Density of states in a two-dimensional electron gas: Impurity bands and band tails

Abstract

We calculate the density of states of a two-dimensional electron gas in the presence of charged impurities within Klauder's best multiple-scattering approach. The silicon metal-oxide-semiconductor (MOS) system with impurities at the interface is studied in detail. The finite extension of the electron wave function into the bulk is included as well as various dependences of the density of states on the electron, the depletion, and the impurity densities. The transition from an impurity band at low impurity concentration to a band tail at high impurity concentration is found to take place at a certain impurity concentration. If the screening parameter of the electron gas is decreased, the impurity band shifts to lower energy. For low impurity density we find excited impurity bands. Our theory at least qualitatively explains conductivity and infrared-absorption experiments on impurity bands in sodium-doped MOS systems and deep band tails in the gap observed for high doping levels in these systems.