半导体器件数值模拟的混合元逼近

THE APPROXIMATION OF THE ELECTROSTIC POTENTIAL BY A MIXED METHOD IN THE SIMULATION OF SEMICONDUCTOR

半导体器件瞬时状态的模型由三个非线性偏微分方程组所决定.一个是关于电子位势的方程外型是椭圆的,另两个是关于电子和空穴浓度方程外型是抛物的,电子位势通过其电场强度在浓度方程中出现,以及相应的边界和初始条件.我们讨论平面区域Ω上的问题:

The transient behaviov of a semiconductor device is described by a system of three qua-silinear partial differential equations,one ellipic in form for the electric potential and twoparabolic in form for the conservation of electron and hole concentrations.The electric ppo-tential appears in the concentration only through its electric field strength,and it is appropriateto choose a numerical method that approximates the electric field strength.The electric po-tential equation is discretized by a mixed finite element method.The electron and hold den-sity equations are treated by a Galerkin method.Optimal order estimates are derived.