  Gallium nitride (GaN) is a typical wide-bandgap semiconductor with a critical
role in a wide range of electronic applications. Ballistic thermal transport at
nanoscale hotspots will greatly reduce the performance of a device when its
characteristic length reaches the nanometer scale, due to heat dissipation. In
this work, we developed a tip-enhanced Raman thermometry approach to study
ballistic thermal transport within the range of 10 nm in GaN, simultaneously
achieving laser heating and measuring the local temperature. The Raman results
showed that the temperature increase from an Au-coated tip-focused hotspot was
up to two times higher (40 K) than that in a bare tip-focused region (20 K). To
further investigate the possible mechanisms behind this temperature difference,
we performed electromagnetic simulations to generate a highly focused heating
field, and observed a highly localized optical penetration, within a range of
10 nm. The phonon mean free path (MFP) of the GaN substrate could thus be
determined by comparing the numerical simulation results with the
experimentally measured temperature increase which was in good agreement with
the average MFP weighted by the mode-specific thermal conductivity, as
calculated from first-principles simulations. Our results demonstrate that the
phonon MFP of a material can be rapidly predicted through a combination of
experiments and simulations, which can find wide application in the thermal
management of GaN-based electronics.
