Cryogenic thermal transport properties from accelerated first-principles calculations: Role of boundary and isotope scattering

Thermal transport properties of materials at low temperatures have been a longstanding research topic. However, experimental thermal conductivity data in this regime are scarce and often limited to specific materials and geometries. The recently developed first-principles anharmonic lattice dynamics methods, which can accurately predict the modal phonon transport properties and thermal conductivity, suffer from significant computational challenges, particularly into the Kelvin temperature range. In this paper, we propose a parameter-free, accelerated first-principles approach for obtaining converged thermal conductivity at low temperatures by leveraging on the maximum likelihood estimation and optimizing phonon frequency cutoffs under relaxation time approximation. Specifically, converged thermal conductivities of Si with different sample sizes are obtained at temperatures as low as 5 K. Due to the dominance of boundary and isotope scattering, the difference in the converged simulation results of Si is within 10% with the experimental measurements at temperatures <20 K. The observed temperature dependence for samples with a 4 mm sample size is proportional to T-1.4 at low temperatures and changes to T-2 when accounting for the finite dimension in the direction of heat flux. When the sample sizes are reduced to the micrometer scale, the temperature dependence is restored to T-3, as predicted in the Casimir limit. Our analysis underscores the dominant influence of boundary and isotope scattering at low temperatures, while the size effect remains significant for samples with centimeter lengths. The proposed computational framework provides reliable tools to investigate thermal transport properties at low temperatures, and our comprehensive analysis yields insights into the temperature and size-dependent behavior of thermal conductivity under cryogenic conditions.