Semiconductor Device Simulation by a New Method of Solving Poisson, Laplace and Schrodinger Equations (RESEARCH NOTE)

In this paper, we have extended and completed our previous work, that was introducing a new method for finite differentiation. We show the applicability of the method for solving a wide variety of equations such as Poisson, Lap lace and Schrodinger. These equations are fundamental to the most semiconductor device simulators. In a section, we solve the Shordinger equation by this method in several cases including the problem of finding electron concentration profile in the channel of a HEMT. In another section, we solve the Poisson equation by this method, choosing the problem of SBD as an example. Finally we solve the Lap lace equation in two dimensions and as an example, we focus on the VED. In this paper, we have shown that the method can get stable and precise results in solving all of these problems. Also the programs which have been written based on this method become considerably faster, more clear. and mote abstract.

Keywords:

Finite difference method , Laplace Equation , Poisson equation , Schrodinger equation , Shotcky Barrier Diode , Vacuum Electronic Devices