1. Introduction

A variety of transparent substrates such as quartz, glass and polymer have been widely used for optical elements and optoelectronic devices including lenses, displays, photodetectors, sensors, and solar cells [1–4]. However, these substrates have refractive indices higher than at least ~1.5, which creates a surface reflectivity of ≥ 4% on a flat single side under normal incident light illumination [5,6]. The Fresnel reflection of the surface causes the reflected glare and deteriorates the optical performance of devices, which leads to a relatively decreased transmission in ideal dielectric substrates without absorption. To avoid these problems, the conventional antireflection coatings (ARCs) with single- or multi-layer thin films have been mainly employed. But, this technique has many drawbacks including thermal expansion mismatch, sensitivity to thickness variations, and interfacial instability in the thin-film stacks as well as only narrow bands of incident wavelengths and angles [7,8]. Furthermore, it becomes limited to the selection of suitable materials with a sufficiently low absorption in the ultraviolet wavelength region [9]. Recently, biomimetic subwavelength structures (SWSs) inspired from the corneas of moth and butterfly eyes [10,11], which have a smaller period than the wavelength of incident light, have attracted great interest as an alternative to the conventional ARC because they can suppress the unwanted surface reflection losses [12–18].

In order to fabricate the antireflective nanostructures, it is very important to form large-scale nanosized etch mask patterns. The lithographic technique based on the self-assembled metal nanoparticles (e.g., Ag, Au, Ni, Pt etc.) formed by thermal dewetting process is relatively simple, cost-effective, and large scalable compared to the e-beam, laser interference, and nanoimprint lithography methods [19–22]. Furthermore, it is possible to obtain the mask patterns with periods shorter than ~200 nm, which can extend the high transmittance region to the shorter wavelength in transparent dielectric materials with no absorption [23–25]. Although many researches on the highly transparent and antireflective surfaces of transparent substrates were performed [9,23–29], there has been very little work reported on the nanostructured glass using thermally dewetted Au nanoparticles, especially with systematic theoretical analysis. Meanwhile, the roughened structures may enhance the hydrophilicity on the surface of transparent substrates [29,30]. The hydrophilic surface, which has some effects such as anti-fog, self-cleaning/easy-cleaning, quick dry, and elimination of light scattering caused by water droplets, is useful in various fields of optical mirrors and lenses, building windows, and optoelectronic devices [27,31]. Thus, it is very meaningful to analyze the optical properties and wettability by applying the SWSs with different shapes, heights, and periods to the surface of glass substrates for optical and optoelectronic applications. In this work, we fabricated the SWSs with different pillar and cone shapes on glass substrates using thermally dewetted Au nanoparticles as the etch mask patterns by inductively coupled plasma (ICP) etching process and investigated their wettability as well as structural and optical properties at the surface. For optical transmission characteristics, the theoretical analysis was also carried out by the rigorous coupled-wave analysis (RCWA) method.

2. Experimental and simulation modeling details

Figure 1 shows the schematic illustration of process steps for the fabrication of pillar- and cone-shaped nanostructures on glass substrates. To fabricate the nanostructures on the surface of glass substrates, the squared and dual-side polished 0.5-mm-thick borosilicate glass (BOROFLOAT® 33, SCHOTT) substrates with a size of 3 × 3 cm² were used. The substrates were ultrasonically cleaned in acetone, methanol, and deionized (DI) water for 10 min and then dried with nitrogen (N₂) gas. The dilute nitric acid rinse was also performed to remove metal contaminants from the surface of substrates. To form the etch nanomask patterns, the gold (Au) thin films with thicknesses of 5, 10, and 15 nm were deposited on the samples by using a thermal evaporator (KVE-T2000, Korea Vac. Tech. Ltd.). The nanosized Au particles were agglomerated on the glass substrate by the thermal dewetting process. This process occurs to minimize the surface energy when the surface energy of Au thin film is larger than the interfacial energy and the surface energy of the underlying substrate due to the thermal heating, like the mechanism of Ostwald ripening [32,33]. The thermal treatment was carried out at the temperature of 600 °C for 3 min under N₂ environment by using a rapid thermal annealing (RTA, KVR-2000, Korea Vac. Tech. Ltd.) system. Using the formed Au nanoparticles as an etch mask pattern, the nanostructures with different pillar and cone shapes were fabricated on glass substrates by using an ICP (Multiplex ICP, STS) etcher system, respectively. After the dry etching, the remaining Au nanoparticles were eliminated by an Au etchant solution. The structural morphology and geometries of the fabricated glass nanopillars and glass nanocones were observed by using a scanning electron microscope (SEM, LEO SUPRA 55, Carl Zeiss). The total (i.e., specular and diffuse) transmittance and reflectance were measured by using a UV-vis-NIR spectrophotometer (Cary 5000, Varian) with an integrating sphere at a near-normal incidence angle of ~8°. Here, the incident light was linearly polarized. For measured samples, the reproducibility (standard deviation) in average total transmittance (T_ave) values at different areas was mostly within the range of ~ ± 0.2% over a wavelength region of 400-1100 nm. The water contact angles were measured and averaged at three different positions on the surface of samples by using a contact angle measurement system (Phoenix-300, SEO Co., Ltd.).

 

Fig. 1 Schematic illustration of process steps for the fabrication of pillar- and cone-shaped nanostructures on glass substrates.

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For the theoretical optical analysis of nanostructured glass substrates, the RCWA simulations were performed using a commercial software (DiffractMOD 3.1, Rsoft Design Group) [34]. The fifth order of diffraction was used to calculate the diffraction efficiency, which can provide the numerically reasonable results due to its sufficient order. To design the theoretical model, the periodic geometry of the nanostructures (i.e., nanopillars, nanocones) on glass substrates is roughly represented in the Cartesian coordinate system by a scalar-valued function of three variables, f(x, y, z). The shape of nanopillars and nanocones is defined by the following equations:

3. Results and discussion

Figure 2 shows the contour plots of the calculated total transmittance variation as a function of wavelength for (i) height and (ii) incident angle of light in glass nanostructures with (a) pillar and (b) cone geometries. The three-dimensional simulation models of the corresponding structures, which are composed of the periodic pattern with a six-fold hexagonal symmetry for simplicity, used in this calculation are shown in each inset of Fig. 2. In RCWA calculations, the period between adjacent nanopillars or nanocones was fixed at 280 nm and their bottom diameter and O_T value were 190 nm and 1, respectively. The thickness of the glass substrate was assumed to be 500 μm. The calculated values at each wavelength were averaged to remove rapid oscillations caused by the interference of light reflected at both side surfaces. For the glass nanopillars, as the height is increased from 0 to 900 nm, there are more oscillations in the transmittance over a wavelength region of 350-1100 nm, indicating the high transmittance values of > 95% (i.e., red parts). This is caused by the interferences at the upper and lower boundaries of cylinder-like nanopillars which act as an effective medium such as a single layer thin film with an abrupt change of the refractive index profile [39]. At relatively low heights of ~100 ±25 nm, the higher transmittance is observed at wavelengths of 370-1100 nm. This may be because the effective refractive index profile can be considered as a gradual distribution from air to the glass substrate via glass nanopillars at a relatively low height though it is abruptly changed at the interfaces of air/nanopillar and nanopillar/substrate. On the other hand, the glass nanocones are nearly independent of their height over a wide wavelength range of 370-1100 nm, indicating the high transmittance values of > 95% at heights above ~200 nm. It is noted that the surface nanostructure with taller and sharper pillars provides a more graded refractive index profile between air and the material to suppress efficiently the surface reflection [16,40], which relatively enhances the transmission in transparent dielectric materials without absorption. As can be seen in (i) and Figs. 2(a) and 2(b), at wavelengths above ~370 nm, the high transmittance values of > 95% are obtained. This is closely related to the cutoff period of nanopillars or nanocones [23]. Furthermore, for lower heights than 50 nm, there is little effect on the transmission property even if the nanostructure is formed on the glass substrate.

 

Fig. 2 Contour plots of the calculated total transmittance variation as a function of wavelength for (i) height and (ii) incident angle of light in glass nanostructures with (a) pillar and (b) cone geometries. The three-dimensional simulation models of the corresponding structures used in this calculation are shown in the insets, respectively.

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To improve the light-absorption efficiency in photovoltaic devices, angle-independent broadband transmission property of the glass substrate as a top surface layer should be explored. The height of both pillars and cones was assumed to be 220 nm in calculations of incident angle dependence. As illustrated in the plots (ii) of Figs. 2(a) and 2(b), the nanocone-shaped surface increases the transmission of the glass substrate (i.e., ~92% due to the reflectivity of ~8% at both sides) more effectively than the nanopillar-shaped surface in the broad ranges of wavelength and incident angle. At wavelengths of 350-1100 nm and incident angles of 0-85°, the T_ave value of glass nanocones is ~84.8%, which is higher than T_ave~83.5% of glass nanopillars as well as T_ave~82.1% of the flat glass substrate. These results can be explained by the fact that the amount of reflected light at the cone-like nanostructured glass surface is lower than those of glass nanopillars and flat glass substrate because the nanocones have the linear and continuous graded effective refractive index profile from air (n_air = 1) to the glass substrate (n_glass~1.5) while the nanopillars, which act as an effective medium such as a single layer thin film, exhibit an abrupt change at the interfaces of air/pillars and pillars/substrate, as mentioned above. We noted that the glasses with nanostructures on one side exhibit a similar tendency in the transmittance as a function of incident angle of light for both incident light directions, i.e., nanostructure surface of glass to air and flat surface of glass to air, though there are slight discrepancies.

Figure 3 shows the measured total transmittance spectra of fabricated glass (a) nanopillars and (b) nanocones with different heights using the thermally dewetted Au nanomask patterns of 10 nm-thick Au film after RTA of 600 °C. The insets show the SEM images of the corresponding structures. For comparison, the total transmittance spectrum of the flat glass substrate is shown in Fig. 3. The etching process was performed with 50 RF power and additional 1000 W ICP power at 5 mTorr in 45 sccm/5 sccm C₄F₈/O₂ plasma. To fabricate the nanopillars with different heights, the etching time was varied. As shown in the SEM images of Fig. 3(a), the pillar-shaped glass nanostructures with different average heights of (i) 130 nm, (ii) 220 nm, and (iii) 350 nm were fabricated at etching times of 100, 180, and 260 s, respectively. The average diameter of the fabricated glass nanopillars was 192 ± 73 nm. For the glass nanopillars with a height of 350 nm, there are oscillations in the transmittance spectrum as shown in Fig. 3(a). This is because there are the light-beam interferences at the upper (air/grating layer) and lower (grating layer/substrate) boundaries due to the abrupt change of the effective refractive index at the top and bottom interfaces in the cylinder-shaped grating structure [23,39]. For the samples with heights of 220 and 130 nm, the oscillations in transmittance spectra were almost not observed because of their low heights. The T_ave values (i.e., ~93.9 ± 0.2%) were higher than T_ave~92.7% of the flat glass substrate. In contrast, the cone-shaped glass nanostructures in Fig. 3(b) were fabricated at etching conditions of 100 W RF power, 5 mTorr, 45 sccm/5 sccm C₄F₈/O₂ mixture gas flow rate, and etching time of 100 s. The glass nanocones with different average heights of (i) 140 nm, (ii) 230 nm, and (iii) 320 nm were formed at different additional ICP powers of 2000, 1500, and 1000 W, respectively. In the case of the higher RF power (i.e., 100 W) with an additional high ICP power, the cylinder-shaped glass nanopillars were changed into the tapered glass nanocones due to the overetching of the nanopillars as well as the erosion of Au nanomask patterns. Thus, the average height became lower and the average bottom diameter was also reduced from 182±61 to 139±39 nm with increasing the additional ICP power from 1000 to 2000 W. As shown in Fig. 3(b), the glass nanocones exhibited the higher transmittance spectra than that of the flat glass substrate over a wide wavelength range of 400-1100 nm. At wavelengths of 300–1100 nm, the T_ave value was slightly increased from 94 to 95% with increasing the average height from 140 to 320 nm. As shown in Fig. 3, the transmittance spectra of the most glass nanocones are higher than those of the glass nanopillars due to its linear and continuous graded effective refractive index distribution between the air and the glass substrate via the nanocone, which is related to the so-called moth eye effect [41]. For both the fabricated glass nanopillars and nanocones, moreover, higher transmittances were observed at wavelengths above ~400 nm compared to the flat glass substrate. This may be ascribed to the diffraction loss at wavelengths of < 400 nm, which is related to the cutoff period of glass nanostructures [23]. It is clear that these experimental results for the variation of the shape and height of glass nanostructures exhibit a similar overall tendency with the calculated data in (i) of Figs. 2(a) and 2(b) over a wide wavelength region of 400-1100 nm.

 

Fig. 3 Measured total transmittance spectra of fabricated glass (a) nanopillars and (b) nanocones with different heights using the thermally dewetted Au nanomask patterns of 10 nm-thick Au film after RTA of 600 °C. The insets show the SEM images of the corresponding structures.

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Figure 4 shows the (a) average diameter and density of nanoparticles and average period of nanopatterns as a function of Au film thickness and SEM images of (b) thermally dewetted Au nanoparticles as mask patterns (top-view) after RTA of 600 °C for 3 min and (c) fabricated glass nanostructures (30°-tilted oblique view) for different Au film thicknesses of (i) 5 nm, (ii) 10 nm, and (iii) 15 nm. The side-view SEM images of the corresponding structures are shown in the insets of Fig. 4(c). As shown in Fig. 4(a) and 4(b), the pattern array of nanoparticles was strongly affected by the thickness of Au films at a given RTA temperature. The average diameter of nanoparticles became larger and the average period between adjacent nanoparticles was increased while their density was reduced as the Au film thickness was increased. The average diameter and period as well as the density were estimated using a commercial image processor (ImageJ 1.42q, NIH). The average diameters and densities of Au nanoparticles were increased and decreased from 70±25 nm and ~46% at 5 nm of Au film to 278±100 nm and ~26% at 15 nm, respectively. The average periods were 106±39, 283±103, and 410±148 nm for Au films of 5, 10, and 15 nm, respectively. For thicker Au films, the islands get bigger and the correlation distance becomes larger because the Au nanoclusters merge together [33], thus reducing the density as can be seen in Fig. 4(b). Therefore, the period, size, and density of mask patterns can be controlled by the metal film thickness. The Au nanopatterns were transferred directly into the underlying glass surface by an ICP dry etching, which produces the glass (i) nanocones or (ii, iii) nanopillars as shown in Fig. 4(c). The etching process was carried out at 5 mTorr for 260 s in 45 sccm C₄F₈ plasma with an additional O₂ gas flow rate of 5 sccm. The RF power was fixed at 50 W with additional ICP power of 1000 W. For Au films of ≥ 10 nm, the nanopillars were formed onto the glass substrates. In the case of the 5 nm-thick Au film, while, the etched profile exhibited the cone-shaped glass nanostructure because the edges were etched much faster than those of the thicker Au films during the etching process in the same etching condition due to the thinner and smaller dewetted Au nanoparticles as the etch mask patterns. Furthermore, the average height of the fabricated glass nanocones was lowered because the etch masks were eroded and removed rapidly. The average heights of fabricated glass nanostructures using different Au film thicknesses of 5, 10, and 15 nm were 250, 350, and 360 nm, respectively.

 

Fig. 4 (a) Average diameter and density of nanoparticles and average period of nanopatterns as a function of Au film thickness and SEM images of (b) thermally dewetted Au nanoparticles as mask patterns (top-view) after RTA of 600 °C for 3 min and (c) fabricated glass nanostructures (30°-tilted oblique view) for different Au film thicknesses of (i) 5 nm, (ii) 10 nm, and (iii) 15 nm. The side-view SEM images of the corresponding structures are shown in the insets of (c). The side-view SEM image of the glass nanostructure for the 10 nm-thick Au film is shown in the inset of Fig. 2(a)

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Figure 5(a) shows the measured total transmittance spectra of the fabricated glass nanostructures using thermally dewetted Au nanoparticles after RTA of 600 °C for 3 min for different Au film thicknesses of 5, 10, and 15 nm. The measured total reflectance spectra of the corresponding glass nanostructures are also shown in the inset of Fig. 5(a). The transmittance also depends on the period of nanopillars and nanocones as can be seen in Fig. 5(a). For Au films of ≥ 10 nm, the transmittance spectra have the oscillations due to the interferences at the interfaces of air/nanopillars and nanopillars/substrate like an effective single layer with the abrupt changes of the refractive index, as mentioned above. Also, the low transmittance region of < 92% was shifted towards the longer wavelengths and became lower and broader with increasing the period. For 5 nm-thick Au films, however, the cone-shaped glass nanostructure with a small average period of ~106 nm exhibited a high transmittance of > 95% over a wide wavelength region of 430-1100 nm without oscillations, indicating the T_ave value of ~95.5% at wavelengths of 300-1100 nm. This is attributed to the reduced Fresnel reflection on the glass surface by the cone-shaped nanostructure which has a linearly graded effective refractive index distribution between air and the glass substrate and its sufficiently small period [17,23]. Similarly, these optical properties were also shown in the measured total reflectance spectra as can be seen in the inset of Fig. 5(a). For comparison, considering only single side with nanostructures by neglecting flat back surface reflection, the calculated average total reflectance (R_ave) of the cone-shaped glass nanostructure with a period of 106 nm was estimated to be ~ 0.7% at wavelengths of 400-1000 nm, indicating a reduction by ~ 80.6% compared to the flat glass (i.e., R_ave~ 3.6%). This R_ave value is lower than ~ 1.7% of the magnesium fluoride (MgF₂) film with a refractive index of 1.38 on the glass substrate as a single layer ARC which is reduced by 58.5% (R_ave~ 4.1% for the flat glass) from the calculated result in other report [42]. To explore the percentage of the incoming solar energy which is transmitted by the glass nanostructures, the solar-weighted transmittance (SWT), i.e., the ratio of the useable photons transmitted to the total useable photons, can be estimated [43]. The SWT is given by

 

Fig. 5 (a) Measured total transmittance spectra of the fabricated glass nanostructures using thermally dewetted Au nanoparticles after RTA of 600 °C for 3 min for different Au film thicknesses of 5, 10, and 15 nm and (b) contour plots of calculated total transmittance as a function of period for glass (i) nanopillars and (ii) nanocones with a height of 250 nm at wavelengths of 350-1100 nm. The measured total reflectance spectra of the corresponding glass nanostructures are also shown in the inset of (a).

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Figure 5(b) shows the contour plots of calculated total transmittance as a function of period for glass (i) nanopillars and (ii) nanocones with a height of 250 nm at wavelengths of 350-1100 nm. In calculations, we assumed that the bottom diameter of both nanopillars and nanocones was increased with the ratio of 0.7 to their period in consideration of the average diameter and correlation distance of the disorderly patterned Au nanoparticles. For both glass nanopillars and nanocones, as the period is increased, the low transmittance region of < 92% is shifted towards the longer wavelength region. When the light with a normal incident angle (θ_i = 0°) enters into the grating structure with a period of Λ, the angle of the reflected diffraction waves θ_r,m in the m-th diffraction order are given by the grating equation [45]:

Figure 6 shows the photograph images of (a) the flat glass substrate and fabricated glass nanostructures for different Au film thicknesses of 5, 10, and 15 nm and (b) water droplets on the samples. For the flat glass substrate, it can be observed that the characters under the sample are nearly not seen due to the reflected white fluorescent light. However, the fabricated glass nanostructure samples yield the transmitted characters together with weak reflected fluorescent lights of different colors. These results confirm their higher transmission property than that of the flat glass substrate in the visible wavelength region of 400-700 nm. The different high transmitted wavelength regions were attributed to the different periods of the glass nanostructures as shown in Fig. 5(a). The fabricated glass nanostructures produced more hydrophilic surfaces with contact angles (θ_c) of 31, 41, and 46° for Au film thicknesses of 5, 10, 15 nm, respectively, compared to the surface of the flat glass substrate (θ_c~65°), which is similar to other report [29]. For contact angle measurements, the standard deviation was approximately ± 2°. This means that the hydrophilicity can be enhanced by the roughness on the hydrophilic surfaces as proposed by the Wenzel’s equation though it is also dependent on the surface energy of materials [47]. Therefore, this glass nanostructure can provide the self-cleaning feature of the dust particles on the surface of optical mirrors and lenses, building windows, and optoelectronic devices as well as the anti-fog function in real environments.

 

Fig. 6 Photograph images of (a) the flat glass substrate and fabricated glass nanostructures for different Au film thicknesses of 5, 10, and 15 nm and (b) water droplets on the samples.

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4. Conclusion

We experimentally and theoretically investigated the optical transmission properties of nanostructures with different pillar and cone shapes on glass substrates by C₄F₈/O₂ ICP etching using thermally dewetted Au nanomask patterns. The transmittance of the fabricated glass nanostructures was dependent on their geometry and shape. The measured data reasonably showed a similar behavior with the calculated results. The glass nanostructures exhibited higher transmittance than the flat glass substrate over a wide wavelength range of 400-1100 nm, indicating the better average transmittance for the glass nanocones compared to the glass nanopillars. Using the Au film of 5 nm, the fabricated glass nanocones with a small period of 106 ± 39 nm improved the average total transmittance and solar weighted transmittance and also produced a more hydrophilic surface. These results can give a better insight into the nanostructures with broadband high transmission properties as well as self-cleaning and anti-fogging functions on the glass substrate for the fabrication of high-performance optical elements and optoelectronic devices.