Piezo-resistance in $n$-type Si$_{1-x}$Ge$_x$ alloys as a function of alloy composition and strain*

We use first-principles electronic structure methods[1,2] to predict the piezoresistance of $n$-type Si$_{1-x}$Ge$_x$ at various alloy compositions and strain configurations. The gauge factor, $G = d\rho/d\epsilon/\rho$, where $\rho$ is resistivity and $\epsilon$ is strain, varies strongly with both composition and strain. Nonlinear changes in resistivity with strain may arise due to changing occupancy of the higher-conductance $L$ valley relative to the lower-conductance $\Delta$ valley, coupled to a change in inter-valley alloy and phonon scattering. [1] F. Murphy-Armando and S. Fahy, J. Appl. Phys., accepted for publication (2011). [2] F. Murphy-Armando and S. Fahy, Phys. Rev. Lett., 97, 096606 (2006)