Temperature gradient effects in an erbium aluminum garnet selective emitter

Spectral control through the use of selective emitters is an important means of improving the efficiency of thermophotovoltaic (TPV) systems. The thin-film selective emitters developed in our laboratory offer a number of potential advantages for use in such systems. It has long been realized, however, that there may exist relatively large temperature gradients across the thickness of these emitters in operation, and that such gradients are likely to have a detrimental impact on emitter performance. Previous efforts at modeling TPV emitter or system performance have either ignored thermal gradient effects or assumed the temperature profile to be linear (1–5). A detailed investigation of the temperature profile and subsequent effects on emitter performance has not yet been given. In this paper, we present results of a detailed theoretical and computational study of the effects of thermal gradients, along with some other film parameters, on the performance of an erbium aluminum garnet ${\mathrm{(Er}}_3{\mathrm{Al}}_5{O}_{12})$ selective emitter. Equations for the internal energy flux within the emitter are developed, under the assumption that heat transfer occurs via conduction and radiation. One face of the emitter is assumed to remain at fixed temperature, as would be the case if a thin emitter were in contact with a massive heat bath. The other face is assumed to experience either “vacuum interface” conditions, where heat transfer from the surface occurs via radiation only, or “lossy” conditions, where additional losses via conduction and convection are included. The temperature profile across the emitter thickness is computed by requiring that energy be conserved everywhere. We investigate the effects of the thermal gradient on the useful output power and emitter conversion efficiency. We also consider the sensitivity of the temperature gradient to the film and substrate physical properties.