Energies of substitution and solution in semiconductors

The tight-binding theory of cohesion in pure semiconductors, based upon universal parameters, is presented and applied to systems with an impurity. Results are given in terms of an energy of substitution, defined as the energy required to remove a single atom from a semiconductor, leaving it as a free atom in the ground state, and replacing it by a free atom of another element; any excess or deficit of electrons is placed at the valence-band maximum. Calculated values are in reasonable accord with the recent measurements by Su and Brebrick J. Phys. Chem. Solids 46, 963 (1985) for Zn, In, and Sn in Ge. Lattice distortions and relaxation energies are also calculated. Agreement with the limited amount of data is mixed but predictions are tabulated for a large array of systems. Relaxation is seen to reduce the misfit energy by a factor of order 4. Comparison of predicted force constants with experiment suggests that the theory underestimates the misfit energy by a similar factor so theoretical energies of unrelaxed substitution provide estimates of the experimental energies of relaxed substitution. Such predictions are in reasonable accord with experiment for homovalent substitutions, which are dominated by misfit energy. For heterovalent substitutions, the enthalpy is dominated by a redistribution of bond polarities in the substitution. Extensive tables of energies of substitution for elements and compounds from the third (silicon), fourth (germanium), and fifth (tin) rows of the Periodic Table are given, permitting direct estimates of the energy change for a wide variety of atomic rearrangements.