Dependence of vibrational density of states and Raman spectra on size in non-polar and polar nano-crystalline semiconductors

The vibrational density of states (VDOS) of Si, diamond, SiC, and InSb clusters has been calculated using the cluster model for various cluster sizes. The results show that the peak frequency of optical-like bands of VDOSs of non-polar nano-crystalline (NC) semiconductors varies with size, but that of polar NC semiconductors does not vary with size. We attribute the origin of this different behavior of non-polar and polar NC semiconductors to different interactions in the optical-like modes of them. That is, the deformation potentials for the non-polar NC semiconductors and electrostatic potentials for the polar NC semiconductors. According to the amorphous crystal (aC) model, Raman spectra are directly related to VDOS. In this Letter, it is verified that the aC model can be applied to NC semiconductors. Calculated VDOS are compared with observed Raman spectra of corresponding samples, which show agreement.