Band structure calculation of Si-Ge-Sn binary and ternary alloys, nanostructures and devices

Alloys of silicon (Si), germanium (Ge) and tin (Sn) are continuously attracting research attention as possible direct band gap semiconductors with prospective applications in optoelectronics. The direct gap property may be brought about by the alloy composition alone or combined with the influence of strain, when an alloy layer is grown on a virtual substrate of different composition. Si-GeSn nanostructures are also promising materials because they are compatible with Si-based technology, and have a high potential in many optoelectronic applications, such as silicon-based Ge/SiGeSn band-to-band and inter-subband lasers. In search for direct gap materials, the electronic structure of relaxed or strained Gel-xSnx and Si1-xSnx alloys, and of strained Ge grown on relaxed Gel_x_ySixSny, were calculated by the self-consistent pseudo-potential plane wave method, within the mixed-atom supercell model of alloys, which was found to offer a much better accuracy than the virtual crystal approximation. Expressions are given for the direct and indirect band gaps in relaxed Gel-xSnx, strained Ge grown on relaxed SixGel-x_ySny, and for strained Gel-xSnx grown on a relaxed Gel_ySny substrate, and these constitute the criteria for achieving a direct band gap semiconductor, by using appropriate tensile strain. In particular, strained Ge on relaxed SixGel_x_ySny has a direct gap for y > 0.12 + 0.20x, while strained Gel-xSnx on relaxed Gel_ySny has a direct gap for y > 3.2x2 - 0.07x + 0.09. In contrast, within the mixed-atom approach the SnxSi1- x alloys never show a finite direct band gap (while the VCA calculation does predict it). Self-assembled quantum dots in 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 f-point and interband optical matrix elements of strained Sn and SnGe quantum dots in Si or Ge matrix are calculated using the eightband 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 (EPM). The calculations show that the self-assembled Sn/Si dots, sized between 4 nm and 12 nm, have indirect interband transition energies between 0.8 to 0.4 eV and direct interband transitions between 2.5 to 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 experiment was also found for SnGe dots grown on Si. However, neither of these are predicted to be direct band gap materials, in contrast to some earlier expectations. In order to extend a creativity in developing a complete suite of Si-base optoelectronic devices, SiGeSn alloys are considered as promising materials for optoelectronic applications because they offer the possibility for a direct band gap and are compatible with Si-based technology, therefore having a perspective of applications for interband lasers and detectors, solar cells, etc. In this work, another possible application of nanostructures based on these materials was considered: to extend the suite of Si-based optoelectronic devices, namely for interband electro-absorption modulators. Using the 8-band k.p method asymmetric double quantum wells have been designed and optimized, by varying the well and barrier widths and material composition, to show large optical transmission sensitivity to the applied bias. Generally, these structures are useful for electro-absorption modulators in the mid-infrared spectral range