Electronic structure and optical properties of Sn and SnGe quantum dots

Abstract

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.

Electronic band structure and effective mass parameters of Ge1-xSnx alloys

“…44 The extraction of k.p effective mass parameters can be obtained by fitting the electronic band structures of k.p method to that of EPM. 36,45,46 Using 8-band k.p Hamiltonian, 47 the band edge dispersion at the C-point obtained by k.p method was fitted to the EPM results by tuning the adjustable Luttinger-like parameters. The 8-band Hamiltonian for a diamond structure is given as where…”

Formation of Ge-Sn nanodots on Si(100) surfaces by molecular beam epitaxy

“…Self-assembled Ge-Sn nanodots (ND) are considered to be a possible candidate for direct band gap materials and have high potential for a variety of applications due to their compatibility with Si technology [1,2]. Ge-Sn ND have been grown on Si substrates by methods of molecular beam epitaxy (MBE) covered with ultrathin SiO 2 films [3,4].…”

Optical properties and size/shape dependence of α‐Sn nanocrystals by tight binding

“…While the treatment of Ge and Si nanocrystals in the litterature is vast and carried out in many frameworks, the available litterature on α-Sn nanocrystals is similarly scarce and only structures up to 20 Sn atoms have been treated by molecular orbital [9], tight binding [10] and ab initio methods [11]. For larger structures, only a combined k · p and effective mass approach exists [12]. Tight-binding is a suitable method for accurately treating nanocrystals with thousands of atoms.…”