3.1. Thin Film Surface Structure
First, we investigated the films surface morphology evolution over time using a scanning electron microscope (Figure 2
). One can find that after long-time storage (more than 7.5 months) cracks appear on almost all the silver films and thicker films have also volumetric inhomogeneities. These defects grow and become much bigger after 19 months in the atmosphere (SEM images of the 25 nm and 70 nm thick silver films are shown separately at lower magnifications (Figure 3
)). We observed through-depth defects (holes) in 25 nm thick film (Figure 3
a) and the emergence of voids (not full depth holes) in 70 nm thick film (Figure 3
In order to investigate the nature of these defects, and make some conclusions on the degradation mechanism (silver films material consumption due to chemical reactions, film surface roughness evolution) and assumptions on the layers stack for ellipsometry model, we measured all the samples using SEM at the cross section (Figure 4
). No significant change in the average films thickness was found. However, after a certain period of time, above the silver film additional growing layers (additional roughness) was observed, which form an inhomogeneous structure in the form of protrusions. As it is shown below, these additional growing layers have nonmetallic optical properties pointing on the products of chemical reactions on the silver surface over time.
Both SEM cross sections (Figure 4
) and stylus profiler measurements (Figure 5
) shows that silver films surface root-mean-square (RMS) roughness is increased monotonically over 19 months. Looking precisely at the SEM cross sections, one can see that very large (order of half film thickness) defects appear on the films’ surface after 19 months. It should be noted that these large defects on the first plan of SEM images (35 nm thick silver film after 19 months, Figure 4
) could be the result of stress relaxation during substrate cleaving process for cross section measurements. One piece of evidence for this is that these defects could be seen on the cleaved (fresh) sidewall surface of 50 nm thick film after 19 months, for example.
The original films were examined by the EBSD method (Figure 6
), which confirms that all the films have a single-crystalline structure with small angles of terraces disorientation.
3.2. Optical Constants
As a result of modeling the ellipsometric data, the dielectric constant dispersions of thin silver films were determined. For simulations, the film array was divided into the main film and the roughness layer (Figure 7
) according to SEM cross section data. The main film was simulated using the Brendel-Bormann model [34
]. For roughness simulation the Bruggeman model was used [35
]. This particular model can be used when inclusions are macroscopic particles, and the matrix cannot be distinguished. Figure 8
, Figure 9
, Figure 10
and Figure 11
show two sets of ε’’ dispersions corresponding to the main layer of the films (a) and the roughness layer (b).
As shown in Figure 8
, Figure 9
, Figure 10
and Figure 11
, ε’’ values (responsible for the losses) at longer wavelengths (600–1000 nm) change over time for all the samples. For the 25 nm film, the losses increase during the first hours right after the deposition process, but then decrease and practically do not change after 1 month, remaining around 0.6 (hereinafter, at 1000 nm) until the expiration of 19 months. For the 35 nm film, the same trend, except for 2 months, when ε’’ increased, is observed. As a result, the value ε’’ decreases down to 0.4 in 7.5 months. For the 50 nm film, ε’’ values stabilized even faster. After 24 h, they stopped changing and stabilized at 0.9. Finally, ε’’ values of the 70 nm film exceed 1.0 right after the deposition process and do not change over time. In general, we can see that the thicker the film, the faster ε’’ values at longer wavelengths stop changing over time. It should be noted that the effect of the roughness layer is negligible in the considered wavelength range, because of the lack of absorption in the roughness layer as seen from the spectrum ε’’ (b).
Changes at the wavelengths around 350–600 nm have a more complex nature because an interband transition occurs here.
At the same time, the absorption values of the roughness layer are nonzero. For the 25 nm film, the interband transition shifts towards longer wavelengths up to 500 nm after 19 months, where the plasmon resonance of the roughness layer is absent. The observed shift can be explained by the growth of size and number of the main film layer defects, which can be seen from the SEM image in Figure 2
and Figure 3
(holes appear). It was observed in [36
] that the defects influence the interband transition position (Lorentz peak), leading to the amplitude increase and the interband transition shift. However, the plasmon resonance position in the roughness layer indicates that some defects will cause absorption peaking at 350 nm. The shape, amplitude and maximum position of the Lorentz band is intrinsically connected to the RMS-to-thickness ratio and originates not only from the contribution of the interband transitions in the Brillouin zone, but also from the intraband transitions as well as surface plasmon-polariton excitations [32
]. For SCULL films the RMS-to-thickness ratio is lower and thus intraband transitions and localized plasmon coupling are limited. This results in a narrow and diminished Lorentz-shaped band.
For the 35 nm film, we observe a similar tendency, when starting from 1 month, the interband transition position in the main film layer is shifted to the wavelength of 450 nm, which is explained by defects size growth on the surface, forming a rough layer. The peaks of the roughness layer for 1 and 7.5 months are characterized by the maximum at 400 nm. It indicates the presence of various-size defects, which leads to absorption existence in the entire range of 350–550 nm. In the plots for 19 months of observations, we see the emergence of a significant interband transition peak with the increased amplitude right-shifted to 500 nm. However, there was no roughness effect, consequently, it is completely determined by the defects of the main film. The influence of its roughness layer, as in the previous two months, is left-shifted with a peak at 350 nm.
For the 50 nm film, no interband transition peaks are observed, which means the morphological defects mainly manifest themselves in the dispersion of the roughness layer. Thus, the defects acquire such a shape that can be completely attributed to the roughness layer, which can seen in the SEM cross section images for these films. This phenomenon is especially visible in the image for the 50 nm film at 19 months. The absorption bands of the roughness layers for the 50 nm film are characterized by a great variety ranging from 330 nm to 400 nm.
For the 70 nm film, an interband transition in the main layer was observed during the first month. After the first month, the transition disappeared. From the SEM cross section images analysis, we conclude that morphological defects form a distinct layer of roughness over time and change optical properties of the roughness layer. At the same time, the absorption bands of the 70 nm thick film roughness layers lie close to each other in the range of 350–360 nm.
The roughness thickness and silver/air ratio used in calculation have been estimated from the SEM cross section images of the films.