Valence band structure calculations of strained Ge$_{1-x}$Sn$_x$ quantum well pFETs

The dependence of valence band structures of Ge$_{1-x}$Sn$_x$ with 0 $\leq$ $x$ $\leq$ 0.2 on Sn content, biaxial strain, and substrate orientation is calculated using the nonlocal empirical pseudopotential method. The first valence subband structure in p-type Ge cap/fully strained Ge$_{1-x}$Sn$_x$ quantum well/Ge (001) and (111) inversion layers are theoretically studied using the 6$\times$6 k$\cdot$p model. A wave-function coupling of a Ge cap with respect to a strained Ge$_{1-x}$Sn$_x$ quantum well, which is influenced by the cap thickness, valence band offset, and confined effective mass, changes the energy dispersion relation in the two-dimensional $k$-space. The increase in Sn content and the decrease in cap thickness increase the hole population in the strained Ge$_{1-x}$Sn$_x$ quantum well to reduce the transport effective mass at the zone center in the Ge/strained Ge$_{1-x}$Sn$_x$/Ge inversion layers.