Calculation of Thermal Conductivity from Molecular Dynamics Simulations

**Jianwei Che**, Tahir Cagin, and William A. Goddard III

Materials and Process Simulation Center, Beckman Institute

California Institute of Technology, Pasadena, CA 91125

Abstract

Based on the fluctuation – dissipation relation in linear response theory, in particular the Green – Kubo relation, we calculated the lattice thermal conductivity through the thermal current auto-correlation functions from classical molecular dynamics (MD) simulations. The quantum corrections were discussed in the harmonic approximation and concluded that these effects are usually small for fairly harmonic systems such as crystalline and strongly covalent materials.

Our calculations find that (at 300 K) ^{12}C isotropically pure perfect diamond has a thermal conductivity 45% higher that natural (1.1% ^{13}C) diamond. This agrees well with experiments that showed a 40% to 50% increasing. Using MD simulations allow us to directly predict the thermal conductivity of novel materials long before experimental measurements can be performed, such as for nanoscale structures. The properties of material thin layers down to the atomic level have been increasingly important recently because of the progress in shrinking the size of electronics. One of the critical issues there is the thermal management at this level. Our calculation is capable of predicting the thermal conductivity of materials from fundamental microscopic information (i.e. atomic interaction and configuration), which can be well utilized in the design of nanoscale functional devices. As one example, we predicted the behavior of the thermal conductivity of a prototype material as a function of layer thickness. The simulation results are compared with our phenomenological model, and find that the continuum phenomenological model is valid even when the layer thickness is quite small (> 6 atomic layers). The results show the importance and limit of continuum model. The second example is to calculate the thermal conductivity of carbon nanotubes. The mechanical and electronic properties of carbon nanotubes have been studied extensively in both theory and experiments, however, the thermal conductivity has only been studied very recently by few experimental groups, primarily because of the technical challenging of preparing high quality samples required by thermal conductivity measurements. To our knowledge, our prediction of carbon nanotube thermal conductivity is the first to date. We find that carbon nanotube has fairly high thermal conductivity along the tube direction, which is comparable to those in pure diamond and in-plane graphite. In the perpendicular direction to the carbon nanotueb, the thermal conductivity is very small, which is also similar to graphite perpendicular direction.

In summary, the calculation of thermal conductivity via MD simulations is a powerful tool to investigate novel materials for which experiments are difficult to perform. The results can be very useful in design of nanoscale functional devices.

Fig.1, Thermal conductivity as a function of layer thickness of a sphalerite structure. The solid lines are the predictions of phenomenological model, the filled circles are the simulated results for the perpendicular direction, and the open circles are the simulated results for the parallel direction. The dashed curves are the phenomenological model modified by an order parameter.

Fig.2, The thermal conductivity of carbon nanotube (10,10) as a function of the periodic simulation cell length along the tube direction. The Error bars are estimated from (2t/t_{run})^{1/2}.