Research of thermal properties of nanomaterials on the silicon basis by the Green-Kubo method using the EDIP potential

Physical and mathematical models of processes of thermal conductivity in silicon nanomaterials with use of an interaction potential of EDIP are constructed. The molecular dynamics method was used as the simulation method. In this work the formalism of Green-Kubo, which connects an autocorrelation function of a heat flux with a thermal conductivity, is used. The simulation was performed using the software package LAMMPS. The EDIP potential was used for the description of interaction of atoms of system. The integration step was $0.1$ fs. Autocorrelation functions, radial distribution functions, phonon distribution functions were constructed by results of calculations. Researches showed a possibility of use of the offered mathematical model and the considered potential for simulation of thermal conductivity processes.
Dependences of a thermal conductivity of silicon on temperature (in the range from $50$ to $1000$ K) for crystals of various sizes ($4 \times 4 \times 4$, $4 \times 4 \times 40$, $4 \times 4 \times 144$) are defined. The results of computer simulation showed that the coefficient of thermal conductivity decreases with increasing temperature. It's confirmed by the experimental studies, the results of which are given in [41, 42].
At temperatures above the Debye temperature the calculated values of the coefficient of thermal conductivity coincide with the experimental data [41, 42]. This suggests the possibility of application of the constructed models for calculation of thermophysical properties of nanosystems and predicting values of these parameters for macro-systems.