A numerical method for a transient quantum drift-diffusion model arising in semiconductor devices

2008 ◽  
Vol 7 (4) ◽  
pp. 485-493 ◽  
Author(s):  
Tomoko Shimada ◽  
Shinji Odanaka
Keyword(s):  
Numerical Method ◽  
Diffusion Model ◽  
Semiconductor Devices ◽  
Drift Diffusion Model ◽  
Drift Diffusion

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.

SEMICONDUCTOR DEVICES UNDER CIRCUIT BOUNDARY CONDITIONS

1994 ◽  
Vol 04 (03) ◽  
pp. 439-453 ◽  
Author(s):  
CHRISTIAN SCHMEISER
Keyword(s):  
Boundary Conditions ◽  
Diffusion Model ◽  
Iteration Method ◽  
Thermal Equilibrium ◽  
Existence Of Solutions ◽  
Semiconductor Devices ◽  
Electrical Circuit ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Stationary Version

A stationary version of the standard drift-diffusion model for the flow of electrons and holes in semiconductor devices is considered. The boundary conditions are, to a certain extent, capable of describing the influence of the surrounding electrical circuit as opposed to the usual mathematical assumption of prescribed voltages. The existence of solutions and the convergence close to thermal equilibrium of a decoupled iteration method are proved.

EXISTENCE OF STATIONARY SOLUTIONS TO AN ENERGY DRIFT-DIFFUSION MODEL FOR SEMICONDUCTOR DEVICES

2001 ◽  
Vol 11 (05) ◽  
pp. 827-840 ◽  
Author(s):  
WEIFU FANG ◽  
KAZUFUMI ITO
Keyword(s):  
Mathematical Model ◽  
Equilibrium State ◽  
Diffusion Model ◽  
Hydrodynamic Model ◽  
Semiconductor Devices ◽  
Stationary Solutions ◽  
Drift Diffusion Model ◽  
Drift Diffusion

We analyze a mathematical model for semiconductors derived from the hydrodynamic model under the massless assumption. This model augments the classical drift-diffusion model by including temperature as a dependent variable. We establish the existence of stationary solutions near the equilibrium state.

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