Ab-initio vibrational properties of SiGe alloys

We report on the vibrational properties of Si1-xGex alloys by means of a pseudopotential density-functional study. We employ randomly generated supercells, and a wide range of Ge concentration (x = 19, 50, 81%) to investigate the alloys. Accordingly, Si atoms were occasionally replaced by Ge atoms in an otherwise perfect 32 Si atom supercell, with the atomic and volumetric degrees of freedom being allowed to relax. The dynamical matrix of 32 atom supercell was determined directly from the ab-initio code. Calculated Raman spectra were obtained averaging over 15 SiGe supercell configurations for each Ge concentration. The experimental three main wide bands were reproduced. The calculated Si-Si and Ge-Ge frequencies shift linearly with Ge concentration. The Si-Si frequency downward shift agrees well with experimental data, while the agreement is not so good for Ge-Ge mode. The highest Si-Ge frequency occurs when Ge composition reaches 50%, which agrees with experimental data. However the asymmetry of the downward frequency shift is not reproduced, which may be due to the limited size of the supercell