Phonon Dispersion and Specific Heat in FCC Structure

FCC구조에서 포논분산과 비열

A model for the phonon dispersion relationship for cubic zinc sulfide structure, for example SiC, is developed in terms of two unknown force constants. Born model that incorporates bond bending and bond stretching, is used for the force constants. The force constants are determined by fitting to experimental data. Using only the nearest-neighbor coupling results in $6{\times}6$ sized dynamic matrix. The eigenvalues of dynamics matrix for each wavenumber in 3-D ${\kappa}$ space correspond to frequencies, 3 for optical phonon and 3 for acoustic phonon, which is so-called dispersion relation (${\kappa}$-${\omega}$). The density of state is determined by counting the states for each frequency bin, and the properties such as specific heat and thermal conductivity can be obtained. The specific heat is estimated on this model and compared with experiment and other models, i.e. Debye model, Einstein model and combined Debye-Einstein model. In spite of the simple bond potential model, reasonable agreements are found.