1. Introduction

To have brilliant colors comparable to colors produced by nature is a goal that humans have been tirelessly pursuing. The commercial pigments in most cases derive their colors from selective light absorption which is connected to their chemical structure. The generation of saturated colors out of non-toxic materials with high ultraviolet (UV) and chemical stability is difficult to achieve [1–3]. Alternatively, a structural color is a color based on spectrally selective light scattering from nanostructures, and thereby depends only on the refractive index distribution and can be produced from non-absorbing and environmentally friendly materials [4,5]. Moreover, different colors could be produced from the same starting materials by changing the structural parameters. At the same time, many structural colors, particularly those based on translational symmetry, are iridescent, thereby changing their color depending on the direction of the incident light and the angle of observation [5–7]. To substitute the conventional pigments, which often are toxic and suffer from fading under UV-irradiation, non-iridescent structural colors from non-toxic and transparent materials have to be developed with sharp spectral characteristics thus a high spectral selectivity to improve the color saturation. However, it is very challenging to achieve such omnidirectional spectral selectivity.

Non-iridescent structural colors based on a disordered arrangement of monodisperse spherical particles (can be air pores embedded in a homogenous matrix), also called direct/inverse photonic glass (PhG/IPhG), have attracted a lot of attention due to a straightforward production procedure [6,8–16]. These types of structures are obtained directly as a layer on a variety of surfaces [11,17] after evaporation of the solvent. Due to the disordered isotropic arrangement, the color impression of such conventional PhGs is independent of the angle of observation, but has a smooth reflection transition, namely poor spectral selectivity. The first-order scattering approximation, Mie scattering and Ewald sphere construction can be used to analyze the reflection from structural colors [18–23]. In contrast to long-range ordered structures, a PhG possesses only a short-range order, analogous to the liquid or amorphous state. The corresponding spatial distribution of the permittivity has a spatial Fourier transform (FT) with a shape of a spherical shell in reciprocal space, the radius of which correlates with the inverse of the interparticle distance [9]. The transition from empty Fourier space inside the spherical shell to the shell maximum is relatively smooth in conventional PhGs/IPhGs [6,10,12,14,21,24]. Thus, the transition from the long wavelength weak-scattering to short wavelength strong-scattering regime is relatively smooth as well. Such a smooth transition in the reflection spectrum leads to a mixture of different reflected colors and, therefore, results in a low color saturation [21]. A single thin shell hollow sphere leads to improved backscattering thus good spectral selectivity and is, thus, promising for structural colors [19]. Recently, Kim et al. [25] demonstrated structural colors based on the PhG out of hollow nanospheres, but the much larger shell thickness still leads to a smooth transition in the reciprocal space, thus, low reflection spectral selectivity for colors. Recently, we have used the motif optimization and demonstrated improved blue color saturation with a direct PhG made from hollow spheres [26]. In order to achieve a better color saturation, the hollow sphere shell thickness had to be <5% of the particle diameter to achieve a sharp FT transition [21]. Such a thin shell can hardly bear mechanical stresses. For the isolated hollow sphere based PhGs, the weak Van der Waals forces between spheres as well as between the color film and substrate after preparation results in very weak adhesion, thus a low scratch stability [11,17,27,28], which will inhibit the future applications such as outdoor paintings, screens etc.

In this work, we theoretically and experimentally show our new concept for a non-iridescent structural color out of surface-templated inverse PhG [29] (ST-IPhG) via atomic layer deposition (ALD). The film thickness can be precisely controlled for the highest color saturation, where the color saturation is defined via the chromaticity point in the CIE diagram in respect to the outer perimeter of the color space, which represents the pure, fully saturated colors. By neglecting the contact points of the inner cores, the ST-IPhG can be considered as a PhG out of conformally coated hollow spheres. The effective motif diameter in this case becomes larger than the inter-particle distance which conceptually differs from the homogenous [10,30] and core-shell particle PhGs [6,24–26,31] or IPhGs [20,24]. This paves an easy way to manipulate the size of the motif without changing the interparticle distance, impossible for direct PhG. We have adjusted the coating thickness and investigated the corresponding effects in order to obtain a sharp transition in the reflection spectrum. The prepared ST-IPhG shows a sharper reflection transition in comparison to the conventional full sphere PhG and suppressed reflection in the longer wavelength region, and, thus, a highly saturated blue color. Our results show that the substructure of the particle, which is much smaller than half wavelength of light, helps to compensate the absence of long-range order and achieve high color saturation. This approach also allows us to further increase the shell thickness. The thicker, denser and solid connected shell is beneficial for higher mechanical stability [27,28].

2. Theory and simulations

The PhG is a particular system which possesses only a near range positional order, but no long-range order in its lattice. Correlated to the real space structure (Fig. 1(a)), in reciprocal space (Fig. 1(b)) such a PhG is represented by the multiplication of the structure factor S with the form factor P=(F_m/V)², where F_m is the motif Fourier Transform (FT) and V is the motif volume) [21]. In our previous works [21,22], we showed that the scattered power from a scattering volume increases proportionally to the square of the overlap between the FT of the permittivity perturbation F{Δɛ(r)} with the Ewald sphere [21,22]. Thus, the light-reflection transition between the no-scattering and back-scattering is determined by the steepness of F{Δɛ(r)} function.

 

Fig. 1. Calculated FTs and scattering efficiency of PhG structures made of different motifs and corresponding simulated reflection spectra. The real space (a) and corresponding reciprocal space (b) representations of a PhG structure made of solid spheres (dashed curve), coated solid sphere (dotted curve) and ST-IPhG, (solid curve). (c) Scattering efficiency per particle for those three kinds of PhGs. Simulated reflection spectra of the (d) solid sphere PhG, (e) coated solid sphere PhG and (f) ST-IPhGs. Insets are the corresponding simulation structures. In figures (d-f) k_l (star) and k_m (colored circle) are shown in respect to each other on the k axis. (g) The corresponding CIE points (solid circle, solid square, hollow circle) are calculated based on these spectra. The paths next to these points indicate how the position in the CIE-diagram changes when the structures in (d), (e) and (f) are scaled with a factor from 1.0 to 0.8. The paths start from the CIE-diagram points of (d), (e) and (f), and both ended with a scaling factor of 0.8. ‘w’ represents the white point.

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The approximate function of radial distribution of ${\cal S}$ can be derived from solving the Ornstein-Zernike integral equation by choosing the hard sphere Percus-Yevick approximation [21]. It can be calculated for PhGs with different packing density (ρ) which is defined as the volume fraction occupied by motifs. Here, we use ρ of 55%, which is an approximation of the value obtained experimentally from hard sphere direct PhGs [32]. The structure factor is determined by the interparticle distance and the statistical parameters of the disordered packing. A main peak is located at k_l=1.15×2π/d for the interparticle distance d. For the FT of a full sphere with diameter d [21], the function always has the first-zero point k_m (colored dot in Fig. 1(b)) located at 1.43×2π/d, thus at the right side of the main peak of the structure factor (indicated by the star in the top graph of Fig. 1(b), ɛ=2.56). The first zero point of the FT of a solid sphere motif can never be tuned to the left side of the main peak of the structure factor by scaling the structure or changing the dielectric strength of PhG/full IPhG [21]. Previously, we have shown the motif FT can be tailored by choosing a core-shell particle. In particular, a non-monotonous dielectric distribution along the radial direction can shift the zero point of the FT motif to the required k position. A particular interest is represented by particles with hollow core as no second material is required in this case. However, the structure factor of PhG out of hollow spheres was correlated to the full particle size, thus very thin shells of <10% of the particle radius were required to shift the motif zero point to required position in respect to the structure factor. Now we show a system for which the structure factor is not determined by the full size of the motif but rather by the size of its inner core. In such system, the lattice is fixed and the motif size is larger than interparticle distance which conceptually differs from the homogenous [10,30], core-shell particle PhGs [6,24–26,31] or IPhGs [20,24]. This offers an easy way to manipulate reciprocal space distribution by simply varying the shell thickness by conformal coating. To shift the first zero point of the motif FT to the left side of the main lattice FT peak the shell thickness will not be limited to a very small value, as was the case in the hollow sphere system [21,25,26]. In Fig. 1(b), the normalized amplitude F_m/V of a PhG structure made of solid spheres (dashed curve), coated solid sphere (dotted curve) and coated hollow sphere (coated solid sphere after calcination of the organic core, solid curve) with a coating thickness h/d = 7.65% (compare to 4∼5% in references [21,26]), ɛ_s=5.29 and background material of air (ɛ_b=1) are shown. Here, we assume the amorphous TiO₂ with a dielectric constant of 5.29 and disregard the index dispersion. Since the coating is still much thinner than the sphere radius, for the analytical calculation, we simplified the motif of the conformally coated PhG to that of a fully coated core-shell sphere by neglecting the absence of a coating in the small contact points between the spheres. Thus, the diameter of the spherical particles assumed in the simulations was d, employing a permittivity ɛ. Onto these spheres of size d, which determined the structure factor of the PhG lattice, a thin shell of thickness h with a permittivity of ɛ_s was considered in the simulations. As can be seen from Fig. 1(b), for the coated solid sphere the first-zero point of the motif FT is positioned right at k_l which eliminates the peak of the PhG-FT upon multiplication in reciprocal space. However, for the hollow shell PhG, achieved by calcination of the polymeric template, the zero point of the motif FT assumes a position left of the k_l, thereby pulling the product function S·P effectively to zero left of its peak with a steeper slope and lower intensity in the low k region. Thus, the ST-IPhG shows a steeper transition from low scattering to strong scattering and lower scattering efficiency in longer wavelength region.

To confirm the theoretical predictions, we have numerically simulated these structures as shown in Figs. 1(d)–1(f). The reflectance spectra are obtained by the brute-force 3D finite integration simulation [33] for the solid sphere PhG (Fig. 1(d), d = 196 nm), the coated solid sphere PhG (Fig. 1(e), d = 196 nm, h = 15 nm) and the ST-IPhG (Fig. 1(f), h = 15 nm). The simulation volume is 2×2×6 µm³ with N = 3348 spheres. The PhGs are then excited by a plane wave incident vertically from air. The lateral sides of the simulation volume are mirrors such that the structure is effectively periodically continued in both lateral directions. The light can exit the simulation volume only through the open boundaries at the top and the bottom. The match layer is lying on the substrate with refractive index equal to the effective refractive index of the PhG. The homogeneous substrate material is then terminated by an open boundary condition. The reflected and transmitted powers are calculated as Poynting vector integration over the upper and lower boundaries, respectively. In these simulations, the motif is a conformally coated structure without any structural simplification, e.g., the fact that some coating is missing in the contact areas is considered. As can be seen from the reflection spectra, the ST-IPhG shows much steeper reflection transition from weak reflection to strong reflection and also a lower reflection in the long wavelength region. The corresponding CIE 1931 chromaticity diagram points were calculated based on the simulation reflection spectra (Fig. 1(g) and Appendix). In such a diagram a fully saturated color originating from monochromatic light can be found on the outer perimeter while a completely unsaturated color is represented by the white point ‘w’ in the center of the diagram [34]. The closer a point to the outer perimeter of the color space, the higher the color saturation. For our simulation spectra, the corresponding points locate at x = 0.25, y = 0.28 (solid circle), x = 0.29, y = 0.27 (solid square), x = 0.19, y = 0.16 (hollow circle) for the solid sphere PhG, the coated solid sphere PhG and ST-IPhG, respectively. The ST-IPhG has a point much closer to the outer perimeter than the full-sphere PhG, which means a much better color saturation. In addition, the coated PhG further moves to the white point which means a loss of color saturation upon coating of the solid spheres. The paths next to these points in Fig. 1(g) indicate the CIE positions which are achieved when each corresponding structure are scaled with a factor from 1.0 to 0.8. The spectra of such structures are just shifted in wavelength, leading to color change. For the solid sphere PhG, the corresponding point first moves towards the outer perimeter and then moves towards the white point ‘w’, where the turning point represents the highest color saturation that can be obtained by the solid sphere PhG, which corresponds to a sphere size of ∼175 nm. For the ST-IPhG, upon scaling, the position gradually moves towards the white point. However, in this scaling factor range, the ST-IPhG always shows better color saturation. For the solid sphere PhG, the non-monotonous dependence of the color saturation on the scaling factor is due to the fact that with the decrease of the sphere size, the strong reflection part in the reflection spectrum moves from longer wavelengths (partially mixed with other colors) into the pure blue region which shows an improved color saturation. Further decreasing the sphere size then moves the reflection out towards the ultra-violet (UV) region reducing the fraction of the reflected blue light. This results in a strong decrease of the blue color saturation.

3. Experimental results

To experimentally verify our predictions from theory and simulations we also prepared polystyrene (PS) solid sphere PhGs by drop-casting and ST-IPhGs via a conformal deposition of TiO₂ by ALD and subsequent removal of the organic phase by calcination. In detail, direct PhGs were produced by drop casting of polystyrene spheres water-based suspension (150 µL) inside a polymer ring onto previously cleaned and heated (60 °C) soda lime glasses (Thermo Fischer Scientific), followed by drying at the same temperature for 15 minutes. To avoid the assemble of the PS particles into a photonic crystal ordered structure, coagulation was induced by adding 1.5 µL of 1 mol/L HCl solution to the PS water-based particles suspension prior to drop cast. The polymer particle sizes and suspension concentration were 172 ± 6 nm, 196 ± 5 nm (Microparticles GmbH) and 5 mg.mL⁻¹, respectively. The direct PhGs were then infiltrated with titanium dioxide by an ALD process performed at 95 °C under a full exposure mode with constant flow of nitrogen (15 sccm) in a home-made reactor (Hamburg University of Technology). An average growth of 0.6 Å per cycle was achieved and the total number of cycles was designed according to the desired film thickness, ranging from 3 to 15 nm. The precursors used were Titanium Iso-propoxide (TTIP, Sigma Aldrich), heated up to 85 °C, and deionized water. The polystyrene core was removed by calcination in air at 500 °C for 30 min with a heating rate of 0.8 °C·min⁻¹.

The thickness of the resulting ALD films was measured by spectral ellipsometry (SENProTM, SENTECH Instruments GmbH) on a Si reference wafer placed close to the samples in the ALD cycle. For color expression, the digital images of the PS solid sphere PhG and the TiO₂ ST-IPhGs are taken simultaneously to ensure the same conditions. The ALD deposition allows to control the film thickness precisely for the highly saturated color. Figure 2 shows the experimental structure of the PS solid sphere PhG with particles size of 172 ± 6 nm (which will be the highest saturation blue structural color from PS direct PhG) and the TiO₂ ST-IPhG with a coating thickness of 15 nm and macro pores defined by the PS former template particles size of 196 ± 5 nm diameter, respectively. The prepared samples are disordered structures with only short range order (see appendix). The coating thicknesses were measured by a spectral ellipsometry on a Si reference wafer placed close to the samples during the ALD cycle. The SEM images (Figs. 2(a) and 2(b)) show that the as-prepared structures have no long-range order as expected for PhG structures. The top view and the cross-sectional SEM images of the ST-IPhG are shown by Figs. 2(c) and 2(d). The SEM image of the original 196 ± 5 nm PS solid sphere (polymeric template for the ST-IPhG) PhG is shown in appendix.

 

Fig. 2. Experimental structures of the solid sphere PhG and the ST-IPhG. Top view (a) and the cross-sectional (b) SEM images of polystyrene (PS) solid sphere PhG. Top view (c) and the cross-sectional (d) SEM images of TiO₂ ST-IPhG.

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The diffuse reflection spectra between 300 nm and 800 nm are measured using UV/VIS spectrometer (Lambda 1050, Perkin Elmer) with 150 mm integrating sphere accessories. The experimentally measured light reflection spectra for the 172 nm PS solid sphere PhG (dot curve) and ST-IPhG (solid curve) are shown in Fig. 3(a). Reflection spectra of 196 nm PS solid sphere PhG and coated solid sphere PhG can be found in appendix. These light reflection spectra demonstrate the same feature as the simulation reflection spectra (Figs. 1(d)–1(f)). The additional reflection drop of the ST-IPhG compared to solid sphere PhG at wavelengths below 360 nm is from the light absorption of TiO₂. The prepared ST-IPhG shows a sharper reflection transition in comparison with the conventional full sphere PhG and suppressed reflection in the longer wavelength region. As can be seen from Fig. 3(b), the TiO₂ ST-IPhG sample (hollow circle) has a position closer to the outer perimeter of the CIE color diagram than the solid sphere (solid circle) indicating a much better saturation in comparison with the full sphere PhG. The achieved color saturation is comparable to the hollow sphere PhG [35]. In Fig. 3(c) we show the colored areas of these two fabricated samples (solid sphere PhG and the ST-IPhG) under identical imaging conditions. To demonstrate the non-iridescent properties both samples are also tilted by 45° keeping the illumination condition fixed. The color is almost absent under white background as expected for structural colors due the fact that the transmitted spectrum is broadband back-reflected from the substrate. In the case of the absorbing black substrate, this transmitted part is broadband absorbed and thus only the part of the spectrum reflected from the PhG itself is observed, resulting in the structural color effect.

 

Fig. 3. The experimentally measured reflection spectra and color impressions. (a) Reflection spectra of PhGs made of 172 nm PS solid spheres (dotted curve) and TiO₂ ST-IPhG (solid curve). (b) The resulting positions in CIE 1931 XYZ color diagram are x = 0.23, y = 0.22 for solid sphere PhG and x = 0.20, y = 0.17 for the ST-IPhG. In addition, the position from hollow sphere PhG [35] also listed as a solid square. The color impressions under white light illumination (c) of the 172 nm PS solid sphere PhG and TiO₂ ST-IPhG viewed at angles of 0° and 45°, respectively. Images in each row represent the same sample with black or white background. Structural colors only show up in thin films when the light transmitted through the film is prevented from reflection by an absorbing black substrate. The digital images of cm sized films are taken simultaneously to ensure the same diffuse white light illumination and viewing conditions for the color comparison.

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4. Coating thickness effect

The first-zero point of the motif FT of a coated sphere PhG (simulations, appendix) can be gradually moved close to the peak positioned at k_l and, thus, nearly eliminates the reflection. The zero point, however, cannot be shifted to the left side of k_l by increasing the coating thickness h. However, for the ST-IPhGs, the first-zero position of motif FT is always positioned at the left side of the k_l. The zero point of the motif FT moves closer to the center of reciprocal space with a larger motif size.

Figure 4 shows the experimentally measured specular reflectance spectra and the corresponding color impressions for samples without (h = 0 nm, solid curve, pentagon) and with TiO₂ thickness of 3 nm (dot curve, square), 6 nm (short dash curve, circle), 9 nm (long dash curve, hexagon), 12 nm (short dash-dot curve, triangle) and 15 nm (long dash-dot curve, star), respectively. The relative position of k_l (red star) and k_m (blue circle) are further shown and the blue arrow indicates the direction of k_m change with coating thickness. For the coated solid sphere PhGs (Fig. 4(a)), the reflection peaks are suppressed in the short wavelength range and the color points in CIE diagram (Fig. 4(b)) move closer to the white point, deteriorating the color saturation, which complies with the theoretical estimation. However, for the ST-IPhGs (Fig. 4(c)), the samples show a much lower reflection in longer wavelength and the reflectivity gradually increases when the deposition thickness is increased from 6 nm to 15 nm. The color saturation is also improved with increasing the coating thickness. Figure 4(e) shows the color impressions of the ST-IPhG with different coating thickness. For comparison, we show digital images of the sample placed on both black and white substrates. As can be seen from Fig. 4(e), the samples with coating thickness of 12 nm and 15 nm show a very good blue color. And, the color maintains when the viewing angle change from 0° to 45°. For the shell thickness h < 9 nm, the structure has weak scattering effect resulting in low reflectivity, due to the partial collapse of the shell structure during burn-out of the polymeric template, thus the color of the samples darkens with decreasing ALD coating thickness.

 

Fig. 4. The experimentally measured reflection spectra and corresponding color impressions. The reflection spectra (a) and corresponding CIE diagram positions (b) of the coated solid sphere PhG. In the CIE diagrams, arrows indicate the color impressions change direction for samples of uncoated (pentagon) and different coatings of 3 nm (square), 6 nm (circle), 9 nm (hexagon), 12 nm (triangle) and 15 nm (star). (c) Reflection spectra of the ST-IPhGs. The relative position of k_l (red star) and k_m (blue circle) are further shown and blue arrows indicate the direction of k_m change with coating thickness. (d) The corresponding points in the CIE diagram of the ST-IPhGs with different coating thickness, which are similar to those in (b), except the core has been removed by calcination. (e) Color impressions of the ST-IPhG samples with different coating thickness and different background.

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5. Conclusion

In conclusion, a non-iridescent structural color with sharp spectral transition cannot be achieved with conventional PhG designs. For that the spherical-particle (motif) structure needs to be well engineered to feature a specific non-monotonous permittivity function with respect to the radius coordinate. That allows shifting the zero point of the particle permittivity distribution in reciprocal space in respect to the peak of the PhG structure factor and thus can be used to sharpen the transition from weak scattering to strong scattering. Here, we devised a new design scheme to realize such a FT feature from disordered ST-IPhGs by conformal deposition of TiO₂ via ALD onto the PhG template which allows to control the film thickness precisely for the high saturation color. In this case, the effective motif diameter becomes larger than the inter-particle distance, which helps to increase the zero-point shift in reciprocal space. The first zero point of the motif FT inherently positioned at the left side of the main peak of the lattice FT. And, the zero point moves closer to the center of reciprocal space with a larger motif size. This avoids the limitation of the shell thickness in hollow sphere PhG for desired sharper FT pattern. The provided thicker, denser and solid connected shell from ALD will be beneficial for mechanical stability in future applications. The achieved theoretical and experimental reflection transitions show a high saturation non-iridescent structural color. More generally, these results show that Fourier space engineering can significantly improve the selectivity of PhG based spectral filter structures. The high pass filter characteristics of ST-IPhGs can be easily shifted with the motif size for other structural colors. Such angle independent spectral filters with high spectral selectivity are also interesting for many related applications such as sunscreens, photovoltaics and radiative cooling.

6. Appendix

The diffuse reflection (solid curve) and the specular reflection (dash curve) of the 172 nm PS solid sphere PhG is shown in Fig. 5(a). The specular reflection spectrum is nearly flat in the wavelength range considered means the sample is not assembled into an opal structure. The top viewed SEM image of 196 nm PS PhG (Fig. 5(b)) also shows the sample only has short range order. The reflection spectra of the as-prepared PhGs can be found in Fig. 6(a). The ST-IPhG shows higher color saturation all show by the CIE diagram (Fig. 6(b)), which is much closer to the perimeter.

 

Fig. 5. (a) The experimentally measured diffuse reflection (solid curve) and the specular reflection (dash curve) of the 196 nm PS solid sphere PhG. (b) Top viewed SEM image of the 196 nm PS solid sphere PhG shows the fabricated sample is a disordered structure. Inset is the corresponding 2D fast Fourier Transform (FFT) image.

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Fig. 6. (a) The experimentally measured reflection spectra of 172 nm PS solid sphere PhG (dotted curve), 196 nm PS solid sphere PhG (dashed curve), coated sphere PhG (dash-dot curve) and ST-IPhG (solid curve). (b) CIE points of 172 nm PS solid sphere PhG (x = 0.23, y = 0.22), 196 nm PS solid sphere PhG (x = 0.25, y = 0.26), coated sphere PhG (x = 0.30, y = 0.31) and ST-IPhG (x = 0.20, y = 0.17).

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Fig. 7 shows the FT of the solid sphere PhG, coated solid sphere PhGs (Fig. 7(a)) and the ST-IPhG (Fig. 7(b)) with different coating thickness h varying from 3 nm to 15 nm, respectively. For the coated solid sphere (Fig. 7(a)), the first-zero position of motif FT can be gradually moved to and eliminate the peak position at k_l by increasing the coating thickness h. Thus, the corresponding scattering curve becomes smooth as shown by Fig. 7(c). For the ST-IPhG samples, the first zero position of motif FT (Fig. 7(b)) starts from the left side of the peak k_l and gradually moved to further in respect of the peak position k_l by increasing the coating thickness h. The scattering intensity (Fig. 7(d)) increases and the scattering transition from weak to strong scattering become steeper. For the shell thickness h < 9 nm, the structure has weak scattering effect resulting in low reflectivity, due to the partial collapse (Fig. 8) of the shell structure during burn-out of the polymeric template.

 

Fig. 7. The calculated FT of the coated solid sphere PhG (a) and the ST-IPhG (b) with different coating thickness, and (c, d) the corresponding scattering efficiency.

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Fig. 8. Cross-sectional SEM images of the ST-IPhG with a coated TiO₂ shell thickness of (a) 6 nm and (b) 9 nm, respectively. The 6 nm sample shows partial collapse of the shell structure during burn-out of the polymeric template.

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Funding

Deutsche Forschungsgemeinschaft (192346071– SFB 986).

Acknowledgments

The authors acknowledge the support from Dassault systemes, with their CST Studio suite. The authors also thank Yen Häntsch for the assistance with the improvement of PhGs fabrication.

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