Electron-nitrogen scattering in dilute nitrides

An n-band Hamiltonian for a dilute nitride system is derived using Anderson's many-impurity model. Using this, an energy-dependent relaxation time for electron-nitrogen scattering is derived, compared, and contrasted to existing theoretical models for the mobility in dilute nitrides. The nonparabolicity of the band structure creates problems when integrating functions of energy over the bands, so modified forms of the density of states in three dimensions and two dimensions that conserve the number of states are derived from the Green's function of the system. The bulk mobility for GaNxAs1-x is calculated for the case of isolated nitrogen and nitrogen pair environments as a function of carrier and nitrogen concentration. In the highly degenerate case, the calculated room-temperature mobilities, excluding other scattering processes, are in good agreement with reported experimental determinations.