In this work, electronic thermal conduction in thin gold film is modeled via the Boltzmann Transport Equation (BTE). The BTE is solved using a Monte Carlo Method (MCM). Temperature profiles for various film thicknesses are computed. Results show that the electronic thermal transport in gold is still diffusion-like at film thicknesses as small as 100 nm, implying that the Fourier law of conduction can be applied at this scale to predict the steady-state thermal heat transfer without comprising the physics. However, the Fourier law does not predict the temperature profiles accurately if the film thickness is reduced to 10 nm or below.

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