Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices

超晶格 热导率 声子 凝聚态物理 玻尔兹曼方程 材料科学 声子散射 散射 热传导 平均自由程 热电效应 镜面反射 弹道传导 热电材料 光学 物理 电子 复合材料 热力学 量子力学
作者
Gang Chen
出处
期刊:Physical review 卷期号:57 (23): 14958-14973 被引量:1068
标识
DOI:10.1103/physrevb.57.14958
摘要

Significant reductions in both the in-plane and cross-plane thermal conductivities of superlattices, in comparison to the values calculated from the Fourier heat conduction theory using bulk material properties, have been observed experimentally in recent years. Understanding the mechanisms controlling the thermal conductivities of superlattice structures is of considerable current interest for microelectronic and thermoelectric applications. In this work, models of the thermal conductivity and phonon transport in the direction perpendicular to the film plane of superlattices are established based on solving the phonon Boltzmann transport equation (BTE). Different phonon interface scattering mechanisms are considered, including elastic vs inelastic, and diffuse vs specular scattering of phonons. Numerical solution of the BTE yields the effective temperature distribution, thermal conductivity, and thermal boundary resistance (TBR) of the superlattices. The modeling results show that the effective thermal conductivity of superlattices in the perpendicular direction is generally controlled by phonon transport within each layer and the TBR between different layers. The TBR is no longer an intrinsic property of the interface, but depends on the layer thickness as well as the phonon mean free path. In the thin layer limit, phonon transport within each layer is ballistic, and the TBR dominates the effective thermal conductivity of superlattices. Approximate analytical solutions of the BTE are obtained for this thin-film limit. The modeling results based on partially specular and partially diffuse interface scattering processes are in reasonable agreement with recent experimental data on GaAs/AlAs and Si/Ge superlattices. From the modeling, it is concluded that the cross-plane thermal conductivity of these superlattices is controlled by diffuse and inelastic scattering processes at interfaces. Results of this work suggest that it is possible to make superlattice structures with thermal conductivity totally different from those of their constituting materials.
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