Matching Items (18)
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- All Subjects: Applied Mathematics
- All Subjects: Gallium Nitride
- Creators: Ringhofer, Christian
- Creators: Vasileska, Dragica
Description
This work is focused on modeling the reliability concerns in GaN HEMT technology. The two main reliability concerns in GaN HEMTs are electromechanical coupling and current collapse. A theoretical model was developed to model the piezoelectric polarization charge dependence on the applied gate voltage. As the sheet electron density in the channel increases, the influence of electromechanical coupling reduces as the electric field in the comprising layers reduces. A Monte Carlo device simulator that implements the theoretical model was developed to model the transport in GaN HEMTs. It is observed that with the coupled formulation, the drain current degradation in the device varies from 2%-18% depending on the gate voltage. Degradation reduces with the increase in the gate voltage due to the increase in the electron gas density in the channel. The output and transfer characteristics match very well with the experimental data. An electro-thermal device simulator was developed coupling the Monte Caro-Poisson solver with the energy balance solver for acoustic and optical phonons. An output current degradation of around 2-3 % at a drain voltage of 5V due to self-heating was observed. It was also observed that the electrostatics near the gate to drain region of the device changes due to the hot spot created in the device from self heating. This produces an electric field in the direction of accelerating the electrons from the channel to surface states. This will aid to the current collapse phenomenon in the device. Thus, the electric field in the gate to drain region is very critical for reliable performance of the device. Simulations emulating the charging of the surface states were also performed and matched well with experimental data. Methods to improve the reliability performance of the device were also investigated in this work. A shield electrode biased at source potential was used to reduce the electric field in the gate to drain extension region. The hot spot position was moved away from the critical gate to drain region towards the drain as the shield electrode length and dielectric thickness were being altered.
ContributorsPadmanabhan, Balaji (Author) / Vasileska, Dragica (Thesis advisor) / Goodnick, Stephen M (Committee member) / Alford, Terry L. (Committee member) / Venkatraman, Prasad (Committee member) / Arizona State University (Publisher)
Created2013
Description
GaN high electron mobility transistors (HEMTs) based on the III-V nitride material system have been under extensive investigation because of their superb performance as high power RF devices. Two dimensional electron gas(2-DEG) with charge density ten times higher than that of GaAs-based HEMT and mobility much higher than Si enables a low on-resistance required for RF devices. Self-heating issues with GaN HEMT and lack of understanding of various phenomena are hindering their widespread commercial development. There is a need to understand device operation by developing a model which could be used to optimize electrical and thermal characteristics of GaN HEMT design for high power and high frequency operation. In this thesis work a physical simulation model of AlGaN/GaN HEMT is developed using commercially available software ATLAS from SILVACO Int. based on the energy balance/hydrodynamic carrier transport equations. The model is calibrated against experimental data. Transfer and output characteristics are the key focus in the analysis along with saturation drain current. The resultant IV curves showed a close correspondence with experimental results. Various combinations of electron mobility, velocity saturation, momentum and energy relaxation times and gate work functions were attempted to improve IV curve correlation. Thermal effects were also investigated to get a better understanding on the role of self-heating effects on the electrical characteristics of GaN HEMTs. The temperature profiles across the device were observed. Hot spots were found along the channel in the gate-drain spacing. These preliminary results indicate that the thermal effects do have an impact on the electrical device characteristics at large biases even though the amount of self-heating is underestimated with respect to thermal particle-based simulations that solve the energy balance equations for acoustic and optical phonons as well (thus take proper account of the formation of the hot-spot). The decrease in drain current is due to decrease in saturation carrier velocity. The necessity of including hydrodynamic/energy balance transport models for accurate simulations is demonstrated. Possible ways for improving model accuracy are discussed in conjunction with future research.
ContributorsChowdhury, Towhid (Author) / Vasileska, Dragica (Thesis advisor) / Goodnick, Stephen (Committee member) / Goryll, Michael (Committee member) / Arizona State University (Publisher)
Created2013
Description
A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters.
ContributorsJones, Jeremiah (Author) / Gardner, Carl (Committee member) / Baer, Steven (Committee member) / Crook, Sharon (Committee member) / Kostelich, Eric (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2013
Description
In vertebrate outer retina, changes in the membrane potential of horizontal cells affect the calcium influx and glutamate release of cone photoreceptors via a negative feedback. This feedback has a number of important physiological consequences. One is called background-induced flicker enhancement (BIFE) in which the onset of dim background enhances the center flicker response of horizontal cells. The underlying mechanism for the feedback is still unclear but competing hypotheses have been proposed. One is the GABA hypothesis, which states that the feedback is mediated by gamma-aminobutyric acid (GABA), an inhibitory neurotransmitter released from horizontal cells. Another is the ephaptic hypothesis, which contends that the feedback is non-GABAergic and is achieved through the modulation of electrical potential in the intersynaptic cleft between cones and horizontal cells. In this study, a continuum spine model of the cone-horizontal cell synaptic circuitry is formulated. This model, a partial differential equation system, incorporates both the GABA and ephaptic feedback mechanisms. Simulation results, in comparison with experiments, indicate that the ephaptic mechanism is necessary in order for the model to capture the major spatial and temporal dynamics of the BIFE effect. In addition, simulations indicate that the GABA mechanism may play some minor modulation role.
ContributorsChang, Shaojie (Author) / Baer, Steven M. (Thesis advisor) / Gardner, Carl L (Thesis advisor) / Crook, Sharon M (Committee member) / Kuang, Yang (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2012
Description
The retina is the lining in the back of the eye responsible for vision. When light photons hits the retina, the photoreceptors within the retina respond by sending impulses to the optic nerve, which connects to the brain. If there is injury to the eye or heredity retinal problems, this part can become detached. Detachment leads to loss of nutrients, such as oxygen and glucose, to the cells in the eye and causes cell death. Sometimes the retina is able to be surgically reattached. If the photoreceptor cells have not died and the reattachment is successful, then these cells are able to regenerate their outer segments (OS) which are essential for their functionality and vitality. In this work we will explore how the regrowth of the photoreceptor cells in a healthy eye after retinal detachment can lead to a deeper understanding of how eye cells take up nutrients and regenerate. This work uses a mathematical model for a healthy eye in conjunction with data for photoreceptors' regrowth and decay. The parameters for the healthy eye model are estimated from the data and the ranges of these parameter values are centered +/- 10\% away from these values are used for sensitivity analysis. Using parameter estimation and sensitivity analysis we can better understand how certain processes represented by these parameters change within the model as a result of retinal detachment. Having a deeper understanding for any sort of photoreceptor death and growth can be used by the greater scientific community to help with these currently irreversible conditions that lead to blindness, such as retinal detachment. The analysis in this work shows that maximizing the carrying capacity of the trophic pool and the rate of RDCVF, as well as minimizing nutrient withdrawal of the rods and the cones from the trophic pool results in both the most regrowth and least cell death in retinal detachment.
ContributorsGoldman, Miriam Ayla (Author) / Camacho, Erikia (Thesis director) / Wirkus, Stephen (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Gallium Nitride (GaN) is uniquely suited for Radio Frequency (RF) and power electronic applications due to its intrinsically high saturation velocity and high mobility compared to Silicon and Silicon Carbide (SiC). High Electron Mobility Transistors (HEMTs) have remained the primary topology for GaN transistors in RF applications. However, GaN HEMTs suffer from a variety of issues such as current crowding, lack of enhancement mode (E-Mode) operation and non-linearity. These drawbacks slow the widespread adoption of GaN devices for ultra-low voltage (ULV) applications such as voltage regulators, automotive and computing applications. E-mode operation is especially desired in low-voltage high frequency switching applications. In this context, Fin Field Effect Transistors (FinFETs) offer an alternative topology for ULV applications as opposed to conventional HEMTs. Recent advances in material processing, high aspect ratio epitaxial growth and etching methods has led to an increased interest in 3D nanostructures such as Nano-FinFETs and Nanowire FETs. A typical 3D nano-FinFET is the AlGaN/GaN Metal Insulator Semiconductor (MIS) FET wherein a layer of Al2O3 surrounds the AlGaN/GaN fin. The presence of the side gates leads to additional lateral confinement of the 2D Electron Gas (2DEG). Theoretical calculations of transport properties in confined systems such as AlGaN/GaN Finfets are scarce compared to those of their planar HEMT counterparts.
A novel simulator is presented in this dissertation, which employs self-consistent solution of the coupled 1D Boltzmann – 2D Schrödinger – 3D Poisson problem, to yield the channel electrostatics and the low electric field transport characteristics of AlGaN/GaN MIS FinFETs. The low field electron mobility is determined by solving the Boltzmann transport equation in the Quasi-1D region using 1D Ensemble Monte Carlo method. Three electron-phonon scattering mechanisms (acoustic, piezoelectric and polar optical phonon scattering) and interface roughness scattering at the AlGaN/GaN interface are considered in this theoretical model. Simulated low-field electron mobility and its temperature dependence are in agreement with experimental data reported in the literature.
A quasi-1D version of alloy clustering model is derived and implemented and the limiting effect of alloy clustering on the low-field electron mobility is investigated for the first time for MIS FinFET device structures.
ContributorsKumar, Viswanathan Naveen (Author) / Vasileska, Dragica (Thesis advisor) / Goodnick, Stephen (Committee member) / Nemanich, Robert (Committee member) / Povolotskyi, Michael (Committee member) / Esqueda, Ivan Sanchez (Committee member) / Arizona State University (Publisher)
Created2022
Description
Wide bandgap (WBG) semiconductors GaN (3.4 eV), Ga2O3 (4.8 eV) and AlN (6.2 eV), have gained considerable interests for energy-efficient optoelectronic and electronic applications in solid-state lighting, photovoltaics, power conversion, and so on. They can offer unique device performance compared with traditional semiconductors such as Si. Efficient GaN based light-emitting diodes (LEDs) have increasingly displaced incandescent and fluorescent bulbs as the new major light sources for lighting and display. In addition, due to their large bandgap and high critical electrical field, WBG semiconductors are also ideal candidates for efficient power conversion.
In this dissertation, two types of devices are demonstrated: optoelectronic and electronic devices. Commercial polar c-plane LEDs suffer from reduced efficiency with increasing current densities, knowns as “efficiency droop”, while nonpolar/semipolar LEDs exhibit a very low efficiency droop. A modified ABC model with weak phase space filling effects is proposed to explain the low droop performance, providing insights for designing droop-free LEDs. The other emerging optoelectronics is nonpolar/semipolar III-nitride intersubband transition (ISBT) based photodetectors in terahertz and far infrared regime due to the large optical phonon energy and band offset, and the potential of room-temperature operation. ISBT properties are systematically studied for devices with different structures parameters.
In terms of electronic devices, vertical GaN p-n diodes and Schottky barrier diodes (SBDs) with high breakdown voltages are homoepitaxially grown on GaN bulk substrates with much reduced defect densities and improved device performance. The advantages of the vertical structure over the lateral structure are multifold: smaller chip area, larger current, less sensitivity to surface states, better scalability, and smaller current dispersion. Three methods are proposed to boost the device performances: thick buffer layer design, hydrogen-plasma based edge termination technique, and multiple drift layer design. In addition, newly emerged Ga2O3 and AlN power electronics may outperform GaN devices. Because of the highly anisotropic crystal structure of Ga2O3, anisotropic electrical properties have been observed in Ga2O3 electronics. The first 1-kV-class AlN SBDs are demonstrated on cost-effective sapphire substrates. Several future topics are also proposed including selective-area doping in GaN power devices, vertical AlN power devices, and (Al,Ga,In)2O3 materials and devices.
In this dissertation, two types of devices are demonstrated: optoelectronic and electronic devices. Commercial polar c-plane LEDs suffer from reduced efficiency with increasing current densities, knowns as “efficiency droop”, while nonpolar/semipolar LEDs exhibit a very low efficiency droop. A modified ABC model with weak phase space filling effects is proposed to explain the low droop performance, providing insights for designing droop-free LEDs. The other emerging optoelectronics is nonpolar/semipolar III-nitride intersubband transition (ISBT) based photodetectors in terahertz and far infrared regime due to the large optical phonon energy and band offset, and the potential of room-temperature operation. ISBT properties are systematically studied for devices with different structures parameters.
In terms of electronic devices, vertical GaN p-n diodes and Schottky barrier diodes (SBDs) with high breakdown voltages are homoepitaxially grown on GaN bulk substrates with much reduced defect densities and improved device performance. The advantages of the vertical structure over the lateral structure are multifold: smaller chip area, larger current, less sensitivity to surface states, better scalability, and smaller current dispersion. Three methods are proposed to boost the device performances: thick buffer layer design, hydrogen-plasma based edge termination technique, and multiple drift layer design. In addition, newly emerged Ga2O3 and AlN power electronics may outperform GaN devices. Because of the highly anisotropic crystal structure of Ga2O3, anisotropic electrical properties have been observed in Ga2O3 electronics. The first 1-kV-class AlN SBDs are demonstrated on cost-effective sapphire substrates. Several future topics are also proposed including selective-area doping in GaN power devices, vertical AlN power devices, and (Al,Ga,In)2O3 materials and devices.
ContributorsFu, Houqiang (Author) / Zhao, Yuji (Thesis advisor) / Vasileska, Dragica (Committee member) / Goodnick, Stephen (Committee member) / Yu, Hongbin (Committee member) / Wang, Liping (Committee member) / Arizona State University (Publisher)
Created2019
Description
Factory production is stochastic in nature with time varying input and output processes that are non-stationary stochastic processes. Hence, the principle quantities of interest are random variables. Typical modeling of such behavior involves numerical simulation and statistical analysis. A deterministic closure model leading to a second order model for the product density and product speed has previously been proposed. The resulting partial differential equations (PDE) are compared to discrete event simulations (DES) that simulate factory production as a time dependent M/M/1 queuing system. Three fundamental scenarios for the time dependent influx are studied: An instant step up/down of the mean arrival rate; an exponential step up/down of the mean arrival rate; and periodic variation of the mean arrival rate. It is shown that the second order model, in general, yields significant improvement over current first order models. Specifically, the agreement between the DES and the PDE for the step up and for periodic forcing that is not too rapid is very good. Adding diffusion to the PDE further improves the agreement. The analysis also points to fundamental open issues regarding the deterministic modeling of low signal-to-noise ratio for some stochastic processes and the possibility of resonance in deterministic models that is not present in the original stochastic process.
ContributorsWienke, Matthew (Author) / Armbruster, Dieter (Thesis advisor) / Jones, Donald (Committee member) / Platte, Rodrigo (Committee member) / Gardner, Carl (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2015
Description
Advances in experimental techniques have allowed for investigation of molecular dynamics at ever smaller temporal and spatial scales. There is currently a varied and growing body of literature which demonstrates the phenomenon of \emph{anomalous diffusion} in physics, engineering, and biology. In particular many diffusive type processes in the cell have been observed to follow a power law $\left \propto t^\alpha$ scaling of the mean square displacement of a particle. This contrasts with the expected linear behavior of particles undergoing normal diffusion. \emph{Anomalous sub-diffusion} ($\alpha<1$) has been attributed to factors such as cytoplasmic crowding of macromolecules, and trap-like structures in the subcellular environment non-linearly slowing the diffusion of molecules. Compared to normal diffusion, signaling molecules in these constrained spaces can be more concentrated at the source, and more diffuse at longer distances, potentially effecting the signalling dynamics. As diffusion at the cellular scale is a fundamental mechanism of cellular signaling and additionally is an implicit underlying mathematical assumption of many canonical models, a closer look at models of anomalous diffusion is warranted. Approaches in the literature include derivations of fractional differential diffusion equations (FDE) and continuous time random walks (CTRW). However these approaches are typically based on \emph{ad-hoc} assumptions on time- and space- jump distributions. We apply recent developments in asymptotic techniques on collisional kinetic equations to develop a FDE model of sub-diffusion due to trapping regions and investigate the nature of the space/time probability distributions assosiated with trapping regions. This approach both contrasts and compliments the stochastic CTRW approach by positing more physically realistic underlying assumptions on the motion of particles and their interactions with trapping regions, and additionally allowing varying assumptions to be applied individually to the traps and particle kinetics.
ContributorsHoleva, Thomas Matthew (Author) / Ringhofer, Christian (Thesis advisor) / Baer, Steve (Thesis advisor) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Taylor, Jesse (Committee member) / Arizona State University (Publisher)
Created2014
Description
From 2D planar MOSFET to 3D FinFET, the geometry of semiconductor devices is getting more and more complex. Correspondingly, the number of mesh grid points increases largely to maintain the accuracy of carrier transport and heat transfer simulations. By substituting the conventional uniform mesh with non-uniform mesh, one can reduce the number of grid points. However, the problem of how to solve governing equations on non-uniform mesh is then imposed to the numerical solver. Moreover, if a device simulator is integrated into a multi-scale simulator, the problem size will be further increased. Consequently, there exist two challenges for the current numerical solver. One is to increase the functionality to accommodate non-uniform mesh. The other is to solve governing physical equations fast and accurately on a large number of mesh grid points.
This research rst discusses a 2D planar MOSFET simulator and its numerical solver, pointing out its performance limit. By analyzing the algorithm complexity, Multigrid method is proposed to replace conventional Successive-Over-Relaxation method in a numerical solver. A variety of Multigrid methods (standard Multigrid, Algebraic Multigrid, Full Approximation Scheme, and Full Multigrid) are discussed and implemented. Their properties are examined through a set of numerical experiments. Finally, Algebraic Multigrid, Full Approximation Scheme and Full Multigrid are integrated into one advanced numerical solver based on the exact requirements of a semiconductor device simulator. A 2D MOSFET device is used to benchmark the performance, showing that the advanced Multigrid method has higher speed, accuracy and robustness.
This research rst discusses a 2D planar MOSFET simulator and its numerical solver, pointing out its performance limit. By analyzing the algorithm complexity, Multigrid method is proposed to replace conventional Successive-Over-Relaxation method in a numerical solver. A variety of Multigrid methods (standard Multigrid, Algebraic Multigrid, Full Approximation Scheme, and Full Multigrid) are discussed and implemented. Their properties are examined through a set of numerical experiments. Finally, Algebraic Multigrid, Full Approximation Scheme and Full Multigrid are integrated into one advanced numerical solver based on the exact requirements of a semiconductor device simulator. A 2D MOSFET device is used to benchmark the performance, showing that the advanced Multigrid method has higher speed, accuracy and robustness.
ContributorsGuo, Xinchen (Author) / Vasileska, Dragica (Thesis advisor) / Goodnick, Stephen (Committee member) / Ferry, David (Committee member) / Arizona State University (Publisher)
Created2015