To optimize solar cell performance, it is necessary to properly design the doping profile in the absorber layer of the solar cell. For CdTe solar cells, Cu is used for providing p-type doping. Hence, having an estimator that, given the diffusion parameter set (time and Temperature) and the doping concentration at the junction, gives the junction depth of the absorber layer, is essential in the design process of CdTe solar cells (and other cell technologies). In this work it is called a forward (direct) estimation process. The backward (inverse) problem then is the one in which, given the junction depth and the desired concentration of Cu doping at the CdTe/CdS heterointerface, the estimator gives the time and/or the Temperature needed to achieve the desired doping profiles. This is called a backward (inverse) estimation process. Such estimators, both forward and backward, do not exist in the literature for solar cell technology. To train the Machine Learning (ML) estimator, it is necessary to first generate a large set of data that are obtained by using the PVRD-FASP Solver, which has been validated via comparison with experimental values. Note that this big dataset needs to be generated only once. Next, one uses Machine Learning (ML), Deep Learning (DL) and Artificial Intelligence (AI) to extract the actual Cu doping profiles that result from the process of diffusion, annealing, and cool-down in the fabrication sequence of CdTe solar cells. Two deep learning neural network models are used: (1) Multilayer Perceptron Artificial Neural Network (MLPANN) model using a Keras Application Programmable Interface (API) with TensorFlow backend, and (2) Radial Basis Function Network (RBFN) model to predict the Cu doping profiles for different Temperatures and durations of the annealing process. Excellent agreement between the simulated results obtained with the PVRD-FASP Solver and the predicted values is obtained. It is important to mention here that it takes a significant amount of time to generate the Cu doping profiles given the initial conditions using the PVRD-FASP Solver, because solving the drift-diffusion-reaction model is mathematically a stiff problem and leads to numerical instabilities if the time steps are not small enough, which, in turn, affects the time needed for completion of one simulation run. The generation of the same with Machine Learning (ML) is almost instantaneous and can serve as an excellent simulation tool to guide future fabrication of optimal doping profiles in CdTe solar cells.

Wurtzite (B, Ga, Al) N semiconductors, especially (Ga, Al) N material systems, demonstrate immense promises to boost the economic growth in the semiconductor industry that is approaching the end of Moore’s law. At the material level, their high electric field strength, high saturation velocity, and unique heterojunction polarization charge have enabled tremendous potentials for high power, high frequency, and photonic applications. With the availability of large-area bulk GaN substrates and high-quality epilayer on foreign substrates, the power conversion applications of GaN are now at the cusp of commercialization.Despite these encouraging advances, there remain two critical hurdles in GaN-based technology: selective area doping and hole-based p-channel devices. Current selective area doping methods are still immature and lead to low-quality lateral p-n junctions, which prevent the realization of advanced power transistors and rectifiers. The missing of hole-based p-channel devices hinders the development of GaN complementary integrated circuits. This thesis comprehensively studied these challenges. The first part (chapter 2) researched the selective area doping by etch-then-regrow. A GaN-based vertical-channel junction field-effect transistors (VC-JFETs) was experimentally demonstrated by blanket regrowth and self-planarization. The devices’ electrical performances were characterized to understand the regrowth quality. The non-ideal factors during p-GaN regrowth were also discussed. The second part (chapter 3-5) systematically studied the application of the hydrogen plasma treatment process to change the p-GaN properties selectively. A novel GaN-based metal-insulator-semiconductor junction was demonstrated. Then a novel edge termination design with avalanche breakdown capability achieved in GaN power rectifiers is proposed. The last part (Chapter 6) demonstrated a GaN-based p-channel heterojunction field-effect transistor, with record low leakage, subthreshold swing, and a record high on/off ratio. In the end, some outlook and future work have also been proposed. Although in infancy, the demonstrated etch-then-regrow and the hydrogen plasma treatment methods have the potential to ultimately solve the challenges in GaN and benefit the development of the wide-ultra-wide bandgap industry, technology, and society.

The quest to find efficient algorithms to numerically solve differential equations isubiquitous in all branches of computational science. A natural approach to address
this problem is to try all possible algorithms to solve the differential equation and
choose the one that is satisfactory to one's needs. However, the vast variety of algorithms
in place makes this an extremely time consuming task. Additionally, even
after choosing the algorithm to be used, the style of programming is not guaranteed
to result in the most efficient algorithm. This thesis attempts to address the same
problem but pertinent to the field of computational nanoelectronics, by using PETSc
linear solver and SLEPc eigenvalue solver packages to efficiently solve Schrödinger
and Poisson equations self-consistently.
In this work, quasi 1D nanowire fabricated in the GaN material system is considered
as a prototypical example. Special attention is placed on the proper description
of the heterostructure device, the polarization charges and accurate treatment of the
free surfaces. Simulation results are presented for the conduction band profiles, the
electron density and the energy eigenvalues/eigenvectors of the occupied sub-bands
for this quasi 1D nanowire. The simulation results suggest that the solver is very
efficient and can be successfully used for the analysis of any device with two dimensional
confinement. The tool is ported on www.nanoHUB.org and as such is freely
available.

Micro Electro Mechanical Systems (MEMS) based accelerometers are one of the most commonly used sensors out there. They are used in devices such as, airbags, smartphones, airplanes, and many more. Although they are very accurate, they degrade with time or get offset due to some damage. To fix this, they must be calibrated again using physical calibration technique, which is an expensive process to conduct. However, these sensors can also be calibrated infield by applying an on-chip electrical stimulus to the sensor. Electrical stimulus-based calibration could bring the cost of testing and calibration significantly down as compared to factory testing. In this thesis, simulations are presented to formulate a statistical prediction model based on an electrical stimulus. Results from two different approaches of electrical calibration have been discussed. A prediction model with a root mean square error of 1% has been presented in this work. Experiments were conducted on commercially available accelerometers to test the techniques used for simulations.

Advanced and mature computer simulation methods exist in fluid dynamics, elec-

tromagnetics, semiconductors, chemical transport, and even chemical and material

electronic structure. However, few general or accurate methods have been developed

for quantum photonic devices. Here, a novel approach utilizing phase-space quantum

mechanics is developed to model photon transport in ring resonators, a form of en-

tangled pair source. The key features the model needs to illustrate are the emergence

of non-classicality and entanglement between photons due to nonlinear effects in the

ring. The quantum trajectory method is subsequently demonstrated on a sequence

of elementary models and multiple aspects of the ring resonator itself.

Positron emission tomography (PET) is a non-invasive molecular imaging technique widely used for the quantification of physiological and biochemical processes in preclinical and clinical research. Due to its fundamental role in the health care system, there is a constant need for improvement and optimization of its scanner systems and protocols leading to a dedicated active area of research for PET. (Geant4 Application for Tomographic Emission (GATE) is a simulation platform designed to model and analyze a medical device. Monte Carlo simulations are essential tools to assist in optimizing the data acquisition protocols or in evaluating the correction methods for improved image quantification. Using GATE along with Customizable and Advanced Software for Tomographic Reconstruction (CASToR), provides a link to reconstruct the images.

The goal of this thesis is to learn PET systems that involve Monte Carlo methods, GATE software, CASToR software to model, simulate and analyze PET systems using three clinical PET systems as a template. Fluorine-18 radioisotope source is used to perform measurements on the modeled PET systems. Parameters such as scatter-fraction, random-fraction, sensitivity, count rate performance, signal to noise ratio (SNR), and time of flight (ToF) are analyzed to determine the performance of the systems. Also, the simulated data are provided as input to CASToR software and Amide's a Medical Image Data Examiner (AMIDE) tool to obtain the reconstructed images which are used to analyze the reconstruction capability of the simulated models. The Biograph Vision PET model has high sensitivity (11.159 cps/MBq) and SNR (12.556) while the Ultra-High Resolution (UHR) PET model has high resolution of the reconstructed image.

This work is concerned with the study and numerical solution of large reaction diffusion systems with applications to the simulation of degradation effects in solar cells. A discussion of the basics of solar cells including the function of solar cells, the degradation of energy efficiency that happens over time, defects that affect solar cell efficiency and specific defects that can be modeled with a reaction diffusion system are included. Also included is a simple model equation of a solar cell. The basics of stoichiometry theory, how it applies to kinetic reaction systems, and some conservation properties are introduced. A model that considers the migration of defects in addition to the reaction processes is considered. A discussion of asymptotics and how it relates to the numerical simulation of the lifetime of solar cells is included. A reduced solution is considered and a presentation of a numerical comparison of the reduced solution with the full solution on a simple test problem is included. Operator splitting techniques are introduced and discussed. Asymptotically preserving schemes combine asymptotics and operator splitting to use reasonable time steps. A presentation of a realistic example of this study applied to solar cells follows.

4H-SiC has been widely used in many applications. All of these benefit from its extremely high critical electric field and good electron mobility. For example, 4H-SiC possesses a critical field ten times higher than that of Si, which allows high-voltage blocking layers composed of 4H-SiC to be approximately a tenth the thickness of a comparable Si device. This, in turn, reduces the device on-resistance and power losses while maintaining the same high blocking capability.

Unfortunately, commercial TCAD tools like Sentaurus and Silvaco Atlas are based on the effective mass approximation, while most 4H-SiC devices are not operated under low electric field, so the parabolic-like band approximation does not hold anymore. Hence, to get more accurate and reliable simulation results, full-band analysis is needed. The first step in the development of a full-band device simulator is the calculation of the band structure. In this work, the empirical pseudopotential method (EPM) is adopted. The next task in the sequence is the calculation of the scattering rates. Acoustic, non-polar optical phonon, polar optical phonon and Coulomb scattering are considered. Coulomb scattering is treated in real space using the particle-particle-particle-mesh (P3M) approach. The third task is coupling the bulk full-band solver with a 3D Poisson equation solver to generate a full-band device simulator.

For proof-of-concept of the methodology adopted here, a 3D resistor is simulated first. From the resistor simulations, the low-field electron mobility dependence upon Coulomb scattering in 4H-SiC devices is extracted. The simulated mobility results agree very well with available experimental data. Next, a 3D VDMOS is simulated. The nature of the physical processes occurring in both steady-state and transient conditions are revealed for the two generations of 3D VDMOS devices being considered in the study.

Due to its comprehensive nature, the developed tool serves as a basis for future investigation of 4H-SiC power devices.

Wurtzite (In, Ga, Al) N semiconductors, especially InGaN material systems, demonstrate immense promises for the high efficiency thin film photovoltaic (PV) applications for future generation. Their unique and intriguing merits include continuously tunable wide band gap from 0.70 eV to 3.4 eV, strong absorption coefficient on the order of ∼105 cm−1, superior radiation resistance under harsh environment, and high saturation velocities and high mobility. Calculation from the detailed balance model also revealed that in multi-junction (MJ) solar cell device, materials with band gaps higher than 2.4 eV are required to achieve PV efficiencies greater than 50%, which is practically and easily feasible for InGaN materials. Other state-of-art modeling on InGaN solar cells also demonstrate great potential for applications of III-nitride solar cells in four-junction solar cell devices as well as in the integration with a non-III-nitride junction in multi-junction devices.

This dissertation first theoretically analyzed loss mechanisms and studied the theoretical limit of PV performance of InGaN solar cells with a semi-analytical model. Then three device design strategies are proposed to study and improve PV performance: band polarization engineering, structural design and band engineering. Moreover, three physical mechanisms related to high temperature performance of InGaN solar cells have been thoroughly investigated: thermal reliability issue, enhanced external quantum efficiency (EQE) and conversion efficiency with rising temperatures and carrier dynamics and localization effects inside nonpolar m-plane InGaN quantum wells (QWs) at high temperatures. In the end several future work will also be proposed.

Although still in its infancy, past and projected future progress of device design will ultimately achieve this very goal that III-nitride based solar cells will be indispensable for today and future’s society, technologies and society.

This dissertation explores thermal effects and electrical characteristics in metal-oxide-semiconductor field effect transistor (MOSFET) devices and circuits using a multiscale dual-carrier approach. Simulating electron and hole transport with carrier-phonon interactions for thermal transport allows for the study of complementary logic circuits with device level accuracy in electrical characteristics and thermal effects. The electrical model is comprised of an ensemble Monte Carlo solution to the Boltzmann Transport Equation coupled with an iterative solution to two-dimensional (2D) Poisson’s equation. The thermal model solves the energy balance equations accounting for carrier-phonon and phonon-phonon interactions. Modeling of circuit behavior uses parametric iteration to ensure current and voltage continuity. This allows for modeling of device behavior, analyzing circuit performance, and understanding thermal effects.

The coupled electro-thermal approach, initially developed for individual n-channel MOSFET (NMOS) devices, now allows multiple devices in tandem providing a platform for better comparison with heater-sensor experiments. The latest electro-thermal solver allows simulation of multiple NMOS and p-channel MOSFET (PMOS) devices, providing a platform for the study of complementary MOSFET (CMOS) circuit behavior. Modeling PMOS devices necessitates the inclusion of hole transport and hole-phonon interactions. The analysis of CMOS circuits uses the electro-thermal device simulation methodology alongside parametric iteration to ensure current continuity. Simulating a CMOS inverter and analyzing the extracted voltage transfer characteristics verifies the efficacy of this methodology. This work demonstrates the effectiveness of the dual-carrier electro-thermal solver in simulating thermal effects in CMOS circuits.