M Julien Pernot

Hitoshi Umezawa

Shin-Ichi Shikata

Tsuyoshi Funaki

P Muret

A Traoré

A Maréchal

J Pernot

D Eon

D Araujo

J Pinẽro

Potential barrier heights at metal on oxygen-terminated diamond interfaces

Keywords: numbers: 73.20.r, 73.30.+y, 73.40.Qv, 73.40.Ns, 85.30.De

A Potential barrier heights at metal on oxygen-terminated diamond interfaces B Electrical properties of ITO Schottky electrodes on oxygen-terminated diamond Bibliography List of Figures ix 4.38 Current-voltage characteristic of annealed (450 • C) Zr Schottky contacts (sample #3) operating at 373 K. The TFE+BL current was calculated for different acceptor concentration to bring out its variation versus N a . . 4.39 RT current-voltage characteristics of as-deposited Zr Schottky contacts (sample #2) together with the expected theoretical (TFE+BL) current. . . 4.40 Effective barrier height (left) and ideality factor (right) versus temperature for as-deposited and annealed Schottky contacts. . . . . . . . . . . . . . . . 4.41 Zero-bias SBH distribution for as-deposited and annealed Zr/O-terminated diamond rectifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.42 SBH distribution at zero-bias and 0.5 V calculated for as deposited and Zr electrodes annealed at 450 • C. . . . . . . . . . . . . . . . . . . . . . . . 4.43 Filtered HRTEM micrograph of annealed (450 • C) Zr/p-diamond contact. The white contrast is ZrO 2 interface layer. . . . . . . . . . . . . . . . . . . 4.44 Barrier heights of metals/p-diamond contacts versus the difference of metals and carbon electronegativities reported by W. Mönch [Mönch 1994] for clean diamond surface and hydrogen terminating surface. . . . . . . . . . . 4.45 Metal/oxidized diamond SBH versus the difference of metals and carbon electronegativites performed for electrodes as-deposited and annealed at temperature ranging from 673 K and 723 K. The square symbols are asdeposited electrodes : Zr this work, Al reported by Koné et al [Koné 2010], Cu and Ag reported by Ueda et al[Ueda 2014], Mo and Ru reported by Ikeda etal [Ikeda 2009], Au reported by Teraji et al [Teraji 2009b]. the round symbols represents annealed MS junctions: Zr this work, Al Mo Ru Ir are reported by Umezawa et al [Umezawa 2012], Au reported by Teraji et al [Teraji 2009b]. . . . . . . . . . . . .

List of Figures

 [Volpe 2009b].

The doping level were ranging between 10 16 cm -3 and 5 × 10 16 cm -3 and the compensation between 10 14 cm -3 and 5 × 10 15 cm -3 . . . . . . . . . . . 2.2 Temperature dependence of the Hall mobility in boron doped diamond together with the scattering modes (ionized impurities ii, neutral impurity ni, acoustic phonon ac, and optical phonon op) reported in reference [Pernot 2010]. The term tot denotes the theoretical moblity taking into account all the scattering processes. Experimental data are illustrated by symbols: (a) N A = 2.5 × 10 17 cm -3 and N D = 10 15 cm -3 , (b) N A = 2 × 10 18 cm -3 and N D = 3 × 10 15 cm -3 , (c) N A = 1.7 × 10 19 cm -3 and N D = 5 × 10 15 cm -3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Theoretical hole density (left), hole mobility (middle), and resistivity (right) calculated for different acceptor concentration N A and a constant compensation level N D using the analytical model reported in reference [Pernot 2010]. 26 2.4 Activation energy as function of boron incorporation reported in the literature [Fiori 2012]. The solid line is the Pearson-Bardeen fitting model:

E a = E a0 -a × N 1/3
imp , E a0 = 0.38 eV, a = 4.7877 × 10 -8 eVcm. . . . . . . 6 Theoretical hole density as function of acceptor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported by Volpe et al [Volpe 2009b], Gabrysch et al [Gabrysch 2008], Werner et al [Werner 1997], and Tsukioka et al [START_REF] Tsukioka | Hall Mobility and Scattering Mechanism of Holes in Boron-Doped Homoepitaxial Chemical Vapor Deposition Diamond Thin Films[END_REF]] . . . . . . . . . . . 2.7 Theoretical hole mobility as function of acceptor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported by Volpe et al [Volpe 2009b], Gabrysch et al [Gabrysch 2008], Werner et al [Werner 1997], and Tsukioka et al [START_REF] Tsukioka | Hall Mobility and Scattering Mechanism of Holes in Boron-Doped Homoepitaxial Chemical Vapor Deposition Diamond Thin Films[END_REF]]. . . . . . . . . . . . 2.8 Calculated p-type diamond resistivity as function of acceptor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported by Volpe et al [Volpe 2009b], Gabrysch et al [Gabrysch 2008],

Werner et al [Werner 1997], and Tsukioka et al [START_REF] Tsukioka | Hall Mobility and Scattering Mechanism of Holes in Boron-Doped Homoepitaxial Chemical Vapor Deposition Diamond Thin Films[END_REF]]. . . . . . 2.9 Temperature dependence of electron mobility in phosphorous doped diamond (N D = 6.8 × 10 16 cm -3 , N A = 8.8 × 10 15 cm -3 ) together with the contributions of the scattering modes (ionized impurities ii, neutral impurity ni, acoustic phonon ac, and intervalley phonon iph) [Pernot 2010]. . 2.10 Theoretical electron densities as a function of donor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported in reference [Pernot 2008]. . . . . . . . . . . . . . . . . . . . . . . 2.11 Theoretical electron mobility as a function of donor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported in reference [Pernot 2008]. . . . . . . . . . . . . . . . . . . . . . . 2.12 n-type diamond resistivity as a function of donor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported in reference [Pernot 2008 (Goodwin & Butler, 1998) [Goodwin 1997].

Introduction

Energy is a crucial resource in our modern societies where economic development and modernization are the main concerns. Besides its necessity in industry as well as in services in order to ensure human well-being such as transport, telecommunications, energy is essential to produce vital resources such as clean water or to guarantee healthcare.

Several primary sources gas, oil, coal, uranium (nuclear) available on our planet, are basically transformed into electricity which is the energy source for industry as well as for household and office appliances (refrigeration, lighting, air conditioners, computers, fax, etc.) [1]. With the world population increasing more specifically in urban areas and furthermore due to emerging economies, world electricity demand is continuously growing [1]. For the next 20 years, the international energy agency estimates the global electricity demand growth to more than 75% expanding from 16400 TWh/year in 2007 to 28900 TWh/year in 2030 [1,2]. Apart from the fact that the continuous and sustainable supply of electricity is jeopardized since primary energy sources are limited, the electricity-related greenhouse gas emission (CO 2 emission) contributes to the average rise of global temperature and then to the current climate change (CO 2 emission due to electricity production should increase about 40% in 2030 expanding from 28.8 Gt/year in 2007 to 40.2 Gt/year in 2030 [1,2]).

In this respect, reducing the environmental impact of electricity production and promoting a management of fossil energy sources are more than ever required to maintain the viability of our modern societies. The sustainable development and the fight against climate change are today international issues [2]. For example, in 2014, France national assembly discussed a law project on Energy "Transition énergétique pour la croissance verte" in order to reduce the greenhouse gas emission by 40%, to increase the amount of renewable power to 32% of total energy consumption, while dividing the latter by two by 2030 [3]. In 2013, the United States administration announced a major climate action to introduce new standards for power plants, more funding and incentives for energy efficiency and renewable, provide more global leadership to reduce carbon emission... [1].

This announcement follows a "Smart Grid" project launched in 2009. The main idea behind the "Smart Grid" concept, is to link all the elements (generators, consumers and those that do both) together for a dynamical energy management. Permanent communications between utility and its customers are expected to optimize energy efficiency and mitigate CO 2 emission [4,[START_REF] Gimelec Industrie | Livre blanc des industriels au service de l'inteligence énergétique[END_REF]. The "Smart Grid" concept is today well accepted since it should allow a greater utilization of renewable energy sources. The European council experts of the Taskforce for Smart Grids mentioned that Smart Grids should play an important role in implementing EU energy policy targeting a share of 75% of renewable energy in gross final consumption. Besides the smart grids favoring renewable energy utilization such as photovoltaic or wind, one can mention the electric vehicles and the hybrid electric vehicles intensively promoted today.

In response to these policies and to the new applications driven by an efficient energy management, power electronics need a "complete makeover". Power electronics represent the main technological bridges used for energy processing from source transformation (coal, fuels, gas, renewable) to the end-users (household, office, industry, etc).

It is well known that the electricity processing through power conversion systems using the well-established silicon technologies, are in major part responsible for approximately 80% of the energy lost along the chain from primary sources to end-users [2]. Over the last decades, wide band gap semiconductors (GaN, SiC, Diamond), which offer better electrical properties, have been identified as the appropriate materials to overcome silicon limitations and to improve the efficiency of the energy chain by minimizing losses.

The transition from silicon to gallium nitride (GaN) and silicon carbide (SiC) devices in power electronics has been already ignited.

Diamond, the ultimate semiconductor for power electronics still at the Research & Development stage, is intensively investigated by several research groups over the world.

Over the last 20 years, the technological progresses achieved in diamond growth, its doping, and its surface treatment, allow today to fabricate various electronics devices (Schottky diode, field effect transistors, bipolar transistors, Metal Oxide Semiconductor capacitor, PIN, etc). Among these diamond-based devices, Schottky diode is the most advanced. Nevertheless, this unipolar device still suffers from several imperfections that must be corrected in order to fabricate a demonstrator with outstanding electrical properties surpassing SiC-based devices (the main wide bandgap material industrialized today) and making the most of the superior electrical and thermal properties of diamond.

The present thesis attempts to contribute to this effort by investigating and enhancing the electrical performance of diamond Schottky rectifiers. In this regard, several open questions must be first considered: (i) Can we demonstrate the superiority of diamond-based rectifiers using the available electronic grade diamond substrates? (ii) Is the elevated ionization energy of dopants redhibitory? (iii) What is the best structure for diamond Schottky diodes? (iv) What kind of metal (Schottky electrode) must be used to reach high performances?. In order to propose workable answers, this report is divided as follows:

Chapter 1: The main wide bandgap (WBG) semiconductors, the share of WBG-based devices in the power electronics market and its expected evolution, will be introduced in this chapter. In a second part, the state of the art of devices based on diamond, the ultimate material for power electronics, will be described.

Chapter 2: The main transport properties (mobility, carrier density, and resistivity) will be investigated over a wide doping and compensation range, and at different temperatures. This work will highlight the influence of dopants ionization energy and of the relevant scattering mechanisms on diamond transport properties.

Chapter 3: The fabrication process of the pseudo-vertical diode structure used (motivated by the unavailability of commercial electronic grade highly conductive diamond substrates) will be introduced. The growth process together with the main characterization techniques used to investigate the epi-layers surface and the volume defects will be introduced. The geometrical considerations, the doping level, the trade-off between serial resistance and breakdown voltage will be presented.

Chapter 4: The electrical characterization of pseudo vertical diamond Schottky rectifiers based on an oxygen-terminated diamond surface covered by the easily oxidizable refractory metals like zirconium (Zr) will be discussed. Zr Schottky contact deposition process together with its interface investigation by High-Resolution Transmission Electron Microscopy (HRTEM) and Electron Energy Loss Spectroscopy (EELS) will be analyzed. The room temperature electrical characteristics followed by their thermal stability will then be presented and discussed. Finally, the electrical characteristics of annealed Zr/oxygen terminated diamond junctions will be investigated.

Chapter 1

Diamond power devices

Introduction

Power electronics is today involved in a mutation process to meet energy efficiency and clean energy policies launched by governments over the world and furthermore to provide answers to the power market evolution related to these policies. Silicon-based devices are today the most advanced and mature technology for power applications ranging from high-voltage direct current (HVDC) converter stations to the flexible ac transmission system (FACTS) devices used in a large number of fields such as to control and regulate ac power grids, the electric drive in transportation systems, variable-speed drivers for motors, interfaces with storage devices of several types... [Tolbert 2005] Depending on the intended field, various Si devices can be used: Thyristors that offer the highest blocking voltage ranging between 10 kV and 8 kV (maximum current about 2.2 kA) and are essentially used for very high voltage applications (grid converter stations) where high frequencies are not required (operating frequency limited at 100 Hz). They have been improved into IGCT (Integrated gate-commutated Thyristor) or GTO (Gate Turn Off) thyristors, which have a higher operating frequency between 100 Hz and 1kHz but a lower blocking voltage (below 8 kV) even maximum current (2 kA). However, IGCT or GTO are used to address a large number applications (Motor control, wind, grid, rail traction...). For power inverters, IGBT (Insulated Gate Bipolar Transistor) is preferentially used because of its best trade-off between high blocking voltage (up to 6 kV) and high operating frequency (about 100 kHz). For small converter power supply and amplifiers, less specific transistors (MOSFET, JFET, Bipolar) are used.

For all these Si-based devices, the first limitation is the low thermal conductivity of silicon limiting the maximum operating temperature to less than 150 • C. This requires a significant thermal management effort (forced air or water-cooled heat sinks for example). On the other hand, for high-voltage applications such as switching in transmission level (blocking voltage higher than 100 kV), the low critical field of silicon (0.3 MV/cm) limiting the maximum blocking capability of Si-based down to 10 kV, stacking packaged devices in series is required [Tolbert 2005]. Besides the need of series stacking with complicated triggering to maintain voltage-sharing between devices [Tolbert 2005] in the stack and the thermal management to maintain devices temperature below 150 • C, it is generally reported that the use of Si-based devices in electricity processing are in major part responsible of 80% of losses over the whole energy chain (from energy generation sources to end users) [Millán 2012].

Chapter1. Diamond power devices 7 Contrary to silicon, the enormous potentiality to save energy using WBG semiconductorbased devices is well recognized. Indeed, most of WBG materials (silicon carbide, gallium nitride, diamond) outstrip silicon in term of physical properties needed for high voltage, high frequencies, and high temperature applications. Their physical and thermal properties, superior to those of silicon may allow smaller, faster, and more efficient power devices.

This chapter will first attempt to give a general overview of main WBG materials and of the expected impact of WBG devices. In a second part, the state of the art of devices based on diamond, the ultimate material for power electronics, will be introduced.

Wide band gap semiconductors

Table 1.1 summarizes the physical properties of candidates for silicon replacement in power applications: Silicon Carbide (SiC), Gallium Nitride (GaN), and diamond. All of these materials have larger critical field and higher thermal conductivity than silicon.

Diamond is outstanding among these candidates due to its high critical field 10 MV/cm (more than 30 times that of Si and 3 more times that of SiC), its higher electron mobility 1000 cm 2 /Vs (comparable to SiC) and hole mobility 2000 cm 2 /Vs (higher than all electron mobilities), and higher thermal conductivity 22 W/cmK (20 times that of Si and 6 times that of copper). As a result, the theoretical Figure Of Merit (FOM) of diamond are much higher than those of its challengers. Figures of merit are generally used to compare materials in view of a specific application field. These FOM are respectively:

Johnson's figure of merit (JF M ): It represents the ability of a material for high frequency and high power transistor applications [Johnson 1965]. This FOM is both applicable to FET and with caution to bipolar transistor.

JF M = F B .v s 2π 2 (1.1)
Keyes' figure of merit (KF M ): It displays the thermal limitation to the switching behavior at high frequency [Keyes 1972].

KF M = λ c.v s 2π. r 1/2 (1.2)
where c is the light velocity. Baliga's figure of merit (BF M ): It defines a material efficiency to minimize conduction losses in power applications [Baliga 1982, Baliga 1989].

BF M = r .µ.F 3

B

(1.

3)

The FOM reported in Table 1.1 are room temperature values calculated for electrons except for diamond where the calculated FOM are those of holes. This was motivated by the fact that p-type diamond is preferentially used for unipolar devices such as Schottky diodes (this thesis) due to the lower ionization energy of the boron acceptor in comparison with the phosphorus donor (confer section 1.4). The FOM reported in Table 1.1 highlights the high BFM of diamond (36 times that of GaN and 139 higher that of SiC), its elevated KFM (2.8 times that of GaN and 7 times that of SiC), and the highest JFM (6 times than those GaN and 3 higher than those SiC). Because of these superior properties, diamond is well now widely considered as the ultimate semiconductor for power applications.

Wide band gap power devices market

As reported by the advanced manufacturing office of US department of energy, WBGbased devices should enhance the energy efficiency in industrial-scale power electronics Chapter1. Diamond power devices 9 and clean energy technologies because of their superior electrical and thermal properties.

Indeed, WBG materials may induce several energy-related benefits in power electronics systems, namely: (i) energy loss reduction up to 90% of those currently occurring in AC-to-DC and DC-to-AC electrical conversions [Tolbert 2005], (ii) higher voltage operation than for Si-based devices, which should greatly enhance the number of high-power applications [Ozpineci 2011], (iii) better tolerance of power systems to high operating temperatures resulting in smaller and lighter systems with reduced life cycle energy use [Ozpineci 2011], (iv) higher frequency operations opening up a range of new applications such as radio frequency (RF) amplifiers [Ozpineci 2011], (v) more reliable and consistent power electronic device operation. These features may find various applications in industrials motors (higher-efficiency, variable-speed drives in motors-pumps, fans) and in grid integration (reduction by 50% of losses upon converting DC electricity generated by renewable sources into AC electricity used for household and offices appliances, accelerate high-voltage DC power lines development more efficient than high-voltage AC transmission lines). Electrical vehicles EV and hybrids HEV (losses reduction by 66% during EV/HEV battery recharging, size reduction of automotive cooling system by 60%), as well as military applications (satellite communications, high frequency and high-power radar) among others, would also benefit from such a technological breakthrough.

6" SiC WAFERS FOR POWER ELECTRONIC APP EXPECTED TO TAKE PLACE IN 2016-2017 CHINESE PLAYERS ARE COMING INTO THE SiC

SiC device sales in %, by applications (Yole Développement, October 2014) not yet fully compatible with their expectations.

Such conservatism heavily impacts our previous oriented plates. However, larger substrate sizes up to 8×8mm 2 plates are commercially available. Finally, highly conductive substrates (boron doping) and heteroepitaxial diamond growth (on iridium substrates as example) on larger surfaces are being intensively investigated by several groups.

General overview

Several groups reported various innovative diamond-based power devices demonstrators using some specific methods to fabricate ever higher performance devices. Since 1997, and the subsequent report of ultraviolet light-emitting pn diodes reported by Koizumi et al [START_REF] Koizumi | Ultraviolet Emission from a Diamond pn Junction[END_REF]] in 2001, diamond has been used in a number of, both unipolar and bipolar devices, (pn junction [Tavares 2005], Schottky-pn diode [Makino 2009],

emitting pin junction [Makino 2008], bipolar transistors [Kato 2013], field effect transistor [Kawarada 1994]...). This part will summarize the most advanced devices and the main technological breakthroughs overcome for each.

Field Effect Transistor FET: Since high operating frequencies are aimed at for such devices, boron doped diamond is preferentially used because of its higher hole mobility (2000 cm 2 /Vs at RT) and lower ionization energy (better electrical conduction) than n-type diamond. However, the ionization threshold of 0.37 eV, is still very high and diamond FET architectures illustrated on Figure 1.5, are designed to benefit from boron doping and to minimize the ON resistance as much as possible. Boron δ-FET (Fig. 1.5, left hand side), which consists of a thin heavily doped (metallic) layer between two intrinsic layers resulting theoretically in high mobility, has been intensively studied by several groups [Elhajj 2008, Tumilty 2009, Chicot 2012, Scharpf 2013, Balmer 2013] : Institut Néel, CEA-LIST, IEMN (France), E6, UCL (United Kingdom), Waseda University (Japan) and Ulm university (Germany). Unfortunately the measured hole mobility in δ-FET is behind expectations and typically lower than 100 cm 2 /Vs at room temperature [Chicot 2012, Balmer 2013]. An alternative to δ-FET is Hydrogen-terminated diamond FET (Fig. 1.5, right hand side) using a 2D hole gas at the surface [Kawarada 1994, Hirama 2006, Hirama 2010, Kasu 2012] Metal Oxide Semiconductor (MOS) structure on diamond and the possibility to control the holes or electrons density in diamond with a gate voltage [Chicot 2013]. This essential breakthrough opens the door toward high power diamond MOS field effect transistor MOSFET fabrication (Fig. 1.5 center hand side).

Bipolar junction: Among the interesting features of diamond devices, PIN junctions and Schottky diodes are the most advanced and continuously improve in order to fully exploit diamond's superior electrical properties. In 2013, Suzuki et al [Suzuki 2013] reported PIN diodes with a sharp and repeatable avalanche breakdown at 920 V (2.3 MV/cm). A high serial resistance leading to low current limited the forward performances of these devices. In 2014, Makino et al [Makino 2014] used highly conducting boron doped diamond (p + ) and phosphorous doped diamond (n -) (Fig. 1.6, left hand side) with hopping conduction to get a low on-resistance and thus enhance the forward current of diamond-based PIN diodes (expending from ∼ 10 -2 A/cm 2 at 10 V to 10 3

A/cm 2 ). However, this new architecture induced a higher reverse current (from ∼ 10 -7

A/cm 2 at 10 V to 10 -4 A/cm 2 ). On the other hand, this new approach has been adopted in the so-called Schottky-pn diodes illustrated on Figure 1.6 (center hand side) with an active n-type diamond sandwiched between the heavily doped p + -type diamond and Schottky electrode. For these devices, a forward current of 60000 A/cm 2 at 6 V (specific resistance of 0.03 mΩ.cm 2 ) was measured and the blocking electric field was 3.4 MV/cm (active n-type layer thickness about 160 nm).

Diamond Schottky barrier diode for high-temperature, high-power, and fast switching applications

Introduction

In recent years, the developments of semiconductor diamond technologies have been remarkable. The diameter of the diamond wafer is increased by more than 1 in., 1) utilizing smart cut and mosaic techniques. 2,3) The residual defects in epitaxially grown single crystal diamond have been clarified by X-ray topography 4) or cathodoluminescence, 5) and the densities of defects have been reduced by ultraflat polishing 6) on h110i miss-cut substrates. 7,8) The doping techniques using boron for p-type and phosphorous for n-type have been established. 9,10) Consequently, the performance characteristics of diodes or field-effect transistors, such as current density, breakdown voltage, thermal stability and switching frequency, have been improved. 11-17) Compared with other wide-gap semiconductors, diamond is the most promising material for future high-power, lowloss, and high-temperature devices 18) because of its superior properties, such as high carrier mobility (4,500 cm 2 V ¹1 s ¹1 for electrons and 3,800 cm 2 V ¹1 s ¹1 for holes 19) ) and high breakdown field (>10 MV cm ¹1 ). Baliga indicated that the conduction or switching loss of a diamond power device can be decreased to 1/100 or 1/10000 of those of a conventional silicon power device from the results of theoretical analysis using material parameters. Huang also crystalline diamond (001) substrate was polished with 2°m iscut toward h110i to enhance the step flow growth. A p-type epitaxial layer of 12 µm thickness was deposited as a drift layer by chemical vapor deposition (CVD) on the p+ substrate. The CH 4 /H 2 ratio, gas pressure, plasma power, and growth temperature used were 2%, 120 Torr, 3.9 kW, and 1000 °C, respectively. To control the acceptor boron concentration in the drift layer, trimethyl boron (TMB) diluted with hydrogen was added during the growth. The boron concentration in the gas phase was 0.45 ppm (B/C). At the end of the growth, TMB gas flow was stopped to decrease the doping concentration at the surface. The doping concen-

REGULAR PAPER

In order to overcome these weak points of the p-i-n junction, Schottky barrier, and merged diodes, we have fabricated the diamond SPND. Figure 7 shows the schematic structure of the diamond SPND. This diode is composed of the n-type active layer sandwiched between the heavily doped hopping p + -type layer and the Schottky metal. Here, we design that the n-type active layer is fully depleted, which is the key structure of the SPND. If the n-type layer is partially depleted, that is, there exists a neutral region in the n-type layer, the device is just the p + -n junction diode merged with n-type Schottky barrier diode tandemly. This structure indicates that the neutral region in the n-type layer is the highest resistive layer and we cannot realize the diode with low on-resistance even when a heavily doped hopping p + -layer with low resistivity is used.

(a) T. Makin however, we obtained the prefactor µ 0 and the low activation energy ¦E of ³20 ³ cm and ³41 meV, respectively, from the fitting of the data to the equation µ = µ 0 exp(¦E/kT). As a result, the resistivity of the n + -type film at RT decreases to ³100 ³ cm, which is lower by 3 orders of magnitude compared with that of the n-type film. Thus, in the case of deep dopants such as those of diamond, the carrier transport in the bulk changes from band conduction to hopping conduction using electron tunneling among the dopant states, and this hopping conduction achieves low resistivity. Generally, in the case of a high doping concentration of over ³10 19 cm ¹3 , most single-crystal semiconductors except diamond have a high concentration of defects and their crystallinity degrades. These defects lead to high roughness on the surface. The devices using such heavily doped layers have unfavorable characteristics; for

E F p + -layer n -layer φ B E C E V E A Depleted region -- metal E D - + + + + + (b) φ qV flat E D + + -- Depleted region E C E V + - p + -layer n -layer + + E A E Fp (c) p + -layer n -layer metal E C metal Schottky electrode n Ib(100) sub. p +

Ohmic electrode

Diamond Schottky diodes

A Schottky diode is a unipolar device using the non-linear current transport behavior of rectifying metal semiconductor junction under applied bias voltage (see Chapter 4).

Such a device behaves like a switch triggered by the bias voltage across its terminals. The vertical structure is one of the best geometrical configurations leading to a low serial resistance. This structure is characterized by a vertical electrical current transport through a stack comprising an active layer and a highly conductive substrate (metallic behavior). In "punch through" configuration, the active layer mainly supports the reverse voltage drop due to a negligible depletion region expansion into the highly conductive substrate. The breakdown voltage (BV) and the specific resistance (R × S) in Chapter1. Diamond power devices 16 this geometry are defined as follows:

BV = E M W -qN W 2 /(2 r ) (1.4) R × S ≈ W/σ + R sub × S + R C × S, with σ = qpµ (1.5)
S, q, E M , W, r , N, p, σ, µ, R sub × S, and R C × S are the diode section, the elementary charge, the avalanche breakdown field, the drift layer thickness, the dielectric constant, the doping level, the carrier concentration, the drift layer conductivity, the carrier mobility, the specific resistance of the highly conductive substrate, and the specific resistance of the ohmic contacts respectively. In vertical diode configuration, both R sub × S and R C × S have to be negligible compared to the specific resistance of the active layer in order to minimize diode serial resistance. The use of a substrate doped above the metallic transition (degenerate semiconductor) allows generally to meet these requirements. Accordingly, besides the geometrical parameter W (active layer thickness)

and S (devices area), the doping level N of diode active layer will define both specific resistance and breakdown voltage. Indeed, a low specific resistance corresponding to a high conductivity will be obtained for a highly doped active layer. Conversely, a highly doped active layer gives rise to a low breakdown voltage. In the case of Si-based devices, where the critical field is lower (0.3 MV/cm), a high blocking voltage implies a high serial resistance.

Moreover, wide band semiconductors such as SiC or diamond (Fig. 1.7), lead to an enhancement of the trade-off between (R × S) and BV because of their high critical field (3 and 10 MV/cm respectively). For example, a specific resistance of 10 -2 Ω.cm 2 involves a BV around 300 V for Si and a BV about 3000 V for SiC and diamond. For diamond devices, the specific on state resistance decreases versus temperature opposite to the case of SiC (Fig. 1.7) for a operating temperature of 250 The Schottky diode, compared to other diamond power devices (Bipolar transistor [Kato 2012], junction field effect transistor [Kawarada 1994, Hiraiwa 2012], Schottky-pn diode [Makino 2014, Makino 2009], is the most promising because of the highest breakdown voltage reported (2.5 kV [Twitchen 2004], 6.7 kV [Butler 2003], 10 kV [Volpe 2010],

8-12 kV [Huang 2004]) and because of recent architectural progress to minimize its serial resistance. Indeed, the high serial resistance of the lightly doped Schottky active layer required to get a high breakdown field is one of the main limitations of such a device.

The use of pseudo vertical (with a heavily boron doped buried layer) or vertical architectures (with a heavily boron doped substrate), allowed a significant reduction of the diamond diode serial resistance. The reported forward current for these diodes architectures are higher than 100 A/cm Aiming to fabricate high performance diamond Schottky diodes, the following chapters will be focused on: (i) the investigation of electronic properties of lightly doped diamond and their dependence on the temperature and on the compensation level, (ii) the geometrical structure adopted, the growth related issues in order to minimize surface and volume defects in diode active layers, (iii) the selection of the Schottky metal, the diamond surface treatment prior to Schottky contact deposition, the electrical characteristics of fabricated devices and their thermal stability.

Introduction

In this chapter, the transport properties of doped diamond will be introduced in order to establish a useful tool, which allows a rapid evaluation of the resistivity versus doping level and compensation for both p-type and n-type diamond. Besides geometrical considerations (shape, thickness l, area S, etc...) generally chosen to minimize the power devices serial resistance (Rs = ρ × l/S) and so favor high forward currents (see Chapter 4), the most important parameter to enhance the latter is the semiconductor resistivity, which depends on the carrier concentration (p) and the carrier mobility (µ) through On the other hand, a high compensation level reduces the mobility values as result of the scattering by ionized impurities [Pernot 2008, Pernot 2010]. At high temperature, carrier mobility is limited by lattice scattering namely, optical phonon for p-type diamond and intervalley phonon for n-type diamond. These works provided the theoretical background and mathematical tools as well as the empirical parameters (acoustic deformation potential, effective coupling constant for optical phonon,) needed to evaluate theoretically the Hall carrier mobility in doped diamond in large range of temperature, doping level, and compensation.

This chapter is a direct follow up of previous works reported in references [Pernot 2008, Pernot 2010]. We will attempt to establish a full picture of the main transport properties (mobility, carrier density, and resistivity) versus doping and compensation level at 300 K and 500 K for both n-type and p-type diamond. This works aims at defining the best trade-off range between all for the intended field of application (high power or high frequency). The analytical Hall transport model reported by Pernot et al. [Pernot 2010, Pernot 2008] and its main results will be introduced first. The carrier concentration, carrier mobility, and resistivity will then be calculated using this analytical model and compared to the experimental data reported in literature. Finally, each of these main transport properties will be plotted versus doping level and compensation ranging from 2.2 Boron doped diamond (p-type)

Theoretical background

Hole transport in diamond occurs mostly within the three uppermost valence bands namely: the light holes (lh) and heavy holes (hh) bands degenerated at the Γ point of the Brillouin zone and the spin-orbit splitter (so) band positioned at 13 meV below these latters [Willatzen 1994]. For the calculations performed here and for those reported in ref [Pernot 2010, Pernot 2006], this small energy splitting was overlooked and the three bands are considered as degenerated at the Γ point of the Brillouin zone. Moreover, the three valence bands are considered to be parabolic with representative effective masses of Ref [Willatzen 1994

+ m * 3/2 hh + m * 3/2 so ) 2/3 = 0.908 m 0 .
The carrier concentration (p) is then determined using the charge balance neutrality equation in the general case of Fermi distribution [Pernot 2001] and the mobility (µ) is evaluated using the classical multi-band equations: µ H = p hh µ hh + p hl µ hl + p so µ so p hh + p hl + p so , (2.1) p i (i = l, h, so) in which lh, hh and so refer to the light, heavy and spin-orbit holes concentration and µ i to their mobility respectively. Moreover, this last expression is simplified since the Hall scattering factor r H is approximated to unity (see ref [Pernot 2010] for the general expression and the motivations for this last assumption). On the other hand, the mobility µ i is calculated using the relaxation time approximation

µ i = eτ i /m * ,
where τ i is average value of the total relaxation time evaluated using the Matthiessen rule:

1 τ i = n 1 τ in , (2.2)
in which τ in is the relaxation time assigned to scattering mechanism n for each band i.

Four main hole scattering mechanisms have been considered : ionized impurity scattering (ii), neutral impurity scattering (ni), acoustic phonon scattering (ac) and non-polar optical phonon scattering (op). The expression of relaxation times corresponding to the different scattering mechanisms enumerated above are reported in reference [Pernot 2010]. acceptor density N A , the acceptor ionization energy E A , and the donor density N D ͑compensation͒ are determined from the fit of p to the experimental data of the Hall density p H = 1 / ͑eR H ͒ with p H = p / r H and assuming the Hall scattering factor r H to be unity. Figure 1͑a͒ shows a comparison between the experimental and calculated values.

Temperature dependence of hole density and mobility

092102-2

Volpe et al. of slightly boron doped diamond layers reported by Volpe et al [Volpe 2009b]. The doping level were ranging between 10 16 cm -3 and 5 × 10 16 cm -3 and the compensation between 10 14 cm -3 and 5 × 10 15 cm -3 .

For these epi-layers where high RT hole mobility were measured (up to 1870 cm 2 /Vs), boron concentration was ranging from 10 16 cm -3 and 5×10 16 cm -3 . On the other hand, the compensation varied between 10 14 cm -3 and 5 × 10 15 cm -3 . Hole concentration increases at high temperature because of the thermal ionization of boron acceptors. Even for these relatively low doping levels, only the ionization regime is observed for the selected measurement temperature range (from 300 K to 750 K). The full boron ionization regime (exhaustion regime where p = N A -N D ) occurs at temperatures above 750 K due to the high ionization energy of boron (0.38 eV). Conversely, the mobility is T -α dependent (α > 0). This feature commonly encountered for most of semiconductors is related to the phonon scattering mechanisms. For lightly doped diamond (N A ≤ 10 17 cm -3 )

with a low compensation level (N A ≤ 10 15 cm -3 ) as shown on Figure 2.2 [Pernot 2010],

the RT hole mobility is limited by acoustic phonon scattering. Noting that the relaxation time of this mode is proportional to ρ m v 2 /(m * 3/2 C 2 a ), where C a = 8 eV is the acoustical deformation potential, ρ m = 3515 kg.m -3 the crystal mass density, and v = 17536 m.s -1 the velocity of longitudinal phonon. Its was then established that the RT hole mobility in boron doped diamond (2000 cm 2 /Vs) is higher than the other semiconductors in column IV (for both electron and hole). Indeed, the high crystal mass density of diamond counterbalances the relatively large C a (8 eV compared to 5 eV for silicon) and the density of states effective mass (0.908 m 0 compared to 0.81 m 0 for silicon) in case of p-type material. For phosphorous doped diamond, i.e. n-type diamond, since the RT electron mobility in slightly doped and low compensating materials is still limited by the (ac) scattering mode, the maximum electron mobility of 1000 cm 2 /Vs is two times lower than the hole mobility, mainly due to the acoustic deformation potential being higher for n-type diamond (C a = 17.5 eV).

for sample B37, N A =2ϫ 10 18 cm -3 and N D =3ϫ 10 15 cm -3 for sample B42, and N A = 1.7ϫ 10 19 cm -3 and N D =5 ϫ 10 15 cm -3 for sample B6. The compensation level has been also determined from the fit of the mobility in Ref. 11. A large discrepancy between N D determined by NE and N D determined by mobility analysis has been found in the case of the most highly doped samples.

Unfortunately, in this work, 11 the neutral impurity has not been introduced in the scattering analysis making the quantitative description of highly doped sample insufficient. In Fig. 3, the mobility temperature dependences of the three samples have been calculated using the same parameters than those determined in the previous section and using impurity parameters determined from the fit of the NE in Ref. 11 given above.

Concerning the B37 sample shown on Fig. 3͑a͒, the low-times lower than the one determined by the mobility analysis ͑2.5ϫ 10 16 cm -3 ͒.

The effect is huge in the case of sample B6 which is the most highly doped. The low-temperature mobility is completely controlled by ni mode up to 600 K leading to a value close to 200 cm 2 / Vs. In this work, the parameters deduced by the NE fit of Tsukioka et al. 8 ͑N A = 1.7ϫ 10 19 cm -3 and N D =8ϫ 10 14 cm -3 ͒ are sufficient to describe the mobility temperature dependence. In their case, for the same reason than for B42 ͑neglecting the ni mode͒, they need to overestimate the compensation with N D = 1.2ϫ 10 19 cm -3 which is more than one hundred times larger than the NE value analysis.

For the three samples, the low-temperature mobility decreases strongly due to a hopping mechanism has already reported in highly boron-doped diamond. 5,9,38 As expected, Moreover, at high temperature, the hole mobility in diamond is limited by optical phonon scattering. The key parameter in this scattering mode is the optical phonon energy, about 165 meV in diamond (63 meV for silicium), which explains the larger mobility of holes in diamond at high temperature (300 cm 2 /Vs [Pernot 2010] at 500 K) in comparison to electrons in Si (150 cm 2 /Vs [Dorkel 1981] at 500 K) and 4H-SiC (30 cm 2 /Vs [Pernot 2005] at 500 K). This is due to the lower phonon population in diamond (high phonon energy). On the other hand, the neutral impurities scattering mode starts to be the limiting mode at RT when the boron acceptor concentration increases as shown on where the theoretical hole density, hole mobility, and resistivity obtained for different doping levels N A (10 15 cm -3 , 10 16 cm -3 , 10 17 cm -3 , 10 18 cm -3 , and 10 19 cm -3 ) are plotted assuming a similar compensation level (N D = 10 14 cm -3 ).

At room temperature (RT), the hole density rises from 10 13 cm -3 to 5 × 10 15 cm -3 when N A varies from 10 15 cm -3 to 10 19 cm -3 . Moreover, the temperature dependence of hole mobility is not affected by acceptor concentration variation if N A lower than 10 17 cm -3 .

As previously discussed, the mobility of holes is limited by lattice scattering (ac+op mode defined by diamond intrinsic properties) in the case of uncompensated lightly doped diamond [Pernot 2010]. At RT, a hole mobility of 1800 cm 2 /Vs (related to acoustic phonon scattering [Pernot 2010]) should be achieved if the doping level is lower than 10 17 cm -3

and the compensation about 10 14 cm -3 . At high temperature, for example 600 K where the full ionization of boron acceptors (exhaustion regime where p = N A -N D ) occurs, hole mobility is limited by optical phonon scattering [Pernot 2010] and a 130 cm 2 /Vs mobility should be obtained. On the other hand, the neutral impurities scattering starts to be the limiting mode at RT when N A ≥ 10 17 cm -3 . For N A = 10 19 cm -3 (for example), the RT hole mobility drops from 1800 cm 2 /Vs (N A ≤ 10 17 cm -3 ) to 300 cm 2 /Vs.

At high temperature, the optical phonon scattering is enhanced and a lower mobility is obtained for heavily doped diamond as shown on Figure 2.3. Using these theoretical hole concentrations and their mobility, the temperature dependence of doped diamond resistivity (ρ = (qpµ) -1 ) has been calculated. Figure 2.3 shows the expected resistivity profile for each N A . The temperature dependence of mobility is characterized by: (i) a decrease stage due to the thermal ionization of boron acceptors, (ii) a minimum value when the exhaustion regime is reached (full boron ionization), and

(iii) an increase stage related to hole mobility diminution versus temperature (constant hole concentration in exhaustion regime). These different stages can be observed on Figure 2.3 for lightly doped diamond (N A ≤ 10 17 cm -3 ) where the exhaustion regime arises below 700 K. Thus, a minimum resistivity should be obtained between 450 K and 600 K if N A ≤ 10 17 cm -3 . For heavily doped diamond (N A ≥ 10 17 cm -3 ), the thermal ionization of boron acceptors occurs over the whole temperature range (from 300 K to 1000 K) and the resistivity decreases with temperature in all cases. However, Figure 2.3

shows that the resistivity of diamond doped at 10 19 cm -3 should be higher than that obtained for N A = 10 18 cm -3 when the temperature is lower than 320 K. This is a consequence of the constant boron ionization energy assumption made for these calculations. For boron doped diamond, the metallic transition happens around a doping level of 5 × 10 20 cm -3 [Klein 2007]. The acceptor band broadening leading to a apparent lower ionization energy as shown on Figure 2.4 [Fiori 2012], can not be neglected for

N A > 10 17 cm -3 .
meV (Lagrange, et al., 1998). The first known studies on boron-doped diamond (Field, 1979) in 1950s were performed on IIb-type * natural and synthetic substrates. The main difficulties encountered in these studies were related to the problem of lack of reproducibility of boron doping over several batches of crystals. However, it was commonly assumed that acceptors "boron" of the atoms is perfectly capable of providing p-type conduction inside the diamond layers because their covalent radius (0.088 nm) and carbon (0.077 nm) are close enough to allow the incorporation of boron into substitutional sites. Initially, the first attempts of boron doping from the gas phase were performed using diborane (B2H6) which, upon decomposition, allows an intake of boron atoms in the gas mixture and thus a possible reintroduction of these in the solid phase (Fujimori, et al., 1986). Subsequently, other attempts at p-doping diamond from the gas phase have been initiated from various other gaseous precursors: Tri-methylborate (B(OCH3)3) (Chen, et al., 1994), Tri-methylboron (TMB, B(CH3)3 higher thermal stability compare to diborane) (Cifre,

E a = E a0 -a × N 1/3
imp , E a0 = 0.38 eV, a = 4.7877 × 10 -8 eVcm.

Additionally to this requirement, i.e. including the ionization energy diminution versus acceptor concentration N A , the electrical properties discussed above are affected by a high compensation level. This is illustrated on figure 2.5 where the temperature dependence of hole density, hole mobility, and the resistivity are calculated for an acceptor concentration of 10 16 cm -3 with different compensation levels. For a compensation ratio k (k = N D /N A ) lower than 10 %, the hole density and mobility versus temperature can be considered as unchanged. Above this compensation ratio limit, both hole density and mobility decrease. For example, for k values around 80 %, the RT hole density decreases from 10 14 cm -3 (k ≤ 10%) down to 10 12 cm -3 . The RT hole mobility drops from 1800 cm 2 /Vs to a value lower than 1000 cm 2 /Vs due to ionized impurities scattering. The resistivity is therefore much higher than that of the uncompensated material. The high temperature mobility is not affected by a high compensation since identical features are obtained.

Aiming to investigate the influence of the doping level and compensation over wide doping and compensation ranges, the hole density and mobility were calculated for N A and N D ranging from 10 14 cm -3 to 10 20 cm -3 . These calculations were done for room temperature (300 K) and 500 K operation. The theoretical curves are compared to experimental data reported by several authors for epi-layers grown on (100)-oriented diamond substrates. Boron ionization energy diminution versus N A was taken into account using the Pearson and Bardeen model established by fitting experimental ionization energies as shown on Figure 2.4 [Fiori 2012]. K. A filled contour plot was adopted. For such a plot, an isovalue, i.e. a constant hole density regardless of doping level and compensation, is described by a given color corresponding to a value indicated on a color bar (left side). Moreover, for a given acceptor concentration N A , the calculations are performed for compensation level N D ranging between 10 14 cm -3 and N A . This upper limit (N D = N A a full compensated material) similar to an undoped material, delimits an uncolored triangle area where the material may be considered as n-type (N D > N A ). On the other hand, the theoretical hole density versus N A and N D are plotted together with symbols corresponding to experimental data reported by various authors for boron doped diamond layer. The value of each symbol is indicated by its face color according to the color bar located on the left side. Thus, a discrepancy between the theoretical calculation and the experimental data Chapter 2. Electrical properties of doped diamond 29 can be rapidly depicted by a color contrast. This type of illustration will be adopted for all theoretical calculations discussed in this chapter (density, mobility, and resistivity).

The theoretical hole density profiles at 300 K and 500 K shown on Figure 2.6 are in good agreement with the experimental data reported by Volpe et al [Volpe 2009b], Gabrysch et al [Gabrysch 2008], Werner et al [Werner 1997], and Tsukioka et al [START_REF] Tsukioka | Hall Mobility and Scattering Mechanism of Holes in Boron-Doped Homoepitaxial Chemical Vapor Deposition Diamond Thin Films[END_REF]].

For uncompensated p-type diamond (N D ≤ 10 14 cm -3 ), the ionization rate (p/N A ) is about 1 % at RT and less than 0.1 % if the compensation ratio k (k = N D /N A ) is higher than 10 %. For example, at a doping level of 10 17 cm -3 , a RT hole density of 10 15 cm -3 may be obtained for a compensation of 10 14 cm -3 (k = 0.1%) and the RT density drops to 10 14 cm -3 for a compensation of 10 16 cm -3 (k = 10%). At high temperature (500 K), the ionization rate is enhanced. For acceptor concentrations lower than 10 17 cm -3 , the exhaustion regime is reached. In this regime, where acceptors are fully ionized, the hole density p is equal to N A -N D thus leading to ionization rate of 1 -N D /N A . In case of low compensated materials (N D << N A ), the ionization rate is therefore 100 % i.e. all acceptor atoms will introduce a carrier in the valence band (p ≈ N A ). This is well illustrated on Figure 2.4 where for a doping level of 10 16 cm -3 , hole density at 500 K is about 10 16 cm -3 when the compensation is lower than 10 15 cm -3 . Above this limit, acceptors compensation significantly reduces hole density leading then to a lower value than previously. For a doping level higher than 10 17 cm -3 , the exhaustion regime occurs at temperature higher than 500 K, and the ionization rate is approximately 10% for a compensation ratio below 10 %.

In summary, the theoretical hole density profile versus N A and N D established a compensation limit around 10 % of the acceptor concentration beyond which p-type diamond RT carrier density decreases due to compensation effect. For a compensation lower than this limit, p-diamond behaves like an uncompensated material at room temperature and 500 K where the exhaustion regime is reached for a doping level below 10 17 cm -3 .

Hole mobility versus N A and N D

As for hole density reported above, the theoretical hole mobility profile versus acceptor concentration and compensation was established for 300 K and 500 K (Fig. 2.7). At room temperature, the theoretical curve predicts a maximum mobility of 2000 cm 2 /Vs for N A lower than 10 17 cm -3 and a compensation N D below 10 15 cm -3 . For a doping level and a compensation out of these ranges, the RT mobility tends to decrease due to neutral and ionized impurities scattering [Pernot 2010]. For instance, the mobility drops from 2000 to 250 cm 2 /Vs when the doping level increases from 10 16 cm -3 to 10 19 cm -3 due to neutral impurities scattering in the case of uncompensated materials (N D ≤ 10 14 cm -3 ).

Conversely, for a given N A such as 10 17 cm -3 , hole mobility is two times lower for a compensation level equal to 10 14 cm -3 (∼ 1800 cm 2 /Vs) than for 10 16 cm -3 (∼ 900 cm 2 /Vs) because of ionized impurities limitation. Moreover, this observation can be generalized for N A ≥ 10 16 cm -3 as a 10% compensation induces a mobility two times lower than the maximum value expected for uncompensated material.

Moreover, the experimental RT hole mobility reported by different authors [Volpe 2009b, Gabrysch 2008, Werner 1997[START_REF] Tsukioka | Hall Mobility and Scattering Mechanism of Holes in Boron-Doped Homoepitaxial Chemical Vapor Deposition Diamond Thin Films[END_REF]] matches well the theoretical mobility values, except for a few samples. Two kinds of discrepancies appear: a lower mobility than the theoretical calculations (for example values with N D = 10 17 cm -3 also reported by

Werner et al [Werner 1997] see Fig. 2.7) and sometimes a higher experimental value than the theoretical one (as example values with N D = 7 × 10 18 cm -3 reported by Werner et al [Werner 1997] confer Fig. 2.7). These discrepancies may result from a wrong acceptor concentration or a wrong compensation level (or both) for these experimental data.

However, another hypothesis would be that the set of scattering processes considered in our calculations is not compete enough. It has to be noticed that only few experimental data do not match the theoretical maps curves. For the majority of these data, a good agreement is obtained even at high temperature, as shown on Figure 2.7 where the theoretical mobility profile at 500 K is plotted together with experimental data (left hand graph). Optical phonon scattering is the limiting mechanism at high temperature for slightly doped layer. Accordingly, the mobility is about 300 cm 2 /Vs for a doping level below 10 17 cm -3 even for high compensation ratios (above 10%). For N A higher than this limit, the influence of neutral impurities starts to be noticeable thus inducing a mobility degradation. This doping level situation may be considered as insensitive to the compensation if the compensation ratio is under 10 %. K. For the doping range and compensation values previously defined as leading to the highest RT mobility (2000 cm 2 /Vs) i.e. when doped diamond behaves as an uncompensated material (N A ∼ 10 15 cm -3 to 10 17 cm -3 and 10 14 cm -3 ≤ N D ≤ 10 16 cm -3 ), the RT resistivity is ranging from 100 and 10 Ω.cm. At 500 K, it decreases to values between 30 and 1 Ω.cm. Away from this ideal N A range, the resistivity is enhanced for low compensation level because of a higher carrier density which counterbalances the low carrier mobility related to neutral impurities scattering [Pernot 2010]. 2.3 Phosphorous doped diamond (n-type)

Experimental setup

In this section, the electrical properties of n-type diamond will be calculated using an identical approach as discussed previously for p-type material. These calculations will be undertaken using the model [Pernot 2006, Pernot 2001] for n-type diamond. Electron densities versus donor concentration (N D ) and compensation (N A ) will be first calculated using the neutrality equation [Pernot 2001] and a constant ionization energy (E d = 0.58 eV) of phosphorous over the whole doping range (10 14 ≤ N D ≤ 10 20 cm -3 ).

For highly phosphorous doped layers, the classical way to estimate E d consisting to fit the temperature dependence of Hall carrier density, is no more appropriated due to hopping mechanism present at relatively high temperature [Matsumoto 2014, Makino 2014].

The reported phosphorous ionization energy calculated taking into account the hopping mechanism, may be considered as constant when the doping level is below 10 20 cm -3

as reported in these references [Matsumoto 2014, Makino 2014]. This is commonly explained as the consequence of the small Bohr radius of phosphorous in diamond which does not favor the electrons wave functions overlapping inducing the impurities band broadening (ionization energy diminution versus doping level). The metal insulator transition has never been observed in n-type diamond.

Additionally to electron density calculation, the theoretical electron mobility versus donor concentration and compensation will be established taking into account the main relevant scattering modes described in Reference [Pernot 2006]: intravalley acoustic phonons (ac), intervalley phonons (iph), ionized impurities (ii) and neutral impurities (ni). As for p-type diamond, the room temperature electron mobility of lightly doped material is limited by acoustic phonon scattering modes. As discussed for p-type doping, this mode depends on crystal mass density ρ, the density of states effective mass m * , and the acoustic deformation potential C a . The high value m * and/or C a favors a low mobility whereas the high crystal mass density may induces a high mobility (µ ac = eτ ac /m * ,

τ ac ∝ ρv 2 /(m * 3/2 C 2 a
)) [Pernot 2001, Pernot 2010]. The high RT hole mobility (2000 cm 2 /Vs) in diamond is related to its crystal mass density (3515 kgm -3 ) which counterbalances the influence of m * and C a [Pernot 2010].

For n-type diamond, the maximum RT electron mobility is about 1000 cm 2 /Vs. This relatively low electron mobility compared to that of holes in diamond, is basically due to the higher acoustic deformation potential C a for electrons (17.5 eV) than for holes (8 eV). It should be mentioned that electron mobility limitations due to this (ac) scattering mode occurs over a wide temperature range as shown on Figure 2.9 for phosphorous doped diamond with N D = 6.8 × 10 16 cm -3 and N A = 8.8 × 10 15 cm -3 . (ac) scattering is predominant until to 700 K. Above this temperature, the mobility is governed by inter valley (iph) scattering. On the other hand, the influence of high phosphorous incorporation (high doping level) together with compensation effects on the electron mobility has been already reported [Pernot 2008]. As discussed for p-type doping, the neutral and ionized impurities scattering modes are enhanced by doping and/or by compensation, leading to a lower mobility value than that of uncompensated and slightly doped n-type diamond [Pernot 2008]. Thus, the variations of the RT electron mobility versus N D and N A were established in reference [Pernot 2008]. computed for N D and N A ranging between 10 14 cm -3 and 10 20 cm -3 . The theoretical calculations have been undertaken for room temperature and 500 K and furthermore compared to experimental data of phosphorous doped diamond films grown on synthetic diamond (111)-oriented substrates and measured by Satoshi KOIZUMI at the National Institute for Materials Science NIMS. The growth conditions of these layers are described in reference [Koizumi 2006]. The phosphorous concentration (N D ) and the compensating center density (N A ) are obtained from the fit of experimental Hall electron densities using the neutrality equation for each sample [Pernot 2008]. The theoretical and experimental values of electron concentration (n) and mobility (µ n ) are compared at 300 K and 500 K for a donor concentration (N D ) and compensation (N A ) ranging between 10 14 and 10 20 cm -3 . Finally, the resistivity maps are calculated and discussed. At RT and 500 K, the theoretical electron density profiles are in good agreement with the experimental data. Moreover, the correlation between the doping level and the compensation reported in reference [Pernot 2008] was demonstrated again since n stays relatively constant (same color means constant value) when N D increases. For the experimental data discussed here, the donor density increase is counterbalanced by a higher compensation level in such a way that an identical carrier concentration is always obtained. For uncompensated n-type diamond (N A ≤ 10 14 cm -3 ), the ionization rate (n/N D ) is lower than 0.1 % at RT thus indicating that less 1 atom over 1000 donors is ionized at RT. At 500 K, for acceptor concentrations lower than 10 17 cm -3 and a compensation of 10 14 cm -3 , the ionization rate is about 10 %. In comparison, for p-type doping, the acceptor are fully ionized in the same doping and compensation ranges and the ionization rate is approximately 100 %. This relatively low ionization rate in n-type diamond is due to the higher phosphorous ionization energy (0.57 eV). The exhaustion regime for n-type diamond occurs then at higher temperature than 500 K for N D range discussed above. Moreover, the ionization ratio is lower than 10% at 500 K for N D ≥ 10 17 cm -3 . As an example, for N D = 10 20 cm -3 , electron density is equal to 10 17 cm -3 thus corresponding to a n/N D ratio of 0.001. This can be ascribed to the constant activation energy assumption over the whole N D range which was made in our calculations. This hypothesis was based on experimental results indicating a constant E a for doping levels lower than 10 20 cm -3 [Matsumoto 2014, Makino 2014]. Moreover, a high compensation level also contributed to reduce the electron density. The compensation effect can be assumed as negligible if the compensation ratio k (k = N A /N D ) is below 10 %. It must noticed that the conduction through only the conduction band have been considered for building the Figure 2.10, and that hopping mechanisms were neglected.

Electron concentration

Electron mobility

The theoretical electron mobility versus donor concentration and compensation was calculated at 300 K and 500 K (Fig. 2.11). A maximum mobility of 1000 cm 2 /Vs at RT and 250 cm 2 /Vs at 500 K may be expected for a doping level lower than 10 17 cm -3 and a compensation below 10 15 cm -3 as shown on Figure 2.11. Out of these N D and N A limits, the mobility decreases as a function of N D and N A due to neutral and ionized impurities scattering [Pernot 2008]. Thus, the mobility drops from 1000 to 120 cm 2 /Vs for doping level increases from 10 16 cm -3 to 10 19 cm -3 in case of uncompensated n-type material (N D ≤ 10 14 cm -3 ).

Moreover, as for p-type diamond, it shows that a 10% of donor compensation induces a mobility twice lower than the maximum value expected for uncompensated material with N A ≥ 10 16 cm -3 . As an example, for N D of 10 18 cm -3 , the mobility of electrons drops from 500 to 250 cm 2 /Vs when the compensation level N A increases from 10 14 cm -3 (k = 0.01%) to 10 17 cm -3 (k = 10%). These theoretical calculations are in good agreement with the experimental data reported in reference [Pernot 2008], expect for some data points for which a lower mobility value compared to our calculations was observed. This kind of discrepancy has been discussed previously in the case of p-type materials. It can be ascribed to additional scattering mechanisms (defects), which were not considered here (neutral impurities, ionized impurities, phonon scattering).

n-type diamond resistivity

Figure 2.12 shows the full picture of n-type diamond resistivity versus N A and N D at 300 K and 500 K. Besides a good agreement with the experimental data, the minimum resistivity at RT and 500 K is always obtained for a N D ranging between 10 18 cm -3 and 10 19 cm -3 and N A lower than 10 15 cm -3 . This feature only observed for n-type diamond is a consequence of the constant ionization energy level assumption underlying our calculations. For 10 15 cm -3 ≤ N D ≤ 10 17 cm -3 and 10 14 cm -3 ≤ N D ≤ 10 15 cm -3 , it was demonstrated that a high mobility around 1000 cm 2 /Vs should be obtained. Unfortunately, this high mobility is counterbalanced by the low ionization rate of phosphorous donor (high ionization energy). At RT, the n-type diamond resistivity is thus ranging between 10 5 and 10 3 Ω.cm for these doping and compensation ranges. At 500 K, the resistivity is still relatively high (10 2 and 10 Ω.cm) compared to p-type diamond in the same doping range where the RT and 500 K resistivity are respectively more than 100 times and 10 times lower than those of n-type materials.

Figure 2.12: n-type diamond resistivity as a function of donor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported in reference [Pernot 2008].

Conclusion

The analytical Hall transport model reported by Pernot et al.[Pernot 2010, Pernot 2008] was used to investigate the main transport properties (mobility, carrier density, and resistivity) as a function of doping level and compensation for both n-type and p-type diamond. For each type of dopant, the theoretical carrier density, carrier mobility, and resistivity profile for a doping level and a compensation ranging between 10 14 to 10 20 cm -3 was calculated for room temperature and at 500 K. These theoretical calculations, in good agreement with experimental data reported by several authors, offer the unique opportunity to estimate the electrical properties of diamond layer for a given doping level and a given compensation. The electrical features of diamond devices can be then preselected and furthermore optimized before their fabrication.

On the other hand, the calculations performed in this chapter delineated a compensation limit and doping range in which carrier density and their mobility are weakly altered as compared to uncompensated materials. For p-type diamond with less than 10% of boron acceptor compensated and a doping below 10 17 cm -3 , a RT mobility close to the maximum of 2000 cm 2 /Vs may be expected. This optimal compensation range and doping range are similar to those of n-type diamond where a maximum RT electron mobility of 1000 cm 2 /Vs should be obtained. Unfortunately, these high mobility values are counterbalanced by the low ionization rates of diamond dopants, thus leading to a high room temperature resistivity for both p-type and n-type materials. Indeed, only 1% of boron acceptors are ionized at RT whereas less than 0.1% phosphorous donors should be ionized. Thus, the RT resistivity of p-type diamond in this low doping range varies between 100 Ω.cm (for N A = 10 15 cm -3 ) and 10 Ω.cm (for N A = 10 17 cm -3 ).

Conversely, for n-type diamond, the RT resistivity is at least 100 times higher with values between 10 5 Ω.cm (for N A = 10 15 cm -3 ) and 10 3 Ω.cm (for N A = 10 17 cm -3 ).

For power unipolar devices such as Schottky diodes where slightly doped active layers are preferentially selected in order to achieve a high blocking voltage, boron-doped diamond (p-type diamond) is therefore more appropriate. At high temperature such as 500 K, the resistivity of p-type diamond is significantly reduced due to the thermal activation of boron acceptors. Such a high operating temperature will then enhance the electrical performance of diamond power devices.

Introduction

This chapter will describe the fabrication process of the pseudo-vertical diode structure used in this thesis. This choice was motivated by the current unavailability of commercial electrical grade highly conductive diamond substrates, probably, at the moment, the major obstacle towards vertical diamond Schottky diodes fabrication (the optimal geometrical configuration).

So far, vertical diamond Schottky diode structures suffer from the propagation of defects such as dislocations [Umezawa 2012, Ohmagari 2011] A/cm 2 ) in forward regime. In this thesis, a pseudo-vertical diode structure was adopted.

Ohmic&contact& Scho,ky&& contact&

Diamond&substrate& p+&layer& p9&layer&

Pseudo&ver<cal& structure& For the pseudo-vertical diode [Kumaresan 2009, Muret 2011], the epitaxial stack of two layers is made. The active layer (p -layer) is grown on a highly conductive epi-layer (p + layer) grown on an insulating diamond substrate. This design is generally used in order to get an electrical behavior close to that of the vertical structure. The active layer is etched back in order to fabricate the ohmic contact on the top of the highly doped layer, thus delineating the pseudo-vertical structure as shown on Figure 3.1. The fabrication process of this structure involves:

1. epitaxy of active and p + layer, 2. ohmic contact fabrication,

Schottky contact deposition.

As for the vertical structure, the diode performance will be in part related to the crystal quality of the p + layer and furthermore to its doping level. A high quality p + layer will favor the minimization of defects inside the active layer (p -layer). Moreover, this layer has to be sufficiently doped to get a metallic behavior to minimize its contribution to the diode serial resistance and achieve a negligible ohmic contact resistance.

In this chapter, the epi-layers growth step and the contact fabrication step will be introduced. The growth process together with the main characterization techniques used to investigate epi-layers surface and volume defects, will be described first, and the obtained results will be discussed. The final step towards pseudo-vertical diode fabrication, the Schottky metal deposition step, will be reported in the next chapter.

Diamond synthesis

Diamond is an allotrope of carbon characterized by a tetrahedral arrangement of carbon atoms bonded together by strong covalent sp 3 -bonds that crystallizes in a variation of face centered cubic structure: the so-called diamond lattice. This confers to diamond its extreme hardness and furthermore its amazing properties such as a high thermal conductivity and a high melting point. HPHT synthesis: this technique is similar to the natural process of carbon crystallization in diamond under the Earth mantle (depths of 140 to 190 km) under extreme conditions where diamond is the thermodynamically stable phase of carbon. General

Electric in USA was the first company to achieve a reproducible and verifiable HPHT diamond growth process around 1955s using the catalytic HPHT methods. Contrary to the logic behind HPHT synthesis, consisting to apply a sufficient pressure to shorten the bonds between graphite layers to force carbon rings to conform to the diamond lattice, the catalytic HPHT method used a solvent material (the catalyst) in order to dissolve graphite layers and build from the dissolved atoms, diamond lattice (the template being provided by a seed) [Ferro 2002]. The solvent acts as a catalyst for the transformation of non-diamond phase in diamond and furthermore as a relative good solvent of nondiamond carbon, lowering the activation energy of the reaction of graphite conversion in diamond [Ferro 2002]. Accordingly, the (P-T) conditions for catalytic HPHT synthesis, Chemical Vapor Deposition (CVD): the CVD process consists in depositing a solid material from gaseous phases at the surface of substrate. This method is widely used in diamond devices processing since it is the main technique allowing diamond synthesis at low pressure and moderate temperature (Fig. 3.2). Furthermore, CVD provides an easier control of diamond electrical properties such as its doping level (in situ doping).

In 1962, Eversole's experiment was one of the first documented reports about CVD diamond. This experiment consisted to diamond growth on a heated natural diamond substrate (from 600 • C to about 1600 • C) from thermally decomposed carbon-containing gas such as carbon oxides or methyl group-containing gas [Ferro 2002].

One of the major steps forward in CVD diamond synthesis was the use of atomic hydrogen in the synthesis reaction chamber, as proposed in the early 1970's. Atomic hydrogen is known to play a number of critical roles in CVD synthesis of diamond, as illustrated on Figure 3.3 [Goodwin 1997]. Atomic hydrogen preferentially etches away non-diamond phases such as graphite and prevents their formation by saturating the dangling bonds, thus making high quality diamond growth possible. Moreover, atomic hydrogen highly contributes to hydrocarbon radicals generation in the gaseous phase. It is also allowed the abstraction of hydrogen from hydrocarbons attached to the surface, thus creates vacant sites on the growing surface [Anthony 1990]. Its concentration should be as much as possible in order to improve both the diamond growth rate and its crystal

Epi-layers growth by MPCVD

This section summarizes the growth processes together with the standard conditions under which the diodes active layers (p -layer) and the highly conductive contact layers (p + layer) have been fabricated in this thesis. The stack comprising the p -layer and the p + layer was grown by MPCVD on Ib (100) HPHT diamond substrates (Sumitomo Electric Ltd). The set of substrates used in thesis is reported in table 3.1. These substrates were finely polished in order to minimize the consequence of scaife polishing (abrasive process) on as-received substrates. Indeed, besides the relatively high roughness (∼ 1.5 nm) induced by scaife polishing method, the as-received substrates have a subsurface damaged area (subsurface hardening), which generally leads to defects (extended defects such as dislocations) in epi-grown layers. Diamond substrates were re-polished by Syntek Co. LtD a Japanese company. The polishing method allowed removing the subsurface hardening zone and led to a lower surface roughness (≈ 0.33 nm). Table 3.1 summarizes the specifications of samples used in this thesis. For each sample, a chemical cleaning was performed prior to growth in order to remove any surface contamination. Diamond samples were cleaned in a hot acid mixture (250 • C) HClO 4 :H 2 SO 4 : HNO 3 (1:3:4 Volume to Volume V/V) followed by a HF:HNO 3 (1:1 V/V) treatment. Moreover, pure hydrogen plasma pre-treatment was performed in situ prior to growth to etch away any remaining non-diamond carbon phases such as graphite and to set the diamond sample temperature to the growth temperature.

Diamond

The highly conductive boron doped diamond (p + layer) was first grown on diamond substrates. This p + layer was then used as a pseudo substrate for diode active layer growth. The key point in this step is the doping level of both the p + and active layers.

The main role of the p + layer is to connect the active layer backside to ohmic contact without inducing an additional resistance. Here, p + layer was grown with a gaseous mixture of CH 4 , B 2 H 6 , and H 2 in a home made NIRIM type reactor (subsection 3.3.1).

The growth conditions were set to achieve a doping level above the critical value for the metallic transition (5 × 10 20 cm -3 [Klein 2007]).

The active layer (p -layer) was then grown on the p + layer in either NIRIM type reactor or a commercial type reactor "PLASSYS BJ 150" (subsection 3.3.1). The p -layers were non-intentionally doped using a gaseous mixture of CH 4 , O 2 , and H 2 aiming at slightly doped layers. In such growth, the boron source was the residual boron atoms (memory effect) in the growth chamber.

Growth reactors

In this work, both a home-made NIRIM type reactor and a bell jar commercial type reactor PLASSYS BJ 150 were used for epi-layers growth. PLASSYS BJ150 is a high-power microwave cavity plasma reactor known to promote high gas temperature (3200 K) needed for an efficient atomic hydrogen production by thermal dissociation of H 2 [Silva 2009] contrary to the NIRIM type reactor where direct electron-impact induced H 2 dissociation mainly occurs [Fiori 2012]. Moreover, the high deposition pressure available together with the strong activation of gaseous phases in the PLASSYS BJ150 lead to high growth rates (several microns per hour). This reactor was used for thick p -layer growth. The main specifications of these reactors are described below.

Home-made NIRIM type reactor: Figure 3.5 shows the schematic diagram of this growth reactor [Fiori 2012]. This home-made reactor is a modified Japanese (NIMS lab)

MPCVD reactor [START_REF] Kamo | [END_REF]]), which is characterized by a plasma ball located at the intersection of a waveguide and the growth chamber. The gaseous mixture is injected from the top of growth chamber composed by an inner (25 mm diameter) and an outer (40 mm diameter) silica tubes. A microwave generator, operating at 2.45 GHz (power range 0 -2 KW), was used as plasma excitation source. The sample holder, formed by silicon substrate coated with a polycrystalline diamond layer, is located on the top of the inner tube fixed to a linear Z-axis guided UHV magnetically coupled metallic transporter. Thus, the deposition temperature can be set by vertically adjusting the sample holder position compared to the plasma ball. A single colour pyrometer (960 nm), with an emissivity set at 0.4, was used to estimate sample temperatures taking in account the contribution of the sample holder.

The growth pressure is set with a throttle valve actuated by a PID controller with five set points. The available pressures are 2.5, 4, 9, 33 and 50 Torr. The 33 and 50 Torr pressures were used for diamond deposition. Conversely, 2.5 and 4 Torr were used respectively for pure hydrogen and pure oxygen plasma ignition. The 9 Torr pressure was used for oxygen plasma etching. on a sample holder with a water-cooling system and a linear Z-axis motion system.

Heavily doped layer

Heavily doping has been intensively investigated at Institut Néel. Several growth set-ups are defined to get high boron incorporation in epi-layer and therefore to reach high electrical conductivity. ) ratios [Fiori 2012] for NIRIM-type reactor.

Accordingly, the heavily doped layer p + layer was grown with a gas mixture of diborane It might be noted that this thin p + layer was grown in order to minimize defects generation and thus improve the quality of the active layer (p -layer) by reducing defects propagation from p + layer in p -layer. On the other hand, the range of p + layer thickness should ensure the electrical transparency of the latter i.e., its contribution in diode serial resistance should be negligible compared to that of the slightly doped p -layer with a thickness higher than 1 µm. Indeed, the theoretical calculations performed in chapter 2, predict a RT resistivity between 10 2 Ω.cm and 10 3 Ω.cm for low compensated (less than 10% of acceptor atoms) boron doped layer with [B] ranging between 10 15 cm -3 and 10 16 cm -3 . For samples #1 and #2, where 1.3 µm thick p -layers were grown (see Table 3.2), the specific resistance of diodes active layer should be ranging from 0.013Ω.cm 2 to 0.13 Ω.cm 2 . Since 100 µm diameter circular electrodes were fabricated (see Chapter 4), the serial resistance related to the active layer is expected to range between 160 and 1700 Ω. Conversely, the resistance induced by the p + layer is roughly 20 Ω and can be considered as negligible compared to that of the p-layer. However, this assumption may be inappropriate for the large area devices (500 × 500 µm 2 ) fabricated on sample #3 (see Chapter 4) for which the resistance related to p -layer lies between 10 and 100 Ω.

([B]/[C] =1200 ppm), methane ([CH 4 ]/[H 2 ] =4%)

Epi-layer surface morphology

The surface morphology of the epi-grown layers was investigated by optical profilometry in order to identify their main topological defects and moreover to estimate their average roughness. Optical profilometry is extremely versatile for carrying out accurate measurements of the shape and texture of all types of surfaces on the micrometric down to nanometric scales. Here, a Veeco 3D optical profiler Contour GT was used to investigate the surface topography of epi-layers. This optical profiler is characterized by fair lateral resolution (0.5 µm) and a very high vertical resolution, below 0.1 nm. Such an optical profiler is a high-speed system (maximum scan speed 92 µm/sec) that allows us to easily investigate a large area. This is one of the main advantages of this system compared to other surface techniques such as Atomic Force Microscopy (vertical resolution about 0.1

Epi-layer thickness

The thickness of epi-grown layers were estimated by ellipsometry measurements. Spectroscopic ellipsometry is a powerful optical technique based on measurement of the change of polarization state of light over a wide spectral range after reflection on the material of interest. This technique is generally used to investigate the characteristics of thin films: their composition, thickness, doping level, electrical conductivity,.... Spectroscopic ellipsometry was demonstrated at Institut Néel [Bousquet 2014] as a powerful non-destructive tool to probe the thickness, the optical parameters and electronic properties of semiconducting and metallic single crystal diamond epi-layers and multilayers. Such a characterization can be performed during sample growth (in situ ellipsometry). Spectroscopic Ellipsometry were performed using a J.A Woollam M-2000 ellipsometer. Ex-situ (after growth) and in-situ (during growth) ellipsometry measurements were therefore performed to estimate epi-layer thickness and furthermore to set hydrogen treatment conditions for growth using PLASSYS BJ 150 reactor. The estimated typical p + layer thickness for all 3 samples using spectroscopic ellipsometry, was about 400 nm corresponding to a growth rate of 26 nm/min.

Summary

A 400 nm-thick heavily boron doped layer was grown on Ib (100) sumitomo HPHT substrates (Table 3.2) with a gaseous mixture of diborane (

[B]/[C] =1200 ppm), methane ([CH 4 ]/[H 2 ] =4%
) and hydrogen using a pressure of 33 Torr and a temperature of 830 • C in a home made NIRIM-type reactor. The growth rate was about 26 nm/min. The obtained epi-layers are free of surfaces defects and characterized by a typical mean roughness of 0.26 nm and Root Mean Square of 0.35 nm. The next step towards pseudovertical structure fabrication is the slightly doped active layer growth, which will be discussed in the next section.

Slightly doped layer

This step is important since electrical performance of the fabricated devices will be closely linked to the crystalline quality of the slightly doped epi-layer. The epi-layers were mainly grown from a gaseous mixture of CH 4 , O 2 , and H 2 . The boron atoms source Chapter 3. Diamond Schottky diodes engineering 54 is related to memory effect i.e. to the residual boron atoms contamination in growth chamber. Oxygen was added in the gaseous mixture to reduce boron incorporation and to improve the quality of the epi-grown layer [Volpe 2009a]. Indeed, oxygen gas is known to give rise to hydroxyl OH species, which reduce boron incorporation rate in epi-grown layer by oxydizing chemically active BH x species originated from B 2 H 6 decomposition [Omnès 2011]. Moreover, oxygen is supposed to contribute to the reduction of the graphitic phases formation on the growing surface and furthermore to increase their etching rate [Frenklach 1991[START_REF] Harris | [END_REF]]. Both NIRIM type and PLASSYS BJ150 reactors were used for diodes active layers growth. The p -layers growth on sample #1 and #2 was performed with NIRIM type reactor. For sample #3, the PLASSYS BJ150 reactor was used to get a thicker film. The growth conditions set-up together with the surface morphology (roughness, unepitaxial defects) of epi-grown layers, will be discussed in this part.

Main surface defects

The main surface defects usually encountered on epi-grown diamond surfaces, as shown on The growth conditions used in the NIRIM type reactor were based on those defined in reference [Volpe 2010] to get high crystal quality using that same reactor. Volpe et al. Unfortunately, these conditions led to a high density of surface defects such as UC defects, which are not suitable for large area device fabrication. Consequently, the growth conditions were adjusted in order to minimize surface contamination.

The p -layer was therefore grown with 0.75% of CH 4 and 0.25% of O 2 in hydrogen gas, On the other hand, it is well admitted that high power density plasma leading to a high atomic hydrogen density, allows getting a defect free surface [Achard 2011]. Thus, aiming at fabricating large area devices on defect free surface, the PLASSYS BJ 150 reactor was used to grow the p -layer in the case of sample #3. The growth conditions together with the obtained results will be discussed in the next part.

Growth in PLASSYS BJ 150 (sample #3)

The main documented reports about CVD diamond grown in PLASSYS BJ 150 were published by the French group from "Laboratoire des Sciences des Procédés et des Matériaux" (LSPM). The influence of various process parameters such as the deposition pressure, substrate temperature, and methane concentration were intensively investigated by this group in order to get both a large growth rate (several microns per hour) Chapter 3. Diamond Schottky diodes engineering 57 and a high quality diamond thick film (several hundreds of microns). The most optimal growth conditions which preferentially favored the (100) direction growth were CH 4 /H 2 ratio of 4 %, a deposition pressure of 200 mbar, and a temperature of 850 • C [Achard 2005, Silva 2009]. The growth rate under such conditions was about 6 µm/h.

Starting from these conditions, we investigated growth conditions using a gaseous mixture of methane, oxygen, and hydrogen in order to identify the best set leading to the lowest number of defects on the epi-layer surface.

The first optimization step before p -layer growth was the definition of hydrogen plasma treatment conditions. Apart from the fact that it etches non-diamond phases prior to the growth, hydrogen plasma treatment allows rising up the diamond sample temperature to the target value. According to the conditions used (pressure, power, duration), the etching phenomenon occurring during hydrogen plasma treatment can be enough to completely remove the p + layer previously deposited onto diamond sample, leading therefore to a strong residual boron level in growth chamber. In situ ellipsometry measurements were then performed to identify less aggressive hydrogen plasma treatment conditions. For a treatment temperature about 890 • C and a gas flow of 500 sccm, the etching rate was 2 nm/min using a pressure of 150 mbar and 6 nm/min for a pressure of 200 mbar. The etching rate was found to be lower than 1.5 nm/min for a pressure of 110 mbar. Thus, hydrogen treatment step was performed using a 500 sccm gas flow, a 110 mbar pressure, and a temperature of 900 • C. The microwave power was 1800 W and the treatment duration was 20 min. Moreover, the influence of the methane concentration in the gaseous mixture on the epi-layer surface state was investigated. Non-intentionally diamond doped layers were grown on substrate with 7 %, 5%, and 4% of methane in gaseous mixture. These growths were performed using a pressure of 150 mbar, a deposition temperature of 900 • C, and a fixed O 2 /H 2 ratio of 0.75%. The total gas flow was 500 sccm. Figure 3.12 shows the typical surface morphology of epi-layers obtained for these different CH 4 concentrations.

The surface texture of the epi-layer obtained with 7% of CH 4 was non-uniform. It seems to be a consequence of an inhomogeneous growth occurring under these conditions. Moreover, the round hillocks (RH) defects mainly appeared for a lower methane concentration as shown on Figure 3.12 (case B and C). The RH defects density onto the layer surface was significantly reduced for 4% of CH 4 in total gas flow. The number of defects is reduced when a deposition pressure of 200 mbar was used (Fig. 3.13).

A":"7"%"of"CH 4" B":"5"%"of"CH 4" C":"4"%"of"CH 4" 235"μm" 170"μm"

Summary

1.3 µm-thick p -layers were grown on sample #1 and #2 with 0.75% methane and 0.25% of oxygen in hydrogen gas using a pressure of 50 Torr and a temperature of 910 • C. These growths were performed in the NIRIM type reactor. Moreover, the PLASSYS reactor was used to grow a 2.5 µm on the sample #3 with 4% of CH 4 and 0.75% of O 2 in hydrogen gas, at a pressure of 200 mbar (150 Torr), and a temperature of 940 • C. Table 3.2 summarizes for each samples, the growth conditions and the thickness of epi-layers p - and p + . The epi-layers grown on samples #1 and #2 were mainly contaminated by unepitaxial crystals known to be embedded in CVD layer without any relationship with neither extended neither defects nor substrate imperfections [Tallaire 2008]. Conversely, round hillocks were the predominant defects on the surface of sample #3. These defects were found to be correlated to the growth conditions. In order to investigate the crystal quality of these epi-layers i.e. the extended defects such as dislocations and furthermore point defects such as silicon impurities, a 5 K cathodoluminescence (CL) spectroscopy was performed. Moreover, CL spectroscopy is known to be a non-destructive tool well suited to estimate the doping level. The measurement set-up together with the obtained results will be discussed in the next subsection. [B](cm -3 ) = 3.5 × 10 16 ×

I BE T O I F E T O (cm -3 ) (3.1)
Besides providing an estimate of the doping and furthermore allowing the investigation of points defects linked to silicon or nitrogen incorporation, for example, CL spectroscopy is one of the main non-destructive techniques to investigate extended defects such as dislocations in diamond. Indeed, the radiative extended defects are commonly associated to broad bands in CL spectrum of diamond.

For example, the extended defects such as dislocations are related to the so-called band A emission (Green band 2.3, 2.5 eV, blue band around 2.9 eV [Zaitsev 2010]). Aiming at estimating boron concentration, and in order to investigate silicon or nitrogen incorporation, and furthermore to reveal extended defects such as dislocations in epi-layers growth, cathodoluminescence spectroscopy was performed at 5 K. Indeed, there is a relationship between the probe depth Z (µm) and electron (electron beam) energy E (keV) defined by the acceleration voltage: Z = α × E β (α = 0.02, β = 1.67 [Kanaya 1972]). Probe depths of ∼ 0.94 µm and ∼ 1.84 µm are thus obtained for 10 keV and 15 keV respectively. The radiative electron-hole pair recombination (CL signal) will take place in the volume delimited by these probing depths, as shown in Figure 3.16 where the deposited energy is plotted versus probe depth for a given electron beam energy, as calculated by Monte-Carlo simulations [Volpe 2009a].

Results analysis

Figure 3.17 shows the 5K CL signal (normalized with respect to the FE peak intensity) obtained for both sample #1 and sample#3.

Figure 3.17: 5K cathodoluminescence spectrum for epi-layers growth in NIRIM type (sample #1) and PLASSYS BJ150 (sample #3) reactors.

Besides the excitonic region, The CL spectrum mainly exhibited broad bands around 2.88 eV (FWHM of 0.39 eV) and 3.7 eV (FWHM of 0.44 eV). The SiV center (interstitial Si, carbon vacancy complex) was also observed at 1.681, 1.682 eV [Zaitsev 2010]. The broad band around 2.88 eV is the blue band-A generally encountered for both single crystal and polycrystalline diamond, is well known as a feature of extended defects such as dislocations. Takeuchi et al [Takeuchi 2001] attributed such a band emission to sp 2 defects in diamond structures at incoherent grain boundaries and/or dislocations.

Conversely, the band around 3.7 eV can be related to several origins. reported a band around 3.5 eV (FWHM ∼ 0.5 eV ) as a feature of boron related defects.

Here, since oxygen is added to the gaseous mixture during epi-layer growth, one can assume that such an oxygen or boron incorporation in extended defects can occur.

The CL spectrum of sample #3 mainly exhibited both the band A and another band at 3.7 eV. The CL intensity of these band in sample #1 were negligible compared to those of sample #3. This can be interpreted as a consequence of a higher density of extended defects responsible for these band emissions in sample #3. Moreover, such a high CL intensity of Si centers indicates a higher Si incorporation in p -layer grown on sample #3 while sample #1 can be considered as non-containing any Si according to its negligible Si center peak intensity. Such a silicon incorporation is commonly explained by an interaction of active chemical species such as CH x with the silica present in the growth chamber. This interaction was supposed to be more intense in the PLASSYS reactor (sample #3) where the growth was performed at high pressure and high methane concentration. Moreover, the excitonic region exhibited a lower BE T O CL intensity of excitonic for sample #1 (Fig. 3.18). This indicates a lower boron incorporation in sample #1 compared to sample #3. The estimated boron concentration by using equation( 3.1) is 1.8 × 10 15 cm -3 and 1.2 × 10 16 cm -3 for sample #1 and sample #3 respectively. The obtained doping level for all samples reported in this work are summarized in table 3.4.

The p -layers grown in NIRIM type reactor (samples #1 and #2) have a similar boron concentration which is an order of magnitude lower than in the epi-layer grown in the PLASSYS BJ 150 reactor (sample #3).

Summary

5K CL spectroscopy was performed on epi-layers grown with both NIRIM type and PLASSYS BJ150 reactors. The layers grown in PLASSYS BJ150 reactor exhibited high Si incorporation and furthermore broad bands around 2.9 eV and 3.7 eV, which are assumed to be related to extended defects. On the other hand, the CL spectrum of epilayers grown in NIRIM type reactor yielded a relatively lower radiative recombination point defects (silicon center) and extended defects (band A) when compared to the layer grown with PLASSYS BJ 150 reactor. Layers grown in NIRIM type reactor (samples Chapter 3. Diamond Schottky diodes engineering 65 #1 and #2) have a boron atomic concentration (∼ 10 15 cm -3 ) one order of magnitude lower than the epi-layer grown in the PLASSYS BJ 150 reactor (∼ 10 16 cm -3 ).

Figure 3.18: 5K CL spectrum in the excitonic region for samples #1 and #3.

Ohmic contact fabrication

Ohmic contacts are generally obtained by annealing carbide-forming metals deposited on diamond. Metal-diamond contact leads generally to a potential barrier because of the wide band gap of diamond. Thus, damaged diamond in contact region [Brandes 1999] by forming a carbide interfacial layer allows generating gap states which will lower the metal-diamond barrier height or enhance tunneling transport, or both [START_REF] Tachibana | [END_REF]].

Apart from the carbide-forming metals requirement, ohmic contact will be selected according to the trade-off between various requirements such as a low contact resistivity, a good adhesion, a high thermal stability, and a bondable top-layer [Werner 2003]. The low contact resistivity ρ c = R c × S requirement is generally overcome by using a heavily doped diamond in the contact region. For boron doped diamond, the contact resistivity ρ c can be approximated by a power-law [Werner 2003]: ρ C ∼ N -n A . For metallic contacts such as titanium (Ti) and molybdenum (Mo), n was found to be between 1. [START_REF] Gimelec Industrie | Livre blanc des industriels au service de l'inteligence énergétique[END_REF]

Introduction

This chapter introduces the final fabrication step of pseudo vertical diamond Schottky diodes. The Schottky metal deposition process and the electrical characteristics of the fabricated devices will be discussed. Besides the defects minimization in the diodes active layer as discussed in chapter 3, the electrical performances of diamond-based rectifiers will be correlated to the selected Schottky metal and the interface with diamond.

Schottky metal must be selected to ensure good adhesion, thermally and chemically stable interface, and a potential barrier leading to an optimum forward losses (a low forward voltage drop) and minimal reverse current even at high temperatures. Conversely to an ohmic contact where a high density of gap states (or interface states) is promoted by forming a carbide interface layer, the main issue towards high performance diodes, fully exploiting the diamond's electrical and thermal properties, is to prevent the carbide formation while minimizing the interface states.

In this respect, diamond surface oxygenation, known to be an efficient way to minimize electronic states on diamond surface [Teraji 2009a], was adopted by several research groups as being the first step of the Schottky contacts deposition process [Muret 2011, Umezawa 2012, Ueda 2014]. Unfortunately, the Schottky barrier height on oxygenterminated surface was generally larger than 2 eV (high forward losses). On the other hand, according to the Schottky electrodes selected, the rectifiers can be thermally unstable (alteration of the rectification behaviors) due to dissociation of oxygen bonds.

Such thermal dissociations of the oxygen bonds was observed for inert metals such as gold [Teraji 2009b, Teraji 2014] (above 500 K) as well as for easily oxidizable metals like aluminum due to the thermal instability of the interface layer formed with diamond. An alternative solution to diamond surface oxygenation is reported in references [Teraji 2014[START_REF] Fiori | [END_REF]. It was established that carbide-preformed metals such as tungsten carbide (WC) have a better thermal stability up to 600 K. WC Schottky are annealed in the range of 560 K and 600 K in order to allow interfacial bonding between WC and diamond [Teraji 2014[START_REF] Fiori | [END_REF]]. However, an operating temperature higher than 600 K induced a degradation of WC based diamond rectifiers [START_REF] Fiori | [END_REF]].

In this thesis, a different approach was adopted. Conversely to the radical solution of the carbide-preformed metals, the Schottky metal was selected in such a way to favor a thin oxide interface. Aiming to fulfill this requirement, easily oxidizable refractory metals such as zirconium (Zr) was envisaged as potential candidate. This chapter will be (EELS) will be firstly introduced. The room temperature electrical characteristics followed by their thermal stability will be presented and discussed. Finally, the electrical characteristics of annealed Zr/oxygen-terminated diamond junction will be investigated.

Schottky contact

According to the difference of work functions, a Metal -Semiconductor (MS) junction will be a ohmic contact or a rectifier (Schottky contact). In our case where a p-type semiconductor is used, an ohmic contact is formed when the metal work function (φ m ) is higher than that of the semiconductor (φ s ) whereas a rectifier (Schottky contact) is obtained when φ m < φ s . This is well explained by the Schottky-Mott theory stating that the band alignment of a MS junction is related to a charges transfer from one side to other aiming to force the Fermis levels to coincide.

E FM$ ϕ M$ ϕ s$ Metal$ Semiconductor$ E FM$ ϕ M$ ϕ s$ Metal$ Semiconductor$ Semiconductor$$ valence$band$ Metal$$ valence$ band$ E s$ Acceptor$ Free$hole$ A)$Electrically$isolated$ B)$Ohmic$MS$junc=on$ CB! VB! Vacuum$level!

Ohmic contact

The band structure of an ohmic MS junction is shown on Figure 4.1. For a p-type semiconductor, when φ m > φ s , the band alignment at thermal equilibrium leads to an upward semiconductor band bending at the interface related to a hole accumulation (Fig. 4.1 B)). If such a junction is biased (V) so that holes flow from the semiconductor to the metal, they encounter no barrier. Moreover, in reverse direction, the upward band bending related to hole accumulation at the interface, behaves like an anode (holes source), which will provides a copious supply of holes [Rhoderick 1978]. The resistance (R) of the semiconductor will therefore determine the electrical current (I) via the ohmic law V = R × I.

Schottky contact

When the metal work function is lower than that of the semiconductor (Fig.

φ b = E g /q -(φ m -X s ) (4.1)
where X s is the Electron Affinity (EA) of semiconductor and q the elementary charge.

Under zeros bias and for a slightly doped semiconductor (Fermi level close to acceptor level), V d0 can be approximated as followed qV d0 qφ b -E a , where and E a is the acceptor ionization energy. Under applied bias V, this potential becomes qV d = qV d0 + qV .

Accordingly, the barrier V d is lower under forward bias (Fig. 4.2 A)) thus favoring a carrier injection from the semiconductor to the metal (J sm ). Figure 4.2 B) shows the reverse situation where the diffusion potential increases versus reverse bias V r . The electrical current (J ms ) in this latter case is induced by a carrier injection from the metal to the semiconductor.

Metal& Semiconductor&

E FM& E FS& ϕ b& ϕ b& ϕ b& V d0& + V r& V d0& + V f& V d0& A)&Under&forward&bias&V f && C)&Under&reverse&bias&V r && B)&Under&zero&bias& J sm& J ms&

Real MS contacts

Before introducing the carrier transport mechanisms over a Schottky contact, it has to be noticed that the ideal junctions discussed in subsection 4.2 are rarely encountered in practice. For most of semiconductors, a metallic electrode generally leads to a rectifier.

As discussed in Chapter 3, an ohmic contact is generally obtained by annealing a MS junction in order to damage the semiconductor in the contact region thus generating gap states and so, the lowering of the potential barrier at the interface or an enhancement of tunneling transport, or both [START_REF] Tachibana | [END_REF]]. Moreover, experimental SBHs are generally less sensitive function of the metal work function [Rhoderick 1978] contrary to the ϕ b& [Rhoderick 1978], where Q m is the positive charge on the surface of the metal, Q sa the negative charge associated to the depletion layer.

E FS& E FM& V d0! ϕ s& ϕ M& Interface&layer& CNL & χ s& Q it& Q sa& +! +! +! +! Q m& +! +!
m = -(Q sa + Q it )
The depletion layer and so the SBH will be adjust according to the amount Q it . For a high density of interface states, the barrier defined by the Bardeen limit, is said to be 'pinned':

φ b ≈ φ 0 (4.2)
SBH is then expected to vary between the limits define by the Mott equation and the Bardeen limit. The CNL level is generally about one third of band gap E g for classical semiconductors such as Si where the experimental Bardeen limits for electron and hole SBH are respectively 0.75 eV (E gφ 0 ) and 0.37 eV (φ 0 ≈ E g /3) [Cowley 1965].

For diamond, CNL level related to Heine's concept was found to be 1.4 eV [Mönch 1994].

However, the surface termination (hydrogen or oxygen-terminated diamond) induces an additional dipoles layer in the junction region and highly affects this neutrality level.

Transport mechanisms

A basic schematic view of the non-linear current transport feature of a Schottky contact under an applied bias voltage was introduced in the previous section. Here, the transport mechanisms and the theoretical laws quantifying the electrical current across a Schottky contact will be presented with the emphasis on a p-type diamond.

Bias dependence of Schottky barrier height

The SBH expressions defined previously are only valid for a zero-bias voltage. Once a bias voltage is applied, the SBH changes even for ideal junction because of intrinsic mechanisms such as the image-force (the Schottky effect) and furthermore due to the influence of imperfections in junction area.

Schottky effect

The Schottky effect is a consequence of the requirement that the electric field at MS interface must be perpendicular to the metal (Schottky electrode) since its surface is an equipotential (no parallel current on its surface). Thus, as for metal-vacuum system, This consideration affects the carrier injection from one side to the other by inducing a barrier variation ∆φ im near the interface expressed as followed:

∆φ im = qE m 4π s (4.3)
Accordingly, the Schottky barrier φ b taking into account only the image force, is defined as followed (V j is the voltage drop across MS junction):

φ b = φ b0 - qE m 4π s (4.4)
φ b0 is the zero-bias SBH without the image force lowering and E m is the maximum field in the depletion region:

E m = 2qN A (V d0 + V j ) 0 s (4.5)
The following expressions point out the fact that the SBH is reduced even at zero-bias due to the Schottky effect as illustrated on Figure 4.5. The zero-bias SBH φ 0 b is then given by:

φ 0 b = φ b0 -∆φ 0 im ≈ φ b0 - 2q 3 N A (4π) 2 3 s V d0 1/4 (4.6)
Moreover, when the electric field increase in the junction area i.e. under a reverse bias, the built-in potential barrier is reduced thus favoring the carrier injection from the metal to the semiconductor. Note that in this situation, the carrier injection from the semiconductor to the metal is inhibited by a high potential barrier (diffusion potential).

Under forward bias V f , the SBH is still bias-dependent and conversely to reverse case, it is higher than φ 0 b (confer Fig. 4.5) and the electrical current is defined by a carrier emission from the semiconductor to the metal. The bias dependence of SBH in the forward state is generally expressed as [Mönch 2004]:

φ b (V f ) = φ 0 b + (1 -1/n if ) V f (4.7)
where V f is the voltage drop across the depletion layer and n if is a bias-independent parameter called the ideality factor related to the Schottky effect only [Mönch 2004]:

n if = 1 - ∆φ 0 im 4qV d0 -1 ≈ 1 - 1 4q 2q 3 N A (4π) 2 3 s 1/4 (V d0 ) -3/4 -1 (4.8)
From equation 4.8, n if tends towards unity for a high zero-bias diffusion potential V d0

and so for a high SBH. It has to be noticed that even for a low SBH, n if is generally close to 1 for most of semiconductors. As example, for a p-type diamond doped at 10 16 cm -3 , n if is expected to be 1.005, 1.008, and 1.009 for respectively 2 eV, 1 eV, and 0.9 eV zero-bias barrier height. Thus, the SBH should be less sensible (quasi constant barrier) to forward applied bias voltage if the image force is only considered.

Real Schottky contact

The image force effect is generally not enough to explain the bias dependence of SBH.

Indeed, the static dipoles and the states linked to the imperfections at MS interface also contribute to lower the SBH. The forward state is still described by the linear bias dependence mentioned above but the ideality factor is no longer related to the Schottky effect only. Under reverse bias, the SBH lowering is generally defined using the empirical expression established by Andrews andLepselter [Andrews 1970, Tung 1992]:

φ b (V r ) = φ 0 b -∆φ im -αE m (4.9) = φ 0 b - 2q 3 N A (4π) 2 3 s [V d0 + V r] 1/4 -α 2qN A s [V d0 + V r] 1/2
α is a constant supposed to be related to the density and depth of interface states [Tung 1992, Parker 1968]. The bias dependence of the SBH mainly alters the reverse state since it increases the reverse current by continuously reducing the Schottky barrier height. However, a high reverse electric field in junction area induces carrier tunneling in the semiconductor, which can be the limiting transport mechanism and then define the electrical current.

Forward currrent

The carrier transport across a Schottky barrier under forward bias can contain the contribution of several mechanisms such as the thermionic emission, the recombination in depletion region, the diffusion mechanism, ... .

The thermionic emission and the diffusion mechanism are generally the limiting mechanisms in the forward state. Thermionic mechanism is the thermally excited carrier emission over the top of Schottky barrier whereas the diffusion current depends on drift and diffusion phenomena in the junction region. For most of reported diamond rectifiers, the forward current is generally ascribed to a thermionic emission mechanism without any justification. Aiming to confirm this assumption theoretically for devices operating at room temperature and at high temperatures such as 500 K (the full boron ionization temperature range for slightly doped diamond), both diffusion and thermionic mechanisms will be introduced and the Bethe's criterion will be evaluated for each temperature.

Theoretical background

Let's first consider the general expression of the electric current taking into account both the thermionic mechanism and the diffusion mechanism (the thermionic-emissiondiffusion model [Sze 2007]):

J T ED = qN v v R 1 + v R /v D exp - qφ b k B T exp qV j k B T -1 (4.10)
N v is the effective density of states in the valence band, T is the temperature, k B is the Boltzmann constant, and V j is the forward bias voltage. v R is the thermionic recombination velocity defining the carrier recombination velocity near the metal-semiconductor interface. The maximum value of v R depends on the average thermal velocity [Mönch 2004] as followed:

v max R = < v th > 4 = 1 4 8k B T πm * 1/2 (4.11)
On the other hand, v D is defined as an effective carrier diffusion velocity from the edge of depletion layer (bulk region) to the potential energy maximum in the junction region [Sze 2007, Mönch 2004]. This velocity is approximated as followed [Mönch 2004]:

v D ≈ qD p k B T E i = µ p E i , E i = 2q (V d0 -V j ) N a 0 s (4.12)
µ p and D p are the hole mobility and the diffusion constant, respectively. N a is the doping level, 0 vacuum permittivity, and s the relative permittivity of the semiconductor. v D is dependent on the forward bias V j and tends to decrease versus V j . On the other hand, since the carrier mobility µ p decreases versus T because of the scattering phenomenon (the optical phonon scattering in case of diamond [Pernot 2010] occurring when T is higher than 400 K for slightly doped material), v D will be lower at high temperature whereas the thermal velocity which increases versus the square root of T. Thus, according to the ratio v R /v D , the diffusion or thermionic emission will be the limiting mechanism:

Diffusion current (J D ) v D << v R :
The forward current can be ascribed to the diffusion mechanism if v D is much lower

than v R (v D << v R ).
The current-voltage relationship is then defined as followed:

J D = J 0 dif f exp qV j k B T -1 (4.13)
where J 0 dif f is the saturation current and defined as :

J 0 dif f = qN v v D exp - qφ b k B T (4.14) = qN v µ p E i exp - qφ b k B T Thermionic emission current (J T E ) v D >> v R : If v D is greater than v R (v D >> v R
), the electrical current over a Schottky contact will be related to the thermionic emission. The thermionic current is defined as followed:

J T ED = J T E = J 0 thermo exp qV j k B T -1 (4.15)
The saturation current for a thermionic model is given by :

J 0 thermo = qN v v coll exp - qφ b k B T (4.16) = A * T 2 exp - qφ b k B T
A * is the effective Richardson constant related to the isotropic current flow from both light and heavy holes in case of p-type materials. This constant is expressed as A * = (m * lh + m * hh )A/m 0 , where m * lh is the effective mass of light hole, m * hh that of heavy hole, and m 0 the effective mass of free electron. A = 4qπm 0 k 2 B /h 3 is the Richardson constant for free electron (A = 120 Acm -2 K -2 ). For diamond where three uppermost valence bands have their maximum located at Γ the point of Brillouin zone (heavy and light holes bands degenerated at Γ and the spin-orbit band positioned at 13 meV below), only light and heavy holes are still considered. Indeed, for (100)-oriented boron doped diamond used in this thesis (m * hh = 0.427, m * lh = 0.366, m * hh + m * lh = 0.793 [Willatzen 1994, Pernot 2010]), the Richardson constant commonly used is 90 Acm -2 K -2 suggesting that the spin-orbit band must be unoccupied or its contribution is negligible.

Bethe's criterion

According to the condition defined above (v D >> v R ), Bethe put forward a criterion stating that the thermionic emission theory applies if at the top of the depletion layer, the potential energy changes by more than k B T within a distance of one mean free path λ p [Mönch 2004] :

qE i λ p >> 2k B T π (4.17)
Since the electric field E i right at the interface depends on the doping level and the barrier height (the diffusion potential qV d = q(V d0 -V j )) that encountered the carrier injected from the semiconductor in the metal, Mönch [Mönch 2004] reported that the Bethe's criterion is satisfied for n-type Si within a donor density above 10 16 cm -3 and qV d > 0.4eV.

Figure 4.17 shows the Bethe's criterion for p-type diamond Schottky diodes operating at 300 K and 500 K. The mean free path was calculated using the relaxation-time approximation and the maximum mobility at 300 K (2000 cm 2 /Vs) and 500 K (300 cm 2 /Vs) [Pernot 2010]. For diamond Schottky diodes, Bethe's criterion is satisfied at 300 K if the diffusion potential qV d is higher than 0.05 eV. This low limit which can be assigned to the flat band situation where semiconductor serial resistance is the limiting parameter (ohmic regime), demonstrates that the electrical current over diamond

Schottky diodes (at room temperature) will be a thermionic emission current. This is still true even for devices operating at 500 K if the doping level (acceptor concentration) is higher than 10 15 cm -3 and qV d higher than 0.1 eV.

Forward current

It has been established that the TE mechanism is appropriated to define the electrical current across diamond rectifiers even at high temperature when the doping level is higher than 10 15 cm -3 . Taking into account the bias dependence of the SBH and the bulk resistance Rs, the TE model introduces above, is commonly rewrites as followed:

I = I S exp q(V -R × I) nk B T 1 -exp - q(V -R × I) k B T (4.18)
where I S is the saturation current:

I S = A * ST 2 exp - qφ 0 b k B T (4.19)
S is the diode area and n the ideality factor defined as :

1 n = 1 -β = 1 - ∂φ b ∂V j (4.20)
The ideality factor is a key indicator of rectifiers. If n close to 1 (β → 0), the rectifier can be considered as ideal (abrupt and free of defects).

Reverse current

The reverse current of diamond rectifiers should be then explained by a thermionic emission mechanism. Such a reverse current is bias dependent because of the Schottky effect and expressed as:

J(V j ) = A * T 2 exp - q(φ 0 b -∆φ im (V j ) -αE m (V j )) k B T (4.21)
However, the TE mechanism is enhanced by the tunneling of thermally excited carrier occurring in the thinner extension part of the potential barrier (Thermionic-Field

Emission TFE) when a high electric field is applied. The general expression describing the TFE current was established by Padovani and Stratton [Sze 2007]. Moreover, Honeisen and Mead's expression is an alternative simple way to estimate the TFE current [Rhoderick 1978]. This latter expression will be preferentially used in this work.

Anyway, Honeisen and Mead's expression is commonly rewritten in order to include the Schottky effect. The TFE reverse current is then defined as followed (V = V r + V d0 , E 00 = 18.5 × 10 -15 (N a /(5.7m * )) 0.5 ) [Umezawa 2007]:

J = 2A * (qπT V ) 1/2 qE 00 k 3/2 B exp - q(φ 0 b -∆φ im -αE m ) k B T + q 3 V E 2 00 3(k B T ) 3 (4.22)

Summary

In conclusion, the electrical properties of Schottky contact were introduced. For such a metal/semiconductor junction, the current transport depends on the built-in potential barrier (the Schottky barrier) and the depletion layer induced in the semiconductor side.

The modulation of this layer (and so the potential barrier encountered by carrier flowing from the semiconductor to the metal) i.e. its increase or decrease by applying an external bias (V) gives rise to a non-linear current transport feature as shown on The voltage forward drop has to be as low as possible (lower SBH) in order to minimize the forward losses (P = V × I). For silicon and silicon carbide Schottky diodes, the typical forward voltage drop is ranging between 0.15 V and 0.8 V whereas for most of the reported diamond rectifiers, this voltage drop was higher due to a high SBH (above 2 eV). Moreover, for diamond devices, the serial resistance decreases for a high operating temperature contrary to Si and SiC-based devices. will be defined by:

Bias%V%

• The maximum blocking voltage

• The reverse current

For vertical diamond Schottky diode or the pseudo-vertical structure adopted for our devices, defects such as dislocations [Umezawa 2012, Ohmagari 2011] propagates from the heavily doped substrate (highly conductive substrate) in the diode active layer during epitaxial growth. As consequence, the obtained critical field (2.1 MV/cm [Umezawa 2013],

2.7 MV/cm [Kumaresan 2010]) even with a field plate structure used to avoid the edge field enhancement [Ikeda 2009], is much lower compared to those found for lateral diamond Schottky diodes (7.7 MV/cm [Volpe 2010]) and to the very first value reported for diamond (higher than 10 MV/cm) [START_REF] Landstrass | Device properties of homoepitaxially grown diamond[END_REF]].

For pseudo-vertical devices fabricated in this thesis, a thin highly conductive layer (p + layer) was grown in order to minimize defects generation and then improve the quality of diode active layer (p -layer) by reducing defects propagation from the p + layer in the p -layer. On the other hand, zirconium was identified as the best candidate to form a thermally and chemically stable interface without alter the oxygen passivation layer.

The following parts will introduce the deposition process of Zr Schottky electrodes and discuss their electrical feature using the theoretical laws described in this background section.

4.5 Zr Schottky deposition process The ozone treatment was performed using a 500 mbar of pressure and the duration was 90 min. Second, Schottky electrodes were then defined by a photolithography process followed by an oxygen plasma etching (30 sec) to remove the residual resist and contaminations in the electrodes area (Fig. 4.8 b)). Third, a second ozone treatment using the conditions defined previously was performed to ensure diamond surface passivation subsequently covered to prevent its oxidization. Different electrodes shape and metallic stacks were fabricated on samples reported in this thesis:

• For sample #1, 100 µm diameter circular shaped electrodes were fabricated. The Zr layer was covered with cap layers in order to obtain distinct metallic stacks on the same sample, defined as follows:

-Stack 1 : Zr(20 nm)/Au(20 nm),

-Stack 2 : Zr(20 nm)/Pt(30 nm)/Au(10 nm). • For sample #2, the Schottky electrodes were metallic stack comprising a Zr (20 nm) layer, a Pt (30 nm) layer, and an Au (10 nm) top layer. These electrodes were 100 µm diameter circular shaped. • For sample #3, circular and square shapes electrodes were fabricated as shown on the electrical performances of rectifiers in reverse state because of its maximum bias voltage of 1000 V and its detection limit of 10 -15 A ( 10 -12 A in DC mode for SMU 2601A). Thus, the complete I-V characteristic was obtained by combining the SMU 2601A (Forward regime) and electrometer 6517B (reverse regime) acquisitions. On the other hand, the capacitance measurements were performed using an Agilent E4980A

Ohmic&contact&

Ohmic&contact&

LCR Meter with a AC signal frequency ranging from 100 Hz to 2MHz and a typical AC voltage amplitude of 50 mV. a DC bias can be also applied from -10 to 10 V. For all measurements, a Linkam cooling system (sample holder) with a liquid nitrogen feed, was used to set samples temperature (ranging from -196 • C to 600 • C).

Room temperature (RT) I-V Characteristics

Effective barrier height and ideality factor

The good reproducibility of electrical properties of Zr/p-diamond rectifiers was qualitatively demonstrated previously. This part attempts to highlight this reproducibility quantitatively by investigating the electrical characteristics dispersion of Zr/p-diamond rectifiers fabricated on a given sample and from one sample to the other. The forward characteristics reproducibility of a rectifier depends on the zero-bias Schottky Barrier Height (SBH) φ 0 b and its ideality factor n if the thermionic emission is the limiting mechanism. Accordingly, the RT I-V characteristics previously reported were fitted by a thermionic law to assess to φ 0 b and n. Noting that φ 0 b was calculated using the theoretical value of the Richardson's constant 90 Acm -2 K -2 . Figure 4.16 shows the zero-bias barrier as function of ideality factor for devices fabricated on sample #1 (left), sample #2 (middle), and sample #3 (right). Sample #1 exhibited a unique family of diodes (IA) characterized by an ideality factor about 1.5 and a barrier height ranging from 1.5 to 1.6 eV. Moreover, a linear dependence was observed between φ 0 b and n. Such a linear dependence as reported by W. Monch [Mönch 2004] for most of MS junctions (Ag/n-Si [START_REF] Schmitsdorf | Correlation between barrier height and interface structure of Ag / Si ( 111 ) Schottky diodes[END_REF]], Ag/n-GaN [Sawada 2000], Ti/n-SiC [Suezaki 2001],), was considered as an evidence of the existence of more than one physical mechanism that determining the barrier height. The barrier dependence on ideality factor is therefore written as [Mönch 2004]:

φ 0 b = φ nif b -ϕ p (n -n if ) (4.23)
where n if is the ideality factor determined by the image force effect only (n if ≈ 1.005 for a barrier height of 2 eV). Conversely, φ nif b is the extrapolation of the φ 0 b versus n to n if and represents the zero-bias barrier height if the image force effect is only considered.

Accordingly, the zero-bias barrier heights φ 0 b of rectifiers fabricated on sample #1 were fitted using the equation 4.23 as shown on eV and 2.29 eV were obtained for sample #2 for the family IIA and IIB respectively.

An identical situation was observed for sample #3 (groups IIIA and IIIB). Moreover, a linear relationship was established for group IIIA only. For group IIIB, apart the high ideality factor calculated (n higher than 1.7), the zero-bias SBH was around 1.6 eV. Such a stabilization is generally encountered for other semiconductors when n is higher than 1.4 as reported in ref [Mönch 2004] without any explication. For group IIIB rectifiers in our case, the higher ideality factor suggesting that they were far from an ideal junction, leaves one to believe they may be inhomogeneous and so the simplest thermionic emission model 4.20 was no more applicable. This could be ascribed to the surface of sample #3, which conversely to sample #1 and #2, was widely contaminated by surface defects such round hillocks and a mean roughness of several nanometers (confer Chapter 3). Another possibility could be a non-uniform oxygen-terminated surface leading to a non-uniform ZrO 2 interface layer or the influence of interface dipoles induced by this layer. Anyway, for groups IA, IIA, IIB, and IIIA rectifiers which allowed assessing to the SBH φ nif b , the different values determined, are ranging between 1.81 and 2.3 eV in disagreement with Mott equation (φ b = Egq(φ m -X s )) if a electron affinity (X s ) of 1.7 eV [Maier 2001] is taken for diamond (Mott barrier is then about 3.15 eV). Moreover, if SBH was pinned at charge neutrality level as predicted by Bardeen model, these different groups of rectifiers should be the consequence of different neutrality level related to interface layer. For rectifiers fabricated on sample #1, the most likely explanation of the zero-bias SBH φ nif b which at least 200 meV lower than those of sample #2 and #3, could be the SBH lowering due to annealing (confer section 4.10). The fabricated rectifiers on sample #1 were unintentionally annealed because of self-heating effect during high forward bias voltages characterization electrical leading to a higher sample temperature above 600 K (confer section 4.8).

High field RT I-V characteristics

The RT current-voltage characteristic of Zr/p-diamond Schottky diodes fabricated on samples #1, #2, and #3, was measured for reverse bias ranging from 0 V to -1000 V.

Figure 4.17 shows the typical reverse current observed for a large number of diodes.

Besides these poor performances characterized by a high leakage and a low blocking voltage (below 300 V), at least 5% of Zr/p-diamond rectifiers exhibited a good reverse performances. Figure 4.18 shows the diodes having the best characteristics. The electrical currents were divided by devices section which were 4×10 -4 cm -2 for sample #3

(200 × 200 µm) and 7.85×10 -5 cm -2 for sample #1 and sample #2 (circular electrodes with 100 µm in diameter). The I-V curves obtained reported for sample #3 are characterized by a current density of 110 A/cm 2 at 6 V and a maximum reverse bias of 100 V. where (Ron) is the specific on-resistance, of 244 MW/cm 2 at RT was obtained for Zr/pdiamond. The BFOM is a figure of merit for power semiconductor devices relating the power dissipation to the intrinsic materials parameters [Baliga 1989]. The calculated BFOM, 24 times larger than the Si BFOM limit (10 MW/cm

Summary

Besides their relatively good reproducibility, the as-deposited Zr Schottky electrodes exhibited high performances RT electrical properties. Indeed, the Zr/p-diamond rectifiers fabricated on sample #1 and sample #2 give rise to a high forward current density of 10 3 A/cm 2 (at 6 V) and a breakdown field larger than 7.7 MV/cm. The power figure of merit was above 244 MW/cm 2 and was the largest value reported for diamond Schottky diodes and furthermore not far from the theoretical one (1000MW/cm 2 )

[ Umezawa 2012]. Unfortunately, this reverse performance was obtained for few rectifiers because of the surface and crystal quality of diode actives that must be more investigated in order to fabricate high performance large area Zr/p-diamond rectifiers.

High temperature I-V charactersitics

The electrical performances of Zr Schottky electrodes were investigated using sample #1 on which Zr layer was covered with two distinct cap layers: Au cap layer and (Pt/Au) Chapter 4. Rectification behavior of Zr Schottky electrodes on diamond 99 cap layer. Figure 4.19 shows the typical I-V characteristic measured at high temperatures. Zr/p-diamond junctions exhibited a good rectification behavior in the whole temperature range. On the other hand, all of these high temperature currents had a similar trend in the ohmic regime (high forward bias). Let's remind that this regime was related to the forward current limitation induced by the serial resistance Rs of diodes.

A linear scale revealed that the electrical currents measured at high temperatures is lower than the RT current in ohmic regime (confer Fig. Assuming that the resistance induced by the highly conducting diamond layer (metallic layer) in pseudo-vertical diode structure is negligible compared to that of the active layer, the serial resistance can be ascribed to the diode active layer (p -layer). Diode active layer resistivity is therefore defined as ρ = Rs × S/l, where S is diode area and l the thickness of diode active layer. Accordingly, the temperature dependence of the active layer resistivity was established. To end this temperature dependence study, the I-V characteristic was measured after the thermal cycling measurement. Apart the fact that they are still exhibiting a good rectification features attesting their thermal stability up to 773 K, the electrical characteristic of Zr/p-diamond rectifier was improved as shown on Figure 4.21. By comparing the I-V curves before and after the thermal cycling measurement, the latter was found to be shifted leading then to a higher current at low forward bias (lower Schottky Barrier

Height SBH) than for as-deposited Zr electrodes. This work brought out the possibility to lower the forward losses (lower SBH) by performing an annealing stage.

Cap layer influence

The thermal cycling measurements discussed above was performed using a Zr Schottky

Summary

The high temperature measurements demonstrated the good thermal stability of Zr/pdiamond rectifiers. For Zr Schottky electrodes covered with a (Pt/Au) cap layer, an operating temperature range starting from RT up to 733 K was established. Moreover, for the rectifiers fabricated on sample #1, the current in the ohmic regime was almost temperature independent because of a self-heating effect thus leading to a higher temperature than the set point values and a full boron ionization in diodes active layer.

On the other hand, this study highlighted the possibility to lower the SBH and so the forward losses by performing annealing. The forthcoming sections will be focused on the investigation of the self-heating and the influence of the annealing Zr/p-diamond junctions.

Self heating of Zr/p-diamond rectifiers

Thermal management is a key step for high power devices. This section does not intend to address this topic, but merely demonstrate the heat generation in our devices and investigate its influence on their electrical performances. In the previous section, a discrepancy between the expected resistivity profile and those deduced from high temperature current-voltage characteristics was observed. Indeed, conversely to a resistivity diminution related to thermal ionization of boron atoms as discussed in Chapter 2, diode active layer resistivity tends to increase versus set temperature. This tendency was evidenced by a forward current diminution for a high operating temperature as previously illustrated on Figure 4.24. It must be noticed that such temperature dependence of electrical current was generally encountered for semiconductor as silicon where exhaustion regime (full dopant ionization) takes place below room temperature due to low ionization energy of dopants. Thus, the resistivity tends to decrease versus temperature because of the carrier mobility drop (confer Chapter 2). The fact that Zr/p-diamond rectifiers fabricated on sample #1 behave like classical semiconductors-based rectifiers, suggests that the inner temperatures of the sample were higher than the one of the sample holder (T h ) and ranging in the exhaustion regime. It was then assumed that the devices were affected by a self-heating phenomenon providing sufficient thermal energy to increase diamond sample temperature (T s ) and so reach the full boron ionization regime.

This section attempts to demonstrate this assumption by establishing the self-heating evidences and its influence on the electrical properties of Zr/p-diamond rectifiers. Aiming to carry out these objectives, Zr/p-diamond diodes were measured at low temperature (ranging from 213 K to 300 K) in order to have high serial resistance and thus limited the forward current of the diode. Such low temperatures allow us to observe and investigate the self-heating effect.

Self-heating evidences at 213 K (T h )

Self-heating is a consequence of heat generation related to the Joule effect losses and its storage in a device. The Joule losses represent the power dissipated P defined by and the sample holder cooled with a nitrogen feed. The heat exchange is assumed to exist between diamond and sample holder since the probe station is under vacuum. Thus, thermal resistance of diamond/holder contact should define the heat transfer from one side to the other and vise versa.

P = I × V ,
Before discussing the thermal resistance of this contact, let consider the I-V characteristic of Zr/p-diamond rectifier at 213 K shown on Figure 4.24. The rectifier was biased in a wide range of forward voltage in order to investigate the active layer resistivity in a large power dissipated scale. The electric current was plotted as function of the relative forward bias V bias -V th , where V th is the threshold voltage and V bias is the applied bias voltage. This relative bias allows an easier serial resistance determination and will preferentially adopted in this section as the forward bias. Figure 4.24 shows clear deviation of the measured electrical current in ohmic regime from that expected for constant serial resistance Rs (theoretical I-V curve). The current tends to stabilize towards a level that was at least 10 times higher than the expected value. This augmentation was correlated to the sample temperature increasing. Indeed, by focusing a pyrometer on diamond sample, its temperature variation was observed.

T"pyrometer" on"sample"" >"600"K" Figure 4.24: I-V characteristics of Zr/p-diamond rectifier operating at 213 K initially set via the holder (T h ). measurement times. Unfortunately, the pyrometer was not synchronized with our source meter (Keithley 2601A) and so, a relation between the measured electrical current and the pyrometer temperature was not established. Anyway, it is observed that diamond temperature is higher than 600 K when the current tends to level off. These results demonstrate the presence of self-heating in Zr/p-diamond rectifier where temperature was initially set at 213 K (T h ). It must be mentioned that the electrical current feature shown on Figure 4.25 is independent of the measurement sweep duration and was even observed for fast measurements performed using the set conditions leading to the maximum single measurement rates of SMU (1800 operations per second). On the other hand, the sample holder was heated by the self heating of diamond rectifier and the system defined by diamond and sample holder, exhibited a transient temperature step which converged towards a high temperature. The electrical current increase related to the self-heating points out the diminution of the rectifier active layer resistivity ρ because of thermal ionization of boron atoms. Figure 4.26 shows the resistivity profile versus Chapter 4. Rectification behavior of Zr Schottky electrodes on diamond 106 power dissipated P . According to the power dissipation, three steps can be identified:

• A constant resistivity step for losses lower than 10 -1 W. This resistivity corresponds to the active layer resistivity of a rectifier operating at 213 K without self-heating

• A resistivity decrease step due to the thermal ionization of boron atoms (P ranging from 10 -1 to 10 1 W)

• A weak resistivity increase step (P higher than 10 1 W) where the full ionization regime is reached T"pyrometer" on"sample"" >"600"K"

Full"Boron"ioniza7on"?"

Resis7vity"independent"on"losses"" Resis7vity" decreases"due"to" thermal"ac7va7on" of"Boron"

T"sample">"600"K" Let's remind that the resistivity ρ is related to the carrier concentration p and carrier mobility µ as follows: ρ(T s ) = 1/(q × p(T s ) × µ(T s )). During the thermal ionization of boron atoms, the mobility diminution is counterbalanced by the carrier concentration increase until the full ionization regime (p independent of T) where the minimum resistivity is reached and its trend is inverted leading to a weak increase. The profile reported on Figure 4.26 is in good agreement with this statement. However, the electric field influence on carrier velocity must be considered since the field higher than 10 5 V/cm was reached. The best way to definitely ascribe such a resistivity variation to a temperature variation only is the establishment of a relation between sample temperature and the dissipated power.

4.8.2 Self-heating at T h higher than 213 K

The achievements reported above demonstrate the self-heating of Zr/p-diamond rectifier which temperature was initially set at 213 K. This rectifier temperature increase is observed when the Joule losses were higher than 10 -1 W (forward bias higher than 7.5

V) and the active layer resistivity dropped from 600 Ωcm to 30 Ωcm due to the thermal ionization of boron atoms. For rectifier temperature initially set to a value higher than 213 K, the self-heating is expected to be observed at lower forward bias voltage since a high current level will be obtained at lower bias voltage (device active layer resistivity initially reduced).

T"pyrometer" on"sample"" >"600"K"

Full"Boron"ioniza7on"?" perceptible for a T h set at 300 K. Indeed, at RT, the current variation in the ohmic regime can be neglected since the maximum resistivity is only 1.17 times higher than the minimum value. For a rectifier operating at RT, the forward current in ohmic regime was therefore defined by a minimum resistivity of the diode active layer related to the self-heating. The power level from which this phenomenon started to appear at 213 K, was reached in the thermionic-emission regime for most of the measurements performed at T h close to/or higher than room temperature, thus leaving one to believe that the self-heating ignition must occur in this regime. Thus, the current limitation related to rectifiers serial resistance for operating temperature higher than 300 K will be defined by losses-independent serial resistance which do not correspond to their real resistance because of the self-heating induced by a poor heat exchange between diamond sample and holder. On the other hand, the resistivity profiles exhibited an identical feature for losses higher than 10 W. This identical tendency characterized by a sample temperature above 600 K, was previously assumed to be a consequence of both the full dopant ionization and the carrier mobility diminution arising at high temperature.

Exhaus'on*regime! Before investigating this feature, let us consider the constant resistivity steps prior to self-heating shown on Figure 4.27. These resistivity denoted as ρ real corresponds to the active layer resistivity when there is no self-heating. So, by calculating ρ real at different temperatures below RT, the temperature dependence of Zr/p-diamond rectifier has been established. Figure 4.28 shows ρ real as function of T h . These experimental data are fitted using the theoretical model introduced in Chapter 2 in order to establish the theoretical resistivity temperature dependence. For an acceptor concentration N a of 8 × 10 15 cm -3 and a compensation of 10 13 cm -3 , a good agreement with the experimental data is obtained (Fig. 4.28). Moreover, this fitting allowed to evaluate the theoretical temperature dependence of carrier concentration and their mobility. Thus, a high hole mobility of 1750 cm 2 V -1 s -1 should be reached at RT in good agreement with the experimental hole mobility reported by Volpe et al [Volpe 2009b] (1870 cm 2 V -1 s -1 at 292 K) for epi-layer grown using the same reactor (homemade NIRIM type reactor)

and quasi identical growth conditions. Unfortunately, such a Hall measurement can not be performed for diodes active layers due to the pseudo vertical structure adopted since the buried highly conductive layer (p + layer) should act as a bypass of the active layer. Anyway, the theoretical temperature dependence of resistivity established from experimental data, shows that the minimum resistivity is reached for temperature (T s ) ranging between 400 K and 600 K. For T s higher than 500 K (full boron ionization), the resistivity increases monotonically because of mobility T -α dependence.

Diamond sample temperature T s versus Joule losses P

The theoretical resistivity offers the possibility to estimate diamond temperature for a given Joule losses. The heat exchange between diamond sample and its surrounding environment was assumed to occur with the sample holder in our experimental setup (confer Fig. 4.23). In this simplest configuration, the basic heat equation 4.24 can be used to model the heat transferred from diamond side in sample holder:

T s = T h + R th × P (4.24)
T s , T h , P , and R th are the sample temperature, the holder temperature, the Joule losses, and the thermal resistance of diamond/holder contact respectively. From equation 4.24 and taking the set value of sample holder temperature, the rectifier temperature was calculated in the power dissipation range where thermal ionization of boron atoms happens.

This calculation was made for low temperature measurements where thermal ionization of dopants is clearly observable. Thus, by adjusting the thermal resistance, a good agreement with the theoretical temperature dependence of active layer resistivity is obtained for a R th of 7.5 K/W. Figure 4.29 shows the experimental resistivity versus the sample temperature T s calculated using equation 4.24 for three measurements performed with a holder temperature T s initially set at 213 K, 223 K, and 233 K. Besides the fact that they were perfectly overlapped, the comparison with the theoretical resistivity confirmed that the rectifier temperature variation due to self-heating can be adequately explained using the basic heat equation defined above. Unfortunately, this simple law is no longer sufficient to describe the identical resistivity feature observed when the dissipated power is higher than 10 W. Indeed, the temperature dependence of experiment resistivity established using this latter, started to deviate from the theoretical curve when the losses is above 10 W. Since the sample temperature reach the exhaustion regime for this high losses, the discrepancy with theoretical resistivity demonstrates that identical resistivity tendency for losses higher than 10 W cannot be ascribed to a carrier mobility decreasing only. This discrepancy could be a consequence of the invalidity of the main assumption made to estimate the experimental resistivity of the diode active layer. It was earlier assumed that the resistance induced by the highly conductive layer in pseudo-vertical diode structure was negligible and the serial resistance was ascribed the slightly doped active layer only. In the exhaustion regime,

Full

where the active resistivity is the minimum value, this latter assumption is no more obvious and can be inaccurate. However, this inaccuracy is not the main cause of the forward current limitation when the losses were higher than 10 W. It might be noted that such a power level is obtained at high forward bias voltage (higher than 10 V).

Thus, the influence of the carrier velocity saturation due to high electrical field related to the high forward bias must be taken in account to describe the observed resistivity profile.

High field influence on forward current

The electrical current in a semiconductor is non-ohmic under high electric fields. This is the consequence of hot-carrier phenomenon leading to a non linear relationship between carrier velocity v d and electric field E: Dri$%velocity%(cm/s)

v d (T, E) = µ 0 (T ) 1 + µ 0 (T )E/v sat E ( 4
v d # = " μ 0 × E # v d# ="v sat # Figure 4
.30: Hole-drift velocity versus electric field reported by Reggiani et al [Reggiani 1981] illustrating the linear correlation filed regime and the saturation velocity.

Figure 4.30 [Reggiani 1981] shows the typical temperature and field dependence of hole velocity. The ohmic regime "V d = µ 0 E" (field lower than 10 3 V/cm) and hole velocity saturation at 1.1 × 10 7 cm/s [Reggiani 1981] (field higher than 10 3 V/cm) are highlighted for a sample temperature of 150 K. Moreover, for an electric field higher than 10 5 V/cm (E lim ), it can be assumed that the holes velocity saturation occurred for a Chapter 4. Rectification behavior of Zr Schottky electrodes on diamond 112 diamond temperature lower/or equal to 700 K. Thus, if the electric field E is higher than E lim , the electrical current density J (A.cm -2 ) must be J ≈ qpv sat and the resistivity ρ therefore defined as ρ(E) ≈ E/(qpv sat ). A linear relationship must exist between the calculated resistivity and the electric field if the carrier velocity saturation occurs. For the current-voltage measurements previously discussed, the diode active layer is 1.3 µm thick and the E lim should be reached at around 13 V. The calculated resistivity is linearly correlated to the electric field when E ≥ 2 × 10 5

a)# b)#

V/cm (get at 26 V). This linear feature demonstrates that the electrical current is limited by hole velocity saturation when the forward bias is higher than 26 V. Below this bias voltage, the calculated resistivity is driven by the thermal activation of boron acceptors (resistivity drop) due to diode self-heating. The linear field dependence of resistivity allows assessing to carrier concentration which was 8 × 10 15 cm -3 in good agreement with full boron ionization regime. Indeed, for a forward bias above 26 V (losses higher than 10 W), the sample temperature is higher than 500 K. The theoretical Chapter 4. Rectification behavior of Zr Schottky electrodes on diamond 113 temperature dependence of resistivity established using the experimental data (confer subsection 4.8.2) demonstrates that the exhaustion regime (full boron ionization) occurs in this temperature range ( T ≥ 500 K). In sum, the weak resistivity increase observed for all I-V characteristics (Fig. 4.31 b)) is related to the carrier drift velocity saturation due to high forward field (E ≥ 2 × 10 5 V/cm). This field influence is predominant after the thermal activation of boron acceptors (for T higher than 500 K) due to self-heating.

Summary

The thermal cycling measurement demonstrates the heat generation in Zr/p-diamond rectifier due to joule effect losses. These losses induced the self-heating of the diode because of the poor heat transfer from diamond with its surrounding environment. The self-heating leading to a sample temperature higher than 600 K, demonstrates again the thermal stability of Zr Schottky electrodes and furthermore the full ionization of boron atoms in diode active layer. As a result, the current in ohmic regime (bias > 3

Chapter 4. Rectification behavior of Zr Schottky electrodes on diamond 114 V) and its corresponding active layer resistivity are almost temperature independent for a device operating above 300 K (confer Fig. 4.32) in disagreement with the theoretical serial resistance profile deduced low temperature I-V characteristics. Thus, the electrical current of Zr/p-diamond rectifier operating at high temperature is limited by a minimum serial resistance (∼ 50 Ω) partly related to full boron ionization. Indeed, the resistance of highly conducting layer of pseudo-vertical structure must be not negligible anymore when the full ionization occurs in diode active layer. This assumption is motivated by the expected resistance of active layer only ranging from 10 to 35 Ω when the exhaustion regime is reached (T s > 400 K) and the maximum operating temperature is 800 K.

Anyway, the results coming from this investigation suggests the possibility to thermally ionized boron atoms using the losses in diamond devices. The cooling of diamond power devices could be imagined so that it allows keeping a sufficient amount of heat generated to reach the full boron ionization regime.

Electrical properties of annealed Zr Schottky electrodes

The previous section highlighted the possibility to lower the SBH of Zr/p-diamond rectifiers by performing annealing. This section will focus on the investigation of electrical Thermal stability: The thermal stability of each annealing is defined by the temperature range in which its barrier height can be considered as constant. A Richardson's plot appeared to be the best way to estimate this T range for each annealing performed.

Indeed, from the expression of the saturation current (Is), as defined by the thermionic emission theory, a linear correlation may exist between ln(Is/(ST 2 )) and 1/T as followed: rectifying MS junction with an insulating interface layer, the saturation current related to the thermionic current current must be corrected by a transmission coefficient corresponding to the carrier tunneling probability over this interfacial oxide layer. The transmission coefficient T r is expressed [Card 1971, Altndal 2007] as T r = exp(-αχ 0.5 δ),

ln(Is/(ST 2 )) = - φ 0 b k B 1 T + ln(A * ) ( 4
where α = (4π/h)(2m * ) 0.5 is a constant that depends on the tunneling effective mass m * , χ the mean tunneling barrier height, and δ the thickness of the insulating layer.

The equation 4.26 then rewrites: The calculated transmission coefficients were then around 0.33, 0.13, and 0.17 for respectively as-deposited and annealed electrodes (350 • C and 450 • C). In sum, according to the annealing temperatures, different barrier height can be obtained from Zr Schottky electrodes deposited of oxygen-terminated diamond. For rectifier annealed at 450 • C, apart the good reproducibility, the thermal stability up 450 • C, and the ideality relatively close to 1, the zero-bias SBH is about 0.88 eV which is 1 eV lower than in case of as-deposited electrodes.

ln(Is/(ST 2 )) = - φ 0 b k B 1 T + ln(A * T r) ( 4

Reverse characteristics

The reverse current of Zr/p-diamond rectifier annealed at 450 • C was measured under high applied bias voltage. Let's remind that for as-deposited Schottky electrodes, a maximum field of 7.7 MV/cm within a current level below the detection limit of our measurement set up (10 -9 Acm -2 ) was demonstrated. The reverse current density is higher for annealed rectifier since their SBH is lower. Using the theoretical models defined in section 4.3, namely, the thermionic-emission (TE)

and the thermionic-field emission (TFE) taking in account the barrier lowering (BL) due to Schottky effect, it is observed that this reverse current feature can be adequately explained. At low temperature, the contribution of the TE+BL mechanism and the TFE+BL can be clearly distinguished as shown on Figure 4.36. The electrical current related to the (TE+BL) mechanism only allows estimating the effective acceptor concentration N a and the parameter α related to density and depth of interface states as defined by the empirical expression of Andrews and Lepselter [Andrews 1970, Tung 1992] introduced in the section 4.3. N a and α are respectively 2.9 × 10 16 cm -3 and 0.37 nm, which are in good agreement with the doping level estimated by CL spectroscopy (1.2 × 10 16 cm -3 ) and the thickness of interface layer measured by HRTEM (0.4 nm). The tunneling parameter E 00 (eV) of 1.5 × 10 -3 eV is furthermore deduced from TFE+BL fitting model. E 00 depends on the doping level N a and the carrier effective mass. For diamond devices, this parameter is given by E 00 = 18.5 × 10 -15 (N a /(5.7 × m * )) 0.5 .

Maximum'current'of' K6517B'

Figure 4.37: Current-voltage characteristic of annealed (450 • C) Zr Schottky contacts (sample #3) illustrating the TFE+BL current at 373 K and 473 K.

Thus, taking this expression and the acceptor concentration N a estimated using the (TE+BL) model, the effective mass can be calculated. The theoretical effective mass is defined as m * = m * hh + m * lh [Mönch 2004] (m * hh is the effective mass of heavy hole and m * lh is the effective mass of light hole). For diamond sample oriented in (100) direction, m * hh = 0.427 and m * lh = 0.366 [Willatzen 1994] thus leading to a theoretical m * of 0.793. The fitting performed gives rise to a N a of 2.9 × 10 16 cm -3 and a E 00 (eV) of 1.5 × 10 -3

eV. An effective mass m * = 0.77 close to the theoretical value (0.793) was obtained using these values. This good agreement confirms that the models used were appropriated to describe the experimental electrical current. Thus, at low temperature as well as at high temperature as shown on Figure 4.37 (373 K and 473K), the electrical current under high reverse bias is related to the (TFE+BL) mechanism. Noting that both low temperature and high temperature measurements point out a substantial problem, which is the impossibility to reach the critical field of diamond keeping several orders of magnitude as rectification factor. As example, for a diode operating at 373 K, only a rectification ratio of 3 decades exists when a reverse field of 1.25 MV/cm (fig. 4.38) is reached.

Doping effect

One the most evident solution to enhance the reverse state (i.e. lower the reverse current) could be the diminution of the doping level N a . Figure 4.38 shows theoretical reverse currents calculated using the (TFE+BL) mechanism together with the experimental current for a device operating at 373 K. A doping level below 10 16 cm -3 involves a significant change on the current level. For a N a of 5 × 10 15 cm -3 and 10 15 cm -3 , the TFE+BL reverse current at 373 K of annealed (450 • C) Zr/p-diamond diodes will be approximately about ×10 -1 Acm -1 for a maximum field of 4 MV/cm. It must be noticed that the diminution of acceptor concentration will involve a reduction of forward current.

For the example mentioned above, the forward current will divide by a factor less than ten. A minimum rectification factor of two order of magnitude may be expected for a devices switching from forward state to a reverse field of 4 MV/cm (-1000 V blocking voltage for devices fabricated on sample #3).

Barrier height effect

Another possibility to minimize the reverse current could be a higher barrier height.

An annealing below 450 • C for example at 400 • C should allow getting a higher barrier ranging between 0.9 eV and 1.4 eV. Such an intermediate annealing will cause alone a limited diminution of the reverse current level. It must be combined with a low doping level aiming to get high critical fields in a wide operating temperature range. However, the thermal stability limit will be then defined by the annealing temperature since it was demonstrated that the Zr/p-diamond junction stayed relatively stable below their annealing temperature. Additionally, a higher SBH will give rise to a higher threshold voltage and so a higher forward losses.

Anyway, it is possible to explain the discrepancy between as-deposited and annealed Zr Schottky contact. Since, the reverse current is mainly originated from the thermionicfield emission taking in account Schottky barrier lowering related to image force and static dipoles at the interface, the theoretical current of as-deposited Zr electrical can then be calculated using a zero-bias barrier of 1.84 eV, a Richardson's constant of 33

A.cm -2 K -2 , an acceptor concentration of 2 × 10 16 cm -3 , and a temperature of 300 K.

The experimental and theoretical reverse current for as-deposited Zr electrodes are illustrated on Figure 4.39. The (TFE+BL) current is at least 3 orders of magnitude lower than the detection limit of measurement set up (10 -9 Acm -2 ). is performed as demonstrated by Teraji et al [Teraji 2009b]. The authors reported the main consequences of this desorption namely, the ideality factor increasing because of the apparition of spatial inhomogeneity and furthermore Schottky barrier height decreasing (SBH dropped from 2.2 eV to 0.9 eV after 870 K heat treatment). The SBH diminution due to annealing is a typical feature of diamond rectifiers based on oxygen terminating surface [Ikeda 2009, Liao 2005, Umezawa 2012]. The explanation given in reference [Teraji 2009b], is particularly appropriated for rectifiers where the Schottky electrodes do not react sufficiently with oxygen layer such as Au or Mo, Ru, Ir [Umezawa 2012]. However, the same barrier lowering was generally observed for easily oxidizable metal like Al (SBH of 2 eV for as-deposited electrodes [Koné 2010] and 0.4 eV after 673 K annealing [Umezawa 2012]). This last-mentioned case suggests the requirement of thermally stable interface layer to prevent the oxygen layer desorption when easily oxydizable metals are used.

Detec%on(limit(

For zirconium Schottky electrodes deposited on O-terminated diamond investigated here, the existence of thin ZrO 2 interface layer was demonstrated for as-deposited contact.

Conversely, the electrical properties reproducibility of annealed (723 K) devices regardless of diodes or samples, seems to show that the oxygen layer desorption is no longer true to explain the SBH diminution observed. Aiming to confirm this and to investigate the origin of the barrier decrease occurring for Zr Schottky electrodes, the spatially inhomogeneous potential model established by Werner [Werner 1991] will be first used to inspect the homogeneity of as-deposited and annealed electrodes. On the other hand, HRTEM study results will be introduced and discussed. Finally, the MIGS-and-Electronegativity theory developed by Mönch [Mönch 2004] will be used in order to compare Zr electrodes SBH decrease to those reported in literature. In the situation where the Zr/O-terminated diamond rectifier interface is modified because of the oxygen desorption, the spatially inhomogeneous interface resulting should involve a SBH fluctuation in the junction area. For spatially inhomogeneous rectifier, the classical thermionic-emission theory is no longer adequate to explain the electrical current and furthermore the Schottky barrier [Werner 1991, Tung 1992]. One the main features of a spatially inhomogeneous rectifying junction commonly observed is a temperature dependent zero-bias SBH φ 0 b on one hand, and on the other hand, a temperature dependent ideality factor n deduced from thermionic-emission theory [Werner 1991, Tung 1992]. Let's remind (confer section 4.3) φ 0 b and n must be temperature independent in case of ideal junction. versus temperature. The as-deposited electrodes exhibit a weak φ 0 b increase until to 473 K. Above this temperature limit, the SBH diminution due to heat treatment start to occur. As-deposited electrodes are then assumed to be thermally stable for an operating temperature lower than 473 K. A same feature was observed for rectifier annealed at 623 K for which thermal stability was ensured for a temperature lower than the annealed one. Additionally to the zero-bias SBH augmentation versus T observed in their thermal stability range, the calculated ideality factors for each of these two annealed electrodes are highly dependent versus temperature. For as-deposited electrodes, n dropped from 1.5 (RT value) to 1.15 (523 K). This variation is less visible when 623 K annealing is performed since n decreased from 1.3 (RT) to 1.2. Concerning Zr electrodes annealed at 723 K, both φ 0 b (about 0.9 eV) and n (1.05) are relatively constant as shown on Figure 4.40 and may be considered as temperature independent. This latter annealing gives rise to features that might be expected only for ideal rectifier where the electrical current is defined by a thermionic-emission only.

Thus, the as-deposited Zr/O-terminated diamond electrodes are apparently spatially inhomogeneous. However, apart the SBH diminution falling from 1.94 eV to 0.9 eV, the spatial inhomogeneity of these rectifiers seems to disappear when an annealing is performed. Aiming to confirm this apparent disappearance of the spatial inhomogeneity correlated to the SBH lowering, the analytical potential fluctuation model developed by Werner andGuttler in 1991 [Werner 1991] (Werner's Model) has been applied to our case.

Werner's model

Several analytical models explaining the current transport over inhomogeneous MS junctions were reported in literature. The main idea behind most of theoretical modeling of electrical current across inhomogeneous junctions is to take into account the MS interface influences. Tung [Tung 2014] points out the complexity of this attempt and furthermore the difficulty to get a simplest theoretical model.

Werner model is one of the simplest theoretical models which is used here. This model explains the temperature dependence of φ 0 b and n using the thermionic emission. In Werner's model, the SBH fluctuations due to the spatial inhomogeneities are modeled by a Gaussian distribution characterized by a mean value φ and standard deviation σ s . Chapter 4. Rectification behavior of Zr Schottky electrodes on diamond 126 From this empirical approach, a quantitative expression of SBH is established:

φ b (V j , T ) = φb (V j ) - σ 2 s (V j ) (2k B T /q) (4.28)
SBH in case of spatially inhomogeneous junction is both bias and temperature dependent. At zero-bias, the SBH is therefore expressed as:

φ 0 b (T ) = φ0 b - σ 2 s0 (2k B T /q) (4.29)
Thus, the T-dependence linked to standard deviation σ so may not occur if the standard deviation tends towards zero, i.e. if sharp potential distribution (quasi uniform or uniform barrier height) exists in junction area. Anyway, the theoretical analysis of the deformation of SBH distributions under applied bias reveals a relatively constant distribution for electrodes annealed at 450 • C. Noting that the ideality factor in Werner's model is defined as the result of the deformation of the spatial barrier distribution when a bias voltage is applied. The ideality factor is temperature dependent and expressed as [Werner 1991]:

n(T ) = 1 + ρ 2 - ρ 3 (2k B T /q) (4.30)
ρ 2 and ρ 3 quantify the voltage deformation of Schottky barrier distribution and are originated from the requirement that the ideality factor must be bias-independent which is satisfied by assuming both φb and σ s may vary linearly with bias V j :

∆φ b (V j ) = φb (V j ) -φ0 b = ρ 2 V j (4.31) ∆σ s (V j ) = σ 2 s (V j ) -σ 2 s0 = ρ 3 V j (4.32)
The fit results of ideality profiles obtained for each annealing are previously shown on The parameter ρ 3 describes the narrowing of the gaussian distribution of SBH upon bias voltage [Werner 1991] whereas the coefficient ρ 2 reflects the bias-dependence of the

Summary

The analytical model developed by Werner and Guttler is used to investigate the homogeneity of as-deposited and annealed Zr/O-terminated diamond rectifiers. In the simple model presented above, the barrier fluctuations related to the spatial inhomogeneities and assumed to be gaussian distribution, are characterized by their average and standard deviation. Although this model suffers from arbitrary assumptions not supported by any physical model, it allows to quantify bias and temperature dependence of SBH and ideality factor without considering in details the electrical properties of the interface. The temperature dependence of I-V characteristics demonstrate that the as-deposited Zr/O-terminated diamond rectifiers are spatially inhomogeneous. This spatially inhomogeneous seems to disappear when an annealing is performed. Unfortunately, the Werner's model do not allows confirming this observation. However, this model indicated that SBH distribution in case of annealed electrodes is relatively bias independent and temperature independent. As consequence, the electrical current of annealed (723 K) Zr/O-terminated diamond rectifiers were adequately explained using a thermionic emission theory assuming a constant barrier and a constant ideality factor. Thus, the annealing allowed minimizing the influence of spatial inhomogeneities on rectifiers properties in opposition to the junction deterioration reported in reference [Teraji 2009b, Teraji 2014] due to oxygen desorption.

Annealed Zr/O-terminated diamond interface

The theoretical model previously discussed, demonstrates the fact that Zr electrodes annealed at 450 • C behaves like a rectifier with a homogeneous barrier conversely to as-deposited electrodes. This feature suggests that the oxygen layer initially present on diamond surface still exists after annealing otherwise the resulting electrical properties should be deteriorated. Thus, the interface of Zr/O-terminated diamond rectifier annealed at 450 • C was then investigated by HRTEM and EELS at university of Cadiz, Spain (J. C. Pinero and D. Araujo) as previously made for as-deposited electrodes.

HRTEM investigation demonstrates the existence and the thermal stability of the thin zirconia (ZrO 2 ) interface layer (0.4 nm thick) between as-deposited Zr electrodes and p-type diamond. Figure 4.43 shows the typical HRTEM image of annealed (450 • C) Zr/oxidized diamond interface performed in the same conditions as those used for asdeposited electrodes [Piñero 2014].

The white contrast between diamond and Zr layer still represents the ZrO 2 interface layer and no significant change is observed on its thickness which is always about two atomic layers as established previously after the 450 • C annealing. This result together with the TT"450°C" Since the oxygen desorption not occur for annealed Zr/p-diamond diodes, the observed SBH decrease seems to be due to from a change in junction region which does not affect its interface nature.

MIGS-and-Electronegativity theory

Adsorbed atoms at diamond surface induce a dipole layer as demonstrated by Maier et al. [Maier 2001]. This dipole layer can affect the diamond Electron Affinity (EA) as illustrated for hydrogen and oxygen terminated diamond for which negative (-1.3 eV) and positive (1.7 eV) EA were respectively demonstrated. Thus, a high SBH (above 2 eV) is commonly reported for most of Schottky contacts on oxygen-terminated diamond whereas for diamond surface with hydrogen termination (H-terminated) the barrier height are generally below 1 eV. In 1994, W.

Mönch [Mönch 1994] demonstrated the correlation between the low barrier height observed for metals/H-terminated diamond rectifier and C-H dipoles using MIGS-and-Electronegativity concept (Mönch's model).

Let's remind that Heine's MIGS concept defines a continuum virtual gap states in junction area due to the metal's electron wave functions tailing in semiconductor. These -diamond contacts are rectifying but Au-and Ptlp-diamond contacts were foun ic. The ideality factors n evaluated with the rectifying point contacts ranged from

.01 to 1. t (0) and evaporated contacts ( A ) on hydrogen-terminated { loo} surfaces from Kaw ].

Figure 4.44: Barrier heights of metals/p-diamond contacts versus the difference of metals and carbon electronegativities reported by W. Mönch [Mönch 1994] for clean diamond surface and hydrogen terminating surface.

Mönch's model deals with Heine's MIGS theory and Pauling's electronegativity concept to describe the charge transfer across rectifying MS junction. This model predicts a linear correlation between SBH and the difference X m -X s of the metal and the semiconductor electronegativities:

φ 0 b = φ * 0 -S x (X m -X s ) (4.33)
φ * 0 is the Charge Neutrality Level (CNL) at MS interface defined by Heine's MIGS theory. The slope parameter S x is calculated from the expression A x /S x -1 = 0.1 ( r -1) 2 , where r is the electronic part of the static dielectric constant of semiconductor and A x = 0.86 when the Miedema's electronegativity scale is used [Mönch 1994]. Miedema's Chapter 4. Rectification behavior of Zr Schottky electrodes on diamond 132 electronegativity scale is preferentially used within Monch's model to describe interfaces formed by solid materials. The author explained this choice by the fact that Pauling's scale should be applied when a local and molecule-like bond picture is more adequate [Mönch 1994, Mönch 2004]. For metals and clean surface diamond junctions, the zero-bias SBH φ 0 b should be related to the difference of electronegativities as φ 0 b = 1.4 -0.3 (X m -X s ). This theoretical linear correlation is in good agreement with the experimental data as reported by Mönch [Mönch 1994] on Figure 4.44. In case of Metals/hydrogen terminated diamond junctions, a similar linear trend was demonstrated (φ 0 b = 0.017-0.37 (X m -X s )). The slope parameter was identical to the theoretical value whereas the φ * 0 is found to be smaller than the CNL of MIGS theory (1.4 eV) by approximately 1 eV thus leading to a shift down of SBH of Metals contacts on hydrogen terminated diamond Figure 4.44. This deviation from the CNL defined by MIGS theory [Mönch 1994] only was ascribed to C-H bonds inducing negatively charges on diamond side since carbon atoms have a larger electronegativity than hydrogen (H +0.06 -C -0.06 ).

The situation is inverted for oxygen terminated diamond surface where the positively charge part is on diamond side [Maier 2001]. Indeed, the electronegativity of carbon and oxygen are respectively 2.54 eV and 3.44 eV (Pauling's scale). On the other hand, the Schottky electrodes can react with oxygen (covalent bond) and then affect the initial charge repartition of dipoles induced by oxygen-carbon bonds. Easily oxidizable metals such as zirconium (Zr) illustrates this scenario since this metal always formed with oxygen -terminated diamond surface a thin zirconia interface layer (about two atomic layers). Thus, aiming to compare diamond rectifiers based on oxygen termination to those investigated by Mönch [Mönch 1994], the SBH reported in literature authors for different metallic electrodes were collected and plotted as function of the difference of metals and carbon electronegativity, as shown Figure 4.45. This plot is performed for asdeposited and annealed Schottky contacts (673 K to 723 K) reported by several groups.

Conversely to H-terminated and clean p-type diamond surface, the generally linear tendency described by the SBH in case of oxygen termination as shown Figure 4.45, is characterized by a positive slope for both as-deposited (φ b = 2.33 + 0.21 (X m -X s )) and annealed electrodes (φ b = 1.45+0.23 (X m -X s )). Noting that such a positive slope must be expected for n-type semiconductor [Mönch 2004]. The MIGS-and-Electronegativities is apparently not appropriated for O-terminated diamond surface.

Summary & Discussion

The analytical models discussed namely the potential fluctuation model developed by

Werner and Guttler [Werner 1991] and the MIGS-and-Electronegativity concept established by Mönch [Mönch 1994], are not enough or are not appropriate to address the origin of Schottky barrier diminution due to annealing as observed for zirconium electrodes and for most metals reported in literature (Figure 4.45). Moreover, the SBH diminution due to annealing is a common feature of easily oxidizable metals (Zr, Al)

as well as for noble metals (Ir, Au, Ru). Such a SBH diminution seems not happens for Ag and Cu electrodes since it was reported there were thermally stable up to 873 K at least [Ueda 2014]. For Zr, Mo, Ru and Ir Schottky electrodes, besides their thermal stability, it was reported that their exhibited a good electrical properties reproducibility Chapter 4. Rectification behavior of Zr Schottky electrodes on diamond 134 even after 673 K annealing [Ikeda 2009, Umezawa 2012]. On the other hand, their SBH dropped by approximated 1 eV. Taking in account the different oxidation features of these metallic electrodes, it could be assumed that the oxygen desorption is not the major cause of the SBH diminution. Annealing could favor the establishment of chemical bonds between Schottky metals and O-terminated diamond thus probably lead to oxide-type interface as for Zr electrodes. This might affect the positive charges on diamond side due to oxygen bonds in such a way that the SBH decreases. An effective diminution of O-terminated diamond EA due to these positive charges attenuation can be considered. However, Zr electrodes seems counterbalanced this assumption since an oxide interface layer always existed for as-deposited and annealed electrodes.

In this regard, Muret et al. (confer annex A for the submitted paper), improved the dipole-layer approach established by Tung [Tung 1992] to give analytical expressions of Schottky barrier height and ideality factor in case of inhomogeneous junctions. In Tung's model, the barrier inhomogeneity is treated as a perturbation induced by dipole layer with a varying dipole moment per area [Tung 1992]. Inhomogeneities are then ascribed to small regions (patches) with a low SBH embedded in an interface with an uniform high SBH. Using this concept, Muret et al. (confer annex A) demonstrates that the disappearance of interface dipoles initially present at Zr/oxygen-terminated diamond interface due to annealing, explain the SBH diminution observed here. The authors showed that:

• (i) As-deposited Zr Schottky electrodes interfaces have moderated density (few 10 6 cm -2 ) of lowered barrier patches with sizes larger than the Debye length.

Their barrier heights inhomogeneities are assumed to be a consequence of distinct oxygen terminations, which generate a strong sensitivity to the shrinkage of the current channels inside the lightly doped layer close to the interface. Indeed, apart the fact that diamond surface could be not entirely covered by oxygen layer, it is well established that oxygen adsorption on diamond surface give rise to several terminations such as carbonyl (C=O), hydroxyl (COH), carboxyl (O=COH) group [Klauser 2010, Notsu 2000] and eventually epoxide (COC) [Fink 2009]. It was demonstrated through theoretical calculations that these different terminations may induced different electron affinities as reported in references [Sque 2006[START_REF] Robertson | [END_REF]]. Thus, according to the geometrical distribution of these different bonds, the SBH of a metal/O-terminated diamond junction could be spatially inhomogeneous. properties which eventually promoted one of them after annealing.

Conclusion

Pseudo vertical diamond Schottky diodes based on zirconium contacts have been developed. The fabricated rectifiers highlighted the possibility to reach high forward current density (10 3 A/cm 2 at 6 V) and very low leakage current (under 10 -9 A/cm 2 ) up to 1000 V corresponding to an electric field larger than 7.7 MV/cm in diode active layer.

An unprecedented BFOM larger than 244 MW/cm 2 is then obtained due to self-heating leading to full dopants ionization. Moreover, the dispersion of zirconium Schottky electrodes electrical characteristics is extremely weak even for large diode area and regardless on samples because of an identical interface for all of the fabricated devices. Noting that zirconium Schottky electrodes were deposited on oxygen terminated diamond surface in order to favor oxide interface layer formation. The high-resolution transmission electron microscopy and the electron energy loss spectroscopy performed in collaboration with Cadiz university (Spain), demonstrates the existence of a thin oxide interface layer about two atomic layers. This layer, assumed to be zirconia (ZrO 2 ), is thermally stable and still exists even for Zr/diamond rectifier annealed at 450 • C, thus preventing from the oxygen passivation desorption required to reduce as much as possible the interface states. On the other hand, a thermal cycling measurement up to 500 • C points out the self-heating and our rectifiers inducing the full boron ionization in active layer. It was also observed that the SBH could be lower by performing an annealing. A 450 • C annealing allows to reduce the Schottky barrier height down to 1 eV. The SBH diminution due annealing is presumed to be a consequence of a structural change of ZrO 2 interface layer (about 0.4 nm) existing between Zr and oxygen terminated p-type diamond interfaces for as-deposited electrodes as well as for annealed electrodes.

Zr/p-diamond rectifiers annealed at 450 • C are thermally stable up to 500 • C. The reproducibility of forward characteristics whatever of samples and their reverse current are satisfactory explained by both thermionic-emission and thermionic-field emission mechanisms taken in the image force effect. The analytical potential fluctuation model developed by Werner and Guttler [Werner 1991] demonstrates that annealing minimizes the influence of spatial inhomogeneities of Zr/O-terminated diamond rectifiers in such a way that the rectifiers annealed at 450 • C behave like an ideal junction (abrupt and homogenous) characterized by a temperature independent ideality factor (n = 1.05) and Schottky barrier heights (φ b = 0.9 eV). Unfortunately, the empirical models discussed (Werner and Guttler [Werner 1991] model and the MIGS-and-Electronegativity concept established by Mönch [Mönch 1994]), are not enough to address the origin of Schottky barrier diminution due to annealing observed for zirconium electrodes. Muret et al (confer annex A for the submitted paper), improved the dipole-layer approach established by

Tung [Tung 1992] to evidence the origin of barrier lowering after annealing. It was then demonstrated that Zr electrodes annealing at 450 • C induces the complete cancellation of interface dipoles initially present at as-deposited Zr/oxidized diamond interface thus resulting in almost homogeneous interfaces with ideal behavior and barrier height as low as 0.96 V.

Zirconium Schottky electrodes demonstrate the superior performances and the advantage to form a thermally oxide interface layer between diamond and Schottky metals. In this regard, the conductive oxides could be considered as potential candidates for diamond rectifier fabrication. This was demonstrated for Indium Tin Oxide (ITO) electrodes deposited on oxygen terminated diamond by sputtering and annealed at 250 • C (confer Annex B). The electrical characteristics of ITO contacts were reproducible and thermally stability up 600 • C. However, the electrical performances (high barrier height (above 2 eV and a lower blocking voltage 300 V) were less interesting than those Zr electrodes.

General conclusion and outlook

This thesis is focused on the fabrication of high power diamond Schottky diodes and on the investigation of their electrical properties. Diamond growth and its doping are today well mastered. The diamond surface passivation which is required to reduce as much as possible the interface states, more specifically the oxygen-terminated diamond surface, is also well mastered. The advent of vertical architectures (diode active layer grown on heavily doped diamond substrate) and pseudo-vertical (stack of diode active layer and heavily doped layer grown on insulating substrate) allowed minimizing the high serial resistance related to the high ionization energy of acceptor-type dopants (boron doped diamond) preferably used for diamond-based rectifiers fabrication. Besides these geometrical configurations favoring high forward currents, diamond Schottky diodes (pseudo-vertical or vertical) were limited by i) the quality of the active layer altered by defects propagation from heavily doped layer thus leading to lower blocking voltage (maximum critical field of 3 MV/cm reported) than the theoretical values (theoretical values of critical field of 10 MV/cm), ii) the quality of metal/diamond interface together with its thermal and chemical stability. Schottky metal selection and surface pretreatment are crucial to get low enough barrier heights (low forward voltage drop and so low losses), low defects density at interfaces (low leakage current), and a thermally stable interface (high operating temperature).

In this thesis, we demonstrated that a pseudo vertical diamond Schottky diode based on an oxygen-terminated surface covered by an easily oxidizable metal such as zirconium (Zr) combined with a heavily doped layer with optimal thickness allow overcoming these limitations. We first found a trade-off between the thickness of heavily doped layer and its doping level in order to minimize defects generations and thus improve the quality of the active layer to be epitaxially grown on top of it (Less defect propagation). We then showed that the selected Zr metallic electrodes gave rise to a thermally stable thin zirconia interface layer. Zr/oxidized diamond rectifiers (pseudo-vertical structures) exhibited better performance than the current state of art: a high forward current density (1000 A/cm 2 at 6 V), a critical field above 7 MV/cm (1000 V blocking voltage with a leakage current less than 1 pA), a Baliga's power figure of merit above 244 MW/cm 2 (the highest value reported to date), a good reproducibility regardless of diodes and samples, the possibility to get barrier heights below 1 eV by annealing, and a thermal stability up to at least 500 • C. Moreover, the reverse current of annealed Schottky electrodes, must be investigated in order to defined the best annealing temperature (Schottky barrier height)

and doping level (previously introduced as a way to minimize the reverse current). Optimal values must be established in order to fully exploit diamond's outstanding properties whilst getting the best trade-off between the forward current, forward voltage drop, and reverse current. Zirconium electrodes were deposited on epi-layers grown on highly doped diamond substrates (N a ∼ 10 19 cm -3 ) provided by the French lab "Laboratoire des Sciences des Procédés et des Matériaux" (LSPM). Figure 4.46 shows the first results obtained for different contact sizes which demonstrates again the high performance of Zr electrodes.

The electrical current was lower at RT because of the high resistance of both active layer

I. INTRODUCTION

Metal-semiconductor interfaces are necessary to implement sensors and electronic devices, and diamond does not escape to this need. Building well defined interfaces at nanometer scale is specially necessary for electrical rectifiers, which can gain high benefits from the bulk properties of boron doped diamond like its very high thermal conductivity, hole mobility and electrical breakdown field 1,2 if specific properties of the interface are also fulfilled. These are mainly good adhesion, thermal and chemical stability at elevated temperatures, compatible with the superior possibilities of diamond, and potential barriers ensuring both low electrical losses under forward voltage and minimal reverse currents even at high temperatures.

Several attempts have been proposed, relying either on materials which react with the bare surface of diamond to form carbides, like silicon 3 or refractory metals and compounds 4-6 , even hetero-epitaxially grown on diamond 7 , or metals on either the oxygenated or hydrogenated surface of diamond 8-12 . In the first case, potential barriers near or higher than 2 eV, stable at temperatures higher than 500 have been obtained but reverse current densities and ideality factors were much greater than expected from the thermionic mechanism alone at least at room and moderate temperatures, and some of these contacts were ohmic. These poor rectifying current-voltage characteristics has been assigned to inhomogeneous and defective interfaces, specially with carbide forming metals 8,13 . Lower potential barriers are implemented on the hydrogen-terminated diamond surfaces due to the dipole H +ϑ -C -ϑ responsible for the negative electron affinity of these surfaces, where ϑ is the averaged fraction of the elementary charge per atom. But the chemical stability is not guaranteed at temperatures as high as in the first case, and reverse current densities turn out to be hardly weaker than 10 -7 A/cm 2 at room temperature, still higher than the thermionic limit. plane, the current density can be written from the previous expression, in the case of a voltage V j applied to the junction 19,22 :

J z,2 = e 0 N M v coll 1 + v coll /v dif f exp (-e 0 Φ B /k B T ) [exp(e 0 V j /k B T ) -1] (2)
with N M being the effective density of states at the majority carrier band edge, k B the Boltzmann constant, T the absolute temperature, v coll the collection velocity at interface

k B T
2πm * , due to the thermionic effect and equal to one quarter of the thermal velocity, m * the conduction effective mass of majority carriers, and v dif f their diffusion velocity. The previous expression takes into account the two transport mechanisms of majority carriers which work in series, due respectively to the thermoionic velocity at interface and diffusion velocity inside the depletion zone, whereas it neglects bulk recombination. The diffusion velocity simplifies into the product of the majority carrier mobility by the electric field at interface if the band bending exceeds some k B T /e 0 units and is generally not the limiting factor for the direct current, as confirmed in the samples under study from the comparison of the two velocities. The numerator of the first factor in Eq. ( 2) can be rewritten A * T 2

where A * = (4πe 0 k 2 B m 0 /h 3 ) × (m * /m 0 ), the first quantity inside the parenthesis being the Richardson constant for emission of electrons into vacuum with a mass m 0 at rest, A R = 120 A cm -2 K -2 . Because v dif f decreases with the increase of the forward bias voltage V j , the pre-exponential factor of Eq. ( 2) becomes voltage dependent. Other reasons for such an effect involving also the factor exp (-e 0 Φ B /k B T ), are (i) the image force lowering of the barrier, (ii) tunneling through the top of the barrier eventually assisted by the electric field, (iii) voltage drop inside an interfacial layer between the metal and semiconductor, (iv) charging interface states in equilibrium with the semiconductor and (v) a spatially inhomogeneous barrier as discussed further. However, the second effect is noticeable only in heavily doped semiconductors, a case which is not achieved in this study since the boron concentration of the lightly doped layer is close to N A = 5×10 15 cm -3 . As one almost always wants to characterize the Schottky contact with a single potential barrier, the more common approximation consists in keeping only the zero bias voltage barrier height Φ 0 B in the first exponential factor of Eq. ( 2) and gathering all the voltage dependent effects into the last factor. Since all these effects contribute to a slope of the logarithm of the current which is smaller than e 0 /k B T , an ideality factor n larger than one is introduced in the denominator of the exponent of exp(e 0 V j /k B T ) and often considered as a constant at least for a given temperature. Such an hypothesis is strictly valid in the case of an interfacial layer where the voltage drop is a constant fraction 1 -1/n of the band bending U = Φ 0 B -V j -V dop (with e 0 V dop being the energy difference between the Fermi level and majority carrier band edge in the bulk semiconductor) mainly determined by the oxide capacitance and density of interface states 23 when mechanisms (ii) and (iii) are combined. But it is not adequate if the interfacial layer either allows tunneling of carriers as the main transport mechanism or does not display any additional barrier for majority carriers because of band alignments similar to those occurring in type II heterostructures, or in the case of barrier inhomogeneities and even with image force lowering. Other effects, which are due to quantum reflexion, transmission and phonon scattering of carriers at the interface are voltage independent and generally very weakly temperature dependent so that it is convenient to lump them into an effective Richardson constant A * * which is weaker than A * by some tens of percent in the case of intimate Schottky contacts 24 , yielding the standard value of 90 A cm -2 K -2 usually considered for diamond. This effective Richardson constant can be further severely decreased because of the attenuation by a factor α of the collection velocity v coll due to additional scattering of carriers by charged centers and roughness, and transport mechanisms through the interfacial layer when they exist. Finally, the non ideal current density is rewritten as :

J z,3 = αA * * T 2 exp - e 0 Φ 0 B k B T exp e 0 V j nk B T -1 (3)
Experimental current-voltage characteristics can then be accounted for by such an expression with the ideality factor n as an adjustable parameter, provided αA * * is known and the series resistance R s is adjusted in order to fit the additional voltage drop R s I z appearing in the total measured voltage V = V j + R s I z . This is done in Fig. 2 for the three interfaces near room temperature. Two kinds of deviation between experimental data and the theoretical laws may appear as it can be seen on Fig. 2 ; the first one is due to a non constant ideality factor as long as the voltage drop in the series resistance is negligible (typically below 0.5 A/cm 2 in these diodes at room temperature) and the second one is due to less common transport mechanisms which are discussed in the following. It is worthwhile to notice that the rectification ratios are more than twelve decades and that no generation-recombination current is detected on these current-voltage characteristics, which would have involved a symmetrical behavior of the absolute value of the current around the origin at low voltages. c), in good agreement with the theoretical ones, but current densities above a few A/cm 2 turn out to be higher because of conductivity modulation due to hole injection from the heavily doped layer. Full lines rely on models which incorporate barrier height lowering and are described in section IV, with Eq. ( 7) for the cases (b) and (c), while Eq. ( 14) is used for the case (a). Horizontal arrows mark the flat band situation in each junction. The effect of image force lowering is displayed in the inset for the case (a). In the hatched area, self-heating becomes important. The second one is the preliminary indication of the presence of barrier inhomogeneities, a conclusion similar to that obtained in ref. 26 about silicides-silicon interfaces, also implying additional consequences which have to be analyzed more thoroughly.

Zero voltage barrier heights and averaged ideality factors are displayed in Fig. 4 as a function of temperature. On the first hand, the former quantities experience indeed an increase with temperature with generally an asymptotic behavior towards highest temperatures, while the latter ones are decreasing, starting from very different values at room temperature (which are reported in Table I) and displaying very different negative slopes.

As noticed previously, such variable ideality factors cannot be ascribed to a voltage drop within an interfacial layer bearing an additional barrier to that built in the semiconductor, because they would not be coherent with oxide interfacial layers which still exist at the three interfaces. On the other hand, experimental data plotted in Fig. 2 deviate from the simulated curves drawn in dash-dot lines on the basis of a constant ideality factor when voltage drop in the series resistance and other effects remain negligible. A first attempt to fit more accurately experimental results uses an alternative definition of the current density, which is also more physically meaningful. It consists in using a temperature and voltage dependent barrier height Φ B (T, V j ), so that the current density can be rewritten more usefully for the homogeneous barrier case:

J z,4 = αA * * T 2 exp - e 0 Φ B (T, V j ) k B T exp e 0 V j k B T -1 (4)
Introducing an inhomogeneous barrier which follows a Gaussian spatial distribution in the

xy plane of the interface, characterized by an average value Φ B (T, V j ) and a standard deviation σ Φ (V j ), permits to derive 21,26 a law similar either to Eq. ( 3) or ( 4), with an effective barrier given in the second case by :

Φ B (T, V j ) = Φ B (T, V j ) - e 0 σ 2 Φ (V j ) 2k B T (5)
For each temperature, it is always possible to convert Eq. ( 4) into Eq. ( 3) through the definition of a voltage independent barrier height, conveniently taken at V j = 0, and a voltage dependent ideality factor n(T, V j ), valid in all situations, the inverse of which being evaluated from the derivative of the logarithm of the current density given by Eq. ( 3) and ( 4) when the reverse saturation current is neglected:

k B T e 0 d(ln J z ) dV j = 1 n(T, V j ) = 1 - dΦ B (T, V j ) dV j = 1 + dΦ B (T, U) dU (6)
However, in this first level model, no explicit dependence of the parameters is given as a function of junction voltage V j or band bending U . Some cases of potential barrier distributions have been analyzed analytically by R. T. Tung 27 , who showed that the dependence of the parameters of Eq. ( 5) was not linear with the band bending and hence with the junction voltage, on the basis of a physical representation of the barrier lowering by a fictitious dipole located at interface. An additional source of non ideality may be present if a spreading resistance effect occurs, involving inhomogeneous current density inside the semiconductor because of current crowding near the pinch-off patches with a lowered barrier and located close to the interface 28,29 . This effect is normally expected to be relevant at current levels where the series resistance voltage becomes larger than some k B T /e 0 . But the combination of multiple barriers and incomplete ionization of doping impurities may induce deviation from the ideal current-voltage characteristic at much smaller currents because of severe weakening of the carrier concentration and narrowing of the current paths in the lowest barrier patches which cannot be assessed easily from the comparison to a voltage drop in an averaged series resistance. This kind of non ideality will be discussed in the next section. (c') and as a dash-dot curve for (a'), but using a non physical parameter in the last case. The full curve adjusted on (a') data exploits Eq. ( 17) and related ones with more meaningful parameters at the expense of a worse agreement with data (see text).

In the simple model presented above, the barrier fluctuations are characterized by their average and standard deviation but are not supported by any physical model. Such an approach prevents to work out the detailed electrical properties of the junction, specifically the behaviors of the barrier lowering and ideality factor with voltage and temperature, unless arbitrary hypothesis are made. Therefore, the reasons for these barrier inhomogeneities have to be analyzed more accurately and an analytical model which will generalize that developed by R. Tung 27 will be implemented in the next section, concurrently with a realistic simulation of some potential fluctuations at interface. But within the framework of the simple approach developed in the present section, it is already possible to derive the two parameters Φ B (∞, 0)

and σ Φ (0) at zero voltage from the fit of these quantities according to Eq. ( 5), which are renamed respectively Φ 0 B,∞ and σ 0 Φ for sake of simplicity and displayed in the Table I, for the three types of interface. The average barrier height at infinite temperature Φ 0 B,∞ decreases by about 0.5 V after each anneal while the standard deviation σ 0 Φ of the barrier fluctuations goes through a maximum after annealing the interface at 350 . But the deficiency of the present model is confirmed by the different behaviors of the ideality factor with temperature plotted in Fig. 3 which cannot be explained. These discrepancies confirm the need for a more accurate model of the effect of potential fluctuations at interface upon current-voltage characteristics.

Meanwhile, an unusual result which ensues from the calculation of the current densities necessary to draw the fitting curves in Fig. 2 can be already pointed out. At some current threshold, flat bands are reached (see the arrows in the same figure) and it is necessary to consider that accumulation occurs at the interface to explain the continuous increase of the current densities beyond this threshold. Such a behavior matches Eq. (1) which states the proportionality of the current to a velocity and carrier concentration at interface. For example in the case (c), flat bands are reached at a voltage of 0.63 V, corresponding to an initial band bending of 0.97 -0.38 = 0.59V (here V dop =0.38 V) plus the barrier increase of 0.04 V demonstrated in the next section, and the current density calculated directly with the hole concentration given by formula (1) in ref. 1 , assuming a compensation of 20% (donor concentration N D = 10 15 cm -3 ) and Eq. ( 1), with a collection velocity ten times smaller than that for an intimate contact, yields 0.4 A/cm 2 , very close both to the experimental one and that calculated by Eq. ( 4). In cases (b) and (a), still at 300K, flats bands are reached respectively at lower current densities indicated in Fig. (2), which cannot be calculated with the help of the initial model because the apparent barrier heights deduced presently are largely underestimated and would produce irrelevant band bending. Therefore, assessing these values needs to wait for more accurate and physically relevant models which will be developed in the next section. In Eq. ( 2) and subsequent ones, the barrier height has been introduced for convenience and it was often believed as an impassable limit in Schottky diodes. Such a statement is not true as everyone can be convinced if he realizes that Eq.

(2) and subsequent ones all derive from Eq. ( 1) where the current is controlled by a carrier concentration. Band curvature reversal and occurrence of accumulation regime are possible and even necessary to reach high currents, up to more than thousand times that those got at flat bands, in these interfaces made on oxygen-terminated diamond, because firstly of the low values of the effective Richardson constant, secondly of the wide forbidden bandgap of diamond and thirdly of the large ionization energy of acceptors. In such a regime, diffusion flow is inverted close to the interface, the barrier seen by majority carriers is canceled and consequently, the models relying on Eq. ( 2) and following ones, and on the properties of barrier height inhomogeneities, specially their voltage dependence, become inappropriate.

Conversely, current crowding near the pinch-off patches with a lowered barrier may become a major source of non ideality. If possible, these mechanisms have to be incorporated into the forthcoming models or else, at least kept in mind to assess the applicability of the following developments.

IV. POTENTIAL BARRIER INHOMOGENEITIES AND IDEALITY FACTOR

A. Potential fluctuations due to randomly distributed discrete charges and dipoles

The electrostatic potential experienced by mobile carriers originates from fixed charges scattered inside the space charge zone and interface. For modeling purposes, it is often derived from constant bulk charge concentration in the space charge zone and homogeneous charge density at interface. This view is correct for mechanisms characterized by lengths larger than the Debye length λ D = ε SC ε 0 k B T /(e 2 0 N A ), where ε SC and ε 0 are respectively the relative permittivity of the semiconductor and the vacuum permittivity, and when average laws are evaluated, but may fail if some physical property of carriers experiences microscopic fluctuations. Indeed, when the effects of potential inhomogeneities are at stake, the discrete nature of fixed charges accommodated within the metal/semiconductor or metal/oxide/semiconductor (MOS) structure must be taken into account and the average distance between these discrete charges have to be compared to λ D . Here, λ D amounts to 40 nm at 300 K and 52 nm at 500K. Three locations have to be considered: (i) inside the depletion zone, the average distance between ionized acceptors is 58 nm, very close to λ D . Only those which are at such comparable distances from the interface influence the potential barrier height, as clearly evidenced in a following subsection. (ii) The oxygen terminations bonded to the carbon atoms of the (001) diamond surface are making up the negative part of the interface dipole, really present at the interface up to some annealing temperature, an inverted situation in comparison to what happens on the hydrogenated diamond surface, due to the sign change of the electronegativity difference between carbon and oxygen or hydrogen respectively. The positive counterpart of this dipole lies within the first and second carbon layer just below the surface, resulting in a potential jump through the surface of ∆q d di N di /(ε i ε 0 ) where ∆q is the charge transfer, d di the dipolar distance, N di the site density and ε i the relative interface permittivity 21 . This potential jump is directly reflected by the electron affinity change provided by oxygen terminations. In average, it can be estimated close to 1.7 V because the smaller difference between electron affinities of the free (2 × 1) reconstructed surface and the oxygenated surface 30 is probably due to already electron depleted bonds in the last carbon layer of the former one. Taking into account the 30 percent coverage measured by X-rays photo-electron spectroscopy 31 on our samples treated by UV-ozone, equivalent to 5 × 10 14 sites per cm 2 , a whole distance normal to the interface of roughly d di = 0.1 + 0.2 = 0.3 nm and ε i = 2, the estimated charge transfer turns out to be 2×10 -20 C, that is ϑ =0.13 electronic charge. However, it is known firstly that there are several oxygen terminations, at least ether (C-O-C), carbonyl (C=O), hydroxyl (C-OH) and carboxyl (O=C-OH) groups 32-35 as individual adsorbates and eventually epoxide (bridged oxygen between two adjacent carbons) 36 in case of UV-ozone treatment as done on our samples. The electron affinities calculated theoretically for the three first terminations are different 34,37 . Secondly, all the sites are not occupied (in our case, about 30 percent, like when oxygen plasma treatment is applied to the diamond surface 31 ) but when adjacent sites are provided with an oxygen termination, polymerization along chains may occur 32 . Therefore, the dipole strength resulting from these various adsorbates and able to modify the potential barrier height is far from being homogeneous at least over a scale length of few nanometers and also along a much larger scale if the various terminations are arranged in macroscopic domains, resulting in effective laterally non-uniform electronic affinity. An other reason which may lead to scattered patches with different barrier heights would be the chemical inhomogeneities like often present when carbide formation occurs 13 , which might also happen if the chemical composition of the interfacial oxide layer or its thickness were not homogeneous throughout the interface, although no evidence of such properties exists in the present case. And last but not least, extrinsic defects such as emerging dislocations cannot be excluded as sources of locally lowered barrier height like revealed at CoSi 2 /n-Si(001) interfaces by ballistic electron energy microscopy 38 . On the contrary, the intrinsic dipole due to charge transfer across the interface because of an eventual misalignment of the charge neutrality levels in the two materials is supposed to be homogeneous because it results from the occupation of gap states which are delocalized in the plane of the interface and will not participate in potential fluctuations. (iii) As evidenced in the following, discrete charged centers exist inside the oxide of MIS structures and are expected to be also present in the thin interfacial oxide of the Schottky contacts. These cases are treated quantitatively in the next subsections and are brought face to face to experimental and simulation results. for the electron affinity of oxygen-terminated p-type diamond 30,41 , E G = 5.45 eV for the diamond band gap and φ F = (E i -E F ) /e 0 = 2.35 V deduced from the difference between intrinsic and Fermi energy levels in bulk boron-doped diamond, assuming no charge in the oxide. The discrepancy comes from this last hypothesis which is not verified, implying that the real situation comprises a positive charge inside the parenthesis of the last term in

V F B = Φ MS -Q is (0) + Q ox /C ox , where C ox is the oxide capacitance density, Q is (0)
and Q ox being respectively the charge per unit area in interface states at flat bands and the product of the total charge per unit area within the insulator by the ratio of the barycenter of this charge to the insulator thickness 39 . To reconcile the two values, a total number of positive charges per unit area must amount to 2×10 13 cm -2 within the 25 nm thick oxide layer.

The centers which accommodate charge may experience change of their charge state if some mechanisms are occurring, like carrier emission from interface states lying in the common forbidden gap of the two materials, and also transport by hopping and tunneling across some thickness of the insulator. Such effects give rise to transient capacitances in the MIS structure because of the rearrangement of all the individual electric dipoles necessary to comply with the rule of a constant whole electric dipole if the MIS is submitted to a constant voltage 39 . Isothermal spectra are displayed in Fig. 5(b) and (c) as a function of the characteristic emission time. They are obtained from the Fourier transform of the transients which are recorded after two filling pulses lasting respectively 1 ms and 100 ms. They show a two peaks structure, the slower peak being higher for the longer filling pulse. This response can be viewed as the projected spectrum of states on the interface energy scale inasmuch both states located at interface and some oxide states as well may exchange holes with the valence band of diamond. Differential spectroscopy is here unnecessary just because emission from discrete interface states in the common bandgap largely dominates that from a hypothetical continuum since peaked structures clearly appear in Fig. 5, and an accurate calibration of the energy scale is not needed. The smaller filling pulse duration t p = 1 ms has been chosen to ensure complete filling of interface states even with capture cross sections as low as 10 -19 cm 2 , whereas the larger t p = 100 ms is able to involve additionally either injection or extraction of carriers trapped in discrete states localized within the insulator at some distance from the interface. The important point consists in the different behaviors followed by the two peaks as a function of t p : the first occurring at the shorter emission time is very weakly sensitive to t p and consequently related to an interface state whereas the second one increases with t p , involving carrier transport through some insulator slice. This is the demonstration that at least one discrete state exists inside the oxide. An order of magnitude of the distance d of these centers from the interface can be estimated from the inverse of the attempt-to-escape time checked by Jain and Dahlke for traps in Si/SiO 2 interfaces 42 and given by ν 0 exp(-qd), with ν 0 10 16 s -1 and α 1.05 Å-1 , yielding roughly

ζ 0 , that is 4u im (ξ -ξ 0 ) 2 + ν 2 + (ζ + ζ 0 ) 2 + 4u im (ξ + ξ 0 ) 2 + ν 2 + (ζ + ζ 0 ) 2
or replacing either one or two of the previous terms by

- 4u im (ξ ∓ ξ 0 ) 2 + ν 2 + (ζ + ζ 0 ) 2 + 4u im (ξ ∓ ξ 0 ) 2 + ν 2 + (ζ -ζ 0 ) 2
at either one location +ξ 0 or both locations ±ξ 0 to simulate either one or two elementary dipole due to negative oxygen termination beyond the interface and its positive counterpart on the diamond side. A 3-dimensional view of potential barriers in several cases is given in solutions of the quartic equation, and can be expressed as

ζ sad ≈ χ(U ) [ζ 0 -2χ(U )] with χ(U ) = u 1/2 im 2k B T e 0 -1/4 U -k B T e 0 -1/4
, and results in δΦ sad B,1 ≈ 4 u im / (ζ 0ζ sad ). The resulting effects of this barrier height lowering will not be treated in detail here. In the three first cases, the distribution function of potential barrier heights is then calculated with a fixed value of ζ 0 and random values of ξ 0 around a mean ξ 0 according to a normal law with a standard deviation σ ξ , to assess the possible values of Φ B (T, V j ) and σ Φ (V j ), the characteristic parameters of the inhomogeneous barrier.

In a first step, the parameter σ Φ (0) is adjusted to match the values displayed in Table I at a medium temperature, typically 500 K with realistic values of ζ 0 , ξ 0 and σ ξ . More specifically, ζ 0 λ D spans the range 0.2 to 0.46 nm and (ξ 0 λ D ) -2 the range 1.5 × 10 12 cm -2 to 3 × 10 14 cm -2 , the two later limits featuring respectively a positive charge density inside the oxide layer and the dipole density at the oxygen terminated surface. Accordingly, the average distances ξ 0 between point charges or dipoles span a range limited by 0.08 and 0.007 (in λ D units) respectively. Therefore, the barrier height fluctuations are occurring along a microscopic scale, well below the Debye length. In a second step, the band bending is changed and the values of Φ B (T, U) and σ Φ (U ) are evaluated as a function of the band bending U . In all the cases and whatever the temperature, as suggested in 26 , the increase of the average barrier height Φ B (T, V j ) and the decrease of the standard deviation σ Φ (V j ) with increasing forward voltage and correlative decreasing band bending is fully confirmed, although the barrier height distribution is not symmetric and cannot be strictly depicted by a normal law. The trends followed by the two terms of Eq. ( 5) both contribute to an increase of the barrier height with forward voltage which can be also interpreted as an increase of the ideality factor, thus inducing a lower current density in comparison to that anticipated with the help of a constant ideality factor like sketched with dash-dot lines in Fig. 2. At variance with the hypothesis used in ref. 26 , neither the variation of Φ B (T, V j ) nor that of σ Φ (V j ) 2 is linear with V j or U , a law which would have resulted in a constant ideality factor, in contradiction both with experimental and simulation results. An other major feature is the relative insensitivity of the ideality factor to the density of point charges or dipoles (ξ 0 λ D ) -2 , the former starting from 1.01-1.02 for band bending corresponding to zero voltage bias and growing up to 1.05-1.15 when the band bending U becomes close to a few k B T /e 0 like shown in Fig. 7, irrespective of the temperature. The barrier height variations which are deduced from the ideality factor match very well those of the image force lowering as clear in Fig. 7 too. This result coming from the simulated inhomogeneous barrier height with repulsive elementary charges or dipoles demonstrates that the image force lowering and its changes with the band bending is the main source of the variation of the average barrier height with the applied voltage, because barrier height enhancement does not contribute significantly to the whole barrier experienced by carriers responsible for the current, except for a reduced effective area. Such a result validates this hypothesis already done in ref. 27 . The whole variation amounts to about 40 mV like inferred in ref. 21 for the image force lowering alone.

It is thus possible to derive a universal law featured by a solid line in Fig. 7 that may be used to derive current density-voltage characteristics with the help of Eq. ( 4) and ( 6). The first important result coming out from this simulation turns out to be the better agreement of the simulated current density sketched in solid line in the inset of Fig. 2 in the case (c) where the barrier height correction has been taken into account. The second one is the insensitivity of the ideality factor to temperature, a property which matches rather well the behavior of the interface (c) in Fig. 4 (c'), in contrast to the absolute variations in data (a') and (b'), although the ideality factor (c') remains slightly higher than the values evaluated from the image force lowering alone. Taking all the arguments evidenced and discussed in the present subsection, one must conclude that microscopic barrier inhomogeneities resulting from repulsive elementary point charges or dipoles which have been however, experimentally evidenced, cannot account for most of the properties of the interfaces presently studied, and that an other type of barrier inhomogeneity must be present. The calculation of barrier height fluctuations due to barrier height lowering ∆ p at circular patches with radius R 0 or linear ones with width L 0 and their effect on the current-voltage characteristics relies on the same principle as previously, except for the weight of each dipole which has to be 2πε SC ε 0 ∆ p R 2 0 to induce the desired barrier change at circular patches which will be only considered in the following because close to those happening naturally in inhomogeneous interfaces. Additionally, only patches with a lowered barrier are considered as demonstrated in the previous subsection. This method, known as the dipole-layer approach, has been implemented analytically by R. T. Tung 27 and summarized later by W.

Mönch 21 . For a single circular patch with radius R 0 and barrier lowering ∆ p embedded into a homogeneous area characterized by a constant barrier height Φ hom B , a single parameter containing the two characteristic quantities R 0 and ∆ p , which is called the patch parameter γ p = 3(∆ p R 2 0 /4) 1/3 can be defined. Integrating Eq.(1) over the whole area A with the hypothesis of a parabolic shape of the potential around the saddle point restores the form of Eq. ( 3). But the new barrier height is Φ hom This choice was justified by the negligible contribution of patches characterized by a barrier height enhancement to the whole current as we checked in the previous subsection. In order to generalize such an approach, allowing to match continuously any intermediate behavior between the two previous cases, the patch parameter distribution function will be chosen

as N (γ p ) = Dp √ 2πσ p exp -(γp-γ 0 ) 2 2σ 2 p
, characterized by a standard deviation σ p of the patch parameter around the central value γ 0 and an areal density D p . Depending on γ 0 , the function N (γ p ) depicts either a peaked distribution around the central patch parameter, or half a Gaussian law decreasing from its maximum at γ p = 0 when γ 0 = 0 or even a decreasing Gaussian tail with a non zero initial slope if γ 0 < 0. After summation of all the currents dependent on any positive value of γ p from zero to infinite, this procedure further allows to derive the following expression where only the last factor contains the effects of inhomogeneities while the others give the ideal thermionic current density of a homogeneous barrier height Φ hom B :

J patchy z = α A * * T 2 exp - e 0 Φ hom B k B T exp e 0 V j k B T -1 × 1 + 2 √ 2π k B T D p σ p η 2/3 9 e 0 U 2/3 exp - γ 2 0 2σ 2 p 1 + √ 2π e 0 < δΦ sad p,0 > k B T exp 1 2 e 0 k B T < δΦ sad p,0 > 2 (7)
where the standard deviation < δΦ sad p,0 > of the distribution of the saddle point of the barrier Φ sad p is:

< δΦ sad p,0 >= σ p U η 1/3 + k B T γ 0 e 0 σ p (8)
But the current density deviates notably from the ideal thermionic law only if the factor inside the braces of Eq. ( 7) is larger than unity. As one is interested in this case, a reasonable approximation consists in neglecting the unity terms inside the braces, so that the effective barrier height can be deduced from the exponent of the exponential factors, which turns out to be 1 2

e 0 k B T < δΦ sad p,0 > 2 - γ 2 0 σ 2 p
inside the braces of Eq. ( 7) and logarithm of the preexponential factor :

Φ ef f B (T, U) = Φ hom B - e 0 2k B T σ 2 p U η 2/3 + γ 0 U η 1/3 - k B T e 0 ln 4π D p σ p η 2/3 9 U 2/3 < δΦ sad p,0 > (9)
This last equation is similar to Eq. ( 5) with the new quadratic average < δΦ B > of barrier fluctuations

< δΦ B >= σ 2 p U η 2/3 + 2k B T e 0 γ 0 U η 1/3 1/2 (10)
and an additional term which has a little influence due to the logarithm and a null value for D p in the 10 10 cm -2 range, but may give a non negligible contribution to the ideality factor appearing in next formula when the barrier inhomogeneity level is low. But the main issue is the dependence of < δΦ B > on temperature which is different from that given by Eq. ( 5) and results in a shift of the high temperature asymptote of the effective barrier in From Eq. ( 6), ( 8) and ( 9), the ideality factor can be calculated as: (11) where k Φ is between 1/3 and 2/3 according to the respective dominance of either the first or the second term in < δΦ B >. This ideality factor increases with decreasing band bending and therefore with increasing applied voltage as long as flat bands are not reached, so that current-voltage characteristics plotted in a semilogarithmic diagram experience a downwards curvature, as in Fig. 2 2) respectively to Eq. ( 7) for interfaces of kind (b) and (c) and Eq. ( 14) for interface of kind (a) as a function of voltage.

n(T, U) -1 n(T, U) = e 0 3k B T U σ 2 p U η 2/3 + k B T e 0 γ 0 U η 1/3 -k Φ k B T e 0 U = e 0 3k B T U < δΦ B > 2 - γ 0 3η 1/3 U 2/3 -k Φ k B T e 0 U
D p Φ hom B,2 annealing temp. V V 1/3 cm 2/3 V 1/3 cm 2/3 V cm -2 V (a) < 300
as a function of temperature, like shown in Fig. (4), where evolutions of the ideality factor are markedly different for the three interfaces in Fig. (4a'), (4b') and (4c'). All these features can be reproduced by the laws demonstrated above, specially the ideality factor variations with temperature which are strongly influenced by the central patch parameter γ 0 in Eq. ( 11). In the case (a), a good agreement with Eq. ( 11) can be obtained as depicted by the full curve in Fig. (4a') at the expense of a negative central patch parameter which would induce an apparent barrier Φ app B larger than the homogeneous one Φ hom B , obviously leading to an incoherent physical situation. Moreover, the direct adjustment of the current density according to Eq. ( 7) turns out to be impossible because this expression is unable to account for the curvature of the current density-voltage characteristic (a) in Fig. may no longer be the Debye length but much more, and the approximations of a parabolic potential at the bottom of the lowered barrier patches depicted by the patch parameter γ p would cease to be valid. Secondly, strong variations of the ideality factor with temperature like in Fig. (4a) suggests that diamond resistivity may play a role because acceptors are progressively ionizing in this temperature range.

E. Barrier domains with multiple sizes and inhomogeneities of the current density

When the lateral size of barrier inhomogeneities largely exceeds the Debye length, the previous model relying on a parabolic potential at the bottom of the patches with a lowered barrier is no longer relevant. These different areas with distinct barrier height can be treated as independent of the band curvature because the pinch-off of the channels where the current flows becomes negligible. Then, the total current is simply obtained by summation of all the currents like in a parallel circuit of the corresponding paths. But such a model is unable to fit the downward curvature experienced by the logarithm of the current density as a function of voltage in interfaces of kind (a) and yields merely an ideal behavior as soon as the lowest barrier is shifted below the others by some k B T /e 0 because the corresponding current flow dominates the others. But this current inhomogeneity due to carrier crowding at the saddle points and lowest barrier domains remains when the z coordinate move away from the interface and therefore have a dramatic influence on the total voltage applied to the junction for a given current, specially when carrier freeze-in occurs, inducing large variations of the ideality factor with temperature. This effect is relevant both for barrier domains much larger than the Debye length where no pinch-off occurs and for pinched-off patches, and the voltage drops in these shrunk channels must be subtracted from the total applied voltage. In the pinched-off case, the diameter of patches is always much smaller than the lightly doped layer thickness t l so that the spreading resistance can be approximated by ρ(T ) 4 √ A p-o ef f,i /π with a good accuracy 45 , ρ(T ) being the resistivity of the lightly doped diamond layer. Therefore, the non pinched-off and pinched-off forward currents which flow respectively through individual areas A i and A p-o ef f,i under an applied voltage V a read:

I non-p-o i = A i α A * * T 2 exp - e 0 k B T Φ hom B -∆Φ -V a + I non-p-o i ρ(T )/λ i (13a) I p-o i = A p-o ef f,i α A * * T 2 exp   - e 0 k B T   Φ hom B -γ p U i η 1/3 -V a + ρ(T ) 4 A p-o ef f,i /π I p-o i     (13b) with A p-o ef f,i = 4 π k B T γp 9 e 0 η U i 2/3 and U i = Φ hom B -γ p U i η 1/3 -V a -V dop + ρ(T ) 4 √ A p-o ef f,i /π I p-o i ;
the lowest barrier spreading over the areas A i with size much larger than the Debye length being Φ hom B -∆Φ. If the current inhomogeneity remains the same along the whole with

∆V non-p-o ≈ ρ(T ) A non-p-o (A non-p-o ∆V ) 1/2 αA * * T 2 exp - e 0 k B T Φ hom B -∆Φ -V a + ∆V non-p-o (14b)
and J p-o = J patchy z from Eq. ( 7), with

V j = V a -∆V p-o where ∆V p-o ≈ π 6 ρ(T ) k B T e 0 1/2 η U 1/3 1.77γ 0 + σ 2 p /(γ 0 + √ 2σ p ) π γ 0 + √ 2σ p /3 × αA * * T 2 exp - e 0 k B T Φ hom B - e 0 2k B T < δΦ B > 2 -V a + ∆V p-o (14c)
and

U ≈ Φ hom B - e 0 2k B T < δΦ B > 2 -V a -V dop (14d)
It must be noticed that the patch density D p does not appear in ∆V p-o because both the conductance and current are proportional to it, so that it is canceled in the framework of the previous approximation. From these expressions, it is easy to guess that the lower the temperature, the higher the effect of the smallest barrier, like in previous models. If the non pinched-off current dominates, the apparent barrier lowering would be ∆Φ -k B T e 0 ln (A d /A non-p-o ), inducing a linear decrease of the effective barrier as temperature is lowered, whereas alternatively Eq. ( 9) would be valid, at least when ∆V remains small regarding V a . At sufficiently high temperature, the increase of the effective barrier would be linear with temperature when the non pinch-off current dominates, an effect which is not clearly detected in Fig. (4a), indicating that the pinch-off current might be the major one. Such a view is confirmed by the absence of any "S-shaped" current-voltage characteristic in From experimental data displayed in Fig. ( 8), it seems that the general trend involving a linear relationship between effective barrier height and ideality is still valid. Such a property can be checked from the integration of the central expression in Eq. ( 6) with V a replacing V j . It results in a linear relationship between the effective barrier and ideality factor function if the ideality factor does not depend on the band bending. Such a condition is only approximately achieved, but better and better when higher and higher band bending are used, like those deduced from these data and reported in Table III. In such conditions, the voltage drop ∆V remains negligible and the ideality factor is close to a constant value when the band bending changes. In such an approximation, K and C being constants, one gets from the integration of Eq. ( 6) :

n(T, V a ) -1 n(T, V a ) = K Φ ef f B (T, V a ) + C (15)
Therefore, the observed linear correlations in Fig. 8 can still be justified but the integration constant is not known and can be replaced by the term proportional to γ 0 in Eq. ( 12) only if the model relying on a patchy barrier height with a negligible voltage drop inside the lightly doped layer is relevant. In the opposite case, specially when non pinched-off zones dominate, the second member of the previous equation would be K (Φ hom B -∆Φ) with an ideality factor close to unity if the previous condition applies, since the current would be essentially thermoionic in nature. In the general case, an uncertainty remains about the physical meaning of the extrapolated barrier and its eventual difference with Φ hom B . When the voltage drop inside the lightly doped layer is not negligible, approximate expressions of the ideality function can be drawn separately from the previous equations when either

I non-p-o = A d J non-p-o z or I p-o = A d J p-o z
dominates, which turns out to be respectively:

Y non-p-o = n a (T, V a ) -1 n a (T, V a ) ≈ e 0 k B T ∆V non-p-o (16a) or Y p-o = n b (T, V a ) -1 n b (T, V a ) ≈ e 0 3k B T U σ 2 p U η 2/3 + γ 0 3 U U η 1/3 1 + e 0 k B T ∆V p-o + e 0 k B T ∆V p-o (16b)
When the ideality factor has to be studied as a function of temperature, measurements should be done at constant current density, because in such a case the product of αA * * T 2 and exponential factors in Eq. (16a) and in the term ∆V p-o of Eq. (16b) can be considered as almost invariant, making any parameter adjustment much easier. In each case, these expressions shows that the ideality factor may become very sensitive to temperature, specially because it follows the variations of the resistivity ρ(T ) which are very important in the range where freezing out of carrier occurs, typically from 300 K to 550 K in this study. Involvement of the voltage drop due to the flow of current through the narrow bottlenecks which lengthen the lowered barrier regions inwards the lightly doped layer is able to explain qualitatively the strong negative slope of the ideality factor in Fig. (4a'). The general case relies on the combination of the two kinds of current with a proportion P = I p-o /(I p-o + I non-p-o ) and on Eq. ( 6), giving the global ideality function:

Y = n(T, V a ) -1 n(T, V a ) = P Y p-o + (1 -P ) Y non-p-o (17)
The best match to the four data at highest temperatures is obtained with P = 72% and plotted as a full curve in Fig. (4a'), confirming the previous hypothesis about the dominance of the pinched-off current. The discrepancy at the lowest temperatures is commented in the following. But it must be stressed that the first term in Eq. ( 17) is unable to account for the ideality factor variation, which are mainly due to the second term despite its smaller weight. It is thus confirmed that the non pinched-off currents contribution is necessary to explain both the current density-voltage curvature and the ideality function shape with temperature in interfaces of kind (a). The more important voltage drop ∆V non-p-o in these interfaces is also able to explain why flat bands are reached at a lower current density (see Fig. 2) in comparison to interfaces of kind (b) and (c) in which the patch and channel densities are so high (see Table II) so that the voltage drop remains negligible in this bias domain.

At sufficiently high forward bias, band curvature can be inverted in some areas or even in the whole diode, as the reader can realized from the comparison of Φ hom B (in Table II) minus V dop = 0.38 V to the applied voltage in Fig. (2), so that the previous expressions can no longer be used. From Eq. ( 10 one to some tens of mW in the range of interest), but is rather due to the injection of carrier by the heavily doped layer, involving a conductivity modulation due to the increase of carrier concentration above the equilibrium one and occurrence of a diffusion current starting from this heavily doped layer. This effect is evidenced from the comparison of the current-density data and curves simulated with a constant series resistance in Fig. expected to be organized in domains displaying distinct electron affinities 31-34,36,37 , resulting in distinct barrier heights, and that the same kind of oxygen terminations can exist on different samples. This dispersion matches that of the various molecules and bonds presented in subsection IV A and probably also the lack of full coverage by oxygen related molecules.

The linear relationship of Eq. ( 12) or ( 15 III, the lowest being about 0.2 V below that indicated in Table II. This local barrier lowering may agree the quantity ∆Φ invoked in subsection IV E over areas with lateral size larger than the Debye length to built the last electrical model detailed in the previous subsection. It can be concluded that, despite some minor imperfect agreements between experimental data and models of inhomogeneous barriers detailed in this section and their limitations to the depletion regime of Schottky junctions, more informations and deeper physical insight into the situation of these metal-diamond interfaces have been gained and can be reinvested in barrier height models discussed in the next section. The most important quantity which can be extracted from the analysis of electrical characteristics of Schottky diodes is obviously the true potential barrier height at an interface free of inhomogeneities and it has been defined at the beginning of this study as Φ hom B . It is always underestimated if the barrier height is measured from the slope of a Richardson plot and a relevant value Φ hom B needs to be deduced either from adjustment of the measured barrier height as a function of temperature, or from the direct adjustment of the currentvoltage density with the appropriate model chosen among those described in this section, or from the statistics of barrier heights as a function of ideality factors in a set of diodes, or preferably from several methods.

V. BARRIER HEIGHT MODELS AT METAL-OXYGENATED DIAMOND IN-

TERFACES

The barrier heights issue at metal-diamond interfaces belongs to the long time debated topic of how the Fermi level position is determined at semiconductor surfaces and interfaces, discussed as early as in the thirties by Sir Nevill Mott 46 concerning the rectification theory and by Walter Schottky 47 . Because this first model, which stated the linear dependence of the barrier height upon the metal work function with a unity slope, did not comply with the huge amount of data gathered since its publication, other explanations have been proposed to justify the weaker dependence experimentally observed, known as Fermi level pinning. New barrier height models have been progressively introduced within the framework of the "metal induced gap states" principle 48 or its generalization to "interface induced gap states" 21 in order to link band alignment and either the work function or electronegativity of the metal at the broadest possible panel of metal-semiconductor interfaces. All rely on the existence of an interface state density localized in the first elementary cells of the semiconductor which is neutral when the Fermi level coincides with an energy level Φ 0 characteristic of the semiconductor and referred as to the neutral level, defined here as the energy difference between such a level and the valence band edge at interface. Deviations from this position and from neutrality occur if a metal having an electronegativity different from that of the semiconductor is put in intimate contact with the semiconductor surface, assuming that the interface states inside the semiconductor remain invariant. This last hypothesis leads to a negative feedback effect due to the reaction of the charge inside interface states onto the voltage jump due to the double layer of the areal dipole astride the interface, which induces a linear relationship between the barrier height and the difference of the metal and semiconductor electronegativities X m -X s , with either a positive slope S X on a n-type semiconductor, or a negative one, -S X , on a p-type semiconductor as here:

e 0 Φ hom Bp = Φ 0 -S X (X m -X s ) ( 1 8 a )
where

S X = A X 1 + (e 2 0 / ε i ε 0 ) D is d di (18b)
with D is the interface state density and A X a coefficient which depends on the electronegativity scale, equal to 0.86 if the Miedema scale is used 21 . This theory was rather successful for intimate metal-semiconductor contacts, which have been better and better controlled at an atomic scale for the seventies, sometimes with an epitaxial metal layer. However, some dispersion still remained, which was not attributable to experimental uncertainties. This is specially true for diamond, which has not been the subject of extensive reports since the nineties, excepted to evidence the wide range of barrier heights existing for the same including that of a hydrogenated diamond surface 17 . This is the second shortcoming. Incidentally, it is difficult to believe that the energy distribution of "interface induced interface states" may remain the same when going from the hydrogenated then air-exposed diamond surfaces to oxygenated ones, as it is well known that the former is provided with adsorbates and conducting whereas the later is not 55 . An other approach, relying on physico-chemical quantities able to influence interface bonding, is necessary.

In the last twenty years, scientists performed modifications of the Schottky barrier heights by means of various ad-atoms and/or physical, chemical and thermal treatments applied to the surface generally before metal deposition excepted for annealing. They realized that these changes are dependent on bonding between interface atoms, and that chemical interactions cannot be ignored between atoms in the neighborhood of the interface. A first improvement of the theory has been brought by R.T. Tung who showed that potential energies in the solids and through the interface were more appropriate to describe band alignment 28 10) can be discussed more thoroughly. First, it is useful to notice that neither the first term in Eq. (19a), which also scales the abscissa in this diagram, nor the second term can account for the observed trend if this later term is supposed to be proportional to the former one because the slope would be increased above one when the ionization energy is held constant. Therefore, one is forced to conclude that hidden physical parameters able to govern this second term might be involved. These are the nature of the bonds and interlayer, the charge transfer across them, their polarizability, and the interface structure with a special attention to the interlayer thickness and relative permittivity. In the case of metals like Pt, Ir and Au, oxide formation is very unlikely since the enthalpy of formation is either positive or close to zero, whereas an oxide is present when Zr, as shown at the beginning of this study, and most probably Al, are used. If the interlayer is supposed to be a dielectric consisting of a ionic solid, its thickness t ox is added to the bond length d bl so that the total dipolar distance

1. 1

 1 SiC devices sales by applications in 2013 its expected evolutions in 2018 and 2020 reported by Yole développement. . . . . . . . . . . . . . . . . . . 1.2 Market segmentation in power electronics reported by Yole développement illustrating device revenues distributesd by voltage range in 2013. . . . . . 1.3 Annual SiC & GaN device market size to 2020 reported by Yole développement. 11 1.4 Diamond Band diagram together with the main dopants. . . . . . . . . . . 1.5 Different architectures of diamond field effect transistors (FET) investigated today: delta-FET (left), Metal Oxide Semiconductor FET (MOS-FET middle), H-terminated FET (right). . . . . . . . . . . . . . . . . . . 1.6 Schematic diagram of Schottky p + -i-n + diodes (left) [Makino 2014], Schottkynp diodes (center), and boron doped diamond Schottky diodes (right) [Umezawa 2014]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Specific on-state resistance and Breakdown voltage [Umezawa 2012] for Si,SiC and diamond vertical Schottky diodes. . . . . . . . . . . . . . . . . 2.1 Temperature dependence of the Hall hole density (a) and mobility (b) of slightly boron doped diamond layers reported by Volpe et al

2 . 5

 25 Theoretical hole density (left), mobility (center), and resistivity (right) calculated at a constant acceptor concentration N A with various compensation levels N D using the analytical model reported by Pernot et al [Pernot 2010]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46 3 . 4

 34 Epi-layers schematic stacking. . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 (a) Schematic diagram of NIRIM type reactor [Fiori 2012] together with its picture (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 (a) Schematic diagram of PLASSYS BJ150 reactor together with its picture (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Incorporated boron vs. ([B]/[C]) in the gas mixture at different ([CH4 ]/[H 2 ]) ratios [Fiori 2012] for NIRIM-type reactor. . . . . . . . . . . . . . . . . . 3.8 Typical surface morphology ( Top view and 3D view) of p + layer obtained by optical profiler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Differential Interference Contrast images (DIC) of main surfaces defects encountered on epi-growth layers [Fiori 2012]. From left to right : Unepitaxial Crystallites (UC), Pyramidal Hillocks (PH), Flat-topped Hillocks (FH), and Round Hillocks (RH). . . . . . . . . . . . . . . . . . . . . . . . 3.10 Typical surface topography obtained by optical profilometry. The main defects such as Unepitaxial Crystallites (UC), Pyramidal Hillocks (PH), and Round Hillocks (RH) are illustrated. . . . . . . . . . . . . . . . . . . 3.11 SEM image of unepitaxial crystals contamination on epi-layer surface. . List of Figures vii 3.12 Typical surface morphology obtained using a deposition temperature around 900 • C, a 150 mbar pressure, various methane concentration. The gas flow was 500 sccm and oxygen molar ratio was set to 0.75%. A : 7% of CH 4 under 150 mbar, B : 5% of CH 4 under 150 mbar, C : 4% of CH 4 under 150 mbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13 Typical surface morphology obtained using a deposition temperature about 900 • C, a 200 mbar ( 150 Torr) pressure, 4% of CH 4 in gaseous mixture. 3.14 Diamond band diagram with main intrinsic and extrinsic transitions. . . . 3.15 Schematic diagram of CL system used . . . . . . . . . . . . . . . . . . . . 3.16 Deposited energy versus depth in diamond calculated by Monte-Carlo [Volpe 2009a] 62 3.17 5K cathodoluminescence spectrum for epi-layers growth in NIRIM type (sample #1) and PLASSYS BJ150 (sample #3) reactors. . . . . . . . . . 3.18 5K CL spectrum in the excitonic region for samples #1 and #3. . . . . . 3.19 Schematic diagram of process flow towards pseudo-vertical structure fabrication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.20 SEM images of etched diamond. A: an etching wall illustrating the epilayers deposited, B : the surface state of etched parts where etches peaks appeared. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1 Band structure of ohmic metal/p-type semiconductor junction at thermal equilibrium: A) Electrically isolated metal and p-type semiconductor, B) band alignment at thermal equilibrium. . . . . . . . . . . . . . . . . . . . . 4.2 Band structure of metal/p-type semiconductor Schottky junction at thermal equilibrium: A) Electrically isolated metal and p-type semiconductor, B) band alignment at thermal equilibrium. . . . . . . . . . . . . . . . . . . 4.3 Band structure of metal/p-type semiconductor Schottky junction at thermal equilibrium (middle), under forward bias (left), and under reverse bias (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Band diagram of metal-semiconductor junction with an interface layer. . . 4.5 Schematic diagram of metal/p-type semiconductor junction illustrating the Schottky effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Bethe's criterion for p-type diamond Schottky diodes operating at 300 K and 500 K. The criterion was illustrated for different acceptor concentration. 4.7 Current-voltage (I-V) characteristic of Schottky diode. . . . . . . . . . . . 4.8 Schematic diagram of Schottky contact deposition process. . . . . . . . . . 4.9 Schematic diagram of sample #1. . . . . . . . . . . . . . . . . . . . . . . . 4.10 Schematic diagram of sample #2. . . . . . . . . . . . . . . . . . . . . . . . 4.11 Picture of sample #3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Filtered HREM micrograph of Zr/oxidized diamond interface. The white contrast is ZrO 2 type oxide layer which remains constant along the interface [Piñero 2014]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 Picture of the probe station used for devices characterization. . . . . . . . 4.14 I-V characteristics of Zr/oxidized Schottky contacts fabricated on sample #1 illustrating the thermionic current and the serial resistance limitation (left) together with the electrical currents of 27 diodes (right) demonstrating the good reproducibility. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.15 I-V characteristics reproducibility for large area Zr Schottky contacts fabricated on sample #3: 200 × 200 µm 2 diodes (left), 300 × 300µ m 2 diodes (middle), 500 × 500 µm 2 diodes (right). . . . . . . . . . . . . . . .

  Contents 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Wide band gap semiconductors . . . . . . . . . . . . . . . . . 1.3 Wide band gap power devices market . . . . . . . . . . . . . 1.4 State of art of diamond devices . . . . . . . . . . . . . . . . . 1.4.1 Diamond substrate . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 General overview . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Diamond Schottky diodes . . . . . . . . . . . . . . . . . . . .

Figure 1

 1 Figure 1.1: SiC devices sales by applications in 2013 its expected evolutions in 2018 and 2020 reported by Yole développement.

Figure 1 . 2 :Figure 1 . 3 :Figure 1 . 4 :

 121314 Figure 1.2: Market segmentation in power electronics reported by Yole développement illustrating device revenues distributesd by voltage range in 2013.

Figure 1 . 5 :

 15 Figure 1.5: Different architectures of diamond field effect transistors (FET) investigated today: delta-FET (left), Metal Oxide Semiconductor FET (MOSFET middle), H-terminated FET (right).

Fig. 1 .

 1 Fig. 1. (Color online) Cross sectional image of diamond VSBD with a thick field-plate.

Fig. 7 .

 7 Fig. 7. (Color online) Schematic diagram of the diamond SPND.

Fig. 2 .Fig. 3 .Figure 1

 231 Fig. 2. (Color online) Schematic diagram of the diamond p + -i-n + junction diode.

  Schottky diodes are used in silicon-based power conversion systems because of their fast recovery time and of their low turn-on voltage (low forward voltage drop) leading to lower power losses and faster switching than conventional PN or PIN junction diodes. Indeed, besides their lower forward voltage drop 0.15 V to 0.45 V (0.6 V -1.7 V for PN diodes), current transport in Schottky diodes is related to majority carrier contrary to bipolar devices such as PN junction diodes where minority carrier injection in the active area was the main current transport mechanism. Schottky diode can thus switch rapidly from forward to reverse bias without minority carrier storage effects (reverse recovery effects) usually encountered for conventional bipolar silicon based technologies. Schottky diodes are characterized on one hand by their serial resistance and their blocking voltage, both related to semiconductor electrical properties. On the second hand, their forward voltage drop and the reverse leakage current will basically depends on the quality of the rectifying metal-semiconductor interface.

Chapter1.Fig. 1 .Fig. 2 .

 12 Fig. 1. Trade-off characteristics of R on S and BVBD for Si, SiC and Diamond SBDs.

ρ

  = 1/(qpµ). The high ionization energy of the impurities used to dope diamond, namely Boron for p-type with an activation energy about 380 meV and Phosphorous for n-type with an activation energy about 570 meV, gives rise to a low ionization rate at room temperature and so to a resistive material. Moreover, according to the current situation of electronic grade diamond samples size basically (3 × 3 mm 2 ), the processing of diamond power device demonstrators, which may compete with Si or SiC based devices, requires the minimization of doped diamond resistivity as much as possible without excessively altering its outstanding electrical properties.The common way to improve the conductivity of doped diamond and get a low resistivity is the increase of carrier concentration via a higher doping level or a high operating temperature. However, the carrier concentration enhancement solutions are counterbalanced by a limitation of carrier mobility due to scattering mechanisms as described by low field Hall transport analysis reported by Pernot et al. for both ntype[Pernot 2006, Pernot 2008] and p-type diamond[Pernot 2010]. The authors investigated theoretically the temperature dependence of the carrier concentration and their mobility using the charge balance neutrality equation and taking into account all relevant scattering mechanisms which limit the mobility: by phonon scattering, scattering by ionized impurities and neutral impurities. The comparison of experimental data together with theoretical calculations, allowed identifying the limiting scattering mechanisms over a wide temperature range. It was established that the room temperature (RT) carrier mobility in slightly doped diamond (with a low compensation) is related to acoustic phonon scattering thus leading to maximum mobility of 2000 cm 2 /Vs for holes and 1030 cm 2 /Vs for electrons. Moreover, the RT carrier mobility decreases as a function of dopant density for both n-type and p-type, due to neutral impurities scattering.

  ]: m * 100 hh =0.427 m 0 , m * 110 hh =0.69 m 0 for the heavy holes, m * 100 lh =0.366 m 0 , m * 110 lh =0.276 m 0 for the light holes and m * so =0.394 m 0 for the spin-orbit holes. The corresponding values for the density of state mass are m * hh = ((m * 110 hh ) 2 m * 100 hh ) 1/3 = 0.588 m 0 and m * lh = ((m * 110 lh ) 2 m * 100 lh ) 1/3 = 0.303 m 0 . Finally, to compute the position of the Fermi level for a given free hole population, we get the total density of state mass m * = (m * 3/2 lh

Figure 2 .

 2 Figure 2.1 shows the typical hole concentration and mobility temperature dependence obtained by Hall effect measurements for lightly boron doped diamond. These resultswere reported by Volpe et al.[Volpe 2009b] for diamond epitaxial layers (epi-layer) grown on Ib HPHT substrate using a similar reactor (homemade NIRIM type reactor, see Chapter 3) and quasi identical growth conditions than those of the epi-layers grown during this thesis for Schottky diodes devices fabrication.

Figure 2 . 1 :

 21 Figure 2.1: Temperature dependence of the Hall hole density (a) and mobility (b)of slightly boron doped diamond layers reported by Volpe et al[Volpe 2009b]. The doping level were ranging between 10 16 cm -3 and 5 × 10 16 cm -3 and the compensation between 10 14 cm -3 and 5 × 10 15 cm -3 .

FIG. 3 .Figure 2 . 2 :

 322 FIG. 3. Temperature dependence of the hole Hall mobility ͑R H ͒ in boron-doped homoepitaxial diamond. ͑a͒ Symbols are experimental data of sample B37 from Ref. 11. The solid lines show the theoretical contribution of various scattering modes and the total mobility ͑tot͒ with N A = 2.5ϫ 10 17 cm -3 and N D = 10 15 cm -3 . ͑b͒ Symbols are experimental data of sample B42 from Ref. 11. The solid lines show the theoretical contribution of various scattering modes and the total mobility ͑tot͒ with N A =2ϫ 10 18 cm -3 and N D =3ϫ 10 15 cm -3 . ͑c͒ Symbols are experimental data of sample B6 from Ref. 11. The solid lines show the theoretical contribution of various scattering modes and the total mobility ͑tot͒ with N A = 1.7ϫ 10 19 cm -3 and N D =5ϫ 10 15 cm -3 . The scattering mechanisms are ii, ni, ac, and op, calculated respectively from Eqs. ͑1͒, ͑4͒, ͑6͒, and ͑7͒.

Figure 2 .

 2 Figure 2.2 b) for [B] = 2×10 18 cm -3 and Figure 2.2 c) for [B] = 1.7×10 19 cm -3 . Accord-

Figure 2 . 3 :

 23 Figure 2.3: Theoretical hole density (left), hole mobility (middle), and resistivity (right) calculated for different acceptor concentration N A and a constant compensation level N D using the analytical model reported in reference [Pernot 2010].

Figure 1 - 1 :

 11 Figure 1-1 : Value of activation energy as a function of boron incorporation reported in the literature. Pearson-Barden fitting model: = × , = 0.38 eV, = 4.7877 × 10 eV.cm.

  26

Figure 2 . 4 :

 24 Figure 2.4: Activation energy as function of boron incorporation reported in the literature [Fiori 2012]. The solid line is the Pearson-Bardeen fitting model: E a = E a0a × N

Figure 2 . 5 :Figure 2 .

 252 Figure 2.5: Theoretical hole density (left), mobility (center), and resistivity (right) calculated at a constant acceptor concentration N A with various compensation levels N D using the analytical model reported by Pernot et al [Pernot 2010].

Figure 2 . 6 :

 26 Figure 2.6: Theoretical hole density as function of acceptor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported by Volpe et al [Volpe 2009b], Gabrysch et al [Gabrysch 2008], Werner et al [Werner 1997],and Tsukioka et al[START_REF] Tsukioka | Hall Mobility and Scattering Mechanism of Holes in Boron-Doped Homoepitaxial Chemical Vapor Deposition Diamond Thin Films[END_REF]

Figure 2 .

 2 Figure 2.7: Theoretical hole mobility as function of acceptor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported by Volpe et al [Volpe 2009b], Gabrysch et al [Gabrysch 2008], Werner et al [Werner 1997],and Tsukioka et al[START_REF] Tsukioka | Hall Mobility and Scattering Mechanism of Holes in Boron-Doped Homoepitaxial Chemical Vapor Deposition Diamond Thin Films[END_REF]].

2. 2 .Figure 2 .

 22 Figure 2.8 shows the p-type diamond resistivity versus N A and N D at 300 K and 500

Figure 2 . 8 :

 28 Figure 2.8: Calculated p-type diamond resistivity as function of acceptor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported by Volpe et al [Volpe 2009b], Gabrysch et al [Gabrysch 2008], Werner et al [Werner 1997], and Tsukioka et al [Tsukioka 2006].

  FIG. 1. Experimental Hall electron mobility as a function of temperature ͑logarithmic scale͒ for sample No. 1 ͑symbols͒. The solid lines show theoretical contribution of various modes and total ͑tot͒ mobility with N D = 6.8ϫ 10 16 cm -3 and N A = 8.8ϫ 10 15 cm -3 . The different scattering mechanisms are ionized impurities ͑ii͒, neutral impurities ͑ni͒, acoustic phonons ͑ac͒, and intervalley phonons ͑iph͒.

Figure 2 . 9 :

 29 Figure 2.9: Temperature dependence of electron mobility in phosphorous doped diamond (N D = 6.8 × 10 16 cm -3 , N A = 8.8 × 10 15 cm -3 ) together with the contributions of the scattering modes (ionized impurities ii, neutral impurity ni, acoustic phonon ac, and intervalley phonon iph) [Pernot 2010]. Such a mobility simulation has been performed again in this work aiming to evaluate the n-type diamond resistivity as function of donor concentration and compensation level. The theoretical electron concentration (n) and their mobility (µ n ) has been first

Figure 2 .

 2 Figure 2.10 shows the theoretical electron concentration versus N D (donor concentration)and N A (compensation) at 300 K and 500 K together with symbols (circle) corresponding to the experimental data obtained for phosphorous doped diamond layer grown on (111)-oriented Ib substrate[Koizumi 2006, Pernot 2008].

Figure 2 .

 2 Figure 2.10: Theoretical electron densities as a function of donor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported in reference [Pernot 2008].

Figure 2 .

 2 Figure 2.11: Theoretical electron mobility as a function of donor concentration and compensation at 300 K and 500 K. The symbols are experimental data reported in reference [Pernot 2008].

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Diamond synthesis . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Epi-layers growth by MPCVD . . . . . . . . . . . . . . . . . 3.3.1 Growth reactors . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Heavily doped layer . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Slightly doped layer . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Cathodoluminescence spectroscopy . . . . . . . . . . . . . . . . 3.4 Ohmic contact fabrication . . . . . . . . . . . . . . . . . . . . 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3 . 1 :

 31 Figure 3.1: Pseudo vertical Schottky diode structure.

Figure 3 .

 3 Figure 3.2 shows the Pressure-Temperature (P-T) phase diagram of elemental carbon together with the main techniques for diamond synthesis [Bundy 1980]. Under normal conditions, as shown on Figure 3.2, the thermodynamically favored carbon phase is graphite. The graphite structure is characterized by carbon atoms (sp 2 hybridization) bonded in sheets of hexagonal lattice linked to each other by weak Van der Waals forces. Contrary to diamond, graphite is soft, slippery, and metallic due to its sp 2hybridization. Despite the low energy difference between diamond and graphite phases (less than 0.025 eV/atom at room temperature[Anthony 1990]), the diamond phase exists under normal conditions because a high activation energy is necessary to promote the structural transition from diamond to graphite, leading to extremely slow reaction kinetics. Diamond is said to be metastable under normal conditions and it may remain such for an almost indefinitely long time thanks to this kinetic stability.

Figure 3 . 2 :

 32 Figure 3.2: The P-T phase and reaction diagram of elemental carbon [Bundy 1980].

  shown on Figure3.2, are much lower compared to HPHT methods. Metal catalysts such nickel or cobalt are commonly used in catalytic HPHT synthesis consisting to compress with huge hydraulic presses at high temperature, a metal-solvated carbon (graphite) mixture in the presence of a diamond seed. HPHT diamonds are generally Ib type i.e. they contain a high nitrogen (N) concentration in single substitutional form (N>5 ppm).Diamond crystals are generally classified in types Ia, Ib, IIa, and IIb according to the concentration and clustering of Nitrogen atoms. The types IIa and IIb may often be considered as free of nitrogen because of their very small concentration of nitrogen (below 5 ppm). The main features of IIb diamonds is their small amount of uncompensated boron leading to p-type conductivity. Moreover, diamond containing nitrogen in single substitutional form are called type Ib while those containing aggregated nitrogen atoms in either platelet or tetrahedron forms, are classified as type Ia (most of natural diamonds are type Ia). Besides their Ib type, HPHT diamonds have many crystal defects and impurities (metallic contamination) not suitable for electrical application. They are mainly used in industrial applications such as cutting and drilling. However, HPHT diamonds may be used as substrate in diamond-based devices processing for high quality epitaxial diamond growth by a CVD process.

Figure 3 . 3 :

 33 Figure 3.3:Dimer opening & Carbon insertion(Goodwin & Butler, 1998)[Goodwin 1997].

Figure 3 . 4 :

 34 Figure 3.4: Epi-layers schematic stacking.

Figure 3 . 5 :

 35 Figure 3.5: (a) Schematic diagram of NIRIM type reactor [Fiori 2012] together with its picture (b).

Figure 3

 3 Figure 3.6: (a) Schematic diagram of PLASSYS BJ150 reactor together with its picture (b).

Figure 3 .

 3 7 shows the typical incorporated boron atoms concentration versus ([B]/[C]) ratio and methane concentration in gaseous mixture ([CH 4 ]/[H 2 ]) reported by A. Fiori [Fiori 2012] for epi-layers grown using a pressure of 33 Torr and a substrate temperature of 830 • C in our home-made NIRIM-type reactor. The incorporated boron concentrations were estimated by Secondary Ion Mass Spectroscopy (SIMS).For a gas mixture with 4% of methane in hydrogen and a ([B]/[C]) ratio at least 10 3 ppm, a high boron incorporation above the metal transition level ∼ 5×10 20 cm -3 can be expected (Fig.3.7). Apart from their relatively high growth rate (13 and 30 nm/min), these conditions were proposed as the most efficient to lower the density of defects such as dislocations.

Figure 3 . 7 :

 37 Figure 3.7: Incorporated boron vs. ([B]/[C]) in the gas mixture at different ([CH 4 ]/[H 2 ]) ratios[Fiori 2012] for NIRIM-type reactor.

  and hydrogen, using a pressure of Chapter 3. Diamond Schottky diodes engineering 51 33 Torr and a temperature of 830 • C. An hydrogen plasma treatment (one hour) was performed prior to the growth using 200 sccm (standard cubic centimeter per minute) H 2 gas flow, a pressure of 33 Torr and a temperature of 880 • C. The total gas flow and the growth duration were respectively 300 sccm and 15 min. The typical thickness of p + layer was ranging between 200 nm and 500 nm.

Chapter 3 .Figure 3 . 8 :

 338 Figure 3.8: Typical surface morphology ( Top view and 3D view) of p + layer obtained by optical profiler.

Figure 3 .

 3 Figure 3.8 shows the typical surface topography of p + epi-layers and furthermore their typical texture (3D view). P + layers are generally free of surface defects. Moreover, one can estimate over a complete 3D surface, the mean roughness Sa and the Root Mean Square (RMS) roughness of these epi-layers using such a surface image. The typical values of Sa and RMS obtained for p + layers are around 0.26 nm and 0.35 nm

Figure 3 .

 3 9, are Unepitaxial Crystals (UC), Pyramidal Hillocks (PH), Flat-top Hillocks (FH), and Round Hillocks (RH). FH defects are truncated PH characterized by a quadrilateral basis and (111) lateral facets. PH hillocks are sometimes topped by UC defects.Conversely, RH hillocks have a conical shape with an elliptical basis. RH defects are commonly difficult to observe due to their small size. Tallaire et al.[Tallaire 2008] carried out some investigations about the relationship between such surface defects and extended crystallographic defects. The hillocks type defects (PH, FH, RH) were found to result from extended crystallographic defects: a bunch of dislocations formed at the interface between the substrate and the layer. Conversely, UC defects were found to be embedded in CVD layer without any relationship with neither extended defects nor substrate imperfections. The nucleation of these defects in CVD epi-layers depends on growth conditions and their inhibition requires an efficient suppression of non-diamond phases[Tallaire 2008]. 3.3.3.2 Growth in the NIRIM type reactor (samples #1 and #2)

Figure 3 .

 3 Figure 3.9: Differential Interference Contrast images (DIC) of main surfaces defects encountered on epi-growth layers [Fiori 2012]. From left to right : Unepitaxial Crystallites (UC), Pyramidal Hillocks (PH), Flat-topped Hillocks (FH), and Round Hillocks (RH).

using a 33 Figure 3 .Figure 3 .

 3333 Figure 3.10: Typical surface topography obtained by optical profilometry. The main defects such as Unepitaxial Crystallites (UC), Pyramidal Hillocks (PH), and Round Hillocks (RH) are illustrated.

Figure 3 .Figure 3 .

 33 Figure 3.12: Typical surface morphology obtained using a deposition temperature around 900 • C, a 150 mbar pressure, various methane concentration. The gas flow was 500 sccm and oxygen molar ratio was set to 0.75%. A : 7% of CH 4 under 150 mbar, B : 5% of CH 4 under 150 mbar, C : 4% of CH 4 under 150 mbar

3. 3 . 4

 34 Cathodoluminescence spectroscopyCathodoluminescence (CL) spectroscopy is an optical characterization technique generally used to investigate defects and among which dopants in a semiconducting material. CL spectroscopy allows the analysis of light emitted by a material under electron beam excitation. Such a light emission is due to radiative intrinsic or extrinsic (assisted by gap states) electron-hole pair or exciton recombinations. An exciton is an electron -hole pair linked by electrostatic attraction that can diffuse in crystal (free exciton). In doped semiconductors, a part of the so-called Free Exciton (FE) will be bound to neutral impurities (dopants or carrier traps) via Van der Waals interactions (Bound Exciton BE). BE formation is more efficient at low temperature since most of the impurities are neutral and furthermore because of their lower energy compared to free exciton. Accordingly, CL measurements are generally performed at low temperature to favor such BE exciton radiative transition in order to investigate the natures of impurities on which they are localized. For indirect gap semiconductors such as diamond, FE and BE recombinations are assisted by phonon (conservation of crystal momentum). Indeed, the minimum of diamond conduction band is shifted by 0.76 π/a in the (100) direction of the first Brillouin zone (Fig.4.13). Transverse Acoustic TA (∼ 87 meV[Warren 1966]), Transverse Optic TO (∼ 141 meV[Warren 1966]), and Longitudinal Optic LO (∼ 162 meV[Warren 1966]), are the main phonon involved in the excitonic transitions in diamond[Dean 1965]. The transition energy was then defined by ν = E g -E xω ph for FE transition and ν = E g -E x -E bω ph

Figure 3 .

 3 Figure 3.14: Diamond band diagram with main intrinsic and extrinsic transitions.

Chapter 3 .Figure 3 .

 33 Figure 3.15 shows the schematic diagram of CL system used in this work. (1) Electron beam generated by a FEI Quanta 200 Scanning Electron Microscope (SEM) gun was SEM$

Figure 3 .Figure 3 .

 33 Figure 3.19: Schematic diagram of process flow towards pseudo-vertical structure fabrication.

-

Chapter 4 .

 4 Rectification behavior of Zr Schottky electrodes on diamond 73 focused on the fabrication and the electrical characterization of pseudo-vertical architecture based on an oxygen-terminated diamond surface covered by Zr metal. Zr Schottky contact deposition process together with its interface investigation by High-Resolution Transmission Electron Microscopy (HRTEM) and Electron Energy Loss Spectroscopy

Figure 4 . 1 :

 41 Figure 4.1: Band structure of ohmic metal/p-type semiconductor junction at thermal equilibrium: A) Electrically isolated metal and p-type semiconductor, B) band alignment at thermal equilibrium.

Figure 4 . 2 :

 42 Figure 4.2: Band structure of metal/p-type semiconductor Schottky junction at thermal equilibrium: A) Electrically isolated metal and p-type semiconductor, B) band alignment at thermal equilibrium. As stated by the Schottky-Mott theory, the potential barrier arises because of a charges transfer from the semiconductor (higher Fermi level) to the metal. The charges transferred, here holes, leave behind uncompensated acceptor atoms and furthermore a positive charges accumulation on the surface of the metal (extra conduction carrier contained

Figure 4 . 3 :

 43 Figure 4.3: Band structure of metal/p-type semiconductor Schottky junction at thermal equilibrium (middle), under forward bias (left), and under reverse bias (right).

  Mott equation. This discrepancy is explained by interface states present in the junction area as suggested by Bardeen in 1947. Interfaces states are commonly ascribed to the imperfections in the junction area (dangling bonds, surfaces defects, etc). In practice, MS junctions can be defined by the Bardeen model shown on Figure4.4. This model assumes the presence of a thin interface layer separating the metal and the semiconductor and a continuous distribution of interface states at the semiconductor surface.

Figure 4 . 4 :

 44 Figure 4.4: Band diagram of metal-semiconductor junction with an interface layer.

Chapter 4 .Figure 4 . 5 :

 445 Figure 4.5: Schematic diagram of metal/p-type semiconductor junction illustrating the Schottky effect.

Figure 4 .

 4 Figure 4.6: Bethe's criterion for p-type diamond Schottky diodes operating at 300 K and 500 K. The criterion was illustrated for different acceptor concentration.

  Figure 4.7: On-state: Under forward bias (on-state), the depletion region decreases. The diffusion potential limiting the carrier injection from the semiconductor bulk (electrically neutral part) to the Schottky electrode, is attenuated. The electrical current increases exponentially versus the forward bias due to a thermionic emission mechanism. When the flat-band situation corresponding to the disappearance of the depletion region (diffusion potential close to zero) is reached, the on-state is characterized by a linear currentvoltage (I-V) relationship ∆I = ∆V /Rs (ohmic regime), where Rs is the semiconductor resistance (diode serial resistance). The on-state is then defined by: • The forward voltage drop ascribed to the threshold voltage (the extrapolation of the linear current part as shown on Figure 4.7) related to the SBH • The serial resistance Rs defined by the semiconductor resistivity and the rectifier design (shape, area, ...)

Figure 4

 4 Figure 4.7: Current-voltage (I-V) characteristic of Schottky diode.

Figure 4 .

 4 Figure 4.8 shows a schematic diagram illustrating the Schottky contact deposition process. First, diamond sample surface was oxygenated by ozone treatment [Teraji 2009a] prior the Schottky electrodes delineation by a photolithography process (Fig. 4.8 a)). This surface oxygenation technique proposed by Teraji et al [Teraji 2009a] consists to expose the diamond surface to a vacuum deep ultraviolet (VUV) light irradiation in an oxygen atmosphere. The VUV light source is a xenon Excimer lamp center at 172 nm.

(Fig. 4 .Figure 4 . 8 :

 448 Figure 4.8: Schematic diagram of Schottky contact deposition process.

Figure 4 . 9 :

 49 Figure 4.9: Schematic diagram of sample #1.

Figure 4 .

 4 Figure 4.10: Schematic diagram of sample #2.

Figure 4 .

 4 Figure 4.11. Zr(20 nm)/Pt(30 nm)/Au(10 nm) stack was adopted for Schottky electrodes. Circular electrodes were 100 nm in diameter. On the sample sample, Schottky contact with various electrodes were fabricated: 500×500 µm 2 , 300×300 µm 2 , 200 × 200 µm 2 .

Figure 4 .

 4 Figure 4.11: Picture of sample #3.

4. 5 . 2 2 •Figure 4 .

 5224 Figure 4.12: Filtered HREM micrograph of Zr/oxidized diamond interface. The white contrast is ZrO 2 type oxide layer which remains constant along the interface [Piñero 2014].

Figure 4 .

 4 Figure 4.12 shows a HREM micrograph of Zr/oxidized diamond interface reported in ref[Piñero 2014]. EELS profiling recorded along the white line (B1, B2, B3, B4) indicated on Figure4.12 allows identifying the white contrast (interface layer) as ZrO 2 (Zirconia) type oxide layer. Moreover, the thickness of this interface layer about 5 Å was found to be homogeneous along the studied interface. These investigations demonstrated the good chemical reactivity of Zr with oxygen present on diamond surface thus ensuring a good adhesion of Zr electrodes and forming a carbide free interface. Zr/ZrO 2 /diamond type contact known as MIS (Metal Insulator Semiconductor) structure is evidenced.

Figure 4 .

 4 Figure 4.13: Picture of the probe station used for devices characterization. The SMU 2601A is characterized a DC measurement mode (bias voltage ranging from -40 V to 40 V) and a Pulse mode for transient I-V tests. This SMU was preferentially used to investigate the forward state of fabricated diodes due to the fact it can source high currents up to 1 A in DC mode and 3 A in Pulse mode. Conversely, the Keithley electrometer 6517B (maximum current restricted at 10 -2 A) was used to investigate

Figure 4 . 4 .Figure 4 .

 444 Figure 4.14 shows the RT I-V characteristics of Zr electrodes with 100 µm diameter fabricated on sample #1. Zr contacts exhibited an good rectification behavior characterized by a rectification ratio larger than 12 orders of magnitude, a reverse current below the detection limit (10 -13 A). The forward current of Zr/p-diamond rectifiers is

Figure 4 .

 4 Figure 4.15 illustrates the I-V curves of different Zr contacts sizes deposited on sample #3. The good rectification behavior and reproducibility of large area diodes fabricated on sample #3 close to those of small devices (sample #1 and #2), demonstrated the uniformity of Zr/oxidized diamond interface over large scales. According to these results and taking in account the HRTEM measurement previously performed (confer section 4.5.2), it can be assumed that the Zr metallic electrodes deposited on oxygen-terminated diamond surface always form a ZrO 2 interface type regardless of samples or devices size.

Figure 4 .

 4 Figure 4.15: I-V characteristics reproducibility for large area Zr Schottky contacts fabricated on sample #3: 200 × 200 µm 2 diodes (left), 300 × 300µ m 2 diodes (middle), 500 × 500 µm 2 diodes (right).

Figure 4 Figure 4 .

 44 Figure 4.16: Effective barrier heights versus ideality factors determined from Zr/pdiamond diodes RT I-V characteristics fabricated on : a) sample #1, b) sample #2, c) sample #3. The solid lines are the linear fits. Since n if can be approximated to 1 (confer 4.3.3), the zero-bias SBH taking in account the image force effect only φ nif b was then calculated. Table 4.1 summarized the obtained results together with those calculated for rectifiers fabricated on sample #2 and #3 on which the same linear correlation was established. Conversely to sample #1, the rectifiers fabricated on sample #2 give rise to two distinct groups (IIA, IIB) of φ 0 b

Figure 4 .

 4 Figure 4.17: Typical high reverse bias characteristic of Zr/p-diamond diodes. The reported I-V curves were performed on samples #1 and #3. Conversely, zirconium Schottky contacts fabricated on samples #1 and #2, exhibited an extremely good rectification behavior characterized by a high current density about 10 3 A/cm 2 at 6 V, a reverse current density less than 10 -8 A/cm 2 up to the maximum voltage | V max |= 1000V available with our measurement setup. According to the drift layer thickness of 1.3 µm, a reverse field (F =| V max | /d) at least 7.7 MV/cm has been reached for Zr/p-diamond diodes without any change in the reverse current level. It must be noticed that the equation used for the electrical field evaluation gives a lower boundary (assumption of an isolating diamond between Zr and p+ layer and so a constant field in the layer). Thus, a Baliga's Power Figure Of Merit BF OM = (V max) 2 / = (RonS),

Figure 4 .

 4 Figure 4.18: High blocking voltage Zr/p-diamond diodes obtained with samples #1, #2, and #3.

Chapter 4 .

 4 Rectification behavior of Zr Schottky electrodes on diamond 98 4.7 Thermal stability of Zr/p-diamond rectifiers A rectifier is characterized by a critical operating temperature limit (T max ) beyond which an alteration of its electrical properties may occur. The thermal stability is basically related to this upper limit T max under which the rectifier can withstand a temperature fluctuation. For diamond rectifiers, it is well known that a transformation of rectifying junctions inducing by carbide interface layer formation or the surface passivation layer desorption (oxygen or hydrogen termination) are the main reasons for diodes electrical performances deterioration at high temperature. The critical limits T max of diamond rectifiers are commonly defined by the temperatures at which such interface transformation arise. Aiming to identify the critical T max for Zr/p-diamond junctions, their current voltage (I-V) characteristic was investigated at different temperatures (T) ranging from 300 K to 773 K.

Figure 4 .

 4 Figure 4.19: High temperature I-V characteristics of Zr/p-diamond rectifier.

Figure 4 .

 4 Figure 4.20: High temperature I-V characteristics of Zr/p-diamond rectifier (left) and the temperature dependence of calculated active layer resistivity (right).

Figure 4 . 4 .

 44 20 spotlights on a linear scale the forward bias range where the serial resistance of Zr/p-diamond rectifiers were calculated together with the resistivity profile. A monotonic increase of diode active layer resistivity with increasing of T was observed in disagreement with the expected resistivity Chapter Rectification behavior of Zr Schottky electrodes on diamond 100 profile for diamond devices. Indeed, as discussed in Chapter 2, the resistivity of boron doped diamond decreases versus T because of the thermal ionization of boron until to the exhaustion regime. When the full ionization is reached, the resistivity increases versus T due to carrier mobility diminution versus T (confer Chapter 2). For a slightly boron doped layer (N a < 10 17 cm -3 ), the full ionization occurs in a temperature range starting from 500K to 800 K.

Figure 4 . 4 .

 44 Figure 4.21: Current-Voltage characteristics before and after the thermal cycling measurments (from 300 K to 773 K). The threshold is lower after thermal cycling leading to higher current at low forward bias.The experimental resistivity reported on Figure4.20 demonstrated that the Zr/p-diamond rectifiers investigated here, behaves like semiconductors such as silicon where the full dopants ionization arises below RT (shallow dopants) and the resistivity only increases with T. The exhaustion regime must be reached for Zr/p-diamond rectifier thus suggesting that the temperature set point (sample holder T holder ) may not correspond to the diode active layer temperature (T sample ). This assumed temperature discrepancy can be a consequence of a self-heating which can provide a sufficient thermal energy to switch in a full ionization regime without a thermal runaway. Zr Schottky electrodes

Figure 4 .

 4 Figure 4.22: High temperature I-V characteristics using a (Au/Zr)/p-diamond rectifier.

4 .

 4 electrodes covered by a stack (Pt/Au) cap layer. The high temperature measurements revealed the influence of the selected cap layer on the thermal stability of Zr/p-diamond Chapter Rectification behavior of Zr Schottky electrodes on diamond 102 junctions. Indeed, conversely to (Zr/Pt/Au) Schottky metallic stack, it was seen that the electrical characteristics of Zr contacts covered directly with Au layer were altered for a operating temperature of at least 523 K. This deterioration shown on Figure4.22, partly display the role of the platinum layer used as diffusion barrier avoiding oxygen migration through the Au layer leading to Zr oxidation, and/or metals intermixing.

Figure 4 .

 4 Figure 4.23: Schematic diagram of probe station illustrating the heat transfer between diamond and the sample holder.

Figure 4 .23 shows Chapter 4 .

 44 Rectification behavior of Zr Schottky electrodes on diamond 104 a schematic diagram of the probe station illustrating the heat transfer between diamond

Figure 4 .

 4 Figure 4.25 shows an example of sample temperature profile as function of pyrometer

Figure 4 .

 4 Figure 4.25: Example of Zr/p-diamond rectifier temperature increase due to selfheating.

Figure 4 .

 4 Figure 4.26: Electrical current measured at 213 K (left) and diode active layer resistivity (right) versus power dissipated.

Figure 4 . 4 .

 44 Figure 4.27: Electrical current measured at different operating temperatures (left) and diode active layer resistivity (right) versus power dissipated. This is clearly illustrated on Figure 4.27 where the I-V characteristics of Zr/p-diamond measured at different T h below 300 K are plotted together with their corresponding resistivity profile. The forward current enhancement related to diode active layer resistivity diminution is always observed. Moreover, this enhancement is no more clearly

Figure 4 .

 4 Figure 4.28: Theoretical carrier concentration (left), carrier mobility (center) versus temperature. The corresponding resistivity versus temperature was plotted together with the experimental data.

Figure 4 .

 4 Figure 4.29: Diode active layer resistivity versus power dissipated (left) and its temperature dependence (right) established using equation 4.24 which was compared to the theoretical curve.

  .25) µ 0 depends on temperature T and corresponds to the carrier mobility defined by the relaxation time approximation (µ 0 = qτ rel /m * ), where τ rel is the relaxation time of lattice scattering. Conversely, v sat is the saturation velocity linked to optical phonon energy and carrier effective mass (v d = ( ω 0 /m * ) 0.5 ).

Figure 4 .

 4 Figure 4.31: Field dependence of experimental resistivity calculated using: a) the I-V characteristic measured for a holder temperature initially set at 213 K, b) I-V characteristics measured for a holder temperature initially set at 213 K, 243 K, and 300 K. The linear field dependence is highlighted.

Figure 4 .

 4 Figure 4.31 a) shows the field dependence of experimental resistivity calculated using the I-V characteristic measured at 213 K (initial temperature prior to the self-heating).

Figure 4 .

 4 Figure 4.32: Temperature dependence of Zr/p-diamond rectifier active layer resistivity together with the theoretical profile deduced from low temperature data.

  performances of Zr/p-diamond Schottky diodes. The rectifiers fabricated on samples #2 and #3 were successively annealed at 350 • C and 450 • C. For each annealing performed, the Schottky diodes are characterized in a wide temperature range.4.9.1 Forward characteristicsRT electrical properties: Figure4.34 shows the current-voltage characteristics of asdeposited and annealed Zr/p-diamond rectifiers fabricated on sample #2. As expected, the annealed Zr/p-diamond rectifiers exhibited a better electrical properties than asdeposited electrodes as reflected by the current density about 150 A.cm -2 for 450 • C annealing, 19 A.cm -2 for 350 • C annealing, and 0.61 A.cm -2 for as-deposited electrodes at 2 V. For each annealing, the effective SBH and the ideality factor (φ ef f B , n) estimated from a thermionic model and the theoretical Richardson constant 90 A.cm -2 K -2 , were (1.97 eV, 1.58) for as-deposited electrodes, (1.4 eV, 1.28) for 350 • C annealed contacts, and (1 eV, 1.16) for 450 • C annealed contacts. Zr Schottky electrodes annealed at 450 • C exhibit a barrier height about 1 eV whereas the as-deposited electrodes have a SBH of 1.97 eV. Besides the diminution of SBH, the annealing leads to a decrease of the ideality factor thus suggesting an improvement of Zr/p-diamond interface.

Figure 4 . 3 (

 43 Figure 4.33: Room temperature current-voltage characteristics for as-deposited and annealed (Zr/Pt/Au) Schottky contacts. Moreover, the rectifiers annealed at 450 • C are reproducible regardless of samples as shown on Figure 4.34 where the I-V characteristics of 18 diodes fabricated on sample #3 (100 µm in diameter diodes randomly selected). The reported I-V curves are perfectly overlapped in thermionic-emission current range. The calculated zero-bias SBH and ideality factor are then weakly dispersed as evidenced by the right graph shown on Figure 4.34. It must be noticed that the ohmic regime (serial resistance) together with the reverse current are spread. The dispersion in ohmic regime can be ascribed to serial resistance fluctuation due to inhomogeneous doping. At the opposite, the dispersion of reverse current is mainly linked to Schottky barrier fluctuation as shown on Figure 4.34.

Chapter 4 .

 4 .26) Rectification behavior of Zr Schottky electrodes on diamond 116 where S, k B , and A * are respectively the diode area, the Boltzmann's constant, and the Richardson's constant. This linear correlation called Richardson's plot, allows us to assess to the zero-bias barrier height φ 0 b from the slope parameter and furthermore the Richardson's constant (intercept with 1/T = 0).

Figure 4 .

 4 Figure 4.34: Current-voltage characteristics for annealed (450 • C) Zr Schottky contacts (sample #3) together with effective Schottky barrier versus ideality factor.

Figure 4 . 4 .

 44 Figure 4.35 shows the Richardson's plot for each case. For as-deposited and annealed electrodes, the experimental values of ln(Is/(ST 2 )) increased linearly versus 1/T in the whole operating temperature range (Fig.4.35) thus attesting a constant slope and so a constant zero-bias SBH. The as-deposited electrodes remain stable up to 250 • C (473 K) while the electrical characteristics of electrodes annealed at 350 • C exhibit a modification for an operating temperature higher than 350 • C (623 K). On the other hand, Zr/p-diamond rectifiers annealed at 450 • C remain stable (no change on I-V characteristics) after a thermal cycling measurement ranging from room temperature to 500 • C (773 K). Its corresponding Richardson's plot is limited to 573 K because of a weak rectification factor (2 to 3 decades are needed to fit the thermionic regime) for a device operating above this limit. The zero-bias SBH for rectifiers annealed at 450 • C is about 0.88 eV which is at least 1eV lower than the as-deposited electrodes. This confirms again the diminution of SBH versus annealing and furthermore the possibility to get a barrier height below 1eV. On the other hand, the calculated Richardson's constants for

Figure 4 .

 4 Figure 4.35: Richardson's plot for as-deposited and annealed (at 350 • C and 450 • C) Schottky contacts.

Figure 4 .

 4 36 shows the typical reverse current profile measured for 500×500 µm 2 square shape Schottky diodes (sample #3) operating at 283 K.

Figure 4 .Chapter 4 .

 44 Figure 4.36: Current-voltage characteristic of annealed (450 • C) Zr Schottky contacts (sample #3) operating at 283 K. The current related to the TE+BL mechanism only and the tunneling current TFE+BL mechanism were highlighted.

Figure 4 .

 4 Figure 4.38: Current-voltage characteristic of annealed (450 • C) Zr Schottky contacts (sample #3) operating at 373 K. The TFE+BL current was calculated for different acceptor concentration to bring out its variation versus N a .

Figure 4 .Chapter 4 .

 44 Figure 4.39: RT current-voltage characteristics of as-deposited Zr Schottky contacts (sample #2) together with the expected theoretical (TFE+BL) current.

4 .

 4 10.1 Homogeneity of Zr/O-terminated junction 4.10.1.1 Zero-bias SBH and ideality factor as function of temperature

Figure 4 .Chapter 4 .Figure 4 .

 444 Figure 4.40: Effective barrier height (left) and ideality factor (right) versus temperature for as-deposited and annealed Schottky contacts.Accordingly, the electrical characteristics of as-deposited Zr electrodes measured at different temperatures and those of electrodes annealed at 623 K (350 • C) and 723 K (450 • C) were fitted with the thermionic model in order to establish their zero-bias SBH and ideality factor profiles versus temperature.

Figure 4 . 4 .

 44 Figure 4.41: Zero-bias SBH distribution for as-deposited and annealed Zr/Oterminated diamond rectifier. Accordingly, the SBH versus T established for each annealing are fitted with the equation 4.29 in order to model the potential distribution in each. The fit results illustrate on Figure 4.40 , shown a good agreement of Werner's model with experimental data in thermal stability range. The calculated mean barrier and standard deviation were summarized inTable 4.2. Figure 4.41 shows the theoretical SBH distribution for each

Figure 4 .

 4 Figure 4.40. A good agreement with the expression 4.30 is obtained and the calculated ρ 2 and ρ 3 are summarized in Table4.2. The 450 • C annealing led to a coefficient ρ 2 of 0.004 and ρ 3 of -0.003 which are respectively 92 and 6 lower than those of as-deposited electrodes.

Chapter 4 .Figure 4 .

 44 Figure 4.42: SBH distribution at zero-bias and 0.5 V calculated for as deposited and Zr electrodes annealed at 450 • C.

Figure 4 .

 4 Figure 4.43: Filtered HRTEM micrograph of annealed (450 • C) Zr/p-diamond contact. The white contrast is ZrO 2 interface layer.

Chapter 4 .

 4 Rectification behavior of Zr Schottky electrodes on diamond 131 virtual states are defined by their neutral level φ 0 (Charge-neutraly level CNL) inducing a Fermi level pinned even for ideal junction.

Figure 4 .

 4 Figure 4.45: Metal/oxidized diamond SBH versus the difference of metals and carbon electronegativites performed for electrodes as-deposited and annealed at temperature ranging from 673 K and 723 K. The square symbols are as-deposited electrodes : Zr this work, Al reported by Koné et al [Koné 2010], Cu and Ag reported by Ueda et al[Ueda 2014], Mo and Ru reported by Ikeda etal [Ikeda 2009], Au reported by Teraji et al [Teraji 2009b]. the round symbols represents annealed MS junctions: Zr this work, Al Mo Ru Ir are reported by Umezawa et al [Umezawa 2012],Au reported by Teraji et al[Teraji 2009b].

Chapter 4 .

 4 Rectification behavior of Zr Schottky electrodes on diamond 135 • (ii) Zr Schottky electrodes annealed at 350 • C are an intermediate state characterized by a much larger density (few 10 9 cm -2 ) of lowered barrier patches with sizes smaller than the Debye length. This different feature compared to as-deposited electrodes, is related to a probable partial cancellation of interface dipoles due to initial oxygen terminations at a nanometer scale. • (iii) Zr electrodes annealed at 450 • C reach a final state where the complete cancellation of interface dipoles occur, resulting in almost homogeneous interfaces with an ideal behavior and a barrier height as low as 0.96 V. Several mechanisms linked to the presence of an oxide layer, can produce this effect: (a) the effective disappearance of the oxygen-carbon dipole layer due to a new bonding arrangement at the diamond interface after annealing; (b) the compensation of the initial dipole layer by positive charges in the oxide, as usually due to extrinsic deep levels, often related to oxygen vacancies; (c) intrinsic gap states within the oxide layer resulting in a new dipole induced by the alignment of the charge neutrality levels in the oxide and diamond; (d) a combination of these mechanisms or a change in the oxide

Figure 4 .

 4 Figure 4.46: Vertical diamond rectifier based on Zr contact and fabricated in the framework on DIAMONIX II project Along with the study of pseudo vertical diamond Schottky diodes using Zr electrodes, vertical diodes are addressed in the framework of French national project DIAMONIX2.

  FIG. 1. HRTEM of interfaces (a) non intentionally annealed and (c) annealed at 450 .

FIG. 2 .

 2 FIG. 2. Current density as a function of applied voltage at 300 K in the three interfaces made of Zr deposited on oxygen terminated diamond (a) with annealing temperature not exceeding 300 ; (b) annealed at 350 ; (c) annealed at 450 . Dash-dot lines are calculated with the help of Eq. (3), αA * * values included in table I which are obtained from fits achieved in the two following figures, and adjusted constant values of the apparent barrier height and ideality factor in each case, that are respectively: (a) 1.83 V and 1.57 ; (b) 1.47 V and 1.29 ; (c) 0.97 V and 1.05. Voltage takes into account the voltage drop in a constant series resistance of 600 Ω in case (a) and 300 Ω in cases (b) and (c), in good agreement with the theoretical ones, but current densities above a

FIG. 3 . 2 .

 32 FIG. 3. Richardson plot for the three same interfaces as in Fig. 2. Averaged barrier heights deduced from the slope of each straight line are respectively: (a) 1.84 V; (b) 1.47 V; (c) 0.95 V; very close to that used in Fig. 2.

FIG. 4 .

 4 FIG. 4. At left, effective barrier heights as a function of temperature in (a) diodes not annealed at temperatures higher than 300 ; (b) annealed at 350 ; (c) annealed at 450 ; full curves are the best fits according respectively to Eq. (5) or Eq. (9) which results essentially in the same behavior for the effective barrier. The point at the highest temperature in data (b) must be discarded because it has been measured at the same temperature as the annealing one, involving an additional annealing time which has induced a further evolution of the interface towards its final state (c). At right, ideality factors for the same diodes after the same respective post-treatments in (a'), (b') and (c') ; the best fits to the ideality factor data obtained with the help of Eq. (11) are displayed in full curves for (b') and (c') and as a dash-dot curve for (a'), but using a non physical

B

  . Evidence of charged centers in oxide layers To check quantitatively the presence of discrete charged centers inside the oxide, a MIS structure Al/ZrO 2 /p-type (001) oriented diamond has been fabricated. The 25 nm oxide layer has been prepared by atomic layer deposition at 100 . The p-layer has a thickness of 2 µm, contains some 10 17 B/cm 3 and has been epitaxially grown on top of a 200 nm p ++ diamond layer itself in epitaxial relationship on a (001) oriented Ib substrate. After etching the p-layer and before the deposit of the last stack Al/ZrO 2 , an ohmic contact is fabricated around the sample on the p ++ layer, ensuring a series resistance close to a few kΩ. In this way, the proper time constant of the MIS structure is inferior to 1 µs. Such a property allows safe measurements of the static, pulsed and transient capacitances at a frequency of 1 MHz, as described in reference 39 . Results of the reciprocal square capacitance as a function of voltage and the isothermal spectra of projected interface states as a function of the hole emission time constant deduced from the first real Fourier coefficient of the capacitance transients at two time window durations are displayed respectively in Fig. 5(a) and Fig. 5(b) and (c). From the extrapolation of the linear part of the curve in Fig. 5(a) to zero ordinates, a flat band voltage V F B of -4.1 V is deduced whereas a value equal to Φ MS = Φ Mχ SC -E G /2e 0 -(E i -E F ) /e 0 = -2.4 V would be calculated with the help of the electron affinity model and Φ M = 4.28 V for the Al work function 40 , χ SC = +1.6eV

FIG. 5 .

 5 FIG. 5. (a) Square of the inverse capacitance density as a function of the gate voltage ; (b) and (c) curves are isothermal transient capacitance spectra respectively after a 1 ms and a 100 ms filling pulse, recorded at a gate voltage of 3 V and temperature of 362 K.

2 ;

 2 d3 nm. The reciprocal attempt-to-escape time at zero insulator thickness ν 0 and the quantum transmission coefficient q are conditioned respectively by the quantum uncertainty about the potential well or barrier height, also close to 2 /G where G is the line width of the resonance 43 , and tunneling transmission coefficient which depends on the square root of the previous quantities. Because the relevant energies are still about 1 eV, the order of magnitude of ν 0 and q are expected not to be largely different in the present case.The evaluated distance d is close to one tenth of the whole insulating layer thickness, a ratio similar to that of the center densities deduced by the transient and static capacitance methods in the MIS structure. Consequently, these point defects behaving as repulsive centers for holes and located inside the oxide layer at the Schottky interfaces under study might not be ignored unless other charged centers or dipoles prevail. C. Effects of local barrier enhancement due to random elementary charges and dipoles close to the interface Electrostatic potential along x and y directions, parallel to the interface, and z, normal to the interface, can be calculated by adding three terms as a function of normalized distances ξ = x/λ D , ν = y/λ D and ζ = z/λ D , and band curvature U in volt: the average potential of the depletion zone Uk B T /e 0ζ k B T /(2e 0 ) the image force potential -u im /ζ with u im = e 0 /(16πε SC ε 0 λ D ) and the potential due to either repulsive elementary charges positioned symmetrically at ξ = ±ξ 0 , ν = 0, and beyond the interface plane by a distance

Fig. 6 ,

 6 Fig. 6, the last one being obtained with an inverted sign before ζ 0 and four random locations of elementary charges within the depletion zone. The three first cases are respectively devised to mimic the mechanisms assumed to be at stake in the transport of carriers at interface, resulting from the repulsive effect of charges located just at interface or close to it inside diamond: (a) with negative oxygen terminations inducing interface dipoles which are supposed to dominate; (b) with a mixed influence of repulsive oxide charges and dipoles

FIG. 7 .

 7 FIG. 7. Ideality factors deduced from the microscopic barrier inhomogeneities model for the three types of interface at 300 K (triangles), 400 K (squares) and 500 K (circles) as a function of the band bending U . Curve (i) is the best fit of data points by 1 + 1/P (U ) with P (U ) = 136.8 U -76.4 U 2 + 28.4 U 3 . The curve (ii) displays the barrier height variation deduced from (i) with help of Eq. (6) which implies that dΦ B / dU = -1/ [1 + P (U )]. Dash-dot curve (iii) shows the image force lowering variations.

D

  . Barrier height and ideality factor of interfaces with lowered barrier patches of size either comparable to or smaller than the Debye length

B 3 1

 3 minus an effective barrier lowering δΦ sad p at the potential saddle point, the ideality factor n is replaced by 1 and an effective areaA ef f = 4πλ 2D Γ/3 affects the current expression. The weight of the patch is proportional tothe dimensionless parameter Γ = γ p η 1/3 U 2/3 where η = ε SC ε 0 / (e 0 N A ). Both the effective barrier lowering 3Γ U = γ p [U / η] 1/3 and area A ef f = 4πγ p k B T 9e 0 [η / U] 2/3 are dependent on the band bending U = Φ hom B -V j -V dop ,while the ideality factor is approximately 1 + Γ, therefore increasing with the forward voltage. The final step consists in introducing a distribution of a variable patch parameter. In the Tung's original work 27 , two cases were worked out : (i) a sharp distribution of lowered barrier patches approximated by a single patch parameter γ 0 and (ii) a broad distribution featured by half a Gaussian law which limited the γ p range to the values pertaining to barrier height lowering alone, that are γ p 0.

  (a) and (b). This model ceases to be valid neat flat bands and beyond because the current calculation relies only on the carrier flow at the saddle points of the potential barrier, neglecting the areas where the barrier is higher than Φ hom B . It must be also stressed that these ideality factor and effective barrier height must be evaluated around the same band bending U = U b if comparison at different temperatures or in different diodes are made. This is often done by assessing the corresponding ideality factor n b at the same

2 .

 2 04±0.14 (9±3)×10 -5 (1.6±0.4)×10 -4 2.26±0.16 (3±1)× 10 6 2.38±0.02 (b) 350 1.68±0.1 (9.0±1)×10 -5 (1.85±0.3)×10 -4 1.87±0.1 (6±2)×10 9 1.90±0.02 (c) 450 0.93±0.04 (5.5±1.5)×10 -5 (1.3±1.2)×10 -5 0.94±0.04 < 10 9 0.99±0.01 TABLE II. Parameters of the Schottky barrier in the three interfaces according to the models detailed in section IV, with Φ app B,1 and σ p deduced from the adjustment of barrier height as a function of temperature according to Eq. (9). Then, γ 0 , and Φ hom B,1 are derived from ideality factors fitted as a function of temperature with respective help of Eq. (11) in the case of interfaces (b) and (c), and Eq. (16b) for interface of kind (a), while D p and Φ hom B,2 come from the direct adjustment of the current densities shown in Fig. (

  FIG. 8. Effective barrier height as a function of (n b -1)/n b , where n b is the ideality factor at band bending U b for 95 diodes fabricated on three distinct diamond stacks elaborated like described in section II, respectively identified by squares (I), pentagons (II) and circles (III). Samples I and II have not been intentionaly annealed while sample III has been annealed at 350 . Dash lines are best linear fits of grouped data IA, IB, IIA, IIB and III according to Eq. (12).

Fig

  Fig. (2a), which otherwise would reveal the existence of two parallel non pinched-off channels, each of ones having its own barrier height and series resistance with the corresponding condition A i /π t l /2 indeed achieved.

  ), barrier lowering vanishes at flat bands for I p-o while it stays constant for I non-p-o and one can think that the effective barrier height remains more or less at the value obtained at flat bands beyond this threshold. But previous models which rely only on barrier lowering are unable to take into account the progressive disappearance of current inhomogeneities in the lightly doped layer due to the general increase of the carrier concentration at the whole interface. Such a behavior would finally lead to a more homogeneous current density and a voltage drop within the lightly doped layer expected to be simply the product of a series resistance and the total current. But even this view fails because voltage drop turns out to be lower in Fig.(2) as if the resistivity were smaller than the predicted one. This discrepancy is neither an artifact of the adjustment procedure nor a selfheating effect which would hardly be justified because of the low dissipated power (typically ± 0.04 0.73 ± 0.08 2.04 ± 0.04 TABLE III. Schottky barriers extrapolated at unity ideality factor at band bending U b in different sets of diodes fabricated on three distinct diamond stacks numbered I, II and III, according to best fits of Eq. (12) and Φ hom B after the γ 0 correction for the interface of kind (b).

( 2 )

 2 and can also be found in the lower value of the current-density derivative compared to the theoretical specific resistance (not shown) at sufficiently high current. It had been probably observed by other authors in Ni/SiC diodes 29 , although they did not give such an interpretation. But this carrier injection which decreases the Fig. (2)resistivity is probably still efficient at lower current density, so that the hole concentration is underestimated even at the bias voltage where ideality factors are measured, at least when complete ionization of acceptors is not achieved. Correlatively, the effective resistivity is overestimated when its equilibrium value is taken into account as done in the present calculation, increasing thoughtlessly the simulated voltage drop and ideality factor in Fig.(4a') at the lowest temperatures. This injection effect probably occurs because the lightly doped layer is only 1.4 µm thick and would disappear for the larger thicknesses suited to higher voltage operation. In any cases, it must be noticed that all the previous models discussed and built in this work are applicable to a range of bias voltages and currents limited by the occurrence of flat bands in the junction.

F.

  Characteristics and origin of barrier height inhomogeneities in the three types of interface The linear relationship between the effective barrier height as a function of the ideality factor function (n b -1)/n b is actually checked for diodes prepared with the same procedure on three different substrates either without intentional post-annealing or annealed near 350 in Fig. (8). The correction of the constant term in Eq. (12) is done only in the case of indisputable relevance of the model of subsection IV D and as it is not certain for interfaces of kind (a), extrapolated barrier heights Φ app B and Φ hom B will be considered as the same in table III. It is noteworthy that the homogeneous barrier height Φ hom B can be different in two families of diodes (IA and IB; IIA and IIB) on the same diamond stack while it turns out to be very similar for two families of diodes (IA and IIA) belonging to two distinct diamond samples, whose the initial surfaces are all oxygen-terminated. Such results confirm that oxygen terminations, which are responsible for the enhanced electron affinity of the oxygenterminated diamond surfaces and highest barrier at interfaces build on such surfaces, are

  ) seems to apply irrespective of the scale of the barrier inhomogeneities in comparison to the Debye length provided ideality factor is measured at high enough band bending, typically two third of the barrier height, as justified in the previous subsection. But because the interface annealed at 350 (Fig. (8, III)) is a matter of the lowered barrier patch model detailed in subsection IV D, the correction which gives the homogeneous barrier from the apparent one is only exerted in this case in table III where the parameters are collected and displayed for all the diodes families. It must be noticed that the coherence of the various Φ hom B values appearing in Tables II and III is reasonable and that an average value of 2.04±0.04 V can be inferred for the interface of kind (b), only about 0.2-0.5 V below the values at stake for the interfaces of kind (a). The relevance of the model relying for interfaces of kind (b) on lowered barrier patches with sizes comparable or smaller than the Debye length and depicted by a patch parameter distribution centered on a peculiar value γ 0 > 0, with a much higher patch density than for unannealed interfaces, demonstrates that the main barrier inhomogeneities take place now along this microscopic scale, contrary to what happened in unannealed interfaces. One must remind that the patch parameters γ p , σ p and γ 0 depends on the one third power of the product of the square radius R 0 and initial barrier lowering ∆ p so that similar values of the two last quantities will not involve necessarily the same R 0 and ∆ p , which can move in opposite directions. From results given in Table II, such statements suggest that the 350 anneal resulted in the partial and random cancellation of the dipoles O -ν -C +ν whose stability is mainly governed by the enthalpy of the thermodynamical chemistry of these species and temperature, leaving the interface in an intermediate state and inducing new barrier lowering with a magnitude equal to the difference of the potential barrier in interfaces of kind (a) and (c), i.e. ∆ p ≈ 1.4 V at a microscopic scale, and increasing considerably the patch density. On the contrary, the initial inhomogeneities in unannealed interfaces of kind (a) likely resulted from the oxygen terminations dispersion over areas with larger size but smaller barrier lowering and much lighter density, with typical ∆ p ≈ 0.3 V, similar to the difference in potential barriers reported for various interfaces of type (a) in Table III. To comply with the similarity of σ p and γ 0 for interfaces of kinds (a) and (b) in Table II, patches area has to be decreased by a factor of nearly five when going from case (a) to case (b), leading to a very good relevance of the model developed in subsection IV D. In the case of interfaces of kind (c) annealed at 450 , these dipoles have completely disappeared, involving a barrier height as low as 0.96±0.04 V (average from Table II) and very low barrier fluctuations, as indicated by a central patch parameter γ 0 one decade smaller than that of other cases, inducing an almost ideal behavior of the current-voltage characteristics. In this last case, residual barrier inhomogeneities could be due to the random influence of the ionized acceptors close enough to the interface, as it can be evidenced according to the model sketched in Fig. (6d) and invoked in subsection IV C, but the calculation will not be developed further and the reader interested in this question may refer to ref. 18 and references therein. An other residual source of barrier inhomogeneities lies in the possible fluctuations of the oxide thickness, because of the link between these two quantities as discussed in the next section. However, as shown by HRTEM and EELS studies in section II, the interfacial layer thickness remains close to two oxide monolayers as an average before and after interface anneal, leading to the very probable hypothesis of a chemical mechanism involving only bonds change between the first oxygen layer and its neighbors. The main consequence of this bonds transformation shows out through the very large change occurring in the averaged barrier heights of interfaces (a) and (c), with a difference near 1.4 V, resulting from the partial or complete cancellation of the dipoles O -ν -C +ν and also other dipole changes as discussed in the next section. The case of the diodes set IIB in Fig. (8) does not comply with any previous models, a fact which suggests that the main part of the current in these diodes is not governed by an exponential law depending on the applied voltage, which was a common hypothesis of all the previous calculations. Therefore, leakage currents like those which might occur in threading dislocations or defects appearing as dark spots in cathodoluminescence images 25 could be responsible for a behavior characterized by rather higher ideality factors and constant apparent barrier height in Fig. (8 IIB). Finally, homogeneous barrier heights Φ hom B,2 appearing in Table II can be considered as the most representative of the physical situation of each interface, except that unannealed interfaces of type (a) may experience two or three different values like mentioned in Table

FIG. 9 .

 9 FIG. 9. Ideal barrier heights as a function of the Miedama electronegativity difference between metal and carbon (assumed to be 5.7 eV) for oxygenated interfaces annealed below 250 (full squares) and for those annealed in the range 400-650 (open squares), together with a linear fit in dotted line in the second case. The dash-dot line (H) is the best fit of barrier data on the hydrogenated surface by Tsugawa 17 et al. as a function of the same abscissa.

metal 8

 8 and with the notable exception of the hydrogenated surface 17 . Such a dispersion has been ascribed to the various structures, terminations, ad-atoms and natures of bond which can exist at the diamond surfaces and interfaces, like already invoked in the case of oxygen termination. Recently, measurements of barrier heights have been published at carefully prepared oxygenated and eventually post-annealed diamond surfaces9,15,49-53 . Together with the present results for Zr-diamond interfaces, ideal barrier heights are plotted in Fig. (9) with error bars added according to the rules discussed in the previous section: either only above the published value when the method underestimated the ideal homogeneous barrier Φ hom Bp , or symmetrical when Φ hom Bp is directly indicated by authors or reassessed with the help of an appropriate method among those discussed in the preceding section. Despite some dispersion, illustrated sometimes in Fig. (9) and (10) with different barrier heights reported for the same metal in literature, two groups of data appear well separated, one for the contacts annealed at typical temperatures less than 250 or as-deposited and an other for contacts annealed at temperatures in the range 400-650 , as a function of the Miedema electronegativity difference between metal and carbon, the last one being left constant at 5.7 eV. Electronegativity is a bulk property, so that it can hardly reflect the change in electron affinity of diamond due to oxygen terminations in the first group. Even if the diamond electronegativity were shifted by about -1.5 eV to take the oxygen terminations into account, although this is not a very sensible operation, the whole set of data does not show clearly any indisputable trend, testifying a first shortcoming. A second one appears if the search for a linear relationship is restricted to the second group of data, which shows a reasonable alignment depicted by the dotted line in Fig. (9), but characterized by a positive slope, in contradiction with Eq. (18a) and what is experimentally found for all other cases

40FIG. 10 .

 10 FIG. 10. Ideal barrier heights as a function of the difference between the ionization energy of diamond and the work function of metals for (i) as-deposited interfaces (full squares) on an oxygenated (100) surface, (ii) for contacts annealed in the range 400-650 (open squares) on an oxygenated (100) surface, together with a linear fit in dotted line, and (iii) for contacts on the hydrogenated (100) surface from ref. 17 . The ionization energy includes the electron affinity shift

  17

  Fig.(10). If the dispersion of data is forgotten in a first approach and the clouds of points related to the three categories of interface in this graph are replaced by their respective barycenters, one can see that they align roughly on the Mott-Schottky line. This trend has been already evidenced in silicides on n-type silicon interfaces 56 . The influence of the cloud related to the hydrogenated surfaces should be minored because Pt, Au, Cu and Ag metals contacts are displayed with zero barrier heights although they should be negative but cannot be actually measured and reported. More accurately, if one observes the barrier heights of each metal (Pt, Au, Mo, Al, Zr) whose contact on diamond has been measured in the two groups of oxygenated interfaces, before and after annealing, the difference is very close to 1.4 ± 0.25 eV for all of them, corresponding to the same change in electron affinity. This common shift indicates that the barrier height for a given metal is primarily controlled by the electron affinity of diamond, with a little influence of the dipole due to interface bonding, reflected in the last term of Eq. (19a), and testifies the disappearance of

  is roughly d bd = t ox + d bl . Then this distance determines the strength of the last term in Eq. (19a) since the charge counterpart of the dipole on the metal side is now located at a slightly larger length than t ox from the last diamond atomic plane and if the charge inside the oxide layer is neglected at first approximation. Moreover, important effects are due to the charge transfer ∆q which is governed by the nature of the bonds, electronegativity difference between the metal and semiconductor, the polarizability of bonds and interlayer thickness, as described in the bond polarization model proposed by R.T. Tung 28 , and also screening which can mainly accounted for by the relative permittivity occurring at the denominator of the last term in Eq. (19a). To get a deeper insight in the problem at least at a first order level of approximation, let us define the abscissa W SM = (I SC (S)φ M ) and take the derivative of the barrier height e 0 Φ hom Bp when the electron affinity, and hence ionization energy are constant:d(e 0 Φ hom Bp ) dW SM = 1 + d(e 0 ∆q d bd N bd /(ε i ε 0 )) dφ M(20)This slope would stay close to one whenever the second term is negligible but can become negative as observed in Fig. (10) if both the second term is negative and its absolute value exceeds unity. Since the main trend occurring when the metal is changed to another one with an increased work function involves a decreased reactivity with oxygen and therefore a thickness reduction or disappearance of the oxide layer, one must wonder what are the resulting effects on the second term of Eq.(20), even if a continuous variation is more artificial than reality. The dipolar distance d bd is obviously decreased while the interlayer permittivity ε i initially near that of high-k dielectric materials is going down closer to unity, resulting in a smaller screening effect. But because theses two parameters are following the same direction of variation and influence the second term by their ratio, the resulting sign of the derivative turns out to be uncertain. Consequently, the fundamental issue relies mainly on the charge transfer ∆q variation, which is dependent on the effective bonding at the metal-semiconductor interfaces 18,28 , including not only orbitals of the two original materials but also atoms or molecules belonging to the interlayer. In such a molecular orbital scheme, metals with the lowest work functions (and also more electropositive) would make more ionic bonds, with a polarizability likely augmented by the presence of additional oxygen bonds inside the interlayer, thus inducing a stronger positive charge transfer ∆q in the orbitals of the last metal atomic layer. Conversely, noble metals (and also more electronegative ones) are expected to share the electrons of their d states in a more equalized way with carbon orbitals, while carbide forming metals would follow a medium behavior. Such a general trend of the charge transfer ∆q which would experience a decrease when the metal work function (and electronegativity) is increased, is able to justify the systematic negative sign of the derivative in the second member of Eq.(20). Consequently, the slope of barrier heights as a function of W SM = (I SC (S)φ M ) can take values smaller than one, as often observed in many semiconductors, and in the case of a magnitude of the absolute value of the last term in the same equation greater than unity, it can become negative as shown in Fig. (10), in contrast to what is known in all other semiconductors. Such a model can also rely on the electronegativity difference between the semiconductor and metal, which mainly governs the dipole strength induced by interface bonding, independent of the interface induced gap states at first order. At a second order level of approximation, the bonding nature of atoms inside the oxide and fixed charges in it will be also able to bring changes in ∆q and these quantities probably contribute to the small deviations visible in Fig. (10) for annealed interfaces, together with the oxide interlayer thickness and permittivity, and changes in the atoms arrangement at interface and in the first diamond atomic layers. The same model also applies to unannealed interfaces, however with larger fluctuations in comparison to a linear behavior. VI. CONCLUSION In this work, interfaces of Zirconium with oxygenated diamond surfaces before and after two kinds of anneal has been characterized on the one hand by HRTEM imaging and EELS spectroscopy, and on the other hand by thorough electrical measurements made on the Schottky junctions. Evidence of an oxide interlayer comprising approximately two Zr and O atomic layers has been obtained. Current-voltage characteristics have been collected at several temperatures in some diodes and analyzed in order to investigate the detailed shape of the current density behavior with applied voltage, the Richardson constant, the apparent barrier height and the ideality factor. Models taking the barrier height and current density inhomogeneities have been implemented and brought face to face with experimental results. From these comparisons, several physical parameters have been estimated. The Richardson constant turned out to be close to one tenth of the standard value, and even one thirteenth when the barrier height disorder reached its maximum value. The effect of different shapes of barrier fluctuations has been studied either numerically in the case of local barrier enhancements or from two analytical models adapted to local barrier lowering and current crowding in the active layer of the diode. In the former case, which happens when fixed repulsive charges are close to the interface like evidenced in metal-ZrO 2 -diamond structures, the image force effect is the only relevant one as far as current-voltage characteristics are concerned. In the later case, it has been shown that barrier inhomogeneities can be characterized by three parameters related to their amplitude and density, and by the homogeneous barrier which is the truly representative physical quantity of the interface from the electrical point of view. It is free of the local and random lowered barrier patches tact, resulted in a larger barrier height (above 2 eV) and a lower breakdown field (300 V). Tin doped Indium oxide (ITO) were deposited on sample #1 to fabricate Schottky contacts with a diameter of 100 µm corresponding to an area S = 7.85 × 10 -5 cm -2 . ITO contacts were deposited by sputtering and annealed at 200 • C during 30 min allowing crystallization. A good reproducibility of I-V characteristics was observed for ITO Schottky electrodes (Fig. B.1). The BFOM in the case of ITO/p-diamond diode was about 8 MW/cm 2 , due to the low breakdown field of 1.5 MV/cm (Fig. B.1). ITO/pdiamond diodes preserved their rectification behavior up to 723 K and were not affected by the thermal cycling study.

Figure B. 1 :

 1 Figure B.1: Electrical properties of ITO/diamond junctions

Table 1 .

 1 1: Physical properties at room temperature of silicon (Si) and major wide band gap materials (SiC, GaN, diamond) used in power electronics and the related figures of merit (Johnson, Keyes and Baliga, see description in the text). In the band gap row, i and d denote respectively an indirect and direct band gap. If temperature dependent, the values are given at room temperature. The FOM were calculated at 300K for electrons except for diamond.

	Chapter1. Diamond power devices

  This limitation was overcome using an oxide to stabilize the hydrogenated surface[Hiraiwa 2012]. In 2014, Liu et al [Liu 2014] reported Ta 2 O 5 /Al 2 O 3 bilayer gate oxide diamond H-FET and Kawarada et al [Kawarada 2014] Al 2 O 3 gate oxide H-FET for high temperature (400 • C) and high voltage (500 V) operations. Additionally to this promising architecture, the French group where this thesis was prepared, reported a

. Such transistors demonstrate high frequency operation up to 45 GHz. The issue of this architecture was the thermal instability of C-H bonds on diamond surface inducing 2D hole gas at Chapter1. Diamond power devices 14 the surface.

  Temperature dependence of the Hall ͑a͒ density ͓1 / ͑eR H ͔͒ and ͑b͒ mobility ͑R H ͒ of boron doped diamond samples 1 ͑circles͒, 2 ͑squares͒, and 3 ͑triangles͒. The temperature dependence of the Hall mobility between 300 and 500 K is indicated on the graph.

		layer. Indee samples, 6 the
		fore growth
		correspondin
		polishing pr
		samples dep
		͑samples 2 a
		cathodolumi
		difference of
		by the polish
		ing mechani
		perature rang
		duced by the
		near room te
		incorporation
	FIG. 1.	to control a
		quality as al
		centers ment
		ence of oxyg
		oxygen durin
		ity in low b
		important is
		vices.
		Finally,
		simulate the
		tronic device
		and a wide b
		perature dep
		+ N A ͒ depend
		hole mobilit
		by:
		͑T,N im

Table II summarizes the experimental values determined from the Hall fit compared with those determined from the C͑V͒ measurements. Figure

1͑b͒

shows the temperature dependence of the Hall mobility ͑R H ͒ between 292 and 800 K.

Sample 1 reaches a Hall mobility of 1870 cm 2 / V s at 292 K which corresponds to the range of the highest experimental values measured in boron doped layers at room temperature. 1-3 Samples 2 and 3 exhibit lower values around 850 cm 2 / V s. Surprisingly, sample 1, which has the highest

Table 3 .

 3 1: Specifications of samples reported in this thesis.

	Sample	Size	Substrate	Orientation	Polishing
	#1	3 × 3 (mm 2 )	Ib HPHT	(100)	Syntek
	#2	3 × 3 (mm 2 )	Ib HPHT	(100)	Syntek
	#3	4.5 × 4.5 (mm 2 )	Ib HPHT	(100)	Syntek

Table 3 .

 3 2: Growth conditions and thickness of epi-layers grown on samples described in this thesis.(1) growth performed with NIRIM type reactor,(2) growth performed with PLASSYS BJ150 reactor

	Layer	Sample		Growth conditions		Thickness
			CH 4 /H 2	O 2 /H 2	[B]/[C]	T	P
		#1
	p +	#2	4%	-	1200 ppm 830 • C	33 Torr	400 nm
		#3
		#1 (1)	0.75%	0.25%	-	910 • C	50 Torr	1.3 µm
	p -	#2 (1)	0.75%	0.25%	-	910 • C	50 Torr	1.3 µm
		#3 (2)	4%	0.75%	-	940 • C	150Torr	2.5 µm

Table 3 .

 3 3: Main excitonic trasition in boron doped diamond.

	Symbol Phonon involved in excitonic recombination Energy (eV)
	FE T O	Transerve Optic phonon (TO)	5.268
	FE T A	Transerve Acoustic phonon (TA)	5.322
	FE LO	Longitudinal Optic phonon (TO)	5.246
	BE T O	Transerve Optic phonon (TO)	5.215
	BE N P	Non Phonon assited transition (NP)	5.356
	BE LO	Longitudinal Optic phonon (TO)	5.193
	for BE transition.

  Mori 1992] reported a broad band 3.75 eV (FWHM of 0.7 eV) as a feature of oxygenrelated defects. In Mori's experiment, this band is supposed to appear due to oxygen diffusion in superficial diamond layer after treatment in CrO 3 + H 2 SO 4 solution at 200 • C by H 2 treatment[Zaitsev 2010]. On the other hand, Lawson et al[Lawson 1995]

The main plausible origins are oxygen-related defects and boron related defects. Indeed, Mori et al Chapter 3. Diamond Schottky diodes engineering 64 [

  and 2.

	A)(Photolithography(process(to(
	define(mask(area(
	p+(layer( p3(layer(	p+(layer( p3(layer(
	Diamond(substrate(	Diamond(substrate(
			Top(view(
	B)(Nickel(mask( deposi>on+(lith3off(	C)(ICP(etching(step(to( delineate(pseudo( ver>cal(structure((
	p+(layer( p3(layer(	p+(layer( p3(layer(
	Diamond(substrate(	Diamond(substrate(	Top(view(
	D)(Photolithography( process(to(define( ohmic((contact(	E)(Ti,(Pt,(and(Au(layers( deposi>on(+(liF3off(
	p+(layer( p3(layer(	p+(layer( p3(layer(
	Diamond(substrate(	Diamond(substrate(
			Top(view(

Table 3

 3

	resistance on

.4 summarizes the main specifications (size, epi-layer growth, thickness, expected doping level estimated by CL and ohmic contact resistance) of the set of samples reported in this thesis. The final step that of Schottky metal deposition, will be introduced in the next chapter. Table

3

.4: Experimental details of growths described in this chapter. Epi-layers growth conditions, their thicknesses (deduced from Ellipsometry), and their expected acceptor concentrations (estimated by CL spectroscopy) are reported. The theoretical Ohmic contact

Table 4 .

 4

	1: Linear fitting parameter of Schottky barrier versus ideality factor obtained
		for distinct diodes groups observed on sample #1, #2, #3.
	Sample	φ nif b	(eV)	ϕ p (eV)	Label
	#1	1.81 ± 0.03	0.47 ± 0.05	IA
	#2	2.16 ± 0.08	0.84 ± 0.23	IIA
		2.29 ± 0.08	0.79 ± 0.15	IIB
	#3	2.01 ± 0.06	0.57 ± 0.13	IIIA
			Level off		IIIB

  Rectification behavior of Zr Schottky electrodes on diamond 97 the largest value reported for diamond Schottky diodes and furthermore not so far from the theoretical one (1000MW/cm 2 ) [Umezawa 2012] for the same breakdown voltage and temperature which should be reached if the effective breakdown voltage was doubled.

2 ) [Umezawa 2012], was Chapter 4.

Table 4 .

 4 2: Mean barrier, standard deviation, and voltage coefficients calculated for as-deposited and annealed Zr/O-terminated diamond rectifiers.

	Zr electrodes	φ0 b (eV)	σ s0 (eV)	ρ 2	ρ 3 (mV)
	As-deposited	1.93	0.071	-0.37	-20
	Annealed	1.54	0.077	0.1	-10
	(350 • C )
	Annealed	0.93	0.056	0.004	-3
	(450 • C )

  3, while n d 1.6 was found with evaporated Al and Pb contacts. The exper lts exhibit a pronounced trend as a function of the electronegativity difference

	Electronegativity (Miedema)
	Electronegativity difference
	1.

-Barrier heights of metal/p-diamond contacts as a function of the difference of the m on electronegativities. Clean-surface data ( 0 ) from

Mead and McGill[16] and Glover [171;

Unepitaxial*crystallite*(UC)** Pyramidal*hillocks*(PH)** Flat:topped*hillocks*(FH)** Round*hillocks*(RH)**

and heavily doped substrates. At high temperature (250 • C), an electrical current of 1 A was measured for 500×500 µm 2 rectifier. Further work is needed. A particular attention must be paid to the rectifier design. Since the boron concentration in diamond substrate used in vertical configuration is still below the metal transition level, its contribution the serial resistance is not negligible and a high temperature will be required to enhance boron ionization rate and so the forward current. The results presented in this thesis demonstrate the possibility to fully ionize boron using self-heating. Accordingly, the devices could be designed in such a way that their self-heating (if any) serves as a heat source to minimize the serial resistance and optimize the forward current.

Appendix A

Potential barrier heights at metal on oxygen-terminated diamond interfaces current density although such a rule is almost true only at vanishing band bending. It is important to notice that various behaviors of the ideality factor as a function of temperature can result from Eq. ( 11), with a trend toward a constant value when the second term inside the brackets dominates at elevated temperatures as one can see in Fig. (3b'), the last term in Eq. ( 11) being negligible except near flat bands and for ideality factors below 1.1. Either neglecting the last term in Eq. ( 9) or lumping it into Φ hom B , a relationship between the effective barrier height and ideality factor n b at the same band bending U b for all the diodes investigated at a given temperature among a set of diodes belonging to a same sample, comes from Eq. ( 9), ( 10) and ( 11):

Therefore, the difference between the effective barrier height Φ ef f 8), which will be commented in the next subsection. However, it must be stressed that all the expressions derived for the effective barrier height and ideality factor within the framework of the present model, that are Eq.( 9) to ( 12), assumed that the factor inside the braces of Eq. ( 7) is largely greater than one. Such a condition implies that the patch density D p must be typically much larger than 10 7 cm -2 , so that one has to wonder whether the value deduced from adjustments has really a physical meaning in each situation.

In one diode alone, the fingerprint of the kind of barrier inhomogeneities breaks out in the behaviors of the ideality factor and to a smaller extent of the effective barrier height depth of the lightly doped layer like assumed in ref. 28 , the voltage drop along the i th non pinched-off channel is simply proportional to a resistance ρ(T )/λ i where λ i = A i /t l . This hypothesis is true in the limit of a diameter of the area with a lowered barrier height well and therefore plays the same role as a negative central patch parameter γ 0 in the effective barrier experienced by the whole current flowing through the pinched-off patches and given in Eq. ( 9). This fact explains why neglecting the confinement of current in channels which stretch out along some part of the lightly doped layer thickness had to be compensated by the occurrence of a negative figure for γ 0 in the simulation results of the previous subsection, leading to an incorrect value because of an inappropriate model applied to interfaces of kind (a).

Averaging all the currents over the whole diode area A d is not tractable analytically. A reasonable approximation consists in calculating separately the total current and an estimate of the whole conductance within the shrunk channels from the integration of all the parallel conductances λ i /ρ(T ) or 4 A p-o ef f,i /π/ρ(T ) appearing in the last term of the exponent of each expression (13a) or (13b), weighted by the distribution

in the later case. It is also assumed like previously that only the lowest barrier for the current flow is efficient and that the barrier lowering is approximated by its quadratic average. For non pinched-off channels, the total conductance would result from the integral of λ i /ρ(T ) weighted by an unknown distribution, so that it is more convenient to introduce a fictitious area A non-p-o ∆V allowing to write the corresponding voltage drop ∆V non-p-o . In the case of the pinched-off currents, two integrals must be evaluated numerically as a function of γ 0 /( √ 2σ p ).

Their ratio appears as a fraction in the next formula and gives the exact value within an error smaller than 10 % . With A non-p-o = i A i representing the true area of the non pinched-off zones, the average current densities in the whole diode area become respectively for the non pinched-off and pinched-off channels: