Modern semiconductor industry and nanotechnology have profoundly impacted the study on thermal transport in dielectric solids such as single-crystal silicon. For these heat conduction phenomena whose characteristic length and time shrink into nano scale, it is efficient to utilize phonon dynamics as a promising approach to investigate the fundamental features of heat transfer at nano scale as well as the distinguished thermal properties of nano-materials. A new computational method is proposed to explore phonon dynamics in single-crystals on the basis of classical Molecular Dynamics technique. This method utilizes the Fourier-Laplace transformation of molecular trajectory, with anharmonicity of molecular vibrations accounted in the investigation on phonon dynamics. Instantaneous mode-dependent energy of phonons and density of vibration state is obtained at each simulated time step. Mode-dependent phonon relaxation is simulated and verified with perturbation method, which gives a way to measure relaxation time of single-mode phonon. The feasibility of the proposed scheme is confirmed by a series of simulations which are carried out in this paper on 1) monatomic crystal of argon with FCC structure and 2) diatomic crystal of silicon with diamond structure, under Lennard-Jones 6-12 potential and Tersoff-1989 model, respectively.

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