Thermal transport near hotspots in cryogenic devices via the phonon Boltzmann transport equation

The hotspots exist widely in cryogenic devices and play a critical role in influencing their electrical performance. Understanding phonon-mediated thermal transport near hotspots in cryogenic devices is essential for device performance in cryogenic technology. Previous studies employed Fourier's law with temperature-dependent thermal conductivity to analyze thermal transport, which cannot fully capture the complex phonon transport at cryogenic temperatures. Here, we develop a method combining first principles with the nonlinear temperature-adaptive phonon Boltzmann transport equation to investigate the underlying mechanism of thermal transport near hotspots at cryogenic temperatures. We demonstrate that ballistic phonons, temperature-dependent variations in phonon properties near the hotspot, and hotspot size are the key factors governing thermal transport at silicon-based cryogenic devices. We reveal that ballistic phonons dominate thermal transport in active regions at cryogenic temperature, and the drastic phonon property variance near the hotspot region contributes to the nonlinearity of temperature rise. We also show that hotspot size has a more significant impact on thermal resistance at cryogenic temperature than at room temperature, consistent with experimental observations. Additionally, our quantitative analysis of phonon-boundary scattering indicates that the impact of silicon film thickness on thermal transport diminishes at cryogenic temperatures in the SOI MOSFET. This work provides a comprehensive analysis of phonon transport near hotspots in cryogenic devices and offers valuable insights for improving electrical performance in cryogenic technology.