First-principle Study for More Accurate Optical and Electrical Characterization of Ge 1-x Sn x Alloy for Si and Group-IV Device Applications

Ge is on increasing demand in the advanced Si-compatible high-speed integrated circuits due to its high carrier mobilities. In particular, its hole mobility is much higher than those of other group-IV and III-V compound semiconductor materials. At the same time, Ge has the local minimum at the ${\Gamma}$ valley, which enables the utilization for optical applications. The fact that Ge becomes a direct-bandgap semiconductor material by applying tensile strain can be a good merit in obtaining higher spontaneous radiation probability. However, engineering the electronic structure of Ge by external mechanical stress through stressors with different thermal expansion coefficients might require a complicated set of processes. Efforts were made to turn it into a direct-bandgap one by incorporating Sn. Carrier mobilities are further enhanced when Sn is substitutionally incorporated into the Ge matrix. Thus, advantageous features are expected in improving both optical and electrical performances. Furthermore, the small bandgap energy and bandgap tunability make $Ge_{1-x}Sn_x$ alloy a promising material for components making up the optical interconnect on Si platform including optical source of near-infrared wavelength. In this work, we study the electrical and optical characteristics of $Ge_{1-x}Sn_x$ alloy as a function of Sn content. To achieve this goal, ab initio calculations of energy-band structures of $Ge_{1-x}Sn_x$ with different Sn fractions have been carried out based on linearized augmented plane wave (LAPW) method with modified Becke-Johnson potential model for more accurate bandgap energy. Then, a novel coding method has been adopted for more reliable overall band structures. The minimum Sn content required for direct- and indirect-bandgap material transition of $Ge_{1-x}Sn_x$, electrical and optical energy bandgaps to investigate the bandgap tunability, as well as effective masses, have been extracted as a function of Sn content. The transition point was found to be 6.9% and succinct reductions of effective masses of electron and hole have been confirmed.