Effect of dimensions on the vibrational frequencies of thin slabs of silicon

Abstract

Calculated frequencies of the long-wavelength vibrations of thin slabs of silicon parallel to the (111) plane show that the in-plane modes decrease almost exponentially in frequency with decreasing thickness of the slab. The out-of-plane modes have frequencies lower than the in-plane modes and decrease in the same fashion as the slab becomes thinner. This result is consistent with the observation that the Raman-active mode shifts toward lower frequencies in laser-annealed, ion-implanted silicon when the recrystallization is not perfect.