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Phonon transport in square-cross-section nanowires is studied using spectral Monte Carlo simulations. Our results show the evolution of the different transport regimes described by Lévy statistics as a function of the surface roughness-to-thermal wavelength ratio σ/λ. More precisely, the relationship between the Lévy index γ describing the mean free path distribution Ψ(Λ) and σ/λ is established for the classical diffusive regime, the superdiffusive regime, and the ballistic regime in the nanowire. Besides the conventional superdiffusive regime that is marked by Ψ(Λ) with a single heavy-tailed peak, we reveal an unconventional superdiffusive subregime featuring Ψ(Λ) with sawtooth oscillations when σ/λ∼0.01. Investigation of the direction of propagation of phonons shows a significant narrowing of the angular distribution around the long axis of the nanowire due to the diffuse scattering at rough boundaries when σ/λ0.1. These results shed light on the transport mechanisms of quasiballistic phonons and will help in nanowire design for specific applications.

In this report we investigate the Kapitza resistance RK at an interface between a classical solid and a 4He quantum crystal, as a function of temperature. We provide a premise for RK based on a combination of two separate mechanisms which occur simultaneously. Owing to the fact that the phonon wavelengths in solid 4He and in the superfluid are of the same order of magnitude, we infer that one mechanism is due to resonant scattering of phonons by nanoscale surface roughness as predicted by Adamenko and Fuks1 for solid/superfluid interfaces. The other mechanism involves the interaction of thermal phonons with mobile vibrating dislocations within solid 4He. The present analysis demonstrates the plausibility of these two mechanisms in solving the long outstanding problem of the Kapitza resistance anomaly of solid 4He in contact with copper for temperatures ranging from 0.4 to 2 K.

In a recent paper, it is shown that the thermal boundary Kapitza resistance between a solid and superfluid helium is explained by resonant scattering of phonons from surface roughness heights, as described in the Adamenko and Fuks (AF) model. We reexamine the original experiments of thermal transfer between a solid (platinum and copper) and superfluid helium conducted by P.L. Kapitza in 1940. In particular, we analyze his experimental results for the different surface treatments of the solid in light of the AF model. Time scales for diffuse scattering of phonons at the interface are estimated. Also the role of a layer of varnish on a copper surface is reinterpreted.

We propose a model for the thermal conductivity of 2D-samples when the mean free paths due to the phonon–phonon interactions exceed the sample dimensions. The physical mechanisms that ensure the stationary heat flux and the stationary nonequilibrium temperature distribution are examined. A recursive equation is derived to quantify the contribution of phonon scattering to the net heat flux in the pure elastic isotropic diffusive regime, as a function of the number of scattering at the boundaries. As the length to width ratio L/W increases above unity, our model shows an increase in the phonon mean free path compared to that predicted by the Casimir model in which the lateral walls are assumed to be black bodies. The present model also reveals that the multiple phonon interactions with the lateral walls lead to a stationary, but non-linear temperature distribution. The dependence of the heat flux and the thermal conductivity on the sample dimensions is then shown to be non-monotonic. This infers that the location of the thermometers on the sample influences experimental measurements of the thermal conductivity.

International audience; A quantum solid (solid 4 He) in contact with a classical solid defines a new class of interfaces. In addition to its quantum nature, solid 4 He is indeed a very plastic medium. We examine the thermal interface resistance upon solidification of superfluid 4 He in contact with a silicon crystal surface (111) and show that dislocations play a crucial role in the thermal interface transport. The growth of solid 4 He and the measurements are conducted at the minimum of the melting curve of helium (0.778 K and ∼25 bar). The results display a first-order transition in the Kapitza resistance from a value of R K,L = (80 ± 8) cm 2 K/W at a pressure of 24.5 bar to a value of R K,S = (41.7 ± 8) cm 2 K/W after the formation of solid helium at ∼25.2 bar. The drop in R K,S is only of a factor of ∼2, although transverse phonon modes in solid 4 He now participate in heat transmission at the interface. We provide an explanation for the measured R K,S by considering the interaction of thermal phonons with vibrating dislocations in solid 4 He. We demonstrate that this mechanism, also called fluttering, induces a thermal resistance R F l ∝ N d T −6 , where T is the temperature and N d is the density of dislocations. We estimate that for dislocation densities on the order of ∼10 7 cm −2 , R F l predominates over the boundary resistance R K,S. These fundamental findings shed light on the role of dislocations and provide a quantitative explanation for previous experiments which showed no measurable change in the Kapitza resistance between Cu and superfluid 4 He upon solidification of the latter. This demonstrates the possibility of using dislocations as an additional means to tailor thermal resistances at interfaces, formed especially with a plastic material.

Kapitza resistance measurements conducted at T > 1 K on silicon and niobium single crystals in contact with helium demonstrate respectively the importance of atomic scale surface roughness and dislocations due to surface damage at the boundary. Two different experimental configurations were used.

The thermoelectric properties of CsSnI3 are analysed with the ab initio first-principle density functional theory (DFT). Seebeck coefficient, electrical and thermal conductivities are calculated in order to determine the dimensionless figure of merit ZT. Knowing that CsSnI3 is one of the perovskite series of materials that undergo complex phase transitions with temperature, the calculations are performed for different common phases. Several phases of CsSnBr3 and CsSnCl3 are also analysed as comparisons. For the same material, comparison of band structures showed that the band gap increases with phase transition from phase — α to phase — β then to phase — γ. And the ZT values show the same trend as the band gaps. CsSnCl3 exhibits a higher ZT value than CsSnBr3 and CsSnI3 at phase-α.

International audience; Kapitza in 1941 discovered that heat flowing across a solid in contact with superfluid helium (

We investigate the impact of phonon grain boundary scattering in our thermal conduction measurements carried out on polycrystalline niobium samples in the superconducting state and of two different sizes. A simple model is developed which takes into account the average grain size d, the Kapitza resistance RK at grain–grain boundaries and the number of grains n over which the measurements are performed. Our model predicts a strong spatial anisotropy in the thermal conductivity for which can account for the discrepancy in our experimental data. The analysis enables the determination of the Kapitza resistance RK at Nb grain–grain boundaries. We show that with increasing temperature the grain boundary resistance remains dominant relative to the bulk thermal resistance.

Heat transfer mechanisms at very small length scales are studied at the boundary between solid and superfluid helium-4 (He II) at temperatures of 1–2 K. We shall show that this configuration is interesting and may prove useful in future heat conduction analysis in microstructures and across film/substrate boundaries. We define two possible heat conduction regimes, namely a classical surface effect regime and a scattering effect regime for the solid/He II system. The distinction between these regimes depends upon the (l/λ) ratio, where the surface roughness extent is l at a given length scale and the phonon wavelength is λ. We analyse our results of heat conduction across solid–superfluid helium interfaces and we show that the conductance can be entirely explained by the scattering effect regime where diffuse phonon scattering from surface irregularities of nanometric scale lengths play a dominant role. We also provide evidence of the existence of a frequency dependence of the heat transmission coefficient and, we compare the heat conduction with that in microstructures.

By measuring the temperature jump in the presence of a heat flux across niobium disks surrounded by He II, we determined the Kapitza resistance, Rk , for different surface roughness and bulk purity. The experiments were conducted from 1.5 Kt oT* , under saturated vapour pressure. The influence of foreign atoms due to the presence of Ti near the interface was also investigated. The importance of Rk on the efficiency of superconducting cavities is discussed.

This paper reports a study of the inertia of rough and vicinal of4He crystals. We have measured the transmission coefficient of ultrasonic waves at frequencies 10, 30, 50 and 70 MHz, across the liquid-solid interface. The experiments are carried out at temperatures ranging between 0.4 and 1.0 K for four crystallographic orientations. Two important phenomena are put to evidence for the first time. We have found the first experimental evidence that the inertia of rough surfaces depends on temperature. For vicinal surfaces, we have shown the strong increase of the inertia as the tilt angle decreases. Our experimental results agree very well with the theoretical predictions.

For bulk solid-solid interfaces, the thermal contact resistance TCR) is generally attributed to a mismatch in the acoustic impedances (density x sound velocity) of each medium [1]. Here, we present a novel study of the TCR for a bulk Silicon crystal (111) in contact with superfluid helium, as a function of the acoustic impedance of the superfluid. The cell design and experimental technique are discussed in [2]. The acoustic impedance is varied by monitoring the pressure of the superfluid. Measurements are carried-out at T~1.8 K, from a few torrs (vapor pressure) up to 25 bars, corresponding to approximately an 80% change in the acoustic impedance of the superfluid. The experiments show no change in TCR over the entire pressure range, indicating a negligible contribution due to the acoustic impedances. A comparison to the diffuse mismatch model [1] is discussed.

An evaporator-type cryogenic heat exchanger is designed and built for introducing fluid–solid heat exchange phenomena to undergraduates in a practical and efficient way. The heat exchanger functions at liquid nitrogen temperature and enables cooling of N2 and He gases from room temperatures. We present first the experimental results of various parameters which characterize the heat exchanger (efficiency, number of transfer units, heat exchange coefficient, etc) as a function of the mass flow rate of the gas to be cooled. An analysis of the Nu–Re diagram is also presented. All experiments were conducted with N2 gas. The scope of this tool is readily extended to research purposes.

In the ballistic regime of transport, we derive the thermal resistance of metal nanowires connected to two heat baths. We find that the thermal resistances for any metal nanowire remain in a narrow and temperature-dependent interval between 0.447/$T$ and 14/$T$ ${\mathrm{m}}^{2}$ K/W. For cross-section edges larger than 20 nm, the thermal resistance can actually be estimated from $\frac{{R}_{0}}{(3\ensuremath{\pi}{n}_{V}^{2}){}^{3}}$, where ${R}_{0}$ is the quantum of resistance and ${n}_{V}$ refers to the electron density. This prediction yields a contact resistance one order of magnitude larger than the one of previous estimations. Significant consequences for application fields such as nanoelectronics, where nanowire sizes involve ballistic transport, are expected.

The thermal contact resistance at a highly polished single-crystal silicon (111)/liquid helium interface has been directly measured from 0.4 to 2.1 K using a single experimental cell. A thermal analysis is presented using the thermal conductivity of the Si which is simultaneously measured. The effect of phonon scattering by nanoscale surface roughness on the observed thermal resistance is investigated. A feature brought to light in our analysis is that the surface roughness which plays an effective role in phonon scattering is temperature dependent. This explains the temperature dependencies of the thermal contact resistance. Comparisons with other experiments are made.

Phonon spectral energy transmission in silicon nanoribbons is investigated using Monte-Carlo simulations in the boundary scattering regime by changing the length and width geometrical parameters. We show that the transition frequency from specular scattering to diffuse scattering is inversely proportional to the edge roughness with a geometry independent factor of proportionality. The increase of the length over width ratio leads to a decrease of the energy transmission in the diffuse scattering regime which evolves as . This trend is explained by developing a model of phonon energy transmission in the fully diffuse scattering regime which takes into account the probability for a diffusively scattered phonon to be directly transmitted from any position on the edge of the nanoribbon. This model establishes the importance of the solid angles in the energy transmission evolution with . The transition from unity energy transmission in the specular scattering regime to reduced transmission in the diffuse scattering regime constitutes a low-pass frequency filter for phonons. Our simulations show an energy rejection rate better than 90% for high , which paves the way for potential high performance filters. Filtering out high frequency phonons is of significant interest for phononic crystal applications, which use band engineering of phonons in the wave regime with low frequencies.

Thermal behavior of superconducting niobium cavities is investigated especially focusing on the Kapitza boundary resistance. First systematic measurements of the thermal boundary resistance are performed on samples with well characterized thermal conductivity (RRR values) and surface morphology (chemically etched or electropolished). The experimental data are used in a simple model, calculating the heat flux to the superfluid helium bath. These results show the relative importance of the Kapitza resistance with respect to the thermal conductivity. Also they indicate that best conditions are reached when using high RRR niobium with rough chemically etched outer surfaces.

Phonon transport in junctions formed between suspended membranes of the same material is studied using Monte Carlo method. The investigation is conducted at 1K for systematically chosen ratios of (d/D) where d is the junction width and D the membrane length. The influence of surface roughness is taken into account. The dependency of the constriction thermal resistance (in μmK/W) is established: RJ ≈ [2.4 + 2.0 × (d /D)−1/2] × 109. The average and frequency dependent transmission coefficients are determined as a function of (d/D). These structural configurations are inherent in thermoelectric; and graphene and silicene related applications.

We present measurements of the Kapitza resistance between a highly polished single crystal silicon surface and superfluid helium from 0.4 K to 2.1 K at svp pressure. The data constitutes the first set of direct measurements using a unique cell configuration for this large temperature range.

Thermoelectricity is considered a promising source of energy since it is able to directly convert heat into electricity. This makes it possible to recover dissipated heat without causing pollution. However, large-scale applicative options are still under restriction because of the dim thermoelectric conversion yield. Therefore, numerous research works are dedicated to improving thermoelectric performance of different materials, which is characterized by the dimensionless figure of merit ZT. A favorable ZT includes simultaneously a satisfying Seebeck coefficient, a high electrical conductivity and a low thermal conductivity. To seek a suitable material with a better thermoelectric performance is the objective of our analyses. With doping technics, different elements can be added into semi-conductors within different concentrations. The charge density could be thus modified in order to change thermoelectric properties. Due to hurdles related to materials synthesis, numerical simulations based on different methods, such as density functional theory (DFT), molecular dynamics (MD), are then implemented to estimate the most promising improvement approach. During this thesis, thermoelectric properties of several materials are investigated for applications in different situations, i.e. CsSnI₃ as a potential candidate with its high electronic conductivity, ZnO as a transparent thermoelectric material, Bi₂Te₃ as a traditional material with further improvements and cellulose as future organic semi-conductor. As DFT concerns only properties of electrons (Seebeck coefficient, electric conductivity, thermal conductivity due to electrons), lattice thermal conductivity is not included herein. Therefore, DFT with finite displacement and MD are used as a complementary method to establish thermal conductivity due to phonons. In this way, this thesis is divided into two parts. In the first part, theoretical backgrounds of DFT are introduced starting with Schrödinger equation. Results of classical DFT simulations are presented afterwards. By using atomic positions from experimental measurements, we launched crystal structure relaxation to ensure that every atom in the system is at its equilibrium position. Electronic band structures are also calculated to validate calculation configurations (cutoff energy, convergence conditions, etc.). A full mapping of Eigenvalues in reciprocal space is realized and thermoelectric properties are calculated by solving Boltzmann transport equations. In the second part, basic theories of phonons are mentioned, followed by introductions of DFT with finite displacements and MD methods. We implemented MD simulations to study the influence of aluminum doping on lattice thermal conductivity for ZnO. We also used DFT with finite displacements method to study lattice thermal conductivity variation of Bi₂Te₃₋ₓSeₓ alloy.; La thermoélectricité est considérée comme une source prometteuse de l'énergie puisqu'elle est capable de convertir directement la chaleur en électricité. Ceci permet de récupérer la chaleur dissipée sans causer de la pollution. Cependant, les options applicatives à grande échelle sont encore en restriction en raison du faible rendement de conversion thermoélectrique. Par conséquent, de nombreux travaux de recherche sont consacrés à l'amélioration de la performance thermoélectrique de différents matériaux, qui est caractérisée par la figure de mérite ZT. Un ZT favorable comprend simultanément un coefficient Seebeck satisfaisant, une conductivité électrique élevée et une faible conductivité thermique. Rechercher un matériau approprié avec une meilleure performance thermoélectrique est l'objectif de nos analyses. Avec les techniques de dopage, différents éléments peuvent être ajoutés dans des semi-conducteurs à différentes concentrations. La densité de charge pourrait ainsi être modifiée pour améliorer les propriétés thermoélectriques. En raison des obstacles liés à la synthèse des matériaux, des simulations numériques basées sur différentes méthodes, telles que la théorie fonctionnelle de la densité (DFT), la dynamique moléculaire (DM), sont ensuite mises en oeuvre pour estimer l'approche d'amélioration la plus prometteuse. Au cours de cette thèse, les propriétés thermoélectriques de plusieurs matériaux sont étudiées pour des applications dans différentes situations, à savoir CsSnI₃ comme un candidat potentiel avec sa haute conductivité électrique, ZnO comme un matériau thermoélectrique transparent, Bi₂Te₃ comme un traditionnel matériau avec d'autres améliorations et la cellulose comme futur semi- conducteur organique. Comme la DFT ne concerne que les propriétés des électrons (coefficient de Seebeck, conductivité électrique, conductivité thermique due aux électrons), la conductivité thermique du réseau n'est pas incluse ici. Par conséquent, DFT avec des déplacements finis et DM sont utilisés comme méthodes complémentaires pour établir la conductivité thermique due aux phonons. De cette façon, cette thèse est divisée en deux parties. Dans la première partie, des contextes théoriques de DFT sont introduits à partir de l'équation de Schrödinger. Les résultats des simulations DFT classiques sont présentés par la suite. En utilisant des positions atomiques issues de mesures expérimentales, nous avons lancé la relaxation de la structure cristalline pour assurer que chaque atome dans le système est à sa position d'équilibre. Les structures de bande d'énergie électronique sont également calculées pour valider les configurations de calcul (énergie de coupure, conditions de convergence, etc.). Une cartographie complète des valeurs propres dans l'espace réciproque est faite et les propriétés thermoélectriques sont calculées en résolvant les équations de transport de Boltzmann. Dans la deuxième partie, les théories de base des phonons sont mentionnées, suivies des introductions des méthodes en DFT avec des déplacements finis et en DM. Nous avons mis en oeuvre des simulations DM pour étudier l'influence du dopage à l'aluminium sur la conductivité thermique du réseau pour ZnO. Nous avons également utilisé la méthode en DFT avec des déplacements finis pour étudier la variation de la conductivité thermique de l'alliage Bi₂Te₃₋ₓSeₓ.

Thermoelectricity is considered a promising source of energy since it is able to directly convert heat into electricity. This makes it possible to recover dissipated heat without causing pollution. However, large-scale applicative options are still under restriction because of the dim thermoelectric conversion yield. Therefore, numerous research works are dedicated to improving thermoelectric performance of different materials, which is characterized by the dimensionless figure of merit ZT. A favorable ZT includes simultaneously a satisfying Seebeck coefficient, a high electrical conductivity and a low thermal conductivity. To seek a suitable material with a better thermoelectric performance is the objective of our analyses. With doping technics, different elements can be added into semi-conductors within different concentrations. The charge density could be thus modified in order to change thermoelectric properties. Due to hurdles related to materials synthesis, numerical simulations based on different methods, such as density functional theory (DFT), molecular dynamics (MD), are then implemented to estimate the most promising improvement approach. During this thesis, thermoelectric properties of several materials are investigated for applications in different situations, i.e. CsSnI₃ as a potential candidate with its high electronic conductivity, ZnO as a transparent thermoelectric material, Bi₂Te₃ as a traditional material with further improvements and cellulose as future organic semi-conductor. As DFT concerns only properties of electrons (Seebeck coefficient, electric conductivity, thermal conductivity due to electrons), lattice thermal conductivity is not included herein. Therefore, DFT with finite displacement and MD are used as a complementary method to establish thermal conductivity due to phonons. In this way, this thesis is divided into two parts. In the first part, theoretical backgrounds of DFT are introduced starting with Schrödinger equation. Results of classical DFT simulations are presented afterwards. By using atomic positions from experimental measurements, we launched crystal structure relaxation to ensure that every atom in the system is at its equilibrium position. Electronic band structures are also calculated to validate calculation configurations (cutoff energy, convergence conditions, etc.). A full mapping of Eigenvalues in reciprocal space is realized and thermoelectric properties are calculated by solving Boltzmann transport equations. In the second part, basic theories of phonons are mentioned, followed by introductions of DFT with finite displacements and MD methods. We implemented MD simulations to study the influence of aluminum doping on lattice thermal conductivity for ZnO. We also used DFT with finite displacements method to study lattice thermal conductivity variation of Bi₂Te₃₋ₓSeₓ alloy.; La thermoélectricité est considérée comme une source prometteuse de l'énergie puisqu'elle est capable de convertir directement la chaleur en électricité. Ceci permet de récupérer la chaleur dissipée sans causer de la pollution. Cependant, les options applicatives à grande échelle sont encore en restriction en raison du faible rendement de conversion thermoélectrique. Par conséquent, de nombreux travaux de recherche sont consacrés à l'amélioration de la performance thermoélectrique de différents matériaux, qui est caractérisée par la figure de mérite ZT. Un ZT favorable comprend simultanément un coefficient Seebeck satisfaisant, une conductivité électrique élevée et une faible conductivité thermique. Rechercher un matériau approprié avec une meilleure performance thermoélectrique est l'objectif de nos analyses. Avec les techniques de dopage, différents éléments peuvent être ajoutés dans des semi-conducteurs à différentes concentrations. La densité de charge pourrait ainsi être modifiée pour améliorer les propriétés thermoélectriques. En raison des obstacles liés à la synthèse des matériaux, des simulations numériques basées sur différentes méthodes, telles que la théorie fonctionnelle de la densité (DFT), la dynamique moléculaire (DM), sont ensuite mises en oeuvre pour estimer l'approche d'amélioration la plus prometteuse. Au cours de cette thèse, les propriétés thermoélectriques de plusieurs matériaux sont étudiées pour des applications dans différentes situations, à savoir CsSnI₃ comme un candidat potentiel avec sa haute conductivité électrique, ZnO comme un matériau thermoélectrique transparent, Bi₂Te₃ comme un traditionnel matériau avec d'autres améliorations et la cellulose comme futur semi- conducteur organique. Comme la DFT ne concerne que les propriétés des électrons (coefficient de Seebeck, conductivité électrique, conductivité thermique due aux électrons), la conductivité thermique du réseau n'est pas incluse ici. Par conséquent, DFT avec des déplacements finis et DM sont utilisés comme méthodes complémentaires pour établir la conductivité thermique due aux phonons. De cette façon, cette thèse est divisée en deux parties. Dans la première partie, des contextes théoriques de DFT sont introduits à partir de l'équation de Schrödinger. Les résultats des simulations DFT classiques sont présentés par la suite. En utilisant des positions atomiques issues de mesures expérimentales, nous avons lancé la relaxation de la structure cristalline pour assurer que chaque atome dans le système est à sa position d'équilibre. Les structures de bande d'énergie électronique sont également calculées pour valider les configurations de calcul (énergie de coupure, conditions de convergence, etc.). Une cartographie complète des valeurs propres dans l'espace réciproque est faite et les propriétés thermoélectriques sont calculées en résolvant les équations de transport de Boltzmann. Dans la deuxième partie, les théories de base des phonons sont mentionnées, suivies des introductions des méthodes en DFT avec des déplacements finis et en DM. Nous avons mis en oeuvre des simulations DM pour étudier l'influence du dopage à l'aluminium sur la conductivité thermique du réseau pour ZnO. Nous avons également utilisé la méthode en DFT avec des déplacements finis pour étudier la variation de la conductivité thermique de l'alliage Bi₂Te₃₋ₓSeₓ.

This thesis aims at characterizing the thermal contact resistance at two interfaces of different nature. The first is a physical interface between Silicon(111) and superfluid Helium-4. The thermal contact resistance is evaluated experimentally for temperatures between 0.3K and 2.0K while varying pressure from the saturated vapor pressure to the Helium-4 solidification pressure (i.e. 25bars). Experimental results, analysed with Adamenko and Fuks model, show that nanoscale surface roughness governs heat transmission at this interface. Furthermore, a first order transition in the thermal contact resistance is revealed due to Helium-4 solidification. The second studied interface is an abrupt constriction created by a micro-junction between two suspended membranes. Even though there is no material discontinuity, Monte-Carlo numerical simulations show the existence of a thermal contact resistance between the membrane and the entrance of the junction. Using simulations we explore the effects of geometry and nanoscale surface roughness in bidimensional and tridimensional micro-structure., L'objectif de cette thèse est de caractériser la résistance thermique de contact au niveau de deux interfaces bien distinctes. La première est une interface physique entre le Silicium(111) et l'Hélium-4 superfluide. La résistance thermique de contact est alors mesurée expérimentalement pour des températures allant 0.3K à 2.0K et en variant la pression depuis la pression de vapeur saturante jusqu'à la pression de solidification de l'Hélium-4 (i.e. 25bars). L'analyse des résultats expérimentaux par le modèle d'Adamenko et Fuks montre la prédominance de la nano-rugosité de surface dans la transmission de la chaleur à l'interface entre ces deux matériaux. Lors de la solidification de l'Hélium-4, une transition du premier ordre dans la résistance thermique est mise en évidence. La deuxième interface étudiée est une forte constriction créée par une jonction de taille micrométrique entre deux membranes suspendues. Sans discontinuité de matériaux, les simulations numériques Monte-Carlo montrent la présence d'une résistance thermique de contact entre la membrane et l'entrée de la jonction dans le régime de diffusion des phonons les parois du système. Les simulations permettent alors d'explorer les effets des dimensions de la jonction ainsi que de la rugosité de surface des micro-structures bidimensionnelles et tridimensionnelles.