Analytical expression for thermal conductivity of superlattices

摘要

The increasing interest in manufacturing nanoscale low thermal conductivity devices has made important to obtain simple expressions that can predict their transport properties. This is more necessary for superlattice structures, where size effects and interface resistance effects can make the models very cumbersome. In this work we propose a simple analytical expression that can predict in-plane and cross-plane values of thermal conductivity of superlattices from an approximate analytical expression that joins a model expansion of the Boltzmann equation with a combination of the acoustic mismatch model and diffuse mismatch model for thermal boundary resistance. The obtained values are compared to experimental data from AlAs/GaAs, Si/Ge, and Si/Si_(0.7)Ge_(0.3) and a reasonable fit is obtained. Special attention is paid to the low thermal conductivity predicted in the Si/Ge large period range, which current microscale models fail to predict but which are approximately described in the present model.