An Improved Computational Procedure for Sub-Micron Heat Conduction

Popular numerical techniques for solving the Boltzmann transport equation (BTE) for sub-micron thermal conduction include the discrete ordinates method and the finite volume method. However, the finite wave speed associated with the BTE can cause large errors in the prediction of the equivalent temperature unless fine angular discretizations are used, particularly at low acoustic thicknesses. In this paper, we combine a ray-tracing technique with the finite volume method to substantially improve the predictive accuracy of the finite volume method. The phonon intensity is decomposed into ballistic and in-scattering components. The former is solved using a ray tracing scheme, accounting for finite wave speed; the latter is solved using an unstructured finite volume method. Comparisons between this new technique and traditional finite volume formulations are presented for a range of acoustic thicknesses, and substantial improvement is demonstrated.