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.

We study the steady-state and ballistic transport properties of semiconducting zig-zag carbon nanotubes (CNTs) using semiclassical Monte Carlo simulation. Electron-phonon scattering is the only type of interaction included in the model. The band structure and phonon dispersion are derived from that of graphene by the zone folding method. Steady-state drift velocity and low-field mobility are calculated for CNTs with wrapping index ranging from n=10 to n=59, i.e., for a diameter range of 0.78−4.62nm. Principally, a transient analysis of transport under uniform driving field is realized and gives the fraction of ballistic electrons as a function of CNT length and the mean free path (MFP) for acoustic and optical phonons scattering. The probability to have ballistic electrons on a given distance appears to be higher for nanotubes of large diameter and depends on the field applied.