1. Introduction

Subwavelength structured optical surfaces have proven their ability to overcome the limitations of classical layer based anti-reflective (AR-) coatings, in particular in terms of broadband capabilities and usability over an extremely wide range of incidence angles [1–5]. The advantageous characteristics of such structured AR-coatings open up a wide scope of applications including the increase of the light output power of light-emitting diodes [6,7], enhance IR-detector efficiency [8], reduce disturbing reflections on flat-panel displays [9,10] and imaging lenses [11], or improve the light harvesting efficiency in photovoltaic systems [12–14] to mention only a few. These subwavelength structures are also found in nature, for example on transparent butterfly wings [15] or on the corneal surfaces of night active insects [16,17]. With respect to the last-mentioned biological model, these AR subwavelength structures are commonly referred to as ‘moth-eye structures’.

Instead of interference effects as used in conventional alternating layer stacks, the AR properties of ‘moth-eye structures’ are based on a gradual decrease of the effective refractive index bridging the transition from the bulk material to the environmental medium. The advantages of graded refractive index (GRIN) AR-coatings were already suggested by Lord Rayleigh [18] in 1879 and are based on avoiding a sharp, step-like transition between interfacing optical media, and therefore allows to minimize Fresnel reflection losses. Southwell [19] compared by simulations different refractive index transition profiles and calculated their antireflection performance. For a linear decrease of the refractive index from 2.4 to 1.6 a reflectance below 0.01% was theoretically calculated, for a quintic profile the reflectance is reduced below 10⁻⁷. Both values are less than typical unavoidable deviations in manufacturing processes. In general, the requirements for appropriate GRIN-AR layers are theoretically well defined, the practical realization is still challenging. One of the first approaches was based on alternating layers of high- and low-index materials in which the thickness of each layer was much smaller than the wavelength of the light used [20]. This stacking sequence can be approximated as an effective continuous transition with a refractive index tuned by the volume ratio of both involved materials. The refractive index of the layer varies effectively between that of the two materials, but especially cannot fall below the value of the low-index material. In particular homogenous, dense materials with a refractive index lower than ∼1.35 in the visible wavelength range are not known. Here, ‘moth-eye’-AR-structures, as uniformly shaped tapered pillars with a periodicity smaller than half of the minimum operating wavelength, have established as an attractive alternative. The small periodicity and the height dependent pillar to space ratio of the structure is offering an effective refractive index gradient from the value of the bulk material down to ∼1 of the ambient air. A similar functionality is also provided by stochastically arranged nanostructures. In the last years, a large number of different technologies have been developed to artificially generate such structured GRIN-AR coatings. An overview of the different fabrication techniques is presented in [21,22].

In opposition to the broad diversity of different manufacturing techniques to create ‘moth-eye’ structures, the transfer to any optical material is still not be solved. A particular challenge concerns the applicability of ‘moth-eye’-structures to optical high-index inorganic glasses, which are crucial for high-end optical systems such as photo cameras, binoculars, microscope objectives or ophthalmological instruments. The limitations of the transferability of the various manufacturing technologies can be attributed to different factors. Generally, Schulz et al. [23] point out, that in a large number of the developed technologies the achievable structure depth or layer thickness is less than 200 nm and to provide an effective index of these structures lower than 1.2 is still challenging. Therefore, some of the layers act rather as a single layer with low index and show only weak gradient characteristics. Furthermore, some technologies do not allow a direct subwavelength structuring of the optical substrate itself but requires an additional layer of a specific material on top of the substrate in which the ‘moth-eye’ structures are formed by micro- and nanotechnologies such as imprinting, lithography or etching steps (e.g. [13,15,24]). In these cases, a step-like transition between the limited refractive index of the ‘moth-eye’ layer and the contacting high-index material is not avoidable and therefore causes reflection losses. Other techniques allow the direct structuring of optical element substrate, for example via dry-etching processes, but most of them are limited to a small selection of bulk materials such as fused silica, selected semiconductor materials or specific polymers [25]. A transfer of the structuring technology to other optical materials is often very challenging, in particular in terms of finding the appropriate process parameters for each new material composition and frequently it is even not possible to find any approach. In particular, the direct etching of precision optical glass is difficult because fluorine compounds are required to remove material. Further restrictions of specific structuring technologies concern the applicable wavelength range. Here for example, statistically distributed AR-structures often show a short wavelength limit, so that the AR-property is lost in the deep blue or UV wavelength range [26].

In order to overcome the mentioned challenges and limitations of ‘moth-eye’- or stochastic-AR-structures on various substrates, in particular on high-index materials different alternative approaches were proposed and developed. In this context the combination of homogeneous interference based thin-film layers with a subwavelength structured top layer has proven advantageous AR characteristics. In one solution [27] of these hybrid AR-systems, a single layer with homogeneous refractive index of an intermediate value (n_layer ∼ 1.56) was sandwiched between a high index substrate (n_sub = 1.84) and an outer layer of a porous film offering a gradient refractive index between 1 and 1.4. More sophisticated hybrid-approaches combined a stack of multiple interference layers of alternating high-low index materials with a final subwavelength AR-structure [3,28–31]. Here, for the low index material of the interference stack typically homogeneous layers of SiO₂ or MgF₂ were used and for the high index layers, materials such as Nb₂O₅, Ta₂O₅ and TiO₂ were applied. Exemplary, porous MgF₂ or porous polymer layers (e.g. PMMA: Polymethylmethacrylate) served as the final subwavelength structured coating. In other hybrid approaches inorganic step-down layer designs combined with organic nanostructures and organic nanostructures covered with inorganic materials were developed to gradual reduce the refractive index of the layer system [24]. Due to the specific material selection necessary for the implementation the last concept cannot be easily and optimally adapted to high index substrate materials.

In this contribution, we introduce an ideally adapted AR-system, offering a continuous gradual reduction of the refractive index in the coating from a high index substrate down to ambient air. The presented approach is not limited only to a few specific materials but it is applicable to a broad material selection and eliminates any step-like transition up to refractive index of the substrate of n_sub ∼2.0. The implementation was demonstrated as an AR-coating for a high-index precision optical inorganic glass, in particular for ‘Schott glass’ N-SF10 with n_N-SF10= 1.727 (@ 600 nm) [32]. The fabrication process involves two main steps. In the first step a GRIN layer of dense silicon oxy-nitride material is deposited on the high index glass. An adjustment of the oxygen to nitride ratio allows to tune the refractive index of the GRIN layer at the contact area to that of the substrate. With increasing growing height the refractive index of the GRIN layer is continuously reduced. In the second step a subwavelength periodic “moth-eye structure” is added to the dense GRIN layer. The specific manufacturing process for these “moth-eye structures” in SiO₂ is based on a combination of block copolymer micelle nanolithography (BCML) followed by a reactive-ion-etching (RIE) process [1,33]. The combined BCML-RIE process offers a high flexibility. In addition to plane substrates and lenses this process is also applicable to microlens-arrays [34] and diffraction gratings [35]. Furthermore, the useable wavelength range can be extended to both the ultraviolet (UV) [36] and to the near-infrared (NIR) [37]. In summary, by the combination of both process steps a continuous transition of the effective refractive index from the value of the high index inorganic glass to ambient air is achieved. In addition to the advantages concerning the AR property of the GRIN layer it also acts as a barrier layer to protect the sensitive high index substrate from corrosion damage potentially originated by disturbing external environmental influences.

2. Concept and implementation of combined dense graded index and ‘moth-eye’ AR-coating

Figure 1(a) shows a three-dimensional graphical representation of the hybrid GRIN-AR-structure. On top of the high index precision glass a dense GRIN layer is deposited. Directly at the interface the refractive index of the GRIN layer is precisely adjusted to the value of the substrate at 600 nm, so that an index discontinuity is avoided.

 

Fig. 1. Fabrication and structure of the hybrid ‘moth-eye’ - dense GRIN layer antireflective coating (ARC). (a) Schematic representation of the entire structure consisting of substrate (blue), dense GRIN layer (color-gradient blue to red), and SiO₂ moth-eye structures. The hybrid ARC offers a smooth transition of the refractive index from the substrate to air (see schematic on the right). (b) Sputter rate and refractive index of the Si_xO_yN_z layer in dependency of the reactive gas composition. (c) Schematic illustration of the fabrication process steps. The substrate (I) is coated with a dense gradient-index layer of Si_xO_yN_z (II). (III) A final layer of homogeneous SiO₂ is coated on top. (IV) A quasi-hexagonal array of gold-nanoparticles is created by BCML and is used as an etching mask in an additional RIE step (V) to manufacture moth-eye structures (VI).

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A variation of the material composition during the deposition process allows a continuous reduction of the refractive index down to the index of SiO₂. The dense GRIN layer is followed by a quasi-periodic ‘moth-eye’-structure made of SiO₂, with a continuous transition of the refractive index. The exact shape of the pillars determines the height dependent fill-factor of the subwavelength structure and therefore the effective refractive index as a function of the height. This leads to an elimination of steps in the refractive index profile and the continuous reduction of the effective index down to the ambient air.

As an exemplary high index precision optical glass we used substrates made of Schott glass N-SF10 which covers a broad wavelength range (refractive index of n = 1.7758 and extinction coefficient of k = 4.6632e-7 @ 404.7 nm and n = 1.6798 and k = 2.0339e-6 @ 2.3254 µm) [32]. The circular shaped plane substrates had a diameter of 25 mm and a thickness of 3 mm. In preparation for the following material deposition process, the substrates undergo a wet chemical cleaning step using isopropyl-alcohol followed by a cleaning tissue process established in optical manufacturing industry.

On all plane N-SF10 substrates and on both surfaces amorphous silicon-oxynitride (Si_xO_yN_z) coatings have been deposited by a reactive pulse sputtering process using a double-ring magnetron system (DRM 400; Fraunhofer FEP) in the bipolar pulse mode. The double ring magnetron system provides homogeneous thickness uniformity on a diameter of up to 8′′ due to the superposition of the two concentric discharge rings [38]. The fabricated coating consists of a GRIN layer of approximately 450 nm thickness made of silicon-oxynitride followed by an additional 450 nm thick homogeneous SiO₂ layer. The amorphous coating were reactively sputtered from a silicon target. Argon was used as inert gas and a mixture of oxygen and nitrogen as reactive gas. The gas flows of O₂ and N₂ were controlled to their aimed mixing ratio. The argon flow was regulated to keep the total gas pressure constant at 0.25 Pa. The constant working pressure is important to eliminate the influence of pressure on the density of the thin films [39]. In detail, the total 450 nm GRIN layer is divided into 157 sub-layers with a thickness of each of about 2.87 nm and with linearly changing refractive index. The refractive index of each sub-layer is tunable by the amount of nitrogen in the reactive gas-mixture (see Fig. 1(b), black inverted triangles). Generally, each refractive index between 1.46 (SiO₂) and ∼2.04 (Si₃N₄) can be selected, so that the GRIN layer can be tailored for most optical glasses. With a nitrogen content of about 43% (N/(N + O)) in the Si_xO_yN_z layer a refractive index of n = 1.72 (@600nm) follows, which fits suitable to the N-SF10 substrate material. A varying gas composition results in changing deposition rates (see Fig. 1(b), red dots). Therefore, deposition time has to be adjusted for each sub-layer (see Fig. 1(b), black dots). On top of the GRIN layer an additional 450 nm thick homogenous SiO₂ layer was deposited as a basic material for the next step of creating the moth-eye structures.

‘Moth-eye’ structures are fabricated in the SiO₂-layer by a combination of BCML and RIE [1,37]. Therefore, spherical micelles were formed by dissolving polystyrene-blockpoly(2)-vinylpyridine (PS-b-P2VP) in toluene and the centers of the micelles were loaded with a gold salt (HAuCl₄). Afterwards the loaded micelles were transferred from the solution to the substrates by spin coating. The resulting mono-micellar film shows a hexagonal pattern with a center distance of ∼105 nm ± 12 nm. After a plasma treatment in which the polymer matrix is removed and a reduction of the gold precursor, a mask of elemental gold nanoparticles remains on the substrate which serves as an etching mask for the following RIE etching process. The height and form of the moth-eye structures are adjusted by different etching protocols, involving the composition of the etching gas and the sequence of the particular etching steps. The BCML-RIE process allows a defined height of the nanopillars between 100 and several hundred nm and the tailoring of the pillars form by Gaussian shaped and/or cylindrical sections [37]. Figure 1(c) shows schematically the individual fabrication steps of the combined process involving the magnetron sputtering of the dense GRIN Si_xO_yN_z layer and the BCML-RIE steps for the ‘moth eye’ generation.

Figure 2 displays SEM (scanning electron microscope) images of the resulting hybrid GRIN-‘moth-eye’ AR-coating. For the SEM images, the sample surface was covered with a thin platinum layer. Figure 2(a) shows a section of the ‘moth-eye’ structured topography captured at an oblique angle of 54°. Uniformly distributed pillars of equal height and with a periodicity significantly smaller than half of the wavelength of visible light are clearly observable. In order to analyze the whole resulting layer stack near to the surface, a focused ion beam (FIB) cut was prepared into the surface (Fig. 2(b)). To achieve a smooth cutting-edge during the FIB-cutting process an additional thin stabilizing platinum layer was applied to the cutting region. On the right side of the image, a region which is not covered by the platinum, the ‘moth-eye’ pillars are clearly visible. In the cross-section of the cutting region the 450 nm thick Si_xO_yN_z GRIN layer is observable. In a selected area of the cutting region the image contrast is enhanced to differentiate clearly between the substrate (light gray), the GRIN transition region (dark gray) and at the top, where the ‘moth-eye’ structures are embedded in the platinum layer.

3. Simulation

To evaluate the design approach of the hybrid graded index structure, especially to simulate the expected wavelength dependent transmission characteristics, model calculations have been performed. For a comparison with measurement data the transmission through the entire sample has to be simulated, in particular comprising the transmission of the GRIN-stacks ${T_{GRIN}}$ on both the front- and back-side of the sample and additionally the influence of the substrate which is described by the internal transmittance $\tau $. For an appropriate simplification of the calculation we decomposed the entire sample into its three contributions, simulate the transmission through each of the contributions separately and finally combine the individual results to a total transmission characteristic T with $T = T_{GRIN}^2\tau $. This approximation is well-suited for transparent materials with low reflectance.

 

Fig. 2. SEM images of the manufactured moth-eye structures under a tilted top-view of 54°. (a) Section of the ‘moth-eye’ structured topography showing uniformly distributed pillars of equal height and with a periodicity significantly smaller than half of the wavelength of visible light. (b) Region of a FIB-cut. For FIB preparation the moth-eye structures are partly coated with platinum. In the cutting region the entire ARC stack comprising the substrate (light gray), the GRIN transition region (dark gray) and at the top the ‘moth-eye’ structures, which are embedded in the platinum layer, are clearly observable. The image contrast is enhanced in the inset to highlight the cross section of the hybrid antireflective coating.

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To simulate the hybrid GRIN-structure on front- and back-side the software UNIGIT [40] was used. Therefore, in detail, the dense GRIN-structure of the varying Si_xO_yN_z layer and the nanopillars were both approximated by extended layer stacks. The combined stack consists of 90 layers representing the 450 nm thick dense GRIN-part and 100 layers were used for the modelling of the nanostructures with a height dependent effective refractive index. The specific index distribution is adapted with respect to the created pillar form. The thickness of the effective index stack describing the nanostructures was adapted to the specific etching depth of the different recipes and varied between 200 and 450 nm. For completeness and with regard to the fabrication process an additional residual SiO₂ layer in between the stack describing the dense GRIN-structure and the stack for the nanopillars has to be taken into account. The thickness of this residual layer was set to be the difference between the 450 nm thickness of the initially deposited SiO₂ layer and the etching depth of the nanostructures. This approach is based on the assumption that the overall thickness of the fabricated structure keeps constant.

For our calculations we assumed normal incidence on the combined GRIN layer stack with a wavelength varying between 400 and 2500 nm in steps of 20 nm. Since measurement data for the extinction coefficient of the fabricated Si_xO_yN_z layer were not available, we simplified our approach and regarded for the calculations only the real part of the refractive indices and exclude absorption effects of the layer-stacks. In the overall calculated transmission curve, the influence of the hybrid GRIN layer stack was counted twice, for the front- and the back-side of the substrate.

With respect to the influence of the N-SF10 bulk material sandwiched between the hybrid GRIN layer stacks, the wavelength dependent transmission of the uncovered substrate was measured. Taking into account, that the transmission of the uncoated substrate is caused by surface reflections and volume absorption effects, the sole absorption influence can be described by the internal transmittance. It is calculated by the measured transmission data divided by the reflection contributions, which are directly derived from the transition of the refraction indices from air to substrate and vice versa. The overall transmission curve is found by combining the resulting measured internal transmittance with the calculated influence of the hybrid GRIN layer stacks. For the overall calculations disturbing scattering effects are neglected.

Figure 3(a) shows the resulting overall transmission spectra calculated for different heights of the ‘moth-eye’-structures. In addition to the calculated results, the measured data for the uncoated N-SF10 substrate is also displayed. All calculated transmission curves show high AR-characteristics over an exceptional broad spectrum ranging from the short visible wavelength range of about 400 nm up to the infrared region of more than 2.4 µm.

 

Fig. 3. Quantitative transmittance characteristics: The double-side structured substrates show high transmittance and low reflectance over a very broad spectral range in comparison to the unstructured N-SF10 substrate (black curve). Different etching depths correspond to different transmittance and reflectance curves. (a) Simulated spectra for different etching depths assuming that the overall thickness of the fabricated structure keeps constant. (b), (c) Measured reflectance and transmittance in the spectral range 400-2500 nm, which closely match to the simulated results. For comparison the measurements of the coated substrate (450 nm GRIN and 450 nm SiO₂) without moth-eye structures are shown (‘GRIN only’, black dashed curve). (d), (e) Detailed view on the measured reflectance and transmittance in the spectral range 500-1200 nm. (f) Transmittance and reflectance in dependency of the angle of incidence (AOI) of a hybrid antireflective coated sample with 300 nm pillar height measured and averaged for different wavelengths between 400 and 1000 nm (red and black dots). For comparison the measured transmittance and reflectance for uncoated N-SF10 is shown (pink and blue triangles).

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In maximum the calculated transmission increases by 12% from 88% for the uncovered substrate up to nearly 100% for the AR-equipped sample at a wavelength of approximately 1 µm. Although the overall transmission decays from the maximum to the infrared wavelength range the transmission increase is still approximately 10% compared to the untreated substrate in this peripheral region of 2.5 µm. The different curves representing the variation in the etch depth show as expected, that the transmission maximum is shifting to the longer wavelength range with increasing depth of the ‘moth-eye’-structure. The features in the curves at 800 nm and at 1400 nm are attributed to the measurement equipment and not to the sample itself. At these specific wavelengths the measurement system is switching between different detectors which results in small dips in the measured curves. As mentioned above, the absorption of the N-SF10 substrate was considered in the simulation by using the measured transmission data of the uncoated substrate, so the small dips also occur in the simulated transmission curves.

4. Results and discussion

Originally, the used etching recipes to create the ‘moth-eye’-structures were developed for bulk fused silica samples [37]. In essential, different heights for the nanostructured pillars can be tailored by adjusting the etching time. For the ‘moth-eye’-structuring described in the present contribution we used sputtered silicon oxide instead of bulk fused silica. Due to a lower density of the sputtered silicon oxide compared to fused silica, the etching times have to be adapted. In detail, we found, that the pillar height in the sputtered silicon oxide is deeper by approximately a factor of 1.17 compared to the corresponding height in fused silica.

Corresponding to the simulations (see Fig. 3(a)), Fig. 3 shows also the measured reflectance (Fig. 3(b)) and transmittance (Fig. 3(c)) for different samples in the range from 400 to 2500 nm. The samples are distinguished by their pillar height. As a reference, also the transmittance and reflectance of the uncoated N-SF10 glass substrate and the coated substrate without moth-eye structures are depicted. In comparison to the uncoated sample a significantly increased transmittance and a strongly decreased reflectance are clearly observable for all samples over the full measured spectrum. In maximum, the transmittance rises by more than 10% and the reflectance decays equivalently. Even in the peripheral regions of the spectrum, at short visible wavelengths around 400 nm and at the infrared range larger than 2 µm, an increase of the transmittance and a corresponding decay of reflectance of more than 6% are observable. An AR-characteristics covering such an extended wavelength range is not available using classical dielectric coatings.

In addition to the surface reflectivity, also the bulk absorption plays a significant role for the overall transmittance. As most high index optical glasses, also N-SF10 shows strong absorption for light at wavelengths below 420 nm. This leads to a significant transmittance drop in the short wavelength range. In the visible and near infrared range the absorption of N-SF10 is low and a high transmittance can be reached. At wavelengths larger than approximately 1.5 µm again an increase of absorption occurs, which accelerates significantly at wavelengths larger than 2 µm, resulting in decreased transmittance. As the thickness of the GRIN stack determines the optimum working wavelength, we choose a thickness corresponding to a transmittance maximum at the far red visible wavelength range for our experiments. For longer wavelengths (>1000 nm) the performance of the GRIN stack decreases and the transmittance and reflectance improvement of the GRIN stack compared to the uncoated substrate is reduced. For completeness, it has to be mentioned, that some of the specific features, in particular in the reflectance curves, can be attributed to measurement or equipment inaccuracies. For example, this concerns the patterns at around 800 nm, 1 µm, 1.4 µm and at 1.6 µm.

A more detailed view shows the reflectance and transmittance spectra of the samples for a reduced wavelength range from 500 nm to 1200 nm (Figs. 3(d) and 3(e)). The lowest AR-improvement corresponds to the shortest height of the nanopillars. With increasing height of the nanopillars the transmittance raises. The best performance is achieved for a height of approximately 320 nm and shows a transmittance higher than 98.2% (>99% for each air/sample interface) and a reflectance lower than 1.3%. While the targeted 350 nm pillar height leads to very similar results a further increase of the profile height leads to a performance decay which is in contradiction to theoretical considerations, predicting a further increase of the transmittance. This experimental finding might be due to introduced structure imperfections, such as increasing variations in the pillar height, which correlates in particular with etching time or the fabrication of longer nanopillars, respectively.

In addition to the advantageous transmission characteristics for normal incidence, the fabricated samples show also a superior transmission and reflection behavior for a broad range of different incidence angles. Figure 3(f) shows the averaged transmittance and reflectance for the sample exhibiting the 300 nm high pillars and measured for different wavelengths between 400 and 1000 nm in dependency of varying incidence angles. For comparison the measured values for the untreated N-SF10 glass are depicted. For these measurements also the contribution of both surfaces of the sample were considered. The measured transmittance stays nearly constant and is higher than approximately 97% up to an incidence angle of 45° and even for an incidence angle of 60° the reflectance keeps below 6%.

5. Conclusion

In conclusion, we fabricated a hybrid antireflection coating on the inorganic high index glass N-SF10 consisting of a dense gradient index layer of silicon oxy-nitride and silicon oxide moth-eye structures by a combination of reactive magnetron sputtering, BCML and RIE etching methods. The resulting coating creates a continuous gradual reduction of the refractive index starting at the substrate down to ambient air. This leads to a very high transmittance and low reflectance over an extreme broad spectral range. The GRIN layer can be adapted to other materials up to a refractive index of about 2.0 by changing the reactive gas composition during the magnetron sputtering process, which makes this approach suitable for almost all inorganic optical glasses. For this reason this method is useful to numerous optical applications like illumination, imaging, communication and sensor systems.