Approximation to Boltzmann transport in semiconductor devices

Abstract

There is hierarchy of models of electron transport in semiconductor device. A complete physical description is provided by the Schrödinger equations, which are numerically too intensive to implement. A simplified model is the drift-diffusion model, which has been successfully used to design devices larger than 0.25μ. The Boltzmann transport equation is a great simplification over the Schrödinger equations model, yet it contains much of the physics; see [1]. The solution of the Boltzmann equation is obtained by computationally expensive Monte Carlo techniques [2]. This motivated several simplified approaches, notably the hydrodynamic model and the drift-diffusion model (see [3] and the references given there). Another approximation to the Boltzmann equation has been developed by Hagan, Cox and Wagner [4] (see also [5; Chap. 11] and the last chapter in this volume).