A model for the lattice thermal conductivity of nanocrystalline materials with arbitrary grain size distribution

Abstract

Nanocrystalline materials are a popular metamaterial used to control heat transport in semiconductor industrial applications. An accurate and reliable theoretical model is urgently needed but challenging for elucidating detailed microscopic heat transfer phenomena. In this study, we develop a mathematical model to predict the lattice thermal conductivity of nanocrystalline materials with arbitrary grain size distribution. The model first obtains the effective scattering rate of grain boundaries in single-grain-size materials, and then integrates the Landauer’s system transmission concept and series transmission concept to become applicable to multiple grain sizes. It takes into account not only intrinsic and grain boundary scattering effects, but also the effects of finite system size and grain size distribution. Numerical samples of silicon nanocrystals with single grain size, dual size, constant grain size distribution, and logarithmic normal grain size distribution are constructed and full-spectrum Monte Carlo simulations are performed for comparison. The excellent agreement observed between model predictions and simulation results validates the accuracy of the proposed theoretical model. This model will be very helpful in designing micron-scale thermal manipulation systems using nanostructures.