Quantization of acoustic-phonon modes in Siedel-White type waveguide nanostructures

Acoustic phonon modes in a rectangular nanoscale waveguide deposited on a substrate (Siedel-White type waveguide) are analyzed analytically in terms of the elastic continuum model and the modes are quantized under the dimensional confinement assumption. The rectangular isotropic overlay structure is assumed to be deposited on a substrate with larger area compared to the overlay, and perfectly rigid. The displacement field inside the rectangular overlay structure is described for structures with nanometer dimensions. The frequency dependence of the modes has been studied along with the modal profiles for different overlay dimensions. The phonon occupation number has been evaluated for a range of dimensions and temperatures and the frequency-quality factor (f.Q) product has been theoretically discussed and evaluated using the parameters for silicon.