P. Pigeat et al., CALCULATION OF THERMAL EMISSIVITY FOR THIN-FILMS BY A DIRECT METHOD, Physical review. B, Condensed matter, 57(15), 1998, pp. 9293-9300
The emissivity variation of a body, according to the modifications of
its surface, has been described by two kinds of arguments. A direct ar
gument consists in adding the energy, leaving each element of volume d
V, considered as independent and incoherent Planckian radiators, weigh
ted by its transmissions and its possible reflections. An indirect arg
ument consists in assuming the validity of Kirchhoffs law. The emissiv
ity is then deduced from the absorption coefficient calculated by usin
g a huge collection of theoretical means. However, in the case of very
thin films deposited on a substrate, the emissivity calculated accord
ing to their thickness does not give the same results, depending on th
e argument used. As a matter of fact, up to now the direct argument di
d not allow a description of interferential phenomena. Such phenomena
are still observed when the film thickness is lower than, or of the sa
me 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 indirec
t method leads to an argument by default, which occults a part of the
physics implied. Here, a direct model is proposed, only based on emiss
ion phenomena. This direct theory allows a description of the interfer
ential behavior in thermal radiation, by taking into account the self-
coherence of the emitted waves, in contrast to the previous direct app
roach. It is shown that this approach accounts for the experimental be
havior of growing thin films. [S0163-1829(98)01812-8].