Band Structure of Strained $\mathrm{Ge}_{1-x}~\mathrm{Sn}_{x}$ Alloy: A Full-Zone 30-Band ${k}\cdot{p}$ Model

Abstract

We extend the previous 30-band k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</sup> p model effectively employed for relaxed Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Sn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> alloy to the case of strained Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Sn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> alloy. The strain-relevant parameters for the 30-band k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</sup> p model are obtained by using linear interpolation between the values of single crystal of Ge and Sn that are from literatures and optimizations. We specially investigate the dependence of band-gap at L-valley and Γ-valley with different Sn composition under uniaxial and biaxial strain along [100], [110] and [111] directions. The good agreement between our theoretical predictions and experimental data validates the effectiveness of our model. Our 30-band k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</sup> p model and relevant input parameters successfully applied to relaxed and strained Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Sn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> alloy offers a powerful tool for the optimization of sophisticated devices made from such alloy.