Quantitative Analysis of Nonequilibrium Phonon Transport Near a Nanoscale Hotspot

Abstract

Understanding thermal transport by phonons near nanoscale hotspots is critical for many engineering applications, especially for nanoscale thermal measurements and nanoelectronics. Previous studies usually adopted the gray phonon Boltzmann transport equation to consider ballistic phonon transport or the multitemperature model to consider selective phonon excitation. However, nonequilibrium phonon transport near a nanoscale hotspot cannot be fully captured by either method. In this work, we employ the more rigorous nongray phonon Boltzmann transport equation to investigate phonon transport near nanoscale hotspots. We first consider hotspots in a one-dimensional system with two phonon modes to extract the underlying physics. Thermal transport is found to be less efficient near these hotspots, leading to significantly smaller effective thermal conductivity. The mechanism behind this is that different phonon modes have different temperatures and are therefore not in equilibrium. Nonequilibrium is caused by both the selective electron-phonon interaction and ballistic phonon transport. For relatively large hotspots, nonequilibrium is primarily contributed to by the selective excitation effect. When the hotspot size further reduces, the contribution from ballistic phonon transport becomes increasingly more important. Furthermore, we quantitatively study the thermal transport of laser-heated hotspots in Raman experiments and Joule heating in fin field-effect transistors (FETs) using the nongray phonon Boltzmann transport equation. We find that the measured thermal conductivity of single-layer graphene can be significantly underestimated if the nonequilibrium effect is ignored. Additionally, the peak temperature rise in a silicon fin FET is much larger than that calculated by the heat-diffusion equation.