The vibrational density of states and specific heat of Si nanocrystals

The vibrational density of states and phonon specific heat of Si nanocrystals are studied by means of a lattice dynamical calculation. The vibrational density of states of Si nanocrystals is distinct from the bulk one at low and high frequencies owing to the finite-size effect. At low frequencies there is an excess of the vibrational modes, while there is a deficit at high frequencies. At low frequencies the dependence of the vibrational density of states on frequency is intermediate between linear and quadratic. The specific heat of Si nanocrystals is enhanced as compared to that of the bulk with a maximal excess at around 90 K. The dependence of the specific heat on temperature deviates from the known T-3-law for crystalline systems at low temperatures.