Investigation of Size Effect on the Emissivity of Thin Films

The size effect on the emissivity of thin films is analyzed via a direct method based on Maxwell’s equations combined with fluctuational electrodynamics. Traditional indirect approaches involve computation of absorption, and the emissivity is then predicted by invoking Kirchhoff’s law. The direct method employed in this work does not require Kirchhoff’s law. Instead, Kirchhoff’s law emerges naturally from the mathematical model. Simulation results reveal that the emissivity of metal films increase above bulk values as the film thickness decreases. This counterintuitive behavior is due to the extraneous contributions of waves experiencing multiple reflections within the thin layer, which are usually internally absorbed for metallic bulks. Conversely, for dielectrics, the emissivity of films decreases as the film thickness decreases due to a loss of source volume. The critical thickness above which no size effect is observed for metals is about a hundred of nanometers, while it is as large as a few centimeters for dielectrics. Finally, a simple approximate expression is suggested for evaluating the critical thickness; this expression can be used as a quick reference to determine if the size effect on the emissivity of thin films should be considered.