Simulation of ballistic and non-Fourier thermal transport in ultra-fast laser heating

Abstract

In this work, the lattice Boltzmann method (LBM) is developed to simulate pico- and femtosecond laser heating of silicon. The temperature fields calculated by the LBM are compared with those obtained from the parabolic heat conduction equation (PHCE) and the hyperbolic heat conduction equation (HHCE). Although the HHCE overcomes the dilemma of infinite thermal propagation speed of the PHCE, it cannot be applied to length scales comparable to the mean free path of energy carriers because of the breakdown of continuum approaches under severe nonequilibrium conditions. The LBM, considering both effects, can be used in both short temporal and spatial scales. From the results of the LBM, it is found that the speed of thermal wave at the ballistic limit is equal to the speed of sound, instead of the value predicted by the HHCE, which is valid only in the diffuse limit. It is also demonstrated that the traditional way of calculating heat flux using the temperature gradient gives rise to physically unreasonable results at the thermal wave front, while the LBM has no such drawback.