Lattice relaxation around substitutional defects in semiconductors

The tight-binding theory of total energies in semiconductors, based upon universal parameters, is modified following the findings on the overlap repulsion by van Schilfgaarde and Sher. The nonorthogonality S of neighboring orbitals is thus taken to vary as 1/d rather than 1/$d^2$, giving a repulsion proportional to 1/$d^3$. An additional repulsion due to nonorthogonality of valence orbitals with neighboring cores is taken to vary as 1/$d^{12}$. The two coefficients are chosen to give the observed equilibrium spacing and bulk modulus of the homopolar materials. The fit gives nonorthogonalities S near the expected value of 0.5. A natural generalization of the repulsion to polar materials predicts spacings and bulk moduli in reasonable accord with experiment in the compounds. The method is then applied to the prediction of lattice distortion around substitutional impurities and energies of substitution. The results are in excellent agreement with the known experimental values.