Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures

Abstract

We report on inelastic light scattering (ILS) by longitudinal acoustic phonons in thin $\mathrm{Si}(001)$ layers (thickness $\ensuremath{\approx}30\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$). Calculations based on the photoelastic model are presented for unsupported and supported layers. We consider ILS by standing longitudinal acoustic modes along [001]. Our calculations take into account the spatial modulations of acoustic, optical, and photoelastic properties. We successively identify their contributions to the scattering efficiency and find that there is a strong interplay between acoustic, optical, and photoelastic cavity effects. The need to consider optical cavity effects is pointed out. It is shown here that they can be included in a convenient way in the scattered electromagnetic fields, by solving the wave equation in the presence of the polarization induced by the photoelastic effect. A detailed analysis of the scattering efficiency (peak frequencies, intensities, and widths) is presented. The dependence of the ILS spectra on film thickness and on substrate characteristics are addressed. Calculations are successfully compared to experimental data for thin Si membranes and silicon-on-insulator structures. It is shown that the inelastic light scattering involves a set of discrete quantized acoustic modes for membranes and a continuum of acoustic modes for silicon-on-insulator structures.