Band-edge alignment ofSiGe∕Siquantum wells andSiGe∕Siself-assembled islands

Abstract

We report on the energy band gap and band lineup of $\mathrm{SiGe}∕\mathrm{Si}$ heterostructures either in the case of coherently strained quantum wells or in the case of $\mathrm{SiGe}∕\mathrm{Si}$ self-assembled islands. We take into account the strain field and the quantum confinement effects through an accurate description of the conduction band including the $\ensuremath{\Delta}$ and $L$ bands. The strain field is calculated using a microscopic valence force field theory. The conduction-band diagram and energies are obtained from a 30-band $\mathbf{k}∙\mathbf{p}$ Hamiltonian accounting for the strain through the Bir-Pikus Hamiltonian. The band-edge description is first given for biaxially strained pseudomorphic $\mathrm{SiGe}$ layers. In $\mathrm{SiGe}$ quantum wells grown on relaxed silicon, the band line-up switches from type I to type II depending on the value of the average valence band offset. Applying the 30-band formalism to the case of heterostructures grown on relaxed silicon germanium buffer layers indicates that a better agreement with experimental data is obtained for a valence-band offset value $\mathrm{\ensuremath{\Delta}}{E}_{v}=0.54x$ where $x$ is the Ge composition. For this parameter, a type-II band lineup is thus expected for all compositions of pseudomorphic $\mathrm{SiGe}$/relaxed Si heterostructures. For $\mathrm{GeSi}∕\mathrm{Si}$ islands, we take into account the strain relaxation in the surrounding Si matrix. A type-II band lineup is predicted for all Ge compositions. The near-infrared interband recombination energy of the islands is calculated as a function of their $\mathrm{SiGe}$ composition.