Phonon spectrum and group velocity calculation of cubic semiconductor quantum dot

Acoustic Phonon Engineering of Cubic Semiconductor Quantum Dot

“…In case of nanostructures, we et al [24] have used elastic continuum approach to get phonon dispersion of cubic quantum dot with cubic crystal. The equation of motion for elastic vibrations is given by (1) Where U = (u, v, w) is the displacement vector, is the mass density of material, is the elastic stress tensor.…”

“…The phonon dispersion is then plotted as a function of . We can multiply the frequency, with to get the dispersion relation [6,24]. Whole procedure is implemented using MATLAB.…”

“…In case of nanostructure we solved the equation numerically instead of analytically with the finite edge boundary condition [6,12,13,24]. We considered a shear wave travelling in the x direction with a particle displacement in the y direction.…”

“…Now we will apply the numerical technique to solve the differential equation (4) with the above mentioned finite edge boundary condition. To solve the equation numerically for phonon dispersion we use finite difference method and follow a general strategy for vibration analysis [6,7,12,13,24].…”

“…Phonon spectrum has also been studied in case of graphene and other nanostructure [2,4]. In our earlier work [24], elastic continuum approach with finite difference method was used to calculate the phonon dispersion of semiconductor cubic quantum dot from which phonon group velocity was found by numerical differentiation. In this research we will coat a cubic quantum dot with acoustically different material and observe the effect of coating on phonon spectra.…”