Frequency domain thermoreflectance (FDTR) imaging is used to create quantitative maps of both in-plane thermal conductance and cross-plane thermal boundary conductance (TBC) for graphene multilayers encased between titanium and silicon dioxide. A graphene flake is encased between a metal layer and a thermally oxidized p-type silicon wafer and a piezo stage is used to raster scan the sample for imaging. For each image pixel, a periodically modulated continuous-wave laser (the red pump beam) is focused to a Gaussian spot, less than 2 um in diameter, that locally heats the sample, while a second beam (the green probe beam) monitors the surface temperature through a proportional change in reflectivity. The pump beam is modulated simultaneously at six frequencies and the thermal properties of the graphene flake are extracted by minimizing the error between the measured probe phase lag at each frequency and an analytical solution to the heat diffusion equation in a multilayer stack of materials. Phase images at six frequencies for the sample are shown in b. Different layers of the graphene flake are clearly shown in 9.9 MHz and 11.3 MHz images. The six phase data points at every pixel are then fitted to our thermal model to generate two thermal property maps of the graphene flake: in-plane thermal conductance and TBC, shown in c. The in-plane thermal conductance map shows an increased conduction of heat in graphene with the number of layers, while the TBC map indicates a constant cross-plane conduction along the flake. Our imaging technique can be used to study thermal transport in graphene and has implications for thermal management in graphene based electronic devices.

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