Transport properties within the Boltzmann transport equation for metallic multi-layer structures as well as bulk materials, were the prime topic of this work. Ab initio total energy calculations for Hydrogen loaded metallic multi-layers were performed in order to shed some light onto problem of H depleted layers at the interfaces that have been experimentally observed. It was explained in connection with structural relaxation of the interface layers. Further on conductivity behavior of Fe/V vs. Mo/V during Hydrogen load was discussed. The difference in, on first sight, rather similar multi-layer structures was explained by the magnitude of Hydrogen induced Vanadium expansion. Problem of variation of conductivity with changed c/a ratio of metals and semiconductors in general was addressed as well. The variations due to change of the Fermi surface of the corresponding materials were observed as well as some intriguing general patterns. The phenomenon could be regarded as piezoresistivity on electronic structure level. For the 3d transition metals variation of conductivity/resistivity through the period was studied. A possible explanation for anomalous behavior of Manganese resistivity due to its much greater lattice constant in comparison to its neighbors in the period is presented. Field of disordered alloys and low dimensional magnetism was touched by discussing Mo/Ru formation energy as well as magnetic nano-wires grown on surfaces. All total energy calculations as well as band structure calculations were performed by using Density Functional Theory based numerical computations. A short but comprehensive review of most common linear-response electron transport techniques is given.

The ultra-short gate (LG < 20 nm) CMOS components (Complementary Metal-Oxide-Semiconductor) face thermal limitations due to significant local heating induced by phonon emission by hot carriers in active regions of reduced size. This phenomenon, called self-heating effect, is identified as one of the most critical for the continuous increase in the integration density of circuits. This is especially crucial in SOI technology (silicon on insulator), where the presence of the buried insulator hinders the dissipation of heat.At the nanoscale, the theoretical study of these heating phenomena, which cannot be led using the macroscopic models (heat diffusion coefficient), requires a detailed microscopic description of heat transfers that are locally non-equilibrium. It is therefore appropriate to model, not only the electron transport and the phonon generation, but also the phonon transport and the phonon-phonon and electron-phonon interactions. The formalism of the Boltzmann transport equation (BTE) is very suitable to study this problem. In fact, it is widely used for years to study the transport of charged particles in semiconductor components. This formalism is much less standard to study the transport of phonons. One of the problems of this work concerns the coupling of the phonon BTE with the electron transport.In this context, wse have developed an algorithm to calculate the transport of phonons by the direct solution of the phonon BTE. This algorithm of phonon transport was coupled with the electron transport simulated by the simulator "MONACO" based on a statistical (Monte Carlo) solution of the BTE. Finally, this new electro-thermal simulator was used to study the self-heating effects in nano-transistors. The main interest of this work is to provide an analysis of electro-thermal transport beyond a macroscopic approach (Fourier formalism for thermal transport and the drift-diffusion approach for electric current, respectively). Indeed, it provides access to the distributions of phonons in the device for each phonon mode. In particular, the simulator provides a better understanding of the hot electron effects at the hot spots and of the electron relaxation in the access.

No description available.

Le développement de la technologie des composants CMOS ultimes à grille ultra-courte (L < 20 nm) se heurte à de nombreuses difficultés technologiques, mais également à des limites thermiques qui perturbent notablement les règles de mise à l'échelle communément employées jusqu'à présent. Les fortes densités de courant obtenues dans des zones actives aussi réduites génèrent un important échauffement local (par effet Joule), lié à l'émission de phonons par les porteurs chauds, qui peut conduire à des réductions très sensibles des performances, voire à des défaillances. Ce phénomène est identifié comme un des plus critiques pour la poursuite de l'augmentation de la densité d'intégration des circuits. Cela est particulièrement crucial dans les technologies SOI (silicium sur isolant), où la présence de l'isolant enterré constitue un frein à l'évacuation de la chaleur. À l'échelle nanométrique, l'étude théorique de ces phénomènes d'échauffement n'est plus possible par des modèles macroscopiques (coefficient de diffusion de la chaleur) mais nécessite une description microscopique détaillée des transferts de chaleur qui sont localement hors d’équilibre. Il s'agit donc de modéliser de façon appropriée, non seulement le transport électronique et la génération de phonons, mais aussi le transport de phonons hors équilibre et les interactions phonons-phonons et électrons-phonons.Le formalisme de l’équation de transport de Boltzmann (BTE) est très bien adapté à l'étude de ce problème. En effet, il est largement utilisé depuis des années pour l'étude du transport des particules chargées dans les composants semi-conducteurs. Ce formalisme est beaucoup moins standard pour étudier le transport des phonons. Une des problématiques de ce travail concerne le couplage de la résolution de la BTE des phonons avec celle des électrons.Ce travail de thèse a développé un algorithme de calcul du transport de phonons par résolution directe de la BTE des phonons. Cet algorithme de transport de phonon a été couplé au transport électronique simulé grâce au logiciel "MONACO" basé sur une résolution statistique (ou Monte Carlo) de la BTE. Finalement, ce nouveau simulateur électrothermique a été utilisé pour étudier les effets d’auto échauffement dans des nano-transistors. L’intérêt principal de ces travaux est de permettre une analyse du transport electro-thermique au-delà d’une approche macroscopique (respectivement formalisme de Fourier pour la thermique et dérive-diffusion pour le courant). En effet, il donne accès aux distributions de phonons dans le dispositif et pour chaque mode de phonon. En particulier, ce simulateur apporte une meilleure compréhension des effets des électrons chauds sur les points chauds et leur relaxation dans les accès. / The ultra-short gate (LG < 20 nm) CMOS components (Complementary Metal-Oxide-Semiconductor) face thermal limitations due to significant local heating induced by phonon emission by hot carriers in active regions of reduced size. This phenomenon, called self-heating effect, is identified as one of the most critical for the continuous increase in the integration density of circuits. This is especially crucial in SOI technology (silicon on insulator), where the presence of the buried insulator hinders the dissipation of heat.At the nanoscale, the theoretical study of these heating phenomena, which cannot be led using the macroscopic models (heat diffusion coefficient), requires a detailed microscopic description of heat transfers that are locally non-equilibrium. It is therefore appropriate to model, not only the electron transport and the phonon generation, but also the phonon transport and the phonon-phonon and electron-phonon interactions. The formalism of the Boltzmann transport equation (BTE) is very suitable to study this problem. In fact, it is widely used for years to study the transport of charged particles in semiconductor components. This formalism is much less standard to study the transport of phonons. One of the problems of this work concerns the coupling of the phonon BTE with the electron transport.In this context, wse have developed an algorithm to calculate the transport of phonons by the direct solution of the phonon BTE. This algorithm of phonon transport was coupled with the electron transport simulated by the simulator "MONACO" based on a statistical (Monte Carlo) solution of the BTE. Finally, this new electro-thermal simulator was used to study the self-heating effects in nano-transistors. The main interest of this work is to provide an analysis of electro-thermal transport beyond a macroscopic approach (Fourier formalism for thermal transport and the drift-diffusion approach for electric current, respectively). Indeed, it provides access to the distributions of phonons in the device for each phonon mode. In particular, the simulator provides a better understanding of the hot electron effects at the hot spots and of the electron relaxation in the access.

The mechanisms of thermal transport in defect-free silicon nanostructures are examined using a combination of lattice dynamics (LD) calculations and the Boltzmann transport equation (BTE). To begin, the thermal conductivity reduction in thin films is examined using a hierarchical method that first predicts phonon transport properties using LD calculations, and then solves the phonon BTE using the lattice Boltzmann method. This approach, which considers all of the phonons in the first Brillouin-zone, is used to assess the suitability of common assumptions used to reduce the computational effort. Specifically, we assess the validity of: (i) neglecting the contributions of optical modes, (ii) the isotropic approximation, (iii) assuming an averaged bulk mean-free path (i.e., the Gray approximation), and (iv) using the Matthiessen rule to combine the effect of different scattering mechanisms. Because the frequency-dependent contributions to thermal conductivity change as the film thickness is reduced, assumptions that are valid for bulk are not necessarily valid for thin films. Using knowledge gained from this study, an analytical model for the length-dependence of thin film thermal conductivity is presented and compared to the predictions of the LD-based calculations. The model contains no fitting parameters and only requires the bulk lattice constant, bulk thermal conductivity, and an acoustic phonon speed as inputs. By including the mode-dependence of the phonon lifetimes resulting from phonon-phonon and phonon-boundary scattering, the model predictions capture the approach to the bulk thermal conductivity better than predictions made using Gray models based on a single lifetime. Both the model and the LD-based method are used to assess a procedure commonly used to extract bulk thermal conductivities from length-dependent molecular dynamics simulation data. Because the mode-dependence of thermal conductivity is not included in the derivation of this extrapolation procedure, using it can result in significant error. Finally, phonon transport across a silicon/vacuum-gap/silicon structure is modelled using lattice dynamics and Landauer theory. The phonons transmit thermal energy across the vacuum gap via atomic interactions between the leads. Because the incident phonons do not encounter a classically impenetrable potential barrier, this mechanism is not a tunneling phenomenon. The heat flux due to phonon transport can be 4 orders of magnitude larger than that due to photon transport predicted from near-field radiation theory.

Gallium nitride (GaN) has been targeted for use in high power (>30 W/mm) and high frequency (>160 GHz) application due to its wide band gap and its large break down field. One of the most significant advances in GaN devices has evolved from the AlGaN/GaN high electron mobility transistor (HEMT). As a result of the large power densities being applied to these devices there can develop intense hot spots near areas of highest electric field. The hot spot phenomenon has been linked to a decrease in device reliability through a range of degradation mechanisms. In order to minimize the effect that hot spot temperatures have on device reliability a detailed understanding of relevant transport mechanisms must be developed. This study focuses on two main aspects of phonon transport within GaN devices. The first area of focus was to establish an understanding of phonon relaxation times within bulk GaN. These relaxation times were calculated from an application of Fermi's Golden Rule and explicitly conserve energy and crystal momentum. This analysis gives insight into the details behind the macroscopic thermal conductivity parameter. Once relaxation times for GaN were established a multiscale phonon transport modeling methodology was developed that allowed the Boltzmann Transport Equation to be coupled to the energy equation. This coupling overcomes some computational limits and allows for nanoscale phenomena to be resolved within a macroscopic domain. Results of the transport modeling were focused on benchmarking the coupling method as well as calculating the temperature distribution within an operating 6 finger HEMT.

The mechanisms of thermal transport in defect-free silicon nanostructures are examined using a combination of lattice dynamics (LD) calculations and the Boltzmann transport equation (BTE). To begin, the thermal conductivity reduction in thin films is examined using a hierarchical method that first predicts phonon transport properties using LD calculations, and then solves the phonon BTE using the lattice Boltzmann method. This approach, which considers all of the phonons in the first Brillouin-zone, is used to assess the suitability of common assumptions used to reduce the computational effort. Specifically, we assess the validity of: (i) neglecting the contributions of optical modes, (ii) the isotropic approximation, (iii) assuming an averaged bulk mean-free path (i.e., the Gray approximation), and (iv) using the Matthiessen rule to combine the effect of different scattering mechanisms. Because the frequency-dependent contributions to thermal conductivity change as the film thickness is reduced, assumptions that are valid for bulk are not necessarily valid for thin films. Using knowledge gained from this study, an analytical model for the length-dependence of thin film thermal conductivity is presented and compared to the predictions of the LD-based calculations. The model contains no fitting parameters and only requires the bulk lattice constant, bulk thermal conductivity, and an acoustic phonon speed as inputs. By including the mode-dependence of the phonon lifetimes resulting from phonon-phonon and phonon-boundary scattering, the model predictions capture the approach to the bulk thermal conductivity better than predictions made using Gray models based on a single lifetime. Both the model and the LD-based method are used to assess a procedure commonly used to extract bulk thermal conductivities from length-dependent molecular dynamics simulation data. Because the mode-dependence of thermal conductivity is not included in the derivation of this extrapolation procedure, using it can result in significant error. Finally, phonon transport across a silicon/vacuum-gap/silicon structure is modelled using lattice dynamics and Landauer theory. The phonons transmit thermal energy across the vacuum gap via atomic interactions between the leads. Because the incident phonons do not encounter a classically impenetrable potential barrier, this mechanism is not a tunneling phenomenon. The heat flux due to phonon transport can be 4 orders of magnitude larger than that due to photon transport predicted from near-field radiation theory.

A fully automated Temperature Dependent Hall (TDH) measurement setup has been assembled for the purposes of this study. This TDH setup is capable of measuring samples in the 20 K to 370 K temperature range. Sample sizes of up to 20 mm × 20 mm can be accommodated by the custom designed and manufactured sample holder. Samples with a resistance in the 1Ω to 250 MΩ range can be measured with this setup provided that the mobility of the sample is greater than 1 cm²/Vs. The computer program controlling the automated measurement processwas written in LabView™ version 6.1. Single crystal Zinc Oxide (ZnO) was the material under investigation in this study. Bulk ZnO samples grown by three different methods, namely pressurized melt growth, seeded chemical vapor transport (SCVT) growth and hydrothermal growth, were measured in the 20 K to 370 K range. The effect of annealing in argon atmosphere in the 550 ºC to 930 ºC range was investigated on all three ZnO types. In addition, hydrogen-implanted layers on semi-insulating hydrothermally grown ZnO were studied. These samples were annealed in the 200 ºC to 400 ºC range and Hall measurements in the 20 K to 330 K range were performed. Programs were written to fit, wherever possible, the obtained temperature dependent carrier concentration and mobility profiles to suitable theoretical models. The carrier concentration data was fitted to a multi-donor single acceptor charge balance equation for the purpose of extracting donor concentrations and activation energies. Before fitting, the data was corrected for the Hall scattering factor and, where necessary, for two-layer effects particularly a degenerate surface conduction channel that developed through annealing on the SCVT-grown and hydrothermally grown samples. The acceptor concentrations of the samples were obtained by fitting the mobility data to a model based on D.L. Rode’s method of solving the Boltzmann transport equation. Scattering mechanisms included in the model were piezoelectric and deformation potential acoustic modes, polar optic modes and ionized impurity scattering. It was found that the mobility data did not fit the model very well without assigning questionable values to other parameters, in this case the deformation potential. Plausible values for the acceptor concentration were however obtained. The carrier concentration data fitted the model well, but due to the large number of parameters to be extracted (up to six parameters in the case of three donors) there was often not much certainty in the extracted values This study shows that TDH analysis is a valuable tool to assess the quality of semiconductors. Bulk and degenerate surface (or interfacial) conduction are separated with relative ease, and shallow defect concentrations as well as compensation level concentrations could be extracted. The generally observed uncertainty in values obtained in the multi-parameter regression of carrier concentration data indicates that supplementary techniques such as photoluminescence are needed to support results obtained by the TDH technique. / Dissertation (MSc (Physics))--University of Pretoria, 2007. / Physics / MSc / unrestricted

Understanding thermal transport across length scales lays the foundation to developing high-performance electronic devices. Although many experiments and models of the past few decades have explored the physics of heat transfer at nanoscale, there are still open questions regarding the impact of periodic nanostructuring and coherent phonon effects, as well as the interaction of strain and thermal transport. Thermomechanical effects, as well as strains applied in flexible electronic devices, impact the thermal transport. In the simplest kinetic theory models, thermal conductivity is proportional to the phonon group velocity, heat capacity, and scattering times. Periodic porous nanostructures impact the phonon dispersion relationship (group velocity) and the boundaries of the pores increase the scattering times. Strain, on the other hand, affects the crystal structure of the lattice and slightly increases the thermal conductivity of the material under compression. Intriguingly, applying strain combined with the periodic porous structures is expected to influence both the dispersion relation and scattering rates and yield the ability to tune thermal transport actively. But often these interrelated effects are simplified in models.<br><br>This work evaluates the combination of structure and strain on thermal conductivity by revisiting some of the essential methods used to predict thermal transport for a single layer of graphene with a periodic porous lattice structure with and without applied strain. First, we use the highest fidelity method of Non-Equilibrium Molecular Dynamics (NEMD) simulations to estimate the thermal conductivity which considers the impact of the lattice structure, strain state, and phononic band structure together. Next, the impact of the geometry of the slots within the lattice is interrogated with Boltzmann Transport Equation (BTE) models under a Relaxation Time Approximation. A Monte Carlo based Boltzmann Transport Equation (BTE) solver is also used to estimate the thermal conductivity of phononic crystals with varying pore geometry. Dispersion relations calculated from continuum mechanics are used as input here. This method which utilizes a simplified pore geometry only partially accounts for the effects of scattering on the pore boundaries. Finally, a continuum level model is also used to predict the thermal conductivity and its variations under applied strain. As acoustic phonon branches tend to carry the most heat within the lattice, these continuum models and other simple kinetic theories only consider their group velocities to estimate their impact on phonon thermal conductivity. As such, they do not take into account the details of phonon transport across all wavelengths.<br><br>By comparing the results from these different methods, each of which has different assumptions and simplifications, the current work aims to understand the effects of changes to the dispersion relationship based on strain and the periodic nanostructures on the thermal conductivity. We evaluate the accuracy of the kinetic theory, ray tracing, and BTE models in comparison to the MD results to offer a perspective of the reliability of each method of thermal conductivity estimation. In addition, the effect of strain on each phononic crystal with different pore geometry is also predicted in terms of change to their in-plane thermal anisotropy values. To summarize, this deeper understanding of the nanoscale thermal transport and the interrelated effects of geometry, strain, and phonon band structure on thermal conductivity can aid in developing lattices specifically designed to achieve the required dynamic thermal response for future nano-scale thermoelectric applications.

The thermal conductivity and electrical resistivity of Zr, ZrC, and ZrN were calculated using first-principles density functional theory (DFT) and the Boltzmann transport equation. The electron-phonon scattering was modeled via the self-energy relaxation time approximation (SERTA), and the phonon-phonon scattering via the analogous single-mode relaxation time approximation (SMRTA). The results obtained from Abinit's electron-phonon coupling code EPH is in good agreement with experimental reference data for Zr and ZrN. Notably, the calculated electrical resistivity of ZrC was found to be significantly lower than the available reference data, likely due to deviations from a perfect Zr/C stoichiometric ratio in the experimental samples. Additionally, it was observed that the calculated lattice thermal conductivity was overestimated at low temperatures, possibly attributed to the neglect of electron-phonon scattering that otherwise appears in metallic systems. / Värmeledningsförmågan och den elektriska resistiviteten för Zr, ZrC och ZrN beräknades med hjälp av täthetsfunktionalteori (DFT) och Boltzmanns transportekvation. Elektron-fononspridningen modellerades via 'self-energy relaxation time approximation' (SERTA), och fonon-fononspridningen via den motsvarande 'single-mode relaxation time approximation' (SMRTA). Resultaten från Abinits elektron-fononkopplingskod EPH stämmer väl överens med experimentella referensdata för Zr och ZrN. Den beräknade elektriska resistiviteten för ZrC visade sig emellertid vara betydligt lägre än all tillgänglig referensdata, troligtvis på grund av avvikelser från ett perfekt Zr/C-stökiometriskt förhållande i de experimentella proverna. Dessutom observerades att det beräknade fononbidraget till värmeledningsförmågan överskattades vid låga temperaturer, vilket möjligen beror på försummelsen av elektron-fononspridning som annars framträder i metalliska system.