Nanoscale Thermal Transport: Understanding Heat Flow from the Ballistic to the Diffusive Limit

Abstract

In the past decade, experiments probing the thermal properties of materials on short time and length scales have observed non-classical behavior, not predicted by the traditional heat equation and Fourier’s law. This so-called “breakdown” of Fourier’s law results from ballistic phonon effects that arise when the characteristic length scale is comparable or less than the phonon mean-free-path (typically a few tens to hundreds of nm). This has spurred many theoretical studies seeking to provide a deeper understanding of nanoscale heat transport, including the role of ballistic and non-equilibrium effects, and to connect the measured thermal characteristics to the fundamental material properties. Beyond scientific interest, nanoscale heat effects have important implications for many emerging technologies, including, for example, heat management in nanoelectronics, phase-change memory, and heat-assisted magnetic recording. In this talk, I will discuss the physics of phonon transport on the nanoscale, how to treat it theoretically, and how it affects measured thermal properties. I will also present recent work to develop a simple and accurate framework to treat phonon transport continuously from the ballistic to the diffusive transport regime, which bridges the rigorous phonon Boltzmann transport equation to the efficient heat equation. Simple approaches are good for providing physical insight, for example explaining why the heat equation works remarkably well down to the nanoscale, and are well-suited for routine experimental analysis and technology design. Continued advances in nanoscale heat transport will further deepen our fundamental understanding of material physics and transport, and enable technological innovations.