Understanding the thermal conductivity and heat transfer processes in superlattice structures is critical for the development of thermoelectric materials and optoelectronic devices based on quantum structures. This letter reports modeling of the heat transfer and thermal conductivity of superlattice structures based on solving the Boltzmann transport equation. Both diffuse and specular phonon scattering processes at interfaces are considered. The modeling results could explain recent experimental data on the cross-plane thermal conductivity of Si/Ge superlattices. Below the critical thickness, thermal conductivity is strongly influenced by diffuse interface scattering of phonons while above the critical thickness, dislocations are the dominant scattering centers in superlattices.

In this article we show that the global thermal resistance to flow between a volume and one point can be reduced to unprecedented levels by shaping the external boundary of each volume element. This degree of freedom is optimized, next to internal features such as the shape and volume fraction of the high-conductivity channels. The volume is covered in a sequence of optimization and assembly steps that proceeds toward larger sizes. The resulting architecture is a leaf-like tree structure with high-conductivity nerves and low-conductivity leaf material. The same constant resistance characterizes the flow from each point on the periphery of the structure to the common sink point. Nearly optimal structures in which the leaf shapes are replaced by needle-like (triangle-in-triangle) shapes are also developed. The fractal-like character of these designs and their relevance to the trend toward fractal-like properties in natural flow structures are discussed in the concluding section of the article.

Understanding the thermal conductivity and heat transfer processes in superlattice structures is critical for the development of thermoelectric materials and devices based on quantum structures. This work reports progress on the modeling of thermal conductivity of superlattice structures. Results from the models established based on the Boltzmann transport equation could explain existing experimental results on the thermal conductivity of semiconductor superlattices in both in plane and cross-plane directions. These results suggest the possibility of engineering the interfaces to further reduce thermal conductivity of superlattice structures.

This article extends to three-dimensional heat flow the constructal method of minimizing geometrically the thermal resistance between a heat-generating volume and one point. Optimized is the geometry of each volume element, and the shape and distribution of high-conductivity inserts. The new feature is the maximization of the amount of heat-generating material that operates at temperatures close to the hot-spot level (Tmax). Volume elements and subsequent constructs acquire optimal shapes where all the external surfaces are isothermal at Tmax. The same, constant thermal resistance separates each surface point (Tmax) and the common heat-sink point (Tmin). The optimized architecture is pine-cone-like, with high-conductivity nerves and low-conductivity filling (and heat-generating) material. The similarities between the constant-resistance structures and the three-dimensional tree networks found in nature are discussed. The analogy between evolutionary flow systems and evolutionary mechanical support systems is reasoned based on the same (constructal) principle of pursuing objective (purpose) subject to global and local constraints.

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