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Abstract
Metamaterials are intriguing candidates for energy conversion systems, and contribute to the control of thermal radiation spectra. Large-scale devices are required to provide high energy flux transfer. However, the surface microstructure of large-scale metamaterials suffers from fabrication defects, inducing optical property degradation. We develop a novel approach to quantitatively evaluate the optical properties of defective 2D metamaterials based on diffraction imaging. The surrogate surface structure is reconstructed from diffraction pattern, and analyzed geometrical features to evaluate the optical properties. This approach shows potential for in-line and real-time continuous diagnosis during industrial fabrication, and high-throughput for large-scale 2D metamaterial.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It is well known that optical properties are determined by material’s intrinsic characteristics and its surface microstructure. The surface microstructure own the advantages such as narrow-band emission spectrum, high-temperature stability, designed adjustability and so on. These were widely used as the thermal radiation spectra control [1–5]. The thermal radiation spectra can be controlled by the interaction between electromagnetic radiation and the structures which include surface plasmon polaritons [6], surface phonon polaritons [7], photonic surface resonances [8] and so on. The well-known microcavity effect, which confines electromagnetic radiation in a cavity chamber, is used to control the optical properties using the microcavity resonant model [9,10]. Such physical phenomenon has a strong relationship to the surface microstructure. In the past decade, with the development of micro-electromechanical system technology, the fabrication of artificially designed materials which called metamaterial has been made possible. The surface of metamaterial is a fabricated two-dimensional (2D) periodic microstructure, which has an extraordinary controllability of the radiation spectra for 2D metamaterial [11]. As the 2D metamaterials are constructed with different materials various extraordinary possibilities emerge, e.g. the graphene-boron nitride hetero-structures realize the negative refraction of all angles [12], and the monolayer 2D silicon carbide acts a prospective candidate for optoelectronic devices [13]. One of the important applications is as a spectrally selective thermal emitter in the thermal energy conversion and thermal management fields [14–16]. For example, the 2D metamaterial is a competitive candidate for morphing the solar spectrum to the optimal spectrum region of solar photovoltaic cells. This is crucial for realizing high-efficiency solar thermophotovoltaic energy conversion systems. The thermal radiation spectra can be controlled by adjusting of the geometrical parameters such as periodicity, cavity size and depth [17].
Metamaterial fabrication usually focusses on the micrometer scale, with the photolithography technology. In the practical energy conversion field, it is essential that the microstructure is fabricated on a large-scale substrate, for a large heat flux transfer. Several microfabrication methods have been proposed to realize large-scale metamaterial fabrication such as nanosphere lithography [18], nanoimprint lithography [19], self-organized super-alloys selective etching [20] and anisotropic anodic etching [21]. These large-scale fabrication methods have advanced owing to their low-cost and high-throughput. They are widely used for manufacturing large-scale metamaterials, thus propelling their commercialization. However, during fabrication, these methods suffer from structural defects, such as distortion, vacancy, collapse, and regional contamination. In general, the performance of metamaterials, i.e. absorption peak intensity, width, and wavelength position, is sensitive to such defects; therefore, it would be degraded from the designed ones. Therefore, quick identification of the surface microstructure condition is essential to diagnose the performance of the degraded area of large-scale metamaterials. The conventional approach to identify defective parts is to examine the condition of the microstructure using a microscope, and then evaluate the optical properties of the defective area using spectroscopy. However, for defective large-scale metamaterials, the localized defects have variations in shape and random distributions. The microscope technique has trade-offs between the diagnosis area and the resolution for identifying the defects. Therefore, the conventional approach is time-consuming for a large-scale metamaterial. In addition, the presence of defects and their distribution are unpredictable in the fabrication process. Conventional diagnosis procedures are ex-situ, which is a challenge to diagnose each product during the industrialized fabrication process.
In this study, we propose a novel approach to reveal the surface microstructure condition using a diffraction imaging system and quantitative evaluation of the optical property degradation, based on the reconstruction of images from the diffraction pattern. The diffraction imaging technology has been developed to reveal the profile of the micro/nanoscale structural features in broad range of physical and biological science, for instance, in-situ probe dynamic phenomena in physical process or high-spatial-resolution images for biological objects [22–25]. The samples are illuminated by laser light and the diffraction patterns are record by a detector. The phase retrieval algorithm is applied to recover the object structure [26,27]. For the defective 2D metamaterial, the reconstruction of surrogate structure is required numerical investigation of geometrical features. Then the optical properties are calculated, which shows a good agreement with the experiment measurements. The proposed method is not constrained by the material; it can perform the diagnosis of metamaterials provided the surface periodic microstructure. The diffraction patterns are obtained by the detector, and the optical properties are calculated by the computer. This can significantly reduce the evaluation time. By scanning the surface with a laser, this approach continuously realizes in-line and real-time diagnosis during the large-scale metamaterial fabrication process. This would provide the possibility to monitor the products in the industrialized fabrication process. Furthermore, the diagnosis area can be easily adjusted by the size of the laser spot. The limitation of the diagnosis area is removed using this approach, which provides high-throughput evaluation for defective 2D metamaterials.
2. Experiment
2.1 Diffraction pattern measurement
The experimental setup for capturing the diffraction pattern from the 2D metamaterials surface microstructure, with reflection-mode, is shown in Fig. 1. A continuous-wave laser beam, with wavelength of 532 nm (9.62 mW output power, TTL modulation), was used as the incident laser source. A black screen with 15 cm square was placed perpendicular to the laser incident direction. The laser beam passes through an aperture of 5 mm at the center of the screen before reaching the metamaterial surface. The laser spot size on the sample surface was approximately 1 mm. The diffracted radiation on the sample surface is then reflected to the screen. The propagated distance is approximately 10 cm, and the diffraction pattern is displayed on the screen. A detector (CMOS sensor, Nikon D3400) capturing the diffraction pattern was placed behind the sample, positioned at 15° from the line of incidence, to capture the complete diffraction pattern images as raw data. To achieve an adequate sampling rate in each dimension, whilst simplifying the data processing, the exposure time was kept to 1s to collect the image data. To avoid the disturbance from external light sources while shooting, the experiment was conducted in a dark room and a self-timer was used. In the horizontal direction, the incident laser beam direction was vertical to the screen and sample, to ensure the zero diffraction spectral order was reflected to the center of the screen aperture. The diffraction pattern image was symmetrical and centralized to satisfy the reconstruction process and to avoid suffering from distortion. In this study, a periodic microstructure array was utilized as a typical metamaterial. Therefore, if the laser beam wavelength less than the aperture size of the microstructure, the dot arrays, which indicate the Bragg peaks in reciprocal space can produces the diffraction pattern. The defective region that affects the optical response in the metamaterial surface produces oscillations among the Bragg peaks on the screen. The diffraction pattern images were captured by the detector, then reconstructed to the surrogate structure, to diagnose the defective 2D metamaterial surface microstructure condition.
Fig. 1. Schematic diagram of the experimental setup for capturing diffraction pattern in 2D metamaterial surface microstructure using reflection-mode.
The samples which used in the experiment were lithographed using reactive ion etching on a silicon substrate, to fabricate the microcavity arrays, then sputtered with platinum [28]. To verify this approach’s effectiveness for defective metamaterial, we used three samples with 2D microcavity arrays. Sample A has perfect microcavity arrays without defects; we categorized this as “defect-less sample.” Sample B has regions where the inclusion material randomly covers the microcavities; we categorized this as “random defect.” Sample C has regions where the microcavities cannot be formed during fabrication; we categorized this as “line random.” The geometrical parameters of the samples are shown in Table 1.
Table 1. Geometrical parameters of the experimental metamaterial.
2.2 Pre-treatment of diffraction pattern images for reconstruction process
The raw data of the diffraction pattern images must satisfy the reconstruction requirement and remove irrelevant disturbances before reconstruction. Four steps were applied on the raw data. First, a beamstop is placed at the center of the diffraction pattern, to eliminate disturbances from the direct beam. Second, it is well known that the diffraction pattern distribution in the frequency domain is distributed from the center to the periphery, from low to high frequency, and the existence of the microcavities and defect information dominate the low frequencies. Besides, the dot arrays on diffraction pattern occurred sight distortion during the laser beam propagation from the irradiation point to the screen, particularly on the periphery of screen. Therefore, considering the trade-off between profile information loss and distortion correction accuracy, the 2048 × 2048 pixel area, which contain the first and second diffraction spectral orders, were selected as the initial data. Third, the linear perspective distortion of the images, due to the detector angle, causes relative distance deviation in the different diffraction spectral orders. The perspective-correct interpolation method [29] was used to keep the image content but deform the pixel grid, and map the deformed grid to the destination images to ensure the diffraction pattern was symmetrical. This maps an accurate structural feature of the surface microstructure. Fourth, the background was eliminated by subtracting the dark field data.
The processed diffraction pattern images are shown in Fig. 2. The diffraction image data were binned with 3×3 pixels to improve the signal-to-noise ratio. These were then embedded to the original pixel size, to avoid introducing the aliasing effect in the reconstruction process. Gaussian filtering was used to suppress Gaussian noise from the sampling and scatter in the detector’s photosensitive element. The experimental process can be regarded as the Fourier transform from the image (real space) to the diffraction pattern (reciprocal space). The reconstruction process was thus considered as the inverse Fourier transform, to recover the object from the diffraction pattern. However, the detector only measured the diffraction pattern intensity distribution, which provides the amplitude distribution but loses the phase distribution. The phase retrieval algorithm was developed to recover the phase distribution information [30]. Given that the algorithm starts with a random phase using Fourier inversion, the accuracy is improved by decreasing the number of unknown variables. The strategy was introduced to impose the “finite support” constraint in each dimension and integrate the oversampling theory using an object with some known intensity distribution. For the 2D metamaterial surface object, the oversampling ratio was 2.6 [31,32]. The reconstructed image size was 128 × 128 µm, which indicates the surrogate structure of the irradiation area. The processed diffraction pattern data were reconstructed using the error-reduction (ER) iterative phase retrieval algorithm [33].
Fig. 2. Processed diffraction pattern images shown on a logarithmic scale and normalized. (a) Sample A, defect-less sample, has clear Bragg peaks without oscillations in the diffraction pattern; (b) Sample B, random defect, with oscillation scatter around the Bragg peaks; and (c) Sample C, line defect, where the oscillation has a strip distribution between the Bragg peaks.
3. Result and discussion
After 1000 iterations with the ER algorithm, the surrogate structural feature images were reconstructed, containing both microcavity arrays and defects. The defects in the reconstructed images included the microcavity connection, distortion, shrink and deletion. To numerically investigate the defective metamaterial surface condition, the reconstructed images were essential for evaluation from the geometrical point of view. The geometrical threshold values of the surrogate structure image were set to filter the defective region and retain the qualified microcavity in the reconstructed images. The threshold setting was considered from two aspects: one is the microcavity area, which avoids damaged microcavity connections and microcavity shrink caused when microcavities cannot form; the other is the microcavity perimeter, which avoids the microcavity area that satisfies the area threshold but has a geometrical distortion. The upper limit of the threshold value was double the microcavity aperture size, to remove the microcavity connections, and the lower limit was half the microcavity aperture size, to remove microcavity shrink. A scanning electron microscope (SEM) was used to observe the surface microstructure condition in the metamaterial samples. To compare the SEM images and reconstructed images at the same scale, a portion of the SEM images, for the samples, and the corresponding reconstructed images are shown in Fig. 3.
Fig. 3. SEM (top) and reconstructed (bottom) images. (a) SEM image of sample A, which has perfect microcavity arrays without the defects. (b) SEM image of sample B, which has regions where the inclusion material covers the microcavities. (c) SEM image of sample C, which has regions where the microcavity cannot be formed causing microcavity connection. (d) Reconstructed image of sample A, which shows the microcavity arrays without defects. (e) Reconstructed image of sample A, which shows the defects distribute as a lump, randomly. (f) Reconstructed image of sample B, which shows the defects distribute as a quasi-stripe.
From the geometrical point of view, the surface microstructure condition can be classified as either a perfect or damaged microcavity. Numerical analysis was realized by defining a geometrical parameter, degree of effectiveness (DOE), which is equal to the ratio of the isolate microcavity unit cell number in the reconstructed image, to the total microcavity unit cell number in the ideal perfect metamaterial. The DOE can quantitatively describe the effective microcavity retention condition, within the diagnosis area, in a large-scale defective metamaterial. For the SEM images, the DOE can be calculated from the ratio of perfect microcavity area to the total diagnosis area. The diagnosis area was equivalent to the laser irradiation area, such that the DOE of sample A, B, and C, calculated from the SEM images, were approximately 100%, 77.1%, and 95.4%, respectively. For the reconstructed images, the border following algorithm, based on connected components, was used to label the microcavity unit cell then count the isolate microcavity unit cell numbers in the reconstructed image [34]. The DOE of sample A, B, and C, from surrogate structures, were 100%, 74.3%, and 93.4%, respectively. The DOE of SEM and reconstructed images have a good agreement, which implies this approach is capable of sufficient quantitative investigation into the defective metamaterial surface condition.
The 2D metamaterial shapes the spectrum of the resonant mode by confining electromagnetic radiation in the resonant cavity. This effect is enhanced according to the photon absorption wavelength. The peak position was fixed by the designed geometrical parameters of the microcavities, and the peak intensity was influenced by the microcavity effect intensity. In a large-scale metamaterial, the perfect microcavity contributes to the designed optical properties, however, these are suppressed by defects. The optical property degradation is embodied by a weakening of the peak intensity, which is caused by microcavity damage, and the microcavity effects disappear. In our research, with the diffraction imaging and geometrical processing of the reconstructed image, the microcavity retention condition in large-scale defective metamaterial can be quantitatively analyzed to a corresponding optical property behavior. The optical properties of the samples are measured using FT-IR (Spectrum-65, Perkin Elmer), implemented with an integrating-sphere with 150 mm in diameter. The hemispherical spectral emittance was obtained from the measurement. The perfect and defective sample regions were measured, corresponding to the designed and measured optical properties. We hypothesize that the damaged regions are deficient in microcavities, in the surrogate structure, such that the optical properties are similar to that of flat metal surface. In the measurement, the optical property degradation can be observed by a weakening of peak intensity of the last peak position from the designed and measured optical properties. According to the microcavity effect and quantitative geometrical analysis, we defined the optical properties of a perfect region ${R_{designed}}$ and the optical properties of a damaged region${\; }{R_{damage}}$, such that the calculated optical properties of a defective region ${R_{calculation}}$ is given by
Fig. 4. Measured and calculated optical properties. (a) Random defect sample, which peaks around 5.7 µm and has optical property degradation of around 22.9% (equivalent DOE: 77.1%). (b) Line defect sample, which peaks around 3.9 µm and has optical property degradation of around 4.6% (equivalent DOE: is 95.4%). Inset shows the peak at a higher resolution.
We have performed the quantitative analysis of the optical property for the defective 2D metamaterial. The optical properties are in good agreement with the experimental measurements. However, the reconstructed images still exhibit some discrepancy compared with the SEM images seen in Fig. 3. The geometrical features of defective metamaterial products are the non-periodic defects randomly distributed in the periodic microstructure arrays, which generate Bragg peaks and oscillation in the diffraction pattern. The principle of the ER algorithm is to generate the random phase information to make the inverse Fourier transformation of the reconstructed images, then compare them with the input data. Due to the absence of precise phase information, the input reciprocal space image correspond to non-exclusive real space images in such a structure, in particular the images contain massive large-scale microstructures. The reconstructed images are regarded as the average of the time domain images in the diagnosis area. The DOE was introduced for quantitative diagnosis of the microstructure retention condition to mitigate any discrepancies in the reconstructed images, thereby realizing the evaluation of the optical properties. To verify the accuracy of this approach, ten points were randomly selected in the experimental measurement area on each sample. The DOE was calculated with this approach, then the average value of the ten points was obtained. The optical measurement data can be converted to the equivalent DOE, which is calculated as one minus the difference between the spectral peak intensity from design to measurement. Because the diagnosis area of integrating-sphere FT-IR is larger than the laser spot size, the equivalent DOE of the experimental measurements can be regarded as the average value of the defective area. The results are shown in Fig. 5. For the defect-less sample, the deviation of the measurement is negligible; the distribution of the measurement point is significantly close to the average value. For the random defect and line defect samples, the defects cause the diffraction patterns to oscillate, which gives rise to the discrepancy in the reconstructed images. The deviation of the measurement increase than the defect-less, but the DOE of the discrete points still surrounding the equivalent DOE. The line defect sample was analyzed in the horizontal and vertical directions; neither of the directions show significant differences in the results. For different types of defects, the average DOE, which was obtained from the diffraction imaging analysis, is in good agreement with the equivalent DOE, which was analyzed from the optical properties experimental measurements.
Fig. 5. The DOE obtained from the proposed method using diffraction imaging and the equivalent DOE analyzed from the optical measurement for defect-less (red), random defect (pink), and line defect (blue) samples. The ten points evaluated from each sample are shown in the left side of the image. The straight line represents the average of the ten scattered points. For the line defect sample, the line defect was analyzed in both horizontal and vertical directions. The equivalent DOE was calculated with the optical measured from the experimental measurement optical properties, as show in the right side of the image.
For conventional coherent diffraction image technology, which reveals the precise profile details for periodic nano/microcrystal [35–37]or non-periodic objects [38–40], the light source energy needs to be as high as possible, such as extreme ultraviolet or X-ray to produce the fine diffraction pattern required for higher resolution images [41–45]. Whereas, the optical properties of metamaterials are affected by the comprehensive microstructure condition. Therefore, this study, does not focus on the precise reconstructed images of the surface microstructure. Instead, the surrogate structure that provides the microcavity retention information are concerned. A visible laser was used in the experiment, sacrificing a portion of the resolution in the reconstructed images but improves the safety and observability. In this study, the reconstructed image can be regarded as the surrogate structure for the optical properties, based on the microcavity effect. By defining the geometrical parameter DOE, we can evaluate the effective region in the reconstructed images and correlate to the optical property degradation even the reconstructed images has a slight deviation from SEM observation images. The optical properties calculated from the DOE, based on the surrogate structure, have a good agreement with the defective regions in measurement, which prove this approach is an effective way to quantitatively diagnose large-scale microstructure conditions.
4. Conclusion
We have established the reflection-mode diffraction imaging experiment to obtain the 2D defective metamaterial diffraction pattern, from which the surrogate structure of the diagnosis region is reconstructed. An effective approach has been proposed to quantitatively diagnose the effective region, based on the geometrical features in the surrogate structure. Then, we can evaluate the optical property degradation in realistic metamaterial products. This approach makes it possible to overcome the challenge of diagnosing large-scale metamaterial optical properties, and numerically investigating the optical property degradation caused by the various defects types and their random distribution. Our study paves the way for the commercialization of metamaterials, given that it can apply to the large-scale industrial production of metamaterials, which relies on in-line production and real-time monitoring of the quality of the optical properties during manufacture. Furthermore, our approach acts as a bridge between the large-scale defective metamaterial microstructure condition and the optical properties, contributing to our understanding of the optical mechanisms of defects in defective metamaterial.
Funding
New Energy and Industrial Technology Development Organization (NEDO)(18101325).
Disclosures
The authors declare no conflicts of interest.
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