Doping and strain dependence of the electronic band structure in Ge and GeSn alloys*

A systematic study of the effect of dopants and strain on the electronic structure of Ge and GeSn alloys is presented. Samples were grown by UHV-CVD on Ge-buffered Si using Ge3H8 and SnD4 as the sources of Ge and Sn, and B2H6/P(GeH3)3 as dopants. High-energy critical points in the joint-density of electronic states were studied using spectroscopic ellipsometry, which yields detailed information on the strain and doping dependence of the so-called $E_{1}$, $E_{1}+\Delta_{1}$, $E_{0}'$ and $E_{2}$ transitions. The corresponding dependencies of the lowest direct band gap $E_{0}$ and the fundamental indirect band gap $E_{ind} $were studied via room-T photoluminescence spectroscopy. Of particular interest for this work were the determination of deformation potentials, band gap renormalization effects, Burstein-Moss shifts due to the presence of carriers at band minima, and the dependence of other critical point parameters, such as amplitudes and phase angles, on the doping concentration. The selective blocking of transitions due to high doping makes it possible to investigate the precise $k$-space location of critical points. These studies are complemented with detailed band-structure calculations within a full-zone $k$-dot-$p$ approach.