Hexagonal Ge / Si 0.25 Ge 0.75 quantum wells: Prediction of quantization and light-emission strength

We investigate heterostructures composed of hexagonal Ge quantum wells embedded within hexagonal <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>Si</a:mi> <a:mrow> <a:mn>0.25</a:mn> </a:mrow> </a:msub> <a:msub> <a:mi>Ge</a:mi> <a:mrow> <a:mn>0.75</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> alloy layers, systematically considering variations in crystallographic orientation, well thickness, and external biaxial strain. This study employs density functional theory together with accurate functionals for calculations of the quasiparticle electronic structure. Overall, the heterostructures exhibit type-I band alignment, with the localization of electron and hole wave functions predominantly within the hexagonal Ge regions. The quantum confinement of both charge carrier types is determined by the orientation and thickness of the Ge layer for three different external strains. The results obtained can be interpreted within a rectangular potential-well model, with characteristic parameters derived from band structures of hexagonal Ge and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>Si</b:mi> <b:mrow> <b:mn>0.25</b:mn> </b:mrow> </b:msub> <b:msub> <b:mi>Ge</b:mi> <b:mrow> <b:mn>0.75</b:mn> </b:mrow> </b:msub> </b:mrow> </b:math> , as well as their strained multiquantum well structures, properly aligned via the branch point energies. Besides confinement energies and subbands, optical transition strengths are also discussed.