Study of phonon modes in silicon nanocrystals using the adiabatic bond charge model

We present theoretical calculations of phonon dispersion in silicon nanocrystals using an approach 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 latter case, nodes and antinodes appear near a frequency of 11 THz. By projecting the nanocrystal modes on the basis of bulk modes, one can show the increasing correlation between the nanocrystal modes and the bulk modes when increasing the dot size. Finally, the frequency shift of Raman spectra calculated as a function of the dot size is found to be in good agreement with sets of experimental data.