L Aigouy

G Tessier

M Mortier

B Charlot

A SCANNING FLUORESCENT PROBE FOR LOCAL TEMPERATURE IMAGING OF MICROELECTRONIC CIRCUITS

A fluorescent particle settled at the extremity of an atomic force microscope tip is used as a scanning temperature sensor. Since fluorescence is an effect that depends on temperature, by collecting the amount on light emitted by the particle as a function of its position on a sample, we are able to map the heat distribution on its surface. To validate the technique, we have imaged the heating of a stripe resistor.

INTRODUCTION

An important and useful application of scanning probe microscopy concerns the study of thermal effects on inhomogeneous materials or microelectronic circuits [START_REF] Pollock | Micro-thermal analysis: techniques and applications[END_REF]. These effects are for example linked to the determination of intrinsic physical parameters of materials such as their thermal conductivity [START_REF] Ruiz | Determination of the thermal conductivity of diamond-like nanocomposite films using a scanning thermal microscope[END_REF] or to the mapping of the thermal conductivity on phase-separated compounds and artificial structures [START_REF] Gorbunov | Probing surface microthermal properties by scanning thermal microscopy[END_REF][START_REF] Lefèvre | 3ω-scanning thermal microscope[END_REF]. Another technological issue is related to the visualization of hot zones in operating microelectronic circuits [START_REF] Mills | Scanning thermal microscopy using batch fabricated thermocouple probes[END_REF]. The visualization of hot zones is an important application since it can allow to determine the position of possible defects and weak points as well as to find out how heat can be dissipated in the circuits.

Until now, scanning thermal probes have mainly used two main types of sensors located at the extremity of atomic force microscope (AFM) tips: a thermocouple or a resistive wire. Thermocouple-based probes are fabricated by several technological steps in clean rooms [START_REF] Mills | Scanning thermal microscopy using batch fabricated thermocouple probes[END_REF]. Two metallic stripes are generally evaporated and connected at the end of the tip to form a thermocouple junction. They allow the determination of the local temperature of a sample with a submicron lateral resolution [START_REF] Shi | Scanning thermal microscopy of carbon nanotubes using batch-fabricated probes[END_REF]. Resistive probes [START_REF] Lefèvre | 3ω-scanning thermal microscope[END_REF][START_REF] Royall | Identification of crystalline and amorphous regions in low molecular weight materials using microthermal analysis[END_REF] are formed by a metallic wire (a platinum rhodium alloy for example) that forms the tip of the AFM. Its section is reduced to the micrometer range to allow the measurement of topographies as well as thermal effects. The temperature variations and heat transfers between the tip and the sample surface are determined by monitoring the variations of the filament resistance. Such a probe has also demonstrated a lateral resolution much smaller than the micrometer [START_REF] Pollock | Micro-thermal analysis: techniques and applications[END_REF][START_REF] Lefèvre | 3ω-scanning thermal microscope[END_REF].

Recently, a technique that employs a layer of europium-based fluorescent dyes spin-coated on a microheater has been developed to monitor temperature variations of the device [START_REF] Van Keuren | Temperature profiles of microheaters using fluorescence microthermal imaging[END_REF]. The fluorescent dyes, spread all over the circuit, emit less light on hot zones than on cold ones allowing to map the temperature distribution on the sample.

In this communication, we will present a technique based on a similar effect, but that employs a single fluorescent particle as a temperature sensor. In our case, the fluorescent fragment is settled at the extremity of an AFM tip and behaves like a scanning thermal probe. By monitoring the fluorescence intensity variations of the particle as a function of its position on the surface of a microelectronic circuit, we are able to determine the absolute temperature of the particle and therefore of the zone of the device it is in contact with.

THE TEMPERATURE DETERMINATION PROCESS

The fluorescent particles are glass ceramic fragments that contain erbium and ytterbium ions [START_REF] Aigouy | Local optical imaging of nanoholes using a single fluorescent rare-earthdoped glass particle as a probe[END_REF]. A scanning electron micrograph of such a particle settled at the extremity of an AFM tip is given on Fig. 1. The particle is glued at the tip end using nanomanipulators [START_REF] Aigouy | Fabrication and characterization of fluorescent rareearth-doped glass-particle-based tips for near-field optical imaging applications[END_REF] with a temperature resistant, UV curable, polymer glue. The particle is excited using a 980 nm laser diode (by a 2photon absorption process). It emits light at different wavelengths: in the visible, fluorescence occurs at 520nm, 550nm and 670nm. The excited energy levels ( 2 H 11/2 and 4 S 3/2 ) involving the 520nm and 550nm lines have the peculiarity of being in thermal equilibrium. This means that the relative population of the two levels depends on temperature.

The relative area of the two fluorescence peaks are therefore linked by an exponential law that directly depends on temperature [START_REF] Alencar | Er 3+ -doped BaTiO 3 nanocrystals for thermometry: influence of nanoenvironment on the sensitivity of a fluorescence-based temperature sensor[END_REF] :

β α + - ≅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ T I I 1 2 ln ( 1
)
where I 2 and I 1 are the area of the peaks located at 520nm and 550nm, α and β are coefficients and T is the temperature. When temperature increases, the peak located at 550nm diminishes more rapidly than the one located at 520nm (see Fig. 2). Therefore, it is possible to determine the temperature of the particle by measuring the amount of fluorescence emitted at 520nm and 550nm. Since the particle is in contact with a sample during a scan, its temperature reflects the temperature of its surface.

The calibration of the coefficients α and β is performed by measuring the fluorescence spectrum of a micron-sized particle deposited on a substrate heated at a known temperature. The thermal conductivity of the particle is 0.8 W.m -1 .K -1 .

THE EXPERIMENTAL SET-UP

The experimental setup is a homemade AFM combined with an optical microscope able to detect the fluorescence emitted by the particle with a high sensitivity. It is sketched on Fig. 3. A 980nm laser diode is focused on the tip extremity and the sample surface. The diode is internally modulated at around 620Hz. Two different interferential filters are placed in front of two photomultiplier tubes (PMT): one is centered at 520nm and the other one at 550nm. The bandwidth of these filters is 10nm. The fluorescence of the peaks can then be measured independently and simultaneously when the tip is scanned on the surface. The fluorescence of the fragment is collected with a high numerical aperture objective followed by a beam splitter that sends the emitted photons towards the two PMTs. Afterwards, the signals are detected by two lock-in amplifiers synchronized to the laser diode modulation frequency and are sent to a computer for recording and processing. The tip is scanned in intermittent contact on the sample surface, in the tapping mode. Its oscillation frequency is around 5kHz (around ten times higher than the fluorescence modulation frequency) and its amplitude is around 10nm.

In order to validate our experimental technique, an operating microelectronic circuit seemed to be a good candidate. Three images are acquired. The first one is the topography of the chip. The second and the third ones are the fluorescence images at the two different wavelengths. As it can be seen in eq. ( 1), the ratio of the two fluorescence images permits to determine if some zones are hotter than others.

VISUALIZING THE HEATING OF AN OPERATING MICROELECTRONIC CIRCUIT

The microelectronic circuit we have tested is a polysilicon resistor stripe implemented on a standard 0.8µm CMOS process. The stripe has a width of 20µm and a height of approximately 600nm. The experiment has been performed at two different DC voltages. The current flowing in the device is therefore constant. We first describe the experimental procedure used to visualize the temperature heating. Afterwards, we will present the experimental results and discuss on the uncertainties and the different factors that can influence the measurements.

Description of the experimental procedure

First, measurements have been achieved when no current is flowing through the resistor. This allows to have a reference for the optical contrast at room temperature. We can expect that two zones made of a different material (for instance, the resistor and the substrate) will have a different optical image at the two wavelengths. Indeed, the reflection coefficient of both the exciting laser beam and the fluorescence lines will not be the same on the resistor and on the substrate. Therefore, even if the temperature of the whole system is the same, the ratio of the two fluorescence images will be different on different materials.

For the second scan, a DC voltage of 25V is applied to the stripe generating a constant current of around 50mA. Under this high current, the stripe is heating and the heat is spreading all around the substrate.

The ratio of the two fluorescence images and its comparison with the reference one at room temperature allows to see if the sample has heated and where. The results are shown on Fig. 4.

Experimental results

The optical image (b) corresponds to the ratio of the fluorescence signals of the particle (I520 / I550) when no current is flowing. The temperature is the same everywhere. Since the polysilicon resistor and the silicon substrate have different optical properties, they appear contrasted on this image. The resistor appears darker than the substrate. The values of the scale bar indicated on the right are arbitrary units.

The optical image (d) corresponds to the same ratio but a current of around 50mA is flowing through the resistor (V=25volts). The stripe is still clearly visible but some features have appeared. First, on the stripe, a gray, curved zone is visible. It corresponds to a hot zone through which the majority of the electrons are probably passing. Second, in the middle, a bright zone is also dominating the image. This area corresponds to a hot zone of the substrate which is created by heat diffusion from the elbow of the stripe nearby. Note that, if we look at the scale bar of Fig 4d, the values are much higher than in the image obtained at room temperature (Fig. 4b), indicating that the whole scanned area has heated. A rough estimation, not detailed here, indicates that the temperature is approximately equal to 70°C on the lower part of the substrate and 90°C in its hot area of the middle. On the stripe, the temperature also varies from around 80°C in the 'cold' zone to 100°C in the hot one. The time necessary to perform a thermal image is around half an hour.

Discussion

The first point we would like to discuss is the influence of the tip on the measurement. Does the tip modify the real temperature of the device? As can be seen on Fig. 1, the size of the particle is smaller than one micrometer and the tip that holds it is very sharp. The point of contact with the surface is therefore very small. Besides, it is intermittent since the tip is oscillating on the surface in the tapping mode. We do not think that the tip perturbs enormously the temperature and the operation of the device, at least no more than most other scanning probe microscope tips that have a spatial extension much larger above the surface.

The other question we can ask is linked to the signal measured by the tip. How close is it to the real temperature of the surface? Indeed, since the tip is in intermittent contact with the sample, the heat transfer mechanisms are complicated. The oscillation amplitude of the tip is around 10nm. During its movement, the time the tip remains in direct contact with the surface depends on the offset used for the feedback mechanism. By varying this parameter and by changing the oscillation amplitude, we do not have observed a noticeable variation of the signals. Besides, almost no significant difference could be observed when the tip was in contact with the surface and when it was situated at several hundreds of nanometers from it. This shows that the heat transfer mechanism in air was important in this experiment. This is not surprising since the size of the device is significantly larger than the tip itself. A different behavior would probably be observed on submicron devices or structures like carbon nanotubes for which air heating is much smaller due to their reduced spatial extension.

Regarding the spatial resolution of the measurements, we can expect it to be of the same order as the particle size in the best case. In principle, a 100nm resolution could be obtained for a 100nm sized particle. Since the tip is very sharp, indirect heating from its far zones and from the cantilever is small. For the device we have studied, it is not possible to determine the real lateral resolution of the method since the heat is diffusing over distances much larger than the particle size. Experiments carried out on smaller circuits will soon be performed.

CONCLUSION

The technique we have developed allows to visualize the hot zones of operating microelectronic circuits. It is based on the measurement of the fluorescence of a submicronsized particle settled at the extremity of an AFM tip. The method permits the determination of the absolute temperature of the device. We are currently performing experiments to determine the limits of the technique in terms of lateral resolution and sensitivity. In particular, we are studying well-defined resistor with integrated diodes which allow the precise temperature calibration of the technique.

L

  . Aigouy, G. Tessier, M. Mortier and B. Charlot A SCANNING FLUORESCENT PROBE FOR LOCAL TEMPERATURE IMAGING ...

Fig. 1 :

 1 Fig. 1 : Scanning electron micrograph of a fluorescent particle glued at the end of an AFM tip.

Fig. 2 :

 2 Fig. 2 : Dependence of the particle fluorescence as a function of temperature.

Fig. 3 :

 3 Fig. 3 : Experimental set-up.

Fig. 4 :

 4 Fig. 4: (a) Topography of the stripe and (b) ratio of the two fluorescence images (I520 / I550) when no current is flowing through the resistor ; (c) topography of the stripe and (d) ratio of the two fluorescence images when a voltage of about 25V is applied. The fluorescence images have been treated using a 3x3 median filter to eliminate noise.

 TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4

ACKNOWLEDGMENTS

The authors strongly thank D. Fournier for stimulating and motivating discussions.


S Pavageau

G Tessier

C Filloy

G Jerosolimski

D Fournier

M L Polignano

I Mica

S Cassette

R Aubry

O Durand

THERMAL IMAGING OF Si, GaAs AND GaN -BASED DEVICES WITHIN THE MICROTHERM PROJECT

Within the european project Microtherm, we have developed a CCD-based thermoreflectance system which delivers thermal images of working integrated circuits with high spatial and thermal resolutions (down to 350 nm and 0.1 K respectively). We illustrate the performances of this set-up on several classes of semiconductor devices including high power transistors and transistor arrays in silicon, gallium arsenide and gallium nitride technologies.

INTRODUCTION

Temperature is one of the key physical parameters which has to be addressed in the field of reliability of electronic devices. This concerns various domains of the semiconductor industry which include both high power devices (mainly GaAs, SiC, GaN and Si technologies) mostly for the telecommunication, aeronautic and aerospace markets but also the microprocessor industry (Silicon exclusively) where the dramatic effect of size shrinking and transistor density has made the heating problem one of the key points of their reliability.

The MICROTHERM project addresses two aspects in the field of thermal management for electronic devices: -Failure analysis: The aim is to make high resolution thermal imaging in order to easily and precisely locate over-heated areas (hot spots) on a defective device. -Reliability Analysis: Here the requirements are to precisely measure the temperature of the active part of a device in order to optimise its working point and life-time and to correctly size the associated cooling system. For this purpose, we have developed a CCD-based Thermal-Photoreflectance system which is able to deliver high resolution images of working integrated circuits. The operation of the integrated circuit itself produces local heat sources modulated at the working frequency f of the device. The circuit is illuminated by a monochromatic visible light. Since surface reflectivity is temperature dependent, the reflected light bears a small modulation at the frequency f, with an amplitude ∆R=∆T.dR/dT. This modulation can be detected with a lock in technique, or its spatially multiplexed equivalent if the CCD camera is triggered at the frequency 4f. The thermal information can then be retrieved from these optical images by a numerical processing.

OPTIMIZATION OF THE ILLUMINATION

The choice of the illumination wavelength is a very important step in the measurement process. It is essential to choose a wavelength for which dR/dT is large to obtain a thermal signal. The optimal wavelength can be very [START_REF] Tessier | Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials[END_REF] drastically modify R(λ) and dR/dT(λ). The setup shown in figure 2 was specially designed to measure these coefficients and therefore enable a rapid choice of the optimal illumination wavelength. In this experiment, a slit is introduced in the Köhler illuminator of the microscope. This line is imaged on the sample surfaced and the reflected light is dispersed by a transmission grating. The prism has a low dispersion compared to that of the grating. Its main role is to deflect the first order of diffraction, which would otherwise not reach the CCD, towards the optical axis. For each material studied here, we have conducted this kind of sensitivity study and chosen an optimal wavelength to conduct thermoreflectance measurements.

In the examples shown below, Si-based transistors (figure 1) were studied at λ=518 nm, whereas GaAs transistors(figure 2) had an optimal thermoreflectance wavelength around 616 nm.

DEFECTS IN TRANSISTOR ARRAYS (ST)

Crystal defects are very harmful in present silicon devices when responsible for a source-to-drain junction piping and hence for a transistor leakage current. In particular, the geometry of the patterns of integrated transistors is found to be a key issue in the formation of crystal defects, both in experiments and in numerical simulations [3, [4]. These effects are difficult to characterise with existing methods. Photoemission spectra can reveal such defects, but the method is relatively slow and lacks sensitivity.

Leakage can induce high current densities and therefore localized heating, which can remain highly confined due to the thermally insulating dielectric environment of some transistor features. Therefore, thermal methods can be an interesting alternative for the study and localization of these defects. Two transistor arrays including patterns critical for defect formation have been constructed and then characterised using our thermoreflectance microscope. However, since this technique measures heating associated to defects, it does not discriminate dielectric breakdown and actual source-to-drain leakage. Both types of defects, buried This is close to the ultimate resolution limit imposed by diffraction at approximately λ/2N.A.=324 nm, where λ=518 nm is the illumination wavelength and N.A. is the numerical aperture of the microscope objective (0.8 in our case). These two parameters set the resolution of the system, provided that the optics and the pixel size of the camera are sufficient to avoid further alteration.

In order to understand the physical processes that occurred in these samples and validate these measurements, post analyses (delayering) were conducted at ST Microelectronics. It appears that no breakdown occurred in non defective structures, as expected. In defective structures, two different phenomena appear to have caused the heating measured here: In one case, source to drain leakage was indeed observed. Another sample showed an oxide breakdown, possibly caused by static discharge, while a third sample had suffered from both effects. Since all these phenomena yield similar measurements, it is difficult to discriminate them. New structures with thicker oxide layers, which should be less subject to oxide breakdowns, have been made and are being characterised by thermoreflectance. After calibration (dR/dT=7.10 -4 K -1 ), the colorbar gives the temperature on GaAs in K. The heating is clearly visible in the source-drain region.

HIGH POWER TRANSISTORS (THALES)

In high power transistors, thermal management problems are crucial. New materials with better thermal properties, associated to thick metallic layers enabling a better evacuation of heat have improved the performances of these transistors. The source-to-drain recess is a specially critical region where most of the heating is produced. However, since the metal layers are very thick, this region is actually a relatively deep (several tens of microns) and narrow (typically 1 to 10 µm wide) recess. Scanning probe measurements are impossible with conventional probes since they cannot reach the bottom of this recess. One of the purposes of Microtherm was to develop probes for this purpose [START_REF] Dobson | Microfabricated temperature standard based on Johnson noise measurement for the calibration of micro-and nano-thermometers[END_REF]. Optical measurements are also difficult since artefacts and resolution degradation occur in this confined geometry. We have measured the temperature of the active regions of these transistors using the two modes described in the inset of figure 1. The image of figure 5 was obtained on a transistor containing 9 intertwined gate, drain and source fingers, with a low frequency modulation of the drain voltage. At F=7.5 Hz, the temperature which is obtained is very similar to that of a device operating in DC regime. Figure 6 shows a simpler transistor with only 2 active regions. In this case, V drain was modulated at a high frequency f=500MHz, sent in periodic bursts with a repetition frequency of F=7.5Hz. The photoreflectance is synchronized with this low repetition frequency, since the sampling rate of the camera is chosen at 4F=30 Hz. In this case, the temperature variation which is measured is not the high frequency component which is actually very small at frequencies above a few 10 MHz as shown in earlier works [START_REF] Filloy | The contribution of thermoreflectance to high resolution thermal mapping[END_REF]. We measure a temperature variation associated to the low frequency modulation F, which is therefore close to the DC temperature component of a circuit working at high frequency F. Similar experiments were conducted at frequencies up to 2GHz, but there is no practical limit to this frequency, since it is relatively easy to apply a low frequency chopping to any high frequency signal.

Pavageau, Tessier, Filloy, Jerosolimski, Fournier, Polignano, Mica, Cassette, Aubry, Durand Thermal imaging of Si, GaAs and GaN -based devices within the Microtherm project

ACKNOWLEDGMENT

This work was funded by the European contract MICROTHERM.

Figure 1 :

 1 Figure 1: Experimental setup for thermal imaging by thermoreflectance. The inset shows the two types of modulation used to power the electronic circuit in these experiments: either a simple low frequency modulation (F), or a high frequency (f) signal modulated by a low frequency carrier (F).

Figure 2 :

 2 Figure 2 : Set up for the measurement of the wavelength dependence of dR/dT(λ).

Figure 3 :

 3 Figure 3:Thermoreflectance image of a non defective structure observed under a x50 objective (50x50 µm).

Figure 4 :

 4 Figure 4: defective structure (135x135 µm). Inset : zoom (42x42 µm) on an image obtained on the same sample 20 minutes later : the shape of the hot spot has changed due to intense heating and source-to-drain leakage. Resolution: 350 nm (FWHM width of the smallest details). These active regions are 6 µm below the Si 3 N 4 surface of the sample.

  , Filloy, Jerosolimski, Fournier, Polignano, Mica, Cassette, Aubry, Durand Thermal imaging of Si, GaAs and GaN -based devices within the Microtherm project under 6 µm of intermetal and encapsulation dielectric were clearly detected with a spatial resolution of 350 nm.

Figure 5 :

 5 Figure5: Thermal image of a GaAs power transistor (Thales) with V gate =V source =0 and V drain modulated between 0 and 2V. After calibration (dR/dT=7.10 -4 K -1 ), the colorbar gives the temperature on GaAs in K. The heating is clearly visible in the source-drain region.

Figure 6 :

 6 Figure 6 : Thermal image of a GaAs transistor (Thales) obtained with a high frequency V drain signal (f=500 MHz), modulated intermittently at f=2.5 Hz.

 TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4


Pierre-Olivier Chapuis

Jean-Jacques Greffet

Karl Joulain

Sebastian Volz

RAREFIED GAS HEAT TRANSFER BETWEEN A NANOMETRIC TIP AND A SAMPLE

We study the heat transfer through air between a nanometric tip and a sample. Using a Monte-Carlo simulation, we show that heat flux densities reach 40 MW.m -2 on the surface under the tip. The modeling shows a spatial resolution of 40 nm for a tip size of the same order. This proves the relevance of using quasiballistic conduction through air as heat transfer channel in applications such as thermally assisted data storage, scanning thermal microscopy and any temperature control techniques out of contact where a good heat localization is needed.

INTRODUCTION

Understanding the heat transfer between a hot tip and a substrate is a key issue in data storage [1], scanning thermal microscopy (SThM) [2][3] and any nanometer scale temperature control. It involves heat conduction at mechanical contact, in the water meniscus as well as in air [4]. For tip temperatures higher than 100°C, the water film contribution disappears and recent works prove that conduction in air becomes predominant [4] [START_REF] Lefèvre | Nanoscale Heat Transfer at Contact Between a Hot Tip and a Substrate[END_REF] in comparison to the heat transfer through the constrictions of the mechanical contact. The tip-sample contact creates a high local flux density just below the tip but the air conduction over microns around the contact point [START_REF] Lefèvre | Nanoscale Heat Transfer at Contact Between a Hot Tip and a Substrate[END_REF] spreads the heat flux reducing the expected resolution. The scanning thermal profiler invented by Williams and Wickramasinghe [2] consists in a hot tip at a nanometric distance of the sample. The size of the tips used in scanning thermal microscopy was quite large until now, as for instance the Wollaston wire tip, which is micrometric [3]. But now true nanometer-scale resolved heat sources are realistic [START_REF] Weaver | communication at the QMTIA05 (Quantitative Micro Thermal Imaging and Analysis) workshop[END_REF]. As we will see, the heat flux transferred through air from the tip to the sample then depends on the sample temperature on a small nanoscale area.

GOAL

We will show that a 40 nm thermal probe can efficiently exchange heat with a sample with a spatial resolution on the order of 40 nm. Different methods as Joule [8] or Peltier heating [4] are possible to heat such a probe. The spatial resolution then depends on the heat spreading in air. The phenomenon cannot be modeled by classical Fourier diffusion because the air mean free path (MFP) is on the order of the average distance between the tip and the sample. It follows that the Fourier's law is not valid. Pure ballistic transfer is neither valid because of the extension of the heat flux on the sample surface: this problem has to be solved in the intermediate regime. 3D effects have also to be included if we want to see the effects of heating a non-symmetric tip. We therefore use a Monte-Carlo approach associated with the linear response theory in order to directly solve space and time dependent problems.

MODELING

P.-O. Chapuis, J.-J. Greffet, K. Joulain and S. Volz

Rarefied gas heat transfer between a nanometric tip and a sample

where m is the diatomic molecular mass. n tip is the number of molecules per unit volume derived from the condition of null molecular flux at the tip surface.

Geometry

We consider the extremity of a pyramidal AFM tip with a square base of l x l with l=40 nm and a height h=20 nm as shown by Figure 1. Heat confinement remains realistic since heat diffusion in the tip generates rapid temperature decay over a few tens of nanometers. Note that the use of specially designed materials such as insulators would be necessary. The distance d between the tip and the surface is in the nanometric range.

Shock computation

The gas is at the ambient temperature T a . We neglect the increase of T a due to the presence of the tip. Thus, we consider that the incident molecules meet molecules coming from the sample surface at T sample or molecules of the gas coming from a far area. Note that T a is here equal to T sample . A molecule leaving the tip flies until undergoing a collision with another molecule or with the sample surface. The path length between two collisions is computed according to an exponential law with a characteristic decay length given by the MFP

Linear response theory

The basis of our model consists in calculating the time evolution of the local heat flux on the sample ( ) q τ is then given by ( )

, ,
2 1 2 2 pot R n π Λ =
which is 55 nm at atmospheric pressure for nitrogen. R pot =0.2075 nm [START_REF] Bird | Molecular Gas Dynamics and the Direct Simulation of Gas Flows[END_REF] denotes its molecular radius.

( ) ( ) ( ) ( ) 0 , , , t R tip th th tip tip m q r t q r t T S q d τ τ τ = - ∫ i τ
The velocities of the collision partners are computed with Boltzmann's law taken at ambient temperature T a . It allows us to define a new velocity and a new direction after the collision for the test-molecule according to the Very Hard Sphere model [START_REF] Bird | Molecular Gas Dynamics and the Direct Simulation of Gas Flows[END_REF]. A molecule may undergo several collisions before it reaches the sample surface. Hot molecules that remain in the gas are discarded and the contribution of collision partners to the tip-sample heat flux is neglected. Finally, the thermal flux received by an element δx.δy of the surface is:

where R th q can be assimilated to a susceptibility. S tip is the area of the heated part of the tip. It is important to see that this model allows us to calculate the heat flux received by the sample when the tip temperature is modified. A realistic case where the tip temperature raises can as a consequence be simulated.

( ) ( )

, , , R th tip E r t q r t T

x y tN δ δ δ =

Kinetic Monte-Carlo approach

where N is the number of emitted molecules and E(r,t) is the net energy transferred by the molecules emitted by the tip and falling in the area δx .δy during the time interval δ t. Each molecule arrives with an energy determined by the Monte-Carlo simulation and leaves the sample area with the sample energy depending on T sample . This energy is the one of a molecule in the air taken at equilibrium at temperature T sample. . Thus:

The susceptibility is computed using a Monte-Carlo approach. The heat transfer is due to air molecules, which are in first approximation nitrogen molecules. A molecule is considered to carry the translational and rotational energy 5 2 B k T where k B is the Boltzmann's constant (reference [START_REF]The accommodation factor is bigger than α=0[END_REF]). Thus, we do not consider the degree of freedom due to internal vibrations of the diatomic molecule at our temperatures. A cold molecule is heated when impacting the hot tip and then flies with a velocity chosen according to a Boltzmann's law at T tip . The emission laws for velocity v and direction described by the cylindrical angles θ and ϕ are derived from the equilibrium molecular flux leaving the probe at T tip :

( ) 2 , 2 2 i B sample i x y mv E r t k T δ δ ∈   = -     ∑
where the index i denotes the incident molecules falling in the δx .δy area. We therefore assume in the calculations that the kinetic energy is fully absorbed at the air-sample interface. Those molecules are considered to leave the tip at the same initial time and the arrival time t is given by their flight time. The calculated susceptibility is a statistical average over N= 10 8 molecules. What is important to notice here is that the heat flux depends on the fixed sample surface T sample .

B tip mv k T tip m t i p B tip v m q n v e d k T d d π π θ ϕ π θ θ θ ϕ - ∞ = = =   =       × ∫ ∫ ∫ v  TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4
P.-O. Chapuis, J.-J. Greffet, K. Joulain and S. Volz

Rarefied gas heat transfer between a nanometric tip and a sample

Results for a tip temperature of 800 K and a sample at T sample =T a =300 K show that heat flux densities reach 40 MW.m -2 on the surface under the tip (see Figure 3). Taking into account that the energy is not completely fully absorbed [START_REF]The accommodation factor is bigger than α=0[END_REF] does not change the results significantly. The imprint of the tip geometry is lost on the heat flux mapping when the height h is higher then 10 nm (case (b)). The decrease of the heat flux density along a section is also less strong when the tip is retracting as shown on Figure 4. The results confirm a spatial resolution on the order of 35 nm when the tip is really close to the sample (insert of Figure 4). This spatial resolution is linked to the size of the hot part of the tip. It should be in consequence the best resolution that an SThM with such a tip could reach.

RESULTS

Levels of heat flux on the sample depend on one hand on the tip-sample distance and on the other hand on heat losses during the molecules collisions. We have tried here to consider the consequences of these two different effects. As shown in Figure 2, the collisions are responsible for the loss of 70 % of the power of the pure ballistic case when the height d is equal to the mean free path of our simulation (near 60 nm).

CONCLUSIONS

Finally, it seems that heat transfer through the air at distances on the order of 10 nm is sufficient to allow noncontact scanning thermal microscopy. We have found the relation between the heat flux transferred by a nanometerscale hot tip and the temperature of the sample that it is thermally probing. A first step in the description of nanometer-scale resolved thermal probes has been achieved. The detection of hot spots in electronic devices would be surely improved if such probes were used.

ACKNOWLEDGEMENTS

Figure 1 .

 1 Figure 1. A skip of the tip. Typical lengths used are l=40 nm and h=20 nm. The distance d is in the nanometric range.

  due to an impulse of molecular flux leaving the tip. The heat flux response q r

Figure 2 .

 2 Figure 2. Full power on the sample normalized by the pure ballistic flux when the tip is retracted. This illustrates the decay of the flux due to collisions.

Figure 4 .

 4 Figure 4. Heat flux density along the section shown in figure 3. Dashed lines show results when collisions are not taken into account. The inset shows the normalized heat flux density.

Figure 3 .

 3 Figure 3. Heat flux density on the substrate. (a) d=0 nm



  TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4

 TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4


S Grauby
email: s.grauby@cpmoh.u-bordeaux1.fr

A Salhi

L-D Patino Lopez

S Dilhaire

B Charlot

W Claeys

B Cretin

S Gomes

G Tessier

N Trannoy

P Vairac

S Volz

Qualitative Temperature Variation Imaging by Thermoreflectance and SThM Techniques

We have studied temperature variations on two dissipative structures with two different techniques. The dissipative structures are constituted of thin (0.35µm) dissipative resistors, the distance between two resistors being equal to 0.8 or 10 µm. On one hand, we have used a thermoreflectance imaging technique which is a wellknown non contact optical method to evaluate temperature variations but whose spatial resolution is limited by diffraction. On the other hand, we have used a Scanning Thermal Microscope (SThM) to study the thermal behaviour of these small dissipative structures. We compare qualitative results obtained by both methods and we present their advantages and limitations for temperature measurements on microelectronic devices.

INTRODUCTION

As integration density of microelectronic circuits goes increasing, there is a need for methods able to measure local temperature variations at submicronic scales.

As a consequence, well-known methods such as infrared imaging [START_REF] Grecki | Application of computer-based thermography to thermal measurements of integrated circuits and power devices[END_REF], liquid crystals or thermocouple measurements [START_REF] Tessier | Quantitative thermal imaging by synchronous thermoreflectance with optimized illumination wavelengths[END_REF] are not adapted to this kind of samples as they offer a bad spatial resolution (5 to 10 µm minimum) regarding the device dimensions. Moreover, a thermocouple implies a contact with the sample that can damage it or disrupt its functioning.

Among the optical methods for submicronic thermal mapping, thermoreflectance [START_REF] Dilhaire | Laser diode COFD analysis by thermoreflectance microscopy[END_REF][START_REF] Bardon | Thermal Management of Electronic Systems III-Eurotherm[END_REF][START_REF] Opsal | Thermal-wave detection and thin-film thickness measurements with laser beam deflection[END_REF] is a useful non contact and non invasive method which presents a good spatial resolution as limited by diffraction to the order of magnitude of the illuminating wavelength.

Nevertheless, when studying structures as thin as a few hundreds nanometers, Scanning Thermal Microscope (STHM) seems the only technique able to reach temperature variation measurements at this scale.

In this paper, we have used the last two methods to qualitatively study the temperature variations on the same samples and we propose to compare their performances.

SAMPLE UNDER TEST

We have studied two kinds of structures constituted by a series of 9 parallel strips resistors which serve themselves as a heat source. Indeed, supplying them with a current, they are submitted to a variation of temperature. The width of each resistor is 0.35 µm. They are covered by a passivation layer made of silicon oxide. The difference between both structures is the spacing between the resistors. In the first one (figure 1), the distance between two consecutive resistors is 10 µm whereas it is only 0.8 µm in the second one (figure 2). These structures are part of a whole test device designed for the evaluation of various temperature measurement techniques; the first one is named C5 while the second one is named C3. The die was implemented using 0.35µm CMOS technology.

THERMOREFLECTANCE MEASUREMENTS

Reflected light coming from the surface of a sample carries information about the thermomechanical behavior of the device under test via parameters such as amplitude, phase, polarization etc... of light. Thermoreflectance is a useful non contact technique to measure temperature variations of a device submitted to a current. Indeed, when an electrical current supplies an electronic device, the latter is submitted to a temperature variation ∆T, which creates a reflectivity variation ∆R at the device surface:

1 R R T T R R T κ ∆ ∂ = ∆ = ∆ ∂ ( 1
)
where R is the sample mean reflectivity and κ is the thermoreflectance coefficient depending on the nature of the material, on the passivation layer thickness [START_REF] Quintard | Laser beam thermography of circuits in the particular case of passivated semiconductors[END_REF], on the light wavelength [START_REF] Heller | Temperature dependence of the reflectivity of silicon with surface oxide at wavelengths of 633 and 1047 nm[END_REF][START_REF] Grauby | Quantitative thermal imaging with CCD array coupled to an heterodyne multichannel lock-in detection[END_REF]… The reflectivity variation implies an intensity variation of the light reflected to the photodetector (CCD camera, photodiode). Thus, measuring the relative variation of photocurrent ∆I/I of the detector, we can deduce the relative variation of reflectivity ∆R/R and then the temperature variation ∆T of the sample if κ is known. Unfortunately, the value of κ is often only known for a few bulk materials at a precise wavelength under specific experimental conditions. Besides, in microelectronic devices, the structure, in particular the passivation layer thickness, has a great influence on this coefficient value and we cannot use the bulk material value. As a consequence, every studied sample and every experimental set-up need a new calibration. Once the value of this coefficient is determined, you can obtain absolute temperature variations.

The set-up is presented in figure 3. The luminous source is LED whose intensity can be modulated. The lenses (L 1 ) and (L 2 ) enable to adapt the size of the luminous beam to the size of the object under study. As we use a polarizing beam splitter (PBS) and as the light emitted by the LED is not polarized, a sheet polarizer (P 1 ) is used to polarize it and to adjust the light intensity to send upon the device under test. After reflection on the sample and crossing twice the quarter-wave plates (P 2 ), the polarisation has been exchanged. As a consequence, the beam is being transmitted in the detection arm ended by a CCD camera. In this arm, the lens (L 3 ) enables to image the sample onto the CCD detector. Its video frequency is fixed and equal to 50Hz. The output signal of the camera is analyzed by a computer to extract the information. All elements L 1 , L 2 , P 1 , P 2 and PBS are included in a microscope. The sample is submitted to a sinusoidal current at frequency f and the flux of the LED is also modulated. Indeed, we use an heterodyne thermoreflectance imaging system [START_REF] Grauby | High resolution photothermal imaging of high frequency phenomena using a visible CCD camera associated with a multichannel lock-in scheme[END_REF]. The heating, due to Joule effect, occurs at f 1 (equal to 2f or f depending on the electrical excitation waveform) and the LED flux is modulated at f 2 = f 1 +12,5Hz. The phenomenon of interest, i.e. the heating of the device initially at f 1 , can then be observed at the blinking frequency f 2 -f 1 =12.5Hz which is easily analyzed by the camera which works at 50Hz. Therefore, during a period of the signal of interest, we take 4 images and we use a classical 4 images algorithm [START_REF] Gleyzes | Profilométrie picométrique. II. L'approche multidétecteur et la détection synchrone multiplexée[END_REF] to deduce the relative reflectivity variation amplitude ∆R/R and phase φ. Moreover, we accumulate several hundreds or thousand images to improve the signal to noise ratio which depends on the square root of the number of accumulated images.

SCANNING THERMAL MICROSCOPY

Thus, scanning thermal microscopy is a promising method that could enable to detect temperature variations on very small structures at submicrometric scale, and in particular here on each resistor individually. Indeed, a SThM can measure the amplitude (and the phase) of the temperature variations induced by the AC current along the electrically excited sample. The SThM is a conventional atomic force microscope (AFM) mounted with a specific probe. The AFM system enables the control of the tip position and the contact force with the sample (Figure 4). Monitoring is performed with a feedback loop between the signal of three x-y-z piezo-electrical ceramics carrying the tip cantilever and four photodiodes tracking a laser beam which is reflected on the mirror of the probe. This probe is constituted of a Wollaston wire shaped into a tip and etched to uncover its core platinum (Pt). The Pt wire is included in a Wheatstone bridge and used as a thermistor, as the resistance of the wire depends on its temperature. The SThM is used in an AC regime. As a consequence, we use a lock-in scheme to measure the amplitude (and the phase) of the first harmonic in the tip voltage. From these measurements, we deduce the amplitude (and the phase) of the temperature at the surface of the sample. The bridge voltage is measured while scanning the surface so that the Pt electrical resistance could be estimated at each point of the sample surface. We estimate the diameter of the tip to be of the order of 5 µm and its contact radius of the order of 50 nm. Therefore, spatial resolution better than the one reached with thermoreflectance techniques can be expected [START_REF] Gomes | Investigation of the electrical degradation of a metal-oxide-silicon capacitor by scanning thermal microscopy[END_REF].

We have already used this technique in AC regime [START_REF] Ezzahri | Dynamical Behavior of the Scanning Thermal Microscope (SThM) Thermal Resistive Probe using Si/SiGe Microcoolers[END_REF] and we have in particular measured quantitative temperature variations on PN Bi 2 Te 3 thermoelectric couples [START_REF] Patiño-Lopez | Characterization of the thermal behaviour of PN thermoelectric couples by scanning thermal microscope[END_REF].

THERMOREFLECTANCE RESULTS

We have first used the set-up described in paragraph 3 on the C5 device with f 1 =300 Hz and f 2 =312,5 Hz. The current supplying the resistors is a few mA, the resistor of C3 or C5 being equal to a few hundreds ohms. The lens L 2 used is a ×50 microscope objective and the LED is a red one emitting at 660 nm. The image of reflectivity, showing a zoom of the central part of C5, is presented in figure 5. Every image we present in this section is the result of accumulation of 40000 images corresponding to an acquisition time of about ten minutes. We clearly see the reflectivity variation to be maximal on the heating resistors (4 resistors in this image). Then, we have used this set-up to measure reflectivity variations on the C3 device in the same experimental conditions. The ∆R/R amplitude image is presented in figure 6. As expected, we can note a higher variation of reflectivity in the heating zone but we do not distinguish the different resistors. This clearly shows that the spatial resolution is too limited.

The use of a LED is then all the more adapted as we can easily find LEDs emitting at various wavelength. As the spatial resolution is limited by diffraction and then linked to the illumination wavelength, it seems logical to use a blue LED (λ=450nm). The other experimental conditions being unchanged, the ∆R/R image is presented in figure 7. And here we can individually distinguish the 9 thin resistors. Nevertheless, it is obvious that we reach the resolution limit.

But we can use a ×100 microscope objective to improve the quality of the image. The result is presented in figure 8 where the 9 resistors are more distinguishable. So, these experiments show that thermoreflectance can be a powerful technique to study the thermal behaviour of highly integrated microelectronic devices. In particular, the use of a LED as light source is very interesting as we can easily change the illumination wavelength to improve the spatial resolution. Indeed, if working with a microscope objective under high magnification conditions (×50 or 100) and with high numerical aperture, we have obtained thermoreflectance images of 0.35 µm structures.

There is still remaining the issue of calibration. There are different materials constituting the device and each needs a calibration of its thermoreflectance coefficient. There exist various methods [START_REF] Tessier | Quantitative thermal imaging by synchronous thermoreflectance with optimized illumination wavelengths[END_REF][START_REF] Grauby | Quantitative thermal imaging with CCD array coupled to an heterodyne multichannel lock-in detection[END_REF][START_REF] Dilhaire | Calibration procedure for temperature measurements by thermoreflectance under high magnification conditions[END_REF] but none is universal and each method must be adapted to the experimental configuration, the calibration sometimes proving quite difficult. Moreover, the signal to noise ratio is not very good and needs to be improved. One solution is to accumulate more images. But then, it takes a lot of time and point thermoreflectance measurements with a photodiode and a lock-in amplifier becomes then a better method. We are now working on another technique combining point measurements with imaging techniques.

STHM RESULTS

We have then used the set-up described in paragraph 4 to study the structures C3 and C5. Here, the device is supplied by a sinusoidal current and the heating occurs at f 1 . A lock-in scheme measures the tip voltage amplitude (and phase) at frequency f 1 . We can adjust the scan size, the scan rate (speed of the tip) and the number of samples by line. We choose the frequency f 1 so that the lock-in time constant should be compatible with the tip scan rate.

We first studied C5 with f 1 equal to 1 kHz, the current supplying C5 is a few mA, the scan size is 30µm×30µm, the scan rate 0.2 Hz and a line is constituted of 256 samples. We clearly see (figure 9) 3 resistors heating. The amplitude is in arbitrary units. The spacing between two resistors corresponds to the expected 10 µm. The thermal signal spread over about 1 µm on each resistor. The tip sweeps the device surface hence the passivation layer and not directly the resistors. So, the temperature signal due to the heating resistors is "filtered" and then smoothed by the passivation layer. The image consequently corresponds to a qualitative surface temperature mapping and not of the active zone.

We have then supplied C3, all the parameters are the same as for C5 apart for the scan size which is first reduced to 15 µm×15 µm. We clearly detect (figure 10) the heating zone constituted by the 9 resistors but we do not see them individually.

Hence, we have once again reduced the scan size to 4 µm and registered the signal on a section of the resistors (figure 11). We detect 3 maxima perhaps corresponding to 3 heating resistors but the signal to noise ratio is poor and other experiments need to confirm these results. The spacing between 2 maxima is a little more than 1µm which is compatible with the 0.8 µm spacing given by the constructor taking into account the result obtained on C5 showing that, under the same conditions, the thermal signal spreads over about 1µm on each resistor, thus reaching the neighboring resistor on C3. The method presents several drawbacks. First of all, if we want to measure microelectronic device temperature, the passivation layer needs to be eliminated to access the active zone or a model must be developed to take it into account but it implies that the passivation layer structure must be perfectly known for every point of the sample.

Moreover, it is time consuming as the whole image (figure 9 or 10 for instance) needs about 20 mn. If we want to reduce it, it is necessary to increase the scan rate and then to reduce the lock-in time constant hence to increase f 1 . But then the thermal signal amplitude decreases and the signal to noise ratio also decreases. This decrease adds to the one due to the passivation layer. Besides, because of the dimension of the Pt core hiding the much smaller contact tip, it is not easy to precisely localize the scanned area before seeing the resulting image, in particular when the scan size is small.

Finally, the tip temperature is not the sample temperature. We have developed [START_REF] Patiño-Lopez | Characterization of the thermal behaviour of PN thermoelectric couples by scanning thermal microscope[END_REF] a model taking into account the tip-sample heat transfer. We plan to use it to deduce the sample surface temperature.

CONCLUSION

We have evaluated two thermal measurement methods in terms of spatial resolution and calibration issue. We have used a very integrated microelectronic device and shown that thermoreflectance can be efficient if using an appropriate optical system. The spatial resolution can then be very good but the main issue is the calibration and the signal to noise ratio. We are now developing a method to improve it while maintaining a small acquisition time; it will constitute a compromise between point and imaging techniques.

As for SThM, again, the passivation layer is an issue as the tip measures the temperature on its surface and not on the active zone itself. It is consequently not obvious to measure the active zone temperature. Moreover, submicrometric spatial resolution for thermal mode is not clearly proved.

Figure 1 :Figure 2 :

 12 Figure 1: Sample 1 (C5) constituted of nine 0.35 µm thin resistors (distance between 2 resistors: 10µm)

Figure 3 :

 3 Figure 3: Modulated thermoreflectance set-up

Figure 4 :

 4 Figure 4: STHM schematic view

Figure 5 :

 5 Figure 5: Relative reflectivity variation amplitude on C5 device.

Figure 6 :Figure 7 :

 67 Figure 6: Relative reflectivity variation amplitude on C3 device with red led.

Figure 8 .

 8 Figure 8. Relative reflectivity variation amplitude on C3 device with blue led and ×100 microscope objective.

Figure 9 :

 9 Figure 9: Qualitative SThM temperature image of the C5 device surface.

Figure 10 :

 10 Figure 10: Qualitative SThM temperature image of the C3 device surface.

Figure 11 :

 11 Figure 11: Qualitative SThM temperature on a section of the C3 device surface.

 TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4

ACKNOWLEDGEMENT

The samples have been provided by the GDR Micro et Nanothermique (n°G2503).

This work has been supported by the Conseil Régional d'Aquitaine and by a FEDER fellowship.


P Vairac

B Cretin

M Genix

B Charlot

S Dilhaire

S Gomes

G Tessier

N Trannoy

S Volz

ULTRA-LOCAL TEMPERATURE MAPPING WITH AN INTRINSIC THERMOCOUPLE

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Temperature and heat flux measurements at submicrometer scales have a broad range of applications related for instance to semiconductor devices, chemical reactions and phase transformations. Existing techniques include thermoelectric probes such as thermocouples, semiconductor diodes and thermistors. Optical techniques such as infrared thermometry [START_REF] Khurana | Analysis of product hot electron problems by gated emission microscopy[END_REF] and surface reflectometry [START_REF] Ju | Short-time-scale thermal mapping of microdevices using a scanning thermoreflectance technique[END_REF] are also state-of-the-art tools. A quite recent metrology is based on a thermocouple or a thermoresistive probe mounted in an Atomic Force Microscope (AFM) [START_REF] Majumdar | Scanning thermal microscopy[END_REF][START_REF] Luo | Sensor nanofabrication, performance, and conduction mechanisms in scanning thermal microscopy[END_REF][START_REF] Pylkki | Scanning nearfield optical microscopy and scanning thermal microscopy[END_REF][START_REF] Leinhos | Micromachined fabrication of Si cantilevers with Schottky diodes integrated in the tip[END_REF][START_REF] Zhang | A thermal microprobe fabricated with waferstage processing[END_REF][START_REF] Mills | Scanning thermal microscopy using batch fabricated thermocouple probes[END_REF][START_REF] Nakabeppu | Microscale real temperature measurement by the AFM using thermal feedback method[END_REF]. It provides thermal and topographical images of sample surfaces with high spatial resolution. The accuracy and the spatial resolution of those measurements are however affected by three main parameters: the coupling between the thermal and topographical signals, the heat transfer in air which spreads the thermal contact over a micrometer scale and the thermal conductivity of the studied materials or of the sub-surface materials. This very last case influences the measurement when the penetration depth of the thermal signal is comparable or greater than the contact radius.

In this paper, we report on the modification of the EFM as a SThM by using a tip contacting a metallic heating surface. The local probing is based on the Seebeck effect. Local investigation seems easy because the radius of the contact between the tip and the sample is estimated to be in the 50-100 nm range depending on the applied contact force. The contact radius can be roughly assimilated to the electrical and thermal contact radii. The heat conduction through the air can be neglected (it is not the case for adsorbed layers). Because the thermal measurement is based on the Seebeck junction effect, surface effects are predominant. The system will therefore not be sensitive to buried materials or impurities. The Debye length (a few nanometers) defines the limit of the measurement area.

Our sample is a CMOS chip including an aluminum top layer. Resistors are buried and will allow us to heat surfaces of various sizes. The temperature calibration is performed with an in-situ sensor. A judicious choice of conducting material for the tip makes it possible to obtain an optimized thermoelectric couple. We present the temperature calibration obtained with our set-up with different thermoelectric couple.

THE EXPERIMENTAL SET-UP

The set-up is derived from an Electrostatic Force microscope (EFM) [START_REF] Rousier | Measurement of the contact potential difference with an electrostatic force microscope[END_REF][START_REF] Cretin | High sensitivity electrical force sensor; application to near-field microscopy and surface characterization[END_REF] using a conductive tip in contact with the sample under test (figure 1). The conductive probe is made with a silicon cantilever with a stiffness K C = 150 N/m (Length = 7 mm, Width = A thin layer of a conductive material is deposited by magnetron sputtering on the assembly to obtain a conductive tip. The set-up uses the classical Optical Beam Deflection method to control the contact force between the tip and the sample. In a first time, in order to perform these measurements the EFM has been implemented with a low cost and single heating stage. This stage is described in figure 2. The heater is a Peltier module, which allows to modify the temperature with an electric current. It is possible to heat or cool the sample with this classical thermal system, and it is necessary to use a radiator to evacuate the heat. Moreover we use a thermistance (TCS 605) to measure the instantaneous temperature. To minimize the thermal drifts, the heater system has been realized in aluminum and Invar (the thermal expansion coefficient of Invar is very low). The Invar part holds the support sample by nylon screws and springs. By this way the differential expansion is directed towards the radiator and the induced displacement on the sample is minimum. This specific stage enables to obtain a mechanical drift below 50 nm/°C, and a temperature range above 100 °C.

THEORETICAL BASIS

The Seebeck effect

In 1821, Thomas Johan Seebeck made the discovery that the creation of an electrical voltage was possible by the difference between two metals having different conductive properties at the other end of the two wires. The Seebeck effect is the heart of thermocouples: if two metals having different Seebeck coefficients are jointed together at one end the presence of a voltage called Electromotive Force (EMF) will be apparent using a voltmeter at the other end. This voltage is due to the temperature gradient between the two sides. As mentioned earlier, this instrumentation will involve the use of the conductive tip of an EFM microscope (Metal A) and a metallic sample (Metal B) for the "fabrication" of an intrinsic thermocouple. The hot junction will be the contact point between the tip and the sample, giving the possibility to perform ultra local temperature measurement. The main effect that is predominantly applicable is the Seebeck effect, where an electromotive force is formed as a result of the proportionality of the thermal gradient between the hot and cold junction materials. The change in voltage between the two junctions is described by taking an integral over the starting / reference temperature to the final temperature. This is shown by the following equation: In metals the Seebeck coefficient is given by the Mott-Jones equation [START_REF] Kasap | Thermoelectric effects in metals: thermocouples[END_REF]:

x F0 3qE T 2 B π²k S - ≈ (2)
With k B the Boltzmann's constant, T the temperature in Kelvin, x a numerical constant dependant on charge transport mechanism, q the charge of an electron, and E F0 the Fermi energy at 0K. Table1 gives the thermal characteristics of some materials. Table1: Seebeck coefficients of selected metals

Metal

The contact point: the hot junction

The contact between the conductive tip and the metallic sample can be considered as the hot junction of the thermocouple. To estimate the size of the contact area, we assumed that the contact is in the elastic regime and we use the classical Hertzian theory. This theory allows to calculate the radius a of the contact area by this formula [START_REF] Johnson | Contact Mechanics[END_REF]: With F the contact force, R the radius of the tip and E * the composite Young's modulus given by the following expression:

3 / 1 * E 4 FR 3 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = a
1 1 2 1 2 E t E t s E s * = - + - ν ν
Where E t , ν t and E s , ν s are respectively the Young's modulus and Poisson ratio of the tip and sample.

In our set-up we use a tip with a 2 µm radius. the standard contact force applied on the sample is estimated by using the stiffness of the associated microcantilever (K C ) and by a variable offset displacement Δz of the sample (F= K C Δz).

Table2 gives the radius of contact for the metallic samples investigated in the case of two contact forces. These calculations demonstrate that with this intrinsic thermocouple method it is possible to perform ultra-local thermal measurement with a resolution of about 100 nm considering that this radius can be assimilated to the electrical and thermal contact radius.

Metal

EXPERIMENTAL RESULTS AND DISCUSSION

The results have been obtained with different thermoelectric couples. We have used two conductive tips made by a thin layer of gold and platinum. Different samples have been investigated such as aluminum, copper and nickel. The figure 5 presents the emf variations obtained with the gold and platinum tips for an aluminum sample versus temperature. The figure 6 shows the results obtained in the case of a copper sample. As expected we demonstrate that the emf voltage variations detected in all the cases depend on the temperature variations. The results are different with the platinum tip compared to those obtained with the gold tip as predicted by the difference in thermoelectric properties of these materials. Nevertheless on these first results we can see that with the same tip but with different samples the evolution of the emf voltage is quite similar. Further investigations are in progress in order to explain this low sensitivity to the sample material.

In a second set of experiments a specific sample, which is a CMOS chip including an aluminum top layer has been investigated. Resistors are buried and allow us to heat aluminum surfaces of different sizes (metal 4). A view of the chip and a scheme of the specific structure under test are given in figures 7a and 7b. From these results we have calibrated the temperature variation obtained by joule effect. We have a temperature variation of 27 °C to 72°C for a current variation of 25 mA in the resistor. We have performed the measurement with the gold tip and as expected the detected emf variation increases as the temperature increases until 72 °C (figure 9). On the same way the emf magnitude measured in this experiment is very close to the one measured in the first experiment with the peltier module and the bulk aluminum sample demonstrating the repeatability of the measurement.

CONCLUSION

This communication reports on our first results concerning the use of an intrinsic thermocouple to perform ultra-local temperature measurements. The intrinsic thermocouple made from an EFM conducting tip put in contact with a conducting sample use the wellknown Seebeck effect. The first results demonstrate that is possible to measure the temperature variation of the sample in contact with the conductive tip by detecting the net emf voltage. We have successfully used this method on a specific CMOS chip showing that this method could be an interesting tool for thermal measurement on IC devices. Further investigations are in progress on this method in order to completely analyze the behavior of this intrinsic thermocouple.

PFigure 1 :

 1 Figure 1: experimental set-up for local temperature probing derived from an EFM.

Figure 2 :

 2 Figure 2: Principle of the heating stage

Figure 3 :

 3 Figure 3: basic principle of the thermocouple.

(

  a , B. Cretin a , M. Genix, B. Charlot b , S. Dilhaire c , S. Gomes c , G. Tessier c , N. Trannoy c and S. Volz cUltra-Local temperature mapping with an intrinsic thermocouple Keep in mind that this is true for one thermal couple). S A-B is the Seebeck coefficient difference between the two metals. The Seebeck coefficient is a material property that is temperature dependant and can be found by dT dV S= .

Figure 4 :

 4 Figure 4: The hertzian contact model.

2 PFigure 5 :

 25 Figure 5: Detected emf in the case of an aluminum sample with to different tips (gold and platinum).

Figure 6 :

 6 Figure 6: Detected emf in the case of a copper sample with to different tips (gold and platinum).

Figure 4 Dissipateur poly 1 PFigure 8 :

 418 Figure 7a: a view of the specific CMOS chip

Figure 9 :

 9 Figure 9: Seebeck voltage detected with a gold contacting tip versus heating current

Table 2 :

 2

		Contact radius	Contact radius
		at F = 75 µN	at F = 150 µN
	Al	113.05 nm	142.43 nm
	Cu	94.52 nm	119.09 nm
	Ni	87.95 nm	110.8 nm

contact radius for different samples

 TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4


S Gomès

O Chapuis

F Nepveu

N Trannoy

S Volz

B Charlot

G Tessier

S Dilhaire

B Cretin

P Vairac

TEMPERATURE MEASUREMENT OF SUB-MICROMETRIC ICs BY SCANNING THERMAL MICROSCOPY

Surface temperature measurements were performed with a Scanning Thermal Microscope. We aim at proving an eventual sub-micrometric resolution of this metrology when using a wollaston wire probe of micrometric size. A dedicated CMOS device was designed with arrays of lines 0.35µm in size with 0.8 µm and 10µm periods. Integrated Circuits with or without a passivition layer were tested. To enhance sensitivity, the IC heat source was excited with an AC current. We show that the passivation layer spreads heat so that the lines are not distinguishable. Removing this layer allows us to distinguish the lines in the case of the 10µm period.

INTRODUCTION

Semiconductor devices, which are continuously reduced for integration, must withstand ever higher electric fields which induce severe degradation or total failure. Spatially high-resolution determination of temperature and detection of local power dissipation in the sub-µm range have then become fundamental for microelectronics. The Scanning Thermal Microscope (SThM) [START_REF] Dinwiddie | Thermal conductivity contrast imaging with a scanning thermal microscope[END_REF] is a relatively new technique permitting such investigations. Indeed this method has permitted to study proximity thermal heat transfers [START_REF] Gomès | Thermal Microscopy : Study of the thermal exchange between a probe and a sample[END_REF][START_REF] Gomès | Scanning Thermal Microscopy: Characterisation and Interpretation of the Measurement[END_REF][START_REF] Lefèvre | Modélisation et élaboration des métrologie de microscopie thermique à sonde locale résistive[END_REF] and materials thermophysical properties [START_REF] David | Characterisation of thin films using scanning thermal microscopy[END_REF], it has also already allowed to map the temperature distribution on active sample surface [START_REF] Fiege | Front-and backside investigations of thermal and electronic properties of semiconducting devices[END_REF][START_REF] Gomès | Investigation of the electrical degradation of a metal-oxide-silicon capacitor by Scanning Thermal Microscopy[END_REF] at a submicrometric scale. Fiege et al. [START_REF] Fiege | Front-and backside investigations of thermal and electronic properties of semiconducting devices[END_REF] have demonstrated that this tool can allow the localization of failures in integrated devices at saturation or in breakdown condition. The SThM has also been used to investigate the energetical aspect of the electric degradation mechanisms inside a metal-oxide-silicon (MOS) structure submitted to an electric stress [START_REF] Gomès | Investigation of the electrical degradation of a metal-oxide-silicon capacitor by Scanning Thermal Microscopy[END_REF]. More recently, it has permitted to measure quantitative temperature variations on PN thermoelectric couples [START_REF] Patino-Lopez | Characterization of the thermal behavior of PN thermoelectric couples by scanning thermal microscope[END_REF]. We aim at proving an eventual sub-micrometric resolution of the SThM when using a wollaston wire probe of micrometric size. A dedicated CMOS device was designed with arrays of lines 0.35µm in size with 0.8 µm and 10µm period. Integrated Circuits with or without a passivition layer were tested. To enhance sensitivity, the IC heat source was excited with an AC current. We show that the passivation layer spreads heat so that the lines are not distinguishable. Removing this layer allows us to distinguish the lines in the case of the 10µm period. In the following, the experimental technique is presented. The results in the case where the passivation layer is present is then adressed. A finite elements based modelling allows us to analyse the data. Then the sample without passivation layer is studied. An explanation for the tip artefact is finally provided.

EXPERIMENTAL SET UP

The experimental set up used in this study results on the combination of a SThM and a device adapted to submit the sample to a DC or AC electric current (Figure 1).

The used SThM is a scanning probe microscope marketed by Veeco Corporation. This SThM is based on an atomic force microscope configuration with a thermal tip. The thermal probe is a thermoresistive probe consisting in a 5 µm diameter and 200 µm length platinum wire bent in form of a loop [START_REF] Dinwiddie | Thermal conductivity contrast imaging with a scanning thermal microscope[END_REF]. We use it in its passive mode: the DC current through the thermal probe has been chosen small enough to not electrically heat the probe. In this mode, the thermal probe is used as a resistance thermometer. It constitutes one of the legs of a Wheastone bridge. As the temperature of the probe changes, the corresponding change in the probe resistance change the voltage balance of the bridge, changing the output voltage (V AB ) of the circuit. The control and the amplification of the output voltage during the scan of an hot sample surface permits to make the thermal image. The contrast of this image translates the variation of the electric resistance (the temperature) of the probe due to variation of the sample surface temperature. The SThM then permits to map qualitatively the temperature distribution of the scanned surface with a thermospatial resolution about 300 nm [START_REF] Gomès | Investigation of the electrical degradation of a metal-oxide-silicon capacitor by Scanning Thermal Microscopy[END_REF].

In the framework of resistive samples study, a second probe put on the electric contact of the considered specimen permits the current injection through the sample in order to heat it by joule effect. The resistive sample can be submitted to a sinusoidal current at a frequency f s . In this case, the internal heating by joule effect of the sample occurs at f = 2f s and the thermal contrast is obtained by measuring the amplitude and the phase of the 2f s V AB harmonic by using a Lock-In Amplifier (LIA).

EXPERIMENTS

The samples

The submicrometric resistive elements are 0.35µm in width and 0.282µm in thickness polysilicone strips resistors. As shown in the Figure 2, the studied structure is composed with nine resistors in parallel and spaced of 10µm or 0.8µm. Resistors are insulated from their polycilicone substrate by a SiO 2 layer. In a first and original configuration (sample1), the resistors are covered by a 3.6µm in thickness SiO 2 passivation layer. AFM images of this sample surface (figure 3) show small topographical features of a few nanometers in height at the surface, this is the signature of the resistors locations under the passivation layer.

RESULTS AND DISCUSSION

The experimental set-up presented in part 2. of this paper has been used to study the temperature fields at the surface of the two samples. can not be distinguished. The wires array can be modelled as one linear heat source as shown in the Figure 6. Figure 7 reveals that the array with a 10µm period still does not allow us to distinguish individual wires. The finite element simulation reported in figure 8 shows one wire in the array. It proves that the temperature field is homogeneous on the surface. Whereas the simulation represents an infinite array, the temperature gradient observed in figure 7 is due to the presence of a cold edge. Figure 8 finally shows that the spatial resolution is larger than 10µm when scanning the passivation layer.

Sample 1: with passivation layer

Sample 2: without passivation layer

Figure 9 gives the topography and the thermal contrast obtained with the SThM for the sample 2 with a 10µm period. The array of nine resistors were submitted to a 11 mA sinusoïdal current at f s = 110 Hz. The contrast of the thermal image clearly shows the heating of the resistors but the real wire width is not found. Due to its large curvature radius the thermal probe cannot follow the surface. As illustrated by the figure 10, this leads to surface dilatation phenomena in the topographical image obtain with the thermal probe. The contrast of the thermal image is also affected by this dilatation effect. The tip-sample heat flux is indeed directly proporptionnal to the thermal contact surface.

µm

Topography

Thermal contraste

This artefact is clearly due to a topography-thermal coupling. Note that the dips on both sides of the wires are insulators. If the surface were flat, heat spreading might also hide the real size of the wires.

CONCLUSION

We showed that the SThM mounted with a 5 microns in diameter platinum wire allows us to detect submicrometric elements but an artefact due to topography-thermal coupling enlarges the size of the wires by a factor of 4. This effect lowers the spatial resolution to 4 microns. When the 3.6 µm passivation layer is maintained, submicrometric elements resolution is even worse than 10µm due to heat spreading in the layer. ICs appear as interesting tools to benchmark the spatial resolution of thermal metrologies such as SThM but the design of the structure has to be modificated. It remains an adequate tool to detect hot spots on ICs surfaces.

Figure 1 :

 1 Figure 1: Experimental set up

Figure 2 :

 2 Figure 2: Electronic microscopy image of the sample

Figure 3 :

 3 Figure 3: Topography of the sample 1 obtained by atomic force microscopy In a second configuration, the passivation layer has been chemically etched. As shown in the figure 4, the AFM images for this sample (sample 2) show that the surface presents large and deep topographical features at the strips locations.

Figure 4 :

 4 Figure 4: Topography image and profile of the sample 2 obtained by atomic force microscopy.

Figure 5

 5 reports the temperature mapping of the wire array with a 0.8µm period. It clearly appears that the wires LIA  TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4

Figure 5 :

 5 Figure 5: Image of the thermal contrast (left) of the wires array with the 0.8µm period. The image size is 100µm x 80µm. The wires are covered by the passivation layer (sample 1). The schematic (right) shows the scanned area as the zone defined by a square .

Figure 6 :

 6 Figure 6 : Finite element modeling of the temperature field (left) around one heat source corresponding to the array in the 0.8µm period case. The colour legend reports the temperature in K. The surface temperature is reported in the graph (right) where the vertical axis refers to temperatures in K and the abscissa to the length in meter of a radius on the surface.

Figure 7 :

 7 Figure 7: Image of the thermal contrast (left) of the wires array with the 10µm period. The image size is 100µm x 100µm. The wires are covered by the passivation layer (sample 1). The schematic (right) shows the scanned area as the zone defined by a square .

Figure 8 :

 8 Figure 8 : Finite element modeling of the temperature field around one wire in the 10µm period case. The top side is on the left.

Figure 9 :

 9 Figure 9: Topographical (top) and thermal (bottom) images (temperature frequency 220 Hz) obtained simultaneously with the SThM at the sample 2 surface.

Figure 10 :

 10 Figure 10: Illustration of the surface dilatation and of the resulting thermal contrast with the SThM probe.

 TIMA EDITIONS / THERMINIC 2005 ISBN 2-916187-01-4

ACKNOWLEDGEMENT

The authors wish to gratefully acknowledge the financial support of the GDR Micro-et nanothermique (GDR CNRS 2503). They are thankful to B. Charlot (TIMA, Grenoble) for supplying the samples.