Published Paper Details:

Lattice Dynamics the concept of a phonon and its properties were first introduced by Debye in 1912. A phonon is defined as a quantum of vibrational energy within a crystal structure. Phonons are considered as a quasi-particle with wave vector q and angular frequency ? s for atomic vibrational polarization s. The energy of a phonon mode is h?s and its momentum is h q. Lattice dynamics is the study of the relationship between these two quantities: ? = ?s(q). In the present study an experimental cum mathematical modeling was performed to study how phonon dispersion curves arise. The continuum model has been employed to explain the phonon dispersion of semiconducting nanostructures. The result shows that for the silicon nanostructures, the ultra-small case of each structure that all branches except the acoustic are flat and dispersion less regardless of whether the system is zero-, one-or two-dimensional. Conversely, the continuum model of the nanotube shows that the group velocity of the low optical modes is much large for k > 1. As the size of the silicon structures increases, these branches are seen to become dispersive in the direction of propagation like the nanotube.