Improved Debye–Callaway model for calculating the lattice thermal conductivity of anisotropic two-dimensional crystals

Thermal management in two-dimensional (2D) materials is pivotal, given their extensive technological utility in miniaturized devices. However, an expedient yet precise method for predicting the thermal transport properties of 2D materials remains to be established. In this study, we derive analytical formulas for calculating the scattering rate of three-phonon Umklapp processes, specifically tailored to 2D materials, based on the continuous elasticity assumption, quasi-harmonic approximation, and central force approximation. These formulas enable the construction of a refined Debye-Callaway model that incorporates the effects of both three-phonon Umklapp scattering and boundary scattering, eliminating the need for any fitting parameters. Notably, we explicitly disentangle the contributions of optical phonons, treating them within a framework analogous to the Einstein model. This improved model facilitates efficient and accurate predictions of the anisotropic lattice thermal conductivities in 2D materials. The results generated by our model for 12 2D crystals show excellent agreement with those from fully first-principles calculations reported in the literature. In particular, this study clarifies how the relaxation time fitting parameter adopted in previous work depends on the crystal structure and dimensional characteristics of the materials. It also provides an understanding of the logarithmic divergence of lattice thermal conductivity with respect to the size of 2D crystals within a framework involving only three-phonon scattering processes and Debye approximation. Owing to its low computational cost and high prediction precision, this model can serve as a valuable tool for high-throughput screening and machine learning applications in the identification of 2D materials with tailored thermal conductivity.