Monte Carlo Simulation of Phonon Transmission in Pure Silicon Nanowire

Compared with bulk Si, thermal conductivity of nanowire decreases sharply, especially at low temperature, which is ascribed to boundary scattering. To study the confinement effects on phonon transport in nanowire, a dedicated Monte Carlo model was built by simplifying the rules of collisions. In the MC model, since specular boundary collision and N (normal) scattering do not change phonon velocity along transport direction, it is rational to neglect their effects on thermal conductivity. While a phonon striking on the boundary diffusely, a random number multiply 2 pi will be used as its new reflection angle, without alternating frequency and the magnitude of wave-vector. If a phonon's incident angle is more than zero, the probability of increasing its speed along propagation direction will be less than 0.5. As for U ( umklapp) scattering, it is hard to decide selection regime and collision process. In simulation, the possibility of U scattering of each phonon was calculated and then do the same as boundary scattering. Therefore, boundary scattering and U scattering provide the main resistances of phonon transport in pure silicon nanowire. The influence on temperature gradient was examined as change the boundary diffusing factor. Silicon nanowires with equivalent diameter of 22nm, 37nm and 56nm over a temperature of 15-315K were simulated. Though the results of 37nm and 56nm nanowire agreed well with experimental data, the 22nm one deviated significantly. By modifying the relaxation time, we got ideal simulation results in the end.