Transport of 29cm−1phonons in hydrogenated amorphous silicon

Abstract

The scattering of 29 cm Ϫ1 phonons in hydrogenated amorphous silicon ͑a-Si:H͒ at 2 K is investigated by means of optically generated heat pulses and the ruby phonon detector. The transport is shown to be governed by elastic spatial diffusion and a diffusion coefficient of ϳ1 cm 2 /s. Resonant scattering by soft oscillators, as well as Rayleigh scattering by microvoids or by the disordered network itself account for the experimental findings. In optically excited a-Si:H, the transmission of 29 cm Ϫ1 phonons is reduced by inelastic scattering, proportional to the optical excitation density in a-Si:H and recovers on a 40-ns time scale. These results are discussed in terms of interaction of 29 cm Ϫ1 phonons with optically generated long-lived very high-frequency phonons in a-Si:H. ͓S0163-1829͑96͒00541-3͔

Dynamics of vibrations in a mixed amorphous-nanocrystalline Si system

“…Also in these experiments we found that the phonon dynamics in a-nc-Si:H is markedly different from that in a-Si:H. The outcome of the transport experiments on a-Si:H is consistent with the results published by Scholten et al, who extensively studied the scattering of 29-cm Ϫ1 phonons in a-Si:H. 11 They showed that in a-Si:H the transport of 29-cm Ϫ1 phonons is governed by elastic spatial diffusion with a diffusion coefficient of ϳ1 cm 2 /s. Encouraged by their analysis, we try to explain the results of the phonon transport measurements on a-nc-Si:H in terms of an elastic diffusion model.…”

“…On the other hand, the trailing edge decays on the same ϳ50-ns time scale for different excitation powers, i.e., much faster than the decay of the R 2 /R 1 signals presented above for a-nc-Si:H for configuration ͑1͒. These observations are in agreement with the results reported for a-Si:H by Scholten et al 11 and are therefore not shown.…”

“…Advantage was taken of the fact that the layers studied were grown on sapphire, which in fact is very dilute ruby, and can be used as an optical detector for 29-cm substrate. 11 A study of the transport of 29-cm Ϫ1 phonons through the a-nc-Si:H layer is of particular interest, as the frequency of these phonons is of the order of the lowest frequency that can be supported by the nanometer-size crystallites present in the a-nc-Si:H film. Under such conditions, the materials microstructure may have pronounced effects on the phonon dynamics.…”

“…The problem is solved using the method of images. 11 To fulfill both boundary conditions, the initial distribution n(x,xЈ,0) has to be symmetric around xϭ0, and antisymmetric around xϭL. This is accomplished by introducing a positive ␦ peak n 0 ␦(xϩxЈ) at xϭϪxЈ, and two negative peaks at xϭ2LϪxЈ and xϭ2LϩxЈ.…”

“…Scholten et al investigated the dynamics of high-frequency phonons in ͑hydrogenated͒ amorphous silicon. 8,10,11 They measured phonon lifetimes more than three orders of magnitude longer than the lifetimes of phonons of the same energy in c-Si. Furthermore, lifetimes appeared to increase with increasing frequency, as opposed to the frequency dependence generally encountered in crystals.…”