A universal model for trends in A1-type defect states in zincblende and diamond semiconductor structures

Abstract

We present a simple and accurate 4-level model derived from sp3s∗ tight-binding calculations on a 64-atom unit cell that quantitatively describes A1-type defect states and their coupling to the lowest Γ1c conduction band state in zincblende and diamond semiconductors. We use a realistic Hamiltonian that quantifies the chemical differences between the impurity and the host atom which it replaces, and that also incorporates local strain effects due to any size discrepancy between the host and impurity atom. The defect state is constructed from a basis that involves only three states: namely an A1-symmetric combination of the host L, X and Σ states, with the matrix elements between the basis states dependent only on the free-atom orbital self-energies and on the material lattice constants. We apply the model to analyse general group III and group V impurities in GaAs, and show that N is the only impurity that generates a strong perturbation. We identify the important role played by each of the three main contributions to the defect Hamiltonian in determining the N resonant state energy and the magnitude of its interaction with the conduction band Γ minimum as well as identifying why the interplay of these different effects leads to boron only weakly influencing the energy gap of GaAs. Finally, we derive simple expressions for the resonant state energy EN and its coupling βN to the Γ minimum, obtaining results in very good agreement with full sp3s∗ tight-binding calculations.