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.

改善热电性能的常用方法是通过增强声子散射来降低热导率。本文基于离散坐标法，开发了一种基于频率的声子辐射输运方程（PRTE）求解器，以模拟具有声子晶体纳米结构的硅薄膜中的声子输运。详细讨论了几何参数对声子传输的影响。此外，使用非线性最小二乘法获得了非线性回归模型，用于预测具有声子晶体纳米结构的薄硅膜的热导率。结果表明，声子晶体纳米结构降低了热导率，这主要是由于具有孔边界的声子向后散射所致，平均自由程较大的声子具有较强的反向散射。当孔的位置固定时，孔构型会影响具有声子晶体纳米结构的硅薄膜中的声子传输。此外，热导率主要由三个几何参数控制，包括[R _⊥， [R _|| 和A _u。此外，所获得的回归模型很好地揭示了热导率与几何参数之间的关系，可以为制备低热导率的硅薄膜提供有用的建议。