Electronic structure and optical properties of Sn and SnGe quantum dots

Self-assembled quantum dots in a Si–Ge–Sn system attract 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 interband optical matrix elements of strained Sn and SnGe quantum dots in a Si or Ge 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 with the continuum mechanical model. The parameters required for the k∙p or effective mass calculation for Sn were extracted by fitting to the energy band structure calculated by the nonlocal empirical pseudopotential method. The calculations show that the self-assembled Sn/Si dots, sized between 4 and 12 nm, have indirect interband transition energies between 0.8 and 0.4 eV and direct interband transitions between 2.5 and 2.0 eV. In particular, the actually grown, approximately cylindrical Sn dots in Si with a diameter and height of about 5 nm are calculated to have an indirect transition (to the L valley) of about 0.7 eV, which agrees very well with experimental results. Similar good agreement with the experiment was also found for SnGe dots grown on Si. However, neither of these is predicted to be direct band gap materials, in contrast to some earlier expectations.