Research Papers: Micro/Nanoscale Heat Transfer

Modeling Electron-Phonon Nonequilibrium in Gold Films Using Boltzmann Transport Model

[+] Author and Article Information
Arvind Pattamatta

Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260-4400ap65@eng.buffalo.edu

Cyrus K. Madnia1

Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260-4400madnia@eng.buffalo.edu


Corresponding author.

J. Heat Transfer 131(8), 082401 (Jun 05, 2009) (8 pages) doi:10.1115/1.3111258 History: Received August 28, 2008; Revised February 25, 2009; Published June 05, 2009

Ultrashort-pulsed laser irradiation on metals creates a thermal nonequilibrium between electrons and the phonons. Previous computational studies used the two-temperature model and its variants to model this nonequilibrium. However, when the laser pulse duration is smaller than the relaxation time of the energy carriers or when the carriers’ mean free path is larger than the material dimension, these macroscopic models fail to capture the physics accurately. In this paper, the nonequilibrium between energy carriers is modeled via a numerical solution of the Boltzmann transport model (BTM) for electrons and phonons, which is applicable over a wide range of lengths and time scales. The BTM is solved using the discontinuous Galerkin finite element method for spatial discretization and the three-step Runge–Kutta temporal discretization. Temperature dependent electron-phonon coupling factor and electron heat capacity are used due to the strong electron-phonon nonequilibrium considered in this study. The results from the proposed model are compared with existing experimental studies on laser heating of macroscale materials. The model is then used to study laser heating of gold films, by varying parameters such as the film thickness, laser fluence, and pulse duration. It is found that the temporal evolution of electron and phonon temperatures in nanometer size gold films is very different from the macroscale films. For a given laser fluence and pulse duration, the peak electron temperature increases with a decrease in the thickness of the gold film. Both film thickness and laser fluence significantly affect the melting time. For a fluence of 1000J/m2, and a pulse duration of 75 fs, gold films of thickness smaller than 100 nm melt before reaching electron-phonon equilibrium. However, for the film thickness of 2000 nm, even with the highest laser fluence examined, the electrons and phonons reach equilibrium and the gold film does not melt.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Nondimensional electron temperature profiles at the front surface of a gold film for L=20 nm and ϕ=13.4 J/m2

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Figure 2

Temporal variation of temperature at the front surface with film thickness for (a) electrons and (b) phonons; tp=75 fs and ϕ=1000 J/m2

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Figure 3

Temporal variation of temperature at the front surface with pulse duration for (a) electrons and (b) phonons; L=20 nm and ϕ=1000 J/m2

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Figure 4

Temporal variation of temperature at the front surface with laser fluence for (a) electrons and (b) phonons; L=20 nm and tp=75 fs

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Figure 5

Variation of maximum electron temperature with laser fluence and film thickness for a pulse duration of 75 fs

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Figure 6

Spatial variation of (a) electron temperature and (b) phonon temperature for tp=75 fs and ϕ=1000 J/m2

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Figure 7

(a) Comparison of melting fluence threshold with experiments; (b) melting threshold fluences for tp=75 fs and L=20 nm




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