  Exact assessment of thermal spreading resistance is of great importance to
the thermal management of electronic devices, especially when completely
considering the heat conduction process from the nanoscale heat source to the
macroscopic scale heat sink. The existing simulation methods are either based
on convectional Fourier's law or limited to small system sizes, making it
difficult to accurately and efficiently study the cross-scale heat transfer. In
this paper, a hybrid phonon Monte Carlo-diffusion method that couples phonon
Monte Carlo (MC) method with Fourier's law by dividing the computational domain
is adopted to analyze thermal spreading resistance in ballistic-diffusive
regime. Compared with phonon MC simulation, the junction temperature of the
hybrid method has the same precision, while the time costs could be reduced up
to 2 orders of magnitude at most. Furthermore, the simulation results indicate
that the heating scheme has a remarkable impact on phonon transport. The
thermal resistance of the heat source (HS) scheme can be larger than that of
the heat flux (HF) scheme, which is opposite from the prediction of Fourier's
law. In the HS scheme, the enhanced phonon-boundary scattering counteracts the
broadening of the heat source, leading to a stronger ballistic effect as the
heat source thickness decreases. The conclusion is verified by a
one-dimensional thermal resistance model. This work has opened up an
opportunity for the fast and extensive thermal modeling of cross-scale heat
transfer in electronic devices and highlighted the influence of heating
schemes.
