An efficient under-relaxation method for simulation of quantum well structures

In a device consisting of thin layers of quantum wells (GaAs) sandwiched between layers of bulk barriers (AlGaAs), the dynamics of carriers are described by a system of coupled nonlinear differential equations consisting of four continuity equations, two current density equations, Poisson, and Schrodinger equation. In this paper, we present a finite-difference numerical method for solving these equations and the results of under-relaxation of the potential, and how the under-relaxation factor is varied during the course of the iterations to increase the convergence rate.