Electronic structure and optical transitions in Sn and SnGe quantum dots in a Si matrix

Self-assembled quantum dots in the Si-Ge-Sn system have attracted research attention as possible direct band gap materials, compatible with Si-based technology, with potential applications in optoelectronics. In this work, the electronic structure near the Γ-point and the interband optical matrix elements of strained Sn and SnGe quantum dots in a Si matrix are calculated using the eight-band k.p method, and the competing L-valley conduction band states were found by the effective mass method. The strain distribution in the dots was found within the continuum mechanical model. The bulk band-structure parameters, required for the k.p or effective mass calculation for Sn were extracted by fitting to the energy band structure calculated by the non-local empirical pseudopotential method (EPM). The calculations show that the self-assembled Sn/Si dots, with sizes between 4 and 12 nm, have indirect interband transition energies (from the size-quantized valence band states at Γ to the conduction band states at L) between 0.8 and 0.4 eV, and direct interband transitions between 2.5 and 2.0 eV, which agrees very well with experimental results. Similar good agreement with experiment was also found for the recently grown SnGe dots on Si substrate, covered by SiO₂. However, neither of these is predicted to be direct band gap materials, in contrast to some earlier expectations.