Mechanically-Durable Antireflective Subwavelength Nanoholes on Glass Surfaces Using Lithography-Free Fabrication

Traditional multilayer antireflection (AR) surfaces are of significant importance for numerous applications, such as laser optics, camera lenses, and eyeglasses. Recently, technological advances in the fabrication of biomimetic AR surfaces capable of delivering broadband omnidirectional high transparency combined with self-cleaning properties have opened an alternative route toward realization of multifunctional surfaces which would be beneficial for touchscreen displays or solar harvesting devices. However, achieving the desired surface properties often requires sophisticated lithography fabrication methods consisting of multiple steps. In the present work, we show the design and implementation of mechanically robust AR surfaces fabricated by a lithography-free process using thermally dewetted silver as an etching mask. Both-sided nanohole (NH) surfaces exhibit transmittance above 99% in the visible or the near-infrared ranges combined with improved angular response at an angle of incidence of up to θi = 60°. Additionally, the NHs demonstrate excellent mechanical resilience against repeated abrasion with cheesecloth due to favorable redistribution of the shearing mechanical forces, making them a viable option for touchscreen display applications.

Table S1: Summary of the parameters that define the initial morphology of the NHs (mean diameter, standard deviation, particle density, average spacing and filled area fraction) for increasing initial silver thicknesses.(a) Schematics of the structure and the geometrical parameters that were varied through a parametrical sweep.Contour plot of reflectance as a function of wavelength and NH depth for the two limit cases: in (b) holes are approaching a cylindrical shape (SR = 0.9) while the structure in (c) is an inverted cone (SR = 0).The mean reflectance in the 400 − 800 nm range depending on the depth is shown in both insets.
Figure S2 summarizes the expected optical behaviour of the simulated structure using COMSOL Multiphysics software.The nanocavities were modeled using a periodic squared array with period P = 100 nm and period ratio P R = D top /P = 1.0 (touching holes) for two limit cases: sidewalls close to vertical with SR = 0.9 (Figure S2b) and pointy bottom with S2c), which is essentially an inverted nanocone.The period was chosen to match the average value obtained from the statistical analysis of SEM measurements after the dewetting process.When the slope ratio is approaching one, equivalent to cylindrical nanohole, an abrupt change of the effective refractive index (RI) n eff along propagation direction occurs.In this case, the reflectance of the nanohole structures can be viewed as equivalent to a single layer coating with thickness d etch and effective RI n eff .The reflectance minima occur at wavelengths satisfying the condition λ min = d etch /4n eff (the orange areas in the contour plot in Figure S2b).The calculated mean reflectance in the 400 − 800 nm range as a function of the depth suggests that NHs with depths between 100 − 150 nm will have the lowest mean reflectance values.To achieve a flatter optical response across wider wavelength range and reflectance below 0.5%, more gradual change of the effective refractive index is needed.By choosing the slope ratio to be equal to zero (i.e., nanocone), the discontinuity in the effective RI for the interface nanocone-bulk glass can be eliminated.Holes deeper than 250 nm will result in less than 0.5% mean reflectance as shown in Figure S2c.As the NH depth further increases up to 500 nm, the average reflectance tends to decrease slowly and the low-reflectance region is broadened towards longer wavelengths.
Figure S3 shows the reflectance of the NHs with fixed period P = 130 nm and slope ratio SR = D bottom /D top = 0, i.e., inverted nanocones.In Figure S3a the mean reflectance the 300 − 1500 nm range is plotted as a function of period ratio P R = D top /P and depth.
Structures with small period ratios (P R = 0.5) are not able to suppress the mean reflectance even for the deepest holes because the air-glass fraction at the upper interface results in change of the effective RI from n air = 1 to n air−hole = 1.27.In order to obtain the lowest mean reflectance values, high period ratios and depths of at least 300 nm are required.Figure S3b shows the mean reflectance as a function of wavelength and depth when the top diameter is equal to the period of the lattice (P R = 1.0).In this case, the n eff = 1.10 at the air-hole interface.The NHs are able to suppress progressively the mean reflectance with increasing the depth and reach below 0.5% values as shown in the inset of Figure S3b.We also compare in Figure S3c the reflectance spectra of two simulated structures with geometric parameters that closely match the experimentally measured dimensions from SEM images.
The simulated spectra follow in good agreement the measured ones and the offset can be  The calculated transmittance and reflectance of the NHs as a function of the top diameter for two depths, 160 nm and 310 nm, that most closely correspond to the fabricated nanoholes with best optical performance in the VIS and NIR is shown in Figure S4a and Figure S4b, respectively.Larger diameters decrease the overall reflection, however, the minimum achieved reflectance is limited by the remaining glass surface at the interface air-hole when the hole diameters are touching and equal to the period of the cell.

Figure S1 :
Figure S1: Top view SEM images and distributions of dewetted silver nanoparticles (AgNPs) on fused silica.The deposition times were 25 (a), 30 (b), 35 (c), and 40 sec (d).Insets represent the histogram of nanoparticle diameters obtained through image analysis with the ImageJ tool.

Figure S2 :
FigureS2: Simulated one-side reflectance R at normal incidence of nanocavities on glass in the 300 -1500 nm range for fixed period P = 100 nm and period ratio P R = D top /P = 1.0.(a) Schematics of the structure and the geometrical parameters that were varied through a parametrical sweep.Contour plot of reflectance as a function of wavelength and NH depth for the two limit cases: in (b) holes are approaching a cylindrical shape (SR = 0.9) while the structure in (c) is an inverted cone (SR = 0).The mean reflectance in the 400 − 800 nm range depending on the depth is shown in both insets.

Figure S3 :
FigureS3: Simulated one-side reflectance R at normal incidence of nanocavities on glass in 300 -1500 nm range for fixed period P = 130 nm and slope ratio SR = D bottom /D top = 0. (a) Contour plot of the mean reflectance in the 300 − 1500 nm wavelength range as a function of period ratio (D top /P ) and depth.(b) The reflectance as a function of wavelength and depth was evaluated for NHs with top diameter equal to the period of the lattice (P R = 1.0).The inset shows the calculated average values of R in the 300 − 1500 nm interval as a function of depth demonstrating that holes with diameters approaching the period can achieve below 0.5% mean reflectance when sufficiently deep.(c) Comparison between measured (solid) and simulated (triangles) reflectance of samples with depth of cavities of ≈ 210 nm and ≈ 310 nm (samples RIE 8 min and RIE 13 min in Figure4in the main text).Parameters of the simulated holes: P = 130 nm, SR = 0.2, P R = 0.9 and D hole = 210 and 310 nm.

Figure S4 :
Figure S4: Simulated one-side mean transmittance and reflectance in the VIS (a) and in the NIR (b) of nanoholes as a function of the top diameter D top .The parameters of the simulated structure in (a) are period P = 130 nm, slope ratio SR = D bottom /D top = 0, depth D = 160 nm, whereas in (b) the depth D = 310 nm.

Figure
Figure S5: (a) Determination of the dry etch rate of fused silica using a linear fit to six nanohole samples.For each sample, six depths were measured and averaged by cross-section SEM scans.Experimentally measured average transmission (left axis, red) and reflection (right axis, blue) in the VIS range (b) and in the NIR (c) as a function of depth that is determined using the calibration line in (a).The values for bare glass are also plotted.

Figure S6 :
Figure S6: Photographs of the bare FS glass and the three NHs samples optimized for (a) VIS and (b) NIR that correspond to the measured spectra in Figure 3 and Figure 4 in the main text.(c) Photographs of bare FS glass (top row), both-sided NHs sample RIE 6 min (middle row) and both-sided NHs sample RIE 13 min (bottom row) at AOIs = 8 • , 30 • , 45 • , and 60 • .