Metamaterial has demonstrated exotic electromagnetic (EM) properties and various applications, for example perfect absorbers. Cascaded perfect absorbers further extend the spectral engineering ability. Perfect alignment of subcells was usually presumed in previous studies. We numerically investigated the effect of lateral misalignments existing in the multiple lithography steps for vertically cascaded metamaterial absorbers and found that the position deviations of the subcells play an important role of the spectral response. As an example, near-unity absorbance reduces to only 30% for a λ/10 subcell misalignment. The detailed investigation of EM field and induced current distributions reveals that the relative position variations of strongly coupled subcells contribute to this phenomenon. The results give us an evaluation that how much registration accuracy is required in multi-step lithography for cascaded metamaterials and on the other side a hint of the potential application of this high position sensitivity.
©2013 Optical Society of America
Metamaterials, which are artificially designed periodic subwavelength structures, have attracted great interests due to the exotic electromagnetic (EM) properties relying on the structures rather than the compositions . Various advanced EM functions have been developed including negative refraction, cloaking, ultra-resolution imaging, etc. A particular branch, metamaterial absorber (MMA), has recently gathered great interests for its ability of unity absorbance of EM waves . It usually consists of an array of metallic subwavelength structure spaced a distance above a ground plane by a dielectric layer, where the ground plane prohibits the transmission and the subwavelength structures suppress the reflection by the perfect impedance match. The resonant frequency of near-unity absorbance can be tuned by manipulating a unit cell and the period. MMAs have rapidly progressed from microwave [2,3], terahertz (THz) [4,5] to infrared . Benefiting from the development of advanced nanofabrication technique, MMAs in the visible range was also demonstrated recently . MMAs have applications in thermal detectors, thermal emitters and biosensors [8,9]. Essentially, MMAs are based on strong EM resonances and therefore the absorption band is usually narrow, typically no more than 20% of the center frequency. Especially in the application as biosensors, narrow-linewidth MMAs are preferred for a high sensitivity. In addition, a recent paper demonstrated the potential application of narrow-linewidth MMAs in a bolometer detector for THz imaging . On the contrary, a broadband absorption is preferred for the application like solar cells . Furthermore, engineering the spectra beyond a single absorption band promises MMAs extra functions and applications. Cascaded MMAs are an effective way for these goals by grouping several cells of single-cell MMAs into a supercell, whose absorption spectra can be seen as a combination of multiple absorption bands that originated from different subcells. Dual-band or flat-top MMAs were firstly demonstrated by simply placing the subcells side by side [11–13]. Then, both laterally [14–16] and vertically [14,17–19] cascaded metamaterials with more than two subcells were proposed to achieve broadband operation. Absorption band as wide as 50% of the center frequency was demonstrated by integrating four subcells laterally or three subcells vertically . In all these work, perfect alignments of subcells were presumed in the device design which is not actual in conventional multiple-step photolithography, where the registration accuracy is approximately 1 μm. We notice that high resolution electron beam lithography was used to accurately stack multilayers in . However, high throughput fabrication techniques like nanoimprint lithography are preferred in practical application, which has similar alignment accuracy as photolithography. Therefore, it is necessary to know the effect of the inevitable misalignments on the performance of vertically cascaded MMAs.
In this paper, we numerically investigate the absorption response of vertically cascaded MMAs considering the misalignments of subcells existing in multi-step photolithography by finite-difference time-domain (FDTD) method. Based on an example of a cascaded MMA experimentally achieved previously , the lateral position deviations of subcells were studied under both polarizations. Absorption responses and EM field distributions have been systematically analyzed. We found that the relative positions of the subcells play an important role of the absorption spectra. The results give us an evaluation of the required registration accuracy in the lithography especially for the fabrication of three-dimensional metamaterials in the visible range.
2. Single-cell MMAs
Single-cell MMAs were first investigated to reveal how the structure dimensions affect the absorption, which helps us understand the misalignment effects in cascaded configurations. We started from a THz MMA that has been experimentally demonstrated and adopted in both laterally and vertically cascaded structures . As shown in Fig. 1, a continuous metal film is used as the ground plane on top of the substrate, and the metal cross array in a square lattice is separated from the ground plane by an intermediate dielectric layer. The absorption spectra were simulated by FDTD method (Lumerical Solutions, Inc.). Au is used as the metal with dielectric constant obtained by the Drude model. The dielectric is modeled as polyimide with a frequency independent refractive index of 1.8 + 0.06i . Three-dimensional simulations of a unit cell were performed with periodic boundary conditions in the xy plane and perfect matching layers in the z direction. Non-uniform meshes were used in the FDTD simulation, where the minimum mesh sizes at the interfaces are 0.2 μm and 0.05 μm in horizontal and vertical directions, respectively. A plane wave was set to be incident in the z direction and reflection (R) was recorded at a plane 100 μm above the metal cross array. Because a thick metal ground plane of 200 nm was used, the transmission is zero. Thus, the absorption is obtained by 1-R. The thickness of the top metal cross is also 200 nm and the thickness of the polyimide is 2 μm. TM and TE polarization waves have the electric field in the x and y directions, respectively.
The simulation results with a frequency resolution of 0.01THz are shown in Fig. 2. Absorption peaks around 5 THz are observed for all cases with a period p from 15 μm to 60 μm. At p = 44 μm, diffraction effect occurs at 6.75 THz where the wavelength approaches the period, and the main absorption peak at 5.53 THz decreases 20% compared to that at p = 32 μm. Similar phenomenon is observed at p = 60 μm with an even smaller absorption. The main absorption peaks at p = (22 ~60) μm show negligible shifts in frequency. It means that the perfect absorption is dominated by the local resonance in a cell rather than the coupling behavior in the periodic cross array. However, the coupling does show an effect at a smaller period such as p = 16 μm and 18 μm, where obvious red shifts of the absorption peaks are observed. To tune the absorption peak, MMAs consisting of cross array with different lengths l of the cross arms were simulated and the results are shown in Fig. 2(b). At a fixed period p = 22 μm, the frequency at the absorption peak increases with the decreasing l. It is the fundamental for the broadband cascaded MMAs, where several subcells with adjacent absorption peaks compose a supercell.
The EM field intensity and induced current distributions at the absorption peak in a MMA (red dot line in Fig. 2(b)) with p = 22 μm and w = 6 μm are shown in Fig. 3. The electric fields have a unit of V/m and the magnetic fields have a unit of A/m. The intensity of incident electric field is set to 1. As seen, both electric field and magnetic field are well confined in the dielectric layer at the resonant absorption frequencies. Hy is localized at the overlapping region of the two cross arms as shown in Fig. 3(b) and 3(c). For each polarization, the cross arm along the polarization direction can be seen as a dipole antenna, resulting in the electric field Ez of the excited surface plasmon resonance located at the edges of the antenna as shown in Fig. 3(e) and 3(f). Because l = 11 μm in Fig. 3(f) is shorter than l = 15 μm in Fig. 3(e), the distance between two maximums of |Ez|2 in Fig. 3(f) is smaller than that in Fig. 3(e). It wouldhelp us recognize absorption resonances in cascaded MMAs as discussed in the following section. In addition, |Hy|2 is more uniformly confined in the dielectric layer but |Ez|2 shows two hot spots around the edges of the cross as shown in Fig. 3(a) and 3(d), respectively. The distributions of induced current Jx are shown in Fig. 3(g)-3(i). The negative values mean inverse direction of current propagation. Jx clearly shows antiparallel currents in two metal layers induced by magnetic resonance, which forms a current loop together with the displacement currents at the ends of the cross as in .
3. Vertically cascaded MMAs
Grouping cells of single-cell MMAs, cascaded MMAs enable engineering the absorption response. It is easy to understand that the laterally cascaded MMAs consisting of subcells side by side can extend the absorption band. The deep subwavelength properties of the subcells ensure slight degeneration of the absorption, although the area filling ratio of each subcell decreases compared to the single-cell MMA [14–16]. Vertically cascaded configuration is particularly attractive because it is able to enlarge the absorption band and keep the spatial resolution [17–19]. However, the multilayer stack of metal films and dielectric layers requires multistep lithography. Whether the alignment affects the whole absorption of cascaded MMAs is a primary question in the design. In this section, lateral alignment issues in MMAs with three vertically cascaded cross arrays are discussed.
The schematic of the structure is shown in Fig. 4(a). Dielectric layer thicknesses h1, h2 and h3, the lengths of the cross arms l1, l2 and l3 are optimized to obtain a wide absorption band as discussed in . The absorption spectra in Fig. 4(b) clearly show the extension of the absorption band. There are three absorption peaks at 4.66 THz, 5.01 THz and 5.53 THz resulting from resonances of three cross arrays. Hy intensity distributions at three frequencies are well differentiated as shown in Fig. 5. The EM waves of different energy bands are confined in different dielectric layers, which could be very attractive to multi-junction solar cells. As shown in Fig. 3, |Hy|2 is mostly confined between adjacent metal layers and symmetrical in the x direction.
Then a lateral shift of the top cross array is assumed in the x direction. As shown in Fig. 6(a), a split of the absorption band is observed for TM polarization incident wave with an increasing Δx. In details, a nearly flat-top absorption band with absorption higher than 90% around 5 THz at Δx = 0 becomes two individual absorption peaks separated by 2.7 THz with a minimum absorption of only 30% at Δx = 6 μm (~λ/10). The changes of the relative positions of the cross arms in different metal layers have an important effect on the electric field polarized in this shifting direction and therefore the absorption spectra. For Δx = 0, 2, 6 μm, distributions of Jx, |Hy|2 and |Ez|2 for the high frequency resonant absorption peaks in the xz plane are plotted in Fig. 7. With the increase of Δx, the part of the EM field confined in the top dielectric layer shifts to the + x direction. Particularly, the lateral extension of Hy intensity becomes small as shown in Figs. 7(d), 7(e) and 7(f). We have known that the lateral extension of the EM field depends on the cross dimension in a single-cell MMA and the absorption peak has a blue shift for a small cross as shown in Fig. 3. The overlap between the top cross and the middle cross decreases with an increasing misalignment Δx, which results in a small effective cross dimension and therefore a change of the field distribution and a blue shift of the absorption peak. It is clearer to see from Ez intensity distributions in Fig. 7(g), 7(h) and 7(i), where the hot spots of the resonances exist at the ends of the overlap region. In addition, two hot spots in Fig. 7(h) and 7(i) localize at the bottom surface of the top metal cross and the top surface of the middle metal cross, respectively, different from Fig. 7(g) with both spots at the bottom surface of the top metal cross. In the case of the cascaded MMA, parallel cross arms in neighboring metal layers in a cell can be seen as a rod pair in the polarization direction of the incident wave. As discussed using resonant LC-circuit model in , antiparallel currents are excited by magnetic resonances can be seen for each metal/dielectric/metal sandwich structure in Fig. 7(a)-7(c).
The lateral shifts of subcells break the degeneration of TM and TE polarizations at the normal incidence. For TE polarization incident wave, the absorption spectra show slight variation in Fig. 6(b). We consider that the relative position of the top cross to the middle cross in a cell in the polarization direction, i.e. Δy, does not change with Δx and thus Ez localizes at the similar position in the y direction. As shown in Fig. 8, two maximums of Ez at Δx = 2 μm and 6 μm are approximately at the same positions in the y direction, which is determined by the ends of the cross arms as mentioned above. Therefore, slight variation of the absorption response occurs with the misalignment in the x direction for TE polarization incident wave.
The misalignments in both x and y directions are also considered. The results of TM polarization (TE polarization has the same results due to the symmetry) are shown in Fig. 9(a). Splitting of the nearly top-flat absorption band is seen as well. The decrease of the peak absorption is even faster than that in Fig. 6(a) but the splitting is slightly slow. We also investigate misalignments of both middle and top cross arrays. For Δx = Δy = 3 μm in the middle cross array and Δx = Δy = 6 μm in the top cross array, the absorption spectrum is shown as red dashed line in Fig. 9(b), which has a wider absorption band than the aligned structure as the green solid line. Actually, the integral absorption is even larger in the case of misaligned subcells. It might be useful in the light trapping design in solar cells.
A vertically cascaded MMA in near IR range is designed and simulated to show the challenge on current fabrication techniques resulting from the misalignment effect. The absorption in Fig. 10 clearly shows that a misalignment of approximately λ/50 causes a visible change of the absorption response. The alignment resolution of the conventional photolithography is far larger than this. Although this effect is not good for large scale industrial production of metamaterial currently, the high sensitivity of spectral response to the component positions shows an interesting application in plasmonic rulers , where a three-dimensional metamaterial was designed to measure nm-scale shift by measuring the variation of the spectral response.
In conclusion, we have numerically studied vertically cascaded metamaterial absorbers and found that the lateral misalignment of the subcells plays an important role of the spectral response. Even a misalignment of λ/50 brings a large influence on the spectral response. The change of the relative positions of subcells that are strongly coupled in a vertically cascaded metamaterial contributes to this phenomenon. The results give us an evaluation that how much registration accuracy is required in multi-step lithography and also show a possible application of this high position sensitivity as nanorulers.
This work is supported by the General Program of the National Natural Science Foundation of China (No. 11274344), the Hundred Talents Program of Chinese Academy of Sciences and the Fundamental Research Project of Shenzhen Science & Technology Foundation (NO. JC201105180781A).
References and links
1. T. J. Cui, D. R. Smith, and R. Liu, eds., Metamaterials-Theory, Design, and Applications (Springer, 2009).
3. P. V. Tuong, J. W. Park, J. Y. Rhee, K. W. Kim, W. H. Jang, H. Cheong, and Y. P. Lee, “Polarization-insensitive and polarization-controlled dual-band absorption in metamaterials,” Appl. Phys. Lett. 102(8), 081122 (2013). [CrossRef]
4. H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010). [CrossRef] [PubMed]
7. K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun 2, 517 (2011). [CrossRef] [PubMed]
9. J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83(16), 165107 (2011). [CrossRef]
10. F. Alves, D. Grbovic, B. Kearney, and G. Karunasiri, “Microelectromechanical systems bimaterial terahertz sensor with integrated metamaterial absorber,” Opt. Lett. 37(11), 1886–1888 (2012). [CrossRef] [PubMed]
11. Y. Ma, Q. Chen, J. Grant, S. C. Saha, A. Khalid, and D. R. S. Cumming, “A terahertz polarization insensitive dual band metamaterial absorber,” Opt. Lett. 36(6), 945–947 (2011). [CrossRef] [PubMed]
12. Y. Zhao, Q. Hao, Y. Ma, M. Lu, M. Lu, B. Zhang, M. Lapsley, I. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012). [CrossRef]
13. J. Hendrickson, J. Guo, B. Zhang, W. Buchwald, and R. Soref, “Wideband perfect light absorber at midwave infrared using multiplexed metal structures,” Opt. Lett. 37(3), 371–373 (2012). [CrossRef] [PubMed]
15. H. Li, L. H. Yuan, B. Zhou, X. P. Shen, Q. Cheng, and T. J. Cui, “Ultrathin multiband gigahertz metamaterial absorbers,” J. Appl. Phys. 110(1), 014909 (2011). [CrossRef]
16. P. Bouchon, C. Koechlin, F. Pardo, R. Haïdar, and J. L. Pelouard, “Wideband omnidirectional infrared absorber with a patchwork of plasmonic nanoantennas,” Opt. Lett. 37(6), 1038–1040 (2012). [CrossRef] [PubMed]
17. Y. Q. Ye, Y. Jin, and S. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in the terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010). [CrossRef]
19. F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012). [CrossRef]
20. T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006). [CrossRef]