Numerical simulation of the distribution of charge carrier in nanosized semiconductor heterostructures with account for polarization effects

A three-level scheme for modeling nanosized semiconductor heterostructures with account for spontaneous and piezoelectric polarization effects is presented. The scheme combines quantummechanical calculations at the atomic level for obtaining the charge density on heterointerfaces, calculation of the distribution of carriers in the heterostructure based on the solution to the Schrödinger and Poisson equations, and the calculation of electron mobility in the two-dimensional electron gas with account for various scattering mechanisms. To speed up the computations of electron density in the heterostructure, the approach based on the approximation of the nonlinear dependence of the electron density on the potential in combination with the linearization of the Poisson equation is used. The efficiency of this approach in problems of the class in question is demonstrated.