Calculation of phonons in [001] and [110] SiGe strained-layer superlattices

Abstract

Abstract In this communication, we present the results of full three dimensional calculations of phonon frequencies in silicon-germanium strained-layer superlattices. We used a modified version of the six-parameter valence force potencial model (VFPM), incorporating the strained nature of the layers. We found that the VFPM reproduces the predicted strain-induced frequency shifts for superlattices grown in the [001] direction extremely well, if longitudinal and transverse polarized phonons are considered separately. We found that the degree of penetration of confined LO phonons into adjacent layers is different for growth in [001] direction and growth in the [110] direction. Confined phonons in [110] superlattices have nearly zero penetration depth into adjacent layers, while the penetration depth for phonons in [001] superlattices is quite significant. This information is crucial when determining layer thicknesses using Raman spectroscopy. It was found that the large penetration depth for [001] superlattices allowed for coupling of interface modes across layers, giving rise to a splitting of these otherwise degenerate modes. The model was found to be unsuitable for modelling strain for superlattices grown in the [110] direction.