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Thermal Conductivity Calculation with the Molecular Dynamics Direct Method I: More Robust Simulations of Solid Materials

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A widespread technique to calculate thermal conductivity κ is the non-equilibrium direct method based on classical molecular dynamics, but despite its popularity there are still open questions regarding the data analysis. Here we use extensive simulations of bulk crystalline silicon with the Stillinger–Weber and Tersoff potentials as a test case to thoroughly examine the sensitivity to simulation parameters and fitting procedures in the solid state. We demonstrate that the transient behavior is well described by the solution to the continuum heat diffusion equation, so that no initial data has to be discarded. We show how best to fit temperature profiles while minimizing artifacts due to the non-linear regions which are usually present. The bulk thermal conductivity, κ , can be obtained by extrapolating to infinitely large systems, and we demonstrate that both periodic and non-periodic boundary conditions give the same value for κ when analyzed correctly using high-quality data. However, in some circumstances simulations with non-periodic boundary conditions do not appear to reach steady-state even after 20 ns. For bulk Si modeled with the Stillinger–Weber potential we obtain κ = 200±4 W/m-K at 500 K.
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Keywords: DIRECT METHOD; HEAT DIFFUSION; MOLECULAR DYNAMICS; SILICON; THERMAL CONDUCTIVITY

Document Type: Research Article

Publication date: October 1, 2011

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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