ABSTRACT
This chapter presents the derivation of the drift-diffusion equations from the Boltzmann transport equation and discusses the physical significance of the parameters associated with these equations. It looks at the numerical solution of the drift-diffusion equations coupled with Poisson’s equation in the domain of the semiconductor device. The chapter examines the Sharfetter-Gummel algorithm for the discretization of the continuity equation and the corresponding Gummel iteration method used to solve the set of coupled equations, which is widely used in conventional device simulation. It describes the drift-diffusion model with a discussion of the inclusion of generation–recombination processes. The chapter explores the application of the drift-diffusion model in understanding the operation of a pn-diode using the solution of the one dimensional drift-diffusion equations. It provides a practical example of the quasi-linearization of Poisson’s equation, as is necessary to obtain stable convergence.
