* Corresponding author. Present address: LET-ENSMA, BP 109, 86960 Futurscope Cedex, France. Fax: # 33-5-4949-8101; e-mail: volz@let.ensma.fr. Physica B 263—264 (1999) 709—712 Lattice dynamic simulation of silicon thermal conductivity S. Volz*, G. Chen Mechanical and Aerospace Engineering Department, University of California, Box 951597, Los Angeles, CA 90095-1597, USA Abstract In this work, we perform MD simulations of the thermal conductivity of bulk silicon single crystals from a computa- tion domain smaller than the phonon mean free path. We impose cyclic boundary conditions in all directions and assume that the phonon scattering is not affected since phonon energy and momentum are conserved through the boundaries. The wavelength cut-off issue due to the system size is corrected via spectral analysis of the heat flux so that the thermal conductivity values become size independent. The consistency of our assumptions is supported by a set of runs probing the sensitivity of the simulation results to temperature and system size.  1999 Elsevier Science B.V. All rights reserved. Keywords: Thermal conductivity; Molecular dynamics; Silicon In this work, we performed thermal conductivity computations of bulk silicon crystals using the mo- lecular dynamics technique (MD) which consists of solving all the particle trajectories of a given sys- tem. If it is taken that the minimum computational size must be of the order of one phonon mean free path, around 100 million atoms should be modeled to retrieve the complete energy transport character- istics. Nevertheless, we will support the idea that the limiting factor to calculate the thermal conductivity is relevant to the phonon wavelength limit imposed by the system size rather than the phonon mean free path. Then, we will use a spectral analysis method [1] to take this wavelength cut-off into consideration. The MD technique gives a deterministic non- quantum description of an N-atom system by calcu- lating the position r  and velocity v  of each atom according to the Newton’s second law. To derive the force term, we choose the Stillinger—Weber po- tential [2] which is reliable to describe the silicon thermal properties. Starting from the variables r  , v  and the interaction force F  , it is possible to derive the three main thermal quantities i.e. temperature, heat flux and thermal conductivity. Temperature seems easy to compute since the Boltzmann distribution function allows the straight- forward derivation of the kinetic energy E  in the following way: E  " 1 2 M    v  " 3 2 Nk  ¹  , (1) where k  is the Boltzmann constant and N is the number of particles in the system. However, the validity of Eq. (1) depends on the condition that the heat capacity is not temperature dependent. 0921-4526/99/$ — see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 4 5 3 - 7