Calculation of thermal emissivity for thin films by a direct method

The emissivity variation of a body, according to the modifications of its surface, has been described by two kinds of arguments. A direct argument consists in adding the energy, leaving each element of volume $dV,$ considered as independent and incoherent Planckian radiators, weighted by its transmissions and its possible reflections. An indirect argument consists in assuming the validity of Kirchhoff’s law. The emissivity is then deduced from the absorption coefficient calculated by using a huge collection of theoretical means. However, in the case of very thin films deposited on a substrate, the emissivity calculated according to their thickness does not give the same results, depending on the argument used. As a matter of fact, up to now the direct argument did not allow a description of interferential phenomena. Such phenomena are still observed when the film thickness is lower than, or of the same order of magnitude as the wavelength of the radiation concerned. On the other hand, the use of Kirchhoff’s law requires delicate handling in the case of mesoscopical structure materials. Besides, the indirect method leads to an argument by default, which occults a part of the physics implied. Here, a direct model is proposed, only based on emission phenomena. This direct theory allows a description of the interferential behavior in thermal radiation, by taking into account the self-coherence of the emitted waves, in contrast to the previous direct approach. It is shown that this approach accounts for the experimental behavior of growing thin films.