Screening in a δ-doped semiconductor

Abstract

The screening of an impurity in the quasi-two-dimensional (2D) electron gas in a δ-doped semiconductor structure is investigated. The screened impurity matrix elements are calculated and compared using three different approaches: the 2D random phase approximation (RPA), the corresponding 2D Thomas–Fermi theory and a quasi-three-dimensional (3D) Yukawa-like screening model. It is found that the 2D Thomas–Fermi theory differs from the RPA result, even in the limit of low q vectors, if more than one subband is occupied. This result is explained analytically by closely examining theq→0 limit of the dielectric tensor. The 2D Thomas–Fermi theory is shown to represent a poor approximation to the RPA whereas the quasi-3D screening model agrees well with the RPA results for not too smallqvectors. Furthermore, this model reduces computing times by orders of magnitude in comparison with the RPA. Thus, our 3D screening model considerably simplifies the calculation of impurity scattering rates in the investigation of the electron mobility in a δ-doping layer.