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The 3$\omega$ method is a dynamic measurement technique developed fordetermining the thermal conductivity of thin films or semi-infinite bulkmaterials. A simplified model is often applied to deduce the thermalconductivity from the slope of the real part of the ac temperature amplitude asa function of the logarithm of frequency, which in-turn brings a limitation onthe kind of samples under observation. In this work, we have measured thethermal conductivity of a forest of nanowires embedded in nanoporous aluminamembranes using the 3$\omega$ method. An analytical solution of 2D heatconduction is then used to model the multilayer system, considering theanisotropic thermal properties of the different layers, substrate thermalconductivity and their thicknesses. Data treatment is performed by fitting theexperimental results with the 2D model on two different sets of nanowires(silicon and BiSbTe) embedded in the matrix of nanoporous alumina template,having thermal conductivities that differ by at least one order of magnitude.These experimental results show that this method extends the applicability ofthe 3$\omega$ technique to more complex systems having anisotropic thermalproperties.

Measurement of anisotropic thermal conductivity of a dense forest of nanowires using the 3$\omega$ method