Size effect on the emissivity of thin films

Abstract

The size effect on the emissivity of thin films is analyzed. There are three methods for calculating film emissivity: the indirect method, the direct method based on the division of amplitude and the 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, based on Maxwell's equations and fluctuational electrodynamics, does not require Kirchhoff's law. Instead, Kirchhoff's law emerges naturally from the mathematical model. A closed form expression for thickness-dependent emissivity of thin films is derived from the direct approach, and it is shown that the three existing methods lead to the same aforementioned expression. Simulation results reveal that the emissivity of metallic films increases 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 can be as large as a few centimeters for dielectrics. A simple approximate expression is finally suggested for evaluating the critical thickness; this criterion can be used as a quick reference to determine if the size effect on the emissivity of thin films should be considered.