Optimum Design Method of Nanostructures for Thermoelectric Materials

Abstract

Thermal design in nanostructures is essential for developing miniaturized thermoelectric devices. The implementation of nanostructural designs utilizes a unique property of heat conduction, which is called as temperature jump on material interfaces. It lets us obtain novel high-performance thermoelectric materials. However, almost all reports proposed thermal-designs have been dependent on heuristic approaches and there is a large demand for constructing the optimal design methods for nanoscale thermal problems. In this paper, we propose a level set-based structural optimization method for thermoelectric materials focused on a nanoscale heat conduction problem. The level set-based method is a useful tool for a nanoscale thermal design, since the boundary effects are essential for developing novel material properties. First, we clarify a nanoscale heat conduction problem based on the Boltzmann transport equation, and define the design problem. Next, we compute a design sensitivity based on the shape sensitivity analysis. Then, we expand the level setbased structural optimization method to the nanostructural heat conduction problem. Finally, we show the validity of our proposed method via a numerical example.