Lattice Boltzmann method (LBM) simulations of phonon transport are performed in one-dimensional (1D) and 2D computational models of a silicon-on-insulator transistor, in order to investigate its transient thermal response under Joule heating conditions, which cause a nonequilibrium region of high temperature known as a hotspot. Predictions from Fourier diffusion are compared to those from a gray LBM based on the Debye assumption, and from a dispersion LBM which incorporates nonlinear dispersion for all phonon branches, including explicit treatment of optical phonons without simplifying assumptions. The simulations cover the effects of hotspot size and heat pulse duration, considering a frequency-dependent heat source term. Results indicate that, for both models, a transition from a Fourier diffusion regime to a ballistic phonon transport regime occurs as the hotspot size is decreased to tens of nanometers. The transition is characterized by the appearance of boundary effects, as well as by the propagation of thermal energy in the form of multiple, superimposed phonon waves. Additionally, hotspot peak temperature levels predicted by the dispersion LBM are found to be higher than those from Fourier diffusion predictions, displaying a nonlinear relation to hotspot size, for a given, fixed, domain size.

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