Application of numerical exciton-wave-function calculations to the question of band alignment inSi/Si1−xGexquantum wells

Abstract

We numerically calculate the two-particle ground-state wave functions for excitons in ${\mathrm{Si}}_{0.7}{\mathrm{Ge}}_{0.3}$ quantum wells in an effective mass model and demonstrate how oscillator strength, binding energy, and electron distribution vary with conduction-band offset and well width. Recombination energies for the two types of excitons involving electrons in different conduction-band valleys are compared. We point out that only due to the very different electron masses in growth direction for ${\ensuremath{\Delta}}_{4}$ and ${\ensuremath{\Delta}}_{2}$ valleys is it possible that the ${\ensuremath{\Delta}}_{2}$-heavy-hole exciton forms the ground state, as was reported in recent photoluminescence experiments at extremely low excitation powers [M. L. W. Thewalt et al., Phys. Rev. Lett. 79, 269 (1997)]. It is shown that those experiments can only be explained with a type-II offset for the ${\ensuremath{\Delta}}_{4}$ conduction band of about 40 meV, in contrast to the common assumption that those data would have proven an offset of at most 10 meV for $x=0.3.$