Phonon transport and equivalent equilibrium temperature in thin silicon films

Abstract

Phonon transport in dielectric film depends on phonon polarization and their frequencies. This requires the solution of frequency-dependent Boltzmann equations for energy transport in dielectric films. In the present study, a frequency-dependent solution of the Boltzmann equation is obtained for a two-dimensional silicon film, and variation of equivalent equilibrium temperature in the film is presented. The influence of film width on phonon transport in the film is examined. The comparison of equivalent equilibrium temperature obtained from the frequency-dependent and -independent solutions is also presented. It is found that ballistic phonons suppress equivalent equilibrium temperature increase in the film. Two-dimensional phonon transport reduces to one-dimensional transport in film as the film width increases to more than twice of the film thickness.

Entropy generation in silicon thin film: Influence of film thickness on entropy generation rate

“…Entropy production in parallel and counter ow system [11] and relativistic binary mixtures [12] were presented incorporating the non-equilibrium transport equation. The ndings of the previous studies [1][2][3][4][5][6][7][8][9][10][11][12] revealed that the characteristics of heat transport for micro-scale analysis were di erent than those of macro-scale analysis. Therefore, micro-scale energy transport, incorporating the phonon radiative transport equation, becomes essential for the thermal analysis of thin lms.…”

“…Considerable research studies were carried out to examine energy transport at micro scale [1][2][3][4][5][6][7][8][9][10] and entropy generation [11,12]. The analytical solution for the phonon radiative transport equation was presented to demonstrate the functional relation between the phonon characteristics and the independent variables such as time and space [1,2].…”

“…The analytical solution for the phonon radiative transport equation was presented to demonstrate the functional relation between the phonon characteristics and the independent variables such as time and space [1,2]. The phonon transport in thin lms was investigated previously [3] and the ndings revealed that equivalent equilibrium temperature provided useful information on the phonon characteristics.…”

Thermal transport across a thin film composite due to laser short-pulse heating

“…Considerable research studies were carried out to examine energy transport in thin lms and laser beam interaction and energy transport at micro/nano scales [2][3][4][5][6][7][8][9][10][11]. A review on ultra-short laser interaction with matter was presented by Gamaly and Rode [12].…”

Phonon transport characteristics across silicon thin film pair: Presence of a gap between the films

“…The energy transport characteristics in thin lms are investigated analytically [20,21] and numerically [22][23][24][25][26]. Even transient phonon cross-plane transport that incorporates frequency dependence in thin silicon lm pair was investigated previously [1,27]; however, the e ect of gap length located between the lm pair was left for a future study.…”