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

Abstract

The drift-diffusion model is considered as one of the most important models which is used to describe the characteristics of semiconductor devices and can be applied to wide range of applications started from micro up to nano scale devices after applying the suitable correction on it. The Poisson, continuity, and current equations are considered as the basic equations for semiconductor devices, these equations are partial differential equations, used in the drift diffusion model. These equations described the semiclassical electron and hole transport in semiconductor in the presence of uniformly applied electric field. In this paper a numerical method (finite difference method) has been used to find the solution of these equations depending on Gummel method and Scharfetter-Gummel scheme, the drift diffusion model is applied after many approximation and suitable boundary condition which has been considered for the pn diode in both equilibrium and non-equilibrium cases at room temperature, from this simulation model a MATLAB program has been prepared to obtained diode parameters as a function of distance at the junction region, these parameters are (conduction band, carrier concentration, electric field and charge density) two diode model has been tested with different doping concentration the first with N_A=N_D and the second with N_A>N_D also the diode characteristic in the forward biased is obtained.