1. Introduction

The recent emergence of metamaterial-based absorbers provides potential routes to realize multifunctional optical devices such as multispectral camouflage [1,2], electromagnetic detecting [3–5], sensing [6–8], thermal radiation [9,10], solar energy utilization and modulation [11–15]. These unique functionalities have been applied by novel proof-of-principle structure designing in ultraviolet [16], infrared [17], or microwave regimes [18]. These metamaterial-based absorbers are usually implemented by periodically arranging the metallic unit cells with pre-designed dimensions in these spectral ranges. In the visible region, metamaterials absorbers, typically made of metals such as gold [19], silver [20,21], chromium [22], titanium [23], or tungsten [24], are able to strongly enhance the light-matter interaction, resulting in significantly absorption in the solar spectrum caused by plasmonic effects. However, there are still some difficulties to overcome, including obstacle to fabricate continuous smooth thin-films [25], fabrication incompatibility with standard semiconductor processing [26], unstable biocompatibility and chemical properties, and poor adhesion to substrate like glass or silicon. For example, metal films can be easily removed from the standard substrate by ultrasonic treatments or even tape due to the inferior adhesion [27]. In addition, spontaneous dewetting of certain metals, such as silver film, can occur even at room temperatures [28] and it will be greatly accelerated when the temperature rises [29]. Another problem is the large magnitude discrepancy between the dielectric constant of the conventional metals and dielectrics (e.g., the real parts of the permittivities of the silica and silver are 2.1 and -28 at 800 nm, respectively). This makes the geometric size of the dielectric component in the metamaterials much larger than the size of the metallic component, which may pose serious fabrication challenges. Hence, for some real-life metamaterial-based absorber application, such as high temperature photovoltaics, metallic absorbers will no longer be the best choice.

On the other hand, periodic metamaterial-based absorbers can be regarded as homogenized anisotropic structures, and their macroscopic optical absorptance is often sensitive to the angle and polarization of incident light due to the structural symmetry. In contrast, different from periodic and disordered structures, various aperiodic structures show great potential in absorber due to their rich structural changes and various unique optical properties [30–32]. Specifically, aperiodic plasmonic metamaterials possess broadband absorption enhancement for flexible compact photovoltaic devices [33–36] and the tunable narrowband thermal emission for artificial thermal physics in switchable thermal sources or temperature regulation [37,38]. These approaches provide a potential candidate for the metamaterial-based absorber. However, metal-free aperiodic metamaterials-based absorber is not easy to achieve due to their usual requirements of plasmonic near-field localizations or strong reflection of metal substrates. The key issue will be whether we can achieve the non-metallic metamaterials-based absorber from a different perspective, such as the lossy features of semiconductor photonic systems.

In the present work, Fibonacci quasiperiodic metamaterials were chosen to demonstrate the broadband absorber from the visible to near-infrared region. The proposed absorber consists of a seven-fold Fibonacci sequence with an alternating composition of heavy doped oxide [ITO (Indium tin oxide)] and lossless dielectric (HfO₂) which can ensure a nearly perfect absorption covering the entire solar spectrum (In the 300-1000 nm wavelength range. The highest absorptance is higher than 99% and the average absorptance is up to 96%). In particular, the designed non-metallic quasiperiodic metamaterial-based absorber can provide efficient absorption band for the wide incidence angle and different polarizations, which is mainly due to the quasi-localized resonances in the Fibonacci systems and the peculiar photonic band structure of the all-dielectric Fibonacci quasiperiodic structures [39]. Moreover, the planar feature gives it many advantages over other two- or three-dimensional nanostructures [40,41], and it can be foreseen that this planar feature is an excellent choice for large-area manufacturing without increasing complexity. In brief, this study presents a feasible method for designing a scalable, non-metallic, aperiodic metamaterials-based absorber with excellent absorption properties in the visible and near infrared ranges of the solar spectrum; thus, the method can promote practical high-temperature applications such as biochemical sensing, thermal sources, thermophotovoltaics, and solar cells.

2. Structural design and experimental procedure

It has been confirmed that in addition to photonic crystals which have periodic structures, quasi-crystals have also caused great attention because of its obvious flexibility, and high feasibility of diversified attractive optical phenomena [42]. The Fibonacci sequence, also known as the golden section sequence, can be generated through a recursive relationship mathematically: S_n = S_n-1 + S_n-2 (n ≥ 2, n${\in} $N*), where S_n is the n^th order sequence. Suppose S₀=A, S₁=B, so that S₂=AB, S₃=BAB, S₄=ABBAB … S₇=BABABBABABBABBABABBAB. For a given frequency range, the photonic band gaps (PBGs) are more than those of strictly periodic structures as a result of the peculiar photonic band structure in Fibonacci quasi-periodic structure. In other words, the slope of the photonic band, representative of the group velocity in one dimensional case, may disappear. Therefore, the photonic state density (i.e., the reciprocal of the group velocity) can be higher than that of the rigorously periodic structure. In addition, if the material of the periodic structure is lossy, the optical absorption will be effectively enhanced in the frequency range of the photon band.

For layers B and A, dielectric HfO₂ and lossy metal-like material ITO were chosen, respectively. As it is known, the optical parameters of thin film materials, especially for ITO, are considerably influenced by the preparation craft. Based on this fact, we performed a variable-angle spectroscopic ellipsometry (J. A. Woollam V-VASE and IR-VASE Mark II) on a 87-nm-thick ITO and a 220-nm-thick HfO₂ film, respectively. Through the measured ellipsometric parameters raw data Ψ and Δ, we obtained their dielectric constants [real dielectric constant (ɛ₁) and imaginary dielectric constant (ɛ₂) (Fig. 6, Appendix A)]. By resorting to the transfer matrix method (TMM) [43,44], the photon band structures of the first three Fibonacci quasi-periodic structures (S2, S3 and S4) under the polarization incidence of TE and TM were respectively calculated, as illustrated in Fig. 1 (see Appendix B for details of the calculation method). As a numerical example, the thickness of dielectric layer (HfO₂) and lossless metallic material (ITO) was maintained at 220 nm and 87 nm, respectively. As expected, due to the Bragg scattering, there is a cut-off frequency in all Fibonacci quasi-periodic structures, which is similar to the rigorously periodic structures. However, more air layers (as demonstrated in the yellow area of Fig. 1) occur in the higher Fibonacci quasi-periodic structures (S4 structure) than the lower order ones (S2 and S3 structures), because the former is more difficult to satisfy Bloch wave condition with the increasing disorder [42]. Furthermore, compared with the lower order Fibonacci quasi periodic structure, the slope of the photonic band of the higher order one is decreased between the cut-off frequency.

 

Fig. 1. Photonic band structures of the (a) S2, (b) S3 and (c) S4 structures under TM polarized incident light, respectively; Photonic band structures of the (d) S2, (e) S3 and (f) S4 structures under TE polarized incident light, respectively. (The yellow areas are the PBGs)

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As demonstrated in Fig. 2(a), the proposed broadband absorber is a Fibonacci structure of one period of S7 (FS7). Different from the traditional absorbers, the proposed absorber can perform perfectly in visible and near infrared wavelengths without metal materials. In order to analyze the physical mechanism underlying the observed absorption, the electric field distribution of FS7 on the xz-plane cross section was calculated by TMM method as shown in Fig. 2(c). In the operating wavelength range, the lossless dielectric layer (HfO₂) is able to enhance the transmission of the light due to the impedance matching. The lossy metal-like material layer (ITO) can effectively absorb part of the incident light as a result of inherent loss. Meanwhile, the layer allows the other part to pass through, and can produce several special absorption cavities through the Fibonacci structure. In this planar FS7 structure, the optical single-wideband resonance in the loss-absorbing cavity is combined with the inherent loss of ITO, thus achieving high efficiency of wideband absorption.

 

Fig. 2. (a) Schematics of FS7. (b) The FESEM picture of the cross section of FS7. (c) Distributions of the electric field intensity (|E|) for FS7 as a function of wavelength at normal incidence.

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In the current work, all the coatings were created by the electron-beam evaporation technique. The lithography-free planar structure based on quasi-period Fibonacci does not involve expensive nanofabrication technology, so it is particularly suitable for large-scale applications. During the sample preparation, all deposition processes were carried out with external substrate heating, and the substrate temperature was kept constant at 200 °C. During the process of HfO₂ deposition, the chamber pressure was 4×10⁻³ pa; And during the ITO deposition, the chamber pressure was 3×10⁻² pa with oxygenation rate at 30 SCCM (Standard Cubic Centimeter per Minute). A multi-channel quartz crystal monitor (Inficon, SQC-310) was used to monitor the thickness of the individual layers. Besides, the cross-section morphology and their scanning energy spectrum of the prepared samples were obtained through the field emission scanning electron microscope (FESEM, Zeiss SUPPA 40). The cross-section morphology of FS7 is demonstrated in Fig. 2(b). At the same time, in order to further understand the characteristic elements of each film in the film structure, we also analyzed the energy spectrum structure of the film under the above process conditions (Fig. 7, Appendix C). The spectra were measured by spectrophotometer (Agilent Cary 5000 with UMA) in which different polarizations and angles of incidence could be selected throughout the whole spectrum measurement process.

3. Results and discussion

In consideration of the loss and dispersion of characteristics, silicon wafers are commonly used as base materials for absorbers, especially for solar absorbers. The measurement (solid) and calculation (dashed line) results [transmittance (T), reflectance (R), and absorptance (A)] of the bare silicon wafer are shown in Fig. 3(a), where A=1-R-T (When the possible scattering in the specular reflection direction is negligible, this extinction is equivalent to the absorption. Our experiments have confirmed the fact that the scattering is beyond the detection limit of our instruments). However, as an absorber, the absorptance is relatively low due to its strong reflection, with only about 64% absorption rate in the 300-1000 nm wavelength range [As is known, the energy of the solar spectrum is mainly distributed in the visible and near infrared bands (especially for 300-1000 nm), as shown in the gray area of Fig. 3].

 

Fig. 3. Experimental (solid line) and theoretical (dashed line) transmittance (T), reflectance (R), and absorptance (A) of (a) the bare silicon wafer, (c) the bare glass, (b) the silicon wafer coated with FS7 and (d) the glass coated with FS7 at normal incidence, respectively. The gray area shows the AM1.5 solar spectrum, normalized to fit the scale of the plot. (e) The photographs and the surface microtopography of the FS7 on silicon wafer and glass, respectively.

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In order to study the spectral performance of the Fibonacci structure, we made a design in terms of the absorber and the optical characteristics of the silicon wafers coated with FS7 is also illustrated as in Fig. 3(b). We can observe that the experimentally results are slightly different from the theoretical ones. The difference may be due to the vertical index variations since ITO grows commonly in graded microstructures. In addition, the intermixed layer formed between two ITO layers may also cause the experimental results to deviated from expectations. Compared with the bare silicon wafers, plating FS7 on silicon wafer in the present study has a superior absorption performance in the visible and near-infrared broad spectrum, which demonstrates that the absorber can obtain a high absorptance, up to more than 99% at 740 nm and the average absorptance is up to 87%.

From the theoretical and experimental results in Figs. 2(c) and 3(b), it can be seen that the transmittance of the designed absorber structure is almost negligible. Therefore, the designed structure of the broadband absorber should be independent of the substrate. In order to avoid the influence of the silicon substrate absorption in the 300-1000 nm band, we chose the glass substrate with almost no absorption in the entire visible and near-infrared range, as demonstrated in Fig. 3(c). When we plated the FS7 on the glass substrate, it can be seen that the simulation result of FS7 on silicon substrate is almost the same as the result of FS7 on the glass which are shown in Figs. 3(b) and 3(d). Compared with the absorber based on the silicon substrate, the absorber with the same structure based on the glass substrate have the same absorption band and absorption characteristics. However, the absorption performance of FS7 on the glass is slightly improved compared to that of the same structure on the silicon substrate. The reason for this might be the difference in surface topography. Just as it is shown in Fig. 3(e), the difference of substrates roughness can cause the difference in surface roughness of FS7 (The surface roughness of silicon wafer is 10 nm, whereas the surface roughness of glass is more than 15 nm). The average absorption rate of FS7 based on glass substrate is about 96%, and the absorption rate remains above 93% over the entire wavelength range of 300-1000 nm. Due to the good adaptability of the proposed absorber to the substrate, we can even evaporate the multilayer film on the flexible substrate (such as aluminum foil substrate) and obtain the flexible broad band absorber. Owing to this simple fabrication process, the broad area and mass production of this designed absorber can be realized.

In the present research, the characteristics of view-angle effect were studied by using TMM simulation. The FS7 based on glass was chosen and the simulation models were established according to the sample schematic diagram as demonstrated in Fig. 2(a). For clarity, we obtained the electric field intensity distribution of FS7 on the x z-plane cross section (see in Fig. 2(c)) at a specific wavelength (740 nm) with different incidence angles and polarizations, as shown in Figs. 4(a) and 4(b). In the condition of different incident angles, both of TE waves and TM waves can maintain good absorption performance. However, the reflection of TM wave at the incident interface (i.e. air/ITO interface) is smaller than that of TE wave under oblique incidence. In general, decreasing the reflected light in absorptive structure tends to increase the absorption, since more energy passes through the absorbing material. Thus, for metamaterial-based absorber proposed here, it has a better angle-independent characteristic in the case of TM wave.

 

Fig. 4. Electric field distributions of FS7 at 740 nm with different incidence angles for (a) TE and (b) TM waves, respectively. (f)-(h) Experimental measured absorbance as functions of the wavelength and incident angle for TE, TM polarized and unpolarized light, respectively. (c)-(e) The corresponding theoretical absorbance spectra for the three cases. (i) Recorded photographs of the corresponding absorption under outdoor ambient light with the incident angles of 15°, 30°, 45° and 60°.

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In this work, the plane waves covering wavelengths of 300-1000 nm were incident along the -Z direction. The simulated complex refractive index of the ITO and the other materials were measured using a spectral ellipsometer (Fig. 6, Appendix A). As it is shown in Figs. 4(c), 4(d) and 4(e), the absorber has a high angular tolerance up to 60° under TE, TM polarized and unpolarized light illumination. The experimental results are basically consistent with the simulation results, as illustrated in Figs. 4(f)–4(h). It can be seen that in the case of TE polarization, although the absorptance decreases to some extent, a good broadband absorption performance can still be maintained with the incident angle increasing. Simultaneously, in the case of TM polarization, the absorption performance of the absorber does not change much with the changing angle, and the absorptance is always maintained above 96%.

Furthermore, the results of the simulated and measured data seem to be in excellent consistency with the experimental observations in Fig. 4(i). Therefore, the proposed broadband absorber possesses a large absorption at a wide viewing angle. It should be emphasized that this conclusion also applies to silicon wafers coated with FS7 (Fig. 8, Appendix D). In addition, the absorption band discussed here is mainly in the visible region. In fact, it remains valid to be extended to the mid-infrared region by properly modulating the parameters of constituent materials (i.e. ITO) by different annealing methods [45].

The proposed broadband absorber designed in this study has good stability and oxidation resistance due to the use of non-metallic materials in the entire film structure. In order to verify this fact, we also conducted the damp heat (DH) tests at a temperature of 85°C, a relative humidity (RH) of 85% on the silicon substrate coated with FS7 and on the glass one, respectively. The Fig. 5(a) shows the results of DH tests for the glass substrate coated with FS7. With the continuous increase of the DH test time, although the absorption performance of the absorber decreases slightly, it still remained at a high level [The change in absorption performance may be due to the change of sample surface morphology with the change of DH test time (Figs. 9 and 10, Appendix E)]. The overall absorption performance of the absorber remains good at the wavelength of 300-1000 nm, the absorptance of which in this range is always higher than 90%. The glass substrate coated with FS7 has good chemical and thermal stability, which can play a very important role in practical applications. Besides, the measured data results seem to be in fine consistency with the experimental results in Fig. 5(b). Of course, the silicon substrate coated with FS7 also possess such performance characteristics mentioned above (Fig. 11, Appendix F). It should be mentioned that the absorption may be further decreased if the temperature is increased to a higher value owing to the thermal response of free carriers in ITO layers and the low deposition temperature (about 200°C) in our experiment. For improving the temperature-stability, increasing the annealing temperature or using thermally stable source materials should be considered as one potential solution [46]. However, more research is needed in this field.

 

Fig. 5. (a) The absorptance of FS7 on the glass for different DH test times. (b) Recorded photographs of 0 hour DH test (Before) and 120 hours DH test (After).

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4. Conclusion

In summary, this study proposes a broadband absorber with good substrate adaptability in visible and near-infrared light generated by metamaterial powered nonmetallic multilayer structures to achieve high-absorption, strong-polarization independence with a large viewing angle. By optimizing the design of the structure parameters, the average absorption rate of the absorber fabricated on the glass substrate can reach 96% in the range of 300 ∼ 1000 nm. The high-absorption properties for TM and TE polarized light are almost unchanged at incident angles up to 60°. In addition, with the advantage of a simple metallic multilayer structure, our designed absorber can be fabricated on a large scale with a protolithic-free, low-cost manufacturing technique. And because the absorber proposed has good adaptability to the substrate, we can also evaporate the multilayer film on various substrates (such as flexible substrate), so as to obtain the flexible broadband absorber. Meanwhile, the designed absorber has a good chemical and thermal stability. Just due to the excellent characteristics of broadband, polarization-insensitive and large-viewing angle, the present designed absorber will be easily applied to solar cells, photoelectric detection and thermal radiation. Furthermore, this structure can be further optimized to apply in a wider band or other bands for perfect absorption.

Appendix A: measurement of material parameters

 

Fig. 6. The material parameters of the film. (a) and (b) are the measured ellipsometric parameters raw data Ψ and Δ of ITO and HfO₂, respectively; (c) and (d) are dielectric constants of ITO and HfO₂ [real dielectric constant (ɛ1) and imaginary dielectric constant (ɛ2)].

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Appendix B: calculation method and explanation

Actually, for Fibonacci quasiperiodic metamaterials, we can treat them as periodic crystal which consists of the Fibonacci sequence as discussed in literature [47]. And then, following a standard approach, the exact dispersion relationship pertaining to 2th-order Fibonacci supercell (i.e. S₂=AB) is given by:

(1)$$\textrm{cos}({2{k_B}d} )= \textrm{cos}({{k_{z1}}{d_1}} )\textrm{cos}({{k_{z2}}{d_2}} )- \frac{1}{2}\left[ {{p_m} + \frac{1}{{{p_m}}}} \right]\sin ({{k_{z1}}{d_1}} )\textrm{sin}({{k_{z2}}{d_2}} )$$

where ${k_B}$ is called the Bloch wavevector, ${k_{z1}}$ and ${k_{z2}}$ are normal wavevectors in A and B layers, ${d_1}$ and ${d_2}$ are thicknesses of A and B layers, ${p_m} \in \{{{p_{\textrm{TE}}},{p_{\textrm{TM}}}} \}$ is a factor that depends on the polarization as ${p_{\textrm{TE}}} = {k_{z2}}/{k_{z1}}$ for TE modes and ${p_{\textrm{TM}}} = ({{k_{z2}}{\varepsilon_1}} )/({{k_{z1}}{\varepsilon_2}} )$ for TM modes, respectively. Similarly, for 3th-order (i.e. S₃=BAB) and 4th-order Fibonacci supercell (i.e. S₄=ABBAB), the Eq. (1) can be modified according to the corresponding number of layers and medium. But for higher-order case, the Eq. (1) becomes so complicated that it is not conducive to solving. And the information about dispersion properties of Fibonacci quasiperiodic metamaterials provided by the Eq. (1) is approximate, and it does not take into account actual truncation of the structure. And thus, the low-order cases are used to study band structure changes of Fibonacci quasiperiodic metamaterials in order to simplify the consideration.

Appendix C: energy spectrum structure

In order to further understand the characteristic elements of each film in the thin film structure (FS7), we chose to prepare a simple Fibonacci structure (S5) under the preparation process of FS7 in the text to perform and analyze the energy spectrum structure for each film, as shown in Fig. 7, “Sn”, “In”, and “Hf” are three chemical elements of tin, indium and hafnium respectively. In this picture, the unit is eV, corresponding to the excitation energy. Here we calibrate the current position by the peak and valley. The content of this element, we can see that the positions of the peaks and troughs of tin and indium are the same, while the peaks and troughs of hafnium are just complementary to it, which proves that the film layer is alternately prepared hafnium oxide and ITO.

 

Fig. 7. The energy spectrum structure of S5.

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Appendix D: properties of the viewing angle effect of FS7 on silicon wafer

 

Fig. 8. (d)-(f) Experimental measured absorbance as functions of the wavelength and incident angle for TE, TM polarized and unpolarized light, respectively. (a)-(c) The corresponding theoretical absorbance spectra for the three cases. (g) Recorded photographs of the corresponding absorption color palette taken under outdoor ambient light with the incident angles of 15°, 30°, 45° and 60°.

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Appendix E: surface morphology of the sample changes with the DH test time for K9 and Si substrate

Figures 9 and 10 show the surface morphology of FS7 on the glass and silicon wafer as a function of DH test time, respectively. The results of Figs. 9 and 10 manifest that the surface morphology of the sample could change significantly with the change of DH test time. Here we have made a possible guess as to the reason for the change in absorption rate. In comparison, Fig. 9 may be more obvious. Figures 9(a)–9(f) are surface topography images at the same scale. It can be seen that the surface “particles” are relatively reduced with the time of the DH test.

 

Fig. 9. The surface morphology of FS7 on glass with (a) 0 hour, (b) 24 hours, (c) 48 hours, (d) 72 hours, (e) 96 hours and (f) 120 hours DH test, respectively.

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Fig. 10. The surface morphology of FS7 on silicon wafer with (a) 0 hour, (b) 24 hours, (c) 48 hours, (d) 72 hours, (e) 96 hours and (f) 120 hours DH test, respectively.

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Appendix F: DH test of FS7 on the silicon wafer

 

Fig. 11. The absorptance of FS7 on the silicon wafer for different DH test times.

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Funding

National Natural Science Foundation of China (11404102, 11704102, 11704104, 61627818, U1804261); Key Scientific Research Project of Colleges and Universities in Henan Province (20B140005); Key Scientific and Technological Project of Henan Province (192102210202).

Disclosures

The authors declare no conflicts of interest.

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