Defect states dominated by localised potentials in semiconductors

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Abstract
The authors have used Green function and direct matrix methods to consider various aspects of the solutions to the localised potential problem. They show that the Green function method can be extended so that the separation of the localised potential can be avoided. The wavefunction in the range of the potential is then obtained in a particularly simple manner, i.e. without recourse to an empirically chosen set of basis functions. The degree of charge localisation has been studied for the typical deep donor and silicon vacancy. It is concluded that in both examples a substantial proportion of the defect wavefunction resides outside the central cell region. In the case of the silicon vacancy, less than half the charge of the t2 state lies within nearest neighbour distance.