Phonon ray tracing calculations of ballistic temperature and heat flux profiles in nanostructures

Phonon ray tracing calculations have been used to quantify phonon boundary scattering in nanomaterials and to interpret thermal conductivity measurements. However, Landauer-based phonon ray tracing methods have not been able to access the temperature or heat flux profiles within nanomaterials, meaning that computationally intensive Boltzmann Transport Equation solvers are needed to gain insight into ballistic transport physics or model nanoscale temperature mapping experiments. Here, we derive and apply phonon Monte Carlo ray tracing methods to calculate the local temperature and local heat flux in semiconducting nanomaterials, with a focus on the ballistic transport regime. The derivation provides a straightforward interpretation of the local temperature in terms of a thermal conductance ratio, and the local heat flux in terms of the difference between forward-and reverse-oriented phonon trajectories crossing a control surface. After validating the method for several common transport regimes and geometries, we apply the method to optimize geometric parameters that lead to locally inverted temperature gradients in porous nanomeshes, and to evaluate the heat focusing capabilities of geometric ballistic phonon lenses. These applications illustrate how phonon ray tracing methods can be used to quantify ballistic thermal profiles and to design nanostructures that exhibit atypical thermal behaviors in the ballistic regime.

Automated summary

Phonon ray tracing calculations have been used to quantify phonon boundary scattering in nanomaterials and to interpret thermal conductivity measurements. However, Landauer-based phonon ray tracing methods have not been able to access the temperature or heat flux profiles within nanomaterials, meaning that computationally intensive Boltzmann Transport Equation solvers are needed. We derive and apply phonon Monte Carlo ray tracing methods to calculate the local temperature and heat flux in semiconducting nanomaterials, focusing on the ballistic transport regime.