Inverse Design in Nanoscale Heat Transport via Interpolating Interfacial Phonon Transmission

TL;DR

This paper presents a novel topology optimization method for nanoscale heat transport that leverages adjoint sensitivity analysis and a new transmission interpolation model to design materials with tailored thermal properties.

Contribution

It introduces the transmission interpolation model (TIM) for smooth material property transitions and applies it to optimize nanostructures for heat management and thermoelectric efficiency.

Findings

Optimized nanomaterials with tailored thermal conductivity.

Enhanced thermoelectric performance through size effect maximization.

Method enables systematic design of heat transport devices.

Abstract

We introduce a methodology for density-based topology optimization of non-Fourier thermal transport in nanostructures, based upon adjoint-based sensitivity analysis of the phonon Boltzmann transport equation (BTE) and a novel material interpolation technique, the "transmission interpolation model" (TIM). The key challenge in BTE optimization is handling the interplay between real- and momentum-resolved material properties. By parameterizing the material density with an interfacial transmission coefficient, TIM is able to recover the hard-wall and no-interface limits, while guaranteeing a smooth transition between void and solid regions. We first use our approach to tailor the effective thermal-conductivity tensor of a periodic nanomaterial; then, we maximize classical phonon size effects under constrained diffusive transport, identifying a promising new thermoelectric material design. Our method enables the systematic optimization of materials for heat management and conversion and, more broadly, the design of devices where diffusive transport is not valid.