Molecular dynamics simulations are performed to estimate acoustical and optical phonon relaxation times, dispersion relations, group velocities, and specific heat of silicon needed to solve the Boltzmann transport equation (BTE) at 300 K and 1000 K. The relaxation times are calculated from the temporal decay of the autocorrelation function of the fluctuation of total energy of each normal mode in the family of directions, where the total energy of each mode is obtained from the normal mode decomposition of the motion of the silicon atoms over a period of time. Additionally, silicon dispersion relations are directly determined from the equipartition theorem obtained from the normal mode decomposition. The impact of the anharmonic nature of the potential energy function on the thermal expansion of the crystal is determined by computing the lattice parameter at the cited temperatures using a NPT (i.e., constant number of atoms, pressure, and temperature) ensemble, and are compared with experimental values reported in the literature and with those computed analytically using the quasiharmonic approximation. The dependence of the relaxation times with respect to the frequency is identified with two functions that follow the functional form of the relaxation time expressions reported in the literature. From these functions a simplified version of relaxation times for each normal mode is extracted. Properties, such as group and phase velocities, thermal conductivity, and mean free path, needed to further develop a methodology for the thermal analysis of electronic devices (i.e., from nano- to macroscales) are determined once the relaxation times and dispersion relations are obtained. The thermal properties are validated by comparing the BTE-based thermal conductivity against the predictions obtained from the Green–Kubo method. It is found that the relaxation times closely resemble the ones obtained from perturbation theory at high temperatures; the contribution to the thermal conductivity of the transverse acoustic, longitudinal acoustic, and longitudinal optical modes being approximately 30%, 60%, and 10%, respectively, and the contribution of the transverse optical mode negligible.
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Thermal Properties for Bulk Silicon Based on the Determination of Relaxation Times Using Molecular Dynamics
Javier V. Goicochea,
Javier V. Goicochea
Department of Mechanical Engineering,
Carnegie Mellon University
, Pittsburgh, PA 15213
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Marcela Madrid,
Marcela Madrid
Pittsburgh Supercomputing Center
, Pittsburgh, PA 15213
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Cristina Amon
Cristina Amon
Department of Mechanical and Industrial Engineering,
University of Toronto
, Toronto, ON, M5S 1A4, Canada
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Javier V. Goicochea
Department of Mechanical Engineering,
Carnegie Mellon University
, Pittsburgh, PA 15213
Marcela Madrid
Pittsburgh Supercomputing Center
, Pittsburgh, PA 15213
Cristina Amon
Department of Mechanical and Industrial Engineering,
University of Toronto
, Toronto, ON, M5S 1A4, CanadaJ. Heat Transfer. Jan 2010, 132(1): 012401 (11 pages)
Published Online: October 22, 2009
Article history
Received:
May 7, 2008
Revised:
July 23, 2009
Published:
October 22, 2009
Citation
Goicochea, J. V., Madrid, M., and Amon, C. (October 22, 2009). "Thermal Properties for Bulk Silicon Based on the Determination of Relaxation Times Using Molecular Dynamics." ASME. J. Heat Transfer. January 2010; 132(1): 012401. https://doi.org/10.1115/1.3211853
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