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Abstract
Moth-eye films have pillars of circular truncated cones with dimensions of one-hundred nanometers as bristles. A moth-eye film coated with gold of 30 nm thickness shows significant broadband light absorption (BLA) over the visible wavelengths. This property stems from the pillars coated with gold, which efficiently confine and localize the light around the pillars. The measured spectra of reflectance, transmittance, and absorptance are supported by those calculated by the finite-domain time difference method. We modeled the pillars as cylinders or circular truncated cones, and calculated their spectra. Among these models, the circular truncated cones coated with gold have the highest BLA property. Gold-coated moth-eye films provide us with a large-area BLA material that is useful for optical devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
A highly efficient light-absorption property is useful for applications in photonics such as filters and light harvesting and emitting devices. However, it is impossible to obtain effective light-absorption using a simple flat surface, even if the material has a large imaginary permittivity. This is because it is impossible to avoid reflection at a flat interface between two media. An option for efficient light absorption is to locate a layer designed for effective absorption between the two media. This layer must have effective complex permittivity, which can only be realized by using designed composite materials, such an effective medium and metamaterials.
A few reports have appeared on broadband light absorption (BLA) property [1–4]. Thin BLA metamaterials based on metallic nanostructures such as particle assemblies, grating, and grooves have been reported [5–16]. The mechanism of the BLA property in the metallic nanostructures has been also discussed both theoretically and experimentally [9,17–19]. We previously reported large-area BLA property of gold-coated natural nanostructures, such as lotus leaves without using any nano-fabrication techniques [20,21]. Among the various nanostructures, arrays of metallic or metal-coated pillars in the shape of wires and cones have been investigated [10,22,23], because it is rather easy to fabricate a wide-area BLA film. Recently we report that the gold-coated cicada wing shows BLA property [24], because array of nanometer-sized cone pillars exists at the cicada-wing surface.
Although natural materials with nanostructure is interesting for scientific research, it is not suitable for practical use, because of low reliability and stability. Thus we adopt a moth-eye film, which is an artificial material with nanostructure similar to the surface of cicada wings. The moth-eye film is commercially available and is used for antireflection stemming from the nanostuture [25–27]. It is a transparent polymer film whose surface has an array of nanometer-sized cone pillars. This surface structure mimics eyes of a moth, whose surface has low reflectivity. As is expected, the gold-coated moth-eye film exhibits the BLA property. The BLA mechanism is also investigated using the finite-difference time-domain (FDTD) method. It was found that the hybrid structure of the dielectric pillar and gold film efficiently confines the light localized in the gaps between the pillars. The gold-coated moth-eye film provides us with a large-area BLA medium that is useful for optical devices.
2. Experiments
The moth-eye film used in this study is MOSMITE$^\textrm {TM}$, provided by Mitsubishi Chemical Corporation, which is made of polyethylene terephthalate (PET). It has an array of nanometer-sized cone pillars (approximately 100 nm in diameter at the bottom) fabricated on the front surface of the film. The density of the pillars is $\sim$ 150 $\mu$m$^{-2}$, corresponding to an inter-pillar distance of $\sim$ 85 nm. It was cut into a size of 10 mm $\times$ 10 mm and fixed on a silica glass substrate 1-mm thick. The back of the film is coated with a transparent adhesive and can be stuck to the plate as it is. Gold-sputtering was performed with an E-1030 sputtering coater (Hitachi). The thickness is monitored by quartz microbalance, and the deposition was made to give a gold film with a thickness of 10 or 30 nm on a flat surface.
The reflection and scattering spectra were obtained with a USB-2000 spectrometer (Ocean Optics) using a halogen lamp as a light source. The light was guided to the sample by an optical fiber (multimode; core diameter of 400 $\mu$m) to illuminate the sample surface at normal incidence with random polarization. Reflected or transmitted light was conveyed to the spectrometer with a multimode optical fiber of 400 $\mu$m in diameter. The reference spectrum was measured with a 1-mm thick silica plate for transmittance and a silver mirror for reflectivity. For the scattering measurements, the back-scattered light was detected at approximately 60$^\circ$ with respect to the surface normal. An SRS-99 diffuse reflectance standard (Labsphere) was used as a reference. The scattered light intensity S was normalized by that from an SRS-99 diffuse reflectance standard, $S_0$ to have a rate of $S/S_0$. Scanning electron microscopy (SEM) observations were performed with an S-4500 (Hitachi).
The numerical electric-field calculations were performed with a software of Lumerical FDTD Solutions. A pulse light was used for illumination with a center wavelength of 450 nm and covering wavelengths in the range of 300–1100 nm. The light was incident along the $z$-axis at normal incidence. The size of the Yee lattice was 1 nm $\times$ 1 nm $\times$ 1 nm. The boundary condition was periodic in the $x$- and $y$-directions and had perfect absorption using perfectly matched layers in the $z$-direction. The transmitted or reflected light spectra were obtained by analysis of the discrete Fourier transform. In this condition, the reflected and transmitted light included back- and front-scattering light, respectively.
3. Results and discussion
3.1 Photographic and SEM image
Figure 1(a) shows an SEM image of a 10-nm-thick gold-coated moth-eye film. An array of pillars of 85 nm in diameter and 200 nm in length is observed on the surface. Inset is a photographic image of the gold-coated moth-eye film. It is lightly gray and rather transparent. This means that the thickness of the gold is not sufficient for the BLA property. Figure 1(b) shows an SEM image of a 30-nm-thick gold-coated moth-eye film. The structure is similar to that of the 10-nm-thick gold-coated moth-eye film, except for the slightly thicker pillars. The inset of Fig. 1(b) is a photographic image of the gold-coated moth-eye film. It is black and exhibits the BLA property despite the gold coating.
Fig. 1. SEM image of gold-coated moth-eye film, (a) 10 nm thick and (b) 30 nm thick. (c) Enlarged view of (b). Inset is a photographic image of the gold-coated moth-eye film (10 mm $\times$ 10 mm).
3.2 Measured spectra
Figure 2(a) shows the reflectance spectra measured for a 30-nm-thick flat, thin gold coating and a moth-eye film covered with a 30-nm-thick gold coating. The flat gold film has high reflectivity, over 80% at wavelengths longer than 700 nm. Its reflectivity is low (less than 50%) in the wavelength range of 400–550 nm because gold has less metallic character in this wavelength range. In other words, the negative permittivity of gold rises and approaches zero when considered from the long wavelength side where the gold shows metallic character. The imaginary permittivity is also higher at this wavelength range. The reflectivity of the moth-eye film stays at 10% or less throughout the measured wavelength range of 400–1000 nm. The transmittance spectra are shown in Fig. 2(b). Both spectra have similar transmittance, $\sim$20%, at wavelengths shorter than 800 nm. The transmittance of the gold flat film decreases with wavelength in the range longer than 800 nm because the negative and real permittivity of gold lowers with increasing wavelength. In contrast, the transmittance of the gold-coated moth-eye film increases with increasing wavelength.
Fig. 2. Measured spectra of (a) reflection, (b) transmittance, and (c) absorptance for a 30-nm-thick gold film and a moth-eye film coated with 30-nm-thick gold coating. Inset is optical geometry for the measurements.
We measured the scattered light intensity $S$ divided by that from an SRS-99 diffuse reflectance standard, $S_0$. The rate $S/S_0$ was less than 2% throughout the wavelength range of visible and NIR wavelengths. Thus, the scattering light is negligible, and the absorptance can be evaluated by subtracting the reflectance and transmittance from unity. Figure 2(c) shows the absorptance spectra. The absorbance of the flat gold film is low, whereas the moth-eye film has high absorptance, over 70% in the visible wavelength range. The spectra are consistent with the appearance of the sample, as shown in the inset of Fig. 1(b). The gold-coated moth-eye film shows the BLA property.
3.3 Calculation model
In order to interpret the experimental results, we modeled pillars of three different shapes and performed FDTD calculations. The models are depicted in Fig. 3. Figure 3(a) shows a bird’s-eye view of the model of the gold-coated moth-eye film. The moth-eye film is made of PET, whose refractive index is 1.57 with no absorption. It is on a silica-glass substrate with a refractive index set as 1.5. The refractive-index dispersion of PET and silica glass is ignored because of no absorption in this wavelength range. For simplicity, we set the pillars to form a square lattice with an inter-pillar spacing $p = 100$ nm, instead of the observed inter-pillar spacing of 85 nm. This is because the inter-pillar spacing does not significantly affect the optical response, as discussed later.
Fig. 3. (a) Bird’s-eye view of the model of the gold-coated moth-eye film. Cross-sectional illustrations of a pillar in (b) model A, (c) model B, and (d) model C.
Figure 3(b) shows the cross-sectional illustration of a pillar in model A. The shape of the pillar on the moth-eye film can be approximated to a circular truncated cone with a top diameter of 50 nm, a bottom diameter of 100 nm, and a height of the cone, $h$. The surface of the PET pillars is coated with sputtered gold. As the sputtering gave a physical thickness of 30 nm on a flat surface, the thickness of the gold coating, $t_1$, at the top and that at the lower horizontal surface can be set as 30 nm. However, it is not straightforward to set a gold thickness of the conical surface because the sputtering beam onto the conical surface is locally oblique. One possible thickness of the gold coating at the conical surface, $t_2$, is given under the assumption that the flux of the sputtered gold is like a beam and is directed perpendicular to the film surface. Here $t_2$ is a thickness at the conical surface in the direction parallel to the film surface. Then, we have a relation, $t_2 / t_1 \sim 25$ nm$/ h$, from geometry consideration. With a thickness of the deposited gold $t_1 =$ 30 nm and $h = 200$ nm, $t_2$ is determined as 4 nm. However, $t_2 =$ 4 nm is not fit to the SEM image in Fig. 1(c).
Another possible $t_2$ is given under the assumption that the sputtered gold is like vapor and is deposited on the conical surface. According to the SEM image shown in Fig. 1(c), which is a high magnification image of the pillars, the thickness of the gold coating on the conical surface in model A is evaluated ranging from 8 to 15 nm. In order to determine the thickness of the gold coating on the conical surface, we calculated transmittance spectra, as shown in Fig. 4, which were obtained for the model A pillars with $t_2 = 4, 8, 10$ nm, inter-pillar distance $p = 100$ nm, and height $h = 200$ nm. Most of the incident light passes through the conical surface because the gold coatings of 30 nm at the top surface and the lower horizontal surface have low transmittance (~ 10 %). The transmittance is governed by the thickness of the gold coating at the conical surface. By comparing the calculated transmittance spectra with that of the measured spectrum shown in Fig. 2(b), we set the thickness of the gold coating at the conical surface as 8 nm.
Model B is a circular truncated cone of gold without the PET pillar. Its shape and size are identical to those of model A. Model C is a cylindrical pillar of gold and PET with a diameter of 84 nm and a height of 230 nm. As the gold coating on the side of the cylinder is set to be 8 nm thick, the total diameter of the gold-coated cylinder of this model is 100 nm.
3.4 Shape of pillars
We calculated the spectra of the models with different pillar shapes. The models are model A with $t_1 =$ 30 nm, $t_2 = 8$ nm, and $h$ = 200 nm; model B; and model C; as shown in Fig. 3. The corresponding spectra are shown in Figs. 5(a), 5(b), and 5(c), respectively. The reflectivity spectrum of a 30-nm-thick flat gold film is also shown for reference. The flat gold film has a higher reflectivity than that of the other models, indicating that the surface structures reduce reflectivity. Although the shapes of models A and B are identical, their reflectivity spectra are different at wavelengths longer than 600 nm, where model A has lower reflectance. This implies that the dielectric cone plays an important role for the reduction of reflectivity. Model C has a higher reflectivity than that of model A over different wavelengths, suggesting that the cone shape is suitable for lower reflectivity.
Fig. 5. Calculated spectra of (a) reflection, (b) transmittance, and (c) absorptance for models A–C and the 30-nm-thick gold film. Arrows are wavelength marks for the snapshots of the calculated electric-field distribution profiles in Fig. 8.
Figure 5(b) shows the transmittance spectra, which include the contribution of the front-scattered light. The transmittance of models A and B is similar to that of the flat gold film in the visible wavelength range. While the reflectivity of model B increases with the increase in wavelength, the transmittance of model B is negligibly small. Figure 5(c) shows the absorptance profiles, evaluated by subtracting the reflectance and transmittance from unity. The absorptance of the gold flat film is the smallest over the wavelength range, suggesting that the pillars on the surface play a significant role for light absorption. While the absorption of model B is slightly higher than that of model A at wavelengths shorter than 600 nm, model A has a higher absorptance at red and NIR light (600–900 nm). The calculated spectra of model A are consistent with the measured ones, except for the lower absorptance at the long wavelengths, from 750 nm to 1000 nm. This stems from higher reflectivity at this wavelength range in the calculated spectra, which is caused by the fact that the reflectivity includes the contribution of backscattering under the boundary condition of the FDTD calculation.
The absorptance spectrum of model C is similar to that of the gold spherical cylinder which shows localized surface plasmon, since the cross-section of the pillars is a circle with a diameter of 100 nm. The model B has broader absorptance band, compared with that of model C. This will stem from the fact that the diameter of the cross-section varies from 50 to 100 nm and their resonance bands are overlapped. Model A has broader absorptance and higher absorption at longer wavelengths. The cross-section of model A is a cylindrical dielectric core covered with a gold shell. Such a dielectric-core/metal-shell structure usually has a strong localized surface plasmon resonance at longer wavelengths, compared with a homogeneous metal cylinder of the same size. Therefore, the dielectric cones of a moth-eye film play an important role for the reduction of reflectivity and the enhancement of absorption at long wavelengths.
3.5 Height dependence
We investigate the optical properties of the cones with different height $h$ in model A. Figure 6(a) shows the reflectivity of pillars with different heights, $h =$ 230, 430, and 630 nm. While the reflectivity is unchanged with the different heights in the visible wavelength range, it is lower for the higher cones at the NIR region, indicating that higher cones have higher light-trapping ability. Figure 6(b) shows the transmittance with different heights. The transmittance is lower for higher cones over the different wavelengths. The absorptance, evaluated from reflectance and transmittance, is plotted in Fig. 6(c). The BLA efficiency, i.e., higher absorptance, is higher for the array of higher cones over the whole wavelength range. This is due to the fact that the longer pillars have stronger localized surface plasmon resonance.
Fig. 6. Calculated spectra of (a) reflection, (b) transmittance, and (c) absorptance for model A pillars with $h =$ 230, 430, and 630 nm.
3.6 Inter-pillar spacing
We show the spectra of model A with different inter-pillar spacing, $p =$ 100, 200, and 300 nm. Figures 7(a) and 7(b) show the reflectivity and transmittance, respectively. The reflectivity is slightly lower for the high-density array, $p = 100$ nm, while the transmittance is similar among the arrays with different $p$. As a result, the absorptance is the highest for the array with the highest density, but the difference is not substantially large.
Fig. 7. Calculated spectra of (a) reflection, (b) transmittance, and (c) absorptance for model A with inter-pillar distance $p =$ 100, 150, and 200 nm.
3.7 Electric field distribution
Finally, we show the electric field distribution of model A calculated using the FDTD method in Fig. 8(a), at three wavelengths, 540, 640, and 840 nm. These wavelengths are peaks or dips in the reflection spectra shown in Fig. 5(a) and they are marked with arrows. The electric field of light penetrates not only in the gap between the cones but also in the moth-eye pillars at a wavelength of 640 nm, at which the absorptance is the highest. The thin gold coating on the conical surface allows the penetration of the electric field in the pillar. This produces the localization of light at the back of the gap, resulting in the low reflectance and high absorptance. In contrast, the degree of penetration in the pillar is lower at a wavelength of 840 nm. This is because of the higher metallic character at this wavelength. Then, the reflectivity is larger than that at 640 nm, as shown in Fig. 5(a).
Fig. 8. Snapshots of the electric field distribution around the pillar of (a) model A and (b) model B at different wavelengths. The corresponding wavelengths are indicated with arrows in Fig. 5.
Figure 8(b) shows the snapshot images of the electric field distribution of model B at three wavelengths, 575, 600, and 840 nm. In model B, where the whole pillar is solely made of gold and the electric field is distributed throughout the gap, the electric field scarcely penetrates into the pillar and the light is reflected, resulting in lower absorptance than that of model A.
The temporal variation of the electric field distribution is given in Fig. 9 and Visualization 1. Light with a pulse length of 2 fs is irradiated on the model A ($t_1 =$ 30 nm, $t_2 =$ 8 nm, $h =$ 200 nm, and $p =$ 100 nm). The illumination light is a pulse and has a center wavelength of 450 nm and a wavelength range of 300–1100 nm. The light energy flow is mostly from upper to lower and it scarcely flow in the opposite direction. The light is localized at the surface structure and gradually relaxed, indicating localized surface plasmon resonance. This behavior can be clearly observed in Visualization 1. This means that the light is captured by the gold-coated moth-eye film and is scarcely released from the gold-coated moth-eye structure, resulting in the BLA property.
4. Conclusion
We have shown that moth-eye films coated with gold have the BLA property over visible wavelengths. This behavior is supported by the FDTD calculations, which were carried out using a model of pillars, circular truncated cones of PET coated with gold on the film surface. We also modeled the pillars as cylinders or circular truncated cones of gold. Among these models, the circular truncated cones of PET coated with gold have the highest absorptance over the wavelength range. According to the electric field distribution calculated using the FDTD method, this absorptance stems from the hybrid pillars, which are suitable for light localization. The gold-coated moth-eye film provides a large-area BLA medium that is useful for optical devices.
Funding
Japan Society for the Promotion of Science (16K13696, 19H02624, 26286058).
Acknowledgments
We thank Mitsubishi Chemical Corporation for providing the MOSMITE$^\textrm {TM}$ film.
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