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Role of Dispersion and Optical Phonons in a Lattice-Boltzmann Finite-Difference Model for Nanoscale Thermal Conduction
Tampere University of Technology, Department of Electronics
A recently presented multiscale model for nanoscale thermal conduction is further developed to include dispersion and optical phonons in the nanoscale. Optical phonons are included as nonmoving heat reservoirs, and dispersion of the acoustic phonons is included by dividing the acoustic phonons into four categories with different group velocities. In the model, only the optical phonons are heated and the energy transfer rate from optical to acoustic phonons is described with a relaxation time. As a test case, a nanoscale hot spot is introduced into a silicon system and thermal conduction to ambient is calculated. The results show a temperature step at the spot boundary, while elsewhere the results agree with thermal diffusion. Optical phonons and dispersion are seen to increase the spot boundary thermal resistance. Moreover, heat transfer near hot spots is seen to be dominated by high heat capacity phonons, while further away from the spot heat conduction is dominated by fast phonons.
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