Nanoscale confinement of phonon flow and heat transport

Efficient thermal management is critical to device performance and reliability for energy conversion, nanoelectronics, and the development of quantum technologies. The commonly-used diffusive model of heat transport breaks down for confined nanoscale geometries, and advanced theories beyond diffusion are based on disparate assumptions that lead to conflicting predictions. Here, we outline and contrast the two predominant formulations of the Boltzmann equation for heat transport in semiconductors, namely, the ballistic and hydrodynamic models. We examine these methods in light of experiments and atomistic calculations of heat fluxes and temperature profiles in phononic systems with nanometer-sized features. We argue that reconciling the hydrodynamic and ballistic formulations is an outstanding necessity to develop a unifying theory of confinement effects on phonon flow, which will ultimately lead to optimal strategies for thermal management in nanodevices.