Abstract
An analysis of the influence of geometry and size on the thermal conductivity in semiconductors, particularized to the study in Si and GaN, is presented. This is done in the framework of a higher-order generalized hydrodynamics (HOGH) of phonons in semiconductors, driven away from equilibrium by external sources. This HOGH is derived by the method of moments from a generalized Peierls–Boltzmann kinetic equation built in the framework of a Non-Equilibrium Statistical Ensemble Formalism. We consider the case of wires (cylindrical geometry) exploring the effect of size (radius), particularly in the nanometric scale when comparison with experiment is done. Maxwell times, which are quite relevant to define the hydrodynamic movement, are evidenced and characterized.
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