A detailed study on phonon transport in thin silicon membranes with phononic crystal nanostructures

A common method to improve thermoelectric performance is to reduce thermal conductivity by enhancing phonon scattering. In this paper, a frequency-dependent phonon radiative transport equation (PRTE) solver, based on the discrete ordinates method, is developed to simulate phonon transport in thin silicon membranes with phononic crystal nanostructures. The influence of geometric parameters on phonon transport is discussed in detail. Besides, a nonlinear regression model is attained for predicting the thermal conductivity of thin silicon membranes with phononic crystal nanostructures using the non-linear least-squares method. The results indicate that thermal conductivity is reduced by phononic crystal nanostructures mainly due to the back scattering of phonons with pore boundaries, and phonons with larger mean free path have stronger back scattering. When the pore placement is fixed, pore configuration affects phonon transport in thin silicon membranes with phononic crystal nanostructures. In addition, thermal conductivity is primarily controlled by three geometric parameters, including r_⊥, r_||, and A_u. Moreover, the obtained regression model reveals the relationship between thermal conductivity and geometric parameters well, which can offer useful suggestions for fabricating thin silicon membranes with low thermal conductivity.