1 Introduction

Anti-reflective (AR) coatings are used in various optical products, such as cameras, microscopes, and display panels [1,2,3]. A multilayer AR coating comprises several stacked layers with varying refractive indices [4]. Among these layers, the top layer contributes the most to AR performance. Decreasing the refractive index (n) of the top layer is necessary to improve AR performance. MgF2 has the lowest refractive index (n = 1.38) but is not sufficiently low for AR coatings [5].

Most low refractive index materials possess a porous structure. The total refractive index of an AR film can be reduced by forming pores containing air (n = 1) in the film. To date, various porous materials, such as CaF2, MgF2, and Al2O3 have been synthesized [6,7,8]. In particular, SiO2 was focused on materials for preparing porous structures [9,10,11]. The use of large amount of air to decrease the refractive index of a film tends to cause considerable scattering of light [12, 13]. Moreover, these materials have unstable refractive indices because their pores adsorb moisture from the air easily [14]. To prevent the adsorption of moisture, hydrophilic Si-OH groups of the film surface are often capped. However, the refractive index of the film increases unless the amount of capping agent is controlled [15, 16].

Many studies have reported that a multi-coating of a porous film that contains SiO2 and whose refractive index is lesser than 1.20 can achieve high transmittance [17, 18]. Therefore, a thin film with n < 1.20 is required for AR coating. However, porous SiO2 thin films prepared via sol–gel reactions often contain large SiO2 particles (several tens of nanometers) in their inner structure and exhibit large Rayleigh scattering, which decreases the transmittance of the film [5, 19, 20]. Therefore, a finely structured thin film of porous SiO2 is required for optical applications. In this study, an easy sol–gel method was used to prepare porous SiO2 thin films. The obtained porous SiO2 films exhibited low light scattering and were humidity resistant. In addition, structural analysis and calculations were conducted, and the factors responsible for the low refractive index and scattering were discussed.

2 Experiment

2.1 Materials

Tetramethyl orthosilicate (TMOS; Tokyo Chemical Industry Co., Ltd.) was used as the silica source. 1-Methoxy-2-propanol (PGME; FUJIFILM Wako Pure Chemical Corporation) was used as a solvent. Triethylamine (TEA; Tokyo Chemical Industry Co., Ltd.) was used as the catalyst for the sol–gel reaction. Hexamethyldisilazane (HMDS; Tokyo Chemical Industry Co., Ltd.) was used for the surface treatment of the porous SiO2 thin films.

2.2 Sample preparation

The typical preparation methods are described in this section. First, PGME (54.43 g) was poured into a polytetrafluoroethylene (PTFE) bottle. H2O (1.731 μL), TEA (36.10 μL), and TMOS (7.310 g) were then added into the bottle at a molar ratio of TMOS: H2O: TEA = 1: 2: 0.01 and stirred for ~27 h at the room temperature. The as-prepared coating liquid containing 4.54 wt% of SiO2 was filtered using a PTFE filter having a pore size of 5.0 μm and then spin-coated onto a substrate. The films thus obtained were heated to 160 °C for 3 h to obtain a film denoted as SiO2_PGME_TEA. After heating, the SiO2_PGME_TEA was treated with HMDS to enhance its hydrophobicity. Subsequently, the film, which was coated on a substrate with 30 mm diameter, was sealed in a closed vessel with HMDS (0.6135 μL) for 24 h at room temperature. Finally, the product was heated at 60 °C for 0.5 h to form SiO2_HMDS.

2.3 Calculation of the refractive index

This research is aimed at obtaining low refractive index thin films. Therefore, the reliability of the refractive index calculation method is very important. The refractive index was calculated with SiO2_PGME_TEA described in Experimental procedure. To calculate the refractive index of a thin film with a low refractive index from its reflectance, a substrate with a high refractive index must be used. This is because the greater the difference between the square of the refractive index of the film and the refractive index of the substrate, the greater the change in reflectance in response to minute changes in the film refractive index, and more reliable the calculation of the refractive index (Eq. (1)) [21].

$$R = \left( {\left( {n_s-n^2} \right)/\left( {n_s + n^2} \right)} \right)^2$$
(1)

R: reflectance; n: refract index of thin film; ns: refract index of substrate

Therefore, J-SF13 with n = 1.74 (HIKARI GLASS Co., Ltd.), which has the highest refractive index among easily available substrates, was used as the substrate. First, the absence of absorption (extinction coefficient; k = 0) in the visible wavelengths (350–800 nm) of SiO2_PGME_TEA was confirmed via ellipsometry. Reflectance measurements at 350–800 nm deposited on J-SF13 substrates were calculated via fitting with Cauchy’s dispersion formula. As a result, the refractive index dispersion shown in Supplementary Fig. S1 was obtained. The refractive index of SiO2_PGME_TEA was n = 1.17 at 550 nm. Furthermore, reflectance of SiO2_PGME_TEA on quartz with nd = 1.52 (HIKARI GLASS Co., Ltd.) and J-BK7A with nd = 1.52 (HIKARI GLASS Co., Ltd.) showed the same refractive index at 550 nm in case of J-SF13 substrate. The refractive index of SiO2_PGME_TEA prepared under the reference conditions was reliably determined as n = 1.17.

The refractive indices of the films prepared by other conditions other than the reference conditions were calculated in the same way as the fitting of refractive index using multiple substrates.

2.4 Analysis equipment

Reflectance and transmittance were measured using a UV–vis spectrophotometer (U-3900; Hitachi High-Tech Science Corporation). Refractive indices at 550 nm were calculated using reflectance and TFCalc (HULINKS, Inc.). The intensity of light scattered from the porous SiO2 thin films coated on quartz substrates was measured using self-assembled equipment composed of an integrating sphere photometer and a light source and was calculated as the sum of intensities of forward- and back-scattered light. The thin films were observed using a scanning electron microscope (SEM, SU9000, Hitachi High-Tech Corporation) and a three-dimensional transmission electron microscope (3D-TEM, JEM-F200, JEOL Ltd.). The pore distribution in the films was analyzed using positron annihilation spectroscopy (PALS-200A, Fuji Imvac Inc.). The contact angles were measured using a contact angle meter (Drop Master DM-501, Kyowa Interface Science Co., Ltd.). Infrared reflection–absorption spectroscopy (IR-RAS) was performed using a spectrometer (FT/IR-6100, JASCO Corporation) with a Vee MAX III variable angle specular reflectance accessory (PIKE Technologies). The packing density of nanoparticles was simulated using Structure of NAno Particles (SNAP) simulation by simulation program SNAP-L ver.3.0.0 (Products Innovation Association).

3 Results and discussions

3.1 Effect of solvent on SiO2 thin films

The relationship between the sol–gel reaction time and the refractive index of the films was investigated. In addition, the experiment was repeated with different solvents namely, PGME, methanol, 1-propanol, and 1-pentanol, to investigate the effect of a solvent on the relationship. Figure 1 shows the relationship between the sol–gel reaction time and the refractive index of the prepared films. In all cases, the refractive index decreased with reaction time. This behavior was consistent with previously reported results [22]. The behavior is attributed to generating a bulky structure that consists of SiO2 and enlarges over time in the reaction mixture. The bulkier the SiO2 structure, the more the number of and larger pores, formed that contain air. Therefore, the refractive index of the thin films decreases over time. The largest decrease in the refractive index was observed when 1-pentanol was used as a solvent. The refractive indices of the thin films prepared using methanol and 1-propanol were almost equal (n ~ 1.20).

Fig. 1
figure 1

Relationship between the sol–gel reaction time and the refractive index of thin films prepared with (a) PGME, (b) methanol, (c) 1-propanol, and (d) 1-pentanol as solvents

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Figure 2 shows the relationship between refractive index of the film prepared from the coating liquid reacted for an arbitrary time and transmittance at 350 nm of the same coating liquid for different solvents. In all cases, the transmittance and refractive index decreased with reaction time simultaneously. As shown in Fig. 1, SiO2 structures grew and aggregated in coating liquid during the sol–gel reaction, which increased the porosity of the SiO2 thin films. Figure 2 provides data to consider how SiO2 fine structure can be formed without particle growth and aggregation, increasing scattering and decreases transmittance. The transmittance corresponding to PGME was higher than that corresponding to methanol and 1-propanol when the refractive indices of the thin films were almost the same; for example, the refractive index was approximately 1.20. The reaction mixture containing 1-pentanol exhibits the highest transmittance. These results indicate that finely structured SiO2 was formed when PGME and 1-pentanol were used as solvents.

Fig. 2
figure 2

Relationship between refraction index of the thin film and the corresponding transmittance at 350 nm of the same coating liquid prepared using (a) PGME, (b) methanol, (c) 1-propanol, and (d) 1-pentanol

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The results showed transesterification occurred between the methoxy group of TMOS and the solvent during the sol–gel reaction. The reactivity of silanes that underwent transesterification was lower than that of TMOS, possibly because silanes contain a bulkier alkoxy group than TMOS. The bulky alkoxy group on the surface of the SiO2 structure prevented the aggregation of the SiO2 particles. The transesterification reaction also prevented the growth and aggregation of SiO2 structures. In addition, PGME is considered a suitable solvent for controlling the refractive index of AR coatings because it tends to reduce the refractive index near 1.20 gradually.

Figure 3 shows the photographs and optical microscopic images of the thin films prepared in this study. As shown in Fig. 3a, b, radial striations can be observed in the SiO2 thin film surface prepared using methanol. In contrast, thin films prepared using 1-propanol (Fig. 3c, d), 1-pentanol (Fig. 3e, f), and PGME (Fig. 3g, h) exhibit smooth surfaces.

Fig. 3
figure 3

Appearance of a thin film prepared using a coating liquid containing (a) methanol, (c) 1-propanol, (e) 1-pentanol, and (g) PGME; b, d, f, and h represent the corresponding optical microscopic images

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From the above results, PGME can be considered a suitable solvent for fabricating porous silica thin films as AR coating from view points of control of refractive index and appearance.

3.2 Effect of the base on the structure of porous SiO2 thin films

To investigate the effect of the base on the structure of SiO2 thin films, SiO2 thin films were prepared using NH3, propylamine (PA), and diethylamino (DEA) in place of TEA in the original preparation method. In each experiment, the refractive index of the thin films was adjusted to n = 1.17 by controlling the reaction time.

Figure 4 shows the cross-sectional SEM images of the thin films. A SiO2 framework comprising small connected particles was observed in all porous SiO2 thin films. In Fig. 4, the diameter of a SiO2 primary particle was considered corresponding to the thickness of the framework. Therefore, the SiO2 primary particle diameter was measured at four points and averaged in each SEM image (Fig. S2). SiO2_PGME_NH3 (Fig. 4a) and SiO2_PGME_PA (Fig. 4b) possessed thick frameworks. The second thinnest and thinnest frameworks were observed in SiO2_PGME_DEA (Fig. 4c) and SiO2_PGME_TEA (Fig. 4d), respectively. The thicknesses of the SiO2_PGME_NH3, SiO2_PGME_PA, SiO2_PGME_DEA, and SiO2_PGME_TEA frameworks, measured using their SEM images, were 15.8, 15.3, 11.0, and 9.8 nm, respectively.

Fig. 4
figure 4

Cross-sectional SEM images of (a) SiO2_PGME_NH3, (b) SiO2_PGME_PA, (c) SiO2_PGME_DEA, and (d) SiO2_PGME_TEA

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Table 1 shows the amount of scattered light at 350 nm by thin films. The amount of light scattered by SiO2_PGME_PA was the highest, whereas that scattered by SiO2_PGME_TEA was the smallest.

Table 1 Amount of scattered light at 350 nm by the porous SiO2 thin films
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Figure 5 shows the viscosity of the reaction mixture to reaction time. The viscosity increased with reaction time for samples prepared using PA, DEA, and TEA catalysts. Notably, the maximum increase in viscosity is observed for TEA. The type of basic catalyst affected the formation of SiO2 because of the inductive effect, steric hindrance of the catalysts and solvent [23]. The pKa values of NH3, propylamine, diethylamine and triethylamine in water are 9.21, 10.53, 10.98 and 10.65, respectively [24]. It means that basicity decreases in the order diethylamine > triethylamine > propylamine > NH3. However, the pKa values listed here are those in water, which have been widely reported, and these values vary with the solvent. It has been reported that tertiary amines may have a higher pKa than secondary amines in organic solvents [25]. This is owing to the stability of the generated cationic species in the solvent and other factors. Therefore, it must be noted that the reaction of this study was carried out in an organic solvent, mainly PGME. Furthermore, the composition of solvent was changed with the progress of reaction owing to methanol produced by hydrolysis. Therefore, discussing the reactivity of the base from the pKa value of a particular solvent is difficult. However, TEA has the highest reactivity in PGME than other bases. This may be because TEA has three alkyl chains, which are electron-donating groups, and the NH(C2H5)3+ generated from TEA has stability in organic solvents owing to its three alkyl chains. SEM images and viscosity measurements showed that small SiO2 nanoparticles were simultaneously generated and interconnected when TEA was used as a basic catalyst.

Fig. 5
figure 5

Viscosity of the reaction mixture containing (a) TEA, (b) DEA, (c) PA, and (d) NH3 as the catalyst to reaction time

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These results indicate that the structure of the porous SiO2 thin films differed depending on the organic base used. In particular, a fine-structured low-scattering film was obtained using a highly basic catalyst (TEA). However, gelation did not proceed when NH3 was used as a basic catalyst. The refractive index of the thin film could be decreased by interlinking small SiO2 nanoparticles using TEA and by growing SiO2 nanoparticles using NH3. In conclusion, TEA is a suitable catalyst for synthesizing porous SiO2 thin films for AR coating.

3.3 Inner and surface structure of a thin film

The Structural characteristics of SiO2_PGME_TEA (n = 1.17) were investigated. Figure 6 shows the pore distribution measured via positron annihilation spectroscopy. Two peaks were observed at 0.48 nm and 2.4 nm. The peak at 0.48 nm could be attributed to the gap in the siloxane framework [26] and that at 2.4 nm could be ascribed to the presence of pores in SiO2 films.

Fig. 6
figure 6

Pore size distribution of SiO2_PGME_TEA (n = 1.17) measured using positron annihilation spectroscopy

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Figure 7 shows a 3D-TEM image of SiO2_PGME_TEA. The colored areas represent pores that were detected by image analysis. Several pores were distributed inside the film. Image analysis also revealed the pore distribution (Supplementary Fig. S3), which showed that the pore diameter was in the range of 2–3 nm. This is consistent with the results induced via positron annihilation spectroscopy. Additionally, porosity was calculated to be 65 vol % via image analysis. Considering that the refractive index calculated from the reflectance measurement was n = 1.17, the porosity of the film was calculated from the Lorentz–Lorentz formula using the refractive index of SiO2 and air and their volume fractions [27]. The porosity calculated using the refractive index was 62.2 vol %. This result indicates that a 3D-TEM structural analysis was appropriate. Therefore, SiO2_PGME_TEA was confirmed to possess abundant pores of diameter 2–3 nm and a high porosity of over 60 vol%. This high porosity was attributed to the bulky colloidal SiO2 structure grown in the coating liquid. If SiO2 in the coating liquid were mono-dispersed spherical particles, the porosity of porous SiO2 thin films would be 49.4 vol%, as calculated using SNAP simulation (Supplementary Fig. S4) [28, 29]. This shows that the SiO2 in the coating liquid possessed a bulky structure formed by connecting small SiO2 nanoparticles. Because bulky SiO2 structures could not be densely packed like mono-dispersed spherical nanoparticles, they formed a highly porous SiO2 thin film.

Fig. 7
figure 7

3D-TEM image of SiO2_PGME_TEA. The refractive indices of the films were adjusted to n = 1.17. Colored areas were detected pores using image analysis

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The size of the pores in SiO2_PGME_TEA (2–3 nm) was smaller than the wavelength of visible light, indicating that SiO2_PGME_TEA can exhibit a low scattering of light [30].

3.4 Enhanced hydrophobicity of SiO2_PGME_TEA

The adsorption of moisture from air into porous SiO2 was reported to increase the refractive index [14]. When porous SiO2 is used for AR coating, increasing the refractive index affects the optical properties. Therefore, the Si–OH groups in SiO2_PGME_TEA should be capped by hydrophobic groups. HMDS was used for capping the Si–OH groups because it is commonly used for hydrophobization [31].

Figure 8 shows the IR-RAS spectra of SiO2_PGME_TEA and SiO2_HMDS. An adsorption band at 1250 cm−1 was observed in SiO2_HMDS spectra, which was assigned to ν (Si–C) [32]. It showed that HMDS was introduced into SiO2_PGME_TEA.

Fig. 8
figure 8

RAS-IR spectra of SiO2_PGME_TEA (a) before and (b) after HMDS treatment

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In addition, the contact angles of SiO2_PGEM_TEA and SiO2_HMDS were measured to be 8.7° and 65°, respectively (Fig. 9). This indicated that SiO2_PGEM_TEA possessed a hydrophilic surface, whereas SiO2_HMDS possessed a hydrophobic surface. These results revealed that HMDS successfully capped the Si-OH group and increased the hydrophobicity of SiO2_PGME_TEA.

Fig. 9
figure 9

Contact angle measurement of SiO2_PGME_TEA (a) before and (b) after HMDS treatment

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The refractive indices of SiO2_PGME_TEA and SiO2_HMDS are listed in Table 2. The refractive index of SiO2_HMDS was higher than that of SiO2_PGME_TEA. It probably indicated that HMDS was introduced into the pores of SiO2_PGME_TEA. Moreover, the changes in refractive indices after keeping the films at 24 °C and 35% relative humidity for 1 d and 7 d were compared. The increase in the refractive index of SiO2_HMDS was smaller than that of SiO2_PGME_TEA for both 1 and 7 d.

Table 2 Refractive indices of SiO2_PGME_TEA and SiO2_HMDS on 0, 1, and 7 d
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Hence, the HMDS treatment prevented an increase in the refractive index of the porous SiO2 thin films via the capping of the Si-OH groups.

4 Conclusion

Porous SiO2 thin films having low refractive indices were successfully prepared via a simple sol–gel method. The choice of solvent and basic catalyst is a key factor for controlling the reactivity of the coating liquid and forming a smooth film that exhibits low scattering. The porous SiO2 thin film fabricated in this study could be used as a broadband AR coating with stacked undercoating and as a lens and sensor in various optical devices.