Strain and band-edge alignment in single and multiple layers of self-assembled Ge/Si and GeSi/Si islands

Strain in coherently embedded Ge/Si islands significantly modifies the band -edge alignment in and around the nanostructures. Our calculations on embed ded flat truncated Ge pyramids show that tensile strain in the surrounding Si causes a splitting of the sixfold-degenerate Delta valleys into the four fold-degenerate Delta (4) and twofold-degenerate Delta (2) valleys. This st rain-induced splitting energy can be larger than 400 meV in stacked Ge/Si i slands. The Delta (2) valleys in the Si constitute the conduction-band mini mum, and the heavy hole in the island constitutes the valence-band maximum. The band gap in the Si above and below the Ge island is smaller than for b ulk Si, in perfect agreement with recent experiments. Relevant energies are worked out as a function of Si interlayer thickness, number of islands, an d Ge concentration in the islands. We compare our calculations of the band- gap energy with photoluminescence experiments on embedded Ge islands, yield ing an average Ge fraction in the nanostructures of 60%.