In our previous works [1-4], we successfully developed and used our lattice Boltzmann method (LBM) to simulate the transient thermal behavior of phonons. This allowed us to study the sub-continuum thermal transport in semiconductors where phonons are the primary carriers or energy. But recently a lot of interest has been developed in the area of micro-fabrication and material processing of thin metallic film structures especially via short-pulse lasers [5-7]. The availability of high power short-pulse lasers on the order of femtoseconds have given rise to several innovative technologies and have brought considerable attention to the transient thermal transport mechanisms occurring in metallic thin films exposed to short laser pulses. In this phenomenon, not only phonons but electrons also play a vital role in the transport of energy. Therefore an effective model to capture the transient sub-continuum thermal transport in thin metallic films should incorporate the dynamics of both carriers of energy, electrons and phonons, without simplifying either of the system. One of the strong candidates to achieve this is to use two Boltzmann transport equations (BTEs), one each for electrons and phonons. BTE assume these energy carriers as quasi-particles and solves for their distribution inside the solid to simulate their dynamics in metals. But the phase space formulation of these BTEs makes them computationally very intensive to solve and also the complex coupling between the two BTEs which still have not been understood very well, makes it very difficult to perform a full-scale coupled BTE simulation for electrons and phonons in metals. This has led us to the development of our coupled LBM scheme where we extended our methodology, developed initially for phonon transport, to electrons and simulate the coupled electrons and phonons systems in the metals. Using this coupled LBM scheme, we demonstrated thin gold film heating via ultra-short laser pulse and studied the effect of electron-phonon coupling on the thermal behavior of the thin gold films where it was demonstrated that the transient thermal profile of the gold exhibit a very high dependence on the coupling factor between the two energy carriers. Sub-continuum effect of huge difference between the temperature levels of the two sub-systems of electrons and phonons at the very short time-scales and ballistic transport of electrons away from the metal surface are also observed in the thin gold film.

References:

[1] S.S. Ghai, W.T. Kim, C.H. Amon, and M.S. Jhon, J. Appl. Phys., 99, 08F906, 2006.

[2] S.S. Ghai, W.T. Kim, C.H. Amon, and M.S. Jhon, Proceedings of International Mechanical Engineering Congress and Exhibition, Orlando, FL, Nov. 5-11, 2005.

[3] R.A. Escobar, S.S. Ghai, M.S. Jhon, and C.H. Amon, Intl. J. Heat Mass. Trans., 49, 97-107, 2006.

[4] C.H. Amon, S.S. Ghai, W.T. Kim, and M.S. Jhon, Phys. A, 362, 36-41, 2006.

[5] I.W. Boyd, Laser Processing of Thin Films and Microstructures," Springer, New York, NY, 1989.

[6] J.K. Chen, J.E. Beraun, L.E. Grimes, D.Y. Tzou, Intl. J. Solids Structures, 39 3199–3216, 2002.

[7] M. Bonn, D.N. Denzler, S. Funk, and M. Wolf, S.-S. Wellershoff, and J. Hohlfeld, Phys. Rev. B, 61 (2), 1101-1105, 2000.