Enhancement of the electronic thermoelectric properties of bulk strained silicon-germanium alloys using the scattering relaxation times from first principles

We use first-principles electronic structure methods to calculate the electronic thermoelectric properties (i.e. due to electronic transport only) of single-crystalline bulk $n$-type silicon-germanium alloys vs Ge composition, temperature, doping concentration and strain. We find excellent agreement to available experiments for the resistivity, mobility and Seebeck coefficient. These results are combined with the experimental lattice thermal conductivity to calculate the thermoelectric figure of merit $ZT$, finding very good agreement with experiment. We predict that 3% tensile hydrostatic strain enhances the $n$-type $ZT$ by 50% at carrier concentrations of $n=10^{20}$ cm$^{-3}$ and temperature of $T=1200K$. These enhancements occur at different alloy compositions due to different effects: at 50% Ge composition the enhancements are achieved by a strain induced decrease in the Lorenz number, while the power factor remains unchanged. These characteristics are important for highly doped and high temperature materials, in which up to 50% of the heat is carried by electrons. At 70% Ge the increase in $ZT$ is due to a large increase in electrical conductivity produced by populating the high mobility $\Gamma$ conduction band valley, lowered in energy by strain.