Lattice distortions and energies of atomic substitution

Abstract

The energies of atomic substitution and the associated excess enthalpies of mixing have been calculated with and without lattice relaxation for both isovalent and heterovalent substitutional impurities in tetrahedrally coordinated semiconductors by using the universal parameter tight binding theory of Harrison. For isovalent substitutional impurities, where experimental data and other theoretical predictions are available, agreement is good. Distortions around isovalent impurities such as indium in gallium arsenide can be readily calculated using the known natural bond lengths for indium arsenide and gallium arsenide. We define corresponding natural bond lengths for heterovalent substitutional impurities (those which come from a different column from that of the atom they replace) by minimizing the total bond energy with respect to interatomic separation. We have used the natural bond lengths calculated in this way to estimate the displacement of the neighbors to a number of impurity systems, and the corresponding reductions in the energy to substitute a free atom for a host atom. When two atoms are exchanged across an interface, relaxation around both atoms must be included and can be large. Such interchanges for heterovalent atoms affect heterojunction band lineups and are therefore of particular interest.