Deep learning molecular dynamics simulation on microwave high-temperature dielectric function of silicon nitride

Abstract

Silicon nitride (<i>β</i>-Si<sub>3</sub>N<sub>4</sub>) is the most promising thermal wave-transparent material. The accurate measurement of its high-temperature dielectric function is essential to solve the "black barrier" problem of hypersonic vehicles and accelerate the design of silicon nitride-based thermal wave-transparent materials. Direct experimental measurements at high temperature are challenging and the accuracy of classical molecular dynamics (CMD) simulations suffers from the choice of empirical potential. In this work, we build a <i>β</i>-Si<sub>3</sub>N<sub>4</sub> model at nanoscale, train the deep learning potential (DLP) using first-principles data, and apply deep potential molecular dynamics (DPMD) to simulate polarization relaxation process. The predicted energy and force by DLP are excellently consistent with first-principles calculations, which proves the high accuracy of DLP. The RMSEs for <i>β</i>-Si<sub>3</sub>N<sub>4</sub>are quite low (0.00550 meV/atom for energy and 7.800 meV/Å for force). According to the Cole-Cole formula, the microwave dielectric function in the temperature range 300-1000 K was calculated by using the deep learning molecular dynamics method. Compared with the empirical potential, the computational results of the DLP are consistent with the experimental results in order of magnitude. It is also found that the DPMD performs well in terms of computational speed. In addition, a mathematical model of the temperature dependence of the relaxation time was established to reveal the pattern of relaxation time varies with temperature. This work calculates the high-temperature microwave dielectric function of silicon nitride by implementing large-scale and high-precision molecular dynamics simulations. It provides fundamental data to promote the application of silicon nitride in high-temperature thermal transmission.