Effects of composition, strain, and atomic disorder on optical phonon frequencies in Si_1-x Ge_x

Optical phonon shift coefficients are studied over the entire composition range of Si_1-x Ge_x, taking into account the effects of composition, atomistic disorder and strain. Ab initio calculations complement various experimental observations found in the literature by revealing that strain effects on the optical phonons-both hydrostatic and biaxial-vary nonlinearly with composition. Additionally, the pure mode frequencies of the highest optical phonon modes in unstrained Si_1-x Ge_x are found to shift linearly with composition, while the mixed-mode frequency shifts quadratically with composition around x=0.5. While atomic randomness affects the composition dependence of the optical phonons, the strain-shift coefficients are approximately insensitive to the local atomic configuration. Short range atomic ordering increases the linear and nonlinear effects.