Anderson localization in doped semiconductors

TL;DR

This paper theoretically analyzes the doping-induced insulator-to-metal transition in bulk semiconductors, modeling it as an Anderson localization transition influenced by Coulomb disorder and screening effects, and calculates the critical doping density.

Contribution

It introduces a detailed theoretical framework for the transition based on the IRM criterion, including analytical and numerical solutions for the critical density.

Findings

Calculated the mean free path from Coulomb scattering by dopants.

Derived an integral equation for localization considering screening effects.

Provided quantitative estimates for the critical doping density for transition.

Abstract

We theoretically consider the problem of doping induced insulator to metal transition in bulk semiconductors by obtaining the transition density as a function of compensation, assuming that the transition is an Anderson localization transition controlled by the Ioffe-Regel-Mott (IRM) criterion. We calculate the mean free path, on the highly doped metallic side, arising from carrier scattering by the ionized dopants, which we model as quenched random charged impurities. The Coulomb disorder of the charged dopants is screened by the carriers themselves, leading to an integral equation for localization, defined by the density-dependent mean free path being equal to the inverse of the Fermi wave number, as dictated by the IRM criterion. Solving this integral equation approximately analytically and exactly numerically, we provide detailed results for the localization critical density for the doping induced metal-insulator transition.