The Application of Evanescent States to Deep Impurities

Abstract

The complex band structure of a semiconductor can be calculated using basis functions appropriate to the impurity problem. These functions diverge at the origin and decay exponentially at large distances. The complex band dispersion relationship relates the decay length of the impurity state to the energy of the impurity and connects to the real band structure at the extremal points such as the Γ, X or L minima. The symmetry of the impurity state plays a central role in determining its properties. The wavefunctions used have been appropriately symmetrized. We show that for states of certain symmetries the relevant complex band connects to the higher minima rather than the Γ minimum. The evanescent states are matched to an impurity wavefunction within a core region. We show that for deep traps the core can have a significant effect on the properties of the impurity. We discuss some of the experimental data which can be understood simply in terms of states connecting to higher minima.