scholarly journals Investigation of The Numerical Solution for One Dimensional Drift-Diffusion Model in Silicon in Steady State

2021 ◽  
Vol 30 (1) ◽  
pp. 46-57
Author(s):  
Rozana Noori ◽  
Mumtaz Hussien
Keyword(s):  
Steady State ◽  
Numerical Solution ◽  
Diffusion Model ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
One Dimensional

scholarly journals Convergence Properties of the Bi-CGSTAB Method for the Solution of the 3D Poisson and 3D Electron Current Continuity Equations for Scaled Si MOSFETs

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 301-305 ◽  
Author(s):  
D. Vasileska ◽  
W. J. Gross ◽  
V. Kafedziski ◽  
D. K. Ferry
Keyword(s):  
Numerical Modeling ◽  
Numerical Solution ◽  
Diffusion Model ◽  
Semiconductor Devices ◽  
Semiconductor Technology ◽  
Electron Current ◽  
Drift Diffusion Model ◽  
Convergence Properties ◽  
Drift Diffusion ◽  
Continuity Equations

As semiconductor technology continues to evolve, numerical modeling of semiconductor devices becomes an indispensible tool for the prediction of device characteristics. The simple drift-diffusion model is still widely used, especially in the study of subthreshold behavior in MOSFETs. The numerical solution of these two equations offers difficulties in small devices and special methods are required for the case when dealing with 3D problems that demand large CPU times. In this work we investigate the convergence properties of the Bi-CGSTAB method. We find that this method shows superior convergence properties when compared to more commonly used ILU and SIP methods.

The combined semi-classical and relaxation limit in a quantum hydrodynamic semiconductor model

2010 ◽  
Vol 140 (1) ◽  
pp. 119-134 ◽  
Author(s):  
Yeping Li
Keyword(s):  
Diffusion Model ◽  
Hydrodynamic Model ◽  
Drift Diffusion Model ◽  
Smooth Solutions ◽  
Drift Diffusion ◽  
One Dimensional ◽  
Quantum Hydrodynamic Model ◽  
Highly Nonlinear ◽  
Isentropic Euler Equations ◽  
Quantum Hydrodynamic

We discuss the combined semi-classical and relaxation limit of a one-dimensional isentropic quantum hydrodynamical model for semiconductors. The quantum hydrodynamic equations consist of the isentropic Euler equations for the particle density and current density, including the quantum potential and a momentum relaxation term. The momentum equation is highly nonlinear and contains a dispersive term with third-order derivatives. The equations are self-consistently coupled to the Poisson equation for the electrostatic potential. With the help of the Maxwell-type iteration, we prove that, as the relaxation time and Planck constant tend to zero, periodic initial-value problems of a scaled one-dimensional isentropic quantum hydrodynamic model have unique smooth solutions existing in the time interval where the classical drift-diffusion model has smooth solutions. Meanwhile, we justify a formal derivation of the classical drift-diffusion model from the quantum hydrodynamic model.

ASYMPTOTIC BEHAVIORS AND CLASSICAL LIMITS OF SOLUTIONS TO A QUANTUM DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS

2010 ◽  
Vol 20 (06) ◽  
pp. 909-936 ◽  
Author(s):  
SHINYA NISHIBATA ◽  
NAOTAKA SHIGETA ◽  
MASAHIRO SUZUKI
Keyword(s):  
Diffusion Model ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Singular Limit ◽  
Drift Diffusion Model ◽  
Planck Constant ◽  
Drift Diffusion ◽  
One Dimensional ◽  
Unique Existence ◽  
Initial Boundary Value

This paper discusses a time global existence, asymptotic behavior and a singular limit of a solution to the initial boundary value problem for a quantum drift-diffusion model of semiconductors over a one-dimensional bounded domain. Firstly, we show a unique existence and an asymptotic stability of a stationary solution for the model. Secondly, it is shown that the time global solution for the quantum drift-diffusion model converges to that for a drift-diffusion model as the scaled Planck constant tends to zero. This singular limit is called a classical limit. Here these theorems allow the initial data to be arbitrarily large in the suitable Sobolev space. We prove them by applying an energy method.

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