Study of phonon modes in silicon nanocrystals using the adiabatic bond chargemodel

Abstract

We present theoretical calculations of phonon dispersion in silicon nanocrystals using anapproach based on the adiabatic bond charge model. To deal with the boundary conditions,two cases are considered: the surface atoms are either free to move or rigidly fixed.In the former case, surface modes appear at low frequencies and, in the lattercase, nodes and antinodes appear near a frequency of 11 THz. By projecting thenanocrystal modes on the basis of bulk modes, one can show the increasing correlationbetween the nanocrystal modes and the bulk modes when increasing the dotsize. Finally, the frequency shift of Raman spectra calculated as a function ofthe dot size is found to be in good agreement with sets of experimental data.