Semiconductor pseudobinary alloys: Bond-length relaxation and mixing enthalpies

Harrison's bonding theory, the valence force field (VFF), and an elastic continuum are combined in a study of the substitution energies ${\ensuremath{\Delta}}_{s}$ and local (first-shell) bond lengths ${d}_{1}$ of isoelectronic impurities in semiconductors. Explicit expressions for ${\ensuremath{\Delta}}_{s}$ and ${d}_{1}$ are derived, which enable us to absorb measured elastic constants into the calculation and to study the chemical effects arising from differences in the covalent radii and polarities. Several models based on VFF alone are also derived for comparison. The full theory and at least five VFF models are found toalculated self-consistently in the Hartree approximation. The degenerate valence-band structure and the matching of the wave function at the interface are taken into account. Without magnetic field we calculate the subband dispersion parallel to the interface. The subbands are found to be strongly nonparabolic and spin split. The calculated classical cyclotron effective masses do not agree very well with those found in cyclotron resonance experiments. We have therefore included the magnetic field in the calculation. The B dependence of the Landau levels is found to be strongly nonlinear. The calculated transition energies are partly in very good agreement with experiment. The dependence of the results on areal hole density, doping concentrations, valence-band discontinuity, etc., is also investigated.