A Green function approach is used with the fluctuation-dissipation theorem to develop a qualitative theoretical model of radiation heat transfer across an evacuated microscale spherical geometry bounded by silicon carbide. The appropriate scalar Green function is presented by employing an impedance boundary condition to describe the electromagnetic spherical interface condition and thus capture the surface modes. This work shows that the spherical boundary can result in spectral conditions for surface mode excitation that depend not only on the dielectric function, but on the sphere radius as well. The surface modes are shown to enhance the radiation significantly and are attributed to surface phonon polariton modes excited at the interface, and surface modes excited by the mechanism of total internal reflection.
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