Measuring thermal conductivity of nanostructures with the 3 & omega; method: the need for finite element modeling

Conventional techniques of measuring thermal transport properties may be unreliable or unwieldy when applied to nanostructures. However, a simple, all-electrical technique is available for all samples featuring high-aspect-ratio: the 3? method. Nonetheless, its usual formulation relies on simple analytical results which may break down in real experimental conditions. In this work we clarify these limits and quantify them via adimensional numbers and present a more accurate, numerical solution to the 3? problem based on the Finite Element Method (FEM). Finally, we present a comparison of the two methods on experimental datasets from InAsSb nanostructures with different thermal transport properties, to stress the crucial need of a FEM counterpart to 3? measurements in nanostructures with low thermal conductivity.