Vibrational spectra ofa-Si: H,a-Si: F, anda-Ge: F: Bethe-lattice calculations

The local densities of vibrational states around Si-H and Si-F bands in $a$-Si are obtained by means of a cluster-Bethe-lattice calculation. Nearest-neighbor bond-stretching and -bending constants are included. The calculations reproduce the peaks observed in the ir spectra of both $a$-Si: H and $a$-Si: F near the upper edge of the TA band (∼210 ${\mathrm{cm}}^{-1\mathrm{}}$). As a result of the calculation, these peaks, however, are seen to have a different origin in the case of $a$-Si: H and $a$-Si: F. In the former, the peak is a resonance vibrating longitudinally to the bond with the H atom rigidly attached to the Si neighbor. For the $a$-Si: F case the resonance has transverse character and corresponds to a mixture of wagging modes of the Si—F bond and TA modes of the $a$-Si matrix. Published ir spectra of $a$-Si: H must be correspondingly interpreted. A calculation of the ir spectrum of $a$-Si: F, in which the absorption strength is not an adjustable parameter, is presented and compared with experiment. The calculations for $a$-Si: F are extended to $a$-Ge: F.