Abstract
A generalized Hydrodynamics, referred to as Mesoscopic Hydro-Thermodynamics, of phonons in semiconductors is presented. It involves the descriptions of the motion of the quasi-particle density and of the energy density. The hydrodynamic equations, which couple both types of movement via thermo-elastic processes, are derived starting with a generalized Peierls-Boltzmann kinetic equation obtained in the framework of a Non-Equilibrium Statistical Ensemble Formalism, providing such Mesoscopic Hydro-Thermodynamics. The case of a contraction in first order is worked out in detail. The associated Maxwell times are derived and discussed. The densities of quasi-particles and of energy are found to satisfy coupled Maxwell-Cattaneo-like (hyperbolic) equations. The analysis of thermo-elastic effects is done and applied to investigate thermal distortion in silicon mirrors under incidence of high intensity X-ray pulses in FEL facilities. The derivation of a generalized Guyer-Krumhansl equation governing the flux of heat and the associated thermal conductivity coefficient is also presented.
Highlights
It has been noticed1 that the ceaseless innovation in semiconductors design creates a demand for better understanding of the physical processes involved in the functioning of modern electronic devices, which operate under far-from-equilibrium conditions
A complete MHT for classical fluids is reported in Ref. 14. In this communication we describe the construction of a MHT of phonons, presenting an in depth study of phonon hydro-thermodynamics in the framework of a nonlinear quantum kinetic theory based on a non-equilibrium statistical ensemble formalism,15–20 referred to as NESEF for short
Elsewhere45 we have considered the question of the contraction of description, where a criterion for justifying the different levels of truncation is derived: It depends on the range of wavelengths and frequencies which are relevant for the characterization, in terms of normal modes, of the hydro-thermodynamic motion in the nonequilibrium open system
Summary
It has been noticed that the ceaseless innovation in semiconductors design creates a demand for better understanding of the physical processes involved in the functioning of modern electronic devices, which operate under far-from-equilibrium conditions. The main interest is centered on the behavior of “hot” carriers (electrons and holes) but the case of “hot” phonons is of interest, in questions such as refrigeration of microprocessors and heat transport in small systems with constrained geometries.2–4 A first kinetic-hydrodynamic approach can be considered to be the so-called classical (or Onsagerian) hydrodynamics, which gives microscopic (mechano-statistical) foundations to, for example, the classical Fourier’s and Fick’s diffusion laws It works under quite restrictive conditions: hydrodynamic motion being smooth in space and slow in time, weak regressing fluctuations, linear flux-force relations (see for example.11) more advanced approaches are required to lift these restrictions because, as noticed, the requirements posited for the analysis of situations aDeceased on October 13, 2012.
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