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Abstract
The authors demonstrate both experimentally and numerically the high tunability that can be achieved in the optical response of sputtered multilayered metal-dielectric thin films. The wavelength dependence of both the transmission and reflectance is analyzed in terms of the geometrical parameters of transparent heterostructures consisting of alternating layers of Ag and SiO2. It is shown that these parameters can be adjusted to induce either a pass-band or a band-gap behavior in the visible range in a submicronic multilayered film.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The so-called physical vapor deposition (PVD) techniques are among the very enabling tools that have been used in a daily basis in the world of microelectronics and nanophotonics [1–5]. They have played a key role in the miniaturization revolution depicted in the Moore’s law [6]. Their capabilities have been successfully incorporated later into research areas such as spintronics [7] and optical materials [8]. Since then, iconic problems like mirrors, anti-reflecting coatings and UV filters have concentrated the research agendas. Systems that two decades ago were studied only either theoretically or numerically [9–11], have been fabricated in the last decade [12–14]. Thus, the study, design, and technological application of single and multilayered thin films, is a field full of possibilities due to the novel behaviors related to scale reduction down to the nano-metric scale [15,16]. In particular, the possibility of tailoring the opacity and/or the degree of transparency in a material, for a purposely chosen frequency band of the electromagnetic spectrum, is of great technological interest [8]. In this letter, we address the study of 1D periodic metal-dielectric bilayers (i.e. SiO2/Ag), fabricated via magnetron sputtering deposition, in order to induce either a pass-band or a band-gap behavior in the visible range in a submicronic thick multilayered film.
SiO2/Ag multilayers are structures that enable to obtain a “dilution” of the metallic optical behavior (e.g. a 200 nm Ag thickness split in 40 layers of 5nm each), which may lead to a tunable transmittance for, a priori, any optical wavelength range [10]. In these systems, the transmittance is enabled due to a resonance enhanced tunneling of electromagnetic waves. According to Scalora et al., who used an analytical approach, a transmission resonance occurs when the condition mL = 2λ is approximately satisfied, where m is an integer and L is the separation between the metallic layers, as a Fabry-Pérot cavity. On the other hand, effective-medium models, which provide insight about the overall metallic or dielectric behavior, are in agreement with that simple relation. Nevertheless, it must be noticed that the validity of these models does not longer hold for thick SiO2 layers (t > 50nm). Hereby, we explore these systems whose geometrical parameters lie in the vicinity of that limit. With this aim, we have fabricated a set of SiO2/Ag periodic multilayers, changing independently the thickness of the Ag and SiO2 layers, as well as the distance L between the Ag layers.
Contrary to the constraints exhibited in both e-beam and thermal evaporation techniques (where the very dissimilar deposition conditions are related to the thermal properties of the materials), in the sputtering process the only relevant feature of a material is whether it is an electrical conductor or not (which simply implies the choice between a DC and an RF power source). Among the various advantages of magnetron sputtering we find: extremely high adhesion of films; high deposition rates, which are very tunable since they are proportional to the power; excellent coverage of steps and small features; ability to coat heat-sensitive substrates; excellent uniformity on large-area substrates; and ease of sputtering any metal, alloy, or compound, into high-purity films [1,2,8].
2. Multilayered thin films deposition and structure
A series of multilayered dielectric-metal (SiO2/Ag) thin films were grown by DC and RF non-reactive magnetron sputtering deposition, at room temperature, under high vacuum. For this purpose, we utilized an AMOD vacuum deposition system (from Angstrom Engineering), using 2.00in in diameter (0.25in in thickness) Ag (99.99% purity, Kurt J Lesker) and SiO2 (99.995% purity, Kurt J Lesker) targets. For each multilayer stack, the deposition was simultaneously carried on glass (for the optical characterization) and on polished Si (100) substrates (for structural characterization). Prior to the stack deposition, the substrates were cleaned in situ under a low energy (i.e. 40 W) Argon RF plasma (Pbase = 1.0 × 10−7 Torr). The SiO2 films were grown using a RF source at 180W, whereas the Ag films were grown under a DC source at 90W, with an 20 sccm Ar flow and a working pressure PAr = 4.2 mTorr in both cases.
Cross-section (i.e. lateral views) images of the multilayer stacks were obtained by means of field-emission scanning electron microscopy (FE-SEM) using secondary electrons (SE) at intermediate probe (accelerating voltage) energy (i.e. less than 7 kV). The cross-section SEM images, as seen in Fig. 1, enabled us to measure the thickness of each layer, and thus to calculate the standard distribution of their thickness. From these measured thickness, we accurately calibrated the deposition rates for each material. The average deposition rates were determined to be 4.1 nm/min for the SiO2 and 40.5 nm/min for the Ag. These deposition rates are greater than the ones typically obtained with evaporation techniques. The observed grain size, however, is much smaller than the thinner Ag layer (i.e. dgrain << 13.5 nm), leading to the observed smooth surfaces.
Fig. 1. Cross-section images, obtained in a field-emission scanning electron microscope (FESEM), showing multilayered [SiO2/Ag]n stacks, for which the geometrical parameters (i.e. SiO2 thickness, Ag thickness and number n of bilayers) have been varied independently, with nominal thickness D = 55 nm for the SiO2 and d = 21 nm for Ag.
Table 1 shows the set of 14 different multilayer stacks that were fabricated using a base nominal thickness DSiO2 = 55 nm for the SiO2 layers and dAg = 21 nm for Ag layers. The average measured values were D = 55.2 nm ± 2.2 nm and 20.7 nm ± 1.5 nm. The stacks differ from each other in the number of SiO2/Ag bilayers (periods), SiO2 thickness and/or Ag thickness, as described in Table 1.
Table 1. Geometrical Parameters for the SiO2/Ag stacks
3. Optical characterization and trends of the optical response
In order to study the optical response of the sputtered multilayered films, the spectral dependence of both the reflectance and the transmittance were recorded by using a UV-Vis-NIR spectrophotometer (Cary 5000 from Agilent) in the 200 nm to 1000 nm wavelength range. Since sputtered thin films exhibit a grain size distribution, both diffuse and specular reflection are thus present, the reflectance measurements were consequently performed incorporating an integrating sphere. Figure 2 shows the wavelength dependence of the reflectance (left column) and the transmittance (right column).
Fig. 2. Spectral response of the reflectance (left column) and transmittance (right column) measured for the multilayered stacks. (a) and (b) show the effect of the number n of periods on the reflectance, and transmittance of the [SiO2/Ag]n stacks, respectively, keeping fixed the thickness of both the SiO2 (D = 55 nm) and the Ag (d = 21 nm) layers. (c) and (d) correspond to the reflectance and transmission response of the [SiO2/Ag]n multilayers under a variation of the Ag thickness, respectively. (e) and (f) show the effect of changes in the SiO2 thickness on the reflectance, and transmittance of the [SiO2/Ag]n stacks, respectively, keeping fixed the thickness d of the Ag layer and being n = 4.
Figure 2(a) and Fig. 2(b) show the effect of the number n of periods on the reflectance, and transmittance of the [SiO2/Ag]n stacks, respectively, keeping fixed the thickness of both the SiO2 (D = 55 nm) and the Ag (d = 21 nm) layers. In every case (i.e. n = 3, 4 and 8), the reflectance gradually drops from 80% in the infra-red to 15% in the blue-violet, going up again in the UV about 240 nm, a low-reflectivity band is thus observed in the 300 nm – 500 nm region. A number of resonances, related to the number of periods (bilayers) is also observed [9]. A minimum value of the reflectance value is observed at ∼325 nm for all the periods. Even in a case where the order of the bilayers has been inverted to [Ag/SiO2], corresponding to sample AMOD074, the overall trend is the same, only being the reflectance 10% larger in the referred band. On the other hand, more pronounced differences (up to 30%) are found in the transmission values when n changes [Fig. 2(b)]. Transmittance responses exhibit a clear pass-band in the 300 nm – 500 nm region. Also a well-defined peak is observed at 325 nm (related to the plasma frequency in silver). It is noticeable that the transmittance amplitude varies inversely with to the number of bilayers n, increasing by 17% from n = 8 to n = 4, and by 13% from n = 4 to n = 3. Inverting the order of the layers to [Ag/SiO2] barely affects the transmittance response.
Figure 2(c) and Fig. 2(d) correspond to the reflectance and transmission response of the [SiO2/Ag]n multilayers under a variation of the Ag thickness, respectively. The studied values are d, 2d, 3d, 2d/3, and 7d/6, keeping the thickness of the SiO2 layer D and the number of bilayers n constant. It is interesting to note that the reflectance for the 2d and 3d stacks is similar to that of a single Ag layer (i.e. very high reflectance in the near-IR and visible region down to 450 nm, with a step-like drop). Here, a number of resonances is also present. By diminishing the Ag thickness to 7d/6, the reflectance drops - from the 99% present in the 2d and 3d stacks, to ∼85% for the 550 nm – 1000 nm region. With a Ag thickness equal to d, the reflectance further drops by 10%. Moreover, for a Ag thickness equal to 2d/3 drastically drops the amplitude to 50% for the 550 nm – 1000 nm region. Adding a couple of bilayers (n = 4 + 2) to a stack with 2d/3 of Ag only leads to a small reduction (∼8%) in the reflectance. On the other hand, the transmittance measurements exhibit a pass-band in the 300 nm – 500 nm region, for all the Ag thickness values, with the transmittance reaching up to 30%. It can be seen that shape of the transmittance band is strongly affected by the Ag thickness: thicker layers are correlated to more square-like shapes. However, the most “squared” profile corresponds to a silver thickness equal to 7d/6 (∼24 nm). The role of the silver thickness is not straightforward since skin-depth related effects are particularly relevant in the measured wavelengths for the Ag thickness (∼20 nm) used in this study [10].
Figure 2(e) and Fig. 2(f) show the effect of changes in the SiO2 thickness on the reflectance, and transmittance of the [SiO2/Ag]n stacks, respectively, keeping fixed the thickness d of the Ag layer and being n = 4 . It is very remarkable that the optical response clearly shows two different behaviors. First, for SiO2 thickness D and D/2, the reflectance follows the trend of a single Ag layer (i.e. very-high/high reflectivity for λ > 550 nm, very-low/low reflectivity for λ < 550 nm). Second, for a SiO2 thickness 2D, the reflectance present a band-like behavior in the range 300 nm - 500 nm, reaching values up to 80%. A widening (towards 550 nm) of such band is observed when a bilayer is “removed” (n = 3). Equally remarkable is the transmission counterpart, seen in Fig. 2(f), where a transmission band is observed for D/2 (300nm-500nm) and D (300nm-500nm) but a band-gap (350 nm – 500 nm) appears for a 2D SiO2 thickness. In this case, changing n from 4 to 3 results in a gap 8% less pronounced. It is worth to notice that AMOD073 and AMOD088 are two samples with the same nominal stack, their slightly different optical responses being related to the dispersion in thickness of the real samples, which highlights how strong is the influence of the SiO2 thickness on the final properties of these systems.
4. Numerical modeling
Since the fabrication and experimental characterization of real samples is very demanding in resources, it would be useful to take advantage of the so-called numerical experiments (i.e. in silico modeling) for further studies on the systems described in this letter. With the aim of validating a simulation model for the multilayered stacks, we have evaluated their reflectance and transmittance spectra by means of a finite-element numerical methodology. Thus, we have performed simulations in the so-called real space, where the 3D electric field distribution is evaluated for the case of light with normal incidence.
The numerical model was built under COMSOL Multiphysics (ver5.4a), a software package based on the finite-element method; taking into account the dielectric function of materials, measured at the bulk [17,18]. Thanks to this software package, we can introduce into the numerical model the Floquet (i.e. periodic) boundary conditions (PBC), which enable the simulations to be carried out over large area samples [19–21]. By means of these conditions, the array can be modeled with a square unit cell containing only one portion of the sample. To achieve this task, we first use one of the cell’s top surfaces as a harmonic port of excitation, which illuminates the portion of the multilayer stack with a monochromatic plane wave. Then, we define the Floquet conditions on the lateral surfaces of the cell, which reproduce the behavior of an infinite stack based on the Floquet theorem. We additionally include two perfectly matched layers (or PML spaces) at the bottom and top of the cell to prevent reflections.
The reflectance and transmittance of the multilayered system can then be obtained by performing a two-port analysis, strategy successfully employed in nano-optics applications [22,23]. Through the analysis of the two-ports, one used for the input and the other for the output of the light, respectively, the numerical solver can generate the scattering parameters or S-parameters [24]. The transmittance and reflectance of light are defined in terms of the S-parameters throughout the relationships:
In order to mimic as much as possible the real structures, the actual (measured) values of the thickness were introduced in the simulations for every stack. The results are showed in Fig. 3.
Figure 3(a) and Fig. 3(b) show the numerical results concerning the effect of the number n of bilayers on the reflectance and transmittance response. It is found that the simulations follow the overall trends exhibit in the measurements. Notably, a transmission pass-band appears in the range 300 nm – 450 nm for all n, with the transmittance amplitude varies inversely with to the number of bilayers n, being 30% the difference between n = 8 and n = 3, as measured.
Fig. 3. Numerical results obtained for the spectral response of the reflectance (left column) and transmittance (right column) in the multilayered [SiO2/Ag]n stacks. (a) and (b) show the numerical results concerning the effect of the number n of bilayers. (c) and (d) correspond to the responses under a variation of the Ag thickness. (e) and (f) show the modeled effect of changes in the SiO2 thickness.
Figure 3(c) and Fig. 3(d) correspond to the simulated reflectance and transmission responses of the multilayers under a variation of the Ag thickness. Here, the trends are also similar to the measurements. The transmittance reproduces the presence of a pass-band in the 300 nm – 500 nm region, for all the Ag thickness values.
Finally, Fig. 3(e) and Fig. 3(f) show the modeled effect of changes in the SiO2 thickness on the reflectance, and transmittance of the stacks. Here again, the simulations reproduce the two behaviors measured in the reflectance (i.e. single-Ag-like and a high-reflectance band in the 300 nm – 450 nm), as well as the “transition” from pass-band to band-gas for the transmittance, well-defined in the 300 nm – 600 nm, as the SiO2 layer becomes thicker.
Once the numerical transmittance spectra were successfully validated with their experimental counterpart, a numerical analysis was performed in order to understand the physical mechanism behind the transmittance band (and peaks) beyond the optical behavior. For this purpose, a complete set of simulations were ran by changing the thickness of the SiO2 layer L of the [SiO2(L)/Ag (21nm)]4, stack. The obtained results unveil in a clear manner the co-existance of two different transmittance mechanisms: the expected transmission of light trough the stack due to the plasma frequency of silver (wavelength ∼325), and the tunneling enhancing resonances. In the first mechanism (appearing only for wavelengths around 325 nm) the stack completely behaves as a transparent dielectric or semiconductor material with a real effective refractive index. Note that all the stacks do present this transmittance peak; their amplitude can only be modified by changing the number of layers of the stacks, which modifies the number of reflectance surfaces (more reflectance surfaces lead to less transmittance).
The second transmission mechanism concerns the tunneling enhancing resonances, which can be resolved or tuned by means of the silicon dioxide layer. As previously indicated, transmittance by tunneling in a four-period stack must present three transmittance-peaks. Results clearly show that both mechanisms overlap for the case of the thin L layers, and splits as L increases. Transmittance by tunneling shifts linearly with the thickness of the SiO2 layers, and a quite simple relationship can be obtained by fitting the peaks positions, as shown in the inset of Fig. 4. On the other hand, for higher thickness, we can remark a second, third and even fourth band-gap appear. Those extra bands conform a set of sub-multiple wavelengths of the first transmittance band.
Fig. 4. Tuning of the transmittance response for [SiO2(L)/Ag (21nm)]4 stacks. The showed numerical results correspond to the wavelength-dependent transmittance for different SiO2 (L) thicknesses. L takes values from 10nm to 400 nm in steps of (390/18) ∼ 21 nm. At low SiO2 thickness, these results reveal the overlap of two different transmittance mechanisms: the Ag transparency at the plasma frequency and the tunneling enhanced resonances. For SiO2 thickness L > 100nm the two contributions split. The inset show the dependency on L of the position of the 3 peaks in the first band (highest wavelengths).
5. Conclusions
In summary, transparent 1D periodic heterostructures, consisting of alternating layers of Ag and SiO2, have been fabricated by magnetron DC and RF sputtering under high vacuum. The characteristic geometrical parameters of these structures (i.e. SiO2 thickness, Ag thickness and number of bilayers) were systematically and independently changed in order to address their influence on the transmittance and reflectance of the stacks. In the case of a variation in the number of bilayers, a clear transmission pass-band is found in the 300-500 nm for the nominal thickness values (D and d), with the amplitude decreasing as the number of bilayers grows. A similar effect has the change of the silver thickness on the transmission amplitude, being also observed that the pass-band region is not modified by the variation of the Ag thickness. Nevertheless, changing the Ag thickness displaces the reflectance response both in wavelength and intensity. Furthermore, it is found that by doubling the thickness of the SiO2 layer, the reflectance response changes from a step-like shape to a high reflectance band in the 300-450 nm, and that the transmission pass-band is turned into a band-gap in the 300-500 nm zone. The trends of all these experimental observations are replicated by the in silico simulations, thus validating the proposed numerical model. From this model we have studied the evolution of the transmittance (wavelength dependence) for several values of the SiO2 thickness, which resulted to be the most influential parameter for tuning the optical response. It is clearly demonstrated the evolution of such response from a pass-band at low SiO2 thickness to the appearance of several band-gaps for thicker values.
Funding
Catedras-CONACYT Project 925 (ID1088); Sistema Nacional de Investigadores (40859).
Acknowledgments
Technical support from Christian Albor at the Materials Characterization Laboratory (CIO) is greatly acknowledged.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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