Two-dimensional density of states for electrons bound to impurities inside inversion layers at the semiconductor-insulator interface

The density of states for electrons bound to Na⁺ impurities inside the inversion layer at the semiconductor-insulator interface of an MOS structure is calculated as a function of impurity concentration. The impurity potential is considered unscreened and the electrical quantum limit is assumed. A simple one-electron Hamiltonian is used and the disorder is treated through a cluster calculation. It is shown that the impurity band has a considerable bandwidth for impurity concentrations in a range of the experimental regime (this result agrees with the experimental findings of Hartstein and Fowler), and that the upper Hubbard band stands well above the lower band at very low concentration (in rough agreement with recent calculation done by Phelps and Bajaj on D^? state).