One-dimensional Semiconductor Device Numerical Simulation Of Finite Volume Element Method And Analysis

With the increasing modern technology, the numerical simulation of semiconductordevices in promoting the development of semiconductor technology of great significance.Consider heat conduction type of mathematical model [1] of semiconductor devices onone-dimensional regionΩ= [a,b]:(T|ˉ) > 0 is the length of time. where (1.1) is the electrostatic potential equation, (1.2)and (1.3) are the electron and hole concentration equations and (1.4) is a temperatureequation. The unknown functions are the electrostatic potentialψ, the electron concen-tration e, the hole concentration p and the temperature T. Equation (1.1) - (1.4) are thecoe?cients appear in the upper and lower bounds are. D_s(x) andμ_s(x) obey the Einsteinrelation D_s(x) = U_Tμ_s(x), where UT is the thermal voltage. N(x) = N_D(x) - NA(x)is a given function, where N_D(x) is the donor impurity concentration and N_A(x) is theacceptor impurity concentration.R(e,p,T) is a recombination term of the electron andhole concentrations including the in?uence of the temperature. For e,p,T, Given theinitial conditions :ψof the initial value by (1.1) and(1.4) calculated; Boundary conditions for:Questions regarding the qualitative analysis of the semiconductor, we can reference[2,3,4]等. These qualitative theory for the modernization of our numerical simulation of semiconductor devices to provide a theoretical basis. Finite volume element methodin heat conduction type of the numerical simulation of semiconductor devices has avery wide range of applications, have a profound physical background, it has been over-whelming majority of workers in math and engineering and technical personnel of thewidespread concern and attention. Regardless of From theory or from the numericalanalysis on the need to conduct an in-depth research.This paper studies the finite volume element method and the upwind finite volumeelement method in one-dimensional heat conduction-type semiconductor device in theapplication of numerical simulation. Will be piecewise linear functions and piecewiseconstant functions, respectively, finite volume element method as the trial function andtest function, Tectonic model of the semiconductor device fully discrete finite volumeelement close to the format and program. And Theoretical analysis, have been H1 normerror estimates.This article is divided into two chapters. The first chapter introduces the one-dimensional numerical simulation of semiconductor devices the finite volume elementmethod, the background and significance, introduce how to construct finite volume ele-ment scheme and convergence analysis carried out. In the second chapter format com-bined with the wind, construction of the one-dimensional heat conduction-type semi-conductor device of the wind finite volume element method, and theoretical analysis,the optimal order H1 norm error estimates, Finally numerical experiments verify thetheoretical results.