Effect of buffer-layer composition on new optical transitions in Si/Ge short-period superlattices.

Abstract

Local empirical pseudopotentials with spin-orbit coupling have been used to calculate transition energies and transition probabilities for the Si/Ge (4:4) superlattice grown on (001) ${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ (0\ensuremath{\le}x\ensuremath{\le}1) buffer layers. The characters of superlattice states close to the band edges are shown in terms of their real-space charge densities and their origin in wave-vector space. Influences of heterojunction-interface bond length and band offset are examined and the individual contributions of compositional modulation and atomic relaxation to the enhancement of matrix elements for cross-gap quasidirect transitions are established. A strain-induced reversal of \ensuremath{\Vert}${m}_{J}$\ensuremath{\Vert}=(3/2 and \ensuremath{\Vert}${m}_{J}$\ensuremath{\Vert}=1/2 valence states is demonstrated in terms of the effects on subband energy levels and polarization-dependence of cross-gap transition probabilities. In the case of the Si/Ge (4:4) superlattice grown on Si, a direct comparison is made between theoretical results and recent electroreflectance data of Pearsall et al. [Phys. Rev. Lett. 58, 729 (1987)]. Comparison is also made between the results of the present empirical-pseudopotential calculations and results of recent local-density, quasiparticle, tight-binding, and effective-mass--type calculations. Predictions are made which can be used to discriminate between different transition assignments which have been given to the same structure in the electroreflectance spectra for the (4:4) superlattice grown on (001) Si.