Abstract

This thesis reports the development of novel scanning thermal microscopy (SThM) probes based on a resistive niobium nitride (NbN) thermal sensor. Electron beam lithography and etching processes have been carried out to integrate the NbN thermal sensor on a non-planar 3D AFM tip. In order to test the novel SThM probe, a commercial AFM system has been modified into a vacuum based SThM setup. The temperature-dependent electrical response demonstrates a very high temperature sensitivity making these probes commercially interesting. Frequency-dependent measurements allowed us to estimate the thermal time constant and thermal properties of the probes.

We also investigated the impact of laser illumination on the NbN-SThM probe's temperature response and found significant heating. This heating is attributed to laser beam absorption via the SThM probe's cantilever. Specifically, we exploited the laser heated SThM probe for thermal measurement in air as well as vacuum conditions. We studied the heat dissipation into three bulk reference samples with dissimilar thermal conductivity under air conditions. These measurements allowed us to achieve the thermal conductivity calibration curve. Furthermore, laser heated SThM probe was utilized to obtain a thermal image of Si-nanowires embedded in the alumina matrix.

A part of the thesis focuses on the active 3ω-SThM method. The point 3ω-SThM experiments have been carried out on bulk samples along with a model based upon a thermalelectrical analogy to study heat transport in vacuum conditions. The obtained experimental results enabled us to extract the thermal contact resistance between the tip-sample system. Finally, we presented the application of these new SThM probes for thermal measurements on DNA nanostructures.

iii

Abstract in French

Cette thèse rapporte le développement de nouvelles sondes de microscopie thermique à balayage (SThM) basées sur un capteur thermique résistif en nitrure de niobium (NbN). Des processus de lithographie par faisceau d'électrons et de gravure ont été réalisés pour intégrer le capteur thermique en NbN sur une pointe AFM 3D non plane. Afin de tester la nouvelle sonde SThM, un système AFM commercial a été modifié en une configuration SThM sous vide. La réponse électrique en fonction de la température démontre une très grande sensibilité à la température, ce qui rend ces sondes commercialement intéressantes. Les mesures en fonction de la fréquence nous ont permis d'estimer la constante de temps thermique et les propriétés thermiques des sondes.

Nous avons également étudié l'impact de l'illumination laser sur la réponse en température de la sonde NbN-SThM et avons constaté un échauffement significatif. Ce chauffage est attribué à l'absorption du faisceau laser par le cantilever de la sonde SThM. Plus précisément, nous avons exploité la sonde SThM chauffée par laser pour effectuer des mesures thermiques dans l'air ainsi que dans des conditions de vide. Nous avons étudié la dissipation de chaleur dans trois échantillons de référence en vrac avec des conductivités thermiques différentes dans des conditions d'air. Ces mesures nous ont permis de réaliser la courbe d'étalonnage de la conductivité thermique. De plus, une sonde SThM chauffée par laser a été utilisée pour obtenir une image thermique des nanofils de Si intégrés dans la matrice d'alumine.

Une partie de la thèse se concentre sur la méthode active 3ω-SThM. Les expériences 3ω-SThM ponctuelles ont été réalisées sur des échantillons massifs avec un modèle basé sur une analogie thermo-électrique pour étudier le transport de chaleur dans des conditions de vide.

Les résultats expérimentaux obtenus nous ont permis d'extraire la résistance de contact thermique entre le système pointe-échantillon. Enfin, nous avons présenté l'application de ces nouvelles sondes SThM pour des mesures thermiques sur des nanostructures d'ADN. v This is the moment to express my gratitude towards all the amazing people, I have met during my Ph.D. journey. It was filled with happiness, excitement, motivation, lots of ups and downs. I would start first by thanking my supervisor Dr. Olivier Bourgeois for allowing me to carry out my Ph.D. within your group. You are a great mentor and your ability to understand the person is great. Thank you for being such a kind-hearted person and sharing your experience as a scientist to a great friend. I owe you countless things that I have learned in these four years. One of the most memorable moment, when we had a competition to balance the beer on our chest in Finland. I am very grateful to being a part of your research family at work. I would now like to express my gratitude to Prof. Jonathan Weaver, Prof. Stéphane Grauby, Dr. Séverine Gomes, Dr. Gilles Pernot, Dr. Laëtitia Marty, and Dr. Gilles Gaudin for being the jury members, careful evaluation of the manuscript and their kind remarks about the thesis.

For the fabrication process, special thanks go to Gwénaelle Julié. She introduced me to different fabrication techniques and tricks to perform experiments on challenging samples such as AFM cantilevers. I am thankful to Jean-Franc ¸ois Motte (problem solver), Thierry Crozes (being really friendly and having interesting conversations), Bruno Fernandez, Thierry Fournier, and Latifa Abbasi for their technical support, suggestions, and friendly behavior. I would like to especially thank Simon Le Denmat that allows us to modify an AFM setup for thermal measurements. He is one of the most organized and hard-working person I have ever met.

I would like to thank our fruitful collaborators Dr. Séverine Gomes (enthusiastic and great mentor), Dr. Jean-Franc ¸ois Robillard and Pierre-Olivier Chapuis.

A big thank you to the TPS group for their continuous support. I would like to extend my sincere gratitude to all the permanent staff, especially Dr. Jean-luc Garden (my KINGinspiring, not only in science), Dr. Jacques Richard, Dr. Hervé Guillou (DNA of TPS group), Dr. Dimitri Tainoff, Dr. Cécile Delacour, Dr. Laureline Porcar, Dr. Laurent Saminadayar, Dr.

Daniel Bourgault, Gaël Moiroux and Emmanuel Andre (great guy).

During my Ph.D., I came across a wonderful fellow. I would like to start with Dhruv Singhal, who suggested me join the TPS group. For almost one decade, he has been there next to vii viii me. I had a wonderful time and learn a lot from him. It's difficult to express all these good times in words. I know, we will continue our brotherhood always. Then, my sir Jessy Paterson, you are my brother too. Without you, I might not able to finish my thesis. I cannot forget the endless beer and amazing conversations. Special mention to Céline Tur (amazing lady), Dr. Adib Tavakoli, Judith Stein (amazing lady too), Charlotte Latargez, Roderic Cravero, Dr.

Jeremie Maire, Dr. Tuyen Nyugen-Duc, Anais Proudhom, Clara Magnin, Victor Dupuit, Victor Doebele, Etienne Niorthe, Anthony Albanese, Clothilde, Boris Brisuda and Sunanda Mitra. I would like to thank you, Mathilde Berard, Christophe Guttin, Anne Gerardin, IT service and electronic service of Institute Néel.

I owe my deepest gratitude to my all friends. Thank you Usasi (supportive and encouraging), Yashpreet (Sweet and kind), Titiksha (motivating), Sukanya (caring), Akshay (cricket companion), Nishu (0/0), Akhil, Raj, Preeti, Vikas, Sumit, Akanksha, Nitika, Siddharth, Vivekanda, Priyank, Vivek (bullshit guy :p), Garima, Monika, Pulkit, Parveen Bhai, Raj Bhai, Saransh, Shanu, Vipul, Naveen, Sahil and all the other people who were a part of this journey. I would also like to thank Klaus Hasselbach director of the MCBT department for his supportive attitude.

Still, there are countless people left to be mentioned who have helped me to reach where I am right now, I acknowledge each and everyone from the bottom of my heart.

In the end, I would like to thank my family: Maa, papa, chacha, chachi, two sisters, and Bhai. A huge thank you to my grandfather, I owe you everything in my life.

Rahul Swami

List of Figures

Measured SThM average T rms

2ω tip temperature for various frequency between out-of-contact and contact with a sapphire substrate (κ sapphire =34 Wm -1 K -1 ) for an AC current of 30µA. Red circles indicate the measured signal in the out-ofcontact mode and red line is used to guide the eyes whereas blue square corresponds to the in-contact measured temperature with blue line to guide the eyes.

The inset shows the zoom-in of the data at low frequency. . . . . . . . . . . . . .

Measured SThM average T rms

2ω tip temperature for various frequency between out-of-contact and contact with SiO 2 substrate for an AC current of 30µA. Red circles indicate the measured signal in the out-of-contact mode and red line is used to guide the eyes whereas blue square corresponds to the in-contact measured temperature with blue line to guide the eyes. . . . . . . . . . . . . . . . . .

Comparison between the measured SThM average T rms

2ω tip temperature as a function of frequency between out-of-contact (Red circles with lines) and in contact (blue square with lines) with Si substrate for an AC current of 30µA. . . . .

Ratio of the of average SThM temperature T rms

2ω between the in-contact and outof-contact is plotted for all the bulk samples used in this work. In the graph, the blue, black, red and green curves represent the S1818 resist, SiO 2 , sapphire and bulk-Si, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.11

Various DNA origami nanostructures that were synthesized and characterized. .

Introduction

Studying local temperature fields and mastering heat transport in nanoscale materials or devices have become crucial in the growth of new technologies. With the advent of nanotechnology, the feature size of the devices has been continuously scaling down to improve performance and be cost-effective. One of the prime example is integrated devices, where localized Joule heating has become a serious issue affecting device reliability [1], [2]. Thus, management of heat generation within the devices is essential for achieving long-term reliability and preventing rapid failure: this kind of application requires materials that can conduct heat efficiently.

On the contrary, to enhance the performance of thermoelectric devices, a reduction in heat conduction is required [START_REF] Tainoff | Network of thermoelectric nanogenerators for low power energy harvesting[END_REF]. In this context, research on novel materials continues for heat management. Overall, all these nanoscale systems somehow rely upon the thermal properties of their constituting materials. Therefore, precise thermal measurements at nanometer scale are essential for the fundamental understanding of heat transport and for the development of optimized novel nanoelectronic, optoelectronic, and innovative thermal nanodevices.

Among various available thermal measurement techniques, Scanning Thermal Microscopy (SThM) is the only method to assess temperature fields with nanometer spatial resolution and high temperature sensitivity. Currently, the resistive thermometer is the most widely used thermal sensor in SThM probes for its convenience and sensitivity. However, the existing resistive sensors exhibit a moderate temperature coefficient of resistance (TCR), which is lower than 2 × 10 -3 K -1 [4]- [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF]. This fact justifies the scope for improving the thermal sensitivity of the SThM probe.

Thus, this thesis is devoted to developing a novel highly sensitive SThM probe based on a niobium nitride resistive thermal sensor [START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF], [START_REF] Nguyen | Niobium nitride thin films for very low temperature resistive thermometry[END_REF]. Moreover, to improve the signal-to-noise ratio, the electrical measurement will be performed in four-wire configuration. Electrical and thermal properties of the NbN-SThM probe will be investigated, followed by electro-thermal measurements on a wide range of materials , from bulk samples to DNA origamis. This project has been performed in the framework of ANR TIPTOP project with collaboration between two In this thesis, we organized the work into six chapters.

Chapter 1 gives an overview of heat transport in solid materials from macroscale to submicrometer scale. Subsequently, various available thermal measurements techniques are introduced. Following, the state-of-the-art SThM technique is presented with a detailed discussion on available thermal probes and the existing thermal transport between the tip and the sample system. The chapter ends with the justification that the NbN resistive thermometer has the potential to significantly enhance the thermal sensitivity of the SThM probes.

Chapter 2 begins with optimizing the electron beam lithography process on a flat surface using a thermally evaporated electron-sensitive resist. Then, we detail the different fabrication strategies conducted during this research project to integrate the NbN thermometer on the nonplanar AFM tip as well as the challenges encountered.

Chapter 3 presents the adaptation of a commercial AFM system for scanning thermal microscopy (SThM) setup that includes the development of a new specific probe holder and lownoise electronics for the acquisition of the thermal probe signal with high accuracy.

Chapter 4 is dedicated to studying the intrinsic and extrinsic properties of the NbN-SThM probe. We measure properties such as the temperature coefficient of resistance (TCR) as well as the thermal conductance of the probe. In addition, the impact of external sources on the NbN-SThM probe's temperature response is detailed.

Chapter 5 presents the point 3ω-SThM experiments carried out on bulk samples along with a model based upon thermal-electrical analogy. We report on the measured thermal contact resistance between the tip-sample system. Finally, we present the thermal measurement conducted on DNA nanostructures using NbN-SThM probes. To the best of our knowledge, it is the first time the thermal conductivity of single DNA origami is measured experimentally.

The chapter 6 of the thesis is devoted to exploiting the laser-heated SThM probe for thermal measurement under air and vacuum conditions. We perform the experiments on bulk reference samples with dissimilar thermal conductivity under air conditions and show the thermal conductivity calibration curve. At the end of the last chapter, we show the preliminary thermal image obtained on Si-nanowires embedded in the alumina matrix.

U

nderstanding and studying heat transport and dissipation phenomena in nanometerscale devices and materials are of great importance for fundamental research and continued demand for improved performance and energy conversion/harvesting in the microelectronic industry. In modern electronic and optoelectronic devices, the feature size has been continuously decreasing and reached down to a single-digit nanometer length scale in order to make them compact, faster, more efficient, and cheaper. As an example, very recently, IBM revealed the world's first 2 nm chip technology in May 2021 [START_REF] Bethany | Ibm unveils world's first 2 nanometer chip technology[END_REF]. This latest breakthrough in the technology allows the installation of up to 50 billion transistors on a chip size of a 1 cm 2 .

It has been well documented that decreasing feature sizes can enhance the capabilities of integrated devices, but at the cost of really high power dissipation within the device. That results in higher operating temperature or the creation of hotspots regions -where the local temperature is significantly high, which can limit the performance of these devices [1], [2].

Consequently, for continuous progress in the micro-electronic industry, reduction of heat dissipation or adequate heat spreading materials are essential. In addition, manipulation of heat flows in nanostructures is central, to utilize them for thermal energy conversion applications and storage technologies, such as solid-state thermoelectric power generation and refrigeration based on the Seebeck and Peltier effects [START_REF] Tainoff | Network of thermoelectric nanogenerators for low power energy harvesting[END_REF], [START_REF] Zardo | Manipulating phonons at the nanoscale: Impurities and boundaries[END_REF], [START_REF] Singhal | Nanowire forest of pnictogen-chalcogenide alloys for thermoelectricity[END_REF]. Therefore, a better understanding of energy transfer at nanoscales and, more specifically, heat is required.

Heat Conduction at Sub-Micro Scale

Heat results from the random motion of energy-carrying particles through objects under a temperature gradient as the objects move towards thermodynamic equilibrium. There are three basic modes of heat transfer processes that occur whenever a temperature gradient exists: conduction, convection, and radiation. Typically electrons, photons, and phonons are the leading heat carriers [START_REF] Phillpot | Introduction to thermal transport[END_REF]. The first mode is referred to conduction heat transfer that occurs across a solid or fluid that is maintained at different temperatures, caused by energy transfer from the more energetic to the less energetic particles in the materials. Secondly, heat convection represents the energy transfer processes when the temperature of a surface is different from that of a surrounding moving liquid. Thirdly, thermal radiation is heat transfer between the surfaces of matter at non-zero temperature without any medium; the energy is carried by electromagnetic waves (photons). In solid materials, heat transport is predominantly carried through conduction due to two main heat carriers, namely, phonons and electrons. In metals, electrons are the primary heat carriers at room temperature, whereas, in semiconductors and dielectrics, heat is transported mainly through phonons at room temperature.

Here we will only discuss the heat transport via conduction. As in this thesis, we are solely interested in studying the thermal properties of solids in the absence of moving fluids and where thermal radiation is negligible compared to heat conduction. The details of radiation heat transfer is given in the section 1.6.3.

Fourier's Law and Thermal Conductivity

The French mathematical physicist Joseph Fourier was the first to experimentally determine the thermal conductivity of a material (steel). In his masterpiece The Analytical Theory of Heat, he presented a rigorous analytical formulation to evaluate the heat propagation in the materials. Most importantly, this mathematical foundation is still applicable for diffusive heat transfer work up to this day [START_REF]Thermal conductivity through the 19th century[END_REF]. It is critical to mention that Fourier's law was empirical. However, the Boltzmann transport equation can now be written as Fourier's law in steady-state phonon transport. Basically, Fourier's law describes the heat conduction processes in a homogeneous medium, where the mean free path (MFP) of the heat carriers is significantly smaller than the size of the object. It relates heat flux to the temperature gradient by:

- → φ = -κ - → ∇ T (1.1)
where

- → φ is the heat flux with units of W.m -2 , thermal conductivity κ has units of W.m -1 K -1 ,
which is considered as temperature-independent material property and -→ ∇ T is the temperature gradient. The negative sign states that the heat flow always occurs from the more heated part towards the less heated one.

Soon after the publication of the analytical theory of heat in 1822, plenty of experimental work have been carried out to measure the thermal conductivity of a wide range of materials.

During those times, experimentalists endeavored to perform thermal conductivity measurements by keeping the material between two parallel walls. One wall was continuously heated with boiling water while the other side was cooled utilizing ice. Then, the heat flux between the walls could be estimated from the magnitude of steam condensed or ice melted. Using the above mentioned-method, scientists were able to determine the thermal conductivity of various materials and get some insights on the dependence of heat flow on crystallographic direction [START_REF]Thermal conductivity through the 19th century[END_REF]. One of the most important discoveries of the 19th century was achieved by James Joule, who experimentally showed that the amount of heat generated in a conductor is proportional to the squared of applied current multiplied with the electrical resistance [START_REF] Joule | Xxxii. on the calorific effects of magneto-electricity, and on the mechanical value of heat[END_REF]. With this discovery, the invention of electrical heaters was possible that allowed us to control the heat for thermal conductivity measurements. In this thesis, we will be utilizing the experimental idea provided by James Joule to generate the heating via electrical current, i.e., creating temperature gradient; and combining it with Fourier's law to measure the thermal conductivity or conductance of materials.

In crystalline solids, atoms are arranged periodically and bonded through chemical bonds.

At temperature T , each atom in solid starts to vibrate around its equilibrium position and perturbs the neighboring atoms, resulting in an energy transfer through atomic vibrations.

Quantum mechanically, these atomic vibrations have discrete energy levels, and each quanta of energy is known as a phonon. The phononic contribution to the thermal conductivity (κ th ) in a solid material can be obtained using the kinetic theory, which is expressed as [START_REF] Chen | Nanoscale heat transfer[END_REF]:

κ th = 1 3 CvΛ (1.2)
where C is the volumetric specific heat, v is the average speed of sound, and Λ is the phonon MFP, which is defined as the average distance traveled by heat carriers between two successive inelastic scattering events. Scattering can always take place at boundaries, impurities, defects, and with other heat carriers. Thus, thermal conductivity is the product of the amount of energy carried by a particle moving with a particular speed and the average distance traveled before losing its energy.

As mentioned earlier, in metals, the majority of heat carriers are electrons. The electronic part of thermal conductivity can be obtained by Wiedemann-Franz law which relates the thermal conductivity (κ e ) to the electrical conductivity (σ ) as:

κ e σ = LT (1.3)
where L is the universal Lorentz constant which has a value of 2.44×10 -8 WΩK -2 , and T is the temperature.

Thermal transport due to phonons: at a macroscale, heat transport is described by a diffusive process. At this scale, the MFP of heat carriers is much smaller than the characteristic dimension of a material, giving rise to frequent scattering inside the material. In another case, when the bulk phonon MFP becomes larger than the characteristic dimension of the system, heat carrier scattering occurs with boundaries. This is the so-called Casimir regime [START_REF] Bourgeois | Reduction of phonon mean free path: From low-temperature physics to room temperature applications in thermoelectricity[END_REF]; the phonon MFP is set by scattering on surfaces. In ballistic thermal transport, the dominant wavelength and the MFP of the phonons should be higher than the characteristic dimension of the system. This limit is achieved at very low temperatures where other scattering effects such as phonon-phonon interaction, electron-phonon interaction, scattering on impurities, etc., are minimized.

Phonon Scattering at Nanoscale

The emergence of new micro-and nano-scale materials and devices have created the need for a detailed study and understanding of the thermal transport mechanisms. The well-known examples are nanocomposites, superlattices, thin films and nanowires [START_REF] Singhal | Nanowire forest of pnictogen-chalcogenide alloys for thermoelectricity[END_REF], [START_REF] Liu | Cross-plane thermal conductivity of self-assembled ge quantum dot superlattices[END_REF]. At low dimensions, thermal transport is affected by two physical effects: (i) phonon confinement and

(ii) enhancement of boundary scattering [START_REF] Chen | Nanoscale heat transfer[END_REF]. Phonon confinement occurs when the system sizes are comparable to the dominant thermal wavelength. That leads to the modification of the dispersion relations and flattening of the phonon bands, consequently reducing the sound velocity. In the case of boundary scattering, the magnitude of the phonon MFP becomes comparable to the characteristics dimension of the materials, which in turn results in the reduction of thermal conductivity as compared to the bulk. Table 1.1 shows the typical size and time scales for heat carriers in solid materials at room temperature [START_REF] Cahill | Thermometry and thermal transport in micro/nanoscale solid-state devices and structures[END_REF].

Electrons in metals Phonons in Insulators and Semiconductors

Wavelength λ(nm) 0.1-1 1-5

Mean Free Path (nm) 10 50-500 Relaxation Time (s) (10-100) ×10 -15

(1-10) ×10 -12 Propagation Speed (m/s) (≈ 10 6 ) (3-10) ×10 3 Table 1.1: Typical length and time scales for energy carriers in solids at room temperature [START_REF] Cahill | Thermometry and thermal transport in micro/nanoscale solid-state devices and structures[END_REF] One of the most prominent examples of boundary scattering is the nanowires, which exhibit a significantly lower thermal conductivity than their bulk counterpart because of enhanced phonon-boundary scattering, making them an excellent candidates for innovative thermoelectric material [START_REF] Singhal | Nanowire forest of pnictogen-chalcogenide alloys for thermoelectricity[END_REF]. Another example of the interest in heat transport studies is the heterostructure materials containing nano-inclusions [START_REF] Paterson | Experimental investigation of heat transport in nanomaterials using electrothermal methods[END_REF]. These materials are currently developed to reduce thermal transport to increase the performance of semiconductors for thermoelectricity.

However, the precise mechanisms of the thermal transport in the heterostructures are still not understood well.

Therefore, in nanoscale materials, both diffusive and ballistic thermal transport must be considered as the MFP of heat carriers is comparable to the characteristics length of the materials. This makes the thermal transport in nanometric scale complicated in terms of theoretical point of view [START_REF] Bourgeois | Reduction of phonon mean free path: From low-temperature physics to room temperature applications in thermoelectricity[END_REF]. There are several examples in literature which have shown that the heat generation at the nanoscale devices is significantly different than the prediction by the Fourier's Law [START_REF] Koh | Frequency dependence of the thermal conductivity of semiconductor alloys[END_REF]- [START_REF] Blanc | Phonon heat conduction in corrugated silicon nanowires below the casimir limit[END_REF].

Notably, in this research work, all the experiments have been carried out near room tem-perature. Thus, we are not expecting to observe the ballistic heat transport in our experiments.

Consequently, only diffusive heat transport will be considered to explain the results. In the following section, we only review the most popular techniques used to measure thermal properties at small length scales.

Thermal Measurement Techniques and Limitations

This section discusses the existing techniques for investigating the heat transport properties of materials based on temperature-dependent phenomena. Generally, two basic approaches have been used for studying heat transfer phenomena. One is based on optical methods and another approach relies on electrical methods. Our intention is not to provide an overview of all available thermal characterization techniques but to summarize some widespread highresolution thermal measurements.

Optical techniques

Optical techniques can produce images with a high temporal resolution since these techniques do not require physical contact with a sample. However, their spatial resolution is limited by the Abbe limit of diffraction to about 1 µm. The well-known optical techniques for thermal measurements are infrared thermometry [START_REF] Christofferson | Microscale and nanoscale thermal characterization techniques[END_REF], Raman thermometry [START_REF] Sandell | Thermoreflectance techniques and raman thermometry for thermal property characterization of nanostructures[END_REF] and thermo-reflectance [START_REF] Cahill | Thermometry and thermal transport in micro/nanoscale solid-state devices and structures[END_REF], [START_REF] Sandell | Thermoreflectance techniques and raman thermometry for thermal property characterization of nanostructures[END_REF].

Infrared thermography is a well-matured thermal imagining technique in the industry.

Any material above the absolute zero temperature emits electromagnetic radiation from its surface. Near room temperature, the electromagnetic radiation is in the range of infrared. This technique is based on measuring the infrared radiation intensity emitted by an object and is able to detect the temperature from cryogenic to 6000 K. It is well suited for materials with high emissivities, such as non-metals. At room temperature, the peak thermal radiation wavelength emitted by an object is in the order of 10 µm [START_REF] Christofferson | Microscale and nanoscale thermal characterization techniques[END_REF].

Raman thermometry [START_REF] Sandell | Thermoreflectance techniques and raman thermometry for thermal property characterization of nanostructures[END_REF] is a non-destructive, contactless technique for measuring thermal conductivity with spatial resolution down to 1 µm. It is based on probing the local temperature by detecting the temperature-dependent inelastic scattering of light, so-called Raman scattering. However, the major limitation of the Raman technique is that it can only be applied to materials that must have non-negligible Raman signals like silicon, graphene, diamond, and carbon. As an example, metals and amorphous materials exhibit poor Raman signals. In addition, the temperature sensitivity is low, which is between 5 to 20 K.

Thermoreflectance [START_REF] Sandell | Thermoreflectance techniques and raman thermometry for thermal property characterization of nanostructures[END_REF] technique includes time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance (FDTR). These techniques have been used to measure the thermal properties of bulk samples, thin-film, and interfaces. In the thermoreflectance method, first, the temperature is modulated using a pulsed or frequency-modulated laser.

Then another laser is used to detect this temperature variation by recording the reflectivity of the sample surface. Thermoreflectance measurements can be performed using the EM radiation from infrared range to UV. That allows to increase the spatial resolution to the order of hundreds of nanometres [START_REF] Tessier | Thermoreflectance temperature imaging of integrated circuits: Calibration technique and quantitative comparison with integrated sensors and simulations[END_REF]. A detailed description of thermoreflectance and Raman thermometry have been presented in Ref. [START_REF] Sandell | Thermoreflectance techniques and raman thermometry for thermal property characterization of nanostructures[END_REF] 1.

Electrical techniques

Thermometry at the nanoscale

The electrical methods are most popular in the heat-transfer community due to their simple experimental setups and high accuracy. Integrated thermal resistors, thermocouples, and noise thermometers are the most common electro-thermal sensors for temperature measurements.

Typically, micro-electronic tools are used to fabricated these electro-thermal sensors onto or buried into the sample. Thermal resistor takes advantage of the temperature-dependent electrical resistance, whereas, in thermocouples, temperature-dependent Seebeck voltage is measured. Johnson noise thermometry depends on the noise generated by thermal fluctuations in the electrical resistor and determines the sensor's temperature.

Thermal conductance technique 3ω method is one of the most developed techniques for measuring the thermal conductivity of solid samples [START_REF] Cahill | Thermal conductivity measurement from 30 to 750 k: The 3-omega method[END_REF]. In principle, the 3ω method employs a one-dimensional thin metal film deposited on a sample that acts both as a heater and thermometer. An alternating current of angular frequency ω is applied through the metal film that results in heating due to the Joule effect. The heat generated in the metal film induces temperature oscillations at angular frequency 2ω. Therefore, temperature oscillation leads to a periodic change in the electrical resistance of the metal film at angular frequency 2ω. Consequently, a voltage at frequency 3ω develops across the metallic line proportional to the temperature oscillation at 2ω. From this temperature oscillation, the thermal properties of the system beneath the metallic line are extracted. This technique has been applied to thin films [START_REF] Liu | Sensitive 3-omega measurements on epitaxial thermoelectric thin films[END_REF], nanowires [START_REF] Bourgeois | Measurement of the thermal conductance of silicon nanowires at low temperature[END_REF] and gives the average thermal conductivity of the sample. One major limitation of this technique is that it does not provide the local thermal conductivity information.

Importantly, the choice of thermal measurement technique is highly dependent upon the Chapter 1. Literature Review 1.3. Scanning Thermal Microscopy (SThM) specific requirements of the task. For example, optical techniques allow generating the highspeed thermal map, whereas 3ω method is suitable for highly sensitive thermal measurements.

Amongst many different existing thermal measurement techniques, Scanning Thermal Microscopy (SThM) is one of the best available tools to probe the temperature and thermal properties of materials with the highest spatial resolution at very small length scales [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF], [START_REF] Majumdar | Scanning thermal microscopy[END_REF]- [START_REF] Zhang | A review on principles and applications of scanning thermal microscopy (sthm)[END_REF].

In particular, the SThM technique permits the thermal characterization of heterostructures with nanoscale spatial resolution. Also, it can detect nanometer-sized hotspots in modern nanoelectronic devices. As a consequence, this technique has a great potential to contribute in the growth of future technologies. In the next section, we will first discuss the SThM technique in detail, starting from the history to the modern SThM experimental setup. Then, the discussion will be followed by explaining the various existing SThM probes and the heat transfer processes between the tip and the sample.

Scanning Thermal Microscopy (SThM)

The invention of the scanning tunneling microscope (STM) and the atomic force microscope (AFM) enable materials study and manipulation at the atomic level. Since then, a variety of novel scanning probe microscopy-based techniques have been developed to explore magnetic, electronic, optical, thermal, chemical, and mechanical properties of materials at a microscopic scale [START_REF] Midha | Batch-fabrication of novel nanoprobes for spm[END_REF]. SThM is an advanced form of a scanning probe microscopy (SPM) technique to investigate the heat transport and local temperature fields in nanoscale materials, structures, and devices.

This part of the thesis is dedicated to the present state-of-the-art of SThM technique in thermal science. It includes a brief history of the technique, principle, development of various probes designed to improve performance. Then, the comparison of different operational modes is presented. After, the description of four major heat transfer mechanisms is discussed. In particular, this part of the thesis has been written with continuous references to the following scientific works [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF], [START_REF] Majumdar | Scanning thermal microscopy[END_REF], [START_REF] Zhang | A review on principles and applications of scanning thermal microscopy (sthm)[END_REF], [START_REF] Borca-Tasciuc | Scanning probe methods for thermal and thermoelectric property measurements[END_REF]- [START_REF] Lambert | Design, fabrication and characterisation of thermally optimised novel sthm probes[END_REF].

Historically, in 1986, Williams and Wickramasinghe were the first ones who introduced the scanning thermal probe. Their probe accounted for mapping the topography images of conducting and non-conducting materials to resolve the shortcomings of the STM technique, which is limited to conducting materials. The thermal probe was fabricated by placing a thermocouple junction at the end of the conventional STM tip, and the technique was known as scanning thermal profiler (STP) [START_REF] Williams | Scanning thermal profiler[END_REF]. In this technique, the temperature of the thermal probe works as an intermediate quantity for maintaining constant tip-sample distance, in a similar way to a STM, where the tunneling current is used to regulate the height of the tip. Although the STP technique could not be used to make the thermal maps of the surface, this was the beginning of the SPM-based technique in thermal science. Afterward, continuous efforts have been carried out in the field of thermal microscopy based on STM [START_REF] Weaver | Optical absorption microscopy and spectroscopy with nanometre resolution[END_REF]. However, the major disadvantage of this technique is that an STM-based system can only be applied to electrically conducting samples.

On the other hand, the AFM technique can be utilized on all kinds of solid materials such as metals, semiconductors, and insulators. Therefore, AFM-based microscopy is preferred over STM. AFM is proven to be a versatile technique as various sensors at the AFM probe tip could be integrated, allowing to study multiple aspects of localized characteristics [START_REF] Midha | Batch-fabrication of novel nanoprobes for spm[END_REF].

The next breakthrough in the field of thermal science took place in 1993 when Majumdar et al. [START_REF] Majumdar | Thermal imaging using the atomic force microscope[END_REF] developed a thermal probe by replacing the conventional AFM probe with two metallic wires to form a thermocouple junction. This probe was adequate to map the surface topography and the thermal map of the metal-semiconductor field-effect transistor simultaneously.

Notably, this AFM-based thermal microscope proposed by Majumdar et al. [START_REF] Majumdar | Thermal imaging using the atomic force microscope[END_REF] could be accounted as a building block for the modern SThM setups. A schematic of the basic SThM setup is shown in Figure 1.1. An SThM setup generally consists of the following components:

• a sharp probe with integrated sensor which can act as a heater and thermometer.

• an AFM control unit for controlling the probe-sample distance or force during the scan.

• a thermal control unit for data acquisition from the thermal probe.

• a heat source either internal (probe itself) or external (laser beam).

Generally, in AFM-based SThM, the optical deflection system is utilized to detect the thermal probe's cantilever deflection, similar to what is used in the conventional AFM technique.

With the knowledge of the cantilever's spring constant, the tip-sample contact force can be determined. In the SThM studies, contact mode is typically performed where a constant force between tip-sample is applied to enable the scanning of the surface. The cantilever deflection generates a signal in the photodetector during the scan. Subsequently, a feedback signal in the AFM control unit is generated, resulting in the movement of either the sample stage or the probe stage, depending on the system. At the same time, variation in the temperaturedependent physical property of the SThM probe is monitored and controlled by the thermal control unit. Finally, topography and a thermal image of the sample can be obtained with high spatial resolution, as shown in Figure 1.2 [5].

Thermal probes

In the SThM technique, the thermal probe is central to the entire system that quantifies its capability, performance, and range of operations. Since 1993, several physical effects have been utilized to fabricate thermal probes that depend on temperature-dependent properties. It includes the thermoelectric voltage [START_REF] Majumdar | Thermal imaging using the atomic force microscope[END_REF][41], electrical resistance [START_REF] Assy | Heat transfer at nanoscale contacts investigated with scanning thermal microscopy[END_REF], [START_REF] Ge | Topography-free sample for thermal spatial response measurement of scanning thermal microscopy[END_REF], thermal expansion [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF], critical current in superconducting junction [START_REF] Halbertal | Nanoscale thermal imaging of dissipation in quantum systems[END_REF] and fluorescence [START_REF] Samson | Ac thermal imaging of nanoheaters using a scanning fluorescent probe[END_REF]. Its spatial and thermal resolutions depend on tip sharpness, tip-sample heat transfer mechanism and thermal environment. Specifically, thermocouple and electric resistance-based thermal probes are the most used in the community due to their easeful implementation, high spatial and temporal resolutions. They can be used to detect temperature as well as thermal conductivity of the materials. Table 1.2 is presented at the end of this chapter that compares the various thermal probes, sensitivity, tip radius, advantages and disadvantages.

Thermocouple probe

Thermocouple-based SThM probes take advantage of the temperature-dependent thermoelectric voltage generated as output across the junction between two dissimilar electrodes. As mentioned earlier, integration of a thermocouple on a scanning probe was first introduced by Williams and Wickramasinghe [START_REF] Williams | Scanning thermal profiler[END_REF]. Followed by Majumdar et al. [START_REF] Majumdar | Thermal imaging using the atomic force microscope[END_REF], who were able to develop the very first thermal system to map topography and thermal images with a submicrometer lateral resolution using a thermocouple based probe. Subsequently, Majumdar and coworkers continued developing probes with improved design, operation, and sharp tips [START_REF] Majumdar | Thermal imaging by atomic force microscopy using thermocouple cantilever probes[END_REF], [START_REF] Lai | Thermal detection of device failure by atomic force microscopy[END_REF]. Luo et al. [START_REF] Luo | Sensor nanofabrication, performance, and conduction mechanisms in scanning thermal microscopy[END_REF] one of them who reduced the thermocouple junction size significantly by deposition of gold (Au) and nickel (Ni) thin films onto the commercially available silicon nitride probes. The first batch fabricated thin-film thermocouple SThM probes were developed by Mills et al. [START_REF] Mills | Scanning thermal microscopy using batch fabricated thermocouple probes[END_REF]. Further, new design and batch fabricated SThM probes were proposed to increase lateral resolution, temperature sensitivity, and improved thermal time response [START_REF] Shi | Design and batch fabrication of probes for sub-100 nm scanning thermal microscopy[END_REF]- [START_REF] Chae | Fabrication of scanning thermal microscope probe with ultra-thin oxide tip and demonstration of its enhanced performance[END_REF]. In 2006, the thermal conductivity of materials was measured using thermocouple probes via the 2ω method [START_REF] Roh | Novel nanoscale thermal property imaging technique: The 2-omega method. i. principle and the 2-omega signal measurement[END_REF]. Furthermore, null-point scanning thermal microscopy has been developed, and its principle is based upon establishing a thermal equilibrium, where heat flux between the tip and the sample becomes zero. This method allows performing quantitative thermometry measurements under ambient conditions by eliminating the parasitic heat transfer through the air gap between the SThM probe and the sample surface [START_REF] Chung | Quantitative temperature profiling through null-point scanning thermal microscopy[END_REF]- [START_REF] Umatova | Quantification of atomic force microscopy tip and sample thermal contact[END_REF]. avoid heat transfer through air and water meniscus. The probe's spatial resolution and Seebeck coefficient were claimed to be about 10 nm and 16.28 µV/K, respectively. [START_REF] Kim | Ultra-high vacuum scanning thermal microscopy for nanometer resolution quantitative thermometry[END_REF]. Generally, the main advantage of a thermocouple probe is the proximity of the sensor with samples. This proximity enables to perform measurements of enhanced radiative thermal transport in the ultra near field [START_REF] Kim | Radiative heat transfer in the extreme near field[END_REF] when the distances between the tip-sample reach to few nm. However, the sensitivity of thermocouple-based probes is low, which could lead to noisy temperature profiles.

Resistive probes

Resistive SThM probes measure the temperature-dependent electrical resistance of the sensitive part of the probe and provide information about the local temperature field of the sample.

In the literature, metallic thin film [START_REF] Mills | Scanning thermal microscopy using nanofabricated probes[END_REF], metallic bent wire [START_REF] Assy | Heat transfer at nanoscale contacts investigated with scanning thermal microscopy[END_REF], [START_REF] Pylkki | Scanning near-field optical microscopy and scanning thermal microscopy[END_REF] and semiconducting silicon doped probes [START_REF] Binnig | Ultrahigh-density atomic force microscopy data storage with erase capability[END_REF] have been used as a resistive thermal sensor in the SThM probe configuration. Generally, such sensors require a high-temperature coefficient of electrical resistance and thermally isolated support, i.e., a cantilever with a relatively low thermal conductance to maximize sensor heating.

Wollaston wire probe

The very first innovative metallic resistive SThM probe was designed by Pylkii et al. [4], [START_REF] Pylkki | Scanning near-field optical microscopy and scanning thermal microscopy[END_REF] in 1994. This SThM probe is made out of the Wollaston wire. The cantilever part consists of a silver shell diameter of 75 µm and a core consists of an alloy of platinum and rhodium of 5 µm in diameter [4]. At the extremity of the cantilever, the wire is bent to form a V-shape tip, The spring constant of the Wollaston wire probe was documented to be 5-20 Nm -1 . Its temperature coefficient of resistivity and thermal response has found to be equal to 1.66

×10 -3 K -1
and 200 µs in air, respectively [START_REF] Assy | Heat transfer at nanoscale contacts investigated with scanning thermal microscopy[END_REF], [START_REF] Lefevre | Probe calibration of the scanning thermal microscope in the ac mode[END_REF]. This probe can work as a temperature sensor and/or heater, depending on the operating mode. With this kind of probe, various thermal behavior of materials have been studied, such as thermal conductivity, phase transitions, and recently the Seebeck coefficient of a material [START_REF] Wilson | Thermal conductivity measurements of high and low thermal conductivity films using a scanning hot probe method in the 3-omega mode and novel calibration strategies[END_REF]. This probe has been attractive for several years due to its high endurance and electrical characteristics. However, the main limitations of this probe are its lack of thermal investigations at nanoscale due to its low spatial resolution below ∼1µm

and the difficulty to adapt the process for batch fabrication.

Microfabricated metallic probes from (KNT)

Microfabricated probes based on palladium (Pd) thermometer integrated on the silicon nitride cantilever (formerly silicon oxide) were developed by Mills et al. [START_REF] Mills | Scanning thermal microscopy using batch fabricated thermocouple probes[END_REF], now known as Kelvin Nanotechnology (KNT) probe. SEM images of the microfabricated metallic thermal probe are illustrated in Figure 1.5. The cantilever of the probe is made of 400 nm thick silicon nitride (SiN), and a thin film of high resistance Pd (50 nm thick) is lithographically patterned at the apex of the tip, which acts as a thermoresistive sensor. This probe consists of two current limiters of nickel-chromium with gold pads for the electrical connection to the thermal unit [5], [START_REF] Dobson | New methods for calibrated scanning thermal microscopy (sthm)[END_REF], [START_REF] Tovee | Nanoscale spatial resolution probes for scanning thermal microscopy of solid state materials[END_REF]. The height of the tip is about 10µm, and the radius of curvature is in the range of sub-100 nm. The height of the tip is an important factor to improve the sensitivity in ambient conditions by minimizing the heat transport via air conduction between the cantilever and the sample. The temperature coefficient of electrical resistance, nominal spring constant and thermal response are 1.2×10 -3 K -1 , 0.35 Nm -1 and few tens of µs [START_REF] Zhang | High temperature imaging using a thermally compensated cantilever resistive probe for scanning thermal microscopy[END_REF].

Doped Silicon Resistive probe

The doped silicon nanoprobe is another type of thermal resistive probe developed by the International Business Machines Corporation (IBM). It was initially designed for data-storage memory applications [START_REF] Binnig | Ultrahigh-density atomic force microscopy data storage with erase capability[END_REF]. Recently, it has been demonstrated to perform nanolithography [START_REF] Garcia | Advanced scanning probe lithography[END_REF]. A schematic of the silicon cantilever with integrated heater/sensor is shown in Figure 1.6, which has a highly phosphorus-doped cantilever region for electrical conduction, and the low-doped region serves as heater/sensor [START_REF] Menges | Nanoscale thermometry by scanning thermal microscopy[END_REF]. Typically these probes have 500 to 700 nm long tips while the radius of curvature is about 10 nm. The nominal spring constant and thermal response is reported to be 0.15-0.20 Nm -1 and 100 µs, respectively. Passive-SThM mode is also referred as temperature contrast mode (TCM). In this mode, a low electrical current flows through the probe while scanning the sample surface and monitoring the electrical voltage of the probe. Importantly, the magnitude of the applied current should be small enough to avoid Joule heating. During the scan, heat flow occurs from the hot/active sample to the probe that causes a temperature variation in the tip, and thus a change in the electrical resistance of the probe [START_REF] Assy | Heat transfer at nanoscale contacts investigated with scanning thermal microscopy[END_REF] which can be written as the following equation:

R p (T ) = R 0 (1 + α(T -T 0 )) (1.4)
where

α = 1 R 0 ∆R p (T ) (T -T 0 ) (1.5)
α is the temperature coefficient of resistance (TCR). R p (T ) is the probe electrical resistance at a temperature T, R 0 is the probe electrical resistance at reference temperature T 0 . This mode has been applied for measuring in-plane temperature profiles and locates hotspots in microand nano-electronics devices [START_REF] Menges | Quantitative thermometry of nanoscale hot spots[END_REF].

Active-SThM mode: In this mode, the probe is heated up either by an external source, i.e.

electromagnetic radiations, or an internal one via Joule effect. Generally, the latter method is the most employed for thermal probe heating. A large amount of electrical current passes through the probe that causes the significant Joule heating in the probe. When the heated probe is in contact with a sample (in air conditions), the heat flows partially into the sample and partially in the air. The amount of heat propagating inside the sample depends on the sample's thermal conductivity and the temperature gradient between the tip-sample [START_REF] Majumdar | Scanning thermal microscopy[END_REF]. That results in the variation of the probe's temperature, which can be extracted from the change in electrical resistance, using Equation 1.4. Moreover, this temperature can be related to the thermal conductivity of the sample through an appropriate thermal model [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF]. Typically, active SThM mode has been used to determine the different thermophysical properties of materials such as thermal conductivity [START_REF] Puyoo | Scanning thermal microscopy of individual silicon nanowires[END_REF], phase transition [START_REF] Nelson | Measuring material softening with nanoscale spatial resolution using heated silicon probes[END_REF], and Seeback coefficient [START_REF] Borca-Tasciuc | Scanning probe methods for thermal and thermoelectric property measurements[END_REF]. In most active-SThM, DC heating is applied to the probe due to its easiness of interpretation of experimental data to extract the thermal transport properties of the materials [START_REF] Borca-Tasciuc | Scanning probe methods for thermal and thermoelectric property measurements[END_REF].

Active 3ω-SThM mode: as previously stated, 3ω method is one of the most developed techniques for measuring the thermal conductivity of solid samples [START_REF] Cahill | Thermal conductivity measurement from 30 to 750 k: The 3-omega method[END_REF]. In principle, the 3ω 1.6. Heat Transfer Mechanisms method employs a thin metal film (large aspect ratio) deposited on a sample that acts as both heater and thermometer. In 1999, Fieged et al. [START_REF] Fiege | Quantitative thermal conductivity measurements with nanometre resolution[END_REF] combined the SThM with 3ω method to perform quantitative thermal measurements with higher accuracy. The basic idea of this technique is the same as classical 3ω: an AC current with an amplitude of I 0 at angular frequency ω is applied through the probe that results in heating due to the Joule effect. The heat generated in the probe causes temperature oscillations (T 2ω ), which varies at 2ω. Therefore, the electrical resistance of the probe is also oscillating at 2ω. Finally, the voltage measurement across the probe contains two harmonic components: ω and 3ω. Generally, the 3ω component is used to extract the thermal information of a sample.

Since the voltage at frequency 3ω is proportional to the temperature oscillation at 2ω, which we refer to the probe's root-mean-square temperature oscillation T 2ω as:

T 2ω = 2V 3ω R 0 I 0 α (1.6)
In 2005, Lefèvre and Volz [START_REF] Lefèvre | 3 omega-scanning thermal microscope[END_REF] performed 3ω-SThM using Wollaston wire probe and proposed a theoretical model along with experimental validation for 3ω-SThM. Following the same idea, Puyoo et al. [START_REF] Puyoo | Thermal exchange radius measurement: Application to nanowire thermal imaging[END_REF] applied the 3ω-SThM using Wollaston and KNT thermal probe to determine the thermal time constant, the thermal exchange radius between the tip-sample, and the thermal image of silicon nanowires.

Thermal penetration depth (TPD) is an important concept to understand and determine the depth of the heat flux lines inside the sample using the 3ω-SThM. It is defined as:

T P D = Λ T P D = κ y ρC p ω H (1.7)
where κ y is the thermal conductivity of a sample in the cross-plane direction. ω H = 2ω is the heating frequency that is twice the frequency (ω) of the driving current. C p is the specific heat of the material with units of Jkg -1 K -1 , and it is defined as the amount of energy needed to increase the temperature of the materials by one degree at constant pressure. TPD is inversely proportional to the heating frequency, which means the length over which the heat flux can go inside the sample can be tuned with the heating frequency.

Heat Transfer Mechanisms

A fundamental understanding of the heat transfer mechanism between the thermal probe and the sample is crucial for performing quantitative thermal measurements. Additionally, the sensitivity and spatial resolution in the SThM techniques also depend on the heat transfer 1.6. Heat Transfer Mechanisms

Chapter 1. Literature Review mechanisms. When the SThM measurements are carried out in the air, the heat transfer mechanisms include heat conduction via direct solid-solid contact, conduction through air between the probe and the sample, heat conduction through the liquid meniscus, and the thermal radiation. In fact, SThM experiments in air conditions result in parasitic heat transfer via air conduction and water meniscus, leading to reduced thermal spatial resolution. Figure 1.7 shows a schematic diagram of heat transfer mechanisms from the hot tip to sample. The effective thermal conductance G ef f ,c between the probe and sample may be described by the following equation assuming that all heat transfer mechanisms are independent [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF], [START_REF] Majumdar | Scanning thermal microscopy[END_REF]:

G ef f ,c = G rad + G air + G w + G ss (1.8)
where G rad , G air , G w and G ss are the thermal conductance through radiation, air conduction, water meniscus and conduction through solid-solid contact, respectively.

Air Conduction

When SThM measurements are not performed in the vacuum environment, air conduction plays a significant role in tip-sample heat transfer. Depending on the temperature gradient exists between the tip-sample system, heat can be transferred from the hot tip to the sample or vice versa. In non-contact SThM mode, the air conduction can be observed quite readily over a few microns distance. Fourier's law can explain the heat conduction between the tipsample. However, at distances smaller or comparable to the mean free path of air molecules (70 nm), ballistic and quasi-ballistic regimes should be considered [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF]. For example, using the Wollaston probe in air, up to 65% of heat transfer has been measured from the probe to the sample via the surrounding air [START_REF] Gomès | Dc thermal microscopy: Study of the thermal exchange between a probe and a sample[END_REF]. The experiments performed using doped silicon probe in air suffer from poor sensitivity because of the small distance between the sensor to the sample [START_REF] Tovee | Nanoscale spatial resolution probes for scanning thermal microscopy of solid state materials[END_REF]. In the case of palladium probe, the tip size is about 10µm, thus, it is suitable for thermal measurement in air conditions. Nevertheless, the thermal transport in air conditions is partly diffusive and ballistic, making the quantitative thermal measurements quite complex.

Water Meniscus

In humid air conditions, a water meniscus appears on the sample surface due to the capillary condensation of humidity. The size of the water meniscus depends on the hydrophilic nature of the sample surface, humidity, and temperature. In the literature, heat conduction via water

Heat Transfer Mechanisms

Chapter 1. Literature Review meniscus is scarcely studied. Majumdar's group [START_REF] Luo | Nanofabrication of sensors on cantilever probe tips for scanning multiprobe microscopy[END_REF] first suggested that the heat conduction through water meniscus is the same order of magnitude as solid-solid conduction. That might be due to the fact that the authors did not consider the thermal conduction at the probe-water and water-sample contacts. Several years later, Shi et al. [START_REF] Shi | Thermal transport mechanisms at nanoscale point contacts[END_REF] found that the heat transfer through water meniscus is negligible compared to air and solid-solid conduction. Following this work, Assy et al. [START_REF] Assy | Temperature-dependent capillary forces at nano-contacts for estimating the heat conduction through a water meniscus[END_REF] investigated the heat transfer through the meniscus using doped silicon and palladium probes. They reported that the thermal conductance of the water meniscus depends on the probe temperature, and it could reach 4% for the doped silicon probe, and 6%

for palladium probe of the total conduction [START_REF] Assy | Temperature-dependent capillary forces at nano-contacts for estimating the heat conduction through a water meniscus[END_REF].

Thermal Radiation

Thermal radiation is the energy emitted by matter at non-zero temperatures. Electromagnetic waves (photons) are responsible for radiative heat transport. Wien's displacement law provides the peak wavelength of the thermal radiation that depends on the temperature; λT=2897 µmK.

When inter-objects distances are greater than Wien's wavelength, the classical theory of radiative heat transfer is valid. It is a so-called far-field radiative heat transfer. In contrast, when the gap size between objects is smaller than Wien's wavelength, near field heat radiative transfer occurs that can be very different from the far-field due to tunneling of evanescent surface waves [START_REF] Mulet | Enhanced radiative heat transfer at nanometric distances[END_REF], [START_REF] Shen | Surface phonon polaritons mediated energy transfer between nanoscale gaps[END_REF].

When the SThM experiment is performed in ambient conditions, in that case, it is impossible to estimate the amount of heat lost by thermal radiation due to the accumulation of thermal radiation with air convection [START_REF] Borca-Tasciuc | Scanning probe methods for thermal and thermoelectric property measurements[END_REF]. In the vacuum condition, it has been reported that the nearfield radiation transfer can be enhanced up to two orders of magnitude [START_REF] Kim | Radiative heat transfer in the extreme near field[END_REF], [START_REF] Shen | Surface phonon polaritons mediated energy transfer between nanoscale gaps[END_REF]. However, this mechanism becomes critical when the temperature gradient between the tip-sample is very high under ultra-high vacuum conditions (10 -9 mbar). Overall, when the SThM experiments are carried out near room temperature, radiation transfer is considered negligible [START_REF] Majumdar | Scanning thermal microscopy[END_REF].

Conduction at the Tip-Sample Contact

In the SThM probe, generally, temperature-sensitive elements are not integrated at the very end of the tip apex. It might result in a short circuit between the tip and conducting sample.

Also, the reproducibility of the measurement will be affected due to the degradation of the tip.

For example, in doped silicon, the sensing/heating part is located at the cantilever, and the palladium probe consists of a temperature sensor near the apex of the tip.

In contact SThM mode, heat transfer through solid-solid conduction between tip-sample plays an important role. The presence of an interface between tip-sample surfaces results in thermal boundary resistance. This thermal boundary resistance mainly depends on the surface roughness, contact force, contact area, chemical bonding between the solid atoms, and mechanical properties of contacting materials. Generally, the effective radius of contact between the tip-sample system is estimated by using mechanical contact theories. These theories estimate the contact area by considering a spherical surface and a flat surface. In addition, SEM imaging can be utilized to measure the radius of curvature of the tip apex. Knowing the contact area between the tip-sample, the thermal boundary resistance can be estimated between solid-solid surfaces using the following relationship:

R c = R th,b πb 2 c (1.9)
where b c is the contact radius, R th,b is a thermal boundary resistance with the unit of m 2 KW -1 . The values of R th,b experimentally determined for solid-solid contacts lie in the range of 5×10 -7 to 5×10 -9 m 2 KW -1 near room temperature. Stoner et al. [START_REF] Stoner | Kapitza conductance and heat flow between solids at temperatures from 50 to 300 k[END_REF] and Haeberle et al. [START_REF] Haeberle | Nanometer-scale heat-conductivity measurements on biological samples[END_REF] showed that the value of R th,b is not always constant due to presence of surface roughness or oxide layers on the sample surface.

The surface roughness of the tip and sample can strongly impact the thermal boundary resistance, i.e., influence the thermal transport. Gotsmann et al. [START_REF] Gotsmann | Quantized thermal transport across contacts of rough surfaces[END_REF] examined the contact force dependence thermal transport via tip-sample in a vacuum. The authors argued that a quantized thermal conductance could occur when the diameter of the heat exchange area is smaller than the transversal phonon coherence length and developed a model taking into account the nanoscale roughness.

Towards a Highly Sensitive Thermal Probe

The development of advanced SThM techniques requires a drastic improvement in the SThM probe sensitivity to detect an extremely small amount of heat flow between the tip apex of the SThM probe and the sample surface.

As discussed in the previous sections, electrical resistance-based thermal sensors are the most widely used for their convenience and sensitivity. Commonly used materials include metallic thin films of platinum (Pt), alloy of platinum-rhodium (Pt90/Rh10) [START_REF] Pylkki | Scanning near-field optical microscopy and scanning thermal microscopy[END_REF], [START_REF] Lefèvre | 3 omega-scanning thermal microscope[END_REF], palladium (Pd) [START_REF] Dobson | New methods for calibrated scanning thermal microscopy (sthm)[END_REF], low doped silicon probes [START_REF] Menges | Nanoscale thermometry by scanning thermal microscopy[END_REF] and alloy of platinum-carbon (Pt-C) [START_REF] Rangelow | Thermal nano-probe[END_REF]. In resistive thermal sensors, a higher temperature coefficient of resistance leads to better sensitivity. Concerning the current existing resistive SThM probes, they can provide a high lateral resolution but exhibit meager thermal sensitivities due to their moderate temperature coefficient between 1 to 2 × 10 -3 K -1 near room temperature. Such low thermal sensitivities compel the need for a high thermal exchange between the probe and the sample, i.e., a strong decrease in heat flux limiting the measurements at a lower temperature gradient. Thus, there is a continued interest in improving the SThM probe's sensitivity to meet the scientific and technical needs to probe the temperature fields and thermal conductivity at low dimensions.

Therefore, the ultimate objective of this work is to elaborate SThM probes with significantly enhanced thermal sensitivity using niobium nitride (NbN) alloy thin films as temperaturesensitive materials that exhibit a high temperature coefficient of resistance low thermal conductivity. In our group, NbN based resistive thermometer has been used extensively for performing nanoscale thermal measurements from room temperature to cryogenic temperature [START_REF] Blanc | Phonon heat conduction in corrugated silicon nanowires below the casimir limit[END_REF], [START_REF] Heron | Mesoscopic size effects on the thermal conductance of silicon nanowire[END_REF], [START_REF] Blanc | Heat transmission between a profiled nanowire and a thermal bath[END_REF]. It has shown a negative temperature coefficient of resistance which can be up to 1 ×10 -2 K -1 [START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF] at room temperature that is about 5 to 10 times higher than the metallic and semiconducting resistive SThM probes. It is essential to mention that throughout this thesis, the temperature coefficient of resistance will be written in absolute value for comparing it with other thermal sensors. Table 1.2 shows the main characteristics of various thermal probes with some advantages and disadvantages.

Summary

In this chapter, an introduction of various available techniques to investigate thermal transport is presented. Often, the majority of the optical techniques are limited by the diffraction limit.

It is challenging to detect hotspots and local thermal properties of nanoscale heterostructures at the nanoscale. Thus, SThM is the only technique to overcome these limitations.

Then, we detailed the SThM technique, including the general principle of measurement and various types of probes. During the development of SThM probes, the radius of curvature has been reduced for obtaining better spatial resolution. However, decreasing the tip apex's size leads to higher thermal boundary resistance between the tip-sample that makes the thermal measurements very difficult at a small scale.

To resolve the temperature sensitivity issue, we propose using a unique type of resistive thermometry based on NbN, which has shown a temperature coefficient of resistivity up to 10 times higher than the existing resistive thermal sensor. In the next chapter, we will present the fabrication process to integrate the high-sensitivity thin films of NbN on the AFM tip. In the first part of this chapter, we will discuss the optimization of the electron beam lithography process on a flat surface using a thermally evaporated electron-sensitive resist. In the second part, we will focus on utilizing the resist for patterning on a nonplanar, suspended AFM cantilever. Finally, we will present the details of several fabrication strategies conducted during this research to integrate the NbN thermometer on the AFM tip as well as the challenges encountered.

Introduction

The fields of energy [START_REF] Tainoff | Network of thermoelectric nanogenerators for low power energy harvesting[END_REF], [START_REF] Zardo | Manipulating phonons at the nanoscale: Impurities and boundaries[END_REF], [START_REF] Singhal | Nanowire forest of pnictogen-chalcogenide alloys for thermoelectricity[END_REF], micro-and nano-electronics [1], fundamental study of quantum effects [START_REF] Tavakoli | Heat conduction measurements in ballistic 1d phonon waveguides indicate breakdown of the thermal conductance quantization[END_REF] and lab-on-chip technologies [START_REF] Consales | Labon-fiber technology: Toward multifunctional optical nanoprobes[END_REF] require innovative and effective nanofabrication strategies. Electron beam lithography (EBL) [START_REF] Grigorescu | Resists for sub-20-nm electron beam lithography with a focus on hsq: State of the art[END_REF] is the most widely employed lithographic technique for fabricating novel nanostructures and prototyping devices at the nanoscale. The ongoing trend in nanotechnology is to fabricate nanostructures on nonplanar 3D architectures that can find application in many areas such as lab-on-chip technologies [START_REF] Consales | Labon-fiber technology: Toward multifunctional optical nanoprobes[END_REF], MEMS (Micro-Electro-Mechanical-System) and nano-electronics [START_REF] Ko | A hemispherical electronic eye camera based on compressible silicon optoelectronics[END_REF]. More specifically, magnetic force microscopy [START_REF] Zhou | Lithographically defined nano and micro sensors using "float coating" of resist and electron beam lithography[END_REF], [START_REF] Sarajlic | Batch fabrication of scanning microscopy probes for thermal and magnetic imaging using standard micromachining[END_REF], tip-enhanced Raman spectroscopy [START_REF] Yeo | Tip-enhanced raman spectroscopyits status, challenges and future directions[END_REF], near-field optical focusing [START_REF] Johnson | Highly reproducible near-field optical imaging with sub-20-nm resolution based on template-stripped gold pyramids[END_REF], scanning single-electron transistor microscopy [START_REF] Martin | Observation of electron-hole puddles in graphene using a scanning single-electron transistor[END_REF] and scanning thermal microscopy (SThM) [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF], [START_REF] Majumdar | Scanning thermal microscopy[END_REF], [START_REF] Zhang | A review on principles and applications of scanning thermal microscopy (sthm)[END_REF], [START_REF] Kim | Ultra-high vacuum scanning thermal microscopy for nanometer resolution quantitative thermometry[END_REF], [START_REF] Dobson | New methods for calibrated scanning thermal microscopy (sthm)[END_REF], [START_REF] Edinger | Novel high resolution scanning thermal probe[END_REF]- [START_REF] Pernot | Frequency domain analysis of 3-omega-scanning thermal microscope probe-application to tip/surface thermal interface measurements in vacuum environment[END_REF] are the well-known examples of the nanofabrication on nonplanar 3D AFM probes. Recently, a considerable amount of literature has been published on EBL for creating nanostructures on irregular surfaces [START_REF] Yamazaki | Electron beam lithography on vertical side faces of micrometer-order si block[END_REF]- [START_REF] Zharik | Nanometer scale lithography with evaporated polystyrene[END_REF]. However, it is still very challenging to perform EBL on nonplanar, 3D architectures because of the lack of uniformity and reproducibility of e-resist films on the substrates. Among various techniques, spin coating is the most widely used method for resist deposition to structure materials and devices because of its simplicity, uniformity, and costeffectiveness. However, one of the key issue of this method is its inhomogeneities of film thickness when used to coat nonplanar, suspended, and 3D substrates, which is due to the presence of edge-bead effects [START_REF] Zharik | Nanometer scale lithography with evaporated polystyrene[END_REF]. On the contrary, it has been reported that e-resist with low-viscosity and low-surface-tension can be coated on nonplanar surfaces [START_REF] Yamazaki | Electron beam lithography on vertical side faces of micrometer-order si block[END_REF] by spin coating. Besides spin coating, several other methods have been demonstrated to deposit resist films on nonplanar surfaces such as spray coating [START_REF] Linden | Spray coating of pmma for pattern transfer via electron beam lithography on surfaces with high topography[END_REF], Langmuir-Blodgett (LB) technique [START_REF] Peterson | Langmuir-blodgett electron-beam resists[END_REF], float coating [START_REF] Zhou | Lithographically defined nano and micro sensors using "float coating" of resist and electron beam lithography[END_REF], monolayer brush [START_REF] Dey | Electron beam lithography on irregular surface using grafted pmma monolayer as resist[END_REF]- [START_REF] Aydinoglu | Grafted polystyrene monolayer brush as both negative and positive tone electron beam resist[END_REF], dip coating [START_REF] Yamada | Single layer surface-grafted pmma as a negative-tone e-beam resist[END_REF], [START_REF] Glass | Micronanostructured interfaces fabricated by the use of inorganic block copolymer micellar monolayers as negative resist for electron-beam lithography[END_REF] and ice lithography [START_REF] King | Nanometer patterning with ice[END_REF]- [START_REF] Zhao | Ice lithography for 3d nanofabrication[END_REF].

The spray coating shows inadequacy to form uniform resist films on samples with sharp edges or corners. The LB technique allows resist coating on curved surfaces but leads to ultra-thin layers that make pattern transfer challenging and inadequate to dry etching processes [START_REF] Peterson | Langmuir-blodgett electron-beam resists[END_REF].

Float coating can provide a uniform layer of resist on relatively large structures, yet it is difficult to obtain homogeneous film on very small structures, such as small holes. Likewise, dip coating has been carried out for resist deposition on irregular surfaces, but this method cannot reproduce the identical or uniform layer of e-resist on nonplanar surfaces. Further, ice lithography (IL) shows the capability to fabricate structures and devices with high-resolution features [START_REF] Han | Nanopatterning on nonplanar and fragile substrates with ice resists[END_REF], [START_REF] Zhao | Ice lithography for 3d nanofabrication[END_REF]. However, its main drawbacks are the requirement for a specifically modified scanning electron microscope (SEM) and ice-resists have an extremely low sensitivity, resulting in a higher cost and long processing time.

To date, the thermal evaporation method is the most efficient way for coating a uniform layer of a resist on nonplanar, bent, suspended, irregular surfaces or 3D architectures [START_REF] Zhang | Electron beam lithography on irregular surfaces using an evaporated resist[END_REF]- [START_REF] Ma | Polystyrene negative resist for high-resolution electron beam lithography[END_REF]. We chose a negative sterol based e-resist named as QuantiScript (QSR-5), developed by Eric et al. [START_REF] Lavallée | Method of producing an etch-resistant polymer structure using electron beam lithography[END_REF]. In this chapter, we first calibrate the deposition for the QSR-5 resist on planar surfaces. Then, we perform state-of-the-art EBL and show that lines structures with a spatial resolution of 100 nm can be readily made on a 2D or flat surface. We then study how the electron exposure dose changes during the lithographic process on QSR-5 resist using different developers, including QSR-5D2 and methyl ethyl ketone (MEK). Afterwards, we apply EBL process on a highly nonplanar geometry, namely a 3D AFM tip. We pattern 800 nm wide gold strips on a pyramid-shaped AFM tip. Following, we will present the various strategies that are carried out to optimize the fabrication process and the challenges that are encountered. Finally, we will show the integration of a niobium nitride (NbN) temperature-sensitive thin film at the apex of a 3D AFM tip along with gold leads on the cantilever dedicated to advanced near field microscopy for nanoscale thermal measurements like SThM.

Experimental Overview

The chapter explains how to pattern temperature-sensitive thin film along with electrical contacts on nonplanar, suspended 3D architectures. We have to employ unconventional nanofabrication strategies to accomplish the patterning on nonplanar AFM probes. In the previous chapter, we have already described the SThM technique in detail and discussed the best criteria for choosing the shape, dimensions, materials and their properties for fabricating the SThM probe. (i) Cantilever's material should have the lowest possible thermal conductivity and be electrically insulating, (ii) highly sensitive thermometer, and (iii) mechanically stiff.

One of the best available choice for fabricating the SThM probes is the silicon nitride (SiN) based AFM probe manufactured by OLYMPUS ™ (Micro Cantilevers), which is displayed in Figure 2.1. These probes have triangular-shaped cantilever, which provides them higher stiffness compared to rectangular-shaped cantilevers. These cantilevers have length and width in tens of microns. The shape of the tip is pyramidal and has a radius of curvature of about 15-20 nm. In addition, the tip and cantilever are made out of SiN that exhibits a low thermal conductivity, and is electrically insulating. For the thermometer, we will integrate the NbN thin film on the AFM probes. To do so, we used an electron-sensitive resist that can be thermally evaporated on suspended structures. Then, the state-of-the-art nano-structuration techniques will be employed, including EBL, sputtering, and dry etching, process tools such as reactive ion etching (RIE), and physical ion beam etching (IBE).

Parameters for Patterning QSR-5 on Flat Surfaces

We first study the physical properties of the thermally evaporated QSR-5 e-resist on planar substrates. This includes surface roughness, electron sensitivity, the contrast of the resist and investigation of the impact on the electron exposure dose during the lithography process with varying the resist developers such as QSR-5D2 and MEK.

The deposition of QSR-5 e-resist was performed using a thermal evaporator based on the Joule effect with an initial base chamber pressure of 2×10 -7 mbar. During the deposition, the temperature of the molybdenum crucible containing the QSR-5 resist (in powder form) was increased gradually up to 130 • C until the desired evaporation rate of 1 • A.s -1 was achieved.

After the resist deposition, the sample was covered in aluminium foil for 24 hours to ensure adequate adhesion. It is essential to perform the deposition of resist at a low base pressure and low evaporation rate to obtain a high-quality resist film. Figure 2.2 (a) and (b) represent the AFM and SEM images of evaporated QSR-5 resist film on a commercially polished SiN (100 nm) film on bulk Si substrate. We observe microscopic rice grain structures with a mean roughness of 15 nm, measured by AFM. However, this granular structure and high roughness of the resist film do not play a critical role in the patterning of QSR-5 resist. As a proof, we can see from the 3D topographic AFM image in Figure 2.2 (c) showing that clean lines of width 0.5µm can be structured using EBL.

To assess the sensitivity and contrast behaviour of the QSR-5 resist, EBL was carried out using an LEO-1530 field emission SEM system. The arrays of lines (length×width: 20 µm×50 nm γ is defined as γ = [log(D 100 /D 0 )] -1 , where D 0 is the maximum electron dose at which the resist does not expose and D 100 is the minimum dose to fully exposed the resist (over all the thickness). Generally, high contrast of the resists are suitable for fabricating steep structures.

Here, the term D 100 is also referring to the electron sensitivity of the resist. The contrast γ for the QSR-5 resist grafted on Au surface and developed in QSR-5D2 and MEK are 0.7 and 2.86, respectively. In the case of resist grafted on SiN surface, the contrast is 0.96 for QSR-5D2 and 1.69 for MEK developer. From the graph of Figure 2.3 (b) and (c), it is interesting to note that the contrast of the resist depends on the way the surfaces are grafted. As a conclusion, the contrast tends to be higher in MEK developers because of the short development time, while the sensitivity of the resist is better in the QSR-5D2 developer. These results are consistent with those of previous studies [START_REF] Lavallee | Evaporated electron beam sensitive organic resist for the back-patterning of x-ray lithography masks[END_REF], [START_REF] Kelkar | Nano patterning on optical fiber and laser diode facet with dry resist[END_REF], [START_REF] Gerbedoen | All evaporation submicron lift-off lithography process with negative e-beam qsr-5 resist[END_REF]. Furthermore, the sensitivity obtained for QSR-5 resist is relatively higher compared to most of the other e-resists that have been used for nanofabrication on unconventional surfaces [START_REF] King | Nanometer patterning with ice[END_REF]- [START_REF] Zhang | Electron beam lithography on irregular surfaces using an evaporated resist[END_REF].

Fabrication on Suspended, Non-planar AFM Cantilevers

Mastering this QSR-5 electron-sensitive negative resist allows to perform micro and nanofabrication on suspended cantilevers. We now show the integration of metallic films on suspended, nonplanar AFM probes using the QSR-5 resist. It consists of several major steps: Au/Ti thin film deposition, dry etching by reactive ion etching (RIE) and ion beam etching (IBE), electron resists deposition, and EBL. The detailed description of the fabrication process is illustrated in

Technique rate of deposition Pressure Thickness

( • A.s -1 ) (mbar) (nm) Thermoevaporator 1 2 ×10 -7 130
Table 2.1: Details of the electron resist deposition.

At first, we installed an AFM probe on a specific holder using a metallic clamp. The additional function of the clamp is to avoid electrical drift during the EBL. A thin film of Ti (as a first layer) of thickness 5 nm and a Au layer of 50 nm (as a top layer) were then deposited using an electron gun evaporator. The latter is a physical vapour deposition device that transforms the solid target into a gaseous phase which produces high-quality thin films with a high yield.

Ti and Au together act as an electrical leads. Au was used for its excellent corrosion resistance and high electrical conductivity, whereas Ti was used as an adhesion layer. Afterward, QSR-5 e-resist was thermally evaporated at a chamber pressure of 2 ×10 -7 mbar and thin film with thickness of 130 nm was achieved. Table 2.1 details the parameters used during the resist evaporation. Next, the electron exposure of 800 nm wide strip was done on a pyramidal-shaped AFM tip with an accelerating voltage of 5 keV and an optimal dose of 400 µC.cm -2 . Thereafter, the development was performed using a QSR-5D2 developer at 30 • C for 12 minutes. The major advantage of using QSR-5D2 developer over MEK is that the optimal dose required for a complete exposure of the resist is about six times less when the development is carried out in QSR-5D2 which translates to time saving of nearly 4 times (as shown in

NbN Thin Films

The next targeted application of our fabrication process is to integrate a NbN resistive thermometer at the apex of the AFM tip for scanning thermal measurements. As a temperaturesensitive material, NbN thin film has been widely used for high-resolution temperature and thermal measurements that can work in a broad range of temperature measurements from mK (e.g., dilution refrigerator) up to 400 K [START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF], [START_REF] Nguyen | Niobium nitride thin films for very low temperature resistive thermometry[END_REF], [START_REF] Heron | Mesoscopic size effects on the thermal conductance of silicon nanowire[END_REF], [START_REF] Tavakoli | Heat conduction measurements in ballistic 1d phonon waveguides indicate breakdown of the thermal conductance quantization[END_REF], [START_REF] Ftouni | Thermal conductivity of silicon nitride membranes is not sensitive to stress[END_REF]. Its low thermal conductivity and high temperature coefficient of the resistance (TCR) that can be up to |1 × 10 -2 | K -1 at room temperature and up to |1| K -1 at cryogenic temperature make NbN an ideal candidate for room temperature as well as low-temperature applications [START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF], [START_REF] Nguyen | Niobium nitride thin films for very low temperature resistive thermometry[END_REF]. It is to note that the TCR for NbN is negative while it is positive for metals. Positive TCR means that an increase in the temperature results in an increase in electrical resistance. It is because of that electrons get more kinetic energy, leading to an increase in scattering, unlike Mott-Anderson Insulators.

NbN thin film is an example of Mott-Anderson insulator and therefore shows a negative TCR [START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF], [START_REF] Nguyen | Niobium nitride thin films for very low temperature resistive thermometry[END_REF]. In the following subsection, we will explain how the electrical conductance behaves with the temperature variation.

Metal-Insulator Transition (MIT)

The first successful theoretical description of metals and insulators is based on the band theory. It allows one to simply distinguish an insulator from a metal based on the filling of the electronic bands at zero temperature. For metals, the highest electronic band is partially filled, whereas the electronic band is completely filled in the case of insulators. In other words, if the Fermi level lies inside the electronic band then the material is metallic while the Fermi level lies in the bandgap it behaves like insulators. However, many materials in nature have shown insulating behaviour experimentally, even though materials have an odd number of electrons per unit cell. According to band theory, these materials should behave like metals instead of insulators, such as NbSi, TiN, and amorphous metal [START_REF] Nguyen | Niobium nitride thin films for very low temperature resistive thermometry[END_REF], [START_REF] Baturina | Localized superconductivity in the quantum-critical region of the disorder-driven superconductorinsulator transition in tin thin films[END_REF], [START_REF] Ovadia | Electron-phonon decoupling in disordered insulators[END_REF]. The reason for the failure of band theory is due to the ignorance of electron-electron interaction in the materials. In order to explain the electronic nature of these materials, Anderson and Mott came up with their respective models to explain it via different physical mechanisms.

According to the Anderson model, a metal can be transformed into an insulating system due to the scattering of non-interacting electrons with randomly distributed impurities induced by the disorderliness of these structures. In other words, he pointed out that if the disorder in a material is strong enough, we can expect high randomness in the potential that leads to very deep potentials wells, i.e., localization of electrons. According to Mott, he imag-ined a crystalline array of atomic potentials with one electron per atom and considered the Coulomb interaction between the electrons. This theory explains how electron-electron interactions could lead the electronically insulating behavior. Mott argued that in these materials, conduction of electrons happens via electron hopping within the lattice site. When the electron moves from its original site to another one already filled with an electron, it will experience Coulomb repulsion. If the electron kinetic energy is much lower than the Coulomb repulsion, the electron would be localized instead of drifting.

Niobium (Nb) shows superconducting behaviour below 10 K. Nb can be turned into an insulator at low temperatures by alloying it with nitrogen (N). This phenomenon is known as a metal-insulator transition (MIT), as explained in the last paragraph. Most importantly, the ratio between N and Nb (x=N/Nb) in the alloying process defines the electrical properties of NbN thin films. As mentioned in Ref. [START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF], if x <0.6, the NbN film behaves like a superconductor with a critical temperature of about 16 K, while x >1.1, the film acts as a Mott-Anderson insulator either at cryogenic temperature range or near room temperature. Further, this temperature range in NbN film can be controlled by playing with the amount of nitrogen content in the alloying process.

As an illustration in Figure 2.6, the electrical resistance is plotted as a function of temperature for four different NbN thin films where we obtained the MIT behaviour at cryogenic temperature range. It is essential to explain the meaning of the legend RR (RR=R 77K /R 300K ) in the graph. RR represents the electrical resistance ratio of the NbN film at temperature 77 K and 300 K. For fabricating the NbN thermometer, the RR ratio is used to quantify the expected electrical properties and estimate the amount of N content in the alloying process. The increasing RR ratio leads to a higher slope in the temperature-dependent electrical resistance.

These thin films of NbN are adapted for low-temperature applications. More details on the fabrication of these NbN films can be found in Ref. [START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF].

Regarding the electronic transport in NbN thin film which acts as MIT material, two phenomena are in the competition. First, the electronic kinetic energy favours the transport of electrons via hopping. While the disorder created by nitrogen favours the localization of electrons. At room temperature, the kinetic energy of electrons is sufficiently high to move from one site to another, so NbN acts as a conductor. At low temperatures, disorder dominates, and NbN shows higher resistance.

Challenges to Integrate NbN on AFM Probes

The fabrication of the NbN based SThM probe can be classified into two major subsequent parts. The first part is the fabrication of the electrical leads made of Ti/Au on the AFM cantilever, and the second part is related to the integration of the NbN thin film at the apex of the tip. To mention that we have the optimized EBL and etching process for patterning the Ti/Au electrical leads on the AFM probes, as detailed in the previous section 2. 4.

For the integration of NbN film, we had to test several potential fabrication processes in order to fabricate SThM probe and evaluate the advantages and drawbacks for each of them. Five different types of fabrication strategies have been tested for patterning the NbN thermometer on the AFM tip. However, only one strategy permits us to integrate the NbN thermometer on the AFM tip with desired shape and dimensions. In the following section, we will focus on the challenges that occurred during the integration of the NbN thermometer.

Preliminary Test

The integration of NbN thin film follows the similar fabrication steps as the fabrication of electrical leads on the AFM cantilever which includes deposition of the thin film, EBL and etching.

NbN thin film is first deposited on top of the electrical leads by DC-pulsed magnetron sputtering, followed by thermal evaporation of the QSR-5 e-resist. The process is continued by exposing the resist on the AFM tip with desired shape and dimension using optimized EBL pa-rameters and subsequently the development step. Finally, the transfer of the NbN thermometer on the AFM tip can be employed using an etching process. However, in the early experience of G. Julié (who is involved in the project since its starting), she observed that the QSR-5 resist film did not adhere satisfactorily to NbN thin film and the reasons will be explained in further sections. Consequently, we were not able to continue the fabrication process. We thus had to find an alternative solution to carry out the integration of the NbN thermometer on the AFM tip. The choice of another strategy was made based on the available sources and flexibility of the techniques.

Strategy 1

One of the critical task in our fabrication process is to overcome the adhesion of resist (negative resist) on the top of NbN. We tried multiple strategies to counter the latter. We decided to use the spin coating technique in place of thermal evaporation. To do that we deposited a positive photoresist named S1818 on the AFM probe, although it has been discussed earlier that spin coating exhibits major issues to coat the AFM tip such as lack of uniformity, reproducibility, and possibility to break the AFM tip. However, the breaking of AFM tip problem can be tackled by reducing the spinning speed.

Thereafter, the resist on the AFM tip is exposed by photolithography and developed. Next, NbN thin film should be coated onto the resist pattern AFM probe by sputtering. Finally, the aim of the process is to lift off the NbN film on top of the resist. The main disadvantage of using photolithography is to have large patterning, resulting in large part of the tip that is covered with NbN.

Strategy 1 is based on the lift-off process of the NbN thin film. The following steps have been employed to deposit the NbN thin film on the AFM probe, as summarized in Figure 2.7.

1. EBL is performed to pattern the gold electrical leads, as discussed earlier.

2. Next, probes are cleaned using reactive ion etching (RIE) to remove resists residue.

3. Spin coating method is utilized to coat a positive photoresist S1818 on the AFM probes using a primer as an adhesion layer. Table 2.2 shows the details of the parameter used during the deposition.

4. The tip of the probe is exposed to white light by using an optical microscope.

Development is carried out using a 1:1 ratio of MICROPOSIT developer and distilled

water for 1 minute. The obtained film of the resist on the probe is shown in Table 2.2: Parameters used for photoresist deposition.

6. NbN thin film is sputtered on the probe using DC-pulsed magnetron sputtering, with a thickness of 70 nm.

7. The final step is the lift-off process. The probe is dipped into the N-Methyl-2-pyrrolidone (NMP) solution to remove NbN from the cantilever along with the photoresist.

In the last step, lift-off of the NbN film from the cantilever is performed using NMP developer.

Strategy 2

As seen in the previous section, an appropriate lift-off of the NbN film could not be achievable using the resist deposited via spin coating. Therefore, to solve this problem, the dip-coating technique has been tested as an alternative of the spin coating for depositing the photoresist that would allow to cover the cantilever's top surfaces, edges, and backside.

Dip coating technique [START_REF] Yamada | Single layer surface-grafted pmma as a negative-tone e-beam resist[END_REF], [START_REF] Glass | Micronanostructured interfaces fabricated by the use of inorganic block copolymer micellar monolayers as negative resist for electron-beam lithography[END_REF] can be described as a process in which the sample of interest (AFM probe) is inserted into the precursor (for example, a resist) with a constant speed and withdrawing slowly from the precursor again at a constant speed under controlled temperature and atmospheric conditions. The thickness of the deposited layer by dip coating mainly depends upon the withdrawal speed and viscosity of the precursor.

MC dip-coating resist is a positive tone resist specific for dip-coating technique, manufactured by MicroChemicals [126]. The use of this resist is ideally suited to cover the whole AFM cantilever. We first validated the dip coating method to deposit resist on a flat SiN wafer. We used the recommended parameters such as dipping speed of the sample inside the resist and soft bake. We obtained a few µm thick layer of resist on the SiN wafer. The exposure of the resist was done using a laser beam of wavelength 385 nm in the SMARTPrint instrument and development in the AZ developer (results are not shown on the flat surface).

Next, we carried out the optimization of the process on the AFM probes. We determined the suitable parameters for the deposition of the resist and its exposure. Following the above mentioned optimization, we tried to replicate the fabrication process for the SThM probe. We first patterned the Ti/Au electrical leads, as described in section 2.4.

Then, the photolithography is performed on the dip coated resist at the AFM tip area, as shown in Figure 2.10 (a). Next, we sputtered the NbN film on the probe and carried out the lift-off step.

Strategy 3

The strategies mentioned earlier are based on the lift-off process for integrating NbN film, which have been shown to be unsuccessful. For this reason, a new fabrication process has to be applied in order to avoid the lift-off step of NbN. As previously demonstrated, QSR-5 resist can be deposited on the gold film and patterned. Then, the idea of the process is to prepare the stacks of NbN, gold, and resist film. In this process, we would expect to obtain the NbN thermometer on the AFM tip along with electrical leads of NbN/Au. This approach will not be ideal for electrical leads because of its high resistance in the range of mega-ohms.

An illustration of the fabrication process is presented in figure 2.11. The concise details of the fabrication process are as follows: 2. NbN thin film was deposited by magnetron sputtering with thickness 70 nm.

3. Evaporation of gold was deposited with thickness of 50 nm.

4. QSR-5 e-resist was thermally evaporated with thickness of 130 nm.

5. EBL was carried out to pattern the tip and cantilever of the AFM probe in four-point probe geometry and developed into QSR-5D2. Then, ion beam etching was used to etch the Au layer from the probe. Afterward, the underneath NbN layer etching was done using RIE with the SF 6 chemistry. The etching rate is about 40 nm/min. Thus etching was performed for approximately 1 minute 30 seconds. However, SF 6 plasma etches the SiN as well. Thus, care has to be taken for this step.

6. QSR-5 was again evaporated on the probe, and the EBL exposure is performed on the whole probe except the AFM tip area to open the window for further etching of gold from the AFM tip using IBE.

Figure 2.12 shows the SEM image of the probe after performing the fabrication process described above. In the final probe, we always observe the resist's grain structure on the cantilever. The possible explanation for the leftover resist is its hardening during the gold etching step using IBE.

The optimized condition for gold etching was bombarding Ar ions on the probe for one minute and stopping the etching process using a shutter. Then we continued the process until finishing the gold etching. To avoid the hardening of the resist, we modified the condition in this step; the bombarding of Ar ions was carried out for a short time (approximately 5 seconds) and the plasma was stopped using a shutter for a long enough time (45 seconds) to cool down the resist. No improvement was observed to avoid the hardening of the resist. Most importantly, we discovered that the attempts to etch gold on the AFM tip were challenging and could not be realized using IBE. One possible direction to etch gold is to use selective wet chemical etching. The disadvantage of this etching is that it will etch the backside gold film on the AFM cantilever that acts as a reflecting layer to carry out the AFM operations. To conclude, the current fabrication process could not provide satisfactory results for fabricating the NbN-based SThM probe.

Strategy 4: Optimized Fabrication Process

In this part, we revisited the fabrication process used in preliminary tests and investigated the possible methods to improve the adhesion of QSR-5 resist on the NbN thin film. One possible reason might be the very smooth surface of the NbN film, which prevents the deposition of QSR-5 resist. To modify the surface roughness of the NbN film, we carried out NbN etching for a short time. The main idea for creating the roughness on a surface is to change the surface energy and promote the adhesion [START_REF] Van Dam | Effect of surface roughness and chemistry on the adhesion and durability of a steel-epoxy adhesive interface[END_REF]. The description of the complete process is given below. Nb target in the presence of Ar/N 2 gas. The detailed description of this step can be found in

Ref. [START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF]. Then, QSR-5 resist is structured again using EBL, followed by development via soaking in MEK developer at 30 • C for 1.5 minutes because of its high contrast, which makes the patterns sharp. Finally, SF 6 plasma etching is carried out for achieving the precise and welldefined patterns of the NbN thermometer at the apex of the AFM tip as shown in Figure 2.14 (c) and (d) (green, false color) using QSR-5 resist as a mask.

Summary

In this chapter, we showed the lithographic capabilities of thermally evaporated QSR-5 e-resist with a combination of EBL technique and dry etching processes on planar and nonplanar suspended surfaces. We achieved rectangular structures with a few hundred-nanometer-wide spatial resolutions on a planar or 2D surface. The impact of two different developers was studied on exposure doses. We found that the sensitivity of QSR-5 resist increased when the development is performed in QSR-5D2 developer compared to MEK. We showed the efficiency of this e-beam sensitive resist by integrating nanofabricated elements on highly nonplanar 3D

architectures: an AFM tip. In our results, we demonstrated the patterning of Au thin film at the apex of the AFM probe.

However, the patterning of NbN thin film on the AFM tip was very challenging. We applied multiple strategies to integrate the NbN film on the AFM tip using lift-off or etching processes.

In the subsections 2.5.2 and 2.5.3, we described in detail the lift-off tests of the NbN film from the cantilever using spin-coated and dip-coated resists, respectively. Our results indicated that the NbN lift-off could not be carried out successfully. It was discovered that deposition of the NbN layer on the sidewalls and backside of the cantilever where the photoresist was absent, avoids the lift-off of NbN.

After testing several ways to pattern the NbN thermometer on the AFM tip, we finally found the best way to fabricate the SThM probe based on NbN thermometer using EBL and dry etching processes that avoids the lift-off step. QSR-5 e-resist is well suited for EBL to write the desired pattern of gold on the probes, such as electrical leads. For NbN patterning, we first had difficulties grafting QSR-5 resist layer on the top of the NbN film. We resolved this problem by introducing roughness in the NbN film surface that promotes the grafting of resist. Finally, we have succeeded in integrating a highly sensitive NbN thermometer at the apex of the tip.

The main advantage of using EBL is that it better defines the patterning of NbN thermometer with desired shapes and dimensions at the nanoscale, more adapted to nonplanar surfaces.

Atomic Force Microscopy (AFM) Technique

The invention of the Nobel prize-winning scanning tunneling microscopy (STM) technique in 1982 developed by Binnig, Rohrer, Gerber, and Weibel [START_REF] Binnig | Tunneling through a controllable vacuum gap[END_REF], introduced a novel concept in microscopy techniques to investigate the structure and materials properties at the atomic scale. The working principle behind the technique is based on scanning a sharp metal tip over the conducting specimen and measure the extremely sensitive tunneling current. The major drawback of the STM technique is its inability to image electrically poor conductors. To address this limitation, Quate, Binnig, and Gerber (1986) introduced an innovative improvement in the measuring principle based on sensing the atomic-scale forces. This technique is known as atomic force microscopy (AFM) [START_REF] Binnig | Atomic force microscope[END_REF] which is capable of examining all kinds of materials, including electrical conductors, semi-conductors, and insulating materials.

The general operating principle of the AFM technique is presented in Figure 3.1. A sharp tip mounted on a micro-cantilever is scanned across the sample in a raster way. During the scan, the short-range interactions between the tip and the sample led to cantilever deflection, which is generally detected via an optical beam deflection (OBD) system (consists of a laser and photodiodes). The topographic images of the sample surfaces in real space can be obtained.

The AFM can be operated in various modes depending on the application. In general, imaging modes are categorized into static and dynamic modes. The static mode is also referred to as a contact AFM mode. In this mode, the topographic information is gathered by establishing the physical contact between tip and sample via sensing the repellent forces. To note that most of the SThM studies are performed in contact-mode. On the other side, dynamic modes refer to non-contact or tapping modes. The surface profile (topography) is achieved by scanning the tip in close proximity to the sample, where the long-range forces (van der Waals, magnetic, electrostatic) induce the variation of the cantilever deflection [START_REF] Nonnenmacher | Scanning force microscopy with micromachined silicon sensors[END_REF].

Tip-Sample Forces

With AFM, we can measure the forces between atoms of the tip and the sample up to a few nanometers separation distance. The force can be classified into attractive and repulsive forces. In this thesis, we will concentrate on the contact AFM mode since thermal measurements are generally performed in contact mode.

Basic components in AFM

To understand the operation of an AFM, we must be familiar with three main components, i.e., piezoelectric scanner, force sensor, and feedback control loop. The piezoelectric scanner allows the movement of the tip across the sample surface, and the force sensor measures the forces between the tip-sample. The feedback control loop obtains the signal from the force sensor and provides the voltage signal to the piezoelectric scanner to maintain a constant force between the tip and the sample.

Piezoelectric scanner -Piezoelectric materials convert electrical potential into mechanical motion. They are also called electro-mechanical transducers. In other words, when an electrical potential is applied across two opposite sides of the piezoelectric material, that results in the deformation of the material's geometry. The magnitude of the deformation depends on the materials, geometry, and applied electrical potential. Typically, a single piezoelectric material changes by 0.1 nm per unit applied volt. Due to their slight variation in the dimensions makes them very useful for accurately controlling AFM measurements' tip motion [START_REF] Voigtländer | Atomic Force Microscopy[END_REF].

Piezoelectric materials can be found in crystalline and poly-crystalline phases. The wellknown examples of the piezoelectric materials are crystalline quartz, and ceramic of lead zirconate titanate (PbZrTiO 3 ), and lead barium titanate (PbBaTiO 3 ). In AFM equipment, ceramicbased piezoelectric materials are used for designing the scanner since ceramics can be transformed into various shapes, sizes, and have a significant expansion coefficient. To date, the tube-shaped piezoelectric scanner is the most widespread in the AFM because it is compact, easy to fabricate, and allows precise control of movement [START_REF] Voigtländer | Atomic Force Microscopy[END_REF].

Force sensor -A force sensor is typically a combination of the AFM probe and the detection system that measures the variation in the AFM probe position during the scan. The force sensor measures the forces in the range of few nN to few hundreds of nN between a small probe and the surface being scanned. Several techniques have been developed for the detection of the AFM probe position [START_REF] Rugar | Force microscope using a fiber-optic displacement sensor[END_REF]- [START_REF] Schönenberger | A differential interferometer for force microscopy[END_REF]. However, the OBD method is the most popular in the AFM setup because of its sensitivity, simplicity, and suitability for ambient and vacuum environments.

Feedback control -It allows maintaining the constant force on the sample while the tip is either scanned or kept still on a given surface region. The feedback loop obtains the signal from the photodiode and compares it with the reference signal. If there is a difference between them, the feedback controller generates a signal to feed it back in the piezoelectric scanner to retain its initial position.

EnviroScope AFM description

The presence of introduced gases. The principle design of the EnviroScope SPM chamber head is depicted in Figure 3.3. A camera is integrated on the top of the microscope head to locate the sample under investigation. The probe is mounted at the one end of a cylindrical piezoelectric tube scanner. The optical system is fixed in this microscope, while the probe is free to scan in all three directions across the sample surface.

In the optical stage, the laser diode emits a laser beam at a wavelength of 670 nm with a power of 1 mW that is focused and reflected on the backside of the AFM cantilever. Then, the laser beam reflected from the cantilever is adjusted to the center position of the photodiode.

During the scan, a slight deflection in the cantilever position is recorded using a photodiode. A feedback signal is generated and used to drive the voltage to the X and Y electrodes of the piezoelectric tube scanner, which results in the horizontal movement to produce a precise raster scanning on the sample surface. A voltage applied to the Z electrode controls the probe position in the vertical direction.

The sample stage consists of magnetic pucks to install the samples and installed onto an

x-y positioning stage. Table 3.1 summarizes the technical specification of the EnviroScope equipment. The sample positioning in the X-Y plane is manual with a range of 6 mm. The maximum sample size of 30 mm can be installed in the X and Y directions, and thickness is limited to 12 mm. Further, a coarse motion is needed between the probe and the sample stage to efficiently exchange the probe and sample. This z-coarse positioning is possible with the use of a stepper motor. Overall, the sample is fixed during the scanning, and the tip can move in X, Y, and Z directions. The limitation of the tip movement in the X and Y direction is 90µm, and 6µm in the Z-direction.

Adaptation of the AFM for SThM

One purpose of this work is to broaden the EnviroScope SPM instrument for quantitative thermal metrology at the nanoscale. In order to achieve this, we have to integrate the thermal control unit in the EnviroScope SPM instrument. Generally, the thermal control unit incorporates some or all of the following elements:

• A specific probe holder to install the SThM probe. Further, the holder is used to establish an electrical connection between the probe and the external electronics.

• Low noise electronics consist of several instruments such as a Lock-in amplifier, a current source, a variable resistance box, and a Wheatstone bridge or a differential bridge (source:

http://neel-2007-2019.neel.cnrs.fr/spip.php?rubrique840&lang=en).

In this thesis, we will use a Stanford SR830 lock-in amplifier, a homemade voltage-tocurrent source LC02, a variable resistance box, and a homemade differential bridge. Figure 3.4

shows the schematic diagram of the AFM-based SThM setup that consists of a thermal probe, AFM control unit, and thermal control unit. A detailed description of each instrument and a specific probe will be presented in the following sections.

Thermal Probe Holder

The first modification in the microscope was to design and manufacture a novel thermal cantilever holder capable of performing resistive thermometry using the four-wire electrical measurements. The most common requirements of the thermal cantilever holder are lightweight, easeful installation and exchange of thermal probe, and compatibility for laser alignment.

A New Home-Made Low-Noise Electronics for Data Acquisition

Voltage-to-current converter

In this work, we used a device developed at Institut Néel (named LC02) that allows us to convert both the DC and AC voltage into DC and AC current, respectively which can provide the stable current from 1 nA to 1 mA. Also, the variation in the current output due to the temperature change is about 1 ppm/ • C, where ppm stands for parts per million. That means the output current from the LC02 device changes by 10 -6 times with one centigrade degree change in temperature.

Lock-in Amplifier

A lock-in amplifier is an essential instrument as a part of the thermal control unit. It is designed to measure very small AC signals down to few nanovolts at a well-defined frequency. It is a very powerful instrument that allows detecting the signal of interest even if it is smaller than the noise signals. Its working principle is based on the concept of phase-sensitive detection (PSD).

To understand the working principle of a lock-in amplifier, we explain a mathematics description below. Typically, the input signal (V in ) in the lock-in amplifier is composed of a signal of interest at angular frequency ω s , and background noise at different frequencies, which can write as:

V in = V s sin(ω s t + φ s ) + noise (3.1)
where V s is the signal of interest. Lock-in measurements require a reference frequency.

Therefore, the lock-in amplifier generates its reference signal,

V ref = V L sin(ω L t + φ L ) (3.2)
Then, the lock-in multiplies the input and the reference signal, such as:

V psd = V in × V ref (3.3) V psd = 1 2 V s V L cos[(ω s -ω L )t + (φ s -φ L )] - 1 2 V s V L cos[(ω s + ω L )t + (φ s + φ L )] + noise (3.4)
The PSD output has two AC signals, one at the difference of frequencies (ω s -ω L ) and another one at the sum frequency of ω s +ω L . By passing the PSD output through a low pass filter, the AC signals will be removed. Since the reference signal ω L and signal of interest ω s are exactly at the same frequency, then the output of the PSD yields a DC signal as follows:

V DC = 1 2 V s V L cos(φ s -φ L ) ∝ V s cos(φ) (3.5)
φ is the phase difference between the signal of interest and the lock-in reference signal. By adjusting φ L we can make φ=0°, then we can measure V s cos(φ). Conversely, φ=90°, results in no output at all. Generally, the commercial lock-in amplifiers consist of two-phase sensitive detectors (PSDs), allowing capturing both signals together. Thus, the first PSD measures the signal at φ=0°and the other at φ=90°. As we know the value of V L , V s cos(φ sφ L ) can be extracted. The output of these two PSDs will be two DC components:

V P SD1 = 1 2 V s V L cos(φ s -φ L ) (3.6) V P SD2 = 1 2 V s V L sin(φ s -φ L ) (3.7)
Often the output of lock-in amplifiers are measured in X and Y, which refer to the in-phase and out-of-phase components, respectively:

X = V P SD1 1 2 V L = V s cos(φ s -φ L ) (3.8) Y = V P SD2 1 2 V L = V s sin(φ s -φ L ) (3.9)
Moreover, the detection limits of digital lock-in amplifiers are mainly dictated by their dynamic reserve, which allows the conversion of a signal from analog to digital (ADC). In this work, we are utilizing an SR830 lock-in amplifier with an ADC resolution of 16 bits, which means it can encode an analog input into 65536 (2 16 ) different numbers. For example, if the lock-in voltage input range is set to 100 mV and we inject a current of 10µA through 1000 Ω resistor. Then, the full-scale sensitivity is set by the chosen voltage range 100 mV, then the least significant bit or resolution is given by 100 mV/2 16 = 152.6 nV.

Differential Bridge

In order to accurately measure the electrical signal and improve the signal-to-noise ratio, various measurement bridges are introduced. In the literature, five types of bridges have been reported to use with the resistive SThM probes [START_REF] Pylkki | Scanning near-field optical microscopy and scanning thermal microscopy[END_REF], [START_REF] Dobson | New methods for calibrated scanning thermal microscopy (sthm)[END_REF], [START_REF] Puyoo | Scanning thermal microscopy of individual silicon nanowires[END_REF], [START_REF] Puyoo | Thermal exchange radius measurement: Application to nanowire thermal imaging[END_REF], [START_REF] Wielgoszewski | A highresolution measurement system for novel scanning thermal microscopy resistive nanoprobes[END_REF]. The classical Wheatstone bridge is the most widely used for SThM measurements [START_REF] Pylkki | Scanning near-field optical microscopy and scanning thermal microscopy[END_REF], [START_REF] Puyoo | Scanning thermal microscopy of individual silicon nanowires[END_REF], [START_REF] Puyoo | Thermal exchange radius measurement: Application to nanowire thermal imaging[END_REF]. It requires two known resistances with additional variable resistance and a resistive thermal probe. The basic principle of using the Wheatstone bridge is based on balancing the bridge. For that, the resistance of the thermal probe is balanced by tuning the variable resistance. During the experiment, a slight variation in the SThM probe temperature can be detected with high sensitivity. The disadvantage of this setup is that it cannot be utilized in a four-wire configuration.

Notably, four-wire geometry provides more localized measurements of the sensor resistance since it does not include the resistance of the electrical leads, contact resistance and external measuring cables.

In the literature, electrical breakdown of the KNT thermal probes has been observed due to the highly electrostatic charge. Thus, Dobson et al. proposed Transformer-isolated Wheatstone bridge [START_REF] Dobson | New methods for calibrated scanning thermal microscopy (sthm)[END_REF] to minimize the electrostatic forces between the tip and the sample. This will allow in-situ measurements of active micro-and nano-electronic devices and prevent the probes from being destroyed. Kelvin bridge is another type of bridge that was originally designed for very low resistance measurement. This setup allows the thermal probe to use in a four-wire configuration resistive probe. Wielgoszewski et al. [START_REF] Wielgoszewski | A highresolution measurement system for novel scanning thermal microscopy resistive nanoprobes[END_REF] used the Kelvin bridge and reported low sensitivity and high noise in the SThM experiment. Modified Wheatstone bridge setup is also proposed by Wielgoszewski et al. [START_REF] Wielgoszewski | A highresolution measurement system for novel scanning thermal microscopy resistive nanoprobes[END_REF] to perform electrical resistance measurement via a four-terminal probe. Moreover, they reported achieving better measurement sensitivity compare to standard Wheatstone and Kelvin bridges.

In this work, we will use a homemade differential bridge setup that can be used for twoterminal or four-terminal thermal probes. As pointed out in previous paragraphs, the classical Wheatstone bridge only allows us to use the probes in a two-wire configuration. In contrast, a four-wire probe can be attached to the Kelvin bridge, but it is specially designed for low resistance measurements. Since we fabricate the SThM probe in a four-wire configuration with the integrated NbN thermometer, expecting a higher electrical resistance. Thus, we chose to work with a homemade differential bridge setup. It is built from three INA103 instrumentation amplifiers. Figure 3.6 illustrates the schematic of a simplified SThM setup with a current source, variable resistance, lock-in amplifier, and the differential bridge that contains two stages. In the first stage of the bridge, the same voltage drops across the variable resistance, and the thermal probe are set, assuming that the variable resistance has a negligible temperature coefficient of resistance. Consequently, the amplified output voltage in the second stage results from the voltage difference between the variable resistance and the thermal probe. The amplification has been chosen so that the signal can be increased for easier detection while keeping it low enough for the output of the second stage of the bridge to avoid the overloading in the lock-in input. Until now, we have described all the integrated parts in the EnviroScope AFM to use as a thermal microscope. Next, we will show the actual SThM setup and use it for characterizing the noise produced in the SThM probe.

Laboratory Environment & Noise Characterization of the SThM Probe

Noise sets the ultimate limit of an experiment sensitivity almost in every area of measurements. In general, noise is defined as the unwanted signals that obscure the signal of interest.

To demonstrate the experiment's sensitivity, it is necessary to measure the actual noise and compare it with the expected noise at the working conditions. In the SThM experiments, mechanical vibrations, electromagnetic radiation, and thermal noise are the interference sources that can limit the thermal measurements' sensitivity.

Concerning the noise of the mechanical vibrations, scanning probe systems are extremely susceptible to environmental vibrations. Thus, scanning probe systems generally consist of vibration-damping systems. Figure 3.8 represents the complete experimental setup at the laboratory. This SThM experimental setup is installed in the specific building with continuous temperature regulation in order to reduce the temperature fluctuations from the environment.

Importantly, the microscope is resting on the vibration-isolated concrete floor separated from the main floor to reduce mechanical vibration noise. The acoustic hood shields the main chamber of the microscope to remove unwanted environmental disturbances. In addition, the setup is equipped with a primary and turbo-pump to create the high vacuum up to 3 × 10 -6 mbar inside the AFM chamber. However, all the electrical equipment including computer, thermal control unit are placed inside the same room that can be potentially sources for electromagnetic disturbances.

Here, we are solely interested to measure the voltage noise in our SThM probe. Since this thesis concerns the electro-thermal measurements.

Johnson-Nyquist noise is more often known as thermal noise. It is an unavoidable electrical noise caused by the random thermal motion of charge carriers that occurs within all electrical circuits at non-zero temperatures. It is a type of white noise that means it does not change with

frequency. The open-circuit noise voltage (v noise (rms)) generated by a resistance R at temperature T can be calculated using the following equation:

v noise (rms) = 4k B T R∆f (3.10)
Where k B is Boltzmann's constant, T is the absolute temperature in Kelvins, and ∆f is the bandwidth in Hz. However, the amplitude of Johnson-noise voltage at any instant is unpredictable, but it obeys a Gaussian distribution.

More precisely, to measure the noise in the SThM probe, we measured the voltage change Generally, electrical noise resulting from random effects forms a Gaussian distribution, which is a bell-shaped curve. temperature-sensitive element (NbN).

Intrinsic Parameters of the SThM probe

In this section, we discuss the current popular methods to extract the resonant frequency and spring constant of the AFM probe used for the fabrication of SThM probe. After that, the experimental procedure is detailed for calibrating the spring constant using thermal noise method.

Spring constant & resonance frequency

Accurate knowledge of the spring constant of an AFM cantilever is of critical importance for topographic imaging of surfaces and force spectroscopy. To date, several methods have been developed for calibrating the spring constant. The most commonly used methods are theoretical dimensional method [START_REF] Sader | Method for the calibration of atomic force microscope cantilevers[END_REF], resonant frequency method [START_REF] Sader | Calibration of rectangular atomic force microscope cantilevers[END_REF] and thermal noise method [START_REF] Hutter | Calibration of atomic-force microscope tips[END_REF]. The dimensional method requires the knowledge of geometrical parameters and material properties to calculate the spring constant. The major limitation of this method is that the stoichiometry of the cantilever can often vary and contains structural defects that lead to significant errors in the spring constant calculations. In the resonant frequency method, the spring constant is determined by measuring the cantilever's resonant frequency and quality factor along with the cantilever dimensions and Young modulus. However, this approach is inadequate to precisely measure the spring constant of the triangular-shaped cantilevers [START_REF] Hutter | Calibration of atomic-force microscope tips[END_REF] due to often variation in the cantilever dimensions. In particular, the thermal noise method is the most efficient way to evaluate the spring constant of triangular-shaped cantilevers. The basic principle of the method consists of determining the spring constant of a cantilever by measuring the mean-square amplitude of the cantilever's deflection < x 2 > at thermal equilibrium. The equipartition principle relates the energy stored in the spring to the thermal energy

as 1 2 k < x 2 >= 1 2 k B T ,
where k is the spring constant, k B and T are the Boltzmann's constant and the reference temperature. The thermal noise method first requires the calibration of the optical beam deflection (OBD) system that relates the photodiode signal in voltage units to induce a variation of the cantilever position in nanometers. For this step, the photodiode signal is monitored during the force-distance curve on a rigid surface such as sapphire. Following, the slope of the force-distance curve gives the deflection sensitivity of the cantilever. After calibrating the OBD detection system of a scanning probe microscope, the thermal noise method can be applied to determine the resonant frequency of the cantilever, and the spring constant of the cantilever can then be extracted. The nominal spring constant and resonant frequency of these AFM probes provided by the manufacturers is 0.15 Nm -2 and 24 kHz, respectively. Gen- erally, micro-fabricated AFM probes may have a slight variation in the reproducibility of the probe dimensions. It is, therefore, necessary to measure the resonance frequency and spring constant of the AFM probe. Importantly, we integrated the thin films of NbN and gold to perform temperature-sensitive local measurements. Therefore, we used the thermal noise method to to determine the accurate spring constant of the SThM probe.

Electro-Thermal Method

This section describes the temperature calibration of the NbN thermometer, which acts as a thermoresistive sensor. We first begin with calibrating the temperature-dependent electrical resistance of NbN sensor patterned on flat SiN substrate and at the AFM tip. This calibration permits us to compare and evaluate the sensitivity of the NbN sensor on flat and nonplanar surface. Next, we will employ the 3ω-SThM method to determine the cut-off frequency and the heat flux through the cantilever. These properties of the probe highly depend on its dimension, geometry, and the material itself. Following, Finite Element Modeling (FEM) simulation will be used to fit the experimental behavior of V 3ω signal in response to frequency under high vacuum conditions. Importantly, with the help of FEM simulation, we will show how the dimensions and materials properties of the cantilever influence the thermal behavior of the probe. In this research work, all the FEM simulation is performed by Gilles PERNOT, Associate Professor at Université de Lorraine.

Calibration of the SThM probe

In resistive SThM probes, the temperature-dependent electrical resistance of the sensitive element (NbN) provides its own average temperature when the probe is in-contact or out-ofcontact with a sample. It can be represented by the following equation, as described in chapter 1:

R p (T ) = R 0 (1 + α∆T ) (4.1)
where

α = 1 R 0 ∆R p ∆T (4.2)
α is the temperature coefficients of resistance (TCR). R p (T ) is the probe electrical resistance at a temperature T , R 0 is the probe electrical resistance at reference temperature T 0 and change in temperature is represented as ∆T = (T -T 0 ). In order to calculate the TCR of the SThM probe, it is required to measure the electrical response with temperature. We used a hot plate to vary the temperature of the NbN thermometer. First, the calibration was carried out on the NbN thermometer patterned on a flat SiN substrate. Second, we calibrated the NbN thermometer integrated at the apex of the AFM probe. The NbN thermometer on the flat substrate as well as on AFM probe are connected to the four-wire gold electrical leads, as shown in the inset of Figure 4.2. The linear I-V experiments are performed at each temperature with a long stabilizing time. An AC current is applied to the outer leads during the measurements, and the voltage drop is monitored between the inner leads. The range of applied current is chosen from 10 nA to 100 nA to avoid overheating. That leads to the power dissipation (P N bN = R 0 I 2 1ω ) of the order few ten's of picowatt. The voltage drop is constantly monitored using a lock-inamplifier; a linear I-V behavior is observed in that current range shows no Joule heating inside the probe.

3ω-SThM Method

In this section, we describe the 3ω method in detail and how to apply this method to measure the thermal time constant and thermal conductance of the probe. The 3ω method is a powerful electro-thermal technique to obtain the thermal properties of various structures, from bulk samples to suspended structures [START_REF] Cahill | Thermal conductivity measurement from 30 to 750 k: The 3-omega method[END_REF], [START_REF] Liu | Sensitive 3-omega measurements on epitaxial thermoelectric thin films[END_REF], [START_REF] Choi | 3-omega method to measure thermal properties of electrically conducting small-volume liquid[END_REF]. This method has been combined with the SThM by Fieged et al. [START_REF] Fiege | Quantitative thermal conductivity measurements with nanometre resolution[END_REF], and further Lefèvre and Volz [START_REF] Lefèvre | 3 omega-scanning thermal microscope[END_REF] provided a thermal model to enhance the sensitivity of thermal measurements and determine the geometrical parameters.

Here, we will detail the basic idea of the 3ω method and express the temperature oscillation related to the thermal conductance of the probe. In 3ω-method, we biased the thermal sensor (NbN) by an AC current of frequency ω, causing heating through the Joule effect at 2ω:

I 1ω = I 0 cos(ωt) (4.3)
where I 0 is the amplitude of applied root mean square (rms) current. The temperaturedependent electrical resistance is already defined in the earlier section, which can be written as:

R p (T ) = R 0 (1 + α∆T ) (4.4)
Since, α∆T 1, the electrical power (P N bN ) generated in the probe by the Joule effect can be approximated as:

P N bN = R 0 I 2 1ω (4.5) = R 0 (I 0 cos(ωt)) 2 (4.6) = R 0 I 2 0 2 (1 + cos(2ωt)) (4.7)
Then, the temperature oscillation in the probe resulting from the dissipated power is:

∆T = P N bN R probe (4.8) = R 0 I 2 0 2 (1 + cos(2ωt))R probe (4.9) = T dc + T 2ω (cos(2ωt + φ)) (4.10)
where R probe represents the thermal resistance of the probe. T dc is the average DC temperature rise in the probe and T 2ω is the temperature of the probe oscillates at the frequency of 2ω. φ is the phase lag between the periodic heating and the temperature response of the probe.

The voltage across the NbN thermometer has two main components of the voltage at ω and 3ω:

V = R p I 1ω (4.11) = R 0 (1 + α∆T )I 0 cos(ωt) (4.12) = R 0 I 0 [1 + α(T dc + T 2ω (cos(2ωt + φ))] cos(ωt) (4.13) = R 0 (1 + αT dc )I 0 cos(ωt) + R 0 I 0 α 2 T 2ω cos(ωt + φ) + R 0 I 0 α 2 T 2ω cos(3ωt + φ) (4.14) = V 1ω + V 3ω (4.15)
For simplicity, we expressed the voltage in terms of harmonics; V 1ω is the ohmic voltage component and V 3ω voltage component at frequency ω and 3ω, respectively. We can notice that the first harmonics of the voltage V 1ω has two components, a large ohmic voltage and a small contribution of the voltage that contains information about the T 2ω . However, it is a very trivial task to separate them. Importantly, the magnitude of the V 3ω only carries thermal information of probe. Since a lock-in amplifier is used to measure V 3ω , thus, we express temperature oscillation in terms of root-mean-square (rms):

T 2ω = 2V 3ω R 0 I 0 α (4.16)
Since the T 2ω is proportional to the electrical power (see equation 4.8). Then, we have:

T 2ω ∝ P N bN ∝ R 0 I 2 0 (4.17) R 0 I 2 0 ∝ V 3ω R 0 I 0 (4.18) V 3ω ∝ I 3 0 (4.19)
The above expression shows that the V 3ω voltage signal is proportional to the third power of the current. Verifying this relation with at least three different frequencies is a simple way to check the proper working of the experimental setup.

Thermal Time Constant

The thermal time constant of a material is defined as the time required to reach thermal equilibrium after a change of temperature of the reference heat bath. Here, we will theoretically calculate the probe's thermal time constant and thermal conductance using the geometry, dimension, and thermal conductivity of the various materials from which the probe is made.

In SThM studies, knowledge of the probe's thermal conductance (G probe ) is critical to evaluate the heat transport through the cantilever and help to build the SThM model. We can determine the G probe by performing the experiment in vacuum conditions when the probe is in and out-of-contact configuration. Moreover, Finite Element Modeling (FEM) has been used to deduce thermal conductance of various SThM probes [START_REF] Tovee | Nanoscale spatial resolution probes for scanning thermal microscopy of solid state materials[END_REF], [START_REF] Leitgeb | Thermal and spatial resolution in scanning thermal microscopy images: A study on the probe's heating parameters[END_REF]. As mentioned in the literature review, various thermal probes have been used for thermal microscopy, and their thermal conductance is reported in Table 4.1 [START_REF] Tovee | Nanoscale spatial resolution probes for scanning thermal microscopy of solid state materials[END_REF], [START_REF] Lee | Thermal conduction from microcantilever heaters in partial vacuum[END_REF], [START_REF] Guen | Microscopie thermique à sonde locale: Etalonnages, protocoles de mesure et applications quantitatives sur des matériaux nanostructurés[END_REF]. 1.87×10 -5 WK -1 /Modeling [START_REF] Tovee | Nanoscale spatial resolution probes for scanning thermal microscopy of solid state materials[END_REF] Doped Si-probe 1.88×10 -5 WK -1 /Experimentally [START_REF] Lee | Thermal conduction from microcantilever heaters in partial vacuum[END_REF] 2.12×10 -5 WK -1 /Modeling [START_REF] Lee | Thermal conduction from microcantilever heaters in partial vacuum[END_REF] Thermocouple probe 5×10 -6 WK -1 /Using the dimensions of probe [START_REF] Kim | Ultra-high vacuum scanning thermal microscopy for nanometer resolution quantitative thermometry[END_REF] Table 4.1: Comparison of the thermal conductance of the various SThM probes.

∼1×10 -6 WK -1 . In addition, we take into account the four electrical gold leads with the following dimensions: length=200 µm, width= 2µm, and thickness=50 nm. The obtained thermal conductance due to the electrical leads is equivalent to ∼6×10 -7 WK -1 . As all the thermal conductances are in parallel, they should be additive, we then estimated the total thermal conductance G probe of the probe to be ∼1.5×10 -6 WK -1 .

The thermal time constant (τ th ) can be defined as the ratio of specific heat to thermal conductance of the system:

τ th = C G probe (4.20)
where C is the heat capacity with a unit of JK -1 .

First, we wish to calculate the mass of the heat source in the probe (see Figure 4.3 (a)) using the relationship mass=volume×density. Note that here we only considered the SiN material for calculation. The density of the SiN is taken from the literature which is 3 gcm -3 [START_REF] Ftouni | Thermal conductivity of silicon nitride membranes is not sensitive to stress[END_REF]. Second, the volume of the heat source is calculated to ∼6×10 -10 cm 3 , using length, width and thickness of 30 µm, 20 µm and 0.8 µm, respectively. Finally, the mass of the heat source is found to be 1.44 ng.

Then, the heat capacity C can be calculated by multiplying the mass with the specific heat of the SiN and found to be 1.15×10 -9 JK -1 . Using equation 4.20, the thermal time constant is estimated to be below 1 ms.

Experimental Evaluation of the Thermal Time Constant

The 3ω-SThM is utilized for determining the thermal time response of the probe. The experiment is performed in high vacuum conditions when the probe is far from the sample. 4.16 is used to determine the rms temperature amplitude of the oscillation in the probe T rms 2ω-o.c and estimated to be ∼ 5.85 K. When the probe is not in contact with the sample under vacuum condition, then, the elec-tric power (P Avg-N bN ) can be equivalent to heat flux (Q probe ) dissipating away from the NbN thermometer along the cantilever to the chip:

P Avg-N bN = Q probe = G probe (T rms 2ω-o.c ) (4.21)
Using equation 4.21, knowing the applied power and measured T rms 2ω-o.c , thermal conductance of the probe can be deduced to be ∼ 1.23 µWK -1 . This value is in very good agreement to the one calculated in section 4.2.3 from the composition of the probe.

FEM simulation

In order to go beyond the analytical calculation of the probe's thermal properties, we also used the Finite Element Method (FEM). It is a well-known numerical technique for solving multiphysics problems. Here, the prime objective of this part is to build a 3D thermal model and compare it to the experimental results. In FEM simulation, the idea is to divide the system geometry into smaller and simpler parts that are so-called finite elements. Each finite-sized element has well-defined equations. Subsequently, all elements recombined into a global system of equations. Then, the solution of the whole system is numerically determined.

For this thesis, G. PERNOT constructed a realistic 3D model of the NbN-SThM probe using FEM, as shown in Figure 4.5. We remind the reader that the cantilever is made of a 800 nm thick SiN layer. We have integrated 70 nm thick film of NbN thermometer at the AFM tip along with 5/50 nm thick Ti/Au electrical leads on the cantilever. Using the symmetry of the probe, only half of probe system was considered to study the thermo-electrical properties.

Impact of AFM-Laser on the SThM Probe Response

This section deals with the induced overheating in a NbN-SThM probe named "JS-10" due to laser illumination. The most common SThM setup is based on AFM equipment, where a laser beam reflects off the backside of the cantilever into a photodiode to control the force between the probe and a sample under investigation. It has already been reported in the literature [START_REF] Marti | Combined scanning force and friction microscopy of mica[END_REF], [START_REF] Ramiandrisoa | A dark mode in scanning thermal microscopy[END_REF] that the laser can create overheating in the AFM probes. Because of the absorption laser beam via AFM probe, even though the probe consists of a reflecting layer. Thus, we investigated the impact of laser heating on the NbN-based SThM probe under air conditions using the SThM setup based on commercial SPM NTEGRA from NT-MDT company at CETHIL, Lyon. This microscope consists of a laser diode that emits a beam of light having a wavelength of 650 nm at a power of about < 1mW. To study the electrical response of the probe, we focused the laser beam on the backside of the cantilever at various positions. The electrical resistance of the NbN thermometer is recorded using the lock-in amplifier in a four-probe configuration.

During the measurements, a small amount of AC current of I 0 =100 nA at the frequency 12 Hz is passed through the probe and AC voltage at frequency ω is recorded by a lock-in amplifier. We have noticed that adding a layer of Ti/Au thin film on the backside of the cantilever helps to improve the laser's reflectivity. That means a small amount of the laser beam is absorbed by the cantilever, and the probe's heating reduced.

Dark Mode: Impact of the Thermo-Mechanical Stress on the SThM Probe Response

In this last section of this chapter, we wish to determine another external source that can influence the electrical resistance of the NbN based SThM probe, i.e., thermo-mechanical stress. As the name suggests, thermo-mechanical stress refers to the property of a material that relates the thermal response to mechanical one and vice-versa. More precisely, this property can be used for assessing the temperature behavior of the probe in response to a change in the applied load. The knowledge of this effect might play a role in the quantitative thermal measurements.

Mostly, the SThM experiments are carried out by placing the tip on a sample with a particular force and study the heat exchange between them. The amount of heat dissipation across the tip-sample interface depends on various factors such as contact area, thermal boundary resistance, surface roughness, temperature gradient, and applied force. As it is known that increasing the applied force led to an increase in the contact area, thus more heat transfer occurs.

However, if we continue to increase the force on a sample, it might be a small possibility to create mechanical deformation in the thermal sensor at the apex of the SThM tip. At the same time, we can expect a large deformation in the electrical leads due to the cantilever bending.

Overall, these deformations can induce some variation in the electrical resistance of the SThM probe (specially in two-wire configuration) with applied load. Therefore, we conducted the dark mode-SThM, proposed by [START_REF] Ramiandrisoa | A dark mode in scanning thermal microscopy[END_REF] to quantify the effect of thermo-mechanical stress in the NbN thermometer.

In dark mode SThM experiment, the SThM probe approaches a sample surface without using a laser beam on the backside of SThM cantilever. The aim of this experiment is to quantify the impact of applied load on the electrical resistance of the SThM probe after contacting the sample. However, to perform the Dark-SThM mode, first the classical SThM mode in NT-MDT SThM setup was performed to guide the thermal probe on the sample using OBD system. Afterwards, the probe was moved to distance of 2 mm far from the sample (bulk-SiO 2 ) to elude the thermal influence between the probe and sample. The laser was then turned off and sample was moved towards the SThM probe using step motor, and voltage signal of the tip was recorded by lock-in amplifier with long stabilization time.

Parameters used during the experiment:

• Sample: a bulk-SiO 2

• No external heating: small AC current to avoid joule heating (I ac =100 nA).

• Electrical resistance of the probe was measured in four-wire configuration using the lockin amplifier. No electrical resistance variation was observed until the distance between the probe-sample was 100 µm. Afterward, the slight change in the electrical resistance of the SThM probe was observed, and the corresponding calculated temperature of the probe was increased by about 0.2 K. A probable explanation for this behavior might be the existing temperature gradient between the SThM probe and the bulk SiO2 (hotter than the probe). As the experiment was performed in air condition and the temperature of the sample was not controlled. However, after establishing the contact with bulk-SiO 2 , the probe was further pushed by 30 µm to estimate the impact of thermo-mechanical stress on the NbN thermal sensor. No deviation in the electrical resistance was observed in the experiment. It was an expected result since we performed the experiment in a four-wire configuration, and the change in NbN thin film dimension was minimal. Therefore, it can be concluded that the impact of thermo-mechanical stress on the NbN SThM probe can be neglected for SThM experiments.

Summary

In this chapter, the intrinsic parameter of the NbN-SThM probe based has been presented.

The thermal noise method was used to determine the nominal spring constant of the probe.

We have reported the slight variation in the resonance frequency as well as nominal spring constant of the SThM probe compared to unexploited AFM probe. We have then experimentally characterized the electrical resistance and temperature coefficient of resistance (TCR) of the NbN thermometer in response to temperature change. The TCR of the SThM probe was recorded to be |4.5 × 10 -3 | K -1 , which is about three times more sensitive than commercially available thermal probes.

Next, we measured the probe's thermal conductance by performing V 3ω measurements un-der vacuum conditions. We have also estimated the probe's thermal conductance from knowledge of the geometry and thermal properties of the probe. The obtained value of the probe's thermal conductance by calculation was in good agreement with the experimental findings.

Moreover, a 3D realistic model of the NbN-SThM probe was presented using FEM simulation.

We enabled to mimic the frequency-dependent V 3ω amplitude of the probe. Moreover, FEM simulation has been carried out to study the influence of SiN's properties on the frequencydependent V 3ω amplitude. We discovered that SiN's properties do not have notable impact on the frequency-dependent behavior of the probe.

Thereafter, the position-dependent laser heating in the probe was discussed under air conditions. The maximum temperature change due to laser was estimated to be ∼ 25 K under air conditions in the SThM probe. In contrast, the SThM probe with an additional reflecting metal layer significantly reduces the heating because of improved reflection (less absorption) of the laser beam off the cantilever. In conclusion, the backside layer on the SThM cantilever as well as the position of a laser, play an essential role in heating the probe. Finally, Dark mode SThM was detailed, and the impact of thermal-mechanical stress was studied. From the experimental finding of Dark mode SThM, we concluded that the thermo-mechanical stress does not affect the sensor's electrical resistance. Therefore, we can neglect the impact of thermal stress during SThM experiments.

Chapter 5

Thermal Measurements in Vacuum

I

n this chapter, the thermal interaction between the probe-sample system is investigated in high vacuum conditions. The first part is dedicated to the fabrication of a specific thermal probe to increase the heat flux between tip-sample system. In the second part, a thermal model based on thermal-electrical analogy describes the various heat transport channels in the SThM experiment. The third part is devoted to the calibration procedure of the NbN based SThM probe for determining the material's thermal conductivity. To do that, we will perform the point contact 3ω-SThM measurements on the bulk reference samples with well-known ther-mal conductivity. That allows us to specify the expected range of thermal conductivity of the materials that can be measured with the NbN-SThM probe. Then, the SThM thermal model will be used to determine the thermal contact conductance at the interface between the probe and the sample. The last part of this chapter is dedicated to applying the SThM method for measuring the thermal conductivity of DNA nanostructures.

Blunt Thermal Probe

This section focuses on enhancing the heat flux between the probe and the sample. As it has been pointed out in chapter 1, commercially available resistive thermal probes can obtain high spatial resolution images but their thermal sensitivities are moderate. This is due to the fact that the contact surface between the probe and the measured sample surface is small, leading to a small heat flux. Consequently, the temperature gradient is not sufficient to be easily detectable. In the literature, several ways have been highlighted to increase the sensitivity of the SThM probe, such as (i) by integrating the thermal sensor with a higher temperature coefficient of resistance (TCR), (ii) increasing the thermal resistance of the cantilever that leads to more localized heating of the tip using low thermal conductivity materials, like SiN or SiO 2 , as pointed out by Shi et al. [START_REF] Shi | Design and batch fabrication of probes for sub-100 nm scanning thermal microscopy[END_REF], (iii) increasing the radius of curvature of the probe that results in lowering the thermal interface resistance between the tip-sample and (iv) in active mode: creating a higher-temperature gradient between the tip and sample by applying ample amount of the current.

To meet these requirements mentioned above, we have implemented point (i) and (ii) by fabricating the SThM probe (SiN cantilever) based on the NbN thermometer, which has a high TCR of |4.5 × 10 -3 | K -1 , as shown in chapter 4. We have chosen specific cantilever made of SiN.

To fulfill the criteria (iii) to reduce thermal contact resistance between the tip and the sample, we decided to increase the radius of curvature of the SThM probe.

How to modify the radius of curvature

A Focused Ion Beam (FIB) is the only existing technology to modify the radius of curvature of an AFM tip in a very controlled way. In recent years, FIB technique has become famous for fabricating micro-and nano-structures with various shapes and geometries in many research areas of science, from material science to biology [START_REF] Kant | Focused ion beam (fib) technology for micro-and nanoscale fabrications[END_REF]. In this technique, the micro-and nanofabrication is carried out by removing solid materials from the sample surface. The operating principle of a FIB technique is somehow analogous to the SEM. FIB uses the beam of ions that focuses on the sample surface instead of electrons in SEM. The focused beam of ions transfers a large amount of energy to the sample surface. Consequently, the sample atoms get high enough energy, leading to the removal of particles from their matrix. Presently, FIB utilizes the gallium (Ga + ) metal as a ion sources and operate with an accelerating voltage between 5 to 30 kV.

To modify the radius of curvature of the SThM tip, we used the dual-beam platforms named as LEO-1530 field emission SEM system, combining a SEM and a FIB column. Initially, the SThM tip has a pyramidal-shaped geometry with a height of 3 µm and a radius of curvature of 20 nm. Finally, we aimed to obtain the tip with a diameter of the flat apex about of ∼250 nm, as shown in Figure 5.1. To do this, one of the most critical parameter to take into account is the angle of the cutting plane for fabricating the blunt tip. As in our AFM equipment, the installed probe has a tilted angle of 12 • relative to the horizontal plane. In this respect, we considered this angle. Then, we intended to dice the tip so that when the probe touches the sample surface, the contact surface between the tip and the sample becomes flat and equivalent to the diameter of the tip (assuming circular).

To fabricate the blunt SThM probe, we first employed the optimized fabrication process to integrate the NbN thin film at the apex of the AFM tip along with electrical gold leads on the cantilever in a 4-wire configuration, as described in chapter 2. Then, FIB was performed by Gwénaelle Julié, and Jean-Franc ¸ois Motte in the cleanroom of the Institut Néel, CNRS to modify the apex of the tip. Figure 5.2 shows the SEM images of the fabricated blunt SThM probe. However, fabricating the blunt SThM probe can enhance the heat flux from the tip to sample while compromising the spatial resolution. It is essential to mention that performing FIB accurately at the apex of the tip is one of the most challenging tasks.

SThM Thermal Model

This section discusses the details of the SThM thermal architecture to understand the different routes of heat transport in vacuum conditions and extract the thermal resistance or thermal conductance of a particular regime of the system. To represent the thermal architecture of a SThM system, we will utilize the thermal-electrical analogy, as employed in electronics. In general, an electric system involves voltage difference, electric current, and electrical resistance.

Similarly, Fourier's law contains a temperature gradient, heat flow, and thermal resistance that can be thought of as voltage difference, current, and electrical resistance in electronics. For example, a temperature gradient (voltage difference) across a metal rod drives a heat flow (current flow) with a rate determined by the thermal resistance (electrical resistance) of the metal. The reciprocal of the thermal resistance is the thermal conductance, which dictates the magnitude of the heat flow. The following subsections will first describe the heat flux inside the semi-infinite sample through the isothermal heat source. Then, a detailed SThM thermal model will be established to describe active contact SThM mode.

Thermal spreading resistance

Spreading resistance describes the resistance to the diffusion heat flow into or out of a homogeneous solid material whose dimensions are much larger than the dimension of the heat source. orders of magnitude larger than the dimension of the isothermal heat source area (circular) [START_REF] Yovanovich | Thermal spreading and contact resistances[END_REF].

R sample = T source -T sink Q (5.1)
where Q is the heat transfer rate, T source , and T sink are the average temperature of heat source and heat sink, respectively. In SThM studies, thermal spreading resistance represents the heat flow from the hot tip to the sample at a lower temperature. Here, the SThM probe's tip can be modeled as a circular heat source with the flat apex. Furthermore, the heat source can be considered to be isothermal due to its small dimensions [START_REF] Puyoo | Thermal exchange radius measurement: Application to nanowire thermal imaging[END_REF]. Then, the thermal spreading resistance of the sample R sample in a SThM system and corresponding conductance G sample = 1/R sample of a sample can be expressed as [START_REF] Yovanovich | Thermal spreading and contact resistances[END_REF]:

R sample = 1 4κb (5.2)
where κ is the thermal conductivity of the sample and b is the global contact radius that takes into account all the mechanisms of heat transfer between the SThM probe and the sample such as air conduction, water meniscus and solid-solid contact. When the experiments are carried out under vacuum conditions, the heat transfer between the probe-sample system occurs through the solid-solid contact. Then, the contact radius can be written as b c .

Measurement Thermal Model

The comparison of the SThM thermal architecture between non-contact and in-contact is presented in Figure 5.4. The probe is operating in active 3ω mode in both cases. The detailed description of 3ω is given in chapter 4. In the non-contact mode, the heat transport can only occur from the tip to the chip body, which is represented as Q probe where the chip body acts as a heat sink at room temperature. G probe represents the thermal conductance through the probe and its magnitude depends on the geometries and thermal properties of the different materials present in the probe.

In the active 3ω-SThM mode, the tip is self-heated by applying a high AC current that results in significant Joule heating. As it has been discussed in chapter 4, we assumed that all electrical power (P N bN ) is dissipated in the NbN thermometer of the SThM probe. The power (P N bN ) is written as:

P N bN = R 0 I 2 0 2 (1 + cos(2ωt)) (5.3)
we can express the average power dissipated in the NbN thermometer:

P Avg-N bN = R 0 I 2 0 2
R 0 is the electrical resistance of the NbN thermometer at the reference temperature and I 0 is the amplitude of the applied AC current. When the tip is not in physical contact with the sample, then the rms temperature oscillation in the probe related to the heat flux and thermal conductance of the probe as:

Q probe = G probe (T rms 2ω-o.c ) (5.4)
where T rms 2ω-o.c is the rms temperature oscillation of the SThM probe where o.c stands for outof-contact. Then, the thermal conductance of the SThM probe can be determined by equating the heat flux through the cantilever (Q probe ) to the average electrical power P Avg-N bN (at low frequency)that is required to achieve the rms temperature T rms 2ω-o.c of the NbN SThM probe above the room temperature:

P Avg-N bN = G probe (T rms 2ω-o.c ) R 0 I 2 0 2 = G probe (T rms 2ω-o.c ) G probe = R 0 I 2 0 2(T rms 2ω-o.c ) (5.5)
In the second scenario, the heated SThM probe is brought into contact with the sample having a lower temperature (assumed to be at room temperature). That results in opening another channel to heat flow from the probe into the sample. Due to the heat transport into the sample, the measured amplitude of rms temperature variation from the probe decreases, as shown in Figure 5.4 (e). Importantly, an additional interface conductance arises between the probe and the sample that is called thermal contact conductance (G c ), as discussed in Chapter 1. It occurs at the interface between two dissimilar materials or the same material with different crystallographic orientations [START_REF] Kapitza | Heat transfer and superfluidity of helium ii[END_REF] leads to temperature discontinuity at the interface. In this configuration, the tip-sample thermal conductance G t-s is calculated as:

Q t-s = G t-s T rms 2ω-i.c (5.6)
where Q t-s represents the heat transfer from the tip to the sample. T rms 2ω-i.c (i.c refers to incontact) is the new measured rms temperature from the SThM probe. G t-s is the combination of two conductance in series, i.e. the thermal contact conductance between the tip-sample (G c ) and the thermal spreading conductance (G sample ). G t-s , can be written as:

1 G t-s = 1 G c + 1 G sample (5.7)
When the SThM probe is in contact with the sample, then, the heat flux through the cantilever to the chip body (Q probe ) modifies as:

Q probe = G probe T rms 2ω-i.c (5.8)
Using the balanced equation between the total heat generated in the probe and the different routes of heat flux, we can write the following equation:

P Avg-N bN = Q probe + Q t-s (5.9) P Avg-N bN = (G probe + G t-s )(T rms 2ω-i.c ) (5.10)
Considering the constant electrical power dissipation at the apex of the tip in both cases when the probe was far from the sample and in contact. Then, the equations 5.5 and 6.6 can be expressed as:

G probe T rms 2ω-o.c = (G probe + G t-s )(T rms 2ω-i.c ) G c × G sample G c + G sample = G probe T rms 2ω-o.c -T rms 2ω-i.c T rms 2ω-i.c G c + G sample G c × G sample = 1 G probe T rms 2ω-i.c T rms 2ω-o.c -T rms 2ω-i.c 1 + G sample G c = G sample G probe T rms 2ω-i.c T rms 2ω-o.c -T rms 2ω-i.c G sample G c = G sample G probe T rms 2ω-i.c T rms 2ω-o.c -T rms 2ω-i.c - 1
By rearranging the equation for G c :

G c = G sample G sample G probe T rms 2ω-i.c T rms 2ω-o.c -T rms 2ω-i.c -1 (5.11)
Similar, we can rearrange the equation for evaluating the G sample :

G sample = G c G c G probe T rms 2ω-i.c T rms 2ω-o.c -T rms 2ω-i.c
-1

(5.12)

In our experiments, we will utilized equation 5.11 to determine the thermal contact conductance G c between the tip and the bulk samples.

Thermal Conductance Measurements

The objective of this part is to experimentally determine the thermal conductance of the probe by performing 3ω-SThM in out-of-contact mode. Then, we will show the calibration of the SThM probe by employing the contact 3ω-SThM method on bulk samples. Here, the term calibration refers to the resulting temperature variation of the hot SThM probe as a function of the sample's thermal conductivity. This calibration allows us to highlight the sensitivity zone of the NbN SThM probe towards the material's thermal conductivity that can be studied. The NbN-SThM probe named ( "JS-21", see Appendix 7) were used to carried out these experiments.

We use the vacuum-based scanning thermal microscope as described in chapter 3 to measure heat-flux between the heated SThM probe and the bulk samples. A set of samples with distinct and well-known thermal conductivities are required to calibrate of the NbN SThM probe [START_REF] Nguyen | Calibration of thermocouple-based scanning thermal microscope in active mode (2-omega method)[END_REF]. Thus, we chose to perform the point contact 3ω-SThM experiments on bulk samples within a thermal conductivity range of 0.2-148 Wm -1 K -1 . The resulting 3ω voltages are recorded when the probe contacts the sample and in non-contact configuration, it is a type of differential measurement.

Measurements of the Probe Thermal Conductance (G probe )

We first studied the frequency behavior of the probe (when the probe is being out-of-contact) within the range of 1Hz to 1kHz by applying the constant AC current of 30µA that results in the Joule heating. Figure 5.5 (a) presents the experimental data of V 3ω voltage of the probe as a function of the electrical frequency in the presence and absence of the laser beam on the backside of the cantilever. It is apparent from the plot that the V 3ω voltage amplitude decreased in the presence of the laser, and the data reveals the impact of the laser. In order to explain the impact of the laser on the V 3ω signal, we will use the following relationship:

V 3ω = T rms 2ω R 0 I 0 α 2 (5.13) T 2ω ∝ P Avg-N bN ∝ R 0 I 2 0 (5.14) V 3ω ∝ R 2 0 I 3 0 (5.15)
where T rms 2ω is the rms amplitude of the temperature oscillation at 2ω, R 0 is the probe electrical resistance at the reference temperature, I 0 is the amplitude of applied AC current and α is temperature coefficient of resistance (defined in chapter 4).

It can be seen clearly from the equation 5.15 that V 3ω voltage is proportional to the electrical resistance (R 2 0 ) of the thermometer. Thus, the impact of the laser beam on the V 3ω voltage amplitude can be explained by considering the DC overheating in the thermal probe via absorption of the laser beam. This increase in the probe's DC temperature due to laser beam in turn decreases the electrical resistance R 0 of the NbN thermometer from 16 kΩ to 15 kΩ. Consequently, we observed the reduction in V 3ω voltage amplitude of the probe in presence of the laser and the corresponding decrease in the amplitude of T rms 2ω temperature oscillations, as shown in Figure 5.5(a) and (b). However, the amplitude of T rms 2ω is still adequate to perform the contact V 3ω -SThM measurements. Next, in order to extract the thermal conductance of the SThM probe, we used the equation 5.5 i.e. P Avg-N bN = G probe T rms 2ω-o.c . In the case where the laser illumination was off, the induced rms temperature oscillation T rms 2ω-o.c (frequency < 5 Hz) in the probe was recorded to be 5.85 K above the room temperature. Note that the induced temperature oscillation in the probe is relatively frequency-independent up to 5 Hz. The calculated average electrical power dissipated in the SThM probe was equivalent to 7.2 µW, using the applied current of 30µA and measured electrical resistance about 16 kΩ. Knowing the induced temperature and power dissipated in the probe, we extracted G probe to be 1.23 µWK -1 in the absence of the laser beam.

Similarly, when the laser was illuminated on the cantilever, the induced rms temperature oscillation in the probe was measured 5 K. However, the average electrical power dissipated in the SThM probe was changed to 6.75 µW due to reduction of the electrical resistance of the NbN thermometer to 15 kΩ, while using the same applied current of 30µA. In this case, we measured G probe to be 1.35 µWK -1 . Consequently, it is essential to estimate the effect of the laser in varying the probe's thermal conductance G probe . Since all the 3ω-SThM measurements will be carried out in the presence of the laser, knowledge of G probe will contribute to quantify the thermal contact conductance (G c ) between the probe and known thermal conductivity sample surface.

Thermal Contact Conductance at the Solid-Solid Interface

The mechanical contact between the SThM tip and the solid surface refers to the solid-solid interface. We already discussed that the heat flux through the heated tip into the solid sample depends on the thermal conductivity of the sample i.e. implies an increase in the thermal conductance at solid-solid contact G t-s with increasing sample's thermal conductivity, as proposed by Majumdar [START_REF] Majumdar | Scanning thermal microscopy[END_REF]. However, the existence of thermal contact conductance G c at the solid-solid interface limits the tip-sample thermal conductance G t-s . Consequently, G c between the SThM tip and the sample surface sets the sensitivity zone of the SThM probe towards the thermal conductivity of materials that can be measured.

The SThM studies could involve the raster scan to produce the topographic and thermal images of the sample or the point-contact measurements. However, it is very challenging to extract quantitative information from the thermal images [START_REF] Bodzenta | Scanning thermal microscopy-a tool for thermal measurement in the nanoscale[END_REF]. Thus, we preferred to perform point contact 3ω-SThM measurements to obtain quantitative results.

The following protocol are utilized to perform the 3ω-SThM.

1. We carried out experiments on various locations on the sample surface with a constant applied force.

2. V 3ω signals were measured as a function of frequency in contact mode as well as in noncontact mode, 20 times each.

3. The average of the 20 experiments that were performed in out-of-contact configuration and similarly for in-contact experiments is taken.

Next, the average T rms

2ω temperature was extracted using equation 5. [START_REF]Thermal conductivity through the 19th century[END_REF], where all the parameters were known such as averaged V 3ω amplitude, electrical resistance of the NbN-SThM probe, applied current and TCR.

We underline that we performed the experiments by inducing the temperature variation of about ∼5 K between the probe and the sample in 3ω-SThM mode, which is significantly lower than the temperature variation used in DC or AC heating active modes. Generally, a temperature gradient of more than 50K between the probe and sample was established for thermal measurements in DC or AC heating modes [START_REF] Zhang | High temperature imaging using a thermally compensated cantilever resistive probe for scanning thermal microscopy[END_REF], [START_REF] Nelson | Measuring material softening with nanoscale spatial resolution using heated silicon probes[END_REF], [START_REF] Pernot | Frequency domain analysis of 3-omega-scanning thermal microscope probe-application to tip/surface thermal interface measurements in vacuum environment[END_REF]. . From the plot in Figure 5.6, we found the difference of 120 mK (at frequency <5Hz) in the temperature oscillation between out-of-contact and in-contact. We can notice that at high frequencies, the amplitude of the T rms 2ω temperature oscillations is similar for both in-contact and out-of-contact configuration. That is because the penetration depth of the heat flux is minimal at high frequency and does not probe the sample.

Measurement of Thermal Boundary Resistance

The interface between two surfaces causes a temperature discontinuity at the junction that results in so-called thermal boundary resistance (R th,b ). The detailed explanation of R th,b is given in chapter 1. According to the literature, R th,b with a unit of m 2 KW -1 can be expressed as [START_REF] Gotsmann | Nanoscale thermal and mechanical interactions studies using heatable probes[END_REF]:

1 G c = R th,b πb 2 (5.16)
In SThM studies, R th,b is associated with G c and area of contact. b is mechanical contact radius between the probe and sample which acts as the scaling factor.

To determine the R th,b between the probe and reference samples, we first used the SThM model derived before to determine G c at the probe-sample interface. The thermal spreading conductance of a bulk system is directly proportional to the thermal conductivity κ (G sample = 4κb c with b c the contact radius), as described earlier. Thus, to calculate the G sample , we used the literature value of the bulk thermal conductivity of sapphire (κ sapphire ) 34 Wm -1 K -1 [START_REF] Paterson | Thermal conductivity and thermal boundary resistance of amorphous al2o3 thin films on germanium and sapphire[END_REF] and the contact diameter of the probe of 250 nm. Then, we obtained G sample to be 17 µWK -1 .

The value of the temperature of the SThM probe T rms 2ω-o.c (out-of-contact) and T rms 2ω-i.c (in-contact) were taken from the experimental results, shown in Figure 5.6. Note that low-frequency values of T rms 2ω were used because the temperature signal is almost independent on the frequency. Using the known values of G sample , T rms 2ω-o.c , T rms 2ω-i.c , and G probe , we estimated G c =1/R c to be 3.72 × 10 -8 WK -1 using the equation 5.11.

We then used the equation 5.16 and measured R th,b to be 1.32 × 10 -6 m 2 KW -1 for the interface between the NbN-SThM tip and sapphire at room temperature. In the literature, the values of R th,b for solid-solid contacts are reported in the range of 5×10 -7 to 5×10 -9 m 2 KW -1 near room temperature [START_REF] Gomès | Scanning thermal microscopy: A review[END_REF], [START_REF] Zhang | A review on principles and applications of scanning thermal microscopy (sthm)[END_REF]. In our case, the obtained value of R th,b is comparatively higher than the earlier studies.

We wish now to perform the experiments on a sample with low thermal conductivity. One of the best choices would be a polymer because the thermal conductivity is usually very low and lies in the range of 0.1-0.3 Wm -1 K -1 . Thus, we carried out the 3ω-SThM experiment in out-of-contact and in-contact mode on the MICROPOSIT S1818 photo-resist (S1818) and repeat the experiment 20 times at various locations. The average temperature rise of the SThM probe is plotted as a function of frequency, as can be seen in Figure 5.7. The temperature difference between the out-of-contact (T rms 2ω-o.c ) and in-contact (T rms 2ω-i.c ) is recorded to 61 mK at low frequency. It is the expected result since the thermal conductivity of the S1818 resist is much lower than the sapphire, thus higher thermal resistance to heat flow is observed from the tip to S1818 resist.

Following, we performed the 3ω-SThM experiment in out-of-contact and in-contact modes with bulk-SiO 2 , having a thermal conductivity of 1.28 Wm -1 K -1 [START_REF] Nguyen | Calibration of thermocouple-based scanning thermal microscope in active mode (2-omega method)[END_REF] and repeated the experiment 20 times at various locations. The experimental data of the rms temperature oscillation T rms 2ω as a function of electrical frequency are shown in Figure 5.8 between non-contact and in-contact. The variation in the average temperature of the probe between T rms 2ω-o.c and T rms 2ω-i.c is 98 mK. This result is in accordance with the predicted higher heat flux exchange between tip-sample as a function of increasing thermal conductivity of sample.

Afterwards, we performed similar 3ω-SThM experiment on the bulk-Si with thermal conductivity κ Si of 148 Wm -1 K -1 and repeat the experiment 10 times at different positions. We plotted the average temperature rise of the SThM probe as a function of frequency, as shown in Figure 5.9. The temperature difference between the out-of-contact and in-contact is recorded to 150 mK at low frequency. This result is significantly positive, since the thermal conductivity of bulk-Si is higher than the S1818 resist and bulk-SiO 2 , thus higher heat dissipation occurred.

In order to compare all the experiments performed on bulk samples, it is convenient to plot the ratio of the average SThM temperature obtained in-contact and out-of-contact on the samples, as suggested by Pernot et al. [START_REF] Pernot | Frequency domain analysis of 3-omega-scanning thermal microscope probe-application to tip/surface thermal interface measurements in vacuum environment[END_REF]. Figure 5.10 shows the ratio T rms 2ω-i.c /T rms 2ω-o.c as a function of electrical frequency. At low frequencies (<5Hz), the results show the clear evidence of higher heat dissipation in the bulk-Si (148 Wm -1 K -1 ) and lowest in the resist (∼0.2 Wm -1 K -1 ), as ex-pected. In addition, at high frequencies (f >100Hz), the ratio of T rms 2ω-i.c /T rms 2ω-o.c goes higher than 1. It can be explained by the fact that at higher frequencies the temperature of the probe is strongly affected by the low-pass behavior of the probe and thus less sensitive to the external environments [START_REF] Pernot | Frequency domain analysis of 3-omega-scanning thermal microscope probe-application to tip/surface thermal interface measurements in vacuum environment[END_REF].

Figure 5.10: Ratio of the of average SThM temperature T rms 2ω between the in-contact and outof-contact is plotted for all the bulk samples used in this work. In the graph, the blue, black, red and green curves represent the S1818 resist, SiO 2 , sapphire and bulk-Si, respectively.

Until now, we have performed 3ω-SThM experiments on S1818 resist, SiO 2 , sapphire and bulk-Si. We next wish to determine the thermal contact conductance between the SThM probe and various samples. A concise details of the procedure is presented below to extract the thermal contact conductance:

• first, calculation of the thermal spreading conductance of the samples are performed using the known thermal conductivity, and assuming the contact diameter of the SThM tip of 250 nm.

• second, we evaluated the values of T rms 2ω-o.c , T rms 2ω-i.c , and G probe from the 3ω-SThM experiments.

• third, the thermal contact conductance G c is determined using equation 5.11.

• finally, thermal boundary resistance is extracted using equation 5.16. Table 5.1 summaries the measured experimental values of G c obtained on various bulk samples that lies in the range of 2 -4.5×10 -8 WK -1 . In the literature, it is already mentioned that the value of G c is not always constant due to presence of surface roughness, tip force and oxide layers on the sample surface [START_REF] Stoner | Kapitza conductance and heat flow between solids at temperatures from 50 to 300 k[END_REF], [START_REF] Haeberle | Nanometer-scale heat-conductivity measurements on biological samples[END_REF]. In our experimental results, we observed the small variation in the G c depending on the sample and observe a trend of the increment in G c when the thermal conductivity of the samples increases. Nevertheless, the dispersion in the obtained G c is not significant if we take into account the fact that materials with thermal conductivities spreading over three orders of magnitude have been measured. Table 5.1: Thermal conductivity of various bulk materials that has been used in this work [START_REF] Nguyen | Calibration of thermocouple-based scanning thermal microscope in active mode (2-omega method)[END_REF], [START_REF] Paterson | Thermal conductivity and thermal boundary resistance of amorphous al2o3 thin films on germanium and sapphire[END_REF]. Summary of the measured quantities in this work by performing 3ω measurements at frequency lower than 5 Hz at room temperature.

Substrate

κ (Wm -1 K -1 ) G sample (WK -1 ) G c (WK -1 ) R th,b (m 2 KW -

Thermal measurements on DNA nanostructures

The discovery of (Deoxyribo-Nucleic-Acid) DNA molecule is one of the most remarkable discoveries that pawed the rise of genetics information. DNA molecule plays a critical role in carrying the biological information of all living beings from its base sequence. These base sequences are made of nucleotides and divided into four different nucleotides in DNA, which are guanine (G), cytosine (c), adenine (A), and thymine (T). DNA double-helix structure occurs due to the pairing of either AT(TA) or GC(CG) via hydrogen bonds. DNA molecule not only defines the genetic code in all living creatures but has also been seen as promising for molecular engineering materials. In 1982, N. Seeman first proposed the design using immobile nucleic acid into holiday junction [START_REF] Seeman | Nucleic acid junctions and lattices[END_REF]. Further, he discussed the theoretical point of view that allows to convert DNA into a two-dimensional nanoscale arrays. Since then, various designs and shapes of DNA structures have been developed and emerged as a promising technology for the bottom-up fabrication of well-defined nanostructures. For his pioneer work, he is widely acknowledged as a founder of DNA nanotechnology. In 2006, Rothemund developed a method that is known as DNA origami, which allows building the DNA nanostructures with a rich diversity in shape, geometry and dimensions [START_REF] Rothemund | Folding dna to create nanoscale shapes and patterns[END_REF]. The origami method is based on the hybridization of a long strand of DNA of genomic origin (so-called scaffold, ∼ 7000 nucleotides long) to other shorter strands (known as staples, 15 to 60 nucleotides long) synthesized to program the folding of the scaffold according to the preconceived scheme. M13mp18 scaffold is the most widely used to construct the DNA origami. It is a single circular strand, made up of 7249 long nucleotides. In order to build a precise geometrical shape of DNA, it is first necessary to define the folding path and length of the scaffold, then the hybridization with complementary staples. For DNA origami assembly, scaffold and staples are mixed in a buffer solution containing positive ions and a stoichiometric ratio is chosen depending on the specific type of DNA origami structure. Then, the mixture is annealed with a well-defined temperature ramp and cooled down gradually to allow the folding of the DNA structure.

With the maturity of DNA origami technology, novel DNA shapes have been designed and employed in various fields such as lithography, nano-electronics, targeted drug delivery, etc. [START_REF] Dey | Dna origami[END_REF]. In recent years, several studies have been carried out to measure the physical properties of DNA molecules, such as electrical conductivity. In particular, a very small studies have been reported on DNA's thermal conductivity [START_REF] Kodama | Heat conduction through a dna-gold composite[END_REF] and most of them are based on the computational approaches [START_REF] Savin | Heat conductivity of the dna double helix[END_REF]- [START_REF] Mahalingam | Thermal conductivity of b-dna[END_REF]. Here, we are interested in studying the thermal property of DNA nanostructures. Since, DNA is one of the smallest object that can be built into desired shapes and dimensions without lithographic processes. We could expect to study molecular 5.4. DNA Chapter 5. Thermal Measurements effects on heat transfer that is not mastered yet. Moreover, the theoretically predicted thermal conductivity of the DNA structures are low that can satisfy the requirement for building molecular thermoelectric devices [START_REF] Maciá | Dna-based thermoelectric devices: A theoretical prospective[END_REF]. And, to our best knowledge, there is no published work that attempt to experimentally measure the thermal conductivity of pure DNA structures.

Preparation of DNA Origami

We purchased the pre-designed DNA origami from the Tilibit group, with various shapes and dimensions called 'PF-2', 'PF-3' and 'PF-6'.

These DNA structures were assembled in the lab. A schematic representations of the shapes and dimension are shown in Figure 5.11 and in order to quantify the quality and purity of DNA origami structures, agarose gel electrophoresis were carried out. AFM technique enables to characterize the 3D shapes of the nanostructures. Since, mica is the well-known substrate for having a flat and clean surfaces. We deposited the DNA nanostructures on mica substrates.

AFM topographic images were carried out using commercial Si AFM probes in liquid for PF-3 and in vacuum environment for PF-2 and PF-6 respectively.

Experimental Procedure & Data Analysis

In this subsection, we begin with the experimental procedure to carry out the reliable 3ω-SThM measurements on the DNA structures. Then, we will present the simple SThM model to deduce the thermal conductivity of DNA structures from the experimental results.

The following experimental procedure is used to perform the 3ω-SThM experiments on the DNA structures.

1. Deposition of DNA samples on the two different substrates: 10µL of DNA origami were spread on the sample, incubate for 5 minutes in air. Then, DNA origami were rinsed with 20µL of deionized water and dried.

2. A topographic image of the surface was realized for positioning the tip on a DNA-free zone.

3. 3ω-SThM measurements were carried out in-contact with the substrate and out-of-contact.

4. Again, topographic imaging was employed for positioning of the tip on the DNA structures.

5. 3ω-SThM measurements were done on the DNA structures and out-of-contact (differential measurement). It is necessary to make a topographic image between each contact measurement in order to reposition the tip on the origami and to estimate the thickness of the DNA samples.

We now discuss the thermal architecture employed for DNA origami studies. It has already been discussed that the non-contact measurements allow estimating the equivalent thermal conductance of the cantilever (see section 5.3.1). Indeed, thanks to the measurement of V 3ω , we can calculate a value of T rms 2ω such as:

T rms 2ω = 2V 3ω R 0 αI 0
Knowing the average AC electrical power injected in the system P Avg-N bN = R 0 I 2 0 2 , we can deduce the value of the cantilever thermal conductance as:

P Avg-N bN = G probe T rms 2ω-o.c
(5.17)

T rms

2ω-o.c is the measured 2ω rms temperature oscillation from the probe at low frequency. Next, 3ω-SThM measurements on DNA-sample system allows us to estimate the contribution of DNA's thermal conductance. To do this, we include the DNA thermal conductance G DN A in series with the substrate. We can write the equivalent thermal conductance of the system as:

G eq = G probe +         1 1 G c + 1 G DN A + 1 G sample        
With G eq = P Avg-N bN (T rms 2ω-i.c-DN A ) where T rms 2ω-i.c-DN A is the new value of temperature oscillation measured in the presence of DNA.

P Avg-N bN =         G probe +         1 1 G c + 1 G DN A + 1 G sample                 T rms 2ω-i.c-DN A (5.18)
Equating equation 5.17 and 5.18: With S the contact surface of the DNA with the tip and t the thickness of the DNA sample.

G probe (T rms 2ω-o.c ) =         G probe +         1 1 G c + 1 G DN A + 1 G sample                 T rms 2ω-i.c-DN A G probe (T rms 2ω-o.c -T rms 2ω-i.c-DN A ) =         1 1 G c + 1 G DN A + 1 G sample         (T rms 2ω-i.c-DN A ) 1 G DN A + 1 G c + 1 G sample = T rms 2ω-i.c-DN A G probe (T rms 2ω-o.c -T rms 2ω-i.c-DN A ) 1 G DN A = T rms 2ω-i.c-DN A G probe (T rms 2ω-o.c -T rms 2ω-i.c-DN A ) - 1 G c - 1 G sample G DN A = G c G sample G probe (T rms 2ω-o.c -T rms 2ω-i.c-DN A ) G c G sample (T rms 2ω-i.c-DN A ) -G c G probe (T rms 2ω-o.c -T rms 2ω-i.c-DN A ) -G sample G probe (T rms 2ω-o.c -T rms 2ω-i.c-DN A ) (5.19)

Results

Two substrates with significantly different thermal conductivity were used to integrate DNA structures and carried out thermal measurements. In addition, these substrates should have a smooth surface to reduce the roughness effect on the SThM measurements. Thus, we chose mica and bulk-Si having thermal conductivity around 0.7 Wm -1 K -1 and 148 Wm -1 K -1 respectively. The contact point 3ω-SThM measurements have to be carried out on the bare substrates. Since the thermal conductivity of the substrates are different, we expect a variation in heat transferred in both samples and therefore different V 3ω voltage amplitude in the SThM thermometer. Then, the DNA nanostructures have to be deposited on both substrates and the SThM experiments have to be performed.

PF-6 DNA on Mica Substrate The experimentally obtained variation in the T rms 2ω temperature oscillation of the SThM probe in-contact and out-of-contact conditions is shown in 5.16. During the experiment, the amplitude of the V 3ω signal was recorded in non-contact condition while keeping a distance of few micrometers from the sample. Second, the same experiment was performed after con-tacting the tip with the sample. All the experiments were repeated 10 times at the same position. The comparison shown in Figure 5. 16 (a) between the DNA-on-mica substrate and mica-substrate indicates the variation in the SThM probe's temperature T rms 2ω at low frequency and have a similar value of the temperature at a higher frequency range.

PF-2 DNA and PF-3 DNA on Si Substrate

We here choose to study the thermal behavior of two different DNA structures, PF-2 (thickness:

61 nm) and PF-3 (thickness: 14 nm). The objective of the 3ω-SThM measurement is to quantify the effect of DNA structure's dimensions on the thermal conductance.

The topographic image of the DNA deposited on the Si substrate is shown in Figure 5.17.

We can notice that DNA on Si substrate aggregates into larger structures instead of individual clusters. In order to solve this issue, several things can be envisaged. First, a structure with larger surface contact area can be designed. A larger contact with the substrate is expected to offer a stronger adhesion force and thus a better stability. Second, coupling agents can be used to enhance the deposition of DNA structures on Si-surface. These strategies will be developed in future work to have a better control on DNA clusters. Thereafter, we employed the point contact V 3ω -SThM experiments on the desired position.

Figure 5.18 highlights the variation of the T rms 2ω temperature oscillation between the PF-2 type DNA and bulk-Si. The solid line represents the data that corresponds to the bulk-Si sample and the dotted line for DNA structure. It can be noticed from Figure 5.18(b) that the out-of-contact T rms 2ω-o.c signals are slightly different when the experiment are performed on bulk-Si and DNA-Si system. This can be explained due to the small variation of induced laser heating that effects the V 3ω signal, as discussed in subsection 5.3.1. However, it is apparent from the graph that heat dissipation is higher in the case of bulk-Si, whereas the addition of DNA nanostructure results in lowering the thermal conductance. At low frequencies (f < 5Hz), the measured temperature difference between contact and non-contact scenarios for PF-2 DNA structures and bulk-Si are 86 mK and 150 mK, respectively.

Next, we studied the DNA (PF-3) nanostructures deposited on Si substrate, as shown in Figure 5.19. We again obtained the cluster of DNA nanostructures on Si-substrate contrary to well-defined geometry of DNA origami. The thickness of DNA cluster is about ∼25 nm.

In the following, we investigate the thermal properties of DNA (PF-3) structures deposited on Si-substrate by conducting point contact measurements. Similarly, we monitored the V 3ω signal in contact and non-contact conditions. All the experiments were repeated 4 times for the Si-substrate and for DNA (PF-3) on Si. The obtained results are shown in Figure 5.20. Again, we observed slight variation in the temperature oscillations in out-of-contact configuration between experiments on Si-substrate and DNA-Si system. It can be attributed to the deviation of the laser position on the probe during the experiments. Nevertheless, we observed the higher temperature difference between in-contact and non-contact for Si-substrate compare to the DNA-Si systems. Thus, these experiments revealed that thermal transport is more favorable in Si-substrate in contrast to the DNA-Si combined system.

Discussions

For estimating G DN A and λ DN A from 3ω-SThM measurements, we used equations 5.19 and 5.20, derived in section 5.4.2. Table 5.2 summarizes all the experimental results obtained on To obtain the average the thermal conductivity of DNA, we averaged out the three measured DNA structures on the substrates.

κ DN A = 1.3 × 10 -2 Wm -1 K -1
This value is in the order of magnitude of those found in the literature [START_REF] Savin | Heat conductivity of the dna double helix[END_REF], [START_REF] Jolfaei | Investigation of thermal properties of dna structure with precise atomic arrangement via equilibrium and non-equilibrium molecular dynamics approaches[END_REF], [START_REF] Xu | Energy transport in crystalline dna composites[END_REF].

Therefore, these measurements are particularly promising in the sense that the model used for these first experiments is quite simple. Many optimizations can therefore be made to the method used. We can then hope to gain precision and rigor on this kind of thermal measurement in SThM. Several axes can be deepened:

• Calculation of a more refined theoretical model, more complete analysis of the thermal boundary conductance, possible modeling by finite element method.

• Design and use of origami shapes more suitable for thermal measurement, for example: cylindrical shape connected in a hierarchical way.

• Optimization of the samples and particularly the adhesion of origami on Si, by surface treatment, for example. (Indeed, the measurements performed so far have been done on 5.6. Discussions DNA "heaps" and not on DNA origami alone. On Si, contrary to mica, origami does not seem to stick to the surface and agglomerate together in heaps).

PF-6 on

λ DN A (Wm -1 K -1 ) | -3.5×10 -3 | 2.3×10 -2 2×10 -2

Summary

In this chapter, we have presented the fabrication of the blunt SThM probe using FIB technique to increase the heat flux across the tip-sample system. Using the SEM technique, we have verified the contact diameter of the tip about to be 250 nm. Then, to investigate the thermal transport through the hot SThM tip to sample, a simple model based on thermal electrical analogy was proposed. Using the SThM model, we experimentally studied the impact of the laser on the probe's thermal conductance (G probe ). We found that G probe increased slightly due to the laser beam illumination. We then determined the thermal boundary resistance R th,b

between the tip and four different sample with known thermal conductivity. We realized that the value of R th,b in the range of 1.1 -2.5 ×10 -6 m 2 KW -1 , as shown in Table 5.1. Further, to show the sensitivity of the NbN-SThM probe, we plotted the ratio T rms 2ω-i.c /T rms 2ω-o.c for four different samples as a function of electrical frequency. As expected, we found the highest heat dissipation inside the bulk-Si within the four bulk samples used in this work.

The next purpose of this study was to investigate the thermal response of DNA nanostructures using 3ω-SThM. Three different pre-designed DNA origami structures were prepared.

One type of DNA structure was deposited on mica, and the other two were deposited on Si substrates. Then, 3ω-SThM measurements were employed on DNA structures along with the SThM model. From these experiments, the average thermal conductivity of DNA nanostructures κ DN A = 2 × 10 -2 Wm -1 K -1 was obtained. Overall, these results of this investigation are significantly crucial for further research in the field of DNA origami technology and studying novel structures at nanoscale for molecular thermoelectric generators. T he last chapter of this manuscript is dedicated to investigating the thermal response of DC laser-heated SThM on the sample with dissimilar thermal conductivities. This chapter is divided into two parts. The first part concerns the interaction of laser-heated SThM probe with three bulk samples, having thermal conductivity from 0.1-148 Wm -1 K -1 in ambient air conditions. In this part, we begin with introducing the simple SThM model to explain heat transport in ambient air conditions along with thermal architecture. Then, we present the sensitivity zone of the NbN-SThM probe as a function of the thermal conductivity of materials and evaluate its performance under air conditions. In the next part, we will show the preliminary thermal map obtained on silicon nanowires embedded in the nanoporous alumina matrix.

Experimental Setup for Ambient Conditions

In the SThM community, most of the experimental work has been done in ambient air conditions [START_REF] Lai | Thermal detection of device failure by atomic force microscopy[END_REF], [START_REF] Chung | Quantitative temperature profiling through null-point scanning thermal microscopy[END_REF], [START_REF] Gomès | Dc thermal microscopy: Study of the thermal exchange between a probe and a sample[END_REF], [START_REF] Assy | Temperature-dependent capillary forces at nano-contacts for estimating the heat conduction through a water meniscus[END_REF]. Thus, this part aims to study the bulk reference samples and obtain Here, all the experiments are carried out using NT-MDT SThM setup at CETHIL, Lyon in ambient conditions. Figure 6.1 shows the schematic diagram of the experimental setup that was used. It includes a current source and lock-in amplifier as a thermal control unit. It will be used for driving the experiment and record the variation in electrical resistance. In SThM studies, the constant current mode is easier and faster to implement because it is a direct measurement in the variation of the electrical resistance by applying a constant current rather than keeping the resistance value constant using a feedback loop. Thus, we decided to use the constant current mode for thermal measurements. In this mode, a constant current is applied through the probe and electrical response is measured between non-contact and in-contact configuration. The obtained electrical resistance was then converted into the temperature using the following relationship, as described in chapter 1:

α = 1 R 0 ∆R p ∆T
where R 0 is the electrical resistance of the resistive (NbN) heating element in the probe at reference temperature T 0 and R p (T ) is the probe electrical resistance at a temperature T. α is the temperature coefficient of resistance (TCR). The change in temperature is represented as

∆T = (T -T 0 ).
From the experiments, we can measure the probe's average temperature ∆T and dissipated power (P N bN ), it is possible to obtain the thermal conductance of the full tip-sample system (G)

in air including all the thermal transport channels air conduction, water meniscus, solid-solid conduction and through the probe.

G = P N bN ∆T (6.1)
In the following section, a simple protocol to perform experiments in air conditions is described along with thermal architecture based on electrical analogy.

SThM Model in Air

It is a common practice in SThM studies to represent the tip-sample system in terms of thermal architecture [START_REF] Menges | Quantitative thermometry of nanoscale hot spots[END_REF], [START_REF] Gomès | Dc thermal microscopy: Study of the thermal exchange between a probe and a sample[END_REF], [START_REF] Zhang | Thermal conductivity measurements of thin films by non-contact scanning thermal microscopy under ambient conditions[END_REF]. In Figure 6.2, we showed a three step protocol to carry out the point contact measurements on bulk reference samples [START_REF] Guen | Microscopie thermique à sonde locale: Etalonnages, protocoles de mesure et applications quantitatives sur des matériaux nanostructurés[END_REF], [START_REF] Guen | Scanning thermal microscopy on samples of varying effective thermal conductivities and identical flat surfaces[END_REF]. In the diagram, we also highlighted the thermal conductance architecture for non-contact and in-contact scenarios.

Note that in the SThM model presented in the last chapter, we considered the constant electrical power dissipation in the probe between in-contact and out-of-contact scenarios. It was because the variation of electrical resistance was minimal when the point measurements are performed in vacuum conditions. However, in air conditions, when the SThM probe contacts the sample surface, we observe a significant variation in the electrical resistance due to heat transport from the tip into the sample through air conduction and solid-solids contact. That leads to a modification in the electrical power of the probe. Consequently, we consider different power dissipation in the thermal probes between in-contact and out-of-contact configurations in air conditions.

We now describe the experimental procedure. In the first step, a temperature difference can be induced in the tip using either internal source (Joule effect) or external (laser) when there is no interaction between the tip and the sample. Then, the electrical resistance has to be monitored and translated into temperature. In this scenario, the thermal conductance through the probe and surrounding gas can be determined by the following relationship: In the second step, the tip moves towards the sample. The heat transfer occurs from the hot In the third step: the signal is measured when the tip is in contact with the sample. The thermal conductance of the system then corresponds to the conductance of the probe G probe , contact conductance G c and of the sample G sample . We ignored the conductance via convection exchanges with the surrounding gas G cc-i.c when the tip is in contact with the sample. In-deed, given the dimensions of the system, convective exchanges are non-existent and only gas thermal conduction occurs under air conditions [START_REF] Guen | Microscopie thermique à sonde locale: Etalonnages, protocoles de mesure et applications quantitatives sur des matériaux nanostructurés[END_REF].

P Avg-N bN -o.c = G probe + G cc-o.c T (d o.c ) = G o.c T (d o.c ) ( 6
P Avg-N bN -i.c = G probe + G sample G c G sample + G c T i.c = G i.c T i.c (6.4)
Following, we can determine the global thermal conductance G global , which is associated with the probe-sample system from the experiment as:

∆G global = G i.c -G o.c ∆G global = G probe + G sample G c G sample + G c -G probe + G cc-o.c (6.5) ∆G global = G sample G c G sample + G c -G cc-o.c (6.6) ∆G global =         G c 1 + G c G sample         -G cc-o.c (6.7)
In order to evaluate G cc-o.c , we have to calibrate the probe under air and vacuum conditions [START_REF] Guen | Scanning thermal microscopy on samples of varying effective thermal conductivities and identical flat surfaces[END_REF]. As defined in the previous chapter, the thermal spreading conductance of the sample is written as:

G sample = 4κb
where κ is the thermal conductivity of the sample and b is the effective radius of the heat exchange area between the SThM probe and the sample. Then, equation 6.7 will be:

∆G global =         G c 1 + G c 4κb c         -G cc-o.c (6.8)
In this scenario, the plot between ∆G global v/s κ can provide a curve having shape close to

A 1 + B κ + C where A = G c , B = G c 4b and C = -G cc-o.c
For quantitative information such as G c and b, it is important to fit the experimental value of ∆G global obtained on bulk reference samples [START_REF] Guen | Scanning thermal microscopy on samples of varying effective thermal conductivities and identical flat surfaces[END_REF] by assuming that G c and b are constant on each reference samples.

Results & Discussion

The idea of the scientific approach is to use samples calibrated in thermal conductivity to proof the efficiency of our NbN-SThM probe for thermal measurements. Here, we used the samples fabricated in the frame work of QuantiHeat project. All samples are highly polished and having surface roughness below 20 nm [START_REF] Nguyen | Calibration of thermocouple-based scanning thermal microscope in active mode (2-omega method)[END_REF]. In this part of the research work, we had the opportunity to conduct experiments on three different bulk reference samples to highlight how the heat dissipation varies in different samples. SThM approach curves will be shown along with the thermal response of the probe. The measurand (∆G global ) will be plotted against the sample thermal conductivity.

To perform the point measurement, we used the following parameters.

1. Heating of the probe by laser: Illumination of laser beam (wavelength 650 nm and power< 1mW) on the backside of the cantilever results in variation in the electrical resistance. The variation in the resistance can be translated to heating of the probe.

2. Position-dependent heating by probe: It is essential to note that the NbN-SThM probe (named "JS-10") used in this study can be heated up to 30K above the room temperature using laser illumination. Depending on the laser position on the cantilever, the induced temperature can be varied. It has been already pointed out by Spiece et al. [START_REF] Spiece | Improving accuracy of nanothermal measurements via spatially distributed scanning thermal microscope probes[END_REF] that the induced temperature due to laser heating in the SThM probe can vary depending on (i) the laser position on the cantilever. We have discussed the influence of laser heating in the SThM probe in Chapter 4.

3. Notably, we also discovered that by changing the laser position about a few hundred's of nm on the cantilever, the induced temperature varies by the small amount from one position to other that can be ignored.

4. The specification of the probe used in this work, we refer the reader to see the Appendix.

Experimental protocol: For the point measurement, we first fixed the distance between the probe and the sample to be 2000 µm. Then, we launched the AFM software in which the sample stage moves towards the probe with a speed of 50 µms -1 . At the same time, we recorded the laser deflection from the backside of the cantilever and the electrical response of the probe in AFM software. Note that there is a small time delay between launching the experiment and recording the data. Figure 6.3 (a) shows the approach SThM curve acquired using NbN-SThM probe on bulk-Si in ambient conditions. At the same time, the electrical resistance of the probe is recorded while the probe approaches the surface, as shown in Figure 6. 3 (b). In order to convert the resistance into temperature, we considered the TCR value to be |4.5 × 10 -3 | K -1 . Figure 6.3 (c) represents the temperature evolution of the probe with distance. We can notice a drop in the probe's average temperature as the probe-sample distance reduces. This temperature variation arises due to the heat transfer through the air gap (mainly conduction) and the solid-solid contact between the tip-sample. One can argue that this temperature variation could come from the movement of laser position when the probe contacts the sample surface. However, we do not expect the variation in laser position by more than a few 10's nm. As we mentioned earlier, the variation in laser position about a few 100's of nm on the cantilever does not affect the temperature variation. Thus, it can be said that this temperature changes in the probe because of heat dissipation into the sample via air conduction and solid-solid contact.

Next, to obtain the thermal conductance of the SThM studied in air, we need to estimate the power dissipated in the probe due to laser beam as well as electric power when the probe was out-of-contact. The average electrical power (R p I 2 0 /2) can be estimated by knowing the electrical resistance of the sensing element (NbN) and applied current. To approximate the power dissipated due to laser beam, we first estimated the induced temperature in the probe by illumination of laser on the cantilever. Second, we used the thermal conductance of the probe G probe = 1.35 × 10 -6 WK -1 that has been measured in vacuum conditions, see chapter 5.

Then, using the following relation, we estimated the power dissipated in the probe via laser in out-of-contact configuration: P N bN -laser = G probe ∆T (6.9)

Then, the total power dissipated in the probe is approximated in out-of-contact by simply adding the laser power and average electrical power.

Thereafter, we used equation 6.1 and plotted the variation in global thermal conductance of the tip-sample system ∆G global with distance, as shown in Figure 6. 3(d). From the graph, we can see an increment in ∆G global by few µWK -1 when the probe contacts the Si surface. Next, our experiments were dedicated to study the heat transport on bulk PMMA and bulk-SiO 2 reference samples. Figure 6.4 shows the results obtained on the bulk-PMMA sample. In this case, the probe was heated up to ∼30 K above room temperature by laser heating. Then, the SThM distance curve and average temperature variation (electrical resistance) were recorded, as shown in Figure 6.4 (a). One can see a clear difference in the probe's average temperature between contact and outof-contact, and obtained value was found to be about 7 K. Next, we carried out the experiment on the bulk-SiO 2 sample with thermal conductivity of 1.28 Wm -1 K -1 . Figure 6.5 detailed the contact point SThM experiment on bulk-SiO 2 sample with thermal conductivity of 1.28 Wm -1 K -1 . During the experiment, there was some drift in the laser position on the cantilever. As a result, we obtained the induced temperature of ∼20K above the room temperature. After, the probe was displaced on the sample surface, and we recorded a temperature variation of ∼10.6 K. That means the tip was cooled down by 10.6 K due to the heat losses into the sample via mainly air conduction and solid-solid contact.

Figure 6.6 shows the fitted experimental data to provide a thermal conductivity calibration curve. We plotted the variation in the global thermal conductance (∆G global ) at the tip-sample interface for three difference bulk samples. It can be noticed that for low thermal conductivity materials, ∆G global is lowest and increases gradually with an increase in thermal conductivity of the samples. These results show the expected trend of heat transfer depending on the materials thermal conductivity. However, no significant difference of the ∆G global between the bulk-SiO 2 and bulk-Si was evidenced.

Next, the experimental data was fitted using equation 6.8 by assuming that G c and b are invariant on all the reference samples. From the fitting, we estimated G c , b and G cc-o.c to be 8×10 -6 WK -1 , 100 nm and 7×10 -6 WK -1 in air conditions. As a conclusion, this calibration curve shows that NbN-SThM probe with sharp tip is sensitive to low thermal conductivity

Preliminary Experiments for Thermal Imaging

One of the most profound application of SThM is to map the temperature or thermal conductivity of a sample depending on the mode used. In this section, we used the vacuum-based SThM probe for performing the experiments, as described in chapter 3. Here, we will show the preliminary attempts to make a thermal contrast map of semiconducting Si-nanowires embedded in an alumina (Al 2 O 3 ) matrix.

Si-Nanowires

In the first chapter, we have introduced that Nanowires have a potential to increase the efficiency of thermoelectric devices by reducing the phonon transport [START_REF] Singhal | Nanowire forest of pnictogen-chalcogenide alloys for thermoelectricity[END_REF], [START_REF] Singhal | Forest of semiconducting nanowires for thermoelectricity[END_REF]. Specially, silicon nanowires have been gained a lot of interest in the field of thermoelectricity. This is because the MFP of phonons varies from 50 nm to 1 mm in bulk-Si [START_REF] Henry | Spectral phonon transport properties of silicon based on molecular dynamics simulations and lattice dynamics[END_REF]. Consequently, fabricating the Si-nanowires, having a diameter smaller than the MFP of phonons, opens up the possibility of building highly efficient thermoelectric devices. Previously, in our group, we have fabricated a large assembly of Si-nanowires embedded in an alumina matrix and reported a diameter dependent reduction in thermal conductivity [START_REF] Singhal | Measurement of anisotropic thermal conductivity of a dense forest of nanowires using the 3-omega method[END_REF].

In this work, we carried out thermal microscopy on Si-nanowires having diameter of ∼100 nm enclosed in Al 2 O 3 matrix. Since, the thermal conductivity difference between Si and Al 2 O 3 (κ Al 2 O 3 = 0.7-2 Wm -1 K -1 ) is about two order of magnitude [START_REF] Paterson | Thermal conductivity and thermal boundary resistance of amorphous al2o3 thin films on germanium and sapphire[END_REF], we expect to obtain a thermal conductivity contrast map using SThM technique.

Results & Discussion

In this study, we used the SThM probe named "JS-7" to employ the SThM measurements.

To begin with, the electrical measurement was done inside the SThM setup under high vacuum conditions by performing the IV characterization of the probe. We measured the electrical resistance of 9.1 kΩ in out-of-contact configuration. After, we illuminated the laser beam (wavelength 650nm and power 1 mW) on the backside of the cantilever and measured the new electrical resistance of the magnitude about 5.2 kΩ. The variation in the electrical resistance can be translated into temperature variation of ∼ 100 K, using TCR of 4.5 × 10 -3 K -1 .

Using the laser heated SThM probe, we carried out the force-distance on the sapphire substrate, as shown in Figure 6.7. A jump in temperature can be seen as the SThM tip contacts the substrate held at room temperature.

Next, the experiments were carried out on the Si-nanowires embedded in the alumina ma- trix. The probe was heated to 100 K via laser heating. Figure 6.8 represents the topography and thermal map obtained using the NbN-SThM probe under vacuum conditions. The scan area of the image is 500×500 nm 2 , with a resolution of 128×128 pixels. The acquisition time for each pixel was 10 seconds. Thus, the time required to obtain these maps was about 7 hours.

A red circle is used to indicate the Si-nanowire in both images. From the thermal image, we can see a contrast between the Si-nanowire and the alumina matrix. This thermal contrast can be attributed to the fact that both exhibit different thermal conductivity. However, this sample contains some topography with surface roughness less than 5 nm. Consequently, the thermal contrast in the image might come from the topography artifacts. Hence, we need to conduct experiments on topography-free samples, having thermal conductivity contrast within the sample to demonstrate thermal imaging capability.

Chapter 7

Conclusions & Perspectives

Scanning thermal microscopy (SThM) has continued to be an important tool for probing local temperature fields with nanoscale spatial resolution. This technique has been used for the precise identification of hotspots in nanoelectronic devices. It also opens up an opportunity to study the thermal behavior of the molecular system that might find application in moleculebased thermoelectric devices. Notably, it is the only existing technique that can probe thermal phenomena down to sub-30 nanometer. In recent years, this technique is becoming mature and continues to be the spearhead for the development of thermal metrology.

In this thesis, we have made a particular effort to describe and discuss the SThM technique from the available thermal probes to the existing thermal physics behind them. Then, we focused on comparing the properties of available commercial resistive SThM probe and pointed out their thermal sensitivity based on the temperature coefficient of resistance (TCR).

The chapter 1 concluded with the fact that there is still room to enhance the thermal sensitivity of the probes. To justify this fact, we proposed to utilize the NbN thermometer, which exhibits high TCR. Thus, a part of this thesis project was focused on building highly sensitive tools to measure the small heat fluxes at nanometer length scale.

In chapter 2, several fabrication strategies were presented to achieve the integration of the NbN thermometer on the AFM tip. The merits and limitations of each strategy were discussed.

Finally, we demonstrated the integration of the NbN thermometer on the commercial SiN AFM probe by performing electron beam lithography (EBL) and etching processes. In the fabrication, the most challenging steps were the grafting of e-resist film on the NbN thermometer and performing EBL experiments on nonplanar AFM probes. We resolved this problem by introducing roughness in the NbN film surface that promotes the grafting of resist. Overall, the thermal evaporation technique is well suited to deposit a uniform layer of QSR-5 e-resist on a nonplanar AFM probe that allows us to define the patterning of NbN thermometer with 123 desired shapes and dimensions at the nanoscale, more adapted to nonplanar surfaces.

Apart from the fabrication of the SThM probe, a commercial AFM equipment has been modified into a vacuum-based SThM setup, as presented in chapter 3. In this regard, a specific tip holder has been designed and developed to perform four-wire electrical measurements using the SThM probe. A low-noise thermal control unit has been incorporated within the AFM equipment for data acquisition from the thermal probe.

In chapter 4, intrinsic and extrinsic properties were characterized under high vacuum and air conditions. Electrical resistance and temperature coefficient of resistance of the NbN thermometer were experimentally determined. The TCR of the NbN-SThM was registered to be 4.5 × 10 -3 K -1 , which is higher than the commercially available thermal probes. The 3ω-SThM experiment was carried out to determine the probe's thermal conductance under high vacuum conditions. In addition, we have also estimated the probe's thermal conductance using the dimensions and thermal properties of the various materials from which the SThM probe is made. The obtained value of the probe's thermal conductance by theoretical calculation was consistent with the experimental results. Moreover, a part of the work has been dedicated to creating a 3D realistic model of the NbN-SThM probe based on FEM simulation. Using FEM, we enabled to reproduce the frequency-dependent V 3ω amplitude of the probe. Moreover, FEM simulations permit us to study the influence of SiN's properties on the frequency-dependent V 3ω amplitude. We discovered that varying the SiN's properties such as thickness, thermal conductivity and specific heat do not have notable impact on the frequency-dependent behavior of the probe.

Further, we have reported a significant DC heating in the NbN-SThM probe due to the laser illumination. In order to diminish the laser heating, we deposited an additional reflecting layer of Ti/Au on the backside of the cantilever. It helped us to improve the laser beam's reflection, which reduces laser heating in the probe.

In the literature, SThM probes with high contact areas have shown the potential to enhance the heat flux across the tip-sample system due to reducing thermal contact resistance. In this context, we have reported fabricating a specific NbN-SThM probe with a large tip apex area.

Then, we have investigated the thermal transport through the hot SThM tip to bulk samples by performing point contact 3ω-SThM. In addition, a simple model based upon thermal-electrical analogy has been applied to determine thermal boundary resistance R th,b under vacuum conditions. We have reported R th,b between the tip and four different samples with known thermal conductivity in the range of 1.1-2.5 ×10 -6 m 2 KW -1 . Also, we have found the higher heat dissipation between the SThM probe (large tip area) and bulk-Si sample, having the highest thermal conductivity within the investigated samples.

Towards the end of chapter 5, the thermal measurement on DNA structures carried out in collaboration with a master intern, Clara Magnin, was presented. We continued to use the SThM probe with large tip apex area on DNA structures. 3ω-SThM measurements were employed on three types of DNA structures deposited on bulk reference samples. From these experiments, the average thermal conductivity of DNA nanostructures κ DN A = 2×10 -2 Wm -1 K -1 was obtained. To our best knowledge, the thermal conductivity of pure DNA structures has never been experimentally measured in the past.

The objective of the last chapter was to exploit the laser heated SThM probe for thermal measurement in air as well as vacuum conditions. We investigated the heat dissipation into three bulk reference samples with dissimilar thermal conductivity under air conditions. Experimental data has been provided to show the variation in the magnitude of SThM tip's temperature after contacting the sample surface. Finally, a thermal conductivity calibration curve has been shown.

At the end of the last chapter, we have presented our preliminary attempts to obtain the thermal map of Si-nanowires embedded in the alumina matrix. The obtained thermal map showed a slight contrast between the Si-nanowire and alumina. In the future, we will use the opportunity to perform thermal mapping on the topography-free samples to demonstrate thermal imaging capability using the NbN-SThM probes.

Future Perspectives

This work allowed us to fabricate the new sensitive thermal probe for scanning thermal microscopy; much work is still required to exploit the maximum benefits from this probe. The first perspective of this work is to refine the parameters during the sputtering of NbN film on the AFM tip to acquire the best nitrogen content for obtaining the highest TCR.

In order to improve the thermal time constant of the probe, a new design will be optimized. To do that, we have to determine the impact of various films and their dimensions by performing the FEM simulation. A realistic 3D model of the NbN-SThM probe has been constructed by G. PERNOT. We further need to exploit the model for optimizing the positioning and dimensions of different elements used in the SThM probe.

For future work, we have to demonstrate the capability of the NbN-SThM probe to detect the temperature fields in passive mode. Also, a part of the work will be concentrated on developing a new process for batch fabrication. In addition, it would be interesting to find new materials with the lowest possible thermal conductivity for fabricating the thermal probe's 125 cantilever to enhance the thermal isolation between the SThM sensor and heat sink.

Finally, one of the perspectives relies on the development of a low-temperature SThM probe. As mentioned in this work, the NbN thermometer has been developed in our group for low-temperature applications down to 20 mK. The most appealing advantage of the NbN thermometer is better sensitivity with TCR about 1 K -1 at 1 K. This will enable the development of ultra-sensitive SThM probe and might opens the opportunities to explore the unraveled physics at a small scale.

List of Abbreviations

1. 1 A 58 xvii 3 . 9

 15839 schematic representation of an AFM-based SThM setup is shown. It includes a probe with an integrated temperature sensor at the tip apex, AFM control unit, and Thermal control unit. The thermal probe is scanned in the lateral directions while the cantilever deflections are monitored using an optical beam deflection system. A balanced Wheatstone bridge is used to sense the variation in the electrical resistance of the thermal probe, adapted from Ref.[START_REF] Gomès | Scanning thermal microscopy: A review[END_REF]. . . . . . . . . . . . 1.2 (a) SEM image of a topography-free sample contains SiN and Au. (b) Topography image and (c) Thermal image. Adapted from Ref. [5] . . . . . . . . . . . . . . . . 1.3 (a) Schematic of thermocouple-based SThM probe. (b) Scanning electron microscope (SEM) images of the SThM probe with an integrated Au-Cr thermocouple [41]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 (a) SEM of the Wollaston probe (b) Detailed description of the Probe. . . . . . . 1.5 SEM image of Pd thermal probe: silicon nitride (SiN) cantilever with thin film Pd resistive sensor at the apex of the tip (commercialized thermal probe from KNT) source: https://www.kntnano.com/probes/. . . . . . . . . . . . . . . . . 1.6 SEM image of doped-silicon thermal probe cantilever, having a very sharp silicon tip [69]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 (a) Schematic description of heat flow channels from the heated tip to a sample at lower temperature (active mode) at different length scales in air conditions. The thermal conductance network for the SThM probe in contact with a sample, adapted from Ref. [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 SEM images of commercial AFM probes manufactured by OLYMPUS ™ (Micro Cantilevers) used in the fabrication process. (a) Top-view of the AFM probe with the triangular-shaped cantilever and tip. (b) Close-up SEM micrograph of the pyramidal-shaped AFM tip with a radius of curvature about 15-20 nm and height of 3 µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii xiv LIST OF FIGURES 2.2 (a) AFM image, where the rice grain structures can be distinguished. (b) SEM image of QSR-5 e-resist film with a thickness of 170 ±15 nm evaporated on SiN substrate. (c) Topographic 3D AFM image of patterned QSR-5 (yellow, false colour shows e-resist step). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3 (a) Topographic AFM images and corresponding height measurements of patterned QSR-5 resist on Au and SiN surfaces. The exposure was carried out at 5 keV, and developed at 30 • C either in QSR-5D2 developer for 12 minutes or in MEK for 1.5 minutes. (a-1) Array of rectangles (length×width: 20 µm×(50 to 500 nm)) of QSR-5 resist patterned on a Au surface, with the exposure dose of 500 µC.cm -2 , developed in QSR-5D2 and (a-2) the exposure dose of 1500 µC.cm -2 and developed in MEK. (a-3) Shows the patterned QSR-5 on SiN exposed at 500 µC.cm -2 and developed in QSR-5D2. (a-4) the exposure is performed at 1500 µC.cm -2 and developed in MEK. (b) and (c) represents the contrast curves of the QSR-5 resist exposed at 5 keV for rectangles of 20 µm×500 nm and the impact of developers is shown on the electron exposure dose. (b) QSR-5 thin film grafted on Au surface (solid dots), and (c) SiN surface (solid triangles) are developed in QSR-5D2 and MEK. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4 Schematic illustration of the steps involved to integrate metallic thin films on nonplanar, 3D commercial AFM probes. (a) SiN based AFM probe with low thermal conductivity and electrically insulating properties. (b) Deposition of egun evaporated Ti/Au with thicknesses of 5 and 50 nm, respectively. (c) Thermal evaporation of QSR-5 negative e-resist with thickness of 130 nm. (d) E-beam lithography and development of resist; Ion beam etching (IBE) process to define the electrical leads of gold on the AFM cantilever and chip. (e) Top-view of the patterned gold strip on the AFM tip. . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5 SEM images of patterned QSR-5 resist AFM probes by EBL and dry etching process, increasing magnifications from (a) to (b). The electron energy and exposure dose of 5 keV and 400 µC.cm -2 are used, respectively. QSR-5 is developed using QSR-5D2 developer for 12 minutes at 30 • C. (c) and (d) show the patterning of Au lines on the AFM probe via performing the Ar plasma step inside Plassys IBE MU400. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6 Electrical resistance versus temperature measurement of four different NbN film from room temperature to 50 mK. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 LIST OF FIGURES xv 2.7 Strategy 1: Schematic representation of the steps involved to integrate thermal sensitive NbN thin films on nonplanar AFM probes based on the lift-off process. (a) (d) shows the patterning of Au thin film for electrical contacts on the AFM cantilever, as described in Figure 2.4. (e) Deposition of S1818 photoresist using spin coating and exposure is performed by projection lithography. (f) Deposition of the NbN thin is carried out by DC-pulsed magnetron sputtering with a thickness of 70 nm. (g) Integration of NbN thin film on the AFM tip after the lift-off step. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 (a) Optical microscopic image of the probe is taken after the photo lithography step. (b) Optical image of the final probe shows the undesirable layer of NbN film on the cantilever. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 (a) An optical microscopic image: resist deposition using dip-coating technique. (b) The photo lithography is performed on the tip area using SMART print instrument. (c) NbN deposition on the probe is employed by sputtering (SEM image). (d) SEM image represents the lift-off of NbN from the AFM cantilever. . 2.10 (a) The dip coating resist on the AFM tip is exposed by optical lithography and developed using AZ developer. (b) The optical image of the probe shows the unsuccessful lift-off of the NbN film from the cantilever. . . . . . . . . . . . . . . 2.11 Strategy 4: Schematic diagram of the fabrication process to integrate the NbN thermometer on the AFM tip. The details of the each step is given in the text. . . 2.12 Strategy 4: SEM images of the probe are after the complete fabrication process. . 2.13 Schematic representation of the steps involved to integrate thermally sensitive NbN thin films on nonplanar AFM probes. (a) (d) shows the patterning of Au thin film for electrical contacts on the AFM cantilever, as described in Figure 2.4. (e) Deposition of the NbN thin film was carried out by DC-pulsed magnetron sputtering with a thickness of 70 nm. (f) Evaporation of QSR-5 e-resist on the top of NbN. (g) Patterning of NbN thermometer via EBL and dry etching (SF 6 plasma). (h) The final design of the SThM probe: top-view of the integrated NbN thin film at the apex of the tip and 4-terminal contact lines. . . . . . . . . . . . . 2.14 SEM images illustrate the integration of the temperature-sensitive NbN film on commercial AFM probes. (a) and (b) Top view of fabricated four-terminal electrical leads of gold (yellow, false color) on AFM chip. (c) and (d) Integrated NbN resistive thermometer (green, false color) at the apex of the nonplanar pyramidalshaped AFM tip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi LIST OF FIGURES 3.1 Schematic view of the atomic force microscope. . . . . . . . . . . . . . . . . . . . 47 3.2 Schematic illustration of the interaction forces between the tip and the sample. . 47 3.3 A schematic of the EnivroScope AFM chamber head. A laser diode is used to emit the beam of photons with a wavelength of 670 nm and power of 1 mW, it reflects off the AFM cantilever and detected by a quadrant photodetector. The piezoelectric scanner is utilized to scan the probe in three different directions relative to the sample surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.4 Schematic representation of an AFM-based SThM setup includes a probe with an integrated temperature sensor at the tip apex, AFM control unit and thermal control unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.5 The geometry of a new SThM cantilever holder constructed in SolidWorks used for thermal measurement, (a) Top view consists of four gold-plated cylinders to establishing the electrical contacts. (b) For driving cantilever oscillations in dynamic operation modes, a dither piezo is integrated on the backside of the holder. (c) and (d) Photographs of the SThM probe installed in the probe holder with the Au wires bonding. (e) and (f) represent the close-up optical images of the wire-bonded gold pads on the SThM chip. . . . . . . . . . . . . . . . . . . . . 52 3.6 Simplified schematic of the SThM setup used for a 3ω experiment. . . . . . . . . 56 3.7 The drawing of the homemade customized flange with 6 BNC connectors is constructed in SolidWorks. The flange has been installed on the side of the AFM chamber to connect the thermal probe with external electronics. . . . . . . . . . 56 3.8 Photographs of the EnviroScope AFM system, which has been modified for thermal microscopy. The top-left photo shows the complete setup of the microscope, including a computer, acoustic isolation box, mechanical isolation base, and electronics. Also, the microscope is resting on the vibration-isolated concrete floor to reduce the noise. The top-right photo shows the opened acoustic box and the EnviroScope chamber with the electronic devices, including the current source, lock-in amplifier, a variable resistance box, and a differential bridge. The bottom-right is the zoomed image of the chamber with BNC cables. The bottom left is the inside view of the chamber, which shows the probe holder made of ceramic glass (white color) with an installed SThM probe and a sample underneath. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement of the noise in the SThM probe inside the scanning thermal microscope setup at a base pressure of 3 ×10 -5 mbar. (a) Solid circles (black) are the voltage response of the thermal tip at 293 K as a function of time, measured using the SR-830 lock-in amplifier. (b) represents the histogram (orange) of the thermal probe corresponding to its voltage response with a Gaussian fit (solid black line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.1 Thermal noise power spectral density of a triangular-shaped SThM probe in the AFM chamber at a pressure of 5 × 10 -6 mbar. The black line shows experimentally measured value, along with Lorentzian fit in the red line. In the inset, a SEM image with the top-view of the SThM probe. . . . . . . . . . . . . . . . . . . 63 4.2 The electrical response and temperature coefficient of resistance (TCR) of the NbN thermometers are illustrated as a function of increasing temperature. (a) NbN thin film of thickness 70 nm was deposited on the flat SiN substrate. The electrical resistance (black dots) with a polynomial fit of second-order (blue dashed line) and TCR (red squares) of NbN thin film are plotted as a function of temperature. The TCR was obtained to be around |8 × 10 -3 | K -1 near room temperature. (b) The black-filled circles represent the experimentally obtained values of electrical resistance of the NbN thermometer, while the blue dashed line is the polynomial fit to the data. The red hexagon represent the TCR of the NbN based SThM probe and obtained value of TCR to be around |4.5 × 10 -3 | K -1 near room temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.3 (a) SEM image of the SThM thermal probe used in this study. The red circle indicates the heat source, the cantilever as a thermal link and the chip body as a heat sink. (b) Drawing of the thermal architecture, heat dissipated from the hot SThM probe to the chip body in vacuum conditions. . . . . . . . . . . . . . . . . 69 4.4 (a) Schematic illustration of a V 3ω SThM setup used here. (b) Verification of the linear behavior of V 3ω and I 3 0 for a particular frequency. (c) The plot represents the V 3ω voltage amplitude variations of SThM probe at various electrical frequencies in vacuum conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.5 Schematic presenting the 3D geometry of the SThM probe built using FEM. . . . 72 4.6 Normalized V 3ω response is plotted against the frequency. The purple line represents the experimental results whereas the black dot connected with solid line stands for the simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.7 Normalized V 3ω response is plotted as a function of frequency. Different parameters are tested to study V 3ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.8 Electrical resistance response and corresponding calculated temperature variation of a SThM probe plotted as a function of the laser positions. The laser with a wavelength of 650 nm and power of < 1mW was applied on the backside of the thermal cantilever. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.9 (a) A schematic diagram of the experimental setup used for performing the Dark mode SThM. In Dark mode SThM, the contact between the tip-sample is established without a laser beam on the cantilever. (b) Electrical resistance variation and corresponding calculated DC temperature change of the SThM probe (no joule heating) are plotted as a function of distance in air conditions. The black dots with connected line stands for electrical resistance and red one corresponds to temperature variation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.1 Schematic illustration of the original AFM probe (a), and (b) FIB modified SThM probe having radius of curvature about 250 nm. . . . . . . . . . . . . . . . . . . . 81 5.2 SEM images of the NbN-SThM probes with flat tip of diameter about to ∼250 nm. (a) Top-view of AFM probe with the triangular-shaped cantilever and tip. (b) Close-up SEM micrograph of the blunt tip with integrated NbN thermometer near the apex of the tip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.3 Heat flux distribution inside a bulk sample whose dimensions are two or more orders of magnitude larger than the dimension of the isothermal heat source area (circular) [146]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.4 Comparison of the SThM thermal architecture between the out of contact (left) and the in-contact (right) regimes in vacuum conditions. (a) Schematic representation of the heat transfer through the probe and (b) corresponding the thermal architecture. (c) The sketch shows T rms 2ω-o.c rms temperature oscillation of the SThM probe (out-of-contact). (d) Schematic of heat transfer interactions between the probe and the sample. (e) the thermal architecture is constructed when the tip is contacted to the sample, and (f) the measured rms temperature T rms 2ω-i.c response from the SThM probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.5 (a) Plot of the SThM V 3ω voltage as a function of electrical frequency in-presence and in-absence of the laser beam on the thermal cantilever (inset shows the zoom-in at low frequency range), and (b) corresponding T rms 2ω signal is plotted as a function frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5. 7

 7 Measured magnitude of the average T rms 2ω tip temperature according to the frequency for the out-of-contact and in-contact with S1818 resist film of 2µm thick on SiO 2 substrate for an AC current of 30µA. Red circles indicate the measured signal in the out-of-contact mode and red line is used to guide the eyes whereas blue square corresponds to the in-contact measured temperature with blue line to guide the eyes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5. 12

 12 Diagram of the model for non-contact measurement. . . . . . . . . . . . . . . . . 5.13 Diagram of the model for the contact measurement on the substrate only. . . . . 5.14 Schematic of the model for the DNA contact measurement . . . . . . . . . . . . 5.15 (a) AFM image highlights the topographic features of the DNA nanostructures deposited on mica substrate (b) Close-up view. The dark brown presents the mica surface whereas lighter part indicates DNA. . . . . . . . . . . . . . . . . . . 5.16 (a) Comparison between the SThM experimental results of T rms 2ω temperature oscillation for DNA-on-mica (dotted line) substrate and mica substrate (solid lines). (b) Zoom-in view of the T rms 2ω signal is plotted as a function frequency. . . xx LIST OF FIGURES 5.17 (a) Illustration of the AFM topographic images of the DNA nanostructures (PF-2) deposited on Si substrate and red box highlights where we performed another AFM image (b) in order to locate the precise position to perform the SThM experiment. (c) The height profile of the DNA nanostructure shows the thickness of the DNA structure of ∼20 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.18 (a) Comparison of T rms 2ω temperature oscillation between PF-2 type DNA and bulk-Si. Dotted lines are representing the data corresponds to DNA where solid lines for bulk-Si. (b) Zoom-in view. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.19 (a) AFM topographic image of the DNA nanostructures (PF-3) deposited on Si substrate and corresponding to the white line the height profile is measured. (b) Height profile of the DNA nanostructure. . . . . . . . . . . . . . . . . . . . . . . 5.20 (a) T rms 2ω temperature oscillation of the SThM probe versus frequency. Dotted lines are representing the data corresponds to DNA where solid lines for bulk-Si. (b) Close-view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 A schematic representation of the SThM setup used in ambient conditions. . . . 6.2 A three-step protocol and equivalent thermal conductance architecture is presented. (1) When tip is far from the sample. (2) The tip approaches the sample, and (3) The tip is in contact. The indices o.c and i.c stand for out-of-contact and in-contact configurations, respectively. . . . . . . . . . . . . . . . . . . . . . . . . 6.3 (a) Approach SThM curves acquired with NbN-SThM probe on bulk-Si in air conditions and (b) measured electrical resistance of the probe. (c) The average temperature of the probe is plotted as a function distance. The inset shows the close up look in the temperature variation of the probe before and after the contact. (d) Variation in the thermal conductance of the probe-sample system ∆G global is plotted as a function of distance. . . . . . . . . . . . . . . . . . . . . . 6.4 (a) Approach curve and average SThM probe temperature were plotted as a function distance in air conditions for PMMA and (b) Global thermal conductance measured as a function of tip-sample distance. . . . . . . . . . . . . . . . . . . . 6.5 (a) SThM distance curve and average SThM probe temperature were acquired as a function distance in air conditions for SiO 2 and (b) Thermal conductance . . . 6.6 The variation in the global thermal conductance between the tip-sample system is plotted against the bulk reference thermal conductivity samples. The black square represents the experimentally measured data and red line denotes the calibration curve deduced by fitting the measured data. . . . . . . . . . . . . . . LIST OF FIGURES xxi 6.7 SThM distance curve was recorded under high vacuum conditions along with the change in SThM tip temperature as a function of distance. When the tip contacts the Sapphire substrate, a change of 1 K in temperature was recorded. . 120 6.8 SThM imaging of Si-nanowires embedded in Al 2 O 3 matrix: (a) Topographic image (b) thermal map. The red circle in the both images indicate the Si-nanowire. 121

  academic research laboratories CETHIL (Lyon) led by Dr. Séverine Gomès and IEMN (Lille) xxv xxvi LIST OF TABLES led by Jean-Franc ¸ois Robillard and one industrial partner CSI.

Figure 1 . 1 :

 11 Figure 1.1: A schematic representation of an AFM-based SThM setup is shown. It includes a probe with an integrated temperature sensor at the tip apex, AFM control unit, and Thermal control unit. The thermal probe is scanned in the lateral directions while the cantilever deflections are monitored using an optical beam deflection system. A balanced Wheatstone bridge is used to sense the variation in the electrical resistance of the thermal probe, adapted from Ref. [6].

Figure 1 . 2 :

 12 Figure 1.2: (a) SEM image of a topography-free sample contains SiN and Au. (b) Topography image and (c) Thermal image. Adapted from Ref.[5]

Figure 1 .Figure 1 . 3 :

 113 Figure 1.3 shows the images of the thermocouple-based SThM probe developed by Kim et al. [41]. They performed the temperature measurement under high vacuum conditions to

Figure 1 . 4 :

 14 Figure 1.4: (a) SEM of the Wollaston probe (b) Detailed description of the Probe.

Figure 1 . 5 :

 15 Figure 1.5: SEM image of Pd thermal probe: silicon nitride (SiN) cantilever with thin film Pd resistive sensor at the apex of the tip (commercialized thermal probe from KNT) source: https://www.kntnano.com/probes/.

Figure 1 . 6 :

 16 Figure 1.6: SEM image of doped-silicon thermal probe cantilever, having a very sharp silicon tip [69].

Figure 1 . 7 :

 17 Figure 1.7: (a) Schematic description of heat flow channels from the heated tip to a sample at lower temperature (active mode) at different length scales in air conditions. The thermal conductance network for the SThM probe in contact with a sample, adapted from Ref. [6].

  the thermal sensitiv-ity is low, temperature profile can be noisy Thermal bending Easy electrical break-down, Thermal bend-ing of cantilever Difficult to do batch fabrication Table 1.2: Thermal probe comparison, thermal sensors, tip radius, advantages and disadvantages.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Experimental Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 Patterning on Flat Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Patterning on AFM Cantilevers . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5 NbN Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5.1 Challenges to Integrate NbN on AFM Probes . . . . . . . . . . . . . . . 34 2.5.2 Strategy 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.5.3 Strategy 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5.4 Strategy 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.5.5 Strategy 4: Optimized Fabrication Process . . . . . . . . . . . . . . . . . 41 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 T his chapter of the thesis is dedicated to the fabrication of the NbN based SThM probe.

Figure 2 . 1 :

 21 Figure 2.1: SEM images of commercial AFM probes manufactured by OLYMPUS ™ (Micro Cantilevers) used in the fabrication process. (a) Top-view of the AFM probe with the triangularshaped cantilever and tip. (b) Close-up SEM micrograph of the pyramidal-shaped AFM tip with a radius of curvature about 15-20 nm and height of 3 µm.

Figure 2 . 2 :

 22 Figure 2.2: (a) AFM image, where the rice grain structures can be distinguished. (b) SEM image of QSR-5 e-resist film with a thickness of 170 ±15 nm evaporated on SiN substrate. (c) Topographic 3D AFM image of patterned QSR-5 (yellow, false colour shows e-resist step).

Figure 2 .

 2 Figure 2.3 (b) and (c) compare the contrast curves for QSR-5 resist exposed at 5 keV and developed either in QSR-5D2 or MEK for rectangles of length×width: 20 µm×500 nm. The contrast curve (γ) describes the sharpness of the resist profile as a function of exposure dose.

Figure 2 .

 2 Figure 2.3: (a) Topographic AFM images and corresponding height measurements of patterned QSR-5 resist on Au and SiN surfaces. The exposure was carried out at 5 keV, and developed at 30 • C either in QSR-5D2 developer for 12 minutes or in MEK for 1.5 minutes. (a-1) Array of rectangles (length×width: 20 µm×(50 to 500 nm)) of QSR-5 resist patterned on a Au surface, with the exposure dose of 500 µC.cm -2 , developed in QSR-5D2 and (a-2) the exposure dose of 1500 µC.cm -2 and developed in MEK. (a-3) Shows the patterned QSR-5 on SiN exposed at 500 µC.cm -2 and developed in QSR-5D2. (a-4) the exposure is performed at 1500 µC.cm -2 and developed in MEK. (b) and (c) represents the contrast curves of the QSR-5 resist exposed at 5 keV for rectangles of 20 µm×500 nm and the impact of developers is shown on the electron exposure dose. (b) QSR-5 thin film grafted on Au surface (solid dots), and (c) SiN surface (solid triangles) are developed in QSR-5D2 and MEK.

Figure 2 . 4 :

 24 Figure 2.4: Schematic illustration of the steps involved to integrate metallic thin films on nonplanar, 3D commercial AFM probes. (a) SiN based AFM probe with low thermal conductivity and electrically insulating properties. (b) Deposition of e-gun evaporated Ti/Au with thicknesses of 5 and 50 nm, respectively. (c) Thermal evaporation of QSR-5 negative e-resist with thickness of 130 nm. (d) E-beam lithography and development of resist; Ion beam etching (IBE) process to define the electrical leads of gold on the AFM cantilever and chip. (e) Top-view of the patterned gold strip on the AFM tip.

Figure 2

 2 Figure 2.4.

  Figure 2.3 (b)).

Figure 2 .

 2 Figure 2.5 (a) and (b) show the SEM images of the structured QSR-5 resist on the AFM tipwith the line-width of 800 nm. Then, the obtained resist patterns are used as a hard mask for dry etching of Ti/Au. To obtain the electrical leads, IBE was conducted at a power of 400 W in Ar atmosphere with a pressure of 0.1 mTorr to remove Ti/Au layers from the unexposed area during the EBL. The electrical resistance between the Au and SiN was measured using two-point probe instrument to detect any short circuit. Then, O 2 plasma was used 2 minutes to clean the resist residues from the AFM probe. Figure 2.5 (c) and (d) demonstrate the well-

  Figure 2.5 (c) and (d) demonstrate the welldefined patterning of Au film on the nonplanar 3D AFM probe with a height of 3 µm via EBL and etching process only.

Figure 2 . 5 :

 25 Figure 2.5: SEM images of patterned QSR-5 resist AFM probes by EBL and dry etching process, increasing magnifications from (a) to (b). The electron energy and exposure dose of 5 keV and 400 µC.cm -2 are used, respectively. QSR-5 is developed using QSR-5D2 developer for 12 minutes at 30 • C. (c) and (d) show the patterning of Au lines on the AFM probe via performing the Ar plasma step inside Plassys IBE MU400.

Figure 2 . 6 :

 26 Figure 2.6: Electrical resistance versus temperature measurement of four different NbN film from room temperature to 50 mK.

Figure 2 . 8 (

 28 a).

Figure 2 . 7 :

 27 Figure 2.7: Strategy 1: Schematic representation of the steps involved to integrate thermal sensitive NbN thin films on nonplanar AFM probes based on the lift-off process. (a) (d) shows the patterning of Au thin film for electrical contacts on the AFM cantilever, as described in Figure 2.4. (e) Deposition of S1818 photoresist using spin coating and exposure is performed by projection lithography. (f) Deposition of the NbN thin is carried out by DC-pulsed magnetron sputtering with a thickness of 70 nm. (g) Integration of NbN thin film on the AFM tip after the lift-off step.

Figure 2 .Figure 2 . 8 :

 228 Figure 2.8: (a) Optical microscopic image of the probe is taken after the photo lithography step. (b) Optical image of the final probe shows the undesirable layer of NbN film on the cantilever.

Figure 2 . 9 (Figure 2 . 9 :

 2929 Figure 2.9: (a) An optical microscopic image: resist deposition using dip-coating technique. (b) The photo lithography is performed on the tip area using SMART print instrument. (c) NbN deposition on the probe is employed by sputtering (SEM image). (d) SEM image represents the lift-off of NbN from the AFM cantilever.

Figure 2 .

 2 10 (b) shows the final result after the complete fabrication process. One can clearly see that the lift-off of the NbN film was not successful, as NbN film was still present on the cantilever. This might be attributed to the variation in the surface quality of the resist on the cantilever due to presence of gold electrical leads. In conclusion of this part, dip coating technique did not improve the lift-off of NbN thin film.

Figure 2 .

 2 Figure 2.10: (a) The dip coating resist on the AFM tip is exposed by optical lithography and developed using AZ developer. (b) The optical image of the probe shows the unsuccessful lift-off of the NbN film from the cantilever.

Figure 2 . 11 :

 211 Figure 2.11: Strategy 4: Schematic diagram of the fabrication process to integrate the NbN thermometer on the AFM tip. The details of the each step is given in the text.

Figure 2 . 12 :

 212 Figure 2.12: Strategy 4: SEM images of the probe are after the complete fabrication process.

Figure 2 .

 2 Figure 2.13 illustrates the full schematic diagram of the fabrication process involved in fabricating thermal probes for SThM. To define the electrical leads of Ti/Au on AFM cantilever and chip, we used the fabrication steps as summarized in Figure 2.4. The resultant patterned structure of Ti/Au is shown in Figure 2.14 (a) and (b). After, NbN thermometer with a thickness of 70 nm is deposited using DC-pulsed magnetron sputtering from high purity (99.95%)

Figure 2 . 13 :

 213 Figure 2.13: Schematic representation of the steps involved to integrate thermally sensitive NbN thin films on nonplanar AFM probes. (a) (d) shows the patterning of Au thin film for electrical contacts on the AFM cantilever, as described in Figure 2.4. (e) Deposition of the NbN thin film was carried out by DC-pulsed magnetron sputtering with a thickness of 70 nm. (f) Evaporation of QSR-5 e-resist on the top of NbN. (g) Patterning of NbN thermometer via EBL and dry etching (SF 6 plasma). (h) The final design of the SThM probe: top-view of the integrated NbN thin film at the apex of the tip and 4-terminal contact lines.

Figure 2 . 14 :

 214 Figure 2.14: SEM images illustrate the integration of the temperature-sensitive NbN film on commercial AFM probes. (a) and (b) Top view of fabricated four-terminal electrical leads of gold (yellow, false color) on AFM chip. (c) and (d) Integrated NbN resistive thermometer (green, false color) at the apex of the nonplanar pyramidal-shaped AFM tip.

46 3. 1 . 2 48 3. 3 53 3. 4

 4612483534 Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.1.1 Tip-Sample Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic components in AFM . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2 EnviroScope AFM description . . . . . . . . . . . . . . . . . . . . . . . . . . . Adaptation of the AFM for SThM . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3.1 Thermal Probe Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.3.2 Low-Noise Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 T his chapter starts with a general introduction to atomic force microscopy (AFM), and goes on to give an overview of a commercial EnviroScope™ AFM equipment that has been modified for SThM measurements. The following sections describe the adaptation of the EnviroScope AFM system for SThM setup that includes the development of a new specific probe holder and low-noise electronics for the acquisition of the thermal probe signal with high accuracy. Finally, the electrical resistance measurement of the new SThM probe will be shown as a function of time to quantify the stability and performance of the probe.

Figure 3 .Figure 3 . 1 :

 331 Figure3.2 shows a schematic of the interaction force F int as a function of the separation distance between the tip and the sample. The force between the tip-sample is negligible when the tip is far away from the sample. As the tip approaches the sample surface, attractive forces between the tip-sample occur. After establishing the contact between the tip-sample, repulsive force occurs. In Figure3.2, a positive interaction force represents the repulsive force between the tip-sample that pushes the tip away from the sample. The negative interaction force stands

Figure 3 . 2 :

 32 Figure 3.2: Schematic illustration of the interaction forces between the tip and the sample.

Figure 3 . 3 :

 33 Figure 3.3: A schematic of the EnivroScope AFM chamber head. A laser diode is used to emit the beam of photons with a wavelength of 670 nm and power of 1 mW, it reflects off the AFM cantilever and detected by a quadrant photodetector. The piezoelectric scanner is utilized to scan the probe in three different directions relative to the sample surface.

Figure 3 . 4 :

 34 Figure 3.4: Schematic representation of an AFM-based SThM setup includes a probe with an integrated temperature sensor at the tip apex, AFM control unit and thermal control unit.

Fig- ure 3

 3 .5 (a) and (b) show the geometry of the probe holder constructed in SolidWorks by Simon Le-Denmat, working at Institut Néel, CNRS, Grenoble. The main body of the cantilever holder is made of Macro®ceramic based-glass with low thermal conductivity, be electrically insulating, strong, rigid, and have zero porosity. This ceramic based-glass is well suited for ambient conditions as well as high-vacuum SThM experiments. In this holder, the thermal probe is installed using a metal clamp with a tightening screw and tilted 12 • relative to the horizontal plane concerning the longest dimension. Since the SThM experiments will be performed using a resistive thermometer in four-wire configuration. We have integrated four gold-plated cylinders to the holder for establishing the electrical connections. In addition, a dither piezo is integrated on the backside of the holder for operating the thermal cantilever in dynamic mode if needed. Figure 3.5 (c) and (d) illustrate the photograph of an SThM probe installed on the probe holder, and Au wires were used to micro-bond the probe to gold plated cylinders. Figure 3.5 (e) and (f) show the close-up optical images of the wire-bonded gold pads on the SThM chip.

Figure 3 . 5 :

 35 Figure 3.5: The geometry of a new SThM cantilever holder constructed in SolidWorks used for thermal measurement, (a) Top view consists of four gold-plated cylinders to establishing the electrical contacts. (b) For driving cantilever oscillations in dynamic operation modes, a dither piezo is integrated on the backside of the holder. (c) and (d) Photographs of the SThM probe installed in the probe holder with the Au wires bonding. (e) and (f) represent the close-up optical images of the wire-bonded gold pads on the SThM chip.

Figure 3 . 6 :

 36 Figure 3.6: Simplified schematic of the SThM setup used for a 3ω experiment.

Figure 3 . 7 :

 37 Figure 3.7: The drawing of the homemade customized flange with 6 BNC connectors is constructed in SolidWorks. The flange has been installed on the side of the AFM chamber to connect the thermal probe with external electronics.

Figure 3 . 8 :

 38 Figure 3.8: Photographs of the EnviroScope AFM system, which has been modified for thermal microscopy. The top-left photo shows the complete setup of the microscope, including a computer, acoustic isolation box, mechanical isolation base, and electronics. Also, the microscope is resting on the vibration-isolated concrete floor to reduce the noise. The top-right photo shows the opened acoustic box and the EnviroScope chamber with the electronic devices, including the current source, lock-in amplifier, a variable resistance box, and a differential bridge. The bottom-right is the zoomed image of the chamber with BNC cables. The bottom left is the inside view of the chamber, which shows the probe holder made of ceramic glass (white color) with an installed SThM probe and a sample underneath.

Figure 3 . 9 :

 39 Figure 3.9: Measurement of the noise in the SThM probe inside the scanning thermal microscope setup at a base pressure of 3 ×10 -5 mbar. (a) Solid circles (black) are the voltage response of the thermal tip at 293 K as a function of time, measured using the SR-830 lock-in amplifier. (b) represents the histogram (orange) of the thermal probe corresponding to its voltage response with a Gaussian fit (solid black line).

Figure 4 . 1 :

 41 Figure 4.1: Thermal noise power spectral density of a triangular-shaped SThM probe in the AFM chamber at a pressure of 5 × 10 -6 mbar. The black line shows experimentally measured value, along with Lorentzian fit in the red line. In the inset, a SEM image with the top-view of the SThM probe.

Figure 4 .

 4 Figure 4.1 shows the thermal noise power spectral of the SThM probe as a function of frequency at a pressure of 5 × 10 -6 mbar. The black line shows an experimentally measured value, along with Lorentzian fit (red line). The resonance peak is obtained at 22.33 kHz, which is lower than the value provided by the manufacture. This change can be explained by the additional mass of NbN and Au thin films on the probe.

Figure 4 .

 4 Figure 4.2 (a) shows the calibration curve of the NbN thermometer deposited on a flat substrate while Figure 4.2 (b) shows the calibration curve of the NbN thermometer integratedat the apex of an AFM probe. Note that the results presented here corresponds to the SThMprobe named "JS-9", see Appendix 7. The electrical resistance of the NbN thermometer is plotted with increasing temperature, where black dots are the experimentally measured value of electrical resistance with the blue dashed line is the second-order polynomial fit. The TCR of the NbN thermometer on the flat surface is obtained to be around |8 × 10 -3 |K -1 near room temperature, which is consistent with the previously published results[START_REF] Bourgeois | Liquid nitrogen to room-temperature thermometry using niobium nitride thin films[END_REF].

Figure 4 .

 4 Figure 4.2 (b) represents the temperature-dependent electrical resistance and TCR of the SThM probe (inset shows the SEM image). We measured the change in the electrical resistance from 4.8 kΩ up to 4 kΩ between the temperature range of 300 K to 340 K, leading to an extracted TCR of |4.5×10 -3 | K -1 near room temperature. We can note that the measured electrical resistance and TCR of the NbN thermometer between the SThM probe and flat surface are different. These variations can be attributed to a high amount of nitrogen contents in the NbN film leads to higher electrical resistance and, consequently, a lower TCR (see equation 4.2) [7].In the case of the SThM probe, a probable reason for the excess amount of nitrogen in the NbN film is potentially due to overheating at the AFM tip (thermally isolated compared to flat SiN substrate) during the sputtering process.In this part, we presented the calibration of only one SThM probe based on NbN thermometer. However, many SThM probes have been fabricated during this research work, and temperature-dependent electrical calibration has been performed. The obtained value of the TCR varies between |4 -5 × 10 -3 | K -1 at room temperature, see Appendix 7.

Figure 4 . 2 :

 42 Figure 4.2: The electrical response and temperature coefficient of resistance (TCR) of the NbN thermometers are illustrated as a function of increasing temperature. (a) NbN thin film of thickness 70 nm was deposited on the flat SiN substrate. The electrical resistance (black dots) with a polynomial fit of second-order (blue dashed line) and TCR (red squares) of NbN thin film are plotted as a function of temperature. The TCR was obtained to be around |8 × 10 -3 | K -1 near room temperature. (b) The black-filled circles represent the experimentally obtained values of electrical resistance of the NbN thermometer, while the blue dashed line is the polynomial fit to the data. The red hexagon represent the TCR of the NbN based SThM probe and obtained value of TCR to be around |4.5 × 10 -3 | K -1 near room temperature.

Figure 4 . 6 WK - 1

 461 Figure 4.3 (a) shows the SEM image of the thermal probe, and the red circle indicates the heat source. If we imagine this probe under high vacuum conditions. Then, the heat flow can only occur through the cantilever to the chip body (heat sink at room temperature). Now, we want to estimate the thermal conductance of the cantilever. For simplicity, we first divide the SiN cantilever into two rectangular plates, having length, width, and thickness of 200 µm, 40 µm, and 0.8 µm respectively. Second, we used the literature value of the thermal conductivity (κ) and specific heat (C p ) of the SiN, which are 3 Wm -1 K -1 and 0.8 Jg -1 K -1 respectively[START_REF] Ftouni | Thermal conductivity of silicon nitride membranes is not sensitive to stress[END_REF]. Using the dimensions and thermal conductivity of the SiN cantilever, we estimated the thermal conductance due to SiN material (G= kS l ; S cross-section area and l is the length) to be

Figure 4 . 3 :

 43 Figure 4.3: (a) SEM image of the SThM thermal probe used in this study. The red circle indicates the heat source, the cantilever as a thermal link and the chip body as a heat sink. (b) Drawing of the thermal architecture, heat dissipated from the hot SThM probe to the chip body in vacuum conditions.

Figure 4 . 4 (

 44 a) illustrates the schematic diagram of the simplified 3ω-SThM experimental setup inside the AFM chamber. A predetermined AC current is supplied through the probe that results in Joule heating. Then, we measured the V 3ω voltage amplitude at various frequencies. In order to confirm the reliability of the experiment, V 3ω signal should be linear with I 3 for a fixed frequency, as shown in equation 4.[START_REF] Paterson | Experimental investigation of heat transport in nanomaterials using electrothermal methods[END_REF]. Measurement results can be seen from Figure4.4 (b). Thereafter, V 3ω voltage amplitude variation is recorded at various electrical frequencies while keeping the heating AC current at a constant value of 30µA.

Figure 4 .Figure 4 . 4 :I 2 0 2 )

 44422 Figure 4.4 (c) shows the V 3ω voltage response of the probe ( "JS-21", see Appendix 7) as a function of electrical frequency in the absence of a laser beam on the backside of the SThM cantilever. The thermal time constant of the probe can be written as τ th = (2πf cut-off ) -1 , where f cut-off is the cut-off frequency at which the V 3ω voltage is attenuated to 1/ √ 2 of the maximum value [41]. The experimentally obtained value of the cut-off frequency is about 60 Hz (Figure 4.4 (c)), and the measured thermal time constant of the SThM probe is about 3∼ms. Next, we used the experimental results presented in Figure 4.4 (c) for determining the

  Figure 4.4 (c) shows the measured V 3ω voltage amplitude of 6.36 mV at frequency of ω: 4.123 Hz. Equation

Figure 4 . 5 :

 45 Figure 4.5: Schematic presenting the 3D geometry of the SThM probe built using FEM.

  Figure 4.6 shows V 3ω voltage amplitude variation in response to frequency. From the

Figure 4 . 7 :

 47 Figure 4.7: Normalized V 3ω response is plotted as a function of frequency. Different parameters are tested to study V 3ω .

Figure 4 .

 4 Figure 4.8 illustrates the experimentally measured electrical resistance response and the corresponding calculated temperature variation of the probe by changing the laser position on the cantilever using TCR of |4.5 × 10 -3 | K -1 . In the graph, we can see the maximum impact of

Figure 4 . 8 :

 48 Figure 4.8: Electrical resistance response and corresponding calculated temperature variation of a SThM probe plotted as a function of the laser positions. The laser with a wavelength of 650 nm and power of < 1mW was applied on the backside of the thermal cantilever.

Figure 4 .

 4 Figure 4.9 shows the electrical resistance variation and corresponding calculated temperature change in the SThM probe ( "JS-10") as a function of distance (in ambient conditions).

Figure 4 . 9 :

 49 Figure 4.9: (a) A schematic diagram of the experimental setup used for performing the Dark mode SThM. In Dark mode SThM, the contact between the tip-sample is established without a laser beam on the cantilever. (b) Electrical resistance variation and corresponding calculated DC temperature change of the SThM probe (no joule heating) are plotted as a function of distance in air conditions. The black dots with connected line stands for electrical resistance and red one corresponds to temperature variation.

Contents 5 . 1

 51 Blunt Thermal Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 SThM Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Thermal spreading resistance . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Measurement Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Measurements of the Probe Thermal Conductance (G probe ) . . . . . . . 5.3.2 G c , Thermal Contact Conductance . . . . . . . . . . . . . . . . . . . . . 5.3.3 Measurement of Thermal Boundary Resistance . . . . . . . . . . . . . . 5.4 DNA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Preparation of DNA Origami . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Experimental Procedure & Data Analysis . . . . . . . . . . . . . . . . . 5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5 . 1 :

 51 Figure 5.1: Schematic illustration of the original AFM probe (a), and (b) FIB modified SThM probe having radius of curvature about 250 nm.

Figure 5 . 2 :

 52 Figure 5.2: SEM images of the NbN-SThM probes with flat tip of diameter about to ∼250 nm. (a) Top-view of AFM probe with the triangular-shaped cantilever and tip. (b) Close-up SEM micrograph of the blunt tip with integrated NbN thermometer near the apex of the tip.

Figure 5 .

 5 Figure 5.3 shows the schematic diagram of the heat spreading via a small heat source into a semi-infinite sample. The thermal spreading resistance can be expressed as:

Figure 5 . 3 :

 53 Figure 5.3: Heat flux distribution inside a bulk sample whose dimensions are two or more

Figure 5 . 4 :

 54 Figure 5.4: Comparison of the SThM thermal architecture between the out of contact (left) and the in-contact (right) regimes in vacuum conditions. (a) Schematic representation of the heat transfer through the probe and (b) corresponding the thermal architecture. (c) The sketch shows T rms 2ω-o.c rms temperature oscillation of the SThM probe (out-of-contact). (d) Schematic of heat transfer interactions between the probe and the sample. (e) the thermal architecture is constructed when the tip is contacted to the sample, and (f) the measured rms temperature T rms 2ω-i.c response from the SThM probe.

Figure 5 . 5 :

 55 Figure 5.5: (a) Plot of the SThM V 3ω voltage as a function of electrical frequency in-presence and in-absence of the laser beam on the thermal cantilever (inset shows the zoom-in at low frequency range), and (b) corresponding T rms 2ω signal is plotted as a function frequency.

Figure 5 . 6 :

 56 Figure 5.6: Measured SThM average T rms 2ω tip temperature for various frequency between outof-contact and contact with a sapphire substrate (κ sapphire =34 Wm -1 K -1 ) for an AC current of 30µA. Red circles indicate the measured signal in the out-of-contact mode and red line is used to guide the eyes whereas blue square corresponds to the in-contact measured temperature with blue line to guide the eyes. The inset shows the zoom-in of the data at low frequency.

Figure 5 .

 5 Figure 5.6 shows the comparison of the T rms 2ω temperature oscillation of the SThM probe (extracted from V 3ω signal) in contact and out-of-contact with the sapphire sample. The red circles are measured temperature oscillations of the probe in out-of-contact configuration, and it corresponds to rms temperature T rms 2ω-o.c above room temperature and blue dots represent the measured temperature in-contact with the sample and corresponds to T rms 2ω-i.c . From the plot in Figure 5.6, we found the difference of 120 mK (at frequency <5Hz) in the temperature

Figure 5 . 7 :

 57 Figure 5.7: Measured magnitude of the average T rms 2ω tip temperature according to the frequency for the out-of-contact and in-contact with S1818 resist film of 2µm thick on SiO 2 substrate for an AC current of 30µA. Red circles indicate the measured signal in the out-of-contact mode and red line is used to guide the eyes whereas blue square corresponds to the in-contact measured temperature with blue line to guide the eyes.

Figure 5 . 8 :

 58 Figure 5.8: Measured SThM average T rms 2ω tip temperature for various frequency between outof-contact and contact with SiO 2 substrate for an AC current of 30µA. Red circles indicate the measured signal in the out-of-contact mode and red line is used to guide the eyes whereas blue square corresponds to the in-contact measured temperature with blue line to guide the eyes.

Figure 5 . 9 :

 59 Figure 5.9: Comparison between the measured SThM average T rms 2ω tip temperature as a function of frequency between out-of-contact (Red circles with lines) and in contact (blue square with lines) with Si substrate for an AC current of 30µA.

Figure 5 .

 5 11 shows the 3D images of various DNA origami nanostructures. This work has been undertaken by C. Magnin during her M1 internship.

Figure 5 .

 5 Figure 5.11: Various DNA origami nanostructures that were synthesized and characterized.

Figure 5 . 12 : 1 Figure 5 . 13 :

 5121513 Figure 5.12: Diagram of the model for non-contact measurement.

Figure 5 . 14 :

 514 Figure 5.14: Schematic of the model for the DNA contact measurement

Figure 5 .

 5 Figure 5.15 shows the topographic images of DNA structures deposited on mica substrate obtained with the SThM probe. The dark brown color on the image represents the mica substrate and lighter part DNA. The purpose of the topographic image is to locate the precise position of DNA nanostructures and then, carried out the contact point V 3ω -SThM experiments. In the experiment, we achieved a spatial resolution of 100 nm despite the blunt tip.

Figure 5 .

 5 Figure 5.15: (a) AFM image highlights the topographic features of the DNA nanostructures deposited on mica substrate (b) Close-up view. The dark brown presents the mica surface whereas lighter part indicates DNA.

Figure 5 .Figure 5 .

 55 Figure 5.16: (a) Comparison between the SThM experimental results of T rms 2ω temperature oscillation for DNA-on-mica (dotted line) substrate and mica substrate (solid lines). (b) Zoom-in view of the T rms 2ω signal is plotted as a function frequency.

Figure 5 .

 5 Figure 5.17: (a) Illustration of the AFM topographic images of the DNA nanostructures (PF-2) deposited on Si substrate and red box highlights where we performed another AFM image (b) in order to locate the precise position to perform the SThM experiment. (c) The height profile of the DNA nanostructure shows the thickness of the DNA structure of ∼20 nm.

Figure 5 .

 5 Figure 5.18: (a) Comparison of T rms 2ω temperature oscillation between PF-2 type DNA and bulk-Si. Dotted lines are representing the data corresponds to DNA where solid lines for bulk-Si. (b) Zoom-in view.

Figure 5 .

 5 Figure 5.19: (a) AFM topographic image of the DNA nanostructures (PF-3) deposited on Si substrate and corresponding to the white line the height profile is measured. (b) Height profile of the DNA nanostructure.

Figure 5 .

 5 Figure 5.20: (a) T rms 2ω temperature oscillation of the SThM probe versus frequency. Dotted lines are representing the data corresponds to DNA where solid lines for bulk-Si. (b) Close-view.

  -MDT SThM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.2 SThM Model in Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.4 Thermal map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.5 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6. 1 .

 1 NT-MDT SThM the calibration curve under air conditions.

Figure 6 . 1 :

 61 Figure 6.1: A schematic representation of the SThM setup used in ambient conditions.

. 2 )

 2 where P Avg-N bN -o.c is the average power dissipated due to laser and Joule effect in the SThM probe, in non-contact configuration. Here, T o.c (d) = T 1 -T RT is the relative temperature between the mean DC sensor temperature T 1 and the heat sink (T RT ) in out-of-contact configuration. G probe and G cc-o.c are the thermal conductance of the probe and surrounding gas by conduction or convention[START_REF] Guen | Scanning thermal microscopy on samples of varying effective thermal conductivities and identical flat surfaces[END_REF]. Here, the indices o.c and i.c represent the out-of-contact and in-contact situations, respectively.

Figure 6 . 2 :

 62 Figure 6.2: A three-step protocol and equivalent thermal conductance architecture is presented. (1) When tip is far from the sample. (2) The tip approaches the sample, and (3) The tip is in contact. The indices o.c and i.c stand for out-of-contact and in-contact configurations, respectively.

Figure 6 . 3 :

 63 Figure 6.3: (a) Approach SThM curves acquired with NbN-SThM probe on bulk-Si in air conditions and (b) measured electrical resistance of the probe. (c) The average temperature of the probe is plotted as a function distance. The inset shows the close up look in the temperature variation of the probe before and after the contact. (d) Variation in the thermal conductance of the probe-sample system ∆G global is plotted as a function of distance.

Figure 6 .Figure 6 . 4 :

 664 Figure 6.4: (a) Approach curve and average SThM probe temperature were plotted as a function distance in air conditions for PMMA and (b) Global thermal conductance measured as a function of tip-sample distance.

Figure 6 . 5 :

 65 Figure 6.5: (a) SThM distance curve and average SThM probe temperature were acquired as a function distance in air conditions for SiO 2 and (b) Thermal conductance

Figure 6 . 6 :

 66 Figure 6.6: The variation in the global thermal conductance between the tip-sample system is plotted against the bulk reference thermal conductivity samples. The black square represents the experimentally measured data and red line denotes the calibration curve deduced by fitting the measured data.

Figure 6 . 7 :

 67 Figure 6.7: SThM distance curve was recorded under high vacuum conditions along with the change in SThM tip temperature as a function of distance. When the tip contacts the Sapphire substrate, a change of 1 K in temperature was recorded.

  Q t-sHeat flow from tip to sampleT rms 2ω-o.crms temperature oscillations in out-of-contact T rms 2ω-i.c rms temperature oscillations in-contact with sample T rms 2ω-i.c-DN A rms temperature oscillations in-contact with DNA T o.c (d) Mean relative temperature (out-of-contact) T i.c (d) Mean relative temperature (in-contact) κ sapphire Thermal conductivity of sapphire κ Si Thermal conductivity of silicon κ DN A Thermal conductivity of DNA P Avg-N bN -o.c Power dissipated in the probe under air conditions (out-ofcontact) P Avg-N bN -i.c Power dissipated in the probe under air conditions (incontact) P N bN -laser Power dissipated in the probe due to laser G cc-o.c Thermal conductance into the environment via gas conduction and convention ∆G global global probe-sample thermal conductance Amplitude of applied rms current

  Heat Conduction at Sub-Micro Scale . . . . . . . . . . . . . . . . . . . . . . . .

	Chapter 1
	Literature Review
	Contents
	1.1

2 1.1.1 Fourier's Law and Thermal Conductivity . . . . . . . . . . . . . . . . . . 3 1.1.2 Phonon Scattering at Nanoscale . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Thermal Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Optical techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Electrical techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Scanning Thermal Microscopy (SThM) . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Thermal probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 Thermocouple probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.2 Resistive probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 Operation modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 Heat Transfer Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.6.1 Air Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.6.2 Water Meniscus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.6.3 Thermal Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.6.4 Conduction at the Tip-Sample Contact . . . . . . . . . . . . . . . . . . . 19 1.7 Towards a Highly Sensitive Thermal Probe . . . . . . . . . . . . . . . . . . . . 20

Table 3 .

 3 1: Technical specification of the EnviroScope SPM instrument.

	Maximum sample dimension	Mode of operation	Chamber pressure	Scan dimensions
	X-Y: 30 mm and Z: 12 mm	Contact and Tapping	3 × 10 -6 mbar	X-Y: 90µm and Z: 6µm

EnviroScope is a commercial scanning probe microscopy (SPM) equipment that can work under various environments such as elevated temperature, air, reduced pressure, and in the

Table 5 . 2

 52

: Summary of the various parameters used in the 3ω experiments and obtained thermal properties of different DNA origami structures.

Acknowledgements

List of Tables 3.5 Summary

In summary, we discussed the working principle of the AFM and the essential components required for understanding the operation. Then, we focused on integrating the thermal control unit to adapt the AFM system for the SThM measurements. We designed and fabricated the new thermal probe holder, which is compatible with performing electrical measurement in four-probe geometry. Following, the laboratory environment is discussed for highly sensitive measurements. Finally, we experimentally characterized the electrical noise of the SThM probe, and the noise is found to be 40 nV/

√

Hz, which is about ten times higher than the expected theoretical noise. and vacuum conditions. To begin with, we discuss the experimental method used to determine the intrinsic parameters of the SThM probe, such as resonant frequency and spring constant. Next, we will show the calibration of the NbN thermometer as a function of temperature. Thereafter, we will theoretically calculate the probe's thermal time constant and thermal conductance using the geometry and composition of the probe. These calculated values will be compared with the experimentally obtained results through V 3ω measurements in vacuum conditions. The following part will focus on estimating the heating in the SThM probe because of the laser beam absorbed by the cantilever. Finally, Dark-mode SThM is described and carried out to study the impact of thermo-mechanical stress on the electrical resistance of the Chapter 4. Probe Characterization modeling, we were able to fit the V 3ω response of the probe that was obtained under high vacuum conditions. Then, we estimated the cut-off frequency to be about ∼38 Hz. As a conclusion, the obtained result from the modeling is in good agreement with the experimental values. The obtained results for the tested parameters are reported in Figure 4.7. No significant difference in V 3ω behavior was found by varying the some physical properties.

Properties Default value Tested value

Length of NbN 1.2 µm 0.25 µm

Thickness of SiN 800 nm 700 nm Table 4.2: Different parameters used for simulation.

After calibrating the temperature response and thermal conductance of the NbN-SThM probe. We wish to study the impact of extrinsic sources which can influence the electrical re-

Summary

In summary, we presented the experiments carried out via the DC laser-heated SThM probe under air and vacuum conditions. In the first part, we investigated the thermal conduction into three samples with dissimilar thermal conductivity. A simple protocol was introduced that allowed us to estimate the thermal conductance of the full tip-sample system (G) under air conditions. We then showed the variation of measurand (∆G global ) with thermal conductivity of the samples and obtained the calibration curve. From the calibration curve, we found out that the sensitivity of the NbN-SThM probe is limited to a few µWK -1 .

Following, the force-distance curve was performed on a sapphire substrate using the laserheated probe. A slight variation in the temperature of the probe was recorded after contacting the sapphire substrate. Finally, the preliminary experiment was presented to obtain the thermal map of Si-nanowires embedded in the alumina matrix. However, more experiments are needed to perform thermal maps of Si-nanowires in an alumina matrix for obtaining a clear thermal conductivity contrast. Furthermore, topography-free samples will be utilized to demonstrate the thermal imaging capability using the NbN-SThM probes.

Appendix

This appendix details the number of NbN-SThM probes were successfully fabricated during this research work. In the table, R 0 stands for electrical resistance at room temperature and TCR refers to temperature coefficient of resistance.

• Temperature range: High refers to room temperature thermometer and low represents the cryogenic thermometry.