Effect of shape in near-field thermal transfer for periodic structures

Abstract

In this paper, the effect of the geometrical shape on the radiative thermal transfer between a periodic array of beams and a planar substrate is investigated. Specifically, we analyze the changes in the thermal transfer that occur when the cross-sectional shape of SiC beams is modified from rectangular to ellipsoidal and finally triangular. Numerical calculations are done based on the rigorous coupled wave analysis. These exact results from this analysis are compared to modified proximity and far-field approximations, which become valid for small and large spacings, respectively. Moreover, these results are also compared to effective medium theory, which becomes increasingly accurate in the limit of small periodicities. We show that a reduction in the periodicity will lead to a reduced thermal transfer for triangular and ellipsoidal shaped beams. Even though, in the limit of very small periodicity, thermal transfer for the case of rectangular shaped beams also decreases by decreasing the periodicity, this decrease is slower as compared to other cross-sectional shapes. Finally, we show that even though changing periodicity will change the magnitude of thermal transfer, the scaling law for its variation with the beam to substrate spacing is primarily determined by the cross-sectional shape rather than the periodicity. We analytically prove this fact by investigating the large and small periodicity regimes.