Optical lineshapes and electronic eigenstates of substitutional defects and vacancies

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Abstract
A scattering-theoretical method for the study of the electronic structure of defects in crystalline solids is developed. The authors' formulation requires the expansion of electronic wavefunctions in a local basis consistent with the band structure of the solid. Appropriately chosen local orbitals are included, even for the analysis of a vacancy. To illustrate the method they perform an exact diagonalisation of the one-electron Hamiltonian for the coupling of four local impurity states to a single electronic band. Their analysis of optical properties includes a comparison with results on internal photoionisation of shallow and deep acceptor levels in silicon. A new simple expression yields excellent fits to the lineshapes of boron, aluminium, indium and zinc impurities. In all these cases inclusion of the p character of the valence bands and the complete treatment of the continuum scattering states is required.