An efficient thermal solver is available in the CMC that allows modeling self-heating in the electrical simulations, which treats phonons as flux and solves the energy balance equation to quantify thermal effects. Using this solver, thermal simulations were performed on GaN-HEMTs in order to test effect of gate architectures on the DC and RF performance of the device. A Π- gate geometry is found to suppress 19.75% more hot electrons corresponding to a DC power of 2.493 W/mm for Vgs = -0.6V (max transconductance) with respect to the initial T-gate. For the DC performance, the output current, Ids is nearly same for each device configuration over the entire bias range. For the RF performance, the current gain was evaluated over a frequency range 20 GHz to 120 GHz in each device for both thermal (including self-heating) and isothermal (without self-heating). The evaluated cutoff frequency is around 7% lower for the thermal case than the isothermal case. The simulated cutoff frequency closely follows the experimental cutoff frequency. The work was extended to the study of ultra-wide bandgap material (Diamond), where isotope effect causes major deterioration in thermal conductivity. In this case, bulk phonons are modeled as semiclassical particles solving the nonlinear Peierls - Boltzmann transport equation with a stochastic approach. Simulations were performed for 0.001% (ultra-pure), 0.1% and 1.07% isotope concentration (13C) of diamond, showing good agreement with the experimental values. Further investigation was performed on the effect of isotope on the dynamics of individual phonon branches, thermal conductivity and the mean free path, to identify the dominant phonon branch. Acoustic phonons are found to be the principal contributors to thermal conductivity across all isotope concentrations with transverse acoustic (TA2) branch is the dominant branch with a contribution of 40% at room temperature and 37% at 500K. Mean free path computations show the lower bound of device dimensions in order to obtain maximum thermal conductivity. At 300K, the lowest mean free path (which is attributed to Longitudinal Optical phonon) reduces from 24nm to 8 nm for isotope concentration of 0.001% and 1.07% respectively. Similarly, the maximum mean free path (which is attributed to Longitudinal Acoustic phonon) reduces from 4 µm to 3.1 µm, respectively, for the same isotope concentrations. Furthermore, PETSc (Portable, Extensible Toolkit for Scientific Computation) developed by Argonne National Lab, was included in the existing Cellular Monte Carlo device simulator as a Poisson solver to further extend the capability of the simulator. The validity of the solver was tested performing 2D and 3D simulations and the results were compared with the well-established multigrid Poisson solver.

A model of self-heating is incorporated into a Cellular Monte Carlo (CMC) particle-based device simulator through the solution of an energy balance equation (EBE) for phonons. The EBE self-consistently couples charge and heat transport in the simulation through a novel approach to computing the heat generation rate in the device under study. First, the moments of the Boltzmann Transport equation (BTE) are discussed, and subsequently the EBE of for phonons is derived. Subsequently, several tests are performed to verify the applicability and accuracy of a nonlinear iterative method for the solution of the EBE in the presence of convective boundary conditions, as compared to a finite element analysis solver as well as using the Kirchhoff transformation. The coupled electrothermal characterization of a GaN/AlGaN high electron mobility transistor (HEMT) is then performed, and the effects of non-ideal interfaces and boundary conditions are studied.



The proposed thermal model is then applied to a novel $\Pi$-gate architecture which has been suggested to reduce hot electron generation in the device, compared to the conventional T-gate. Additionally, small signal ac simulations are performed for the determination of cutoff frequencies using the thermal model as well.

Finally, further extensions of the CMC algorithm used in this work are discussed, including 1) higher-order moments of the phonon BTE, 2) coupling to phonon Monte Carlo simulations, and 3) application to other large-bandgap, and therefore high-power, materials such as diamond.

In this work, an advanced simulation study of reliability in millimeter-wave (mm-wave) GaN Devices for power amplifier (PA) applications is performed by means of a particle-based full band Cellular Monte Carlo device simulator (CMC). The goal of the study is to obtain a systematic characterization of the performance of GaN devices operating in DC, small signal AC and large-signal radio-frequency (RF) conditions emphasizing on the microscopic properties that correlate to degradation of device performance such as generation of hot carriers, presence of material defects and self-heating effects. First, a review of concepts concerning GaN technology, devices, reliability mechanisms and PA design is presented in chapter 2. Then, in chapter 3 a study of non-idealities of AlGaN/GaN heterojunction diodes is performed, demonstrating that mole fraction variations and the presence of unintentional Schottky contacts are the main limiting factor for high current drive of the devices under study. Chapter 4 consists in a study of hot electron generation in GaN HEMTs, in terms of the accurate simulation of the electron energy distribution function (EDF) obtained under DC and RF operation, taking into account frequency and temperature variations. The calculated EDFs suggest that Class AB PAs operating at low frequency (10 GHz) are more robust to hot carrier effects than when operating under DC or high frequency RF (up to 40 GHz). Also, operation under Class A yields higher EDFs than Class AB indicating lower reliability. This study is followed in chapter 5 by the proposal of a novel π-Shaped gate contact for GaN HEMTs which effectively reduces the hot electron generation while preserving device performance. Finally, in chapter 6 the electro-thermal characterization of GaN-on-Si HEMTs is performed by means of an expanded CMC framework, where charge and heat transport are self-consistently coupled. After the electro-thermal model is validated to experimental data, the assessment of self-heating under lateral scaling is considered.

With the high demand for faster and smaller wireless communication devices, manufacturers have been pushed to explore new materials for smaller and faster transistors. One promising class of transistors is high electron mobility transistors (HEMT). AlGaAs/GaAs HEMTs have been shown to perform well at high power and high frequencies. However, AlGaN/GaN HEMTs have been gaining more attention recently due to their comparatively higher power densities and better high frequency performance. Nevertheless, these devices have experienced truncated lifetimes. It is assumed that reducing defect densities in these materials will enable a more direct study of the failure mechanisms in these devices. In this work we present studies done to reduce interfacial oxygen at N-polar GaN/GaN interfaces, growth conditions for InAlN barrier layer, and microanalysis of a partial InAlN-based HEMT. Additionally, the depth of oxidation of an InAlN layer on a gate-less InAlN/GaN metal oxide semiconductor HEMT (MOSHEMT) was investigated. Measurements of electric fields in AlGaN/GaN HEMTs with and without field plates are also presented.

A novel Monte Carlo rejection technique for solving the phonon and electron

Boltzmann Transport Equation (BTE), including full many-particle interactions, is

presented in this work. This technique has been developed to explicitly model

population-dependent scattering within the full-band Cellular Monte Carlo (CMC)

framework to simulate electro-thermal transport in semiconductors, while ensuring

the conservation of energy and momentum for each scattering event. The scattering

algorithm directly solves the many-body problem accounting for the instantaneous

distribution of the phonons. The general approach presented is capable of simulating

any non-equilibrium phase-space distribution of phonons using the full phonon dispersion

without the need of the approximations commonly used in previous Monte Carlo

simulations. In particular, anharmonic interactions require no assumptions regarding

the dominant modes responsible for anharmonic decay, while Normal and Umklapp

scattering are treated on the same footing.

This work discusses details of the algorithmic implementation of the three particle

scattering for the treatment of the anharmonic interactions between phonons, as well

as treating isotope and impurity scattering within the same framework. The approach

is then extended with a technique based on the multivariable Hawkes point process

that has been developed to model the emission and the absorption process of phonons

by electrons.

The simulation code was validated by comparison with both analytical, numerical,

and experimental results; in particular, simulation results show close agreement with

a wide range of experimental data such as the thermal conductivity as function of the

isotopic composition, the temperature and the thin-film thickness.

In this work, transport in nanowire materials and nanowire field effect transistors is studied using a full band Monte Carlo simulator within the tight binding basis. Chapter 1 is dedicated to the importance of nanowires and nanoscale devices in present day electronics and the necessity to use a computationally efficient tool to simulate transport in these devices. Chapter 2 discusses the calculation of the full band structure of nanowires based on an atomistic tight binding approach, particularly noting the use of the exact same tight binding parameters for bulk band structures as well as the nanowire band structures. Chapter 3 contains the scattering rate formula for deformation potential, polar optical phonon, ionized impurity and impact ionization scattering in nanowires using Fermi’s golden rule and the tight binding basis to describe the wave functions. A method to calculate the dielectric screening in 1D systems within the tight binding basis is also described. Importantly, the scattering rates of nanowires tends to the bulk scattering rates at high energies, enabling the use of the same parameter set that were fitted to bulk experimental data to be used in the simulation of nanowire transport. A robust and efficient method to model interband tunneling is discussed in chapter 4 and its importance in nanowire transport is highlighted. In chapter 5, energy relaxation of excited electrons is studied for free standing nanowires and cladded nanowires. Finally, in chapter 6, a full band Monte Carlo particle based solver is created which treats confinement in a full quantum way and the current voltage characteristics as well as the subthreshold swing and percentage of ballistic transport is analyzed for an In0.7Ga0.3As junctionless nanowire field effect transistor.

In this work, the insight provided by our sophisticated Full Band Monte Carlo simulator is used to analyze the behavior of state-of-art devices like GaN High Electron Mobility Transistors and Hot Electron Transistors. Chapter 1 is dedicated to the description of the simulation tool used to obtain the results shown in this work. Moreover, a separate section is dedicated the set up of a procedure to validate to the tunneling algorithm recently implemented in the simulator. Chapter 2 introduces High Electron Mobility Transistors (HEMTs), state-of-art devices characterized by highly non linear transport phenomena that require the use of advanced simulation methods. The techniques for device modeling are described applied to a recent GaN-HEMT, and they are validated with experimental measurements. The main techniques characterization techniques are also described, including the original contribution provided by this work. Chapter 3 focuses on a popular technique to enhance HEMTs performance: the down-scaling of the device dimensions. In particular, this chapter is dedicated to lateral scaling and the calculation of a limiting cutoff frequency for a device of vanishing length. Finally, Chapter 4 and Chapter 5 describe the modeling of Hot Electron Transistors (HETs). The simulation approach is validated by matching the current characteristics with the experimental one before variations of the layouts are proposed to increase the current gain to values suitable for amplification. The frequency response of these layouts is calculated, and modeled by a small signal circuit. For this purpose, a method to directly calculate the capacitance is developed which provides a graphical picture of the capacitative phenomena that limit the frequency response in devices. In Chapter 5 the properties of the hot electrons are investigated for different injection energies, which are obtained by changing the layout of the emitter barrier. Moreover, the large signal characterization of the HET is shown for different layouts, where the collector barrier was scaled.

Studying the electronic band structure is necessary to understand the physics behind electron transport in devices made of the material under consideration. Graphene has been in the limelight of ground breaking research in the recent past and will continue to be in the future, as scientists around the world have been giving special attention to this remarkable material in pursuit of advancement in the semiconductor device industry by making use of many of its fascinating properties.

Although several different approaches have been proposed for the calculation of the band structure, the empirical methods have proven to be more convenient, since we can arrive at a reasonable result close to what has been found experimentally without a huge computational trade-off by varying some relevant parameters. Moreover, a method based on a plane wave basis has been found to be extremely compatible with advanced methods for device modeling and simulation such as a semi-classical Monte Carlo. The purpose of this study is to extract fitting parameters for the calculation of band structure of graphene using the empirical pseudopotential method, which can be used for further research, such as theoretical modeling and simulation of graphene-based devices. Since various methods have been proposed for the calculation of these pseudopotentials, we will also briefly study the effect of different pseudopotentials on the band structure of bilayer graphene.

In mesoscopic physics, conductance fluctuations are a quantum interference phenomenon that comes from the phase interference of electron wave functions scattered by the impurity disorder. During the past few decades, conductance fluctuations have been studied in various materials including metals, semiconductors and graphene. Since the patterns of conductance fluctuations is related to the distributions and configurations of the impurity scatterers, each sample has its unique pattern of fluctuations, which is considered as a sample fingerprint. Thus, research on conductance fluctuations attracts attention worldwide for its importance in both fundamental physics and potential technical applications. Since early experimental measurements of conductance fluctuations showed that the amplitudes of the fluctuations are on order of a universal value (e2/h), theorists proposed the hypothesis of ergodicity, e.g. the amplitudes of the conductance fluctuations by varying impurity configurations is the same as that from varying the Fermi energy or varying the magnetic field. They also proposed the principle of universality; e.g., that the observed fluctuations would appear the same in all materials. Recently, transport experiments in graphene reveal a deviation of fluctuation amplitudes from those expected from ergodicity.

Thus, in my thesis work, I have carried out numerical research on the conductance fluctuations in GaAs nanowires and graphene nanoribbons in order to examine whether or not the theoretical principles of universality and ergodicity hold. Finite difference methods are employed to study the conductance fluctuations in GaAs nanowires, but an atomic basis tight-binding model is used in calculations of graphene nanoribbons. Both short-range disorder and long-range disorder are considered in the simulations of graphene. A stabilized recursive scattering matrix technique is used to calculate the conductance. In particular, the dependence of the observed fluctuations on the amplitude of the disorder has been investigated. Finally, the root-mean-square values of the amplitude of conductance fluctuations are calculated as a basis with which to draw the appropriate conclusions. The results for Fermi energy sweeps and magnetic field sweeps are compared and effects of magnetic fields on the conductance fluctuations of Fermi energy sweeps are discussed for both GaAs nanowires and graphene nanoribbons.