https://doi.org/10.1140/epjb/e2013-40109-1
Regular Article
Mesoscopic hydro-thermodynamics of phonons in semiconductors: heat transport in III-nitrides
1 Departamento de Física, Pontifícia
Universidade Católica de Goiás, 74605-010
Goiânia, Goiás,
Brazil
2 Condensed Matter Physics Department,
Institute of Physics “Gleb Wataghin”, University of Campinas-Unicamp,
13083-859
Campinas, SP, Brazil
a e-mail: cloves@ucg.br
Received:
7
February
2013
Received in final form:
4
March
2013
Published online:
2
May
2013
It is presented a generalized hydro-thermodynamics (called mesoscopic hydro-thermodynamics MHT) of phonons in semiconductors, driven away from equilibrium by external forces, derived by the method of moments from a generalized Peierls-Boltzmann kinetic equation built in the framework of a non-equilibrium statistical ensemble formalism. The resulting MHT involves the enormous set of coupled evolution equations for the densities of the quasi-particles (phonons) and their energy together with their fluxes of all orders. The handling of them requires the introduction of a contraction of description what defines MHT’s of different orders. We illustrate the matter analyzing heat transport by phonons in GaN within the framework of a MHT of first order to obtain a generalized Guyer-Krumhansl equation from which it is analyzed the effect of geometry on the heat transport. It is described the influence of size (from bulk to nanometric scales) on the reduction of the thermal conductivity and the improving of the figure of merit of thermoelectric devices.
Key words: Mesoscopic and Nanoscale Systems
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013