durable, superhydrophobic, antireflection, and low haze glass surfaces using scalable metal...

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Durable, superhydrophobic, antireflection, and low haze glass surfaces using scalable metal dewetting nanostructuring Daniel Infante 1 , Karl W. Koch 3 , Prantik Mazumder 3 , Lili Tian 3 , Albert Carrilero 1 , Domenico Tulli 1 , David Baker 3 , and Valerio Pruneri 1,2 ( ) 1 ICFO-Institut de Ciències Fotòniques, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain 2 ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys, 23,08010 Barcelona, Spain 3 Corning Incorporated, Sullivan Park, Corning, NY 14831, USA Received: 25 February 2013 Revised: 10 April 2013 Accepted: 12 April 2013 © Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2013 KEYWORDS nanostructures, surface modification, antireflective, superhydrophobic/philic surfaces, self-assembly, dewetting ABSTRACT In this paper we report a multifunctional nanostructured surface on glass that, for the first time, combines a wide range of optical, wetting and durability properties, including low omnidirectional reflectivity, low haze, high transmission, superhydrophobicity, oleophobicity, and high mechanical resistance. Nanostructures have been fabricated on a glass surface by reactive ion etching through a nanomask, which is formed by dewetting ultrathin metal films (< 10 nm thickness) subjected to rapid thermal annealing (RTA). The nanostructures strongly reduce the initial surface reflectivity (~4%), to less than 0.4% in the 390–800 nm wavelength range while keeping the haze at low values (< 0.9%). The corresponding water contact angle (θ c ) is ~24.5°, while that on a flat surface is ~43.5°. The hydrophilic wetting nanostructure can be changed into a superhydrophobic and oleophobic surface by applying a fluorosilane coating, which achieves contact angles for water and oil of ~156.3° and ~116.2°, respectively. The multicomponent composition of the substrate (Corning ® glass) enables ion exchange through the surface, so that the nanopillars’ mechanical robustness increases, as is demonstrated by the negligible changes in surface morphology and optical performance after 5,000-run wipe test. The geometry of the nanoparticles forming the nanomask depends on the metal material, initial metal thickness and RTA parameters. In particular we show that by simply changing the initial thickness of continuous Cu films we can tailor the metal nanoparticles’ surface density and size. The developed surface nanostructuring does not require expensive lithography, thus it can be controlled and implemented on an industrial scale, which is crucial for applications. Nano Research DOI 10.1007/s12274-013-0320-z Address correspondence to [email protected]

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Page 1: Durable, superhydrophobic, antireflection, and low haze glass surfaces using scalable metal dewetting nanostructuring

Durable, superhydrophobic, antireflection, and low haze glass surfaces using scalable metal dewetting nanostructuring

Daniel Infante1, Karl W. Koch3, Prantik Mazumder3, Lili Tian3, Albert Carrilero1, Domenico Tulli1, David Baker3,

and Valerio Pruneri1,2 ()

1 ICFO-Institut de Ciències Fotòniques, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain 2 ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys, 23,08010 Barcelona, Spain 3 Corning Incorporated, Sullivan Park, Corning, NY 14831, USA

Received: 25 February 2013 Revised: 10 April 2013 Accepted: 12 April 2013 © Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2013 KEYWORDS nanostructures, surface modification, antireflective, superhydrophobic/philic surfaces, self-assembly, dewetting

ABSTRACT In this paper we report a multifunctional nanostructured surface on glassthat, for the first time, combines a wide range of optical, wetting and durabilityproperties, including low omnidirectional reflectivity, low haze, high transmission,superhydrophobicity, oleophobicity, and high mechanical resistance. Nanostructureshave been fabricated on a glass surface by reactive ion etching through ananomask, which is formed by dewetting ultrathin metal films (< 10 nm thickness)subjected to rapid thermal annealing (RTA). The nanostructures strongly reducethe initial surface reflectivity (~4%), to less than 0.4% in the 390–800 nm wavelengthrange while keeping the haze at low values (< 0.9%). The corresponding water contact angle (θc) is ~24.5°, while that on a flat surface is ~43.5°. The hydrophilicwetting nanostructure can be changed into a superhydrophobic and oleophobicsurface by applying a fluorosilane coating, which achieves contact angles for waterand oil of ~156.3° and ~116.2°, respectively. The multicomponent compositionof the substrate (Corning® glass) enables ion exchange through the surface, so that the nanopillars’ mechanical robustness increases, as is demonstrated bythe negligible changes in surface morphology and optical performance after5,000-run wipe test. The geometry of the nanoparticles forming the nanomaskdepends on the metal material, initial metal thickness and RTA parameters. Inparticular we show that by simply changing the initial thickness of continuous Cu films we can tailor the metal nanoparticles’ surface density and size. Thedeveloped surface nanostructuring does not require expensive lithography, thusit can be controlled and implemented on an industrial scale, which is crucial for applications.

Nano Research DOI 10.1007/s12274-013-0320-z

Address correspondence to [email protected]

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1 Introduction

Optical components and optoelectronic devices use a wide assortment of transparent substrates such as quartz, glass, dielectric crystals and organic polymers. These include lenses, displays, photo-detectors, sensors, and solar cells among many others [1–8]. Their high surface reflectivity (of ≥4% under normal incidence) negatively impacts the optical performance of these elements: Total transmission is reduced in a non- absorptive dielectric. Initially, conventional antireflection coatings (ARCs) with single- or multi-layer thin films were employed to avoid this problem [9]. This tech-nique, based on the cancellation of multiple inter-ferences, has nonetheless many drawbacks comprising durability issues, thermal expansion mismatch, per-formance only at narrow bands of incident wavelengths and angles, poor or reduced substrate adhesion on certain materials, sensitivity to thickness variations and limited laser induced damage threshold (LIDT) [10, 11]. More recently, biomimetic sub-wavelength structures (SWSs) inspired by the corneas of moth and butterfly eyes have attracted great interest [12–17]. In addition to the suppression of undesirable surface reflection losses [18, 19], SWSs can overcome most of the problems that conventional ARCs suffer.

Forming large-scale nanosized etch mask patterns is critical for fabricating the antireflective nanostructures. The lithographic technique based on self-assembled metal nanoparticles (e.g., Ag, Au, Ni, Pt, Cu, etc.) formed by a thermal dewetting process is reasonably straightforward, cost-effective, and scalable to large surfaces compared to e-beam, laser interference, nano-imprint lithography and other top-down fabrication methods [20–22]. In addition, spatial periods of the mask shorter than ~30 nm can be achieved, which can extend the high transmittance region to shorter wavelengths in transparent dielectric materials with no absorption [23]. Even though there has been a lot of work on highly transparent, antireflective surfaces of transparent substrates [10, 24, 25], the research reported on nanostructured glass using thermally dewetted nanoparticles has demonstrated potentially interesting capabilities, but results are only preliminary at this stage [18]. Meanwhile, nanostructuring of trans-parent substrate surfaces may increase repulsion or

attraction of water, i.e., it may enhance hydrophobicity or hydrophilicity [26–28]. Hydrophilic surfaces, which have some properties such as anti-fogging, self-cleaning/easy-cleaning and quick drying, are useful in various fields of optical mirrors and lenses, building windows, and optoelectronic and microfluidic devices. Hydrophobic surfaces stand out for their self-cleaning/easy-cleaning, anti-fingerprint, anti- bacterial and anti-fouling behavior, which are valuable for hospital buildings and automotive windows, displays, large surface smooth interactive panels, as well as marine and aerospace applications.

Fabricating SWSs in transparent materials using techniques based on e-beam or interference lithography [26, 29]—although very precise—is slow and cannot process large surfaces, making it expensive and thus not scalable to an industrial level. The metal dewetting technique is, by contrast, low cost (free of any e-beam or optical lithography), applicable to large surfaces and industrially scalable [30, 31]. A first demonstration of its potential on glass substrates was reported in Ref. [18]. However the study was limited to a few structural geometries, used expensive gold masking, and only investigated the reflectivity and hydrophilic properties, excluding other important parameters, such as haze and angular reflection, which are essential to preserve high quality transparency. A deeper analysis of both the optical and wettability properties of SWSs with different heights, periods, and shapes to the sur-face of glass is needed. We achieve this by changing the thickness of the continuous metal film which then dewets into nanoparticles of different surface density and size. In addition, regardless of the fabrication techniques, the SWSs reported so far have not been proven mechanically stable using durability experi-ments. In this paper tapered nanopillars with different dimensions forming different density SWSs on glass substrates have been fabricated. The manufacturing process relies on the use of thermally dewetted Cu nanoparticles as the etch mask, and glass nanopillar patterns are created by a reactive-ion etching process. We report investigations of the wettability and durability, as well as mechanical and optical properties of the SWSs in this article. Also, a theoretical analysis of optical reflectivity characteristics has been performed by the finite-difference time-domain (FDTD) method.

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By taking advantage of the multicomponent nature of the glass, we chemically modify the SWSs to provide them with mechanical strength. Our paper is the first to combine and demonstrate low omnidirectional optical reflectivity, low haze, and high transmission, together with high mechanical durability, superhydrophobicity and oleophobicity on a nanostructured surface.

2 Results and discussion

Antireflection (AR) surfaces are made by dewetting a thin metal film, then using these metal particles as an etch mask to produce pillars with highly uniform heights and taper angle. Controlling the process variables allows one to tailor the nanostructure, as well as the optical properties. As seen in Table 1 and Fig. 1, thicker initial films lead to fewer and larger dewetted particles.

Similarly, the salient characteristics of the nano-pillars are given in Table 2. The reader must have noted a reduction in the density of particles/pillars after the etching step, which is higher when the size of the dewetted particles is smaller (i.e., for thinner metal layers). This is due to the fact that the smallest metal particles are etched away by the reactive ion

Table 1 Summary of the most significant parameters of the dewetted nanoparticles extracted from SEM image analysis with ImageJ software. Control over density is manifest, as it decreases when thickness is increased.

Sample ID Initial metal

thickness (nm)

Average particle density

(#Particles·m–2)

Average particle

diameter (nm)

KDF 3334 series 4 104 ± 9 47.4 ± 18.6

KDF 3344-C2 5 59 ± 6 57.6 ± 22.3

KDF 3342-A3 6 34 ± 6 77.7 ± 30.6

etching (RIE) process. Also, the dewetted particle diameter in Table 1 corresponds to the apex diameter of the etched nanopillars, calculated by the following equation in combination with the data of Table 2

apex base tanR R h (1)

where h is the pillar height, and , the base angle, is the acute angle between the surface of the substrate and the side of the tapered pillar.

The apex or top diameter of the etched nanopillars could not be resolved from scanning electron micros-copy (SEM) image analysis, and that explains why it has to be calculated. Similarly, now focusing on the data in Table 2, a longer etching time produces taller pillars and increases their base diameter. Likewise, as etching depth increases, some of the nanopillars become fragile and fall off, decreasing the density of pillars. Control over density, height and diameter of the nanopillars is manifest by simply varying initial metal thickness and etching times.

Figure 1 SEM images of the self-assembled dewetted nanoparticles for different Cu thickness (specified in the upper left corner and their respective analysis with ImageJ software). The yellow box in the lower row is the analysed area for particle counting.

Table 2 Summary of the main parameters of the samples studied concerning the fabrication process and the geometry of the resulting nanopillars.

Sample ID Initial metal thickness (nm)

Dry etching time (min)

Pillar height (nm)

Base angle (°)

Pillar density (#Pillars·m–2)

Base diameter(nm)

KDF 3334-A1 4 7 163.0 ± 4.6 79.2 ± 1.5 77 ± 14 92.5 ± 28.6

KDF 3334-A3 4 9 194.1 ± 13.3 79.4 ± 2.1 71 ± 9 96.0 ± 22.1

KDF 3334-B1 4 11 246.3 ± 10.4 80.8 ± 1.8 71 ± 9 101.4 ± 23.4

KDF 3344-C2 5 7 156.7 ± 3.1 77.9 ± 2 45 ± 4 133.1 ± 42.8

KDF 3342-A3 6 7 152.5 ± 4.9 76.7 ± 1.1 30 ± 3 137.9 ± 32.2

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According to spectral reflectance and transmittance measurements shown in Fig. 2 and further summarized in Table 3, sample KDF 3334-B1 provides the lowest average reflectance (~0.4%) among all the samples. Namely, the reflectance of this sample is below 0.75% over the whole visible spectrum. Its haziness and forward scattering ratio (FSR) are far from being the lowest though, as it is the sample that diffuses the most light in transmission. Total average transmittance of KDF 3334-B1 is ~2.7% points higher than that of Corning® chemically strengthened flat glass and is the second best value of all the samples, only ~0.1% points below the maxima, which is a small difference compared to the variation we see across the sample. If all the treated specimens are considered, the maximum average reflectance is ~1.5% and the haze or milkiness is less than 0.9%. As the reader may

have noted, the sum of transmittance and reflectance does not reach 100%: This is due to a light guiding or scattering effect rather than absorption. Further data regarding angular scattering and single-surface

Table 3 Summary of averaged values for the main measured optical properties and forward scattering ratio (FSR) of the different samples.

Sample ID Ravg

(%)Tavg

(%)TDIFFavg

(%) TAXIALavg

(%) Haze(%)

FSR

KDF 3334-A1 0.6 94.8 0.5 94.4 0.5 5.5E-03

KDF 3334-A3 0.6 94.8 0.4 94.5 0.3 4.5E-03

KDF 3334-B1 0.4 94.7 0.9 93.6 0.6 9.0E-03

KDF 3344-C2 0.9 94.6 0.5 94.3 0.8 4.8E-03

KDF 3342-A3 1.5 93.9 0.4 93.3 0.2 4.4E-03

Corning® flat glass

4.1 92.0 — — — —

Figure 2 Measured total reflectance (a), total transmittance (b), axial and diffuse transmittance (c) versus wavelength and haze (d) plots for the different nanostructured samples.

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reflectance extraction from measurement can be found in Figs. S1 and S2, respectively, in the Electronic Supplementary Material (ESM).

The etching process leads to features of roughly the same vertical size and roughly the same base angle. Bigger (4” × 4”) samples were fabricated and reflectance measurements were made at six different points across the surface of each sample. These values showed a maximum absolute difference of ~0.3% points on each specimen, demonstrating that the uniformity achieved in the fabrication process is optimum.

As the plots in Fig. 3 illustrate, the AR nanopillar structured surfaces are not strongly polarization dependent: There is no Brewster angle. On the polar measured angles average, the reflectance from a nanostructured sample is ~3.9% lower than a standard flat glass sample.

The results from measurements are compared with the simulation results, where the average pillar spacing, pillar height, and base angle parameters are those extracted from SEM image analysis and base diameter is varied within the range determined by the standard

deviations (see Fig. 4 and Table 2). When the average size and spacing of the surface features is small compared to the optical wavelength, simulations of periodic arrays of similar features provide a good approximation to the average reflectivity of the surface.

2.1 Wetting properties

Once the structures are created on the surface of the samples by dry etching and the residual metallic particles of the mask are removed, the samples exhibit a hydrophilic and lipophilic behavior. This is due to the fact that, owing to the intrinsic hydrophilicity and oleophilicity of the glass surface, the texturing enhances the wetting property of the surface. Nonetheless, their performance can be fully transformed by activating the samples’ surfaces with Dow Corning® 2634 coating by a simple process [32]. This renders the initially hydrophilic surface superhydrophobic. A maximum water contact angle of 156.3° and a maximum oil contact angle of 117.1° confirm the change to super-hydrophobic and oleophobic states (refer to Table 4 to check all the values).

Figure 3 Plots of the experimental reflectance versus angle of incidence for different polarizations (RS and RP) and the average of the two (R) at a wavelength of 530 nm. A Corning® chemically strengthened flat glass substrate (both experimentally and simulated) and a nanostructured sample were analysed.

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Table 4 Contact angle values for water (H2O) and oil (OIL) drops of 2 L volume on the surface of the different samples, before and after the Dow Corning® 2634 coating was applied.

H2O (º) OIL(º) Sample ID

Before After Before After

KDF 3334-A1 26.2 150.1 15.8 115.9

KDF 3334-A3 27.8 154.3 10.7 117.1

KDF 3334-B1 24.5 156.3 12.1 116.2

KDF 3344-C2 26.3 151.3 11.2 111.6

KDF 3342-A3 27 154.3 9.7 101.3

Corning® flat glass 43.5 115.9 27.6 76.3

2.2 Cratered structures simulation

A close inspection of SEM and atomic force microscope (AFM) height images show that the apex of the pillar has a spherical depression, whose depth appears proportional to the diameter of the pillar. This depression makes a smoother refractive index change between air and the pillars, enhancing the AR effect [19]. The impact of a spherical depression (crater) on the apex of a tapered pillar on the optical transmission and reflection properties of the surface is demonstrated. The cratered top of the pillar is

Figure 4 SEM images of the samples used in this work. Each row represents a different sample. The first column (a) collects top views of thesurfaces, the second column (b) are 45º-tilted views and the last column (c) are fractured cross-section views. Accelerating voltage was 3 kV.

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modeled as a spherical depression in the apex of the cone, where it intersects the edges of the cone’s tip, as shown in Fig. 5.

By simple geometry, the following expression for the sphere radius can be extracted

2 2sphere apex / 2R R d d (2)

If the sphere depth d is expressed as a fraction of the radius of the top of the pillar (d = α·Rapex), the fraction α is bounded as 0 < α ≤ 1, and the resulting expression is

2sphere apex(1 ) / 2R R (3)

From Fig. 5(d), we see that an increase in the spherical depression on top of a tapered pillar shifts the minimum reflectivity to shorter wavelengths. Additionally, the minimum reflectivity value is also reduced. When pillars are topped with a depression depth equal to 30% of the pillar’s apex diameter (d = 0.3 × Dapex) and pillar height equals half the lattice pitch (h = 0.5·), the diameter and pitch for the lowest average reflectivity over the visible range (450–650 nm) increase both by ~19.4% in comparison to a similar pillar structure with no crater on top. In this case, the minimum reflectivity decreases by ~7.6%. On the other hand, for pillars topped with similar craters and twice

the height (h = ), the diameter and pitch for the lowest average reflectivity over the visible range (450– 650 nm) increase both by ~4.4% in comparison to a similar pillar structure with no crater on top. In this case, the minimum reflectivity decreases by ~6.9%, while the average reflectivity remains roughly the same. Figure 6 shows the behavior of the structures in the different simulations. The ESM includes additional simulated reflectivity plots in Figs. S3 and S4 and data in Table S1.

2.3 Mechanical robustness

In order to analyze the structures’ mechanical durability, a wipe test was performed by using a fiber cloth with a crock-meter and applying a force of 9 N over a surface of 2 cm2. The samples were previously subjected to an ion exchange (IOX) chemical process to strengthen the AR structures [33], where Na+ ions in the substrate were replaced by larger K+ ions, thus creating a layer of compressive stress throughout the nanostructure surface. The ion-exchanged nanopillars withstood the wipe test, as can be qualitatively observed in Fig. 7. Even though craters disappeared from top of the pillars, the optical transmission, haze and contact angle measurement results did not change significantly.

Figure 5 Schematic view of the most relevant geometric parameters. (a) Geometry and typical parameters of a crater topped taperedpillar. (b) Cross-section of tapered pillars for series of crater depths d ranging from 1.00Rapex to 0.0. (c) Top view geometry of hexagonally packed tapered pillars. The graph in (d) plots the simulated spectral reflectivity for series of crater depths with Dbase = 200 nm, = 250 nm, = 15°, and h = 125 nm.

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Figure 6 Contours plots of average simulated reflectivity <R> for standard tapered pillars (a), (c) and for tapered pillars with crater (d = 0.3 ×Dapex) on top (b), (d). The height of the pillars corresponds to half the pillar spacing (h = 0.5·, (a), (b)) or the pillar spacing (h = , (c), (d)).

Figure 7 (i) Atomic force microscope images sequence: (a) After dry etching, (b) after the ion exchange (IOX) process, and (c) afterthe IOX process and 5,000 runs of the wipe test. (ii) SEM images of the structure (a) after dry etching and (b) after the IOX process and5,000 runs of the wipe test.

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3 Conclusions

AR properties of nanostructured glass substrates have been investigated both experimentally and theoretically. The chosen structures, tapered nanopillars, are fabricated by dry etching of a thermally dewetted Cu nanomask on the substrates. Thereby, structural parameters such as height, diameter and density of the nanopillars can be altered to impact different optical and fluidic attributes. The average reflectance of the treated samples is lowered over the visible wavelength range over a wide range of incidence angles in comparison to flat glass substrates. We demonstrate an average reflectance of ~0.4%. Cratered nanopillars make the transition from low-refractive-index air medium to high-refractive-index glass substrate smoother, improving thus AR characteristics. Also, the hydrophilic state of the fabricated samples can be switched to the superhydrophobic state by a simple activation of the surface. The multicomponent glass substrates employed in this work allow ion exchange chemical strengthening of the as-fabricated structures, enhancing their durability and robustness.

To summarize, nanostructures with broadband low reflectivity, low haze, high transmission and durability can be fabricated on a large-scale, mass production method that adds extra value and functionality to high- performance optical components and optoelectronic devices.

4 Experimental

Scheme 1 shows the process steps for the fabrication of nanopillars on glass substrates. The substrates used to fabricate the nanostructures were Corning® chemically strengthened glass pieces with a thickness of 0.7 mm and a size of 2” × 2” to 4” × 4”.

4.1 Metal thin film deposition

Copper (Cu) thin films with thicknesses of 4, 5 or 6 nm were deposited on the substrates by using a magnetron sputtering system (ATC Orion 8, AJA International, Inc. or KDF 903i) [2]. The depositions were performed at a base pressure of 10–8 Torr, room temperature, 100 W of DC-power and 25 standard cubic centimeters (sccm) of pure Ar. The working pressure

Scheme 1 Nanostructure fabrication process: Deposition of a thin Cu layer on top of the glass substrate, thermal dewetting and dry etching of the nanostructures.

was of 1.5 × 10–3 Torr, the deposition rate was 0.166 nm/s and the target–substrate distance was 41 cm.

4.2 Dewetting

The samples then underwent a thermal dewetting process, where nanosized metal particles were formed on top of the glass substrate. Dewetting took place because the surface energy of the thin, metallic-Cu film was greater than the interfacial and surface energy of the underlying substrate when thermally heated, so the metal film reduced its surface area by self-collecting into small islands on the substrate surface. Minimization of energy took place when nanoparticles were formed, like in the mechanism of Ostwald ripening [34]. The nanomask was generated by putting the samples in a rapid thermal annealing (RTA) system (e.g., TsunamiTM RTP-600S) at a temperature of 750 °C, typically for 50 to 125 s. During the RTA process, a susceptor of 6” diameter was used to hold small glass. High purity N2 gas was used to prevent oxidation of the metal film in 1 atmosphere.

4.3 Etching

Once the metallic film had been dewetted, the resulting metallic nanoparticles can be used as etch mask. Dry

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etching of the samples was performed by using a RIE system (Plasmalab System 100 or 190, Oxford Instruments) in either RIE mode or inductively coupled plasma (ICP) RIE mode. Etching times were varied to achieve different pillar heights, although the etching parameters were kept constant at the different experiments, for instance, 300 W RF power (875 DCV) at 10 mTorr in 40 sccm Ar/5 sccm CHF3 plasma. Afterwards, the samples were immersed in acidic, e.g., aluminum etchant solution (73% (w/w) phosphoric acid, 3.1% (w/w) nitric acid, 3.3% (w/w) acetic acid and 20.6% (w/w) water, Sotrachem Technic France) for a few seconds to remove any metal residue. Next, the samples were ultrasonically cleaned in acetone, isopropanol, and deionized (DI) water for 10 min, and eventually residual moisture was removed by blowing dry N2 over the surface and placing the substrate in a 120 °C oven for 10 min. The morphology of the nanopillars was examined by a field-emission scanning electron microscope (FEG-SEM, Inspect F, FEI Systems).

4.4 Photometric characterization

The total (i.e., specular and diffuse) transmittance and reflectance were measured in the wavelength range of 390 to 800 nm by using a UV–vis–NIR spectrophoto-meter (PerkinElmer Lambda 950) equipped with a 60-mm- or a 150-mm-diameter integrating sphere. Haze was measured by using a Haze-meter (BYK-Gardner 4601 haze-gloss). Furthermore, angular photometric reflectance behavior to the incidence of both polarizations TE (S) and TM (P) were studied. In this experiment, the goniometer of a SOPRA GES5E ellipsometer was scanned from 20° to 76°. Back face reflection was suppressed by painting the rear surface of the samples with an absorbing black ink.

4.5 Wetting characterization

Water and oleic acid contact angles were measured and averaged at three different positions on the surface of samples by using a drop shape analysis system (DSA-100, Krüss GmbH).

4.6 Simulation

In addition to the experimental results, and in order

to verify them, the structures were also simulated via the numerical analysis technique of finite-difference time-domain (FDTD) [35]. The main parameters were extracted via image-processing analysis of SEM images of the samples, and the average hexagonally packed feature separation〈〉was related to the average feature density〈〉by means of the following equation

2 3 (4)

Using simple trigonometric formulas, the apex radius of the tapered pillars formed on the surface can be related to the base radius by means of Eq. 1. In the simulations, the average pillar spacing, pillar height, and base angle were kept constant, for a number of different pillar base diameters. We used a broad- bandwidth pulse to characterize an extended spectral response (from 200 to 2,500 nm) of the textured surface. We could then use the scale-invariance properties of Maxwell’s equations to extend the analysis to a wide range of surface parameters. Figure 5 depicts the most significant morphological parameters.

Acknowledgements

This work was supported by the Spanish Ministerio de Economía y Competitividad through grant No. TEC2010–14832.

Electronic Supplementary Material: Supplementary material regarding the spectrophotometric measure-ments performed in this work, the mathematical development of the single-surface reflectance extraction from a two-surface reflectance measurement and some 3D-FDTD simulation results and comparison with their experimental counterparts is available in the online version of this article at http://dx.doi.org/10.1007/ s12274-013-0320-z.

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