Modelling of local modes in Si_xGe_{1 - X} and C_xSi_yGe_{1 - X - y} alloys to explore the local clustering of the species

The frequencies of the local vibrational modes due to defects within group IV alloys are affected by the local environment of the defects; therefore by investigating known modes we get an insight into alloy fluctuations near the defects. The local modes are modelled around defects in a range of local alloy arrangements to investigate the effects of clustering alloy species. An interatomic potential has been fitted to phonon frequencies for the pure materials at symmetry points in k-space, to local vibrational modes of lighter elements in otherwise pure local environments and to atomic positions predicted by local density calculations for certain alloy structures. Using this potential, the frequencies of local modes of substitutional carbon are found in Si_xGe_{1 - x} with various values of x. From a stochastic analysis of the local environs to the carbon, the modes are weighted to produce the expected local vibrational spectrum of a Si_xGe_{1 - x} alloy. The experimental local mode line shapes in the alloys deviate sufficiently from those predicted to show that the carbon substitutes preferentially in regions of high silicon content.