Session: K9-11 Phonon Modeling and Machine Learning for Thermal Transport

Paper Number: 114839

114839 - 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 (BTE) 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. Compared to the BTE method, the ray tracing model described here fundamentally determine the phonon transmission coefficients and forward/reverse crossing indices rather than determining the local energy density or local heat flux as a function of time in a volumetric mesh.

We validated our ray tracing method for cross-plane and square nanowire geometries from the ballistic through the diffusive regimes by performing simulations for a range of gray phonon bulk mean free paths. In addition, we find that the bulk finite-element method  results also are in quantitative agreement with our ray tracing calculations in the nanoslot geometry in the diffusive regime. After performing these validations, we apply the method to optimize geometric parameters that lead to locally inverted temperature gradients in porous nanomeshes. These results show that smaller pores, thick films, and multiple pores along the direction of transport lead to large and inverted values of the temperature gradient in the ballistic regime as compared to the traditional diffusive gradients. Lastly, we evaluate the heat focusing capabilities of geometric ballistic phonon lenses. Our ray tracing results show that both the magnitude and the diameter of the focal point can be controlled by the pore size and configuration of the nanostructures. 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.

Presenting Author: Yingru Song Rice University