Mode-resolved logarithmic quasiballistic heat transport in thin silicon layers: Semianalytic and Boltzmann transport analysis
Nonequilibrium phonon transport driven by nanoscale hotspot heating in silicon device layers governs heat dissipation in advanced microelectronics and underscores the need for a better microscopic understanding of such processes. Yet the origin of the frequently observed logarithmic (ln) dependence of the apparent thermal response on hotspot size in crystalline silicon, and the role of individual phonon modes in this regime, remain unclear. Here, we develop a semianalytical, mode-resolved framework in the spectral phonon mean free path (MFP) domain and validate it against a full-phonon-dispersion Boltzmann transport model for heat removal from a 10 x 10 nm^2 hotspot in a thin Si layer (thicknesses of 41, 78, and 177 nm) representative of a silicon-on-insulator transistor. We show that ln-type quasiballistic scaling arises only for modes that lie on a log-uniform conductivity plateau and are diffusive-side or quasiballistic with respect to the hotspot size, whereas fully ballistic long-MFP modes contribute a saturated, nonlogarithmic background, leading to extremely slow suppression of their heat-carrying capability. The resulting phonon-modal nonlocal spectrum establishes spectral selection rules for ln-regime transport in confined Si and provides a compact basis for incorporating mode-selective quasiballistic corrections into continuum thermal models and for interpreting phonon-resolved thermometry experiments.