Theory of the Shallow Impurity States in Semiconductors

Abstract

A formalism is set up to describe the impurity state in a semiconductor, using the Green's-function method which includes fully the electron-electron interaction. This makes possible a systematic investigation of the corrections to the effective-mass equation. It is sometimes assumed that the correction to the long-range screened Coulomb potential of the impurity ion is a short-range potential, whereas it is shown here that there is an additional potential correction that is inversely proportional to the square of the distance at large distances from the impurity. This long-range correction is composed of (i) dipole effects and (ii) second-order effect of the impurity on the electron exchange and correlation.