-V, P-E, PFM (piezoresponse force microscopy)

Keywords: PZT (Pb(Zr FeRAM, XRD, leakage current, I-V, C

1-x ,Ti x )O 3 ), SRO (SrRuO 3 ), ferroelectric, piezoelectric, sputtering, sol-gel,

Outside academy, his kindnesses have made my living in this country much easier.

Then I would like to thank Bertrand VILQUIN. Growing oxides with highly crystalline structures requires great caution and profound understanding of materials. Bertrand is a master of almost every machine. Trained by Bertrand to use every required equipment in clean-room, I was able to manipulate all the machines alone. Numerous discussions with Bertrand helped me determine the research direction and achieve objectives.

By his extensive experiences, Nicolas BABOUX has guided me out of the thorns of electric-property identification. By setting up the equipments in an innovative way, we were able to assess the specific characteristic, making further improvement of oxide fabrication much easier. The codes written by Nicolas were really enjoyable, which have greatly reduced the tedious work of data processing. The discussions were often inspired, many of which have greatly optimized my earlier mediocre method.

Being a member of epitaxy group for three years is my great pleasure. From day one, everyone was so helpful and supportive and language barrier has been greatly reduced. Every colleague has a remarkable experience of the undefeated MBE. Michel and Guillaume definitely lead a great team. JB and Claude can fix every problem without delay. Phillippe is a super responsible guard for everyone's safety. There has been so many happiness and amusement to work with all PhD fellows, from the veteran NIU Gang, who has introduced most of the equipments to me in his last days in lab, to the newbies Hélène and Baba and Jeanne, who will definitely do a better work in the coming years. It is of great joy to work in the same team with JB2 and Lamis for the entire study. I give my best wish to Lucie and Nasser, who will conquer every difficulty to obtain their degrees this year. A big thank to Hélène for her generousness.

My wish also goes to Rahma, Marie, Benjamin and Amaury, and you can still enjoy your life for another year. Special thanks to YIN Shi and Jose for their great help, especially of XRD. I wish you all continue doing great job.

Electric measurement is limited in micro-scale. With the help of Nano-caracterisation group in INSA, we have achieved in manipulating electric signals in nano-scale, offering much more insight. Thanks for the excellent PFM images from Simon and David, which were better and better in the end of the i study. David's AFM images offered incomparable clearness. The discussion with Brice has helped me understand how PFM works. I thank Radek, Pierre, Aziz and Brice for their brilliant work. Their maintenance keeps all the machines in great condition with least interruption. Their substantial experiences of every detail can always bring the machine back when I made a mistake or I was stuck.

I am thankful to Raphaël and Laurent for their IT support. I also thank our wonderful secretaries Thérèse, Patricia and Sylvie, who have fixed a great deal of non-scientific problems, making our research work less stressful.

Three years in Lyon, I've made some friends, not many but they are all great people. I hope you all can enjoy your life and work in the following years. Hope to meet you again.

I would like to express my gratitude to China Scholarship Council for its financial support. Without its help, nothing could happen.

Special thanks to QQ. The discussions can usually pull me out of the closed mind, creating much more possibilities.

I express my hearty thanks to the unconditional support of my parents in all these years, back to primary school. 25 years' study, they are always trying their best to give me the best opportunities.

And, I thank my girlfriend for the company, patience and disturbance during these years in the other side of English Channel.

General Introduction

The outstanding properties of ferroelectric materials such as polarization hysteresis, large dielectric constant and piezoelectric effect can all be applied in electronic devices. Among these applications, nonvolatile memories utilizing the ferroelectric thin films have captured great attentions due to their potential low power consumption and high operation speed. To realize the large scale integration of ferroelectric thin-film memories, which are competitive with various current dynamic random access memories and static random access memories, a comprehensive study of ferroelectric thin-film capacitors has been carried out. Our study includes two parts: the fabrication of epitaxial ferroelectric thin-film capacitors; and effective electrical measurements for the understanding of leakage currents and switching dynamics. The structure of this thesis is described as follows:

Chapter 1 is dedicated to the background of ferroelectric materials, including: historical research, applications, principles of ferroelectricity, Pb(Zr 1-x ,Ti

Historical

The phenomenon of pyroelectricity, or the property of some materials, exhibiting a temperature dependent spontaneous electric dipole moment, was first recorded back to 314 BC. Theophratus noted that a stone, called lyngourions in Greek, could attract sawdust [START_REF] Richards | Theophrastus on stones[END_REF]). In the eighteenth and nineteenth centuries many experiments were carried out in an attempt to characterize the pyroelectric effect quantitatively. These studies eventually led to the discovery of piezoelectricity, which is the production of electrical polarization by application of stress, by J. Curie and P. Curie in 1880.

It was not until 1920 that J. Valasek recognized ferroelectricity by experiments (Valasek 1921) (ADP), which was found to be antiferroelectric 20 years later. These newly discovered ferroelectric series exhibited a much simpler crystal structure, which facilitated theoretical understanding of ferroelectricity [START_REF] Lines | Principles and Applications of Ferroelectrics and Related Materials, Oxford classic texts in the physical sciences[END_REF].

Historical

After the discovery of KDP series, one decade passed without experimental breakthrough. It was thought that a hydrogen bond was prerequisite for a ferroelectric. However ferroelectricity was found in barium titanate BaTiO 3 (BTO) [START_REF] Wul | Compt. Rend. Acad. Sci. URSS[END_REF]. The discovery was important to the study on ferroelectricity for: 1) BTO was a ferroelectric without hydrogen bonds; 2) the crystal structure was perovskite with very high symmetry and had only 5 atoms per unit cell; 3) it was chemically and physically stable; 4) it exhibited ferroelectricity at room temperature; 5) BTO was among the largest single class of all ferroelectrics-the oxygen octahedral ferroelectrics made up from basic BO 6 building blocks (von Hippel 1950, Kwei et al. 1993, Scott 2007). Owing to its exceptional properties, BTO had been the most investigated ferroelectric material for decades. Later ferroelectric behavior was found in KNbO 3 , KTaO 3 (Matthias 1949), and in LiTaO 3 , LiCbO 3 (Matthias and Remeika 1949) and in PbTiO 3 (Shirane et al. 1950).

In the mid-fifties of last century, C(NH 2 )Al(SO 4 )•6H 2 O (GASH) was found to be ferroelectric. Its isomorphs were found to be ferroelectrics soon though T c was not observed since they decomposed before phase transition. Soon the number of discovered ferroelectrics passed 100 [START_REF] Lines | Principles and Applications of Ferroelectrics and Related Materials, Oxford classic texts in the physical sciences[END_REF]. In the 1950s demand for high-capacity computer memories emerged and ferroelectrics seemed to be prime candidates for their bistable polarization used for binary memories. However the problems of reliability and fatigue hampered their application. Eventually magnetic and semiconductor memories were favored.

In 1960s and 1970s, intense studies on ferroelectrics were carried out. During the second half of the 1960s, a large number of new ferroelectrics were discovered. Application of these materials for optical devices evolved. At the same period, since the progress in integrated Si devices advanced, interest of using ferroelectric thin films for non-volatile memories emerged.

In 1980s, processing of complex ferroelectric oxides advanced as sol-gel-derived thin ferroelectric film was achieved (Blum andGurkovich 1985, Dey et al. 1987). In 1987, ferroelectric memory integrated with silicon complementary metal-oxide semiconductor (CMOS) was demonstrated [START_REF] Eaton | Solid-State Circuits Conf. 1988. Dig. Tech. Pap. ISSCC. 1988 IEEE Int[END_REF].

Considerable interest was given to ferroelectrics in 1990s. The possibility of using ferroelectric thin films as nonvolatile memories and new microelectromechanical systems (MEMS) attracted significant interest. However, problems of fatigue and aging hindered its development for memories but piezoelectric MEMS had been in mass production for a variety of devices.

Now the known ferroelectrics are more than 1000, many of which are neither hydrogen bonded nor oxides (Izyumskaya et al. 2007, Scott 2007). In the beginning of this new century, miniaturization has been an essential method to increase the performance of single crystal ferroelectric thin film. Firstprinciple has helped further understand ferroelectric properties (Meyer andVanderbilt 2002, Diéguez et al. 2004).

In recent years, interests of designing innovative electronic devices based on coupling between ferroic orders emerged. Ferroelectricity can be utilized to modulate magnetic properties like: controlling the Curie temperature across an interface; turning magnetism on and off; altering the spin polarization of electrons and changing exchange coupling between magnetic layers (Kanki et al. 2006, Bibes 2012). Bismuth ferrite, BiFeO 3 (BFO) has captured a significant amount of attention for its exceptional properties.

So far, BFO is the only potential candidate that exhibits both antimagnetism with a Néel temperature of 640 K and strong ferroelectricity up to 1100 K. The structure of magnetoelectric random access memories (MERAMs) is demonstrated (Bibes and Barthélémy 2008), which can store 4 logic states per unit.

Besides, energy harvester based on the piezoelectricity attracts many interests in recent years (Bowen et al. 2014).

Applications

Since the discovery of ferroelectricity in Rochelle salt, the research on ferroelectrics has been closely linked to device applications. Rochelle salt was widely used for microphones for its largest piezoelectric effect at that time. In 1940s, Rochelle salt was employed as sound transducer (transfers sound pressure into electrical charges) for submarine sonar systems but then was replaced by the more stable ADP [START_REF] Massa | [END_REF] during World War II. Since its discovery, it seemed to be a perfect candidate for computer memory elements. A polarization of 10 µC/cm 2 corresponds to ∼ 10 14 electrons/cm 2 , so in principle a high density storage with high signal-to-noise ratio could be achieved. The potential of this device was not realized for its short-term fatigue, less well-defined coercive field and a hysteresis loop with not sufficient square shape (Scott andPaz de Araujo 1989, Uchino 2000). In 1960s, a burst of activity accompanied the discovery of a large amount of ferroelectrics. During this period, the development of ferroelectric as memories, optical devices and thermal detectors steadily increased [START_REF] Lines | Principles and Applications of Ferroelectrics and Related Materials, Oxford classic texts in the physical sciences[END_REF]. In 1970s, transparent ceramics were developed which offered possible electro-optic applications. Study on single crystals emerged in this period but devices were still limited to bulk ceramics for their much lower costs.

From 1984, when ferroelectric thin films were fabricated and integrated into semiconductor chips, research started focusing on thin film ferroelectrics (Scott 2007). In late 1980s, development of ferroelectric random access memories started. Ferroelectric random access memory (FeRAM) has been commercialized since late 1990s but remains a relatively small part of the overall semiconductor market. The problem of fatigue and imprint hinders it from replacing dynamic random access memory (DRAM) although FeRAM exhibits lower power consumption and theoretical faster read/write period (Ishiwara et al. 2004). Another type of ferroelectric memory is metal ferroelectric semiconductor field effect transistor (MFSFET), which was proposed before the conventional capacitor-type memory. As the polarization of the ferroelectric changes, the drain current differs which can be used as binary states of a memory unit. Comparing to FeRAM, the "read" operation is non-destructive, but the fabrication cost is higher.

The major application of ferroelectrics is for capacitors, utilizing their high dielectric constants around the curie temperature. Recently, since conventional Si micro-machining technology coupled with silicon oxide and metal, is limited in its ability to produce fine-scale capacitors, ferroelectric seems to be a better alternative and draws a lot attention (Ishiwara et al. 2004). Energy harvesting is also a topic of intense interest since it provides a route for the realization of autonomous and self-powered low-power electronic devices, e.g., wireless sensor networks. Most energy harvesters transform mechanical energy to electric power using piezoelectricity of the material. The use of pyroelectric materials to generate electrical energy from temperature fluctuations is also a research topic (Bowen et al. 2014).

Since all ferroelectrics are pyroelectrics and all pyroelectrics are piezoelectrics, ferroelectrics can be employed in devices using their different properties. Ferroelectrics have also received intense interest due to their high optical transparency and remarkable optical nonlinearity for photonic devices. Table 1.1 lists the devices which use ferroelectrics as the major functioning parts (Haertling 1999[START_REF] Uchino | Ferroelectric Devices, Materials engineering[END_REF][START_REF] Lines | Principles and Applications of Ferroelectrics and Related Materials, Oxford classic texts in the physical sciences[END_REF], Ishiwara et al. 2004, Setter et al. 2006a).

FeRAM

Over the past two decades, FeRAM has evolved from a concept to a commercial memory product used in a variety of consumer and industrial applications, e.g., smart cards, power meters, printers and video games. Compared to other types of nonvolatile memory, such as electrically erasable read-only memory (EEPROM) and battery-backed static random access memory (SRAM), FeRAM exhibits low power consumption, high read/write endurance, fast read-write access and long-term retention (Ishiwara et al. 2004). The first FeRAM was invented in 1988 using PZT. The FeRAM cell consisted of two transistors and two capacitors (2T-2C). Most commercial FeRAM devices currently available employ a 2T-2C cell with a 0.5 µm minimum CMOS feature size. The large cell factor (110) for a 2T-2C device can be reduced by changing the architecture to 1T-1C type. With this change the reference cell is excluded from unit cell in 1T-1C and a single reference cell is used for the entire memory. The quality requirement in terms of switchable polarization, retention and cycling endurance is higher in 1T-1C than in 2T-2C. Additional decrease in cell factor can be achieved by building the capacitor on top of a plug which contacts an underlying access-control transistor (Ishiwara et al. 2004). Table 1.2 lists the road map for 1T-1C FeRAM and the requirements for feature sizes down to 0.1 µm.

MEMS

Kinetic energy can be harvested by MEMS through piezoelectricity. Figure 1.1 demonstrates a cantilever generator. When the cantilever deflects due to external vibrations (e.g., shaking), charges are generated by the ferroelectric film.

There is a lot of interest in developing human-powered energy-harvesting devices. Studies has shown that a 68 kg man walking at 3.5 mph can produce 67 W power [START_REF] Fischer | The human gait[END_REF]. Although not all this energy can be harvested, a group at MIT put a PZT generator in an insole gathering 8.4 mW .

Boeing is developing seats for its airplanes that could harvest the motion of passengers. This energy could be used to power the outlets for laptops and cellphones [START_REF] Carter | [END_REF]).

An advantage of piezoelectric generators is that they are scalable: they can be combined to generate more power and also can be scaled down even to nano-scale to create localized power sources. The performance of energy harvesting is directly related to the piezoelectric coefficients, but the applied stress or strain is also an important factor. The energy output depends on the ability of the piezoelectric material to sustain an applied force or to repeatedly undergo a recoverable strain. The limits in the strength and elasticity of these materials may be the dominant factors in performance rather than piezoelectric coefficients [START_REF] Starner | Low-power Electron[END_REF].

Ferroelectricity

Ferroelectricity originates from the asymmetricity of crystals. There are 32 crystal classes and 11 of them possess a center of symmetry, which exhibit no polar properties. If a uniform stress is applied to these 11 classes of centrosymmetric crystals, the resulting small movement of charge is symmetrically distributed in a manner that relative displacements are fully compensated. Of the remaining 21 noncentrosymmetric classes, all except one exhibit electrical polarity when subject to stress. The effect (and also its converse, the production of strain by application of an electric field) is linear, with reversal of the response under reversal of the stimulus, and is termed piezoelectric effect. Of the 20 piezoelectric classes, 10 are pyroelectric. They possess a spontaneous polarization under certain temperatures. The amplitude of the dipole moment varies when temperature changes. Among pyroelectric crystals, ferroelectrics can be distinguished for the fact that they possess permanent polarization in the absence of electric field and the polarization can shift from one state to another by electric field (when it is sufficient large). The ferroelectricity of ABO 3 type perovskite-crystals origin from B-site ion shift. B-site ions have two stable locations, either slightly above the center or below it. If dipoles in all lattices are in the same direction, the material shows a polarization of the same direction. When this polarized PZT is subject to a sufficient antiparellel electric field, the dipoles will be forced to change direction.

The shift of B-site ions between the two stable states is the origin of the ferroelectricity in perovskite ferroelectrics.

Landau-Ginzburg-Devonshire Theory

The behavior of ferroelectrics is often modeled by free energy. In Landau-Ginzburg-Devonshire theory, the free energy F can be expanded in a power series [START_REF] Kittel | Introduction to Solid State Physics[END_REF]):

F (P ; T, E) = -EP + g 0 + 1 2 g 2 P 2 + 1 4 g 4 P 4 + 1 6 g 6 P 6 + • • • (1.1)
where the coefficients g n are temperature dependent, T is temperature in K and E is external electric field. Odd powers are not included due to the symmetry reason. The value of P in thermal equilibrium condition is given by the minimum of F . At applied electric field E, the equilibrium polarization satisfies the condition:

∂F ∂P = -E + g 2 P + g 4 P 3 + g 6 P 5 + • • • (1.2)
To obtain a ferroelectric state we must suppose that g 2 passes through zero at some temperature T 0 :

g 2 = γ(T -T 0 ) (1.3)
γ is a positive constant, which equals to 1/ε 0 C CW . ε 0 is permittivity of free space ( 8.85419 × 10 -12 F/m ) and C CW is Curie-Weiss constant.

Second-order Transition

If g 4 is positive, g 6 P 5 and higher order terms can be neglected. When E = 0, it is found:

γ(T -T 0 )P s + g 4 P 3 s = 0 (1.4)
So either P s = 0 or P 2 s = (γ/g 4 )(T 0 -T ). For T ≥ T 0 , P s = 0. T 0 here equals Curie temperature T c . For T < T 0 , the minimum free energy F in zero field is at:

|P s | = (γ/g 4 ) 1/2 (T 0 -T ) 1/2
(1.5)

The phase transition schema is plotted in Figure 1.5. The transition is a second-order transition because P goes continuously to 0 at T 0 . The order of transition in PZT depends on its composition (Haun et al. 1989).

First-order Transition

If g 4 is negative, the transition is first order and P s goes to 0 abruptly. g 6 is retained and taken as positive. Otherwise, F will go to minus infinity. The equilibrium condition for E = 0 is given by Chapter 1: Background and Motivation Figure 1.5: Free energy for second-order and first-order phase transition [START_REF] Kittel | Introduction to Solid State Physics[END_REF].

Equation (1.2):

γ(T -T 0 )P s -|g 4 |P 3 s + g 6 P 5 s = 0 (1.6) So either P s = 0 or γ(T -T 0 )P s -|g 4 |P 3 s 2 + g 6 P 4 s = 0 (1.7)
Curie temperature T c is related to T 0 by:

T c = T 0 + 3 16 g 2 4 γg 6 (1.8)
This indicates that when T 0 < T < T c , there will still be two stable polarization states. The transition is plotted in Figure 1.5.

The double well potential is entirely consistent with the hysteresis behavior of ferroelectrics.

PZT Properties

Lead zirconate titanate Pb(Zr 1-x ,Ti x )O 3 (PZT) is a solid solution whose crystalline structure and properties varies with the ratio of PbZrO The most prominent feature of the phase diagram is the existence of "morphotropic phase boundaries" (MPB). In the vicinity of this region, the crystal structure changes abruptly with dielectric constant and electromechanical coupling coefficient becoming maximum. Figure 1.8 shows the dielectric constant and coupling coefficient of PZT as a function of Zr/Ti ratio. The reason why PZT of this composition shows excellent dielectric response and high electromechanical coupling coefficient has not been fully understood. In tetragonal PbTiO 3 , there are 6 possible domain states from < 100 > direction and in rhombohedral PbZrO 3 , there are 8 possible domain states from < 111 > direction. All these 14 possible domain states are equally favorable energetically. The enhanced properties near MPB was attributed to this large amount of possible polarization direction (Damjanovic andDemartin 1997, Hoffmann et al. 2001). However, the apparent continuous phase transitions through the MPB region from tetragonal to rhombohedral are not allowed by symmetry. High resolution of X-ray powder diffraction on homogeneous 1.4. PZT Properties sample of high quality revealed that a narrow stripe of monoclinic phase existed between tetragonal and rhombohedral phases (Noheda et al. 2000ab). Thus in the MPB region, the transition from tetragonal to rhombohedral phase is mediated by a monoclinic phase acting as a "bridge". Close to the MPB, the piezoelectric elongation of the unit cell occurs along the directions associated with the monoclinic distortion instead of the rhombohedral and tetragonal polar directions, indicating the high dielectric property arises from the monoclinic phase (Guo et al. 2000). The width of the MPB stripe is not well defined because of the difficulty in preparing samples of high compositional homogeneity. Ahart et al. (2008) showed that even a pure compound (PbTiO 3 ) could display a MPB under pressure (10 ∼ 20 GP a). In the MPB region, large piezoelectric effects were also observed. Their firstprinciple calculations were consistent with the experimental results. According to their study even at room pressure a pure compound with MPB-like behavior maybe exist, which would lead to great advances in electromechanical applications.

Choice of PZT(52/48)

For the fabrication of FeRAM, many ferroelectric materials have been investigated, among which PZT and SrBi 2 Ta 2 O 9 are the two main materials studied for their high remnant polarization and low coercive field (Kingon 1999, Scott 2000[START_REF] Schwarzkopf | [END_REF]. Although PZT is in commercial production, both materials have disadvantages which have limited their evolutions into mass productions.

For PZT, the main problem is fatigue for capacitors with common platinum electrodes. However, this problem has been greatly eased by using oxide electrodes such as IrO 2 , RuO 2 and SrRuO 3 (Asano et al. 2003, Masuda andNozaka 2003). SBT does not show any fatigue phenomenon up to 10 13 cycles (Scott 2000). SBT also has a lower coercive field, which enables an lower operating voltage. But the high process temperature (about 750 • C) for SBT makes it difficult to process in conjunction with silicon devices (Park et al. 1999). And the crystallization temperature for PZT is less than 650 • C, making it possible for implementing PZT capacitors on CMOS logic circuits.

The phase of Pb(Zr 1-x ,Ti x )O 3 varies with its composition and its properties change accordingly.

The polarization direction of a rhombohedral phase PZT (x < 0.48) is neither perpendicular to the plane, nor parallel to the plane, making it not practical for memory use. When x varies from 0.48 to 1, PZT phase changes from MPB to tetragonal and remnant polarization increases from 30 µC/cm 2 to 55 µC/cm 2 , accordingly. However, coercive field increases noticeably, making low operating voltage more difficult [START_REF] Foster | [END_REF]). Thus we chose PZT(52/48) for its sufficient remnant polarization and low coercive field. INL is involved in projects employing PZT for MEMS as sensors and energy harvesters and PZT(52/48) has an outstanding piezoelectric coefficient compared to other compositions.

Polycrystalline vs Epitaxial

Before 2000 due to technical limitations, most studies on PZT thin films concentrated on its polycrystalline phase and now most research works are dedicated to monocrystalline phase for its superior polarization, higher piezoelectric coefficient and better interface with substrate. Since polycrystalline films usually consist of randomly-oriented crystalline grains, they must be poled in order to preferentially orient the ferroelectric polar domains [START_REF] Ramesh | Thin Film Ferroelectric Materials and Devices[END_REF]. As monocrystalline phase has all the domains appropriately-oriented, its ferroelectric, pyroelectric and piezoelectric response are all better than that of polycrystalline PZT. Monocrystalline phase exhibits high macroscopic uniformity, which makes miniaturization of devices possible.

Polycrystalline film contains many grains of usually different orientations. Grain boundaries are formed between grains. Compared to monocrystalline phase, which possesses no grain boundaries, the leakage current increases several orders of magnitude and the fatigue endurance and breakdown voltage are reduced (Lee and Joo 2002). The polycrystalline PZT films is reported to show a non-square hysteresis loops, in which the coercive field was not well defined. This implies that a higher operating voltage is required (Setter et al. 2006b).

If PZT film is deposited on a substrate with small lattice mismatch, epitaxial growth can be achieved. Since it is monocrystalline, grain boundaries are avoided and its ferroelectric properties are improved due to the single orientation of almost all domains. TEM (transmission electron microscopy) observation has also revealed that contrary to polycrystalline film the interface between the epitaxial PZT layer and the underlying layer is clean and flat; no obvious diffusion between these two layers was observed (Scott 2000). If the in-plane lattice parameter of substrate is slightly smaller than that of PZT, the increased tetragonality (for tetragonal PZT, x > 0.48) is enhanced by the clamping force from the substrate, thus improving its ferroelectric performance.

Based on these information, our aim is to grow epitaxial PZT(52/48) capacitors. The coercive field were 64 kV /cm and 41 kV /cm, respectively.

Several routes have been proposed to improve the film quality. Meng et al. (2000) replaced Zralkoxides with zirconium nitrate, to reduce the relative content of organics in the precursor solution. By modifying the solution, the shrinkage of the film reduced during the thermal treatment, thus reducing the formation of cracks. The coercive field was as low as 45 kV /cm but the remnant polarization was only 11 µC/cm 2 .

Some efforts have been given to lower the process temperature. Perez (2004) demonstrated that at 500 • C, PZT(52/48) was crystallized by distilling the Pb precursor multiple times after dissolving in 2-methoxyethanol and increasing the drying temperature. This procedure provided high chemical homogeneity, thus increasing crystallinity. The remnant polarization and coercive field were 30 µC/cm 2 and 60 kV /cm, respectively. [START_REF] Wu | [END_REF] reported that by adding perovskite PZT nanopowders as seeds into precursor solution, the post annealing could be performed either at lower temperature or for shorter period. The seeded film showed relatively higher crystallinity than unseeded films.

Thick PZT film, prepared by multiple spin coating and annealing processes, often show an oscillating chemical profile. Calame and Muralt (2007) demonstrated that by using gradient-composition solutions for different spin coating layers for compensation, an almost gradient-free 2-µm-thick film was obtained. Its piezoelectric coefficient was larger than the gradient counterpart.

Sputtering

Sputtering has been successful using elemental and alloy targets for the deposition of ferroelectric materials. Usually the deposition rate is low (< 5 nm/min). In recent years, sputtering for PZT has focused on epitaxial growth as well as coverage of large areas.

Through an off-axis magnetron sputtering, Gariglio et al. (2007) deposited 15-nm-thick totally strained PZT(20/80) film on Nb-doped STO substrate. He also found that when the film thickness exceeded 80 nm, it turned to be relaxed. By using a 12-inch ceramic PZT target, Masuda et al. (2001) achieved depositing PZT on a 6-inch substrate. Film thickness and Pb content uniformity showed very low variations.

By controlling O 2 /Ar ratio and heating rate in post annealing, highly oriented ( 111) and (100) PZT films have been achieved on Pt/Ti/SiO 2 /Si by [START_REF] Kalpat | [END_REF]. PZT(111) showed a remnant polarization of 25 µC/cm 2 and coercive field of 65 kV /cm while for PZT(100), the corresponding results

were 20 µC/cm 2 and 35 kV /cm.

When PZT thickness exceeds ∼ 30 nm, it will relax on substrate (Gariglio et al. 2007), which will reduce the ferroelectric properties since the tetragonality decreases. Callori (2013) demonstrated a method to keep PZT strained on substrate by depositing PbTiO 3 /SrRuO 3 superlattice structure. This ferroelectric of more than 100 nm could remain strained on substrate. However the hysteresis loops were not square and the remnant polarization was only 20 µC/cm 2 , less than that of recently reported PbTiO 3 films (Izyumskaya et al. 2007).

PLD

PLD have been intensely investigated for its capacity of growing high quality epitaxial PZT films in recent years. To increase the uniformity, a rotating target and oblique angle of incidence are often employed. The most promising characteristics of PLD for oxide growth are little difference between the film and ceramic target. In addition, high oxygen gas pressure is feasible during growth, which can suppress oxygen vacancies produced due to the volatility of lead in the form of PbO (Izyumskaya et al. 2007). Pintilie et al. (2007) reported high quality epitaxial PZT(20/80) films deposited on SrRuO 3 .

Square-like hysteresis loops were obtained with remnant polarization as high as 105 µm/cm 2 .

Usually, the coverage of PLD is very poor due to the form of the plume. [START_REF] Nguyen | Int. Conf. Mater. Adv. Tehcnologies, ICMAT 2011[END_REF] reported a PZT deposition on a 4-inch silicon-on-insulator (SOI) wafer. The thickness variation was less than 5%. In this chapter, two film growth techniques employed in this work, sputtering and sol-gel, will be presented firstly. The principles of characterization for structural, morphological and electrical properties will be introduced then.

Film Growth Techniques

Two different deposition routes were employed for the fabrication of ferroelectric PZT capacitors. And a lift-off process was used for the deposition of top electrode. In this section, these three techniques will be presented.

Sputtering

Vacuum based thin film deposition technologies can be classified into two major categories: physical vapor deposition (PVD) and chemical vapor deposition (CVD). In PVD techniques, single atom or small clusters occur on the substrate surface independently of the source process. In CVD techniques, molecular species chemically react at the substrate surface resulting in a condensed film as well as the emission of volatile by-products [START_REF] Powell | PVD for Microelectronics: Sputter Deposition Applied to Semiconductor Manufacturing[END_REF].

Sputtering "knocks off" the material to be sputtered via high energy, ionized atoms. Physical sputtering is driven by energy and momentum exchange between ions and atoms in the target. DC (direct current) plasma is used for conductive material deposition. Ions are neutralized after gaining electrons from the cathode. To produce highly insulating oxides, RF (radio frequency) power is applied to avoid the build-up charges on the insulative target surfaces, which lowers the deposition rate. Compared with DC powered sputtering, RF sputtering increases the deposition rate (as well as for conductive material deposition), lowers the required voltage and is compatible with the use of reactive gas, such as oxygen. 13.56 M Hz is the most commonly used frequency for commercial sputtering application.

Sputtering sources often utilize magnetron to confine charged plasma particles near the target. This can enhance both the efficiency of initial ionization process and allowing a plasma to be generated at lower pressures [START_REF] Rossnagel | PVD for Microelectronics: Sputter Desposition to Semiconductor Manufacturing, Thin films[END_REF]. In this work, Alliance Concept AC450 sputtering machine in RF magnetron mode was employed for both PZT and electrode growth.

The advantages of sputtering deposition are [START_REF] Mattox | Handbook of Physical Vapor Deposition (PVD) Processing[END_REF]):

• Ability to deposit a wide variety of metals, insulators, alloys and composites. Especially practical for materials with high melting points.

• Large area coverage (the cost of large target can be high, overlapping mosaic tiles, rods can replace single planar target).

• High step coverage.

• Reproducible deposition control.

• In-situ cleaning of substrate by reversing the potential.

And the disadvantages of sputtering deposition are:

• Due to its relatively violent bombardment, active control for layer-by-layer growth is difficult compared to pulsed laser deposition.

• Inert sputtering gases may be built into the growing film as impurities.

• Most of the sputtering energy is transfered to heat in the target.

• Targets are often expensive.

• Some targets are fragile and may be broken by non-uniform heating.

Sol-gel

Sol-gel process is a chemical solution deposition (CSD) technique used for the fabrication of ceramics and organic-inorganic hybrids. In the initial stages, Budd et al. (1985) demonstrated sol-gel process for the formation of perovskite oxide thin film. Since then, a large variety of perovskite-related compounds have been synthesized as thin films by sol-gel, such as PbTiO 3 (Blum and Gurkovich 1985), BaTiO 3 (Kamalasanan et al. 1991), SrBi 2 Ta 2 O 9 (Boyle et al. 1996), Pb(Mg 1/3 Nb 2/3 )O 3 (Okuwada et al. 1989), (La,Sr)MnO 3 (Taguchi et al. 1992). The main advantages of sol-gel technique are the relatively low cost and the excellent control of film composition through the adjustment of precursor solution stoichiometry. Other advantages include easy fabrication process, high growth rate and large area coverage compared to sputtering, PLD and MBE. The disadvantages of sol-gel process include the difficulty of fabricating ultrathin film (< 30 nm)

and coating 3D surface (Schwartz et al. 2004).

Lithographic Patterning

To fabricate top electrodes for the capacitors, lithography with reversal mask was employed. The advantage of using reversal lift-off is that after reversal the sidewall slope forms an undercut profile which avoids destroying the adjacent electrode in the development step.

The procedure of reversal lift-off is depicted in Figure 2.3 and described as follows:

1. Several drops of reversal resist AZ5214E are drizzled on the sample followed by 30 s of rotation at the speed of 5000 rpm . Then a soft bake is performed at 110 • C on a hot plate to drive off solvents 6. Top electrode is sputtered on the sample surface at ambient temperature.

7. Developer-inert resist is removed by immersing the sample in acetone with ultrasonic during several minutes (then acetone is removed by ethanol).

Characterization Techniques

Characterization Techniques

Film structure directly influences the ferroelectricity of the capacitors. Surface morphology has a great influence on the quality of film. Since a "sandwich" capacitor includes two interfaces between the ferroelectric and the two electrodes and one interface between the bottom electrode and the substrate, small roughness of each surface is the prerequisite of the high quality of subsequent film. We are now going to introduce the instruments for examining the structure and morphology.

Structural Analysis

X-ray diffraction (XRD) is commonly used in material science for probing the atomic and molecular structure of a crystal. XRD is a non-destructive analytical technique.

Since the wavelength of X-ray is comparable to the unit-cell spacing in crystals, X-ray can be diffracted from crystals which have regularly repeating atomic structures. Scattered X-rays interfere with each other either constructively or destructively, producing a diffraction pattern on a detector. The resulting wave interference pattern is the basis of diffraction analysis, which is called Bragg diffraction.

When the phase shift is a multiple of 2π, the interference is constructive, which can be expressed by Bragg's law [START_REF] Guinier | X-Ray Diffraction: In Crystals, Imperfect Crystals, and Amorphous Bodies[END_REF]:

nλ = 2dsinθ (2.1)
where n is an integer, representing the diffraction order, λ is the wavelength of the X-ray, d is the spacing between planes in the atomic lattice and θ is the angle between the incident ray and the scattering planes. A diffraction pattern is obtained by measuring the intensity of scattered waves as a function of scattering angle. To measure out-of-plane lattice parameter, 2θ/ω scan is performed. Scanning through ω axis around (002) peak, a "rocking curve" is obtained, which can be used to evaluate the out-of-plane mosaicity of the thin film. For in-plane measurement, instead of 2θ/ω scan and ω scan, 2θ χ /φ scan and φ scan are used to extract the in-plane lattice parameter and evaluate the in-plane mosaicity, respectively.

A combination of 2θ/ω scan and ω scan is sometimes required to reveal the strain state of thin film by performing asymmetric scan. X-ray is also used to obtain the thin film thickness through X-ray reflectivity (XRR). XRR scan is similar to 2θ/θ scan, but has a very small incident angle (usually 0 ∼ 5°). For incident angles greater than a critical angle θ c , the X-ray beam partially penetrates into the film and partially reflect from the surface. The interference between the rays reflected from the surface of the film and the bottom of the film results in interference fringes. By using Fourier transform, the thickness, roughness and density of the layer can be obtained.

Morphological Analysis

Atomic force microscopy (AFM) is a technique to obtain topographies and other surface informations from a variety of samples. AFM works by scanning a tip along the sample surface. When the tip is brought into proximity of a sample, forces between the tip and the surface lead to cantilever deflection according to Hooke's law. The deflection of the cantilever due to forces acting on the tip is detected by a laser focused on the back of the cantilever. The laser is reflected on a distant photodiode. The movement of the laser spot on the photodiode reveals the sample's topography along with other informations. The sample is mounted on a piezoelectric scanner, which precisely maintains the distance between the tip and the surface or the force on the tip. Veeco CP-II is used to carry out AFM measurement. According to the nature of the tip motion, AFM operation is described in three modes:

• Contact mode: The tip is "dragged" across the surface. The defection of the cantilever is kept constant. In this mode, the image is heavily influenced by frictional and adhesive forces.

• Non-contact mode: The tip does not contact the surface but is oscillated at the resonance frequency. The amplitude of the oscillation is kept constant. In non-contact mode, image quality can be reduced by the surface contaminant (e.g., water) .

• Tapping mode: The tip oscillates up and down as non-contact mode. But at each oscillation downward, the tip touches the surface. The oscillation amplitude is maintained. This method of "tapping" lessens the damage done to the surface compared to contact mode and provides higher resolution compared to non-contact mode. In this work, most of the surface morphologies were measured through tapping mode.

Electrical Characterization

Microscale electrical characterizations of ferroelectrics are widely used to evaluate the properties of the capacitors, including: current-voltage measurement, capacitance-voltage measurement and hysteresis loop measurement. Nano-scale PFM measurement provides the opportunity to investigate domain switching behavior with a resolution of several nm.

Current-Voltage

Low leakage current is an essential prerequisite for a ferroelectric film. It depends on the mobility of free electronic charges in the ferroelectric. An applied voltage results in a leakage current flow through the capacitor. The current-voltage (I-V) measurement is performed by applying a step shaped voltage waveform from 0 to +V max /-V max , as shown in Figure 2.6. The measurement was carried out by Agilent 4156B Semiconductor parameter analyzer. Current response is recorded after performing a voltage of the same waveform to avoid the domain switching current. At each voltage step (V s ), current is monitored after a short period (delay time, t d ). In this work, t d = 0 was employed since we did not observe significant difference of leakage by varying t d .

A typical leakage characteristic is shown in Figure 2.7. According to the amount of leakage, the insulated property of a ferroelectric can be evaluated. By fitting the leakage current to equations of different charge transport mechanisms, the dominant transport mechanism can be found.

Capacitance-Voltage

Ferroelectrics exhibit a nonlinear relative permittivity ε r , which is dependent on field, frequency and temperature. For an ideal ferroelectric, ε r as a function of field is shown in peaks in two small regions around the coercive field E c . The peak value is relatively much higher than ε r at other field, which is near 0. This occurs because during switching, a small field change results in a very large change in polarization (Brennan 1992). Peak value can exceeds 5000 for a high quality ferroelectric (even higher ε r is achieved by Erbil et al. (1996)). Peak value of ε r is frequency dependent. As frequency increase, it decreases and attains to a constant limiting value. It can be explained by the behavior of dipole movement. As frequency increases, dipoles begin to lag behind the change of the field and the accumulation of charges at the interfaces between the sample and the electrode drops [START_REF] Saif | [END_REF].

ε r is also temperature dependent. Elevated temperature disturbs the alignment of dipoles, resulting in a decrease in the peak value of ε r . To perform the capacitance-voltage (C-V) measurement, HP 4284A Precision LCR meter was used. The ferroelectric is under a DC bias voltage (the waveform is similar to that used in I-V measurement), whereas the capacitance is tested with a small AC field. The circuit is shown in Figure 2.9. As the capacitance of a ferroelectric capacitor is small (usually less than 10 nF ), it yields large reactance.

This implies that the effect of the parallel resistance (R p ) has relatively more significance than that of the series resistance (R s ). The low value of resistance represented by R s has negligible significance compared with the capacitive reactance, so the parallel circuit mode C p -G is employed for ferroelectric.

C

Figure 2.9: C-V measurement circuit.

The admittance (reciprocal of impedance) in the parallel circuit is:

Y = G + jB = G -2πf C p j (j 2 = -1) (2.2)
Through ε r = Cd/ε 0 A (d is the thickness of ferroelectric and A is the area), ε r can be obtained and be expressed in two parts: real component ε ′ r and imaginary component ε ′′ r .

ε r = ε ′ r -jε ′′ r (2.3) ε ′ r = Gd/ε 0 A (2.4) ε ′′ r = |B|d/ε 0 A (2.5)
ε ′′ r is attributed to bound charge and dipole relaxation phenomena, which gives energy loss. Loss tangent is used as quality factor, which is the ratio of ε ′′ r to ε ′ r (or |B|/G). C-V curve shape of real ferroelectric is not like Figure 2.8 but resembles Figure 2.10, which contains three parts [START_REF] Mihara | [END_REF], Evans 2011): a linear part ε ′ r l , independent of voltage and frequency; the upper non-linear part (with 2 peaks), linked to ferroelectric switching behavior; the lower linear part, linked to paraelectricity (polarization disappears when external applied field is removed).

P-E Hysteresis Loop

Not long after the discovery of ferroelectricity in Rochelle salt (Valasek 1921) In a PUND pulse train, the first negative pre-switch voltage acts to switch the domains downward (if the voltage is higher than coercive voltage). Then the first the positive voltage "P" switches the domain upward, which includes the contribution due to the domain motion and other parts. Subsequently a second positive voltage "U" is employed to measure the contribution not due to the domain motion. By subtracting the charges during the pulse "U" from the charges during the pulse "P", the switching-up charges can be measured. Combining this with the negative half, a PUND hysteresis loop is formed. By integrating the charges during P and N pulse, a PN loop is obtained which is equivalent to Sawyer-Tower loop and has almost identical shape and characteristic values. Figure 2.14 shows the circuit in PUND measurement. Different from Sawyer-Tower circuit, the charge is not recorded directly, thus the hysteresis loop can not display on the oscilloscope simultaneously. Instead, current response to the whole pulse train is recorded and charges are obtained by integrating the response under each pulse. Amplitude of V max and PUND pulse frequency are manipulated directly in the generator. Retention quality of a ferroelectric capacitor is investigated by varying t r . charges flow to the opposite direction); and leakage current I l , which is almost negligible in Figure 2.16.

And their relations are:

I P = I P -U + I U (I N = I N -D + I D ) (2.6) I U = I p d + I p l (I D = I n d + I n l ) (2.7)
PUND loop can be extracted by combining

P p = 1 A I P -U dt and P n = 1 A I N -D dt (2.8)
PN loop can be extracted by combining

P p = 1 A I P dt and P n = 1 A I N dt (2.9)
where A is the area of the electrode (100 × 100µm 2 for all measurements in this work unless stated otherwise); P p and P n are polarization in positive part and negative part, respectively.

Figure 2.16 shows the PUND loop, PN loop and corresponding currents I P -U and I N -D . From PUND loop, remnant polarization P r and coercive field E c are extracted. From PN loop, maximum polarization P ⋆ is extracted. In this example, P ⋆ is about 50% bigger than P r . If a ferroelectric is more leaky than this one (which can be caused by inferior film quality, approximation to breakdown voltage or elevated temperature), I U (or I D ) will be much larger and P ⋆ is driven up to be many times larger than P r . So for a good ferroelectric (P r from PUND loop and from PN loop are identical), P ⋆ is the maximum displacement at V max , containing both remnant part P r and non-remnant part. For a leaky ferroelectric, besides these two parts P ⋆ also contains the contribution from leakage.

High voltage/current ratio of amplifier is favorable to increase the signal/noise ratio. However, non-zero current may be observed due to the artifact of the amplifier, resulting in incomplete hysteresis loop. This problem can be solved by frequently pressing the "Correct" button or subtracting the average current at 0 V . Square waveform of PUND pulse signal provides higher voltage increasing rate compared to triangular waveform. With PUND pulse train, contributions from domain motion and from leakage can be separated, which makes the evaluation of a ferroelectric capacitor easier and more accurate.

Piezoresponse Force Microscopy

Piezoresponse force microscopy (PFM) is a variant of AFM that images and manipulates ferroelectric domains. The PFM technique is based on the converse piezoelectric effect (CPE). As all ferroelectrics exhibit piezoelectricity, an electric field applied on a ferroelectric results in changes of dimension. To detect the polarization orientation, a conductive tip is in contact with the ferroelectric surface and an alternating voltage is applied on the tip. In response to the electrical stimulus, the domain beneath the tip expands if the polarization is parallel to the electrical field. And the domain contracts when it is anti-parallel to the field. By comparing the amplitude and phase of the tip to the driving signal, the information of the domain can be obtained [START_REF] Alexe | Nanoscale Characterisation of Ferroelectric Materials: Scanning Probe Microscopy Approach, NanoScience and Technology[END_REF]). Figure 2.17 illustrates the ideal phase and amplitude to a 180°domain ferroelectric. The above method of using phase signal to map the orientation of out-of-plane orientation of a ferroelectric is called PFM imaging, which is frequently used to investigate domain switching behaviors.

Domain Structure

For PZT in this work, vertical PFM imaging was employed since the PZT film was crystallized in 00l

direction. First domains of different direction are "written" by a voltage higher than coercive voltage sweeping on the PZT film. Then the switching information is "read" by PFM imaging according to the principle described above. The standard procedure is as follows:

1. Scan a square with various DC bias voltage to determine the coercive voltage.

2. Determine the size of area to be studied (such as 5 × 5 µm 2 , or 20 × 20 µm 2 ). Scan a square on the surface with a sufficient DC bias voltage applied to the tip to switch all the opposing domains thus all domains will point to the same direction. The signal is read by an AC bias.

3. Scan a smaller square inside the previous one with opposite drive voltage to force all scanned domains to point to the opposite direction.

4. Depending on the quality of the film and the scan size, an even smaller square of scan inside the previous zone with the opposite drive voltage to the last one can be performed. Squares scanned with opposite drive voltage will present contrast in phase and amplitude. Contrast nearby a smaller square is usually less obvious because of the increasing difficulty in switching the domain without poling the nearby ones.

5. Retention is investigated by writing 2 or 3 different size of squares on the surface as step two and read the signal some time later.

By performing PFM imaging, topography, phase and amplitude can be obtained simultaneously.

Based on the same principle, local domain can be switched by applying a field larger than coercive field.

This technique is called PFM spectroscopy, in which a small AC signal is carried by a square wave which steps in magnitude with time. As the square wave passes coercive field, domain switches which can be detected by the AC signal. The voltage signal is shown in Figure 2.18.

Step period and interval period can be varied. In this work, every capacitor was fabricated from bottom to top in four steps: 1) preparation of STO substrate; 2) deposition of bottom electrode; 3) deposition of PZT film through sputtering or sol-gel (both required a post annealing for crystallization); 4) deposition of top electrode (another post annealing was required for its crystallization). Growth conditions, including temperature, plasma voltage for sputtering; rotational speed and acceleration for sol-gel, have been varied for optimization. The details of each step will be presented in the following sections.

Substrate Preparation

Before depositing SRO bottom electrode, a chemical treatment was applied to the STO (001) substrate to obtain atomic plane with single termination. Rough surface with two different terminations increases the difficulty of hetero-epitaxial growth, causing more defects in the interface and degrading the film crystal structure. Besides, the growth rate of SRO on the two terminations is found to be different (Koster et al. 2012), which may further increase the surface roughness. Kawasaki et al. (1994) first invented an acidic etching procedure to obtain an atomic flat surface of STO by removing the top SrO layer and contaminations. Now it becomes a standard procedure for thin film growth on oxide substrate as well as on silicon substrate for removing SiO 2 .

Abrupt surface is obtained by using the different chemical properties of the two terminations. SrO reacts with CO 2 and H 2 O, forming SrCO 3 and Sr(OH) 2 , respectively (Ohnishi et al. 2004), which can be dissolved in HF. TiO 2 is very stable in water and its solubility in HF is much smaller than SrO. Thus HF can be used to effectively remove the top-most SrO layer and the Sr(OH) 2 .

Our modified treatment procedure based on Kawasaki's study is described as follows:

1. Rinse in acetone during 10 min with ultrasonic.

2. Rinse in ethanol during 10 min with ultrasonic.

3. Rinse in deionized water during 10 min with ultrasonic.

4. Immerse in pure BOE (buffered oxide etching solution) during 20 s.

5.

Rinse in three beakers of deionized water, each for 1 min.

6. Rinse in ethanol during 3 min with ultrasonic.

7. Dry up with N 2 gun.

8. Anneal at 950 • C in O 2 for 10 h with furnace pre-heated to avoid contaminations.

Deposition of SRO

In this section, at first, the properties of SRO will be introduced. Then the optimization by varying deposition conditions will be presented. At last, the structure characteristics of deposited SRO as bottom electrode will be presented.

Choice of SRO as Bottom Electrode

SRO was chosen as the bottom electrode for all the capacitors in this work for its: a) conductive property without doping; b) high chemical stability; c) comparable perovskite structure, providing a good lattice matching with both STO substrate and PZT thin film.

Hetero-structures of ferroelectric thin films are attractive for the lack of detrimental grain boundaries and SRO makes it achievable. Since Eom et al. (1992) successfully grew epitaxial SRO layer on STO substrate two decades ago, SRO has been widely applied as a conducting layer on complex oxide studies.

SRO is grown by various approaches, mostly by pulsed laser deposition (PLD) (Wu et al. 1993 (1996) observed that from T c (∼ 160 K) to 1000 K, the resistivity of SRO was linearly dependent on temperature, which is important for electrode application.

SRO is chemically and thermally stable. In oxidizing or inert gas atmospheres, it is stable up to 1200 K To obtain high quality hetero-epitaxial structure, SRO has to be grown on a STO substrate with single termination. Contamination will increase the defects in the interface. Besides, SRO grows faster on B-site termination (Koster et al. 2012). Different growth rate causes non-uniform morphology, which will also result in more defects in the subsequent film growth.

Optimization of SRO Growth

All SRO films were deposited on (001) STO substrates by an in-axis sputtering machine. As stated, substrate temperature, plasma voltage, chamber pressure and gas composition all impact the property of deposited thin film. First, we studied the influence of the substrate temperature. Four SRO films were deposited at different temperatures4 from 460 • C to 675 • C on as-received (001) STO substrates5 during 75 min. Plasma voltage were all kept at 109 V , chamber pressure at 0.005 mbar, gas composition of 50 sccm Ar/5 sccm O 2 . Figure 3.4 shows out-of-plane 2θ/ω scans and rocking curves of these four SRO films. The two SRO deposited at relatively lower temperatures showed much smaller intensity of SRO (002)6 peak compared with the other two, indicating that relatively small amount of SRO was crystallized when at less than 600 • C. SRO deposited at 620 • C had more crystalline SRO comparing to the one at 675 • C. And the Kiessig fringes around SRO (002) peak of the one at 620 • C indicated the low roughness of the SRO film surface.

From the rocking curves of these four SRO films, a narrow sharp peak with higher intensity and a broad peak with lower intensity were observed for the two SRO films deposited at relatively lower temperatures. The broad peak indicated that part of the SRO crystal structure exhibited high mosaicity.

The broad peak disappeared at higher temperature. The peak of the SRO film deposited at 620 002) peak and slightly smaller mosaicity (the difference also depended on the film thickness).

X-ray reflectivity (XRR) was performed to extract the film thickness. The thicknesses of the SRO films deposited at 600 • C and 675 • C were 102.4 nm and 97.4 nm, respectively. The thickness of the other two cannot be measured due to their rough surface morphologies (about 100-nm-thick film with rough surface is hard to obtain oscillations in XRR spectrum). From sputtering depositions of SRO, PZT and Pt, it was found that higher temperature caused reduced deposition rate, which could be attributed to the higher mobility and lower adhesion of species to the substrate at higher temperature. Compared with the SRO film deposited at room temperature (at the same conditions used for the four films above), the deposition rate reduced about 25% when at 650 • C.

Out-of-plane lattice parameter were extracted from 2θ/ω scan by fitting the SRO (002) peaks. Full Other deposition parameters such as plasma voltage, pressure and gas composition have also been examined. At 620 • C ∼ 650 • C, plasma voltage mainly affects the deposition rate (higher voltage higher deposition rate) and has little influence in crystalline quality and surface morphology (results shown in next section); chamber pressure has been varied from 0.005 mbar to 0.1 mbar, and deposition rate was found to be inversely proportional to chamber pressure, as shown in Figure 3.7. One possible reason is that as pressure increases the amount of flux increases correspondingly and the mean free path for sputtered species from the target is reduced. As a result, more collisions occur before the sputtered species reach the substrate, thus reducing the deposition rate. In this study, process pressure was kept at 0.005 mbar for all SRO film growth; Oxygen proportion has been tested from 9.1% to 20%, but no obvious difference has been observed. Based on the studies above, the standard sputtering condition for SRO is: voltage, 109 V ; substrate temperature, 620 • C; 7 chamber pressure, 0.005 mbar and gas composition, 50 sccm Ar /5 sccm O 2 . The deposition rate is ∼ 1.4 nm/min.

Growth of SRO with Terraces on Vicinal STO

Since interface significantly influences the properties of thin film and the density of defects, the importance of preparing a flat SRO surface for the subsequent growth of PZT can never be overemphasized. A great effort has been put to produce SRO with terraces of single unit cell in height. As stated, lower plasma voltage can reduce the deposition rate, allowing the attached atoms on the substrate have more time to reorganize, thus reducing the surface roughness. But lower deposition rate also means that the film is kept at high temperature for longer time, which may cause Sr to emerge to the surface, hence making the deposition rate inhomogeneous at different locations (Koster et al. 2012).

In order to find the suitable deposition rate to grow SRO film with terraces of single unit cell

7 When we deposited SRO as bottom electrode in following sections, all SRO were deposited at a temperautre between 620 • C and 650 • C. The reason we did not always use the optimal temperature (620 • C) is that we found this result after we started fabricating PZT capacitors. The quality degradation of SRO deposited at 640 • C ∼ 650 • C was very small for film of less than 30 nm on vicinal STO.

in height as bottom electrode, three SRO depositions of ∼ 10 nm have been processed on vicinal STO substrates using the standard sputtering condition mentioned in previous section except that the voltage was changed to achieve different deposition rates. Plasma voltages were 70 V , 87 V and 109 V respectively for the three depositions. Out-of-plane 2θ/ω scan and rocking curve measurements have been performed for these SRO films, as shown in Figure 3.8. 2θ/ω scan unveiled only (00l) oriented SRO grown on STO substrate for all three films. Intensity of SRO (002) peaks in 2θ/ω scans were very similar, indicating same amount of SRO were crystallized. However the rocking curve showed that SRO film deposited at 70

V had much lower mosaicity. Out-of-plane lattice parameters and mosaicities are shown in Table 3 Deposition rate was greatly influenced by plasma voltage. Every drop of ∼ 20 V reduced the deposition rate in ∼ 50% (see Table 3.1). At 70 V , deposition rate was only 0.228 nm/min.

Surfaces of all three films (in Figure 3.9) showed terraces with single unit cell in height. The terraces of the film deposited at 70 V were slightly more obvious than that of the other two. The roughness of three films were all ∼ 0.3 nm, as shown in Table 3.1.

Bottom electrode for a PZT capacitor thickness is usually between 20 nm and 100 nm (Vrejoiu et al. 2006, Sambri et al. 2012, Eom et al. 1993, Bruchhaus et al. 1991).8 As ∼ 10 nm SRO is not thick enough for the use of bottom electrode, several thicker SRO films were deposited on vicinal STO substrates to investigate the maximum achievable thickness of SRO film with terraces of single unit cell in height. As shown in Figure 3.10, at 109 V , after deposition of 18.9-nm-thick SRO, terraces disappeared.

At 70 V , SRO of 27.7 nm exhibited clear terraces of single unit cell in height, but terraces disappeared when the thickness increased to 32.8 nm. At this deposition condition, the maximum thickness of SRO film with terraces of single unit cell in height is ∼ 30 nm. Deposition rate, surface roughness, out-of-plane lattice parameter and FWHM can be found in Table 3.2. nm, deposited after the interval). This is probably because the growth on the vicinal STO substrate was slightly easier than on the relatively rougher SRO surface at the beginning of the second half deposition.

According to the XRR fitting result, the alternating peak intensities indicated that the density of top SRO layer (deposited after the 15 min interval) was about 9% higher than that of the bottom one.

Reciprocal space mapping (RSM) around the (103) reciprocal lattice points were performed (Fig- With more intervals, deposition at higher rate can achieve same quality of SRO film of same thickness.

SRO Growth as Bottom Electrode

Nine SRO films were deposited on vicinal STO substrates as bottom electrodes for PZT capacitors (four was later used for sputtered PZT capacitors and five for sol-gel-derived PZT capacitors). For the three thinner sputtered PZT capacitor, SRO of ∼ 26 nm9 were deposited (at same condition as in Figure 3.10 (b), but no terraces were observed), and SRO of 35 nm (with terraces, same sample as shown in Figure 3.11) was deposited for 190-nm-thick PZT capacitor. For all five sol-gel-derived PZT capacitors, SRO of ∼ 85 nm10 were deposited. Table 3.3 presents the detailed SRO thicknesses for all nine capacitors. SRO deposited at same condition showed almost identical surface morphology, only one topography is provided. Out-of-plane 2θ/ω scan was performed after the deposition of PZT layer and will be provided in next section with that of PZT in Tables 3.4 and 3.6.

The resistivity of the 85-nm-thick SRO was measured by 4-point probes method. Linear relationship of the applied current and the measured voltage was observed in the whole measurement range. The extracted resistivity was 300 µΩ • cm, which was in agreement with reported result (Klein et al. 1996).

PZT Growth by Sputtering

In recent years, high quality hetero-epitaxial PZT films have been achieved through PLD by several groups (Ramesh et al. 1991, Vrejoiu et al. 2006, Lee et al. 2008). In this study, sputtering has been chosen as the growth route for its larger coverage than PLD. The PZT sputtering started from the optimization of deposition conditions.

Optimization of PZT Growth by Sputtering

At the beginning, attempts have been tried to grow monocrystalline PZT directly by varying deposition conditions (plasma voltage, substrate temperature, chamber pressure, gas composition). However the deposited PZT film turned out to be amorphous regardless of deposition condition. Thus a post annealing was always required to realize the transformation form amorphous phase to crystalline phase.

Temperature Influence

Temperature is the most crucial parameter, because at too low substrate temperature absorbed species on the substrate surface have less energy to diffuse, making a good crystallization difficult during the subsequent annealing process (Li et al. 2009) and too high substrate temperature will cause lead evaporation in the form of PbO, resulting in the formation of pyrochlore phase (Dana et al. 1991, Lee et al. 1996, Chen and Chen 1998). Six PZT films were deposited on 85-nm-thick SRO coated STO substrates with substrate temperature varying from room temperature11 to 650 • C. All PZT were deposited at 71

V during 20 min. The gas composition was 50 sccm Ar and no oxygen. The chamber pressure was 0.005 mbar. The thicknesses were about 60 ∼ 80 nm, and the thickness showed an inverse temperature dependence.

Out-of-plane 2θ/ω scans were performed for all six samples both before and after a rapid thermal annealing (RTA) at 650 • C during 30 s in oxygen. Before RTA, no crystalline PZT phase was observed except the one deposited at 650 • C, in which a pyrochlore phase was observed around 33.9 °. Figure 3.15

shows out-of-plane 2θ/ω scan of these six samples after RTA. PZT deposited from room temperature to 540 • C all crystallized in (00l) direction after RTA. The pyrochlore phase in PZT deposited at 650 • C remained after RTA, although Kwok and Desu (1992) has reported RTA could change pyrochlore phase into perovskite phase.

Focusing on the PZT (002) peak, its highest intensity appeared in the PZT deposited at 150 The leakage current measurement of these PZT as capacitor with an area of 100 × 100 µm 2 was performed, showing that only the PZT deposited at 300 • C was well insulated and all other five capacitors were leaky. Thus 300 • C was chosen as the substrate temperature for later growth of sputtered PZT capacitor.

Gas Composition Influence

The influence of gas composition has also been investigated. In the previous section, all the six PZT films were deposited in 100% Ar atmosphere. Another two PZT were deposited, one in 20% O 2 /80% Ar and another in 100% O 2 to compare with the previous ones. Other deposition parameters and deposition duration were kept same (70V , 0.005 mbar, 300 • C, 20 min). Figure 3.17 shows the out-of-plane 2θ/ω scan results of these two PZT films after RTA. No crystalline PZT phase formed when the sputtering gas contained 20% O 2 . When the sputtering gas contained only O 2 , only a fraction of PZT formed perovskite structure and a small amount of pyrochlore phase was also observed. At both conditions the total gas flux quantity was kept at 50 sccm.

The gas composition had a huge impact on the crystallization process. 100% Ar (50 sccm) was chosen as standard PZT sputtering condition.

Plasma Voltage Influence

Plasma voltage has also been modified to investigate its influence on the crystallization of PZT. One PZT film of 91 nm was deposited at 50 V (during 163 min) and another of ∼ 40 nm was deposited at 138 V (during 19 min), both followed by RTA. Substrate temperature was 300 • C and other parameters were kept same as in Section 3.3.1.1. Figure 3.18 shows the out-of-plane 2θ/ω scan results of these two PZT films after RTA. At 50 V , crystalline PZT (00l) was formed and its intensity was high, indicating large amount amorphous PZT was crystallized after RTA. At 138 V , PZT (00l) was formed, accompanied with several different pyrochlore phases, which were formed due to the low surface mobility at high deposition rate (Scott 2000). The out-of-plane lattice parameter c P ZT of PZT deposited at 50 V extracted from PZT (002) peak was 4.067 Å, much smaller than PZT deposited at 71 V in section Section 3. Compared to SRO sputtering, plasma voltage showed much greater impact in crystallization in PZT sputtering. 71 V was chosen as the PZT plasma voltage.

Growth and Structural Characterization of Sputtered PZT

After modifying the substrate temperature, gas composition and plasma voltage (chamber pressure has not been varied, a typical pressure of 0.005 mbar was applied to PZT sputtering process), four PZT films of different thicknesses from 40.5 nm to 190 nm were deposited on SRO/STO. The miscut angle of these STO substrate is ∼ 0.05°. Different thicknesses were achieved by adjusting the deposition duration.

Deposition condition was: at 71 V , in a 0.005 mbar chamber with 50 sccm Ar on 300 • C substrates. Since 190-nm-thick PZT was deposited on a SRO film with terraces of single unit cell in height, its PZT surface roughness was smaller than other three thinner PZT films. And blurred terraces12 with same width was observed, as shown in Figure 3.23. As PZT thickness was about 50 times of the unit cell height and surface peak-to-valley value was even larger than unit cell height, the observed blurred terraces of the same form before deposition indicated that the growth mode of PZT in this deposition condition was layer-by-layer.

PZT Growth by Sol-gel

Sol-gel process for growing PZT film was the most widely used method since 1980s for its simplicity, low cost and large area coverage (Yi et al. 1988[START_REF] Dey | [END_REF], Melnick et al. 1990). The growth conditions have been highly developed. In this work, PZT film was also fabricated through sol-gel method to compare with sputtered PZT.

Optimization of PZT Growth by Sol-gel

The growth procedure of PZT by sol-gel solution is only slightly modified according to the suggested procedure by sol-gel solution supplier Mitsubishi Materials (see flowchart in Figure 2.2). Acceleration and rotational speed of spin coating have been tested on STO substrates before growing PZT capacitors.

Firstly, acceleration rate is an important parameter, concerning the solution diffusion process. At low acceleration from 500 rpm/s ∼ 2000 rpm/s, the solution could not totally diffuse over the surface, and it turned out to be a visible bumpy topography. A high acceleration 5000 rpm/s was chosen for the spin coating procedure.

Secondly, rotational speed of 6000 rpm, 3000 rpm and 1500 rpm have been tested. It turned out that rotational speed not only had an effect on the thickness of the film, but also led to the formation of different phases. A separation of phase was observed at lower rotational speed. XRD analysis indicated a rotation-dependent structural phase, i.e., a phase transition from tetragonal phase for the 6000 rpm film to a bi-phase (tetragonal + pseudo-cubic 13 ) structure for the 3000-rpm and 1500-rpm films. RSM around (103) reciprocal space points are provided in Figure 3.24. The thickness of 6000-rpm, 3000-rpm and 1500-rpm PZT film were 33 nm, 45 nm and 65 nm, respectively. Ellipsometry pointed out the stoichiometric ratio of Ti/Zr decreased from bottom to top for the 1500 rpm grown thicker PZT (Liu et al. 2014).

For the purpose of producing monocrystalline PZT, rotational speed of 6000 rpm was chosen as standard procedure. Each rotational cycle lasted 15 s as the suggested procedure. After every spin coating, the sol was dried on a heater at 325 • C for 5 min. A post annealing was carried out after each 3 ∼ 4 spin coating cycles at 650 • C in oxygen for 1 min (see process flowchart in Figure 2.2).

Growth and Structure Characterization of Sol-gel-derived PZT

Four PZT films of different thicknesses were deposited on the 85-nm-thick SRO (shown in Figure 3.14 c)) with the conditions described in previous section. The thicknesses were simply controlled by varying 13 The corresponding phase in bulk PZT of the same composition is rhombohedral phase. the numbers of spin coating cycle. Four depositions of 1, 2, 4 and 6 cycles were carried out and the corresponding thicknesses14 are 33 nm, 67 nm, 133 nm and 200 nm. For the 33 nm, 67 nm and 133 nm PZT, only one RTA was carried out after required thickness was obtained. For the 200 nm one, another RTA was imposed after three spin coating cycles.

Top electrode for these samples required another RTA of 1 min for its crystallization. To compare the influence of this 2nd annealing (1st is the annealing for PZT crystallization), another PZT of 100 nm was fabricated and annealed in the same way in the 1st annealing. 2nd annealing for the top electrode of this 100-nm-thick PZT was carried out in a tubular furnace in air during 3 h instead of 1 min RTA in oxygen.

Out-of-plane 2θ/ω scans and rocking curve measurements were carried out for these five samples, as shown in Figure 3.25. All PZT films crystallized only in (00l) direction except the 100-nm-thick one, in which a fraction of pyrochlore phase also formed. The mosaicity of 100-nm-thick PZT was 1.74 °, much bigger than that of others.

A φ scan of 360°around (103) plane of STO, SRO and PZT was performed for the 200-nm-thick sol-gel-derived capacitor, as shown in Figure 3.26. The overlapping of peaks indicated that both the PZT layer and SRO layer were grown epitaxially.

Out-of-plane lattice parameters and mosaicities were extracted from Figure 3.25, as shown in and the process of recrystallization was accompanied by relaxation. Due to this destructive annealing, the mosaicity of 100-nm-thick PZT was bigger than that of others and during the recrystallization pyrochlore phase was formed.

From Table 3.6, it is noticed that c P ZT increased slightly with thickness. Usually tetragonality (c/a) shows an inverse thickness dependence (Lee et al. 2007), due to the reducing clamping effect from the substrate on the epitaxial film. Nagarajan's work (Nagarajan et al. 1999(Nagarajan et al. 2006) ) on PLD-derived PZT showed that, as thickness varied under ∼ 150 nm, c P ZT was almost stable. And as thickness continued increasing, c P ZT was obviously reduced in the order of 0.02 Å. Another possible reason for the stable c P ZT with thickness here can be derived from the varying chemical profile in sol-gel-derived PZT. Sol-gelderived PZT usually exhibits a gradient of composition. Calame and Muralt (2007) showed within one spin coating layer of 250 nm, Zr/(Zr+Ti) ratio varied from 0.45 to 0.60. Thus from the bottom to top of each spin coating layer, tetragonality decreased as Zr/(Zr+Ti) increased. And a P ZT at the bottom of each spin coating layer was smaller than a P ZT at the top. A clamping force was applied on the top of the layer by the bottom of the layer above, thus the tetragonality was kept as thickness increased. It is also possible that the PZT might be totally relaxed, in which condition tetragonality would not change with thickness.

Surface morphologies of these five samples were measured by AFM, as shown in Figure 3.27 (surface morphologies of underlying SRO was shown in Figure 3.14 c). All samples exhibited good topography with RMS less than 1 nm except the 100-nm-thick PZT, confirming the destructive effect of the long annealing duration. Grain size of 100-nm-thick PZT was 2 ∼ 3 times bigger than that of other four samples. It can be assumed that before the 3 h annealing, 100-nm-thick PZT exhibited a similar crystalline structure and topography as others and the destructive annealing changed the PZT physical properties. Bigger grains were formed during the recrystallization.

Grain density of the 133-nm-thick PZT was much smaller compared to 33-nm-thick, 67-nm-thick and 200-nm-thick PZT. Figure 3.27 (c) was obtained before the 1 min RTA for top electrode. After

Growth of Top Electrodes

After SRO bottom electrode and PZT film were deposited, top electrode was fabricated through reversal lift-off procedure (depicted in Figure 2.3). Three conductive materials, SRO, Pt and ITO, were employed as top electrode to investigate their influences on capacitor's electrical properties. Since the SRO top electrode was same as bottom, a sample with the stack SRO/PZT/STO was fabricated to verify the crystalline structure of the top SRO. Top SRO was found to crystalline also in (00l) direction, with reduced amount of crystal structure compared to the bottom SRO.

Due to the size of sample, only large ones (1 × 1 cm 2 ) were fabricated with three different top electrodes. For a capacitor with three types of top electrodes, the three conductive materials were deposited in the sputtering chamber by covering part of the surface. Then the samples were cut into two parts, one with ITO top electrode and another with SRO and Pt top electrodes. Two parts experienced different RTA as described above. Table 3.8 lists the top electrodes of each capacitor.

Summary

In this chapter, the growth details of PZT capacitors both by sputtering and by sol-gel have been presented. Epitaxially grown PZT were achieved both by sputtering and by sol-gel. Out-of-plane parameter c P ZT in sol-gel-derived PZT (∼ 4.11 Å) was larger than that of sputtered PZT (∼ 4.09 Å). In both cases, PZT were relaxed on SRO/STO. But the degree of relaxation was unknown. Further study of the Zr/ Ti ratio in depth or deposition on a substrate with big mismatch will help understand the strain state between PZT and SRO. Mosaicity of sol-gel-derived PZT (∼ 0.75°) was about 25% smaller than that of

200 √ √ 100 √ sputtered PZT.
Grain size and surface roughness of PZT morphology from both growth routes were comparable.

Through sputtering, high quality PZT with layer-by-layer growth mode was achieved on a SRO film with terraces of single unit cell in height. And its surface roughness was smaller than both sputtered PZT deposited on SRO without terraces and sol-gel-derived PZT.

Sol-gel-derived PZT is highly reproducible in terms of crystal structure and surface morphology.

Sputtered PZT in same conditions of various thicknesses also showed similar crystalline structure and surface morphologies and deposition rate was similar with a variation less than 10%. But several times (less than 20%), the deposition rate could decrease as big as 40%. One possible reason is that the PZT target is frequently loaded and unloaded due to the overwhelming demands for deposition of different materials. The condition of the target (like electrical contact between the target and voltage generator) may change even we keep using the same target holder. Further optimization is required to stabilize the deposition rate to improve the reproductivity of sputtered-PZT films.

Bibliography

Aaltonen, T., M. Ritala, T. Sajavaara, J. Keinonen, and M. Leskelä (2003) In this chapter, firstly, leakage current of both sputtered and sol-gel-derived PZT capacitors will be presented and be fitted according to different charge transport mechanisms. Secondly, relative permittivity of these capacitors will be reported. Then, P-E loops of these capacitors will be presented, and P r and E c at different fields will be shown. At last, PFM results of these ferroelectric films will be demonstrated.

Leakage Current

Leakage current is a crucial issue in ferroelectric capacitors concerning reliability such as thermal breakdown. In an ideal capacitor the conductance of an insulating film is assumed to be null. Real insulators, however, show some degree of carrier conduction when the electric field or temperature is sufficiently high (also some contributions across the interface). For a ferroelectric thin film capacitor, the leakage current can be very large, even covering the contribution of polarization. Therefore, to study the mechanism of charge transport in ferroelectric thin films is of great importance.

Ferroelectrics are often treated as insulators. Many works [START_REF] Robertson | [END_REF], Doolittle et al. 2003, Pintilie and Alexe 2005) regard ferroelectrics as wide bandgap semiconductors, making it easy to adapt well founded theories for semiconductors. However, how to include the semiconductivity is still a difficult problem when analyzing experimental data. Simplified models based on semiconductivity may ignore important effects or limit the range of parameters. For instance, polarization is considered as two uniform sheets of opposite charges posing at a distance ("dead" layer, non-ferroelectric) from the ferroelectric-metal interface (Dawber et al. 2003). Zubko et al.'s work (2006b) found that this assumption will become invalid when space charge level exceeds ∼ 10 19 cm -3 .

Typically, PZT is p-type in bulk and the metal-ferroelectric interface can be n-type due to oxygen deficiency (Yarmarkin et al. 2000, Smyth 1996). Scott (2000) stated that in all ferroelectric thin-film capacitors the conduction was predominantly due to electrons injected from the cathode, not due to holes, despite the p-type character of the film. But Stolichnov et al.'s work (1998) on Pt/PZT/Pt capacitors showed the conduction was supported by holes. Wouters et al. (1995) also found that the hole barrier was smaller than the electron barrier in their study on Pt/PZT/Pt capacitors. Scott (2000) pointed out that n-type perovskite ferroelectric films could be formed when growing in reducing atmospheres. When oxygen is lost in the form of neutral O 2 , it leaves behind electrons, thus the vacancies turn out to be donors. The binding energy is around 1.0 eV . In appearance n-type perovskite has a darker outlook compared to p-type.

Leakage Current Mechanisms

Charge transport in a metal-ferroelectric-metal (MFM) capacitor is usually complicated and composed of various mechanisms since electrons, holes and ions can all contribute to it, resulting in nonlinear integral equations for total leakage current. Among these mechanisms, many are borrowed directly from the theories for metal-semiconductor junction. Pintilie and Alexe (2005) classified these mechanisms into two groups: (i) interface-dominant mechanisms: Schottky emission and Fowler-Nordheim tunneling (FN); (ii) Bulk-dominant mechanisms: ohmic contact, Frenkel-Poole emission (FP), space-charge-limited currents (SCLC) and ionic conduction. For an ultra-thin ferroelectric capacitor, a ferroelectric tunnel junction (FTJ) is formed and the dominant conduction mechanism is direct electron tunneling (Kohlstedt et al. 2005, Tsymbal andKohlstedt 2006).

The regular method to identify which mechanism is involved in one or a series of specific samples is to fit different models to the experimental data. Sometimes more than one mechanism fit the data.

Measurements at different temperatures or of different thickness samples may help further identify the conduction mechanism.

In the following sections we will first present I-V characteristics of the sputtered capacitors and sol-gel-derived ones. Then we will fit each transport mechanism1 to our data. According to the fitting result, we will see which mechanism is compatible with the leakage current. 2000). Φ M (Pt) = 5.7 eV (Michaelson 1977) and Φ M (ITO) = 4.4 eV (Park et al. 1996).

However the required energy to go over the barrier is lowered due to image-field correction. Schottky attributed the phenomenon to the attraction between the electrons already injected to the ferroelectric from the cathode and the electrons still at the cathode. The lowered amount is [START_REF] Sze | Physics of Semiconductor Devices[END_REF]:

∆Φ = ( qE 4πε opt ε 0 ) 1/2 (4.1)
It should be noted that E is the maximum field drop in the junction, which might be ten times of the average field. Due to the lack of knowledge about the maximum field drop, the average field (V /d) was used instead for all the calculations in this work. ∆Φ is about 0.8 eV (Scott 2000). Thus the barrier between the bottom SRO and PZT film is around 0.5 eV . ε opt is the optical permittivity of the ferroelectric. ε opt may be smaller than ε ∞ (relative permittivity when frequency is infinite, usually the minimum relative permittivity of the material). During the emission, if the electron transition time from the interface to barrier maximum is shorter than the dielectric relaxation time, the medium does not have enough time to be polarized, and ε opt < ε ∞ is expected [START_REF] Sze | Physics of Semiconductor Devices[END_REF].

According to [START_REF] Sze | Physics of Semiconductor Devices[END_REF], the leakage current of Schottky emission is:

J = A * T 2 exp   -q Φ B -qE/4πε opt ε 0 k B T   (4.2)
where A * is Richardson constant, q is elementary charge and k B is Boltzmann's constant. At a given temperature, ln(J) ∝ (β SE /T )E 0.5 . The slope (β SE /T ) = q 3/2 /(k B T 4πε opt ε 0 ) and ε opt can be extracted from the data.

Fowler-Nordheim Tunneling (FN)

Tunneling is the most common conduction mechanism through good insulators under high field.

Different from direct tunneling, FN tunneling only crosses a partial width of the barrier. The interface acts as a thin blocking contact in thermal equilibrium. At low voltages, virtually the entire applied voltage is across the interface thus a very high field is built up. When this field is high enough (about 400 kV /cm for ferroelectric oxides (Scott 2000)), electrons can flow through the barrier [START_REF] Sze | Physics of Semiconductor Devices[END_REF]. This tunneling is mainly dependent on the field at the interface and independent of temperature 2 [START_REF] Lampert | Current injection in solids[END_REF]. The tunneling current is given by [START_REF] Sze | Physics of Semiconductor Devices[END_REF]:

J ∝ E 2 exp - 4(2m * ) 1/2 3h (qΦ B ) 3/2 qE (4.3)
where h is reduced Planck constant or Dirac constant, equal to the Plank constant divided by 2π and m * is effective carrier mass. According to Equation (4.3), ln(J/E 2 ) ∝ -β F N (1/E). The slope [START_REF] Sze | Physics of Semiconductor Devices[END_REF], leakage current due to ohmic conduction is given by:

β F N = 4(2m * ) 1/2 q 1/2 Φ 3/2 B /3h.
J ∝ E exp -∆E ac k B T (4.4)
where ∆E ac is activation field of electrons.

Frenkel-Pool Emission (FP)

For electrons which are generally trapped in local sites, thermal fluctuation can give them enough energy to get out and move to conduction band. This is the mechanism of Frenkel-Poole emission. Under electric field, the electrons need less energy to get into conduction band as they are pulled by the field.

The leakage current is [START_REF] Sze | Physics of Semiconductor Devices[END_REF]:

J ∝ E exp   -q Φ B -qE/πε opt ε 0 k B T   (4.5)
At a given temperature, ln(J/E) ∝ (β F P /T )E 0.5 .

β F P = q 3/2 /(k B T √ πε opt ε 0 ) = 2β SE .
The barrier reduction here is roughly twice as in the case of Schottky emission, since the barrier lowering is about twice due to the immobility of the positive charge (Scott 2000).

4.1.1.2.3 Space-Charge-Limited Current (SCLC)
The space-charge-limited current (SCLC) results from carriers injected into the ferroelectric, where no compensating charge is present [START_REF] Sze | Physics of Semiconductor Devices[END_REF]. Pointed out by Scott (2000), after reaching a threshold, the leakage current is no more limited by the mechanisms mentioned above but by the injected space charges. 3 At high field range, ejected electrons are distributed over a region of space, forming a continuum of charges. As the SCLC is formed, the amount of excess carriers won't affect the current.

Traps in the film can lower the drift mobility, thus lowering SCLC (Lampert 1956, Many andRakavy 1962). When trap densities is as high as 10 18 cm -3 , SCLC is lowered to almost unmeasurable level (Rose 1955).

According to Mott-Gurney law [START_REF] Mott | Electronic processes in ionic crystals[END_REF], the SCLC is given by:

J(V ) = 9ε opt µV 2 8d 3 (4.6)
where µ is the carrier mobility.

SCLC dependency on film thickness d is not accurate. Instead, an accommodation or mutual diffusion length a ′ is excluded for correction. Thus thickness is replaced by (d -2a ′ ) (Scott 2000).

Mayer's work on Si indicates that a ′ is about 10% of d (Mayer et al. 1965).

Lampert gave more precise theoretical equations for SCLC. And two different equation are assigned to different field regions [START_REF] Lampert | Current injection in solids[END_REF].

In the relatively low field range, the current is given by:

J(V, d) = 9 8 qt R µ n µ p τ V 2 d -3 (4.7)
where t R is recombination time, µ n and µ p are the mobility of electrons and holes, and τ is the density of recombination centers.

Interface Schottky emission J = A * T 2 exp -q Φ B - √ qE/4πεoptε 0 k B T ∝ T 2 exp +β SE √ E/T -qΦ B /k B T Fowler-Nordheim tunneling J ∝ E 2 exp - 4(2m * ) 1/2 3h (qΦ B ) 3/2 qE ∝ E 2 exp(-β F N /E) Bulk Ohmic conduction J ∝ E exp -∆Eac k B T ∝ Eexp (-β OC /T ) Frenkel-Pool emission J ∝ E exp -q Φ B - √ qE/πεoptε 0 k B T ∝ Eexp +2β SE √ E/T -qΦ B /k B T Space-charge-limited current J = A 0 V n d m ∝ E n d -(m-n)
β SE , β F N , β OC , A * , A 0 , m and n are positive constants.

In higher voltage range, the current regime changes to:

J(V, d) = 125 18 ε 0 ε opt t R µ n µ p V 3 d -5 (4.8)
The cube-law at higher field is due to double injection [START_REF] Lampert | Current injection in solids[END_REF]. Scott et al.'s work (1994) on PZT showed transition from V 2 to V 3 and V to V 3 directly were both possible. The transition field between the V 2 -dependence and V 3 -dependence is given by (Scott 2000):

V th = constant d 2 2µ n µ p (4.9)
Rose's theoretical work (1955) indicates that the voltage dependence of a even higher power is possible:

J(V, d) = A 0 V n d m (4.10)
where A 0 , n and m are all constants. n can exceed 3 when the space charge density approaches a uniform distribution between cathode and anode. Shin et al.'s work (1999) on sol-gel-derived PZT capacitor showed that n was 5.06 (at 40 • C).

Summary

According to the five charge transport mechanisms described above, Table 4.1 lists the equations of each mechanism and corresponding dependence parameters. nm with SRO top electrode. Forward J l (response to voltage applied from 0 to V max ) and reverse J l (response to voltage applied from 0 to -V max ) were identical for all four capacitors. J l of 40.5-nm-thick capacitor was about 4 orders of magnitude bigger than other three thicker capacitors. In Figure 4.1, the three thicker capacitors have similar amount of leakage current at same field.

Leakage Current of Sputtered Capacitors and Fitting Results

The variation of leakage is not only due to the thickness. The leakage current of capacitors on the same sample at different locations also varies slightly. Generally, thin capacitor (less than 50 nm) exhibited relatively higher J l . We attribute this to the difference of defect density. PZT forms columnar grains from bottom to top during the crystallization. As thickness decreases, the density of defects which penetrate the thickness increases, thus J l increases.

Our J-E measurement was carried out on 100 × 100µm 2 large capacitors for all the samples, and the defect density is different from capacitor to capacitor even on the same sample for sub-50 nm capacitor.

For 40.5-nm-thick sample, about 80% of the capacitors exhibited insufficient insulated characteristics.

For the three thicker samples, the amount of J l were similar when top electrode changed. The impact of top electrode on leakage current was minor. Capacitors of three different top electrodes showed leakage of similar quantity and shape. Forward J-E curve and reverse J-E curve were of little difference and were exact the same for SRO/PZT/SRO capacitors. Now we are going to fit various models with only forward J l .

Schottky Emission

Figure 4.4 shows the leakage current of four sputtered capacitors with SRO top electrode. From 40 kV /cm to 800 kV /cm, ln(J l ) is linearly dependent on E 0.5 . The slopes β SE /T = q 1.5 /k B T √ πε opt ε 0 of four curves were extracted and ε opt for four capacitors were calculated, presented in Table 4.2. Leakage currents of capacitors with Pt top electrode and ITO top electrode are presented in Figure 4.5 and ε opt were extracted and presented in Table 4.2. The starting point of linear dependency for 136-nm-thick capacitor with Pt top electrode and for 120.6-nm-thick capacitor with ITO top electrode were higher than others. The bumps observed in these two samples at low field range were due to the dielectric polarization. Since these bumps were small, they were usually covered by leakage current (more discussion in next subsection). Leakage current of sputtered PZT capacitors with Pt top electrode and ITO top electrode showed similar linear dependency at high field and the extracted m * had similar small values. Fowler-Nordheim tunneling is excluded from the charge transport mechanism.

Ohmic Conduction

Figure 4.7 shows that below ∼120 kV /cm, current was linearly dependent on field. When field passed 120 kV /cm, leakage current increased more rapidly. The different slopes are attributed to the same reason, stated before. For relatively thick (> 100 nm)capacitors, the slopes were of little difference.

For 40.5-nm-thick capacitor, the slope was much larger. It may be due to the increased density of defect penetrating the thickness. For all sputtered capacitors of different thicknesses with different top electrodes, linear dependence on field had been observed at low field. [START_REF] Sze | Physics of Semiconductor Devices[END_REF] stated at low voltages, current was carried by thermally excited electrons hopping from one isolated state to the next. This mechanism yields an ohmic characteristic, linearly dependent on field, indicating at low field, the predominant charges are thermally generated.

Frenkel-Pool Emission

Leakage currents are plotted according to Frenkel-Pool emission in Figure 4.9. From 360 kV /cm to 800 kV /cm there was a linear dependency and ε opt were extracted and presented in Table 4.4. fitting quality from 300 to 800 kV /cm, and Schottky emission showed a better fit at medium field ( 100∼ 300 kV /cm). ε opt extracted from the fitting to SE was much smaller than that from the fitting to FP.

The extracted ε opt from FP was much larger than the experimental results from Huang et al. (2000), Deineka et al. (2001), Peng et al. (2011). Thus interface-dominant SE is more consistent with the data at medium and high field than bulk-dominant FP emission.

Space-Charge-Limited Current As stated before, the thickness dependence is impossible to investigate with only one J-E curve from each capacitor, since leakage varies from capacitor to capacitor of same thickness. So the quantitative investigation of thickness dependence on leakage current was not carried out. According to the fitting results with different mechanisms, Figure 4.13 shows the well fitted region of each mechanism. Interface-dominant SE mechanism was well fitted to the data in large range (from ∼ 50 to 800 kV /cm) and the extracted ε opt was consistent with experimental results; Ohmic conduction was fitted to the data from 0 to ∼ 150 kV /cm ; SCLC was fitted to the data in two regimes in the range of ∼ 200 to 800 kV /cm, E 2 in lower range and E 3 in higher range; FN was not compatible as the extracted m * was out of range even it was fitted to the data from ∼ 600 to 800 kV /cm ; FP was well fitted to the data from ∼ 200 to 800 kV /cm, but extracted ε opt was out of the experimental range. Top electrode was found to have little influence on charge transport, so we estimate that the top electrode interface has little influence to leakage. The 40.5-nm-thick sputtered capacitor showed much larger leakage compared to other thicker capacitors. At ∼ 200 to 800 kV /cm, both Schottky emission and space-charge-limited current fitted the data, and further study at various temperatures may detect the appropriate mechanism. with SRO top electrode were all too leaky to be measured.) For 67-nm-thick, 133-nm-thick and 200-nm-thick PZT capacitors, J-E curves were different from that of sputtered ones; leakage current were not symmetric for both SRO-top-electrode and Pt-top-electrode capacitors; below 300 kV /cm, leakage was quite small and from 400 kV /cm upward leakage increased rapidly. The 100-nm-thick capacitor, which experienced 2 h annealing in furnace, exhibited similar J-E curve as sputtered capacitors and the forward and reverse J-E curves were symmetric for it. Top electrode also showed minor influence on leakage current. In Figure 4.14, as top electrode changed from SRO to Pt, J-E curves did not change obviously for 133-nm-thick and 200-nm-thick capacitors. Between 100 and 300 kV /cm, there was a "negative resistance region" for 67-nm-thick, 133-nmthick and 200-nm-thick capacitors. They are usually due to double injection or trap filling and trap emptying (Ridley and Watkins 1961[START_REF] Ridley | Proc. Phys. Soc[END_REF], Scott et al. 1994). The 100-nm-thick capacitor, which experienced much longer annealing for the crystallization of top electrode, did not show the negative resistance. In Figure 4.3, we notice that leakage current of 136-nm-thick sputtered capacitor with Pt top electrode in the range between 100 and 300 kV /cm also showed a similar shape, but the Resistance did not drop to negative. These abnormal leakages actually were much smaller (2 ∼ 3 orders of magnitude less) than the "normal" leakages. We attributed these bumps between 0 and 200 kV /cm to dielectric polarization. As an external field was applied to the capacitor, corresponding dielectric polarization was formed. At the beginning point of measurement, the field change was the highest, thus a large amount of dielectric polarization occurred between 0 and 200 kV /cm. Then as the field change was stable, the current due to dielectric polarization was also stable. This current J d was relatively small and was usually covered by the leakage current part J l . So only when the capacitor was well insulated, we could observe the "negative resistance region". In chapter 5, the leakage current will be further analyzed, according to which, the current J U (or J D , current response to pulse "U" or pulse "D" in PUND measurement) is equivalent4 to J d . Figure 4.15 shows J U in PUND measurement. From the ratio of J U in PUND

Leakage Current of Sol-gel-derived Capacitors and Fitting Results

.9 ± 0.2 N/A N/A 1.1 ± 0.1 0.4 ± 0.1 N/A N/A 133 12.0 ± 1.0 13.0 ± 0.5 15.2 ± 2.0 N/A 1.3 ± 0.1 1.4 ± 0.1 0.8 ± 0.1 N/A 200 13.8 ± 1.0 23.5 ± 0.5 15.5 ± 1.0 22.3 ± 2.0 1.0 ± 0.1 0.4 ± 0.1 0.9 ± 0.1 0.5 ± 0.1 100 6.4 ± 0.2 6.6 ± 0.2 N/A N/A 4.4 ± 0.1 6.2 ± 0.2 N/A N/A
measurement to J d in I-V measurement in Figure 5.12, the equivalent maximum value of J d is ∼ 1.2 µm/cm 2 , which is compatible to the bump peak observed in Figure 4.14. Thus in our case, in this region the resistance is not negative. The bump is due to dielectric polarization and it can only be observed when leakage current is less than ∼ 1 uA/cm 2 in this region. Now, we will plot the leakage according to each charge transport mechanism. Because J d is difficult to be separated from leakage current,5 leakage current fitting was performed to (J l + J d ).

Schottky Emission

Figure 4.16 plots the leakage in ln(J) vs E 0.5 form. Linear fitting was applied to the curves and ε opt was extracted, as shown in Table 4 E -1 form. Linear fitting was applied to the high field range. However the extracted m * /m was between 5 × 10 -7 and 1 × 10 -4 (estimating Φ B = 0.5 eV ), which was out of the range. Similar m * were found from Pt-top-electrode capacitors. So FN tunneling is also excluded from the charge transport mechanism.

Ohmic Conduction

Figure 4.18 shows the J-E curves of sol-gel-derived capacitors with both SRO top electrode and

Pt top electrode at low field range. Leakage current was linearly dependent on field from 0 to 30 kV /cm, which was smaller than the range of sputtered capacitors. This is because the smaller leakage current is partly covered by the current due to dielectric polarization. Space-Charge-Limited Current According to the fitting results above, the well fitted mechanisms are plotted in Figure 4.21. In low field range (0 to 30 kV /cm), Ohmic conduction was compatible; In high field range (from ∼ 500 to 800 kV /cm), both FP and SCLC were well fitted to the data. In the range between 50 kV /cm and 500 kV /cm, due to the existence of J d , none of the mechanisms mentioned above satisfied the leakage current. We extended the fitting range of ohmic conduction, FP and SCLC with dash lines. 33-nm-thick capacitor was too leaky to be measured. Top electrode also showed little influence on leakage as it did for sputtered capacitors.

Frenkel-Pool Emission

Conclusion

Low leakage currents were observed for sputtered PZT capacitors with a thickness between 100 nm and 200 nm. The amount of current density were compatible with reported results for high quality PZT capacitors (Zubko et al. 2006a, Vrejoiu et al. 2006, Pintilie et al. 2007, Boerasu et al. 2013). For solgel-derived capacitors, under 300 kV /cm the leakage were even one or two orders of magnitude smaller than sputtered capacitors but at higher field it increased faster. By fitting various models to the leakage currents, it was found that charge transport mechanism was complicated, varying with applied field range. At low field (0 ∼ 100 kV /cm) J l of both sputtered and sol-gel-derived capacitors showed a linearly dependent on V , which was due to Ohmic conduction. From ∼ 200 kV /cm to 800 kV /cm, SCLC was well fitted for capacitors of both types. In this range, other transport mechanisms were also successfully fitted to the data (SE for sputtered capacitors and FP for sol-gel-derived capacitors). Capacitors of sub-50 nm exhibited much higher leakage or were even too leaky to be measured with the top electrode size of 100

× 100 µm 2 .
Theoretically, bulk and interface properties can be separated by testing capacitors with asymmetric electrodes. According to the results of sputtered capacitors, J-E curves were totally symmetric from capacitors with symmetric structure SRO/PZT/SRO. Even for Pt/PZT/SRO structure, J-E curves were almost symmetric. For sol-gel-derived samples, J-E curves were not symmetric for SRO/PZT/SRO capacitors and change of top electrode did not affect on the J-E curves. So the influence of top electrode on leakage current is very small. We also notice that among all well fitted models (see Figures 4.13 Under high voltage, the breakdown was always from the top electrode (negative branch of J l surged), probably due to the fact that more defects existed in the top interface. It is estimated that that bottom electrode provides a better morphology, thus the bottom interface has less defects than the top one.

Usually, leakage current J l consists contributions from several different conduction mechanisms.

For example, V 2 dependency of J l may be due to the double injection or single injection in the trapfilled limit. Vertical jumps in a J(V ) curve can arise from breakdown or from field-induced emptying of filled traps (Scott 2000). Due to the complexity of transport mechanisms, J(V ), J(T ), J(d) and J(t) measurements together would help distinguish the different mechanisms.

Capacitance-Voltage Characteristics

The "butterfly" shape of a Capacitance-voltage (C-V) curve is the signature of ferroelectrics. C-V measurement is routinely used to obtain the permittivity of the ferroelectrics. Ferroelectric capacitors with high relative permittivity permit the electronic industry to continue increasing the chip bit-density since their areas can be reduced as relative permittivity increases.

Capacitance was measured through the method illustrated in chapter 2. It is reported in many articles (Zhou andNewns 1997, Stengel andSpaldin 2006) that a dead layer is formed at ferroelectricelectrode interface due to the presence of defects, thus the film is divided into two parts: effective ferroelectric with thickness d ef f and thickness of the sum of the two dead layers at the two interfaces d dl . Dead layer's relative permittivity ε ′ r dl is much smaller than that of the effective part. d dl is first evaluated and then ε ′ r of PZT is extracted. The linear capacitance C l (mostly from the effective part) can be expressed by:

1 C l = d ef f 1 ε 0 ε ′ r l A + d dl 1 ε 0 ε ′ r dl A = αd ef f + β (4.11)
where ε 0 is the permittivity of free space, A is the surface of the capacitor. α and β (> 0) are the slope and intercept of the plot of reciprocal C l as a function of thickness.

ε ′ r l can be extracted from the slope α. Then d ef f can be extracted by:

d ef f = 1 C l -β /α (4.12)
And the relative permittivity, ε ′ r , of PZT capacitor can be obtained by:

ε ′ r = Cd ef f ε 0 A (4.13)
where C is the measured capacitance from C-V measurement.

Relative Permittivity of Sputtered Capacitors

Capacitance-voltage (C-V) characteristics were performed at 1 kHz for sputtered PZT capacitors with SRO top electrode, as shown in Figure 4.22. Loss tangent of three thicker capacitors were between 0.01 and 0.1 as field varies. For 40.5-nm-thick capacitor, loss tangent exceeded 10 at high field. Loss tangent exhibited similar value for capacitors with same thickness as top electrode changed and in the following of this section, they will not be provided.

According to Equations (4.11) and (4.12), to obtain the linear capacitance ε ′ r l and effective thickness d ef f of the PZT capacitors, reciprocals of the linear capacitance C l of these four capacitors were extracted and plotted in Figure 4.23.

By fitting the reciprocals of C l in Figure 4.23, ε ′ r l was found to be 179 ± 15 and d dl was about 1 ∼ 2 nm for all these four sputtered capacitor with SRO top electrode. Then ε ′ r of PZT capacitors can be obtained by Equation (4.13). ε ′ r of these four sputtered capacitors with SRO top electrode were extracted, as shown in Figure 4.24. Maximum permittivity seemed to be similar for SRO-top-electrode Then we extracted the linear permittivity ε ′ r l for Pt-top-electrode and ITO-top-electrode sputtered PZT capacitors, by calculating the slope of C l 's reciprocals, as shown in Figure 4.25. ε ′ r l for capacitors with Pt top electrode and ITO top electrode were 173 ± 15 and 155 ± 15, respectively. d dl was less than 3 nm for all these capacitors. Plot of ε ′ r for sputtered capacitors with Pt top electrode and ITO top electrode is provided in Figure 4.26.

Sputtered PZT with Pt top electrode had similar permittivity as that of SRO-top-electrode capacitors in all thicknesses. ITO-top-electrode capacitors exhibited a much smaller permittivity.

Relative Permittivity of Sol-gel-derived Capacitors

C-V curves of sol-gel derived PZT capacitors have also been measured. Linear capacitances C l of five capacitors of different thicknesses were extracted from C-V curves and their reciprocals are plotted in Figure 4.27. Linear permittivity ε ′ r l were extracted to be 178 ± 15 for SRO-top-electrode capacitors and 174 ± 15 for Pt-top-electrode capacitors. Loss tangent for all these capacitors with both top electrodes were similar, with values between 0.01 and 0.1 as field varied, same to that of sputtered capacitors.

Conclusion

Through C-V characteristics of the PZT capacitors, it is found that: 1) ε ′ r l was almost invariable for both sputtered and sol-gel-derived capacitors with various top electrodes (∼ 170) ; 2) Maximum relative permittivity of sputtered capacitors showed no thickness dependency. The value was between 900 and 1300, which were in agreement with reported results (Perez 2004, Klee et al. 2010, Boerasu et al. 2013);

3) Maximum relative permittivity of sol-gel-derived capacitors (with SRO top electrode) decreased with thickness and maximum relative permittivity of thicker sol-gel-derived capacitors was much smaller than that of sputtered capacitors with equivalent thicknesses; 4) Dead layer thickness was less than 3 nm for all capacitors; 5) Loss tangent of sputtered capacitors and sol-gel-derived capacitors were similar (0.01 ∼ 0.1, except the leaky 40.5-nm-thick sputtered capacitor), regardless of top electrode. Film of sub-50 nm with 100 × 100 µm 2 top electrode exhibited considerably reduced qualities (40.5-nm-thick sputtered capacitor was extremely lossy and 33-nm-thick sol-gel-derived capacitor was too leaky to be measured).

Ferroelectric Hysteresis Loops

Hysteresis P-E loop is the unique feature of ferroelectrics. Measuring the P-E loop of a ferroelectric capacitor allow us to evaluate its ferroelectric properties. Large P r and low E c are favorable for the fabrication of ultrathin capacitors of high reliability. PUND measurements at various voltages were performed for the three thicker PZT films with SRO top electrode (40.5-nm-thick capacitor was too leaky to be measured at higher voltages). P r and E c were extracted from PUND loops, as shown in Figure 4.30. Polarization was saturated starting from 300 kV /cm to 900 kV /cm for 120-nm-thick and 190-nm-thick PZT, with the variation within 1 µC/cm 2 (136-nm-thick PZT has been measured only at 500 kV /cm).

P-E loops of Sputtered Capacitors

In Figure 4.30, E c were symmetric from 100 kV /cm to 500 kV /cm for all sputtered PZT capacitors.

Under higher voltage, 190-nm-thick PZT showed a higher E n c . Figure 4.31 presents the PUND loops of these capacitors with Pt top electrode and ITO top electrode, measured at 500 kV /cm. 40.5-nm-thick capacitor with Pt top electrode was not as leaky as that with SRO top electrode, but still had a much smaller P r compared to that of thicker capacitors.

And it also turned to be leaky under higher electric field. All ITO-top-electrode capacitors exhibited a much larger E c , which will be discussed in chapter 5 . not be extracted precisely. There is a semi-empirical scaling law,

E c ∝ d -2/3 (4.14)
Equation (4.14) is successful in describing the thickness dependence on E c in the last several decades for films of 100 nm ∼ 200 µm (Scott 2000). According to some variations (Janovec 1958, Kay andDunn 1962) of this thickness dependence, the external charges are assumed to reside on a plane of negligible thickness at the interfaces, compensating for the polarization inside the ferroelectric. However, in realistic cases charges are distributed over a small finite region in the metallic electrodes. This spatial charge distribution leaks to a voltage drop in the metallic electrodes, and a compensating depolarization potential across the ferroelectric film is formed to ensure the whole structure is equipotential (Mehta 1973). Equation

P-E loops of Sol-gel-derived Capacitors

Four sol-gel-derived PZT capacitors (except the 33-nm-thick capacitor, which showed huge leakage current) have been also investigated under PUND pulse trains. PUND loops were measured as maximum electric field was kept at 500 kV /cm , as shown in Figure 4.33. 7 From the shape of hysteresis loops, we noticed that capacitors with thickness more than 100 nm had more square-like loop, indicating the domain motion occurred in a narrow electric field range near coercive field. These sol-gel-derived capacitors have also been measured at various voltages. P r and E c were extracted, as shown in Figure 4.34. For the 67-nm-thick PZT capacitor, P r increased almost linearly as drive voltage increased. For 100-nm-thick, 133-nm-thick, increment of P r was smaller as V max increased.

P r of 200-nm-thick capacitor exhibited much better saturation quality.

Sol-gel-derived capacitors with SRO top electrode exhibited symmetric PUND loops or loops with small asymmetricity. Pt-top-electrode sol-gel-derived capacitors exhibited negative asymmetricity

(|E p c | < |E n c |)
, which was opposite to the positive asymmetricity, observed in sputtered capacitors with Pt top electrode. The value of E c was comparable to that in sputtered capacitors.

At 2250 kV /cm, the 200-nm-thick capacitor with SRO top electrode broke down, and the same sample with Pt top electrode broke down at 2925 kV /cm. It was usually found that Pt-top-electrode capacitors had higher breakdown field.

Conclusion

By performing PUND measurement, the switching behavior of these ferroelectric capacitors have been investigated. Except sub-50 nm capacitors, all showed PUND loops with square-like shapes. P r were between 25 and 40 µC/cm 2 for all capacitors except sub-50 nm ones, which were among the highest 7 Pr of 200-nm-thick capacitor increased to 40 µC/cm 2 after various measurements (sometimes at elevated temperature) after 3 months. The reason was unknown. Pr of other samples, which have been measured much less, did not change. values in recent reported results for thin-film PZT(52/48) capacitor (Lee et al. 2005, Kim et al. 2006, Chen et al. 2007, Dekkers et al. 2009). Along with the I-V and C-V results, we found that PZT film of both growth routes with a thickness more than 100 nm exhibited excellent electrical properties in terms of low leakage, high maximum relative permittivity, small loss tangent and high remnant polarization.

Asymmetric stack structure affected imprint property of the capacitor. However the asymmetricity in sputtered Pt/PZT/SRO capacitors and in sol-gel-derived Pt/PZT/SRO capacitors were opposite.

Thicker capacitor was better saturated under higher field than thinner ones. These capacitors can stand 1000 kV /cm without obvious degradation.

No obvious dependence of P r on thickness was observed, which might due to our limited thickness range. The relatively smaller P r exhibited in thin capacitors (40.5-nm-thick sputtered capacitor and 67-nm-thick sol-gel-derived capacitor) was attributed to their worse quality (may be higher throughoutthickness defect densities). Kim et al.'s work (2006) on PZT(52/48) showed that P r increased from only 3 µC/cm 2 to 50 µC/cm 2 as thickness varied from 40 nm to 1.5 µm. However, Kijima's study on PZT ranging from 25 nm to 100 nm showed almost identical P r (22 µC/cm 2 ) for all capacitors (Ishiwara et al. 2004). Larsen et al.'s work (1994) on PZT(51/49) of various thicknesses (from 120 nm to 690 nm) showed similar P r for all capacitors (∼ 20 µC/cm 2 ). Yanase et al.'s work (1999) on totally strained BTO showed that from 12 nm to 79 nm, the variation of P r was very small and he attributed the thickness dependence of ferroelectricity to the imperfection of the crystal structure at the ferroelectric-metal interfaces.

Piezoresponse Force Microscopy

Macro-scale ferroelectric characterization techniques (I-V, C-V, PUND) are of limited capacities in studying domain-level properties of ferroelectric thin films. The application of PFM permits non-destructive, high resolution, local imaging at nano-scale, providing us an unique opportunity for the investigation of domain dynamics. As the scale decreases to the size of a tip, huge leakage current in macro-scale characterization can be greatly reduced or avoided. PFM can also be easily used to investigate the stability of the switched domains (retention measurement). and the domains were manipulated by the voltage applied on the film. The three squares from big to small were written by a voltage of 5 V , -5 V and 5 V one by one. We notice that the most outside zone which had not been not written showed a phase response similar to the zone which was written by -5V .

PFM Imaging of Sputtered PZT Films

This similarity indicated that after the film was fabricated, it showed a strong polarization preference for the upward direction. Same result was observed by Jung et al. (2005) for their as-fabricated PbTiO 3 .

According to Ahn et al.'s work (2005) on PbTiO 3 , all as-fabricated film with a thickness more than 12 nm exhibited upward polarization.

PFM Imaging of Sol-gel-derived PZT Films

PFM study of sol-gel-derived films were also carried out. Figure 4.37 shows the topography, amplitude response and phase response of five sol-gel PZT films. All these films showed clear contrast in squares written by opposite DC bias voltages in phase response except the 100-nm-thick film, which was annealed in tubular furnace for 3 hours (other four only experienced short time RTA annealing). We have to bear in mind that 33-nm-thick PZT film in Macro measurement was too leaky to be tested. As PFM studies nano-scale domain properties, ferroelectric film which is leaky in macro-scale measurement still can clearly demonstrate converse piezoelectric effect and ferroelectric property. It was noticed that all non-written areas (the most outside part) of the four sample (except 100-nm-thick one) had a positive polarization, which was the as-fabricated state of these films, similar to sputtered films. For 100-nm-thick PZT film, its reduced response compared to other films indicated the long period annealing changed the crystalline structure which affected its domain behaviors.

The converse piezoelectric effect that 200-nm-thick PZT film exhibited was more obvious than others, indicated by the sharp contrast and homogeneous color both in positive-and negative-voltageswritten areas in phase response. This was compatible with its good PUND shape and more saturated polarization quality. For 33-nm-thick, 67-nm-thick and 133-nm-thick films, the contrast in phase were less strong than that in 200-nm-thick PZT film. showed the typical response of piezoelectric material both in amplitude and in phase.

For the 33-nm-thick film, which was too leaky to be measured in macro-scale measurements, coercive electric field was as big as 1000 kV /cm while the others range from 100 kV /cm to 250 kV /cm.

The much higher observed E c might be due to leakage, since the film was much leaky than others and a large amount of charges might flow across the film during the measurement, forming a fake high E c .

Retention of Sol-gel-derived PZT Films

All domains in five samples were re-read after some time to check the retention quality. Figure 4.39 shows the phase response to the AC drive bias.

The phase response of 200nm-thick film showed no degradation after 3 h which was much better than the slightly reduced contrast in the three thinner films.

100-nm-thick PZT film acted differently. The central up-domain remained pointing upward without any relaxation as time passed while the down-domains switched upward gradually, indicating that even the domains could be manipulated by external field but the domains exhibited a strong upward preference. Just after 5 min of writing, a lot down-domains have already switched back. After 4 h, most of its domains have switched upward. The bad quality of 100-nm-thick film was directly linked to the damaging annealing in furnace for 3 h.

Conclusion

Film of about 200 nm PZT fabricated by both routes showed great converse piezoelectric effect while thinner sol-gel-derived films exhibited reduced converse piezoelectric effect. All as-fabricated PZT films showed an upward polarization. This might be due to the clamping force from underlying SRO layer.

200-nm-thick sol-gel-derived film showed high retention without and degradation after 3 h while thinner sol-gel-derived films exhibited degraded retention quality. Long period post annealing in furnace showed a destructive effect on the film piezoelectricity.

Summary

In this chapter, the electrical properties of both sputtered and sol-gel-derived capacitors have been investi- charge transport mechanism in ferroelectrics. Maximum of relative permittivity were between 600 and 1300, which were in agreement with literature for PZT(52/48). Thickness of dead layer was estimated to be less than 3 nm for all capacitors, meaning that very few defects existed at the interface. All capacitors with PZT of 100 to 200 nm exhibited square-like P-E loops. P r of all capacitors (except sub-50 nm)

were between 25 and 40 µC/cm 2 , which were in good agreement with reported results. Capacitors with symmetric structure SRO/PZT/SRO showed no imprint, regardless of growth route; capacitors with Pt top electrode showed some degree of imprint; capacitors with ITO top electrode showed broadened P-E loops. PZT capacitors of about 200 nm of both types showed great saturation quality. 200-nm-thick solgel-derived film showed good converse piezoelectric effect and long period retention without degradation while thinner ones showed inferior qualities.

Frequency Dependence of Coercive Field

P-E loops are usually measured at line frequencies of 60 Hz (USA) or 50 Hz (Europe) by Sawyer-Tower method for convenience. With readily accessible apparatuses, reproducible values of E c and P r can be extracted. In this work, we used PUND measurement for its ability to separate the switching part from the whole charge flows. The hysteresis loops were routinely measured at an equivalent frequency of 250

Hz. The frequency of PUND measurement is defined as follows, one cycle contains the non-zero drive voltage part of pulse "P" and pulse "N", thus f = 1/4t inc , as illustrated in Figure 5.1. E c is found to be frequency dependent. Since ferroelectric capacitors will be employed as memories, which operates at hundreds of M Hz, it seems essential to figure out their exact relationship. In practical applications, a small V c (relative big E c for an ultrathin film can also provides a small coercive voltage V c ) at high frequency is favorable to memory applications, since computer memory components usually work under several volts. For a 100-nm-thick ferroelectric capacitor with E c = 100kV /cm, V c is 1 V but the operating voltage is usually about three times of V c to ensure that all domains are switched. The reason that why E c is dependent on frequency is that domain switching takes a short period to accomplish. When the input signal frequency is too high, short voltage rising time t inc leaves domains insufficient time to achieve switching. Thus a longer period is needed to accomplish switching, which means higher E c is observed. Domain switching involves domain wall motion except at extremely high fields or extremely small capacitors (Scott 2000). Domain motion encounters a certain resistance or viscosity which increases with frequency. Due to the apparatus limit, we could not collect the output current when f exceeded 250 kHz.

According to Hashimoto et al. (1994) , at even higher frequency, E c will exceed the maximum input field and only part of the domains will switch, thus P r will drop and PUND loop looks like an irregular oval. When a reversal field (bigger than E c ) is applied on a ferroelectric capacitor, needle-like nucleus form near the interface between electrode and PZT and often at imperfect sites (Merz 1954). Then new domains grow throughout the thickness, accompanied by domain wall (DW) movement (forward or lateral, depending on the material). In the last several decades, there have been several models proposed to describe this frequency dependence, giving different importance to nucleation and DW movement. Now we will introduce these models and then fit them to our data.

I-O Model

Ishibashi and Orihara's model (Ishibashi and Orihara 1995) is based on the Kolmogorov-Avrami model [START_REF] Kolmogorov | Selected works of AN Kolmogorov[END_REF], Avrami 193919401941). In I-O model, the limiting factor in switching is assumed to be domain wall movement, including both forward and sideways growth (Scott 2006).

In I-O model, the relation between E c and f is described as follows:

E c ∝ f D k (5.1)
where D is dimensionality of domain motion and k is a parameter connected with input signal waveform. Dimensionality D = 1 means that domain boundary moves along one direction after the formation of plate-like nuclei; D = 2 means that the boundary moves two dimensionally after forming cylindrical nuclei; D = 3 means that the boundary moves three dimensionally after forming spherical nuclei, illustrated in Figure 5.5 (Ishibashi and Takagi 1971).

In Figure 5.6, our result is plotted in log -log form according to Equation (5.1). No linear fit c) are correspondent to one, two and three dimensional cases, respectively. rc is the radius of nucleus. [START_REF] Prasertchoung | Pulse switching and scalling effects in ferroelectric capacitors[END_REF] is possible to meet the data. Jung et al. (2002) showed a good fit to PZT, BTO, SBT and KNO 3 by applying I-O model to their data. However, the frequency range of their data was limited between 100

Hz to 100 kHz. When the bulge is at a critical radius of R * , the critical nucleation energy is:

∆G * = 4πγ B 2 γ (E∆P ) 2 (5.2)
where ∆P is the polarization change effected by the passing domain wall, which equals to 2P r for a fully polarized case.

As domain switching is assumed to be essentially affected by nucleation, domain wall sweeping time is short compared to the nucleation motion via the bulge formation. Switching rate under an AC field, is given by:

f = f 0 exp - ∆G * k B T (5.3)
where k B is Boltzmann constant and T is temperature in K.Thus we can obtain:

lnf = lnf 0 - 1 k B T πγ B 2 γ P r 2 1 E c (5.4)
where f 0 is the limiting switching frequency, above which the critical bulge can not form and the switching motion will be hindered.

The model was fitted to our data, as shown in According to Poykko and Chadi (1999), [START_REF] Ganpule | [END_REF], Tybell et al. (2002), γ is about 0.1 ∼ 0.2 J/m 2 . From the slope in Figure 5.7, we obtained that γ B = 0.068 ∼ 0.095 J/m 2 .

From the intercept in Figure 5.7, the limiting switching frequency f 0 was also extracted to be 400 kHz (the corresponding t inc = 0.625 µs). 400 kHz is much smaller than the speed of memories used nowadays. Tsurumi et al. (2001) have measured frequency dependence for PZT capacitors of different sizes and have found f 0 was dependent on the capacitor size. Small capacitor exhibited a higher f 0 . As the capacitor area in this work is 100 × 100 µm 2 , which is relatively huge comparing to the capacitors in commercial use. For capacitor with lateral size of sub-micron, f 0 can increase several orders of magnitude.

L-Y-D Model

In L-Y-D (R. Landauer, D. R. Young and M. E. Drougard) theory [START_REF] Landauer | [END_REF], nucleation is considered as extremely unimportant because domains do not contribute to the displacement current until they are created (Jung et al. 2005). In L-Y-D model, E c is related with the ramp rate, dE(t)/dt, as follows:

ln dE(t) dt = ln νE c b n k=1 (-1) k+1 k!E k c α k - α E c (5.5)
where ν is a rate constant which is independent of field and polarization, b = ln(1/2) and α is activation field, which is related to the threshold field needed to initiate nucleation. Equation (5.5) is practical for triangular input form since the rise rate is kept constant.

P-K Model

Pulvari and Kuebler (1958) assumed that domains nucleated on the cathode or anode and propagated through the thickness. In P-K model both nucleation and domain wall motion are considered important.

E c and ramp rate are related as follows:

ln dE(t) dt = ln κE 2 c - α E c + δ (5.6)
where κ is proportional to the displacement mobility and is dependent on temperature and film thickness. Fitting result is shown in Figure 5.9. Between 50 Hz and 400 kHz P-K model was well fitted to the data but was not successfully fitted to the low frequency range.

Conclusion

E c was found to be frequency dependent and it can be several times bigger at high frequency. P r was stable at different frequencies as long as applied field exceeds E c . After applying four models to our data, which have different emphases on nucleation or domain wall movement, the fitting results showed L-Y-D have the best fit in all frequency range measured and was successful in predicting the minimum limit of Scott (2006) estimated the critical lateral area to be 100 µm 2 for KNO 3 and 1 µm 2 for PZT.

Prasertchoung 's work (2006) on polycrystalline PZT capacitors from 225 µm 2 to 0.19 µm 2 showed that with a quasi-square PUND drive pulse, P r of capacitors with different sizes exhibited similar value (∼ 30 µC/cm 2 ). Switching time was in the range of ns for all capacitors and smaller capacitors exhibited faster switch, but of the same order.1 Activation field α dropped dramatically as the size of capacitor dropped.

Different Contributions in P-E Loop

PUND measurement separates the switching part (I P -U and I N -D ) from the non-switching part (I U and I D ). In this section we will investigate these two parts quantitatively through the comparison of I-V measurement with switching part and the comparison of C-V measurement with non-switching part.

This allows us to further understand the shape of a P-E loop.

Switching Part

In the previous chapter, the leakage currents were recorded in the condition that the capacitor had experienced applied field of the same sign (positive or negative). Thus all the domains had already been switched and no switching charges flowed during the I-V leakage measurement. If a reversal field (> E c ) is applied to the capacitor prior to the I-V measurement, a small peak will be observed, as shown in The current with switching, J tot s , consists of three parts: switching current, J s ; leakage current, J l ; and dielectric current, J d , which is due to the dielectric polarization of the capacitor. These three components are illustrated in Figure 5.11. The switching current J s can be obtained by performing twice I-V measurement with domain pre-switched to the same and opposite direction.

J s = J tot s -J tot ns (5.7)
J tot ns = J l + J d . Compared to leakage current J l , non-switching current J d is usually very small and omitted, thus J tot ns ≈ J l . J d can be roughly estimated by performing an I-V measurement (without switching) with increasing voltage and another with decreasing voltage. Since leakage current J l is usually much bigger than J d , it is difficult to obtain J d precisely.

Since J s from I-V measurement and J P -U and J N -D from PUND measurement are both due to the domain switching behavior, the amount of polarization from both measurement should be the same. Figure 5.12 depicts these two kinds of current. First we notice that, the amount of J P -U (or J N -D ) is about 4 orders of magnitude larger than that of J s . The great difference in quantity is because that the field was applied in different ways in these two measurements. In dynamic PUND measurement, field was applied with a frequency of 250 Hz. In static I-V measurement, the equivalent frequency was only 0.0125 Hz. Secondly, it is found that E c from I-V measurement was smaller than that from PUND measurement. This is because domain switching was relatively slow comparing to the field varying rate in dynamic PUND measurement. But in the static I-V measurement, at each voltage, the long step period allows more domains to be switched. It is also clear that the peaks from both measurements have the same shape. The peak in positive field are wider and has a smaller maximum value in both measurements.

Lastly, as the capacitor has a asymmetric structure Pt/PZT/SRO, |E p c | > |E n c | is observed in both cases. By integrating J s , a P-E loop is obtained, as shown in Figure 5.13 along with PUND loop and PN loop. (Since the J l and J d is very small in Figure 5.12, J s ≈ J tot s ). This P-E loop have almost the same shape as PUND loop except that E c from this loop are slightly smaller than those of PUND loop, due to the different frequencies in two measurements. As we can see from Figure 5.13, for the P-E loop, integrated of J s , when field passes E c , polarization is almost stable. This means that the capacitor is well saturated at about 2E c and higher field does not cause noticeable domain switching. This means that the difference between this P-E loop and PN loop is not due to the domain switching. (The maximum value in PN loop, P ⋆ , is usually called saturation polarization, which is usually not correct.) In this case, J l is almost zero, and the part (P ⋆ -P r ) is mainly due to the dielectric polarization of the capacitor.

Theoretically, P r from the P-E loop, integrated of J s , should be slightly larger than that of PUND loop. Because when the applied field passes E c by a margin, all switchable domains align their directions with the long lasting field. Then the ferroelectric capacitor is well saturated in this condition.

In Figure 5.13, we notice that the P r from the P-E loop, integrated of J s , actually is slightly smaller than that of PUND loop. This is due to the I-V measurement. The realistic current response to each voltage step is non-linear, as shown in Figure 5.14. However the measured current is constant under each voltage step. Even we set delay time t d = 0, there might be a small amount of charges which could not be measured at the beginning of each step due to limit of response speed. I-V leakage current measurement at various temperatures was also performed for the same capacitor, as shown in Figure 5.15. E c slightly dropped with temperature, which was in consistent with the PUND measurement results at various temperatures (see Figure 5.19). The switching peaks in I-V measurement are rarely reported (we have only found the the reports from [START_REF] Ryu | Synthesis and Characterization of Ferroelectric (1-x)SrBi2Ta2O9-xBi3TaTiO9 Thin Films for Non-volatile Memory Applications[END_REF] and Evans ( 2011)), because a pre-switch field is usually applied to the capacitor when measuring leakage current, as we did in chapter 4. The reason also can be the large leakage (e.g., 40.5nm-thick sputtered PZT capacitor), which will mask the small switching current (only several nA for a 100 × 100 µm2 capacitor). And even a high quality capacitor can exhibit relatively high leakage current. 2

It may also be due to the measurement set-ups. Peaks will disappear when delay time t d is big enough (0.5 s for our sol-gel-derived capacitors) as all domain switching behaviors complete during this period.

Non-Switching Part

As stated in the previous subsection, PUND loop is the manifestation of domain switching exclusively and the polarization between P r and P ⋆ (maximum polarization in PN loop) is due to dielectric polarization (not due to paraelectric polarization). We use (PN-PUND) loop to evaluate this part, which is obtained by sutracting PUND loop from PN loop. C-V measurement meters the capacitance of an insulator. Now we are going to compare the measured result quantitatively from these two methods since both of them originate from dielectric polarization.

In Figure 5.16, P-E curves of three types of dielectrics are plotted with correspondent C-E curves.

For a simple dielectric, polarization is a linear function of external field with a constant capacitance, as

shown is Figure 5.16 (a). For a paraelectric, at lower electric field it exhibits a higher dP/dE slope, due to the formation of non-permanent dipoles, as shown in Figure 5.16 (b); at higher electric field, it shows only linear dielectric effect. Figure 5.16 (c) shows the P-E loop and C-E curve of a ferroelectric.

A ferroelectric capacitor can be deemed as a paraelectric with memory. Polarization P due to dielectric effect can be extracted from C-V measurement by equation:

P = C(V )dV A (5.8)
where A is the area of the capacitor.

Conclusion

A usually seen P-E loop (PN loop here) has been separated into three parts: PUND part which is the integration of switching charges; (PN-PUND) part, which is due to the dielectric polarization; and contributions from leakage. For a well insulated capacitor, the leakage contribution is very small. For a slightly leaky capacitor, P ⋆ is apparently bigger than that of its insulated equivalent.

By comparing I-V and C-V measurement results with PUND measurement results quantitatively, we have found that two bumps in I-V measurement are due to domain switching behavior and the difference between PN loop and PUND loop is due to the dielectric polarization of the capacitor.

The peak shape and location in I-V curve and C-V curve are close connected to PUND loop shape. For example, wider peak in I-V curve or in C-V curve (see the curve of 40.5-nm-thick capacitor in Figure 4.24) means field need to pass E c by a margin to switch all the domains. Similarly, PUND loop shows a less square-like shape (dP/dE is smaller) for this type of capacitor (see the loop of 40.5-nm-thick capacitor in Figure 4.29).

By combining P-E loop extracted from J s in I-V measurement and P-E extracted from capacitance, we can obtain a similar loop to PN loop. The main difference is that E c is smaller due to the reasons mentioned before. [START_REF] Pintilie | [END_REF] showed that E c measured by static method4 is smaller than that in normal dynamic mode and it was compatible with the E c in I-V and C-V results.

Electrical Characterization at Various Temperatures

PUND measurement has also been carried out at low temperature under vacuum circumstance and on a heated substrate holder in air. Figure 5.19 shows PUND loops of 200-nm-thick sol-gel-derived PZT capacitor with Pt top electrode measured at various temperatures. P r decreased with temperature due to pyroelectric effect. And E c also decreased with temperature. Pyroelectric coefficient was calculated to be as large as -50 nC/cm 2 K -1 , equivalent to the reported value -48 nC/cm 2 K -1 (Xiao et al. 2008) and bigger than -18 nC/cm 2 K -1 of PZT(30/70), reported by Zhang and Whatmore (2001). The transition of PZT from cubic phase to tetragonal or rhombohedral phase is either of first order or of second order (see Landau-Ginzburg-Devonshire theory in chapter 1), depending on the composition of PZT (see Figure 5.20). According to Haun et al. (1989), PZT(52/48) transition is of second order.

From Equation (1.3) we know that for a second order transition, remnant polarization P r can be expressed by:

P 2 r = γ(T c -T ) g 4 = T c -T g 4 ε 0 C CW (5.10)
where g 4 is Landau-Ginzburg-Devonshire coefficient, C CW is Curie-Weiss constant. Figure 5.21 plots the P 2 r vs. T . From the linear fitting result, the x-intercept indicates that T c ≈ 385 • C. This is consistent with the phase diagram in Figure 1.7 and in agreement with our XRD measurement from room temperature to 800 • C on a sol-gel-derived PZT film (not provided in this dissertation).

C-V measurement has also been carried out on the same sample from 100 K to 473 K, plotted in Susceptibility χ of the ferroelectric satisfies the Curie-Weiss law, as described by (Zubko et al. 2006):

1 ε ′ r ε 0 ≈ 1 χ = 2(T c -T ) ε 0 C CW (5.11)
The reciprocals of ε ′ r (at E = 0) extracted from Figure 5.22 are plotted in Figure 5.23. By fitting the data, the Curie-Weiss constant C CW was extracted to be 4.56 × 10 5 K -1 and 4.20 × 10 5 K -1 for the results measured at low temperature and at high temperature, respectively, which is similar to 4.44 × 10 5 K -1 , reported by Zubko et al. (2006). As temperature approaches to T c , ε ′ r will be several times bigger than that at room temperature (Haun et al. 1989), but its value will not become several orders of magnitude larger. Thus in Figure 5.23, T c should be on the left proximity to the x-intercept from the linear fitting. The value of this extracted T c is consistent with T c extracted from PUND measurement in Figure 5.21.

Relaxation

As ferroelectric capacitor is mainly used in memories, relaxation and retention are important parameters since a memory should have a high stability. Stored information in the capacitor should remain for enough long period without obvious decay.

In the PUND measurement, the period between the opposite drive voltages is t r (see Figure 2.13).

In chapter 4, t r = 1 ms for all the measurements. t r has been varied from 1 ms to 60 s to investigate the relaxation of the capacitor (the period between pulse "P" and "U" and between "N" and "D", t int , was kept as 1 ms, see Figure 2.13). Figure 5.24 shows the remnant polarization P r as a function of t r . As t r increased from 1 ms to 100 ms, P r dropped from 26 to 20 µC/cm 2 and after ∼ 5 s P r was stable at around 18 µC/cm 2 , which was 69.2 % of P r at t r = 1 ms. This suggested that relaxation did happen in a short period after the domain switching had completed. The remained polarization was still big enough to be distinguished from different states. It should be noted that the measurement was carried out on a sol-gel-derived capacitor, which experienced 3 h annealing for both the crystallization of PZT film and the crystallization of top electrode.

According to the results in chapter 4, long duration annealing in furnace could damage both the crystalline structure of both bottom SRO layer and PZT film. Thus the relaxation quality of other capacitors discussed before should be better than this one.

Imprint

Retention is the ability of a ferroelectric capacitor to retain the polarization sign and the magnitude originally written. It is a measure of self-life, as opposed to fatigue, which measures loss of polarization after repetitive switching. Retention is an even more crucial issue, concerning the reliability of the ferroelectric capacitor. For practical applications, the retention time must be longer than 10 years [START_REF] Ishiwara | Ferroelectric Random Access Memories: Fundamentals and Applications[END_REF].

Retention losses occur when the back-switching happens from the interface and penetrates through the thickness. Gruverman and Tanaka (2001) stated that the presence of a polarization-independent builtin bias at the interface of ferroelectric and bottom electrode triggered the back-switching of domains. It is found that at elevated temperatures, retention losses are more obvious Shimada et al. (1997).

Since retention measurement is greatly time-consuming, due to limitations we have not carried out this measurement on the PZT capacitors.

Imprint

Imprint describes the preference of one polarization state over the other. Imprint leads to a shift of P-E loop on the field axis, and strong imprint can cause a loss of P r . Imprint can lead to a read/write failure of the capacitor.

For the explanation of imprint in ferroelectric capacitors, there are mainly two types of mechanism: defect dipole alignment model [START_REF] Arlt | [END_REF]; interface screening (Grossmann et al. 2002).

In the former model, an internal bias is assumed to exist due to the gradual alignment of defect dipoles consisting of acceptor ions and oxygen vacancies. When the domains are switched by an external field, these aligned defect dipoles remain in their positions, causing a shift of P-E loop. In the later model, a thin layer with suppressed ferroelectric properties is assumed to exist in the interface between the ferroelectric and electrodes (depicted in Figure 5.25). An electric field E if is formed inside the interface layer. E if is responsible for the charge separation within the interface which is due to Frenkel-Poole emission [START_REF] Ishiwara | Ferroelectric Random Access Memories: Fundamentals and Applications[END_REF]). Grossmann et al.'s work (2002) showed great agreement between experiment and simulation. To further study the impact of annealing, we fabricated a capacitor with SRO top electrode without performing RTA to top electrode. It is found that the PUND loop showed a big positive asymmetricity and

(|E p c | + |E n c |)/2
was around 200 kV /cm which was about twice of usually observed value. The maximum value of ε ′ r was found to be greatly reduced (∼ 35% less) without performing second annealing. (The result was not provided here.) Since top electrodes were deposited at room temperature by sputtering and they were amorphous before RTA, it can be assumed that after the RTA the interface between the top electrode and PZT film was changed thus the field formed inside the interface, E if , also changed, shifting the P-E loops.

According to these results, the much bigger E c and reduced ε ′ r observed in capacitors with ITO top electrode might due to the 2nd RTA instead of the use of ITO.

Influence of Bottom Electrode Thickness

The thickness of bottom electrode SRO varied form 25 nm to 85 nm for all the capacitors presented in chapter 4, and all SRO/PZT/SRO capacitors exhibited symmetric P-E loops without obvious imprint.

The thickness of top electrode was much thicker (∼ 150 nm) to sustain the microprobe while carrying out electrical measurements. Since thinner bottom electrode can reduce the roughness of its surface and are more strained on substrate, high quality epitaxial growth for ferroelectric layer can be easier on a thinner bottom electrode.

A 200-nm-thick sol-gel-derived capacitor with bottom electrode of only 18.9 nm was fabricated to compare the influence of bottom electrode thickness, when it dropped to less than 20 nm. Figure 5.27 shows the PUND loops of this sample and the PUND loops of another 200-nm-thick sol-gel-derived capacitor with 85-nm-thick bottom electrode (the same sample mentioned in chapter 4 and in previous sections of this chapter) for comparison. The capacitor with 18.9-nm-thick bottom electrode with SRO top electrode exhibited an obvious shift of PUND loop. ε ′ r of both capacitors were found to be similar (not provided here). and Pt top electrode) were found to be identical. But the result of E c showed that the thickness of bottom electrode did have an impact on the imprint quality of the capacitor. For the capacitor with 18.9-nmthick bottom SRO layer with Pt top electrode, the imprint was very small, which was different from the result we observed previously from capacitors with relatively thicker bottom electrodes.

According to these results, we found that SRO/PZT/SRO capacitor exhibited no imprint when bottom SRO electrode exceeded 25 nm; and when bottom SRO was less than 18.9 nm, SRO/PZT/SRO capacitor showed imprint but Pt/PZT/SRO showed no imprint. Capacitor with no imprint of both symmetric and asymmetric stack structure can be fabricated by varying the bottom electrode thickness. Further study is needed to find out the minimum bottom electrode thickness at which it can both acting as a good electrode and prevent diffusion.

Summary

In this chapter, frequency dependence of E c was investigated and it is found that higher frequency increased E c but did not change P r . Four models have been applied to the experimental results: D-C, L-Y-D and P-K model all showed a good fit in the range from 50 Hz to 250 kHz and L-Y-D model (only considering domain wall movements) successfully predicted the minimum limit of E c at frequencies below 50 Hz.

A typical P-E loop was decomposed into two parts (for a good insulated capacitor, the contribution from leakage is negligible): ferroelectric polarization and dielectric polarization, by comparing I-V and C-V with PUND results quantitatively. P 2 r was found to linearly decrease with temperature and maximum of ε ′ r was found to increase with temperature, which were consistent with literature. Imprint property of the capacitors have been investigated through three aspects: top electrode, post annealing and the thickness of bottom electrode. They all showed influences on imprint. and longer retention than thinner sol-gel-derived PZT films. It was found that E c was highly dependent on frequency. Three different models were successfully fitted to E c at different frequencies. Imprint property was found to be dependent on three aspects: top electrode (or stack structure asymmetricity); post annealing procedure; and bottom electrode thickness.

To summarize, we have developed procedures to grow high quality epitaxial PZT films on SRO/ STO templates through two routes. By building an effective electrical set-up, domain switching behaviors and leakage current mechanisms of these films have been evaluated. Of both growth routes, films of 100 ∼ 200 nm have shown low leakage, considerable P r and convincing switching proofs of 180°domains while films of ∼ 200 nm have shown better electrical qualities in terms of retention and saturation. Sub-50 nm films have shown inferior qualities.

The precise composition of our PZT films is unknown despite the fact that the sputtering target and sol-gel solution both contains PZT(52/48). Sol-gel-derived PZT film has been reported to have a gradient composition, which reduces its piezoelectricity. Chemical contents could be analyzed in depth in future, and the diffusion will also be clear especially for ultralthin bottom electrode (< 20 nm), which can help us further optimize deposition procedures to improve the PZT quality.

To further understand the charge transport mechanisms, I-V measurement at various temperatures need to be added since more than one model fit the data in high field range now. For PUND measurements, the wave form used in this thesis was triangular. To increase the switching speed, quasi-square signal with high ramp rate could be employed, which is usually used in commercial devices. By analyzing the switching current, switching time can be extracted, which is an important factor for FeRAM devices.

Maximum of switching current should be analyzed because it affects the reliability of the device.

According to our results, for a 100-nm-thick PZT capacitor, with E c about 70 kV /cm, the operating voltage is about 2 V (about 3E c ). However, at high frequency the required operating voltage is much higher since E c is frequency dependent. This undesirable high operating voltage is mainly due to our large capacitor surface (100 × 100 µm 2 ). According to Tsurumi's work, E c is strongly dependent on capacitor area. With a new acquired mask for lithography, the area of top electrode can be reduced by more than 3000 times thus E c at the same frequency can be greatly reduced. Besides, fabrication of smaller capacitors will allow us to study the size effect of area. As a result of the decreasing lateral size, defect density in each capacitor drops, making the realization of thinner workable capacitor possible, thus reducing the operating voltage. With the current large area, capacitor with a thickness under 100 nm is vulnerable to high leakage. For ultrathin PZT film, which is strained on substrate, many properties such as MPB region and T c will shift due to the compressive force and its ferroelectricity may be enhanced. In this thesis, all capacitors on the same sample share the same PZT film. The drawback of this structure is crosstalk, which may greatly reduce the memory reliability especially when the memory element density increases. With existing lithographic techniques, the area of capacitor is hard to reduced to less than 0.01 µm 2 . To fabricate individual addressable ultrahigh-density ferroelectric memories, new lift-off masks should be investigated. To produce individual capacitors, the mask should stand high deposition temperature and can be easily removed without damaging the ferroelectric elements. A Korean group has succeeded in fabricating PZT capacitors with diameter of 64 nm, density of 176 Gb/inch 2 by using anodic aluminum oxide membranes with regular pores.

Further studies on MEMS for sensors, energy harvesters will be based on this work by using the magnificent piezoelectricity of PZT(52/48). By replacing bulk STO substrate with STO buffered Si substrate, which is compatible with the current production technology, the integration of epitaxial PZT on Si and its properties will be studied. For FeRAM application, PZT(20/80) is a better candidate because it offers a mismatch of 1.19% on STO substrate (0.57% mismatch with bulk SRO), which could be more easily strained than PZT(52/48) does (our PZT films were relaxed). PZT(20/80) also offers a higher P r and strained state will further improve its ferroelectric property.

Even though PZT offers great piezoelectricity, pyroelectricity and ferroelectricity and highly tunable properties by varying Zr/Ti ratio and has already been commercialized in a variety of devices, there is a strong impetus to find alternative lead-free materials of compatible properties due to the harmful effects of lead. In further works, BTO, BSTO and other materials will be introduced.

a

  lattice parameter along x-axis Å a ′ accommodation or mutual diffusion length nm α the slope of reciprocal of C l as a function of thickness

4 .

 4 24 ε ′ r as a function of field of sputtered PZT capacitors with SRO top electrode. . . . . . . . 4.25 Reciprocal of C l as a function of thickness of sputtered capacitors with Pt top electrode and ITO top electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.26 ε ′ r as a function of field of sputtered PZT capacitors with Pt top electrode and ITO top electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.27 Reciprocal of C l as a function of thickness of sol-gel-derived capacitors with SRO top electrode and Pt top electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.28 ε ′ r as a function of field of sputtered PZT capacitors with SRO top electrode and Pt top electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.29 PUND loops of sputtered capacitors with SRO top electrode. . . . . . . . . . . . . . . . . 4.30 P r and E c as a function of field for sputtered capacitors with SRO top electrode. . . . . 4.31 PUND loops of sputtered capacitors with Pt top electrode and ITO top electrode. . . . . 4.32 P r and E c as a function of field for sputtered capacitors with Pt top electrode and ITO top electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.33 PUND loops of sol-gel-derived capacitors with SRO top electrode and Pt top electrode. . 4.34 P r and E c as a function of field for sol-gel-derived capacitors with SRO top electrode and Pt top electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.35 PFM images of 190-nm-thick sputtered PZT film. . . . . . . . . . . . . . . . . . . . . . . 4.36 PFM loops of 190-nm-thick sputtered PZT film. . . . . . . . . . . . . . . . . . . . . . . . 4.37 PFM images of sol-gel-derived PZT films of various thicknesses after writing opposite squares.103 4.38 PFM loops of sol-gel-derived PZT films of various thicknesses. (100-nm-thick PZT is listed apart from others for the reason that it has experienced 3 h post annealing while others have experienced only 1 min RTA.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.39 PFM retention of sol-gel-derived PZT films of various thicknesses. . . . . . . . . . . . . . 5.1 Definition of frequency in PUND measurements. . . . . . . . . . . . . . . . . . . . . . . . 5.2 PUND loops of 200-nm-thick sol-gel-derived PZT capacitor with Pt top electrode measured at different frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 E c as a function of frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Domain switching stages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Dimensionality of domain growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi 5.6 Plot of E c at various frequencies according to I-O model. . . . . . . . . . . . . . . . . . . 115 5.7 Plot of E c at various frequencies according to D-C model. . . . . . . . . . . . . . . . . . . 116 5.8 Plot of E c at various frequencies according to L-Y-D model. . . . . . . . . . . . . . . . . 117 5.9 Plot of E c at various frequencies according to P-K model . . . . . . . . . . . . . . . . . . 118 5.10 Leakage current of normal I-V measurement and and I-V measurement with domain switching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.11 Schematic of three compositions of J tot s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.12 Comparison of I-V leakage current and switching current J s in PUND measurement. . . . 121 5.13 Comparison of integration of J s in I-V measurement with PUND loop and PN loop. . . . 121 5.14 Schematic of I-V measurement with switching. . . . . . . . . . . . . . . . . . . . . . . . . 122 5.15 J tot s at various temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.16 P-E curve and corresponding C-V curve of three different types of capacitors. . . . . . . . 123 5.17 P-E loop, extracted from C-V curve, compared with PUND loop, PN loop and (PN-PUND) loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.18 C-V curve extracted from J P and J U in PUND measurement, compared with C-V curves measured at three frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.19 PUND loops measured at various temperatures. . . . . . . . . . . . . . . . . . . . . . . . . 126 5.20 Polarization as a function of temperature for PZT of various compositions. . . . . . . . . 127 5.21 P 2 r as a function of temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.22 ε ′ r as a function of temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.23 Reciprocals of ε ′ r as a function of temperature. . . . . . . . . . . . . . . . . . . . . . . . . 128 5.24 Relaxation of polarized domains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.25 Interface screening model for imprint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.26 PUND loop and ε ′ r of puttered capacitors experienced different 2nd RTA. . . . . . . . . . 132 5.27 PUND loops of a 200-nm-thick capacitor with 85-nm-thick bottom SRO layer and of another 200-nm-thick capacitor with 18.9-nm-thick bottom SRO layer. . . . . . . . . . . . 133 5.28 P r and E c of PUND loops from two 200-nm-thick capacitor with bottom electrode of different thickness, measured at various fields. . . . . . . . . . . . . . . . . . . . . . . . . . 134 xvii List of Tables 1.1 Applications of ferroelectric materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The roadmap for 1T-1C FeRAM memory and target requirements. . . . . . . . . . . . . . 3.1 Lattice parameters, surface morphologies, deposition rate of SRO of ∼ 10 nm deposited at different plasm voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Parameters extracted from XRD and AFM and deposition rates. . . . . . . . . . . . . . . 3.3 Thickness, deposition conditions and morphology parameters of SRO bottom electrodes. . 3.4 Out-of-plan lattice parameters and mosaicities of sputtered PZT films and underlying SRO films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Surface morphology parameters of sputtered PZT films of different thicknesses. . . . . . . 3.6 Out-of-plan lattice parameters and mosaicities of sol-gel-derived PZT films and underlying SRO films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Roughness and grain size of sol-gel-derived PZT surfaces. . . . . . . . . . . . . . . . . . . 3.8 Top electrode types for each PZT capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Possible conduction mechanisms in ferroelectric capacitors. . . . . . . . . . . . . . . . . . 4.2 ε opt of sputtered PZT capacitors extracted according to Schottky emission. . . . . . . . . 4.3 m * extracted by estimating Φ B = 0.5 eV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 ε opt of sputtered PZT capacitors extracted according to Frenkel-Pool emission. . . . . . . 4.5 ε opt of sol-gel-derived PZT capacitors extracted according to Schottky emission. . . . . . . 4.6 ε opt of sol-gel-derived PZT capacitors extracted according to Frenkel-Pool emission. . . . . 5.1 Fitting quality and suitable capacitor sizes of four different models. . . . . . . . . . . . . . xix

  x )O 3 (PZT) properties and the state-of-the-art of PZT deposition techniques. Then the motivation of this work is provided. Chapter 2 introduces the two different deposition methods (sputtering and sol-gel) for PZT and patterning technique used for top electrodes. The routinely used electrical measurements (current-voltage, capacitance-voltage and ferroelectric hysteresis loop) are presented in details. In the last, the principle and procedures of PFM (piezoelectric force microscopy) measurement are introduced. Chapter 3 describes the growth details of PZT capacitors by sputtering and sol-gel, respectively. The physical properties in terms of crystallinity and surface morphologies of each layer are shown here. Chapter 4 compares the leakage current, relative permittivity and hysteresis loops of capacitors obtained from both deposition methods with different thicknesses and different top electrodes. Then the PFM results of these PZT films are provided.Chapter 5 studies the electrical properties of PZT capacitors in details. Firstly, the frequency dependence of coercive field is investigated and the results is fitted according to different models. Secondly, the different contributions in a ferroelectric hysteresis loop are separated. Thirdly, hysteresis loop and capacitance results measured at various temperatures are presented. At last, the relaxation and

Figure 1 . 1 :

 11 Figure1.1: Schematic of piezoelectric cantilever vibration harvester(Muralt 2004).

Figure 1 . 2 :

 12 Figure 1.2: Grouping of crystal classes (Defaÿ 2013).

Figure 1 . 3 Figure 1 . 3 :

 1313 Figure 1.3 shows the displacement in pyroelectrics, ferroelectrics and antiferroelectrics. A pyroelectric displacement is independent on external field, but only on temperature. Ferroelectric shows a irreversible displacement which remains after the applied field is removed when T < T c . Antiferroelectric has neighboring lines of ions displaced in opposite directions when T < T c and shows no remnant

  Figure 1.4 shows the crystalline structure of Pb(Zr 1-x ,Ti x )O 3 (PZT). Above Curie temperature T c , PZT is paraelectric (polarized under field and removal of field resulting in zero polarization) and the crystal is cubic. B-site ions are in the center of the lattice and the polarization is zero. Below T c , PZT lattice is tetragonal.

Figure 1 . 4 :

 14 Figure 1.4: Schematic of PZT crystalline lattice and the origin of permanent dipole in tetragonal lattice. Image adapted from Wikipedia (2010).

   illustrates the connection between ferroelectric switching and double-well potential. Starting from the state polarized downward, which is corresponding to the state that polarization in the left side of the double-well potential. When a positive field is applied to the ferroelectric, the right side of the double well deepens and the left side becomes shallower. As the field increase to an amount large enough, the barrier between the two wells disappears and the polarization switches to the up state. A larger field will cause the right side deepens and left side shallower, and polarization increases. The amount of polarization will reach a saturated value as field continues increasing.

Figure 1 . 6 :

 16 Figure1.6: The ferroelectric hysteresis loop, associated with potential subject to an applied field[START_REF] Callori | PbTiO3 Based Ferroelectric Superlattices with Conventional and Novel Dielectric Components[END_REF].

3

 3 and PbTiO 3 . PbTiO 3 undergoes a first-order phase transition from cubic paraelectric phase to tetragonal ferroelectric phase as temperature decreases passing 490 • C. At room temperature: a = b = 3.904 Å, c = 4.152 Å (Iijima et al. 1986). PbZrO 3 is antiferroelectric. At room temperature PbZrO 3 is orthorhombic with lattice parameters: a = 5.886 Å, b = 11.749 Å and c = 8.248 Å (Kong et al. 2001). T c is 230 • C, at which temperature a transition from cubic paraelectric phase to orthorhombic antiferroelectric phase occurs. Figure 1.7 shows the phase diagram of PZT solid solution, first obtained by[START_REF] Jaffe | Piezoelectric ceramics, Non-metallic solids[END_REF]. Above T c , PZT is cubic over the whole range of compositions. Below T c , PZT in Ti-rich region is tetragonal and in Zr-rich region is rhombohedral (two phases HT and LT, depending on the temperature). When x is close to 1, there is a region in which PZT is orthorhombic and the solid solution is antiferroelectric.

Figure 1 . 7 :

 17 Figure 1.7: Phase diagram of PZT. Strokes denote the MPB. Image adapted from Waser et al. (2006).

Figure 1 . 8 :

 18 Figure 1.8: Dielectric constant and electromechanical coupling coefficient of PZT as a function of Zr/Ti ratio. Image adapted from Carter and Norton (2013).

Figure 2

 2 of sputtering. Positively charged ions (usually ionized inert gas such as Ar + ) from plasma are accelerated by the electrical field superimposed on the target and strike on the target. During the collision, the kinetic energy and momentum of the ions transfers and distributes among many atoms in the target. A small fraction of target atoms/ions are dislodged as part of the collision chain. Sputtered target atoms travel to the substrate which is usually several cm away and adhere to it, forming a thin film. The bombardment of the cathode with ions caused emission of secondary electrons, which are then accelerated toward the anode and gain enough energy to ionize more gas atoms.

Figure 2 . 1 :

 21 Figure 2.1: Schematic of sputtering process.

Figure 2 .Figure 2 . 2 :

 222 Figure 2.2 illustrates the sol-gel process. In our Mitsubishi Materials sol-gel solution, lead acetate anhydrous, zirconium precursor and titanium precursor are dissolved in 1-butanol, with the ratio Pb:Zr:Ti = 110:52:48. 10% excess of lead is the compensation to its loss during the thermal treatment due to the volatility of PbO. A few droplets of PZT solution are drizzled over the substrate through a pipette. The substrate is rotated at high speed (normally from 1000 to 8000 rpm) during 15 ∼ 30 s. Following the

Figure 2 . 3 :

 23 Figure 2.3: Reversal lift-off procedure for the deposition of top electrode.

2 .

 2 Resist is exposed to UV under reversal mask during 3 s. The photo active compound diazonaphtoquinone sulfonate in the exposed parts releases N 2 molecules and turn to be indene carboxylic acid, thus soluble in alkaline developer. 3. Reversal bake at 120 • C during 2 min make the exposed areas in last step inert while the unexposed areas remaining photo-active. 4. Flood exposure of 20 s turns unexposed areas in the 2nd step soluble. 5. The sample is immersed in AZ 726 MIF developer (component: tetramethylammonium hydroxide) during 40 ∼ 50 s to remove the alkaline soluble areas and then in deionized water to remove the developer residues.

Figure 2 .

 2 4 shows the geometry of Rigaku SmartLab 4-circle diffractometer. The X-ray sources are Cu Kα 1 photons, with a wavelength of 1.5406 Å. A 2-bounce Ge (220) monochromator is used to reduce the beam divergence, improving signal to noise ratio.

Figure 2 . 4 :

 24 Figure 2.4: Geometry of Rigaku SmartLab 4-circle diffractometer.

Figure 2 Figure 2 . 5 :

 225 Photodiode

Figure 2 . 6 :Figure 2 . 7 :

 2627 Figure 2.6: Voltage waveform for typical I-V measurement.

Figure 2 . 8 :

 28 Figure 2.8: εr as a function of field for an ideal ferroelectric. Image adapted from Evans (2010).

Figure 2 . 10 :

 210 Figure 2.10: Schematic of different contributions in a C-V curve. Data from 190-nm-thick sputtered PZT capacitor with SRO top electrode.

  , the switchable polarization in ferroelectric materials has been usually measured by a Sawyer-Tower set-up (Sawyer and Tower 1930), which is still widely used nowadays. Sawyer and Tower used a Braun tube to obtain oscillograms, which was made by 2 pairs of plates: one pair to steer the beam in X and the other in Y. A 60 Hz sinuous alternative signal was used to switch the polarization in Rochelle salt. By measuring the deflections in Y axis, polarization-electric field (P-E) hysteresis loops were obtained.

Figure 2 .Figure 2 . 12 :Figure 2 .

 22122 Figure 2.11: Schematic connection of Sawyer-Tower circuit in 1930. C = 0.7 M f ; R 1 = 450000 Ω; R 2 = 3180 Ω; R 3 = 31800 Ω. Image adapted from Wikipedia (2010).

Figure 2 .Figure 2 . 15 :

 2215 Figure 2.15 shows the corresponding currents to PUND pulse train. For a good ferroelectric, I U is much smaller than I P . When the sample is leaky, I U is considerably high and even can be much bigger than I P -U . I P (or I N ) contains three parts: switching current I P -U (or I N -D ); non-switching current I d , which is due to the dielectric polarization of the capacitor (as the drive voltage changes, an amount of

Figure 2 .

 2 Figure 2.16: PUND loop, PN loop and corresponding currents.

Figure 2 .

 2 Figure 2.17: Ideal output phase and amplitude in PFM imaging. Image adapted from Proksch and Kalinin (2008).

Figure 2 .

 2 Figure 2.18: Drive voltage for PFM spectroscopy.

  Figure 3.1 shows the surface morphology of as-received STO substrate. Irregular terraces of roughly 2 Å revealed the alternating terminations of SrO and TiO 2 . Blurred morphology indicated that contamination (H 2 O and CO 2 ) worsened the surface.

Figure 3 . 1 :

 31 Figure 3.1: Topography of as-received STO substrate.

  The final annealing is implemented to totally remove the remnants in previous treatments and to facilitate the re-crystallization of top-most layer. The duration of etching and annealing can be modified depending on the miscut angle of the substrate surface (small miscut angle substrate requires less etching duration). Figure3.2 shows the surface morphology of STO substrate after treatment. Flat TiO 2 surface with terraces of single unit cell replaces the mixture of SrO and TiO 2 .

Figure 3 . 2 :

 32 Figure 3.2: Topography of STO substrate after chemical treatment.

(

  Bensch et al. 1990).Of the well-known ruthenates series Sr n+1 Ru n O 3n+1 , SrRuO 3 is the infinite-layer compound (n = ∞), having an orthorhombic structure at room temperature, with lattice parameters a 0 = 5.5670 Å, b 0 = 5.5304 Å, c 0 = 7.8446 Å,(Jones et al. 1989, Gan et al. 1999). It also exhibits a lightly distorted pseudo-cubic perovskite structure with lattice parameter a pc = 3.93 Å, α = β = 90°, and γ = 89.6°. The lattice mismatch of SRO and STO is exceptionally small (1.01%) and the lattice mismatch of SRO and PZT is also fairly small (2.80%), which facilitates the hetero-epitaxial growth of PZT on STO.The crystallographic relationship between the orthorhombic and the pseudo-cubic structures is illustrated in Figure3.3. The orthorhombic distortion arises from the rotation of RuO 6 octahedrons around [001] pc and [010] pc at room temperature. 2 At 547 • C, the orthorhombic phase of bulk SRO transforms to tetragonal phase with RuO 6 octahedrons rotated only around [001] pc . When rising to 677 • C, it transforms into cubic phase with RuO 6 octahedrons no more rotated. And for about 50-nmthick epitaxial SRO film, orthorhombic-cubic transition 3 temperature decreases to 280 • C due to the strain applied by STO substrate (Choi et al. 2010).

Figure 3 . 3 :

 33 Figure 3.3: Crystal structure of SRO. SRO has a Pbmn orthorhombic pervoskite structure with √ 2apc × √ 2apc × 2apc unite cell Dimensions, where apc denotes the pseudo-cubic lattice parameter. The black dotted and solid squares represent the unite cell of orthorhombic and pseudo-cubic structures, respectively. Oxygen octahedral tilt angle θ SRO is illustrated by the blue dash lines (Aso et al. 2013).

  width at half maximum values (FWHM) were extracted from the rocking curve scans. Both are plotted in Figure3.5. SRO film deposited at 460 • C and 540 • C showed similar out-of-plane lattice parameter and similar FWHM (0.09°). Film deposited at 620 • C and 675 • C had larger out-of-plane lattice parameters, indicating that they might be better strained on STO substrates. Mosaicity of SRO deposited at 620 • C was much smaller than that of other three.

Figure 3 . 5 :

 35 Figure 3.5: Out-of-plane lattice parameters and mosaicity of SRO deposited at different temperatures.

Figure 3 . 6 :

 36 Figure 3.6: Surface morphologies of SRO films deposited at the substrate temperature of (a) 460 • C; (b) 540 • C; (c) 620 • C; (d) 675 • C.

Figure 3 . 7 :

 37 Figure 3.7: Deposition rate at different chamber pressures. All three SRO film were deposited at 620 • C ∼ 650 • C, with voltage of 173 V and gas composition of 50 sccm Ar / 5 sccm O 2 .

Figure 3 . 8 :

 38 Figure 3.8: Out-of-plane 2θ/ω scans and rocking curves of SRO deposited at different voltages. Insect shows 2θ/ω scan of SRO deposited at 109 V from 20 °to 50 °.

Figure 3 . 9 :

 39 Figure 3.9: Surface morphologies of SRO films deposited on vicinal (001) STO substrates. (a) 11.9 nm SRO deposited at 109 V ; (b) 8.8 nm SRO deposited at 87 V ; (c) 10.6 nm SRO deposited at 70 V ; (all films were deposited at 650 • C with chamber pressure of 0.005 mbar and a gas composition of 50 sccm Ar and 5 sccm O 2 ). Insets show the corresponding STO surface morphologies after chemical treatment.

Figure 3 .

 3 Figure 3.10: Surface morphologies of SRO of (a) 18.9 nm deposited at 109 V ; (b) 27.7 nm deposited at 70 V ; (c) 32.8 nm deposited at 70 V . All deposition were carried out at 650 • C, and thickness were measured by XRR. The insets show the corresponding surface morphologies after chemical treatment of STO substrates.

  intervene intervals every several minutes into the deposition process. At the start of the deposition, large numbers of 2D nuclei form small islands on the surface. Due to the limited mobility of the adatoms and short-time for relaxation, after the arrival of new atoms, the growth mode changes from layer-by-layer mode to multilevel 2D growth mode, forming larger islands. With the increasing surface roughness, finally film is growing in 3D mode. An interval following a period of deposition allows the adatoms to have more time for relaxation and keep the surface smoothness. The island size is kept small and multilevel growth is prevented. Bachelet achieved ∼ 60 nm SRO with terraces of single unit cell in height.A deposition of SRO film during 130 min at 70 V with 15 min interval was carried out. During the 15 min interval, the plasma was stopped and other conditions (pressure, gas composition and substrate temperature) were kept unchanged. Figure3.11 shows the surface morphology of this film. Terraces of single unit cell were clear. The surface roughness was only 0.24 nm, smaller than the 27.7-nm-thick SRO deposited without interval. And grain size was smaller than that of the 27.7-nm-thick one (from smaller scale of AFM results, not provided here). Extracted data of deposition rate, roughness and FWHM are shown in Table3.2.

Figure 3 .

 3 Figure 3.11: Surface morphologies of 35 nm SRO deposited during 130 min with a 15 min interval in the middle. The insect shows the surface morphology after chemical treatment of STO substrate.

Figure 3 .

 3 Figure 3.12 shows the XRR result of this SRO film. Fitted curve revealed that the bottom SRO layer (deposited before the interval) had a slightly bigger thickness (17.8 nm) than the top SRO layer (17.2

Figure 3 .

 3 Figure 3.12: XRR result and fitting to 35-nm-thick SRO deposited during 130 min with 15 min interval in the middle.

Figure 3 .

 3 Figure 3.13: RSM around (103) reciprocal lattice points of a) 27.7 nm SRO deposited during 100 min; b) 35 nm SRO deposited during 130 min with 15 min interval in the middle. Both SRO were deposited at 70 V at 650 • C substrate and shows terraces of single unit cell in height.

Figure 3 .Figure 3 .

 33 Figure 3.14 c) for five sol-gel-derived PZT capacitors. The 35-nm-thick SRO (with terraces) exhibited smaller grains compared to the islands in other SRO surfaces. Its surface roughness (RMS) was also smaller than others, as shown in Table3.3 with growth parameters and peak-to-valley values.

Figure 3 .

 3 Figure 3.14: Surface morphologies of SRO bottom electrode for a) 40.5-nm-thick, 120.6-nm-thick and 136-nm-thick sputtered PZT capacitors; b) 190-nm-thick sputtered PZT capacitor; c) five sol-gel-derived PZT capacitors.

Figure 3 .

 3 Figure 3.15: Out-of-plane 2θ/ω scans of PZT films deposited at different temperatures during 20 min on 85-nm-thick SRO on as-received (001) STO substrates. Deposition parameters as follows, voltage: 71 V ; chamber pressure: 0.005 mbar; flux: 50 sccm Ar and 0 sccm O 2 .

Figure 3 .

 3 Figure 3.16 presents the rocking curves of these PZT films. FWHM were 1.58, 1.71, 2.60, 1.85 for PZT deposited at 150 • C, 300 • C, 460 • C and 540 • C, respectively. The mosaicity of PZT deposited at 460 • C is larger than the other three.

Figure 3 .

 3 Figure 3.16: Rocking curves around (002) of PZT films deposited at different temperatures during 20 min on 85-nm-thick SRO on as-received (001) STO substrates.

Figure 3 .

 3 Figure 3.17: Out-of-plane 2θ/ω scans of PZT deposited in two different gas compositions: 20% O 2 /80% Ar; 100% O 2 . At both conditions the total gas flux quantity was kept at 50 sccm.

Figure 3 .

 3 Figure 3.18: Out-of-plane 2θ/ω scans of PZT deposited at 50 V and at 138 V . The peak at 46°corresponds to bulk SRO, which might be the result of PZT bombardment on the SRO surface at high plasma voltage.

Figure 3 .Figure 3 .

 33 Figure 3.19: Out-of-plane 2θ/ω scans and rocking curves around (002) of PZT films of different thicknesses deposited on SRO/STO. Out-of-plane 2θ/ω scan was carried out from 20°to 50°and no pyrochlore phase was observed.

Figure 3 .

 3 Figure 3.21: RSM around (103) reciprocal lattice points for 190-nm-thick sputtered PZT sample.

Figure 3 .

 3 Figure 3.22: Surface morphologies of sputtered PZT of various thicknesses. All topographies were obtained before the deposition of top electrode except 136-nm-thick PZT which was measured after the deposition of top electrode.

Figure 3 .

 3 Figure 3.23: Surface morphologies of 190-nm-thick PZT capacitor: (a) substrate after chemical treatment; (b) after deposition of 35-nm-thick SRO during 130 min with 15 min interval in the middle; (c) after deposition of 190-nm-thick PZT. (scanning area: 5 µm × 5 µm)

Figure 3 .

 3 Figure 3.24: RSM around (103) reciprocal lattice points of PZT deposited at the rotational speed of a) 6000 rpm; b) 3000 rpm; c) 1500 rpm.

Figure 3 .Figure 3 .

 33 Figure 3.25: Out-of-plane 2θ/ω scans and rocking curves around (002) of sol-gel-derived PZT of different thicknesses. A small peak at 44.8°of 200-nm-thick PZT is observed, which corresponds to a-domain PZT (4.04 Å).

Figure 3 .

 3 Figure 3.27: Morphologies of sol-gel-derived PZT films of (a) 33 nm, (b) 67 nm, (c) 133 nm, (d) 200 nm and (e) 100 nm .

Figure 3 .

 3 Figure 3.28: Out-of-plane 2θ/ω scan of capacitors after the deposition of top electrode.

  4.1.1.1 Interface-dominant Mechanisms 4.1.1.1.1 Schottky Emission (SE) Schottky emission process is the carrier transport of electrons with sufficient energy to overcome the ferroelectric-electrode barrier Φ B = Φ M -χ. Φ M is electrode work function (voltage differencebetween its conduction band and vacuum level, around 4.8 eV for SRO(Scott 2000) and χ is electron affinity of PZT (voltage difference between its conduction band and vacuum level, around 3.5 eV (Scott

Figure 4 .

 4 Figure 4.1 shows the J-E characteristics of sputtered PZT of various thicknesses from 40.5 nm to 190

Figure 4

 4 Figure 4.1: J-E characteristics of sputtered PZT capacitors with SRO top electrode. Forward J-E is plotted with filled circles and reverse J-E with open circles. 40.5 nm in black, 120.6 nm in blue, 136 nm in olive and 190 nm in red.

Figure 4 .

 4 2 shows the forward J-E characteristics of 190-nm-thick sputtered PZT capacitors with SRO top electrode at seven different locations. The variation range is same to that of the three thicker capacitors in Figure4.1. Since it was inappropriate to investigate the thickness dependence with only one J-E curve for each sample, we only extracted the slopes of the curves as they always kept the same shape. In the leakage current investigation, thickness dependence is neglected. The dependence of thickness can be achieved by measuring a large amount of capacitors systematically on the same sample or several samples with same thickness and the size of capacitor should be small enough to minimize the influence of defects.Pintilie et al.'s work (2007) on PZT(20/80) deposited by PLD showed that films with thickness varying from 50 nm to 230 nm exhibited similar amount of leakage current.

Figure 4 .

 4 Figure 4.3 shows the J-E characteristics of these sputtered PZT capacitors with Pt top electrodeand ITO top electrode. As the "sandwich" structure was no more symmetric, forward J-E curve differed from reverse J-E curve, but the difference was insignificant. J l of 40.5-nm-thick capacitor with Pt top electrode and ITO electrode was much smaller, compared to the same capacitor with SRO top electrode.

Figure 4 . 2 :

 42 Figure 4.2: Forward J-E characteristics of 190-nm-thick sputtered PZT capacitor with SRO top electrode on seven different locations.

Figure 4 . 3 :

 43 Figure 4.3: J-E characteristics of sputtered PZT capacitors with Pt top electrode (left) and ITO top electrode (right). Forward J-E is plotted with filled circles and reverse J-E with open circles. 40.5 nm in black, 120.6 nm in blue, 136 nm in olive and 190 nm in red.

Figure 4 . 4 :

 44 Figure 4.4: Leakage characteristics of sputtered PZT capacitors with SRO top electrode plotted in ln(J) -E 0.5 form. 40.5 nm in black, 120.6 nm in blue, 136 nm in olive and 190 nm in red.

Figure 4 . 5 :

 45 Figure 4.5: Leakage characteristics of sputtered PZT capacitors with Pt top electrode (left) and ITO top electrode (right) plotted according to Schottky emission. 40.5 nm in black, 120.6 nm in blue, 136 nm in olive and 190 nm in red.

Figure 4 . 7 :Figure 4 . 8 :

 4748 Figure 4.7: Leakage characteristics of sputtered PZT capacitors with SRO top electrode at low field. 40.5 nm in balck, 120.6 nm in blue, 136 nm in olive and 190 nm in red.

Figure 4 . 9 :Figure 4 . 10 :

 49410 Figure 4.9: Leakage characteristics of sputtered PZT capacitors with SRO top electrode plotted in ln(J/E) -E 0.5 form. 40.5 nm in balck, 120.6 nm in blue, 136 nm in olive and 190 nm in red.

Figure 4 .Figure 4 . 11 :

 4411 Figure 4.11 shows the leakage currents of sputtered PZT capacitors with SRO top electrode plotted in log-log form. Starting from ∼ 200 kV /cm, J ∝ E 2 . At higher field (400 ∼ 600 kV /cm), the dependence transfered to E 3 except the 40.5-nm-thick capacitor.

Figure 4 .

 4 Figure 4.12 shows the leakage current of 4 sputtered PZT capacitors with Pt top electrode and ITO top electrode plotted in log -log form. The dependency on E was similar to SRO-top-electrode capacitors. The transition field from E 2 to E 3 was also ∼ 400kV /cm. For 136-nm-thick capacitor with Pt top electrode, leakage dependence on field transfered from E 2 to E 5 directly.

Figure 4 . 12 :

 412 Figure 4.12: Leakage characteristics of sputtered PZT capacitors with Pt top electrode (left) and ITO top electrode (right) plotted in logJ -logE form. 40.5 nm in balck, 120.6 nm in blue, 136 nm in olive and 190 nm in red.

Figure 4 . 13 :

 413 Figure 4.13: Well fitted charge transport mechanisms in different field ranges for sputtered PZT capacitors.

Figure 4 .

 4 Figure 4.14 shows I-V characteristics of sol-gel-derived PZT capacitors of various thicknesses from 67 nm to 200 nm with SRO top electrode and Pt top electrode. (More than three 33-nm-thick capacitors

Figure 4 .

 4 Figure 4.14: J-E characteristics of sol-gel-derived PZT capacitors. Forward J-E is plotted with filled circles and reverse J-E with open circles. 67 nm in black, 133 nm in olive, 200 nm in red and 100 nm in grey.

Figure 4 .

 4 Figure 4.15: J U from PUND measurement. Data from 200-nm-thick sol-gel-derived capacitor with Pt top electrode.

. 5 .

 5 According toHuang et al. (2000),Deineka et al. (2001), Peng et al. (2011), only the ε opt of 100-nm-thick capacitor was in the range. Thus SE is excluded from the charge transport mechanism.Fowler-Nordheim Tunneling

Figure 4 .Figure 4 . 16 :

 4416 Figure 4.17 plots the leakage of sol-gel-derived capacitors with SRO top electrode in ln(J/E 2 ) vs

Figure 4 . 18 :

 418 Figure 4.18: Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode and Pt top electrode at low field. Forward I-V is plotted with filled circles and reverse I-V with open circles. 67 nm in black, 133 nm in olive, 200 nm in red and 100 nm in grey.

Figure 4 .

 4 Figure 4.19 plots the leakage in the form of J/E vs E 0.5 according to FP emission. 100-nm-thick capacitor showed a much smaller slope, compared to other three capacitors. From ∼450 to 800 kV /cm, linear fit was applied to all curves and Table4.6 lists the extracted ε opt . Except the 100-nm-thick capacitor, all ε opt were in the range according to the experiments ofHuang et al. (2000),Deineka et al. (2001),Peng et al. (2011). Thus FP is compatible to the charge transport mechanism in the field between ∼450 to 800 kV /cm.

Figure 4 . 19 :

 419 Figure 4.19: Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode (left) and Pt top electrode (right) plotted in ln(J/E) -E 0.5 form. Forward I-V is plotted with filled circles and reverse I-V with open circles. 67 nm in black, 133 nm in olive, 200 nm in red and 100 nm in grey.

Figure 4 .

 4 Figure 4.20 plots the leakage in log -log form. The slope was much bigger than that of sputtered

Figure 4 . 20 :

 420 Figure 4.20: Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode (left) and Pt top electrode (right) plotted in logJ -logE form. Forward I-V is plotted with filled circles and reverse I-V with open circles. 67 nm in black, 133 nm in olive, 200 nm in red and 100 nm in grey.

Figure 4 . 21 :

 421 Figure 4.21: Well fitted charge transport mechanisms in different field ranges for sol-gel-derived PZT capacitors. Areas inside the dash lines means that in this field range leakage current is possibly due to this charge transport mechanism.

and 4 .

 4 21), only Schottky emission (for sputtered capacitors) was interface-dominant mechanism.

Figure 4 .Figure 4 . 23 :Figure 4 .

 44234 Figure 4.22: Capacitance-field curves and loss tangent of sputtered PZT capacitors with SRO top electrode.

Figure 4 . 25 :

 425 Figure 4.25: Reciprocal of C l as a function of thickness of sputtered capacitors with Pt top electrode (left) and ITO top electrode (right).

Figure 4 .

 4 Figure 4.26: ε ′ r as a function of field of sputtered PZT capacitors with Pt top electrode (left) and ITO top electrode (right).

Figure 4 . 27 :Figure 4 .

 4274 Figure 4.27: Reciprocal of C l as a function of thickness of sol-gel-derived capacitors with SRO top electrode and Pt top electrode.

PFigure 4 .

 4 Figure 4.29: PUND loops of sputtered capacitors with SRO top electrode. Inset shows the PUND loop and PN loop of 40.5-nm-thick capacitor with SRO top electrode.

PFigure 4 . 30 :Figure 4 .

 4304 Figure 4.30: Pr and Ec as a function of field for sputtered capacitors with SRO top electrode. For the plot of Ec, mean value of positive coercive field E p c and negative coercive field E n c is plotted. Error bar is used to indicate the degree of asymmetricity of hysteresis loop (asymmetricity = E p c -E n c ). Positive value means the loop shifts along positive direction on field-axis (E p c > E n c ).

Figure 4 . 32 :

 432 Figure 4.32: Pr and Ec as a function of field for sputtered capacitors with Pt top electrode (left) and ITO top electrode (right).

  (4.14) expects much higher E c for ultrathin (<10 nm) ferroelectric capacitors, which is inconsistent with experimental data.Dawber et al. (2003) included the depolarization field E d , and his modified scaling law well fitted the data from 1 nm to 1 µm for polyvinylidene fluoride (PVDF) ferroelectric film. Compared to Dawber's data for PZT from 50 nm to 5 µm(Dawber et al. 2003), which was well fitted (log(E c ) ∝ -0.66 log(d)), our data from SRO-top-electrode and Pt-top-electrode sputtered capacitors is in the same fitting line.

Figure 4 .

 4 Figure 4.33: PUND loops of sol-gel-derived capacitors with SRO top (left) electrode and Pt top electrode (right).

Figure 4 . 34 :

 434 Figure 4.34: Pr and Ec as a function of field for sol-gel-derived capacitors with SRO top electrode (left) and Pt top electrode (right).

Figure 4 .

 4 Figure 4.35 shows the topography, amplitude and phase response of the 190-nm-thick 8 sputtered PZT film after "writing". The clear contrast shown in phase image indicated that the film was piezoelectric

Figure 4 .

 4 Figure 4.35: PFM images of 190-nm-thick sputtered PZT film.

4. 4 . 2

 42 Switching Spectroscopy of Sputtered PZT Films

Figure 4 .Figure 4 .

 44 Figure 4.36 shows the PFM switching spectroscopy of 190-nm-thick sputtered PZT film. Both the phase loop and amplitude loop (direction: anticlockwise) were obtained by taking the average of 10 loops from different locations on the film. The difference between the top and the bottom in the phase loop was around 180°, indicating that the c-domains in the PZT film were switched up and down by the drive voltage. The response of amplitude showed a drop near the coercive field to almost zero, at which point,

Figure 4 .

 4 Figure 4.37: PFM images of sol-gel-derived PZT films of various thicknesses after writing opposite squares. (100-nm-thick PZT is listed apart from others for the reason that it has experienced 3 h post annealing while others have experienced only 1 min RTA.)

Figure 4 .

 4 Figure 4.38 shows the PFM switching spectroscopies of the five PZT films. All of these five PZT films

  gated. All films (except sub-50 nm) showed low leakage, regardless of growth route and top electrode. At low field range, sol-gel-derived capacitors showed one or two orders of magnitude lower leakage. Charge transport mechanism has been analyzed by fitting various models to leakage data and the fitting results showed that at different field range the dominant mechanism was different, showing the complexity of

Figure 4 .

 4 Figure 4.38: PFM loops of sol-gel-derived PZT films of various thicknesses. (100-nm-thick PZT is listed apart from others for the reason that it has experienced 3 h post annealing while others have experienced only 1 min RTA.)

Figure 4 .

 4 Figure 4.39: PFM retention of sol-gel-derived PZT films of various thicknesses. (100-nm-thick PZT is listed apart from others for the reason that it has experienced 3 h post annealing while others have experienced only 1 min RTA.)

Figure 5 . 1 :

 51 Figure 5.1: Definition of frequency in PUND measurements. Left shows a complete voltage signal of PUND measurement and right defines one cycle of signal.

Figure 5 .Figure 5 . 2 :

 552 Figure 5.2 shows PUND loops measured at different frequencies. As frequency decreased from 250kHz to 250 Hz (t inc increased from 10 µs to 1 ms), E c was greatly reduced and P r kept unchanged.When the input frequency continued dropping to 25 Hz, the change in E c was indistinguishable and P r increased a little. This is because a small amount of domains which were non-switchable at relatively high frequency switched due to the long lasting field applied on the capacitor. And P ⋆ increased 30% (in

E

  c extracted from PUND loops are plotted in Figure 5.3. Measurement at various frequencies was carried out on a 200-nm-thick sol-gel-derived PZT capacitor with Pt top electrode. Positive asymmetricity was observed at all frequencies measured. When f increased from 0.025 Hz to 50 Hz, E c kept stable.As f continued increasing, E c increased in a roughly exponential manner.

Figure 5 . 3 :

 53 Figure 5.3: Ec as a function of frequency. Data from 200-nm-thick sol-gel-derived PZT capacitor with Pt top electrode.

Figure 5 . 4 :

 54 Figure 5.4: Domain switching stages. Nucleation, usually at anode or cathode. (b) Needle-like domains move parallel to the applied field; (c) Lateral growth. The speed-limiting parameter can be (a), (b) or (c) for different materials (Ishiwara et al. 2004).

Figure 5 . 5 :

 55 Figure 5.5: Dimensionality of domain growth. (a), (b) and (c) are correspondent to one, two and three dimensional cases, respectively. rc is the radius of nucleus.[START_REF] Prasertchoung | Pulse switching and scalling effects in ferroelectric capacitors[END_REF]

Figure 5 . 6 :

 56 Figure 5.6: Plot of Ec at various frequencies according to I-O model.

Figure 5 . 7 :

 57 Figure 5.7: Plot of Ec at various frequencies according to D-C model.(E nc is not plotted here, which shows similar result.)

Figure 5 .Figure 5 . 8 :

 558 Figure 5.8 shows the fitting result of L-Y-D model to our data. According to this fit, n = 3 for both curves. L-Y-D model had a good fit in all frequency range and succeeded in predicting a minimum limit for E c as frequency continued decreasing when passing 50 Hz.

Figure 5 . 9 :

 59 Figure 5.9: Plot of Ec at various frequencies according to P-K model

E

  c at low frequency. However, sub-50 Hz is not useful for memory devices. D-C, L-Y-D and P-K model all exhibited good fit to the data from 50 Hz to 400 kHz. I-O model failed to fit the data. D-C model clearly pointed out the limiting frequency f 0 . Table 5.1 presents the features of 4 models and the fitting quality of each model.As the capacitor size decreases below a critical area, the limiting factor shifts to nucleation as there are less nucleation sites. P-K model is more applicable for small capacitors comparing to L-Y-D model.Jung et al.'s work (2005) showed that P-K model fitted better than L-Y-D model (measured in the range between 1 kHz and 1 M Hz). Because in L-Y-D model, nucleation is considered to be unimportant.

Figure 5 .

 5 Figure 5.10. The two ramps are due to the domain switching movement.

Figure 5 . 10 :

 510 Figure 5.10: Leakage current of normal I-V measurement and and I-V measurement with domain switching.

Figure 5 .

 5 Figure 5.11: Schematic of three compositions of J tot s .

Figure 5 .

 5 Figure 5.12: Comparison of I-V leakage current and switching current Js in PUND measurement. Data from 200-nm-thick sol-gel-derived PZT capacitor with Pt top electrode.

Figure 5 . 13 :

 513 Figure 5.13: Comparison of integration of Js in I-V measurement with PUND loop and PN loop. Data from 200-nm-thick sol-gel-derived PZT capacitor with Pt top electrode.

Figure 5 . 14 :

 514 Figure 5.14: Schematic of I-V measurement with switching. t d was set to be 0 if not stated.

Figure 5 .

 5 Figure 5.15: J tot s at various temperatures. Data from 200-nm-thick sol-gel-derived PZT capacitor with Pt top electrode.

Figure 5 .

 5 Figure 5.16: P-E curve and corresponding C-V curve of three different types of capacitors. (a) simple capacitor; (b) paraelectric capacitor; (c) ferroelectric capacitor.

Figure 5 .Figure 5 .Figure 5 .Figure 5 .

 5555 Figure 5.17 depicts the P-E loop, integrated of capacitance and PUND loop, PN loop. The difference between PN loop and PUND loop, (PN-PUND) loop is also plotted here by integrating I U and I D . P-E loop, integrated of capacitance resembles the (PN-PUND) loop but the slope in (PN-PUND) loop is higher in low field range.

Figure 5 .

 5 Figure 5.19: PUND loops measured at various temperatures. Data from 200-nm-thick sol-gel derived PZT capacitor with Pt top electrode.

Figure 5 .

 5 Figure 5.22. As temperature increased, maximum of ε ′ r increased and the linear part did not change. E c decreased with temperature, which was consistent with the PUND results in Figure 5.19.

Figure 5 .Figure 5 .Figure 5 .

 555 Figure 5.20: Polarization as a function of temperature for PZT of various compositions. PbTiO 3 and PZT(20/80) are of first order transition while PZT(30/70), PZT(40/60) and PZT(50/50) are of second order transition (Haun et al. 1989).

Figure 5 . 23 :

 523 Figure 5.23: Reciprocals of ε ′ r as a function of temperature. Data from 200-nm-thick sol-gel derived PZT capacitor with Pt top electrode. Low temperature measurement was carried out in vacuum and high temperature measurement was carried out in air.

Figure 5 . 24 :

 524 Figure 5.24: Relaxation of polarized domains. Data from 100-nm-thick sol-gel-derived PZT with SRO top electrode. This 100-nm-thick capacitor experienced twice annealing in furnace for 3 h for the crystallizations of PZT and top electrode, which is not the same 100-nm-thick capacitor mentioned in previous chapters.

Figure 5 . 25 :Figure 5 .

 5255 Figure 5.25: Interface screening model for imprint. (a) A sketch of a ferroelectric capacitor with thin interface layers; (b) An enlargement of the interfacial region, showing the driving force of E if of imprint (Ishiwara et al. 2010).

Figure 5 .

 5 Figure 5.27: PUND loops of a 200-nm-thick capacitor with 85-nm-thick bottom SRO layer and of another 200-nmthick capacitor with 18.9-nm-thick bottom SRO layer. Left shows the PUND loops of these two capacitors with SRO top electrode. Right shows the PUND loops of these two capacitors with Pt top electrode.

Figure 5 .

 5 Figure 5.28 shows the P r and E c extracted from PUND measurements at various voltages of these two capacitors with different thick bottom electrodes. P r from both sample (both with SRO top electrode

Figure 5 . 28 :

 528 Figure 5.28: Pr and Ec of PUND loops from two 200-nm-thick 5 capacitor with bottom electrode of different thickness, measured at various fields. Left shows the results of these two capacitors with SRO top electrode. Right shows the results of these two capacitors with Pt top electrode.

Fatigue

  is one of the most important factors for FeRAM devices, which we have not yet studied. Capacitors with Pt top electrode usually showed degraded switching behaviors after 10 4 cycles. Oxide electrodes such as IrO 2 , RuO 2 and SrRuO 3 could greatly improve fatigue property to 10 10 cycles without degrading. Fatigue quality of these capacitors with different top electrodes will be investigated in next work.

  Schematic of piezoelectric cantilever vibration harvester. . . . . . . . . . . . . . . . . . . . 1.2 Grouping of crystal classes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Schematic representation of structural phase transition and dipole movement in response to field of pyroelectrics, ferroelectrics and antiferroelectrics. . . . . . . . . . . . . . . . . . 1.4 Schematic of PZT crystalline lattice and the origin of permanent dipole in tetragonal lattice. .11 Schematic connection of Sawyer-Tower circuit in 1930. . . . . . . . . . . . . . . . . . . . . 2.12 Schematic connection of Sawyer-Tower circuit nowadays. . . . . . . . . . . . . . . . . . . . 2.13 PUND pulse train signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14 Schematic connection of the circuit used in PUND measurement. . . . . . . . . . . . . . 2.15 Drive voltage, corresponding currents and polarizations in PUND measurement. . . . . . . 2.16 PUND loop, PN loop and corresponding currents. . . . . . . . . . . . . . . . . . . . . . . 2.17 Ideal output phase and amplitude in PFM imaging. . . . . . . . . . . . . . . . . . . . . . Topography of as-received STO substrate. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Topography of STO substrate after chemical treatment. . . . . . . . . . . . . . . . . . . . 3.3 Crystal structure of SRO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Out-of-plane 2θ/ω scans and rocking curves of SRO films deposited at different temperatures. 3.5 Out-of-plane lattice parameters and mosaicity of SRO deposited at different temperatures. 3.6 Surface morphologies of SRO films deposited at different temperatures. . . . . . . . . . . . 3.7 Deposition rate at different chamber pressures. . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Out-of-plane 2θ/ω scans and rocking curves around (002) of SRO deposited at different voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Surface morphologies of SRO films of ∼ 10 nm deposited at different plasma voltages on vicinal (001) STO substrates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 360°φ scan of (103) plane of STO substrate, SRO layer and PZT layer of 190-nm-thick sputtered capacitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.21 RSM around (103) reciprocal lattice points for 190-nm-thick sputtered PZT sample. . . . 3.22 Surface morphologies of sputtered PZT of various thicknesses. . . . . . . . . . . . . . . . . 3.23 Surface morphologies of each layer of 190-nm-thick PZT capacitor. . . . . . . . . . . . . . 3.26 360°φ scan of (103) plane of STO substrate, SRO layer and PZT layer of 200-nm-thick sol-gel-derived capacitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.27 Morphologies of sol-gel-derived PZT films of different thickness. . . . . . . . . . . . . . . . 65 3.28 Out-of-plane 2θ/ω scan of capacitors after the deposition of top electrode. . . . . . . . . . 66 4.1 J-E characteristics of sputtered PZT capacitors with SRO top electrode. . . . . . . . . . . 77 4.2 Forward J-E characteristics of 190-nm-thick sputtered PZT capacitor with SRO top electrode on seven different locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.3 J-E characteristics of sputtered PZT capacitors with Pt top electrode and ITO top electrode. 78 4.4 Leakage characteristics of sputtered PZT capacitors with SRO top electrode plotted in ln(J) -E 0.5 form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.5 Leakage characteristics of sputtered PZT capacitors with Pt top electrode and ITO top U from PUND measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.16 Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode and Pt top electrode plotted in ln(J) -E 0.5 form. . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.17 Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode plotted in ln(J/E 2 ) -E -1 form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.18 Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode (left) and Pt top electrode (right) at low field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode and Pt top electrode plotted in logJ -logE form. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.21 Well fitted charge transport mechanisms in different field ranges for sol-gel-derived PZT capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.22 Capacitance-field curves and loss tangent of sputtered PZT capacitors with SRO top electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.23 Reciprocal of C l as a function of thickness of sputtered capacitors with SRO top electrode.

	P ⋆	maximum displacement	µC/cm 2
	J P ∆P	current response to pulse P polarization change effected by the passing domain	µA/cm µC/cm 2
	J U	current response to pulse U wall	µA/cm
	J N J D q q x Contents current response to pulse N current response to pulse D elementary charge reciprocal space along x-axis List of Figures	µA/cm µA/cm 1.60218 × 10 -19 C Å -1
	J P -U q z J N -D R p J tot s J tot ns J d J l J s k k B κ λ m m * µ µ n µ p n n n ν P P P P U P N P D P n P p R s R * r c T t dec t inc t int t R t r τ V V ac V c V max V s Φ M Φ B ∆Φ χ ω Abbreviations Symbols List of Figures List of Tables General Introduction reciprocal space along z-axis = J P -J U parallel resistance = J N -J D current with domain switching in I-V measurement current without domain switching in I-V measure-ment current due to dielectric polarization leakage current current due to domain switching parameter in I-O model Boltzmann's constant constant wavelength of the X-ray positive constant effective carrier mass carrier mobility mobility of electrons mobility of holes diffraction order positive constant reflective index rate constant polarization polarization response to pulse P polarization response to pulse U polarization response to pulse N polarization response to pulse D the difference polarization response between pulse N and pulse D the difference polarization response between pulse P series resistance critical radius of the bulge in domain motion radius of nucleus temperature transition temperature Curie temperature delay time period of voltage from 0 to -V max period of voltage from 0 to +V max period between identical neighboring pulses recombination time period between opposite neighboring pulses density of recombination centers voltage alternating voltage coercive voltage maximum voltage applied on the capacitor step change of voltage electrode work function ferroelectric-electrode barrier lowered amount of barrier electron affinity angle between the reflected ray and the scattering planes admittance (reciprocal of impedance) in the parallel circuit 1 Background and Motivation 1.1 3.24 RSM around (103) reciprocal lattice points of PZT deposited at different rotational speeds. µA/cm Å -1 µA/cm Ω µA/cm µA/cm µA/cm µA/cm µA/cm 8.61733 × 10 -5 eV K -1 Å kg cm 2 /(V • s) cm 2 /(V • s) cm 2 /(V • s) µC/cm µC/cm µC/cm µC/cm µC/cm µC/cm µC/cm Ω m m K or °T0 K or °Tc K or °td s s s s s s V V V V V eV eV eV eV °Y S iii v xiii xix xxi 1
	and pulse U 3.25 Out-of-plane 2θ/ω scans and rocking curves around (002) of sol-gel-derived PZT of different
	P r	remnant polarization	µC/cm
	P s	saturation polarization	µC/cm
	viii		vii

1.5 Free energy for second-order and first-order phase transition. . . . . . . . . . . . . . . . . 1.6 The ferroelectric hysteresis loop, associated with potential subject to an applied field. . . 1.7 Phase diagram of PZT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Dielectric constant and electromechanical coupling coefficient of PZT as a function of Zr/Ti ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Schematic of sputtering process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Schematic of sol-gel process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Reversal lift-off procedure for the deposition of top electrode. . . . . . . . . . . . . . . . . 2.4 Geometry of Rigaku SmartLab 4-circle diffractometer. . . . . . . . . . . . . . . . . . . . . 2.5 Schematic of AFM operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Voltage waveform for typical I-V measurement. . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Typical J-E curve of a ferroelectric capacitor. . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 ε r as a function of field for an ideal ferroelectric. . . . . . . . . . . . . . . . . . . . . . . . 2.9 C-V measurement circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Schematic of different compositions in a C-V curve. . . . . . . . . . . . . . . . . . . . . . . 22.18 Drive voltage for PFM spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.19 Phase and amplitude response in PFM spectroscopy. . . . . . . . . . . . . . . . . . . . . xiii 3.1 3.10 Surface morphologies of SRO of 18 ∼ 35 nm deposited at different voltages. . . . . . . . . 3.11 Surface morphologies of 35-nm-thick SRO deposited during 130 min with a 15 min interval in the middle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 XRR result and fitting to 35-nm-thick SRO deposited during 130 min with 15 min interval in the middle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13 RSM around (103) reciprocal lattice points of two SRO of ∼ 30 nm, one of them with 15 min interval in the middle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14 Surface morphologies of SRO bottom electrode for PZT capacitors. . . . . . . . . . . . . . 3.15 Out-of-plane 2θ/ω scans of PZT films deposited at different temperatures. . . . . . . . . . 3.16 Rocking curves around (002) of PZT films deposited at different temperatures during 20 min on 85-nm-thick SRO on as-received (001) STO substrates. . . . . . . . . . . . . . . 3.17 Out-of-plane 2θ/ω scans of PZT deposited in different gas compositions. . . . . . . . . . . 3.18 Out-of-plane 2θ/ω scans of PZT deposited at 50 V and at 138 V . The peak at 46°corresponds to bulk SRO, which might be the result of PZT bombardment on the SRO surface at high plasma voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19 Out-of-plane 2θ/ω scans and rocking curves of PZT films of different thicknesses deposited on SRO/STO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3thicknesses. A small peak at 44.8°of 200-nm-thick PZT is observed, which corresponds to a-domain PZT (4.04 Å). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv electrode plotted according to Schottky emission. . . . . . . . . . . . . . . . . . . . . . . . 79 4.6 Leakage characteristics of sputtered PZT capacitors with SRO top electrode plotted in ln(J/E 2 ) -E -1 form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.7 Leakage characteristics of sputtered PZT capacitors with SRO top electrode at low field. . 81 4.8 Leakage characteristics of sputtered PZT capacitors with Pt top electrode and ITO top electrode at low field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.9 Leakage characteristics of sputtered PZT capacitors with SRO top electrode plotted in ln(J/E) -E 0.5 form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.10 Leakage characteristics of sputtered PZT capacitors with Pt top electrode and ITO top electrode plotted in ln(J/E) -E 0.5 form. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.11 Leakage characteristics of sputtered PZT capacitors with SRO top electrode plotted in logJ -logE form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.12 Leakage characteristics of sputtered PZT capacitors with Pt top electrode and ITO top electrode plotted in logJ -logE form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.13 Well fitted charge transport mechanisms in different field ranges for sputtered PZT capacitors. 84 4.14 J-E characteristics of sol-gel-derived PZT capacitors. . . . . . . . . . . . . . . . . . . . . . 85 4.15 J 4.19 Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode and Pt top electrode plotted in ln(J/E) -E 0.5 form. . . . . . . . . . . . . . . . . . . . . . . . . . 88 xv 4.20

  1.1 Historical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 1.3 Ferroelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 PZT Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 PZT Deposition: State of the Art . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

  The detailed crystal structure of Rochelle salt was unknown and seemed complicated. Between 1935 and 1938, a series of ferroelectrics were produced. Scientists discovered that the crystals that were isomorphous to potassium dihydrogen phosphate, KH 2 PO 4 (KDP), seemed to show ferroelectricity below T c . The only exception was ammonium salts, e.g., (NH 4 )H 2 PO 4

. He discovered that Rochelle salt (first produced in about 1675, in La Rochelle, France) exhibited a spontaneously polarized phase which was similar to the already discovered ferromagnetism. An extremely large dielectric constant and piezoelectric response appeared near Curie temperature T c . The term ferroelectricity was not commonly used before early 1940s because Rochelle salt had been the only ferroelectric material for more than one decade.

Table 1 . 2 :

 12 The roadmap for 1T-1C FeRAM memory and target requirements(Ishiwara et al. 2004).

	Generation (µm)	0.5 (current)	0.35	0.25	0.18	0.13	0.1
	Architecture	2T-2C	1T-1C	1T-1C	1T-1C	1T-1C	1T-1C (3D)
	Density (M b)	1	16	64	256	512	2000
	PZT thickness (nm)	200	180	140	100	80	65
	Capacitor area (µm 2 )	3.0	1.5 ∼ 1.0	1.0 ∼ 0.5	0.33 ∼ 0.13	0.14 ∼ 0.07	0.06 ∼ 0.03
	Cell factor	63	63 ∼ 30	30 ∼ 15	20 ∼ 8	16 ∼ 8	12 ∼ 6
	Cell size (µm 2 )	15.8	8.0 ∼ 3.7	1.9 ∼ 0.9	0.65 ∼ 0.26	0.27 ∼ 0.14	0.12 ∼ 0.06
	Operating voltage (V )	5/3.3	3.3	2.5	1.8	1.5	1.2
	Read/write (cycles)	10 10 /10 16	10 16	10 16	10 16	10 16	10 17
	Data retention (yr)	10	10	10	10	10	10
	Switching time (ns)	<10	<10	<10	<10	<5	<5
	Access time (ns)	70	50	30	20	15	10
	Active current (mA)	<15	<15	<15	<15	<15	<15
	Energy/bit (pJ)	2.3/1.4	0.68	0.19	0.04	0.02	0.02

  The hysteresis loop is obtained through the phase response. Figure2.19 shows a typical phase response and amplitude response in PFM spectroscopy. Based on the fact that PFM spectroscopy manipulates domain locally, this technique can investigate the domain switching behavior in nano-scale, much smaller than in PUND measurement. Phase and amplitude response in PFM spectroscopy.The aim of this chapter is to present the growth details of epitaxial Pb(Zr 0.52 ,Ti 0.48 )O 3 , which is in the region of MPB, on SrTiO 3 (STO) substrate with an interlayer of SrRuO 3 (SRO) as bottom electrode by two growth routes, sputtering and sol-gel. The crystal structure of both bottom electrode and PZT film were characterized by XRD. AFM was performed for morphological characterization of each layer. .1. Substrate Preparation parameter) which can increase PZT tetragonality by the clamping force applied. SRO was selected as bottom electrode for its conductive property, compatible structure (pseudo-cubic), close lattice parameter (between STO and PZT), which could facilitate the hetero-epitaxial growth and its chemical stability.For both growth routes (sputtering and sol-gel), PZT films have been grown from less than 50 nm to around 200 nm in order to investigate the thickness influence and to figure out the thinnest workable PZT capacitor. As the metal-ferroelectric interface plays an important role on the PZT properties and different metallic materials exhibit different work functions, three conductive materials, SRO, Pt and ITO (indium tin oxide) have been employed as top electrode to study their influence on PZT capacitor's electric properties.

	0 Drive field Fabrication and Structural -90 0 90 Phase E p c Phase (deg) E n c Amplitude Amplitude (a.u.) Figure 2.19: Chapter 3 Characterizaton

3.1 Substrate Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Deposition of SRO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Choice of SRO as Bottom Electrode . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Optimization of SRO Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Growth of SRO with Terraces on Vicinal STO . . . . . . . . . . . . . . . . . .

3.2.4 SRO Growth as Bottom Electrode . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 PZT Growth by Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Optimization of PZT Growth by Sputtering . . . . . . . . . . . . . . . . . . . . 3.3.1.1 Temperature Influence . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.2 Gas Composition Influence . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.3 Plasma Voltage Influence . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Growth and Structural Characterization of Sputtered PZT . . . . . . . . . . . 3.4 PZT Growth by Sol-gel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Optimization of PZT Growth by Sol-gel . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Growth and Structure Characterization of Sol-gel-derived PZT . . . . . . . . . 3.5 Growth of Top Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The capacitor stack structure is top electrode/PZT /bottom electrode/substrate, which is often labeled as metal-ferroelectric-metal (MFM) stack. First, STO (001) was chosen as substrate for its shared perovskite structure, slightly smaller lattice parameter (-3.68% of PZT 52/48 a-axis lattice 3

  , Rijnders et al. 2004, Lee et al. 2004), sputtering(Eom et al. 1993, Jiang et al. 1998, Gan et al. 1999), molecular beam epitaxy (MBE)(Tian et al. 2007) and metal organic chemical vapor deposition (MOCVD)(Takahashi et al. 2002). PLD can achieve good quality through layer-by-layer deposition(Choi et al. 2001),

but the coverage is usually very poor

[START_REF] Defay | Ferroelectric Dielectrics Integrated on Silicon[END_REF]

. In this work, SRO is deposited by sputtering for its much larger achievable area and higher homogeneity compared to PLD. SRO exhibits good conductivity. At room temperature, the resistivity of SRO (100 nm) is around 220 µΩ • cm

(Klein et al. 1996

). 1 Allen et al.

  .1. As plasma voltage decreases, deposition rate dropped significantly and out-of-plane lattice parameter c SRO slightly decreased.

							Raw data						Raw data
							Fit peak STO					Fit peak
							Fit peak SRO
							Cumulative fit peak
							109 V 11.9 nm
	Intensity (a.u.)						87 V 8.8 nm
							70 V 10.6 nm
	44.0	44.5	45.0	45.5	46.0	46.5	47.0	47.5	22.5	22.6	22.7	22.8	22.9	23.0
			2theta/omega (deg)						omega (deg)

Table 3 . 1 :

 31 Lattice parameters, surface morphologies, deposition rate of SRO of ∼ 10 nm deposited at different plasm voltages.

	Voltage	Thickness	RMS Deposition rate	c SRO	FWHM
	(V)	(nm)	(nm)	(nm/min)	(Å)	(°)
	109	11.9	0.27	0.992	3.987	0.09
	87	8.8	0.34	0.489	3.983	0.08
	70	10.6	0.35	0.228	3.980	0.03

Table 3 . 2 :

 32 Parameters extracted from XRD and AFM and deposition rates.

	Thickness	Voltage	Deposition rate	RMS	Peak-to-Valley	c SRO	FWHM	Terrace
	(nm)	(V )	(nm/min)	(nm)	(nm)	(Å)	(°)
	18.9	109	1.050	0.45	1-2	4.004	0.09
	27.7	70	0.277	0.54	1-2	3.984	N/A	√
	32.8	70	0.273	0.52	1-1.5	3.999	0.10
	35	70	0.269	0.24	0.3-1.5	3.986	0.10	√

Table 3 . 3 :

 33 Thickness, deposition conditions and morphology parameters of SRO bottom electrodes.

		PZT Thickness	SRO Thickness	Voltage	Deposition Rate	RMS	Peak-to-Valley	Terrace
		(nm)	(nm)	(V )	(nm/min)	(nm)	(nm)
	Sputtering Sol-gel	40.5 120.6 136 190 33 67 100 133 200	27.5 26 25.5 35 ∼ 85 85 ∼ 85 ∼ 85 ∼ 85	70 70 70 70 109 109 109 109 109	0.275 0.260 0.255 0.269 1.417	0.63 0.63 0.66 0.24 0.84	1.5 ∼ 2 1.5 ∼ 2 1.5 ∼ 2 0.3 ∼ 1.5 1 ∼ 3	√

  • C and 300 • C. At room temperature and 460 • C, its intensity decreased slightly. As substrate temperature increased to 540 • C, only a fraction of amorphous PZT phase transfered to crystalline phase by RTA.

	PZT (001)	SRO (001)	STO (001)			PZT (002)	SRO (002)	STO (002)
			Room temperature
			150 C
	Intensity (a.u.)		300 C
			460 C
			540 C
			650 C		Pyrochlore
	20		25	30	35	40	45	50
				2theta/omega (deg)

  3.1.1, which was 4.089 Å. It indicated that PZT deposited at 50 V was probably more relaxed due to the low deposition rate. c P ZT of PZT deposited at 138 V was 4.091 Å.

	PZT (001)	SRO (001)	STO (001)	@ 50 V @ 138 V		PZT (002)	SRO (002)	STO (002)
	Intensity (a.u.)
					Pyrochlore
	20		25	30	35	40	45	50
				2theta/omega (degree)

Table 3 . 4 :

 34 Out-of-plan lattice parameters and mosaicities of sputtered PZT films and underlying SRO films.Out-of-plane 2theta/omega scans and rocking curve measurements were carried out for these four PZT films, presented in Figure3.19. All these PZT films were mono-crystalline in (00l) direction. No pyrochlore phase was observed. Out-of-plane lattice parameters and FWHM were extracted from PZT (002) peaks, as shown in Table3.4. All PZT films had similar out-of-plane lattice parameter. Mosaicity of these films were also similar.

		PZT Thickness	SRO Thickness	c P ZT	c SRO	FWHM (PZT)	FWHM (SRO)
		(nm)	(nm)		(Å)	(Å)		(°)			(°)
		40.5	27.5		4.070	4.000		1.30		0.10
		120.6	26		4.093	4.001		1.08		0.10
		136	25.5		4.084	4.009		1.01		0.11
		190	35		4.084	3.978		1.20		0.09
		40.5-nm-thick PZT
		120.6-nm-thick PZT									40.5-nm-thick PZT
	PZT (001)	STO (001) 136-nm-thick PZT SRO (001) 190-nm-thick PZT					PZT (002)	SRO (002)	STO (002)		120.6-nm-thick PZT 136-nm-thick PZT 190-nm-thick PZT
	Intensity (a.u.)
	20	25	30	35		40		45	50	-2	-1	0	1	2
			2theta/omega (deg)							Delta Omega (deg)

Table 3 . 5 :

 35 Surface morphology parameters of sputtered PZT films of different thicknesses (surface roughness before the deposition of PZT is presented here also).

	PZT thickness	SRO thickness	RMS (SRO)	RMS (PZT)	Grain Size	Peak-to-valley
	(nm)	(nm)	(nm)	(nm)	(nm)	(nm)
	40.5 120.6 136 190	27.5 26 25.5 35	0.63 0.63 0.66 0.24	0.77 0.73 0.48 0.38	20 ∼ 30 20 ∼ 30 20 ∼ 30 20 ∼ 30	1 ∼ 3 1 ∼ 2.5 1 ∼ 1.5 0.4 ∼ 1.8

Table 3

 3

	.6. c SRO of 100-nm-thick PZT sample was much smaller, compared to others and its value of
	3.939 Å was close to SRO bulk value, 3.93 Å, indicating it was mostly relaxed on STO substrate. All
	SRO were deposited in same condition and 200-nm-thick PZT experienced once more RTA than others

Table 3 .

 3 6: Out-of-plan lattice parameters and mosaicities of sol-gel-derived PZT films and underlying SRO films. It is reasonable to attributed the abnormal c SRO in 100-nm-thick PZT sample to the long annealing duration for the top electrode. During this 2nd annealing, SRO layer was thermally activated

	PZT Thickness	SRO Thickness	c P ZT	c SRO	FWHM ( PZT) FWHM (SRO)
	(nm)	(nm)	(Å)	(Å)	(°)	(°)
	33 67	∼ 85 85	4.097 4.104	3.986 3.972	0.35 N/A	0.09 N/A
	133 200 100 15	∼ 85 ∼ 85 ∼ 85	4.110 4.119 4.108	3.984 3.981 3.939	0.73 0.75 1.74	0.06 0.09 0.36
	during the sol-gel procedure but still exhibited similar c SRO as 33-nm-thick, 67-nm-thick and 133-nm-
	thick did.

Table 3 .

 3 7: Roughness and grain size of sol-gel-derived PZT surfaces.

	PZT Thickness	SRO Thickness	RMS (SRO) RMS (PZT)	Grain Size	Peak-to-valley
	(nm)	(nm)	(nm)	(nm)	(nm)	(nm)
	33 67 133 200 100	∼ 85 85 ∼ 85 ∼ 85 ∼ 85	0.84	0.38 0.46 0.41 0.66 1.63	10 ∼ 20 25 ∼ 35 20 ∼ 40 15 ∼ 20 50 ∼ 70	0.5 ∼ 3 1 ∼ 2 0.5 ∼ 2 0.5 ∼ 2 2 ∼ 4
	this 2nd RTA, grain densities of the 133-nm-thick PZT was found to be at the level of 200-nm-thick
	PZT while performing PFM measurement. As sol-gel-derived PZT crystallizes from bottom through the
	thickness to top, forming columnar grains (Amanuma et al. 1994), the low grain density was attributed to

the insufficient annealing during the sol-gel growth. The 133-nm-thick PZT only experienced once RTA for crystallization as the 33-nm-thick and 67-nm-thick PZT did and the 200-nm-thick PZT underwent twice RTA. The annealing for top electrode crystallized the amorphous phase of 133-nm-thick PZT near the surface, increasing its surface grain density. RMS results and grain sizes of these five samples are provided in Table

3

.7.

  All three top electrodes were deposited by sputtering at room temperature. The thickness was around 150 nm. Through the reversal mask, six different sizes (100×100µm 2 , 150×150µm 2 , 200×200µm 2 , 300×300µm 2 , 400×400µm 2 , 600×600µm 2 ) of top electrodes were deposited in arrays. To crystallize the top electrode, SRO and Pt experienced 1 min RTA at 650 • C in oxygen, crystallizing in (00l) and (111) direction, respectively. ITO required a different annealing procedure for crystallization(Morgan et al. 1998, Rogozin et al. 2004, Higuchi et al. 1994). RTA at 250 • C during 1 min in oxygen was performed for ITO crystallization. In 2 O 3 (222) was observed in out-of-plane 2θ/ω scan.

	3.6. Summary
				Pt (111)
	Intensity (a.u.)		(222)
			3
			O
			2
			In
	20	25	30	35	40	45	50
				2theta/omega (deg)

Pintilie et al.'s work (2012)

suggested that different top electrodes generated different amount of top interface traps, which affected the leakage current of the capacitor thus forming different ferroelectric hysteresis loops.

  Leakage Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Leakage Current Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	Chapter 4
	Electrical Characterization
	Rev. B. Condens. Matter 53 (8), 4393. Amanuma, K., T. Hase, and Y. Miyasaka (1994), Appl. Phys. Lett. 65 (24), 3140. 4.1 4.4.5 Retention of Sol-gel-derived PZT Films . . . . . . . . . . . . . . . . . . . . . .
	Aso, R., D. Kan, Y. Shimakawa, and H. Kurata (2013), Sci. Rep. 3, 2214. 4.4.6
	Bachelet, R., F. Sanchez, J. Santiso, and J. Fontcuberta (2008), Appl. Phys. Lett. 93 (15), 151916.

, Chem. Mater. 15 (9), 1924.

Allen, P., H. Berger, O. Chauvet, L. Forro, T. Jarlborg, a.

Junod, B. Revaz, and G. Santi (1996)

, Phys.

Bensch, W., H. Schmalle, and A. Reller (1990), Solid State Ionics 43, 171. Bruchhaus, R., D. Pitzer, O. Eibl, U. Scheithauer, and W. Hoesler (1991), in MRS Proc., Vol. 243

(Cambridge Univ Press) p. 123. 4.1.1.1 Interface-dominant Mechanisms . . . . . . . . . . . . . . . . . . . . . 4.1.1.2 Bulk-dominant Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Leakage Current of Sputtered Capacitors and Fitting Results . . . . . . . . . . 4.1.3 Leakage Current of Sol-gel-derived Capacitors and Fitting Results . . . . . . . 4.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Capacitance-Voltage Characteristics . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Relative Permittivity of Sputtered Capacitors . . . . . . . . . . . . . . . . . . . 4.2.2 Relative Permittivity of Sol-gel-derived Capacitors . . . . . . . . . . . . . . . . 4.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Ferroelectric Hysteresis Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 P-E loops of Sputtered Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 P-E loops of Sol-gel-derived Capacitors . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Piezoresponse Force Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 PFM Imaging of Sputtered PZT Films . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Switching Spectroscopy of Sputtered PZT Films . . . . . . . . . . . . . . . . . 4.4.3 PFM Imaging of Sol-gel-derived PZT Films . . . . . . . . . . . . . . . . . . . . 4.4.4 Switching Spectroscopy of Sol-gel-derived PZT Films . . . . . . . . . . . . . . .

Table 4 .

 4 1: Possible conduction mechanisms in ferroelectric capacitors[START_REF] Sze | Physics of Semiconductor Devices[END_REF].

	Dominated by	Process	Expression	Dependence (E, T or d)

Table 4 .

 4 2: εopt of sputtered PZT capacitors extracted according to Schottky emission.

	PZT Thickness (nm) Top electrode	10 4 ×slope SRO	10 4 ×slope Pt	10 4 ×slope ITO	εopt SRO	εopt Pt	εopt ITO
	40.5 120.6 136 190	5.4 ± 0.1 8.4 ± 0.1 6.7 ± 0.2 5.7 ± 0.2	8.2 ± 0.2 6.7 ± 0.2 13.8 ± 0.3 8.7 ± 0.3	8.1 ± 0.3 8.9 ± 0.3 7.0 ± 0.2 N/A	7.3 ± 0.1 3.2 ± 0.1 3.0 ± 0.3 4.8 ± 0.1 4.7 ± 0.1 1.1 ± 0.1 6.5 ± 0.2 2.8 ± 0.1	3.3 ± 0.1 2.7 ± 0.1 4.4 ± 0.1 N/A

Table 4 .

 4 3: m * extracted by estimating Φ B = 0.5 eV .Peng et al. (2011), n for PZT is about 2.3 ∼ 3.1, thus ε opt is about 5.3 ∼ 9.6. The extracted ε opt are consistent with these experimental results. Leakage characteristics of sputtered PZT capacitors with SRO top electrode plotted in ln(J/E 2 ) -E -1 form. 40.5 nm in black, 120.6 nm in blue, 136 nm in olive and 190 nm in red.

	PZT thickness (nm) 40.5 120.6 136 190	10 -7 × Slope -1.80 ± 0.2 -3.2 ± 0.2 -8.7 ± 0.3 -9.7 ± 0.4	m * /m (1.1 ± 0.1) × 10 -4 (3.6 ± 0.1) × 10 -4 (2.6 ± 0.1) × 10 -3 (3.3 ± 0.1) × 10 -3

Fowler-Nordheim Tunneling

Figure 4.6 plots the leakage current according to Fowler-Nordheim tunneling. From ∼ 650 kV /cm to 800 kV /cm, leakage current is ln(J/E 2 ) proportional to 1/E. By estimating Φ B ≈ 0.5eV , m * are extracted and presented in Table 4.3. As m * is out of the range, FN is excluded from the charge transport mechanism.

Table 4 .

 4 4: εopt of sputtered PZT capacitors extracted according to Frenkel-Pool emission.

	PZT Thickness (nm) Top electrode	10 4 × slope SRO	10 4 × slope Pt	10 4 × slope ITO	εopt SRO	εopt Pt	εopt ITO
	40.5 120.6 136 190	2.7 ± 0.1 6.8 ± 0.1 4.1 ± 0.2 4.2 ± 0.2	5.3 ± 0.2 4.3 ± 0.1 11.3 ± 0.1 5.9 ± 0.1	5.6 ± 0.1 7.1 ± 0.3 4.1 ± 0.2 N/A	129.0 ± 5.0 18.0 ± 0.3 55.0 ± 3.0 47.0 ± 2.0	30.0 ± 1.0 47.0 ± 2.2 6.7 ± 0.1 25.0 ± 0.4	28.0 ± 0.5 4.1 ± 0.2 52.0 ± 2.6 N/A

Table 4 .

 4 5: εopt of sol-gel-derived PZT capacitors extracted according to Schottky emission.

	PZT Thickness (nm)	10 4 × slope	10 4 × slope	10 4 × slope	10 4 × slope	εopt	εopt	εopt	εopt
	Direction of E	forward	reverse	forward	reverse	forward	reverse	forward	reverse
	Top electrode	SRO	SRO	Pt	Pt	SRO	SRO	Pt	Pt
	67	15.3 ± 1.0	22

  Leakage characteristics of sol-gel-derived PZT capacitors with SRO top electrode plotted in ln(J/E 2 ) -E -1 form. Forward I-V is plotted with filled circles and reverse I-V with open circles. 67 nm in black, 133 nm in olive, 200 nm in red and 100 nm in grey.

					E (kV/cm)
			1000	667	500		400	333	286	250
			SRO					FN
		e	-24
		e	-29
	)
	2
	(A/V	e	-34
	2
	J/E
		e	-39
		e	-44
								Sol-gel
			1.0E-8	1.5E-8	2.0E-8		2.5E-8	3.0E-8	3.5E-8	4.0E-8
					E	-1	(m/V)
	Figure 4.17:

Table 4 .

 4 6: εopt of sol-gel-derived PZT capacitors extracted according to Frenkel-Pool emission.capacitors in Figure4.11 except the 100-nm-thick capacitor. SCLC is consistent with the experimental data in the range from ∼500 to 800 kV /cm.

	PZT Thickness (nm)	10 4 × slope	10 4 × slope	10 4 × slope 10 4 × slope	εopt	εopt	εopt	εopt
	Direction of E	forward	reverse	forward	reverse	forward	reverse	forward	reverse
	Top electrode	SRO	SRO	Pt	Pt	SRO	SRO	Pt	Pt
	67 133 200 100	14.5 ± 1.0 10.4 ± 2.0 12.5 ± 2.0 3.8 ± 1.0	20.1 ± 1.0 11.1 ± 2.0 20.2 ± 2.0 3.8 ± 1.0	N/A 14.4 ± 2.0 12.7 ± 1.0 N/A	N/A N/A 20.8 ± 2.0 N/A	4.1 ± 0.3 7.9 ± 1.5 5.5 ± 0.9 60.5 ± 16.0	2.1 ± 0.1 7.0 ± 1.3 1.7 ± 0.2 59.8 ± 16.0	N/A 4.1 ± 0.6 5.3 ± 0.4 2.0 ± 0.2 N/A N/A N/A N/A

Table 5 .

 5 1: Fitting quality and suitable capacitor sizes of four different models.

	Model	I-O	D-C	L-Y-D	P-K
	Limiting factor	DW nucleation	DW	DW & nucleation
	Low (≤ 50 Hz) Middle (50 ∼ 250k Hz) Suitable for (size of capacitor) Fitted range	N/A	√ N/A	√ √ large	√ large and small

1.3. Ferroelectricity

2.1. Film Growth Techniques

The resistivity of 110-nm-thick Pt film is 12 µΩ • cm (Aaltonen et al.

2003).2 In this dissertation, the Miller indices for SRO are based on the pseudo-cubic structure.3 It is difficult to discriminate the tetragonal and cubic phases because it involves only small oxygen atom displacements with RuO 6 octahedrons rotated around SRO [001] direction(Vailionis et al. 2007).

At each temperature, two or three SRO were deposited at the same time, film deposited at same temperature showed similar results.

To investigate the influence of substrate temperature, thick SRO film (∼ 100 nm) were deposited to mainly study the crystalline quality. Substrates were only cleaned by acedone and ethanol, not chemically treated by BOE solution.

According toJiang et al.'s work (1998) on SRO's orientation on vicinal (001) STO, 95% SRO exhibited (001) domain and 5% possessed (010) or (100). In this work, we use (001) as the out-of-plane direction of deposited SRO for simplicity.

Lee et al. (2007) deposited PZT(20/80) on 4-nm-thick SRO coated STO and obtaines square hysteresis loops with remnant polarization of 85 µC/cm 2 .

All three SRO films were deposited at the same time, thickness exhibited ∼1.5 nm variation due to the different location on the substrate holder.

XRR measurement was performed to one of these five films. The thickness variation is within 2 nm according to our previous depositions at the same condition.

Room temperature refers to the condition that the heater is off.

More than 10 topographies were measured at different locations of this PZT film and all showed blured terraces.

Thickness of one spin coating cycle film was measured by XRR. Thickness of multiple spin coating cycles is simply to multiply the number of cycles by 33 nm.

Annealed for 3 h for top electrode instead of 1 min RTA, which was applied to other sol-gel-derived PZT films and sputtered PZT films.

Since the I-V measurement was carried out in a static way and ionic conduction is a transient phenomenon, it was excluded from the transport mechanism.

Providing Φ B is independent of temperature.

SCLC densities in solids are orders of magnitude less than those in vacuum tubes(Scott 2000).

J U = J l + J d ≈ J d , because leakage current in dynamic PUND measurement is relatively much smaller for a good insulated capacitor.

Set a sufficient delay time in I-V measurement can exclude J d .

Different from the variation in J-E curves, C-E curves are much more reproducible for all capacitors with same thickness. So thickness dependence can be investigated here.

The PFM imaging of other sputtered PZT films have not been carried out yet. Retention quality of these sputtered PZT also has not been measured.

He stated that the obtained switching time might be of the set-up, not of the PZT.

[START_REF] Pintilie | Ferroelectrics -Physical Effects[END_REF],Vrejoiu et al. (2006) demonstrated that a high quality epitaxial PZT showed a larger leakage current comparing to defective PZT. They stated that the reason can be the higher mobility in high quality PZT than in the defective film.

For all the capacitors in this thesis, leakage current was quite small in PUND measurement at Emax < 1000 kV /cm, except

40.5-nm-thick sputtered capacitor and 33-nm-thick sol-gel-derived capacitor.

A certain field is appled to the capacitor after a poling precedure. The amount of polarization is calculated by integrating the current. Procedure is repeated with varying the field. A P-E loop can be obtained by connecting the polarization at each field. Detailed procedure inPintilie et al. (2012).

This sample is the same shown in Figure4.34.

Acknowledgements

This work would have remained unfinished without the help of numerous people. I give my thankfulness to all these great people.

First and foremost I would thank Prof. Yves ROBACH. Without his guidance, I couldn't finish this work on time. In the beginning, he guided me into the oxide field. And at the end, he showed me how to develop a logical well-structured thesis. Through the research, he is always helpful and of great patience.

Abbreviations

1T-1C one transistor and one capacitor 2T-2C

Influence of Top Electrode

In chapter 4, the P-E loops of sputtered and sol-gel-derived PZT capacitors with three different top electrodes (SRO, Pt, ITO) have been presented (see Figures 4.29,4.31 and 4.33) It should be noted that for the capacitors with symmetric stack structure, SRO/PZT/SRO, the SRO above and beneath are not of the same quality. The bottom SRO was deposited at around 620 • C on STO substrate. It was crystalline without post annealing. The top SRO was deposited at room temperature on relatively rougher PZT layer. An additional post annealing was required to crystallize the amorphous top SRO and XRD result showed the amount of crystalline SRO on top was much less compared to that of the bottom SRO.

Capacitors with ITO top electrode always showed a much bigger E c (see Figure 4.31), which was unfavorable. It should be noted that ITO was annealed at 250 • C in N 2 during 1 min by RTA. SRO and Pt top electrodes were annealed in O 2 at 650 • C for 1 min by RTA. This difference may also cause the broadening of its P-E loop.

Influence of Post Annealing

To verify the influence of post annealing, two capacitors, one with SRO top electrode and another with Pt top electrode, part of both experienced the RTA at 650 • C in O 2 and another part of both experienced the RTA, which was designed for ITO top electrode. The PUND results and ε ′ r are shown in Figure 5.26. For capacitors, both with SRO top electrode and with Pt top electrode, the annealing at 250 • C in N 2 broadened the PUND loop. After both annealing procedures, P r were similar and the maximum value of ε ′ r was smaller in 250 • C N 2 RTA, which was similar to the reduced ε ′ r of capacitors with ITO top electrode (see Figure 4.26).

We noticed that the the different annealing procedure showed different effect in imprint. For capacitors with SRO top electrode, P-E loop was always symmetric after 2nd annealing in O 2 . But when the annealing was performed in N 2 , the imprint was so great that the domains strongly preferred to switch "down" when external field was removed. A deformed PUND loop was obtained (blue dash in Figure 5.26). By applying a positive offset voltage (mean value of the two coercive voltages) to the whole

Conclusion and Perspectives

In this thesis, PZT(52/48) capacitors grown by two methods, sputtering and sol-gel, were studied. For each method, the thickness of capacitors varied from sub-50 nm to ∼ 200 nm to investigate the thickness effect and find out the thinnest workable PZT capacitor. In order to investigate the influence of top electrode, three different conductive materials (SRO, Pt and ITO) were employed.

Initial work was on the optimization of sputtering SRO as bottom electrode. By varying deposition conditions, a set of parameters were obtained for growing smooth (RMS < 1.0 nm) SRO film with high crystallinity and low mosaicity (∼ 0.1°). In order to grow epitaxial SRO layer by layer on vicinal STO, which offers flat interface with subsequent PZT film and reduces defect densities, we further lowered the plasma voltage and introduced an interval in the middle of sputtering process. In this condition, SRO layer of more than 30 nm with terraces of single unit cell in height was achieved. In the next growth stage, by optimizing deposition conditions, epitaxial PZT films were achieved by both methods. Smooth surface (RMS < 0.8 nm) were obtained for all films and the mosaicity of sputtered PZT films were about 1.1°, which was about 25% bigger than that of sol-gel-derived films. By lowering the plasma voltage and posing an interval into the middle of sputtering process, a 190-nm-thick PZT film (RMS = 0.38) even exhibited terraces of single unit cell in height.

After the fabrication process, electrical properties of these capacitors were investigated through current-voltage (I-V), capacitance-voltage (C-V) and hysteresis loop measurements (PUND) and piezoresponse force microscopy (PFM). For capacitors with a PZT layer of 100 ∼ 200 nm, which was well insulated, the amount of leakage did not show thickness dependence. By fitting various charge transport models to the leakage data, we found that: at low field range, leakage was due to ohmic conduction for both types of capacitors; at higher field range, the leakage mechanisms were different for the capacitors made by different routes. Due to the complexity of leakage current in ferroelectrics, two mechanisms fitted this field range for both types of capacitors. Top electrode seemed to have very small influence on leakage current. The thickness of dead layer for all capacitors was found to be less than 3 nm. Maximum relative permittivity ε ′ r of all capacitors were between 600 and 1300, which were compatible with previous reports.

P r of capacitors with a thickness of 100 ∼ 200 nm was between 30 and 40 µC/cm 2 , which were in great agreement with reported results. Thicker capacitors showed better saturation quality than thinner ones. For PZT with a thickness of around 200 nm, P r exhibited a high saturation quality for both types of capacitors. PFM results revealed that 200-nm-thick sol-gel-derived PZT showed better piezoelectricity