Raman spectra of isotopic-disordered group IV semiconductors: A first principles approach

We present theoretical results of the off-resonance Raman spectra, phonon d ensity of stales and self-energies of isotopic-disordered diamond, Si, Ge, and alpha-Sn. Modern first-principles techniques are used to obtain the lat tice-dynamical properties which are the base of our calculations. We simula ted isotopic-disordered systems using supercells containing up to 512 atoms per unit cell and compared our results with the virtual-crystal approximat ion (VCA) and the coherent-potential approximation (CPA). We show the equiv alence of CPA and supercell methods when using as input the same lattice-dy namical quantities, whereas the VCA fails to obtain the correct trends. We proved that supercells of the size of a few hundred atoms are sufficient to describe the main disorder-induced features in good agreement with experim ental results.