Iteration Methods

Abstract

The set of equations solved in this work is similar to [1, 2, 3]. One possible strategy for the solution of the SE-BTE-PE system is to solve each equation independently and successively and to consider the coupling between the equations by an outer loop. This constitutes a nonlinear relaxation scheme comparable to the classical Gummel loop [4, 5]. The outer loops are repeated until a self-consistent solution is obtained. In literature the multisubband Monte Carlo (MC) method is often used to solve the BTE [1, 2, 3] (Fig. 11.1 (left)). However, the nonlinear relaxation schemes with the MC method converge slowly. Moreover, a true DC solution of BTE is impossible with the transient MC method. In contrast, the BTE in this work is solved with a new deterministic method based on the Fourier expansion of the distribution function (see Chap. 9 ). Such nonlinear relaxation methods (Fig. 11.1 (right)) with the new deterministic method to solve BTE converge linearly with simulation time similar to the Gummel loop in the classical drift-diffusion based TCAD device simulators [4, 6], and thus much faster than an MC algorithm with its square root dependence [7]. In addition, the deterministic relaxation method yields a true DC solution.