DISCRETIZATION METHOD OF HYDRODYNAMIC EQUATIONS FOR SIMULATION OF GaN MESFETs

A finite discretization method in two dimensions has been developed and used to model electron transport in wurtzite phase GaN MESFETs. The model is based on the solutions of the highly-coupled nonlinear hydrodynamic partial differential equations. These solutions allow us to calculate the electron drift velocity and other device parameters as a function of the applied electric field. This model is able to describe inertia effects which play an increasing role in different fields of micro and optoelectronics where simplified charge transport models like drift-diffusion model and energy balance model are no longer applicable. Results of numerical simulations are shown for a two-dimensional GaN MESFET device which are in fair agreement with other theoretical or experimental methods.

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A SHOCK-CAPTURING UPWIND DISCRETIZATION METHOD FOR CHARACTERIZATION OF SiC MESFETs

International Journal of Computational Methods ◽

10.1142/s0219876208001509 ◽

2008 ◽

Vol 05 (02) ◽

pp. 341-349

Author(s):

H. ARABSHAHI ◽

M. R. BENAM

Keyword(s):

Hydrodynamic Model ◽

Nonlinear Partial Differential Equations ◽

Two Dimensions ◽

Shock Capturing ◽

Balance Model ◽

Discretization Method ◽

Transport Models ◽

Inertia Effects ◽

Upwind Discretization

A finite difference shock-capturing upwind discretization method in two dimensions is presented in detail for simulation of homogeneous and nonhomogeneous devices. The model is based on the solutions to the highly coupled nonlinear partial differential equations of the full hydrodynamic model. These solutions allow one to calculate the electron drift velocity and other device parameters as a function of the applied electric field. The hydrodynamic model is able to describe inertia effects which play an increasing role in different fields of micro- and optoelectronics where simplified charge transport models like the drift-diffusion model and the energy balance model are no longer applicable. Results of numerical simulations are shown for a two-dimensional SiC MESFET device, and are in fair agreement with other theoretical or experimental methods.

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COMPARISON OF TWO-VALLEY HYDRODYNAMIC MODEL IN BULK SiC AND ZnO MATERIALS

Modern Physics Letters B ◽

10.1142/s0217984909020916 ◽

2009 ◽

Vol 23 (23) ◽

pp. 2807-2818 ◽

Cited By ~ 1

Author(s):

H. ARABSHAHI ◽

REZAEE ROKN-ABADI ◽

S. GOLAFROZ

Keyword(s):

Energy Balance ◽

Hydrodynamic Model ◽

Energy Balance Model ◽

Balance Model ◽

Future Research ◽

Hydrodynamic Models ◽

Drift Diffusion ◽

Transport Models ◽

Inertia Effects ◽

Zno Semiconductor

This report reviews the feasibility of two-dimensional hydrodynamic models in bulk SiC and ZnO semiconductor materials. Although the single-gas hydrodynamic model is superior to the drift-diffusion or energy balance model, it is desirable to direct the efforts of future research in the direction of multi-valley hydrodynamic models. The hydrodynamic model is able to describe inertia effects which play an increasing role in different fields of micro and optoelectronics where simplified charge transport models like the drift-diffusion model and the energy balance model are no longer applicable. Results of extensive numerical simulations are shown for SiC and ZnO materials, which are in fair agreement with other theoretical or experimental methods.

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Flexible categorization in perceptual decision making

Nature Communications ◽

10.1038/s41467-021-21501-z ◽

2021 ◽

Vol 12 (1) ◽

Cited By ~ 1

Author(s):

Genís Prat-Ortega ◽

Klaus Wimmer ◽

Alex Roxin ◽

Jaime de la Rocha

Keyword(s):

Decision Making ◽

Network Models ◽

Drift Diffusion Model ◽

Perceptual Decision Making ◽

Drift Diffusion ◽

Perceptual Decision ◽

Attractor Dynamics ◽

Attractor Model ◽

Sensory Evidence ◽

Winner Take All

AbstractPerceptual decisions rely on accumulating sensory evidence. This computation has been studied using either drift diffusion models or neurobiological network models exhibiting winner-take-all attractor dynamics. Although both models can account for a large amount of data, it remains unclear whether their dynamics are qualitatively equivalent. Here we show that in the attractor model, but not in the drift diffusion model, an increase in the stimulus fluctuations or the stimulus duration promotes transitions between decision states. The increase in the number of transitions leads to a crossover between weighting mostly early evidence (primacy) to weighting late evidence (recency), a prediction we validate with psychophysical data. Between these two limiting cases, we found a novel flexible categorization regime, in which fluctuations can reverse initially-incorrect categorizations. This reversal asymmetry results in a non-monotonic psychometric curve, a distinctive feature of the attractor model. Our findings point to correcting decision reversals as an important feature of perceptual decision making.

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Informing cognitive abstractions through neuroimaging: The neural drift diffusion model.

Psychological Review ◽

10.1037/a0038894 ◽

2015 ◽

Vol 122 (2) ◽

pp. 312-336 ◽

Cited By ~ 86

Author(s):

Brandon M. Turner ◽

Leendert van Maanen ◽

Birte U. Forstmann

Keyword(s):

Diffusion Model ◽

Drift Diffusion Model ◽

Drift Diffusion

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Incorporating photon recycling into the analytical drift-diffusion model of high efficiency solar cells

Journal of Applied Physics ◽

10.1063/1.4902320 ◽

2014 ◽

Vol 116 (19) ◽

pp. 194504 ◽

Cited By ~ 48

Author(s):

Matthew P. Lumb ◽

Myles A. Steiner ◽

John F. Geisz ◽

Robert J. Walters

Keyword(s):

Solar Cells ◽

Diffusion Model ◽

High Efficiency ◽

Drift Diffusion Model ◽

Drift Diffusion ◽

High Efficiency Solar Cells ◽

Photon Recycling

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A Discretization Scheme for a Quasi-Hydrodynamic Semiconductor Model

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202597000475 ◽

1997 ◽

Vol 07 (07) ◽

pp. 935-955 ◽

Cited By ~ 23

Author(s):

Ansgar Jüngel ◽

Paola Pietra

Keyword(s):

Finite Elements ◽

Mixed Finite Elements ◽

Exponential Fitting ◽

Discretization Scheme ◽

Drift Diffusion Model ◽

Drift Diffusion ◽

Current Conservation ◽

Numerical Tests ◽

Finite Elements Methods ◽

Degenerate Type

A discretization scheme based on exponential fitting mixed finite elements is developed for the quasi-hydrodynamic (or nonlinear drift–diffusion) model for semiconductors. The diffusion terms are nonlinear and of degenerate type. The presented two-dimensional scheme maintains the good features already shown by the mixed finite elements methods in the discretization of the standard isothermal drift–diffusion equations (mainly, current conservation and good approximation of sharp shapes). Moreover, it deals with the possible formation of vacuum sets. Several numerical tests show the robustness of the method and illustrate the most important novelties of the model.

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PERFORMANCE LIMITS OF SIMULATION MODELS FOR NOISE CHARACTERIZATION OF MM WAVE DEVICES

Fluctuation and Noise Letters ◽

10.1142/s0219477507003957 ◽

2007 ◽

Vol 07 (03) ◽

pp. L299-L312

Author(s):

ALI ABOU-ELNOUR

Keyword(s):

Boltzmann Transport Equation ◽

Simulation Models ◽

Two Dimensions ◽

Boltzmann Transport ◽

Performance Limits ◽

Drift Diffusion ◽

Model Equations ◽

Accuracy Of Results ◽

Noise Characterization

Based on Boltzmann transport equation, the drift-diffusion, hydrodynamic, and Monte-Carlo physical simulators are accurately developed. For each simulator, the model equations are self-consistently solved with Poisson equation, and with Schrödinger equation when quantization effects take place, in one and two-dimensions to characterize the operation and optimize the structure of mm-wave devices. The effects of the device dimensions, biasing conditions, and operating frequencies on the accuracy of results obtained from the simulators are thoroughly investigated. Based on physical understanding of the models, the simulation results are analyzed to fully determine the limits at which a certain device simulator can be accurately and efficiently used to characterize the noise behavior of mm-wave devices.

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Speed, Accuracy, and the Optimal Timing of Choices

The American Economic Review ◽

10.1257/aer.20150742 ◽

2018 ◽

Vol 108 (12) ◽

pp. 3651-3684 ◽

Cited By ~ 36

Author(s):

Drew Fudenberg ◽

Philipp Strack ◽

Tomasz Strzalecki

Keyword(s):

Sequential Sampling ◽

Decision Time ◽

Optimal Timing ◽

Drift Diffusion Model ◽

Drift Diffusion ◽

Prior Beliefs ◽

Constant Cost ◽

Speed Accuracy ◽

Decision Times ◽

Choice Probabilities

We model the joint distribution of choice probabilities and decision times in binary decisions as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant cost per unit time for gathering information. We show that choices are more likely to be correct when the agent chooses to decide quickly, provided the agent’s prior beliefs are correct. This better matches the observed correlation between decision time and choice probability than does the classical drift-diffusion model (DDM), where the agent knows the utility difference between the choices. (JEL C41, D11, D12, D83)

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