Tunable Split-Disk Metamaterial Absorber for Sensing Application

nanomaterials

Article Tunable Split-Disk Metamaterial Absorber for Sensing Application

Yusheng Zhang , Peng Lin and Yu-Sheng Lin *

School of Electronics and Information Technology, Sun Yat-Sen University, Guangzhou 510006, China; [email protected] (Y.Z.); [email protected] (P.L.) * Correspondence: [email protected]

Abstract: We present four designs of tunable split-disk metamaterial (SDM) absorbers. They consist of a bottom gold (Au) mirror layer anchored on Si substrate and a suspended-top SDM nanostructure with one, two, three, and four splits named SDM-1, SDM-2, SDM-3, and SDM-4, respectively. By tailoring the geometrical conﬁgurations, the four SDMs exhibit different tunable absorption resonances spanning from 1.5 µm to 5.0 µm wavelength range. The resonances of absorption spectra can be tuned in the range of 320 nm, and the absorption intensities become lower by increasing the gaps of the air insulator layer. To increase the sensitivity of the proposed devices, SDMs exhibit high sensitivities of 3312 nm/RIU (refractive index unit, RIU), 3362 nm/RIU, 3342 nm/RIU, and 3567 nm/RIU for SDM-1, SDM-2, SDM-3, and SDM-4, respectively. The highest correlation coefﬁcient is 0.99999. This study paves the way to the possibility of optical gas sensors and biosensors with high sensitivity.

Keywords: tunable metamaterial; metal-insulator-metal absorber; plasmonic sensor

1. Introduction Recently, gas sensing technology reveals good prospects with the aggravation of environmental pollution. There are mainly two approaches, including electrochemical Citation: Zhang, Y.; Lin, P.; Lin, Y.-S. sensing [1] and nondispersive infrared (NDIR) sensing [2]. The electrochemical sensor Tunable Split-Disk Metamaterial has been widely employed in commercial products. However, it is limited by large power Absorber for Sensing Application. Nanomaterials 2021, 11, 598. https:// consumption, poor selectivity, and hysteresis [3]. Rather than the electrochemical sensor, doi.org/10.3390/nano11030598 the infrared (IR) sensor is used to detect gas molecules owing to the specific absorption spectrum of gas molecules in the near to middle IR wavelength. It gradually becomes a Received: 6 December 2020 mainstream of research for its high selectivity and lower hysteresis, but it still suffers from Accepted: 30 December 2020 poor absorption characteristics and selectivity in the mixed environment where various Published: 4 January 2021 gases and water vapor coexist. In view of this point, some literature has reported using metamaterial absorber with high selectivity to enhance the absorption characteristics in the Publisher’s Note: MDPI stays neu- mid-IR wavelength range [4–8]. Metamaterials, composed of periodic or random structures tral with regard to jurisdictional clai- with subwavelength feature size, exhibit unique electromagnetic and optical characteristics, ms in published maps and institutio- such as negative refraction index [9], perfect absorption [10–12], and so on. Owing to their nal affiliations. extraordinary electromagnetic properties, metamaterials are widely explored for optical filters, waveguides, polarizers, resonators, and absorbers [13–18] spanned from microwave, terahertz (THz), and IR to visible spectra ranges [10,19–22]. The various surrounding gas molecules including water vapor have their own ab- Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. sorption spectra, which will make the electromagnetic resonance of the IR metamaterial This article is an open access article absorbers shift or decrease the resonance intensity. However, it is difficult to meet the distributed under the terms and con- requirements of high selectivity owing to the fact that the electromagnetic characteristics of ditions of the Creative Commons At- metamaterial absorbers are fixed once fabricated on rigid substrates. Therefore, an actively tribution (CC BY) license (https:// tunable metamaterial in the mid-IR wavelength range becomes a feasible approach. The creativecommons.org/licenses/by/ controllable methods of tunable metamaterials include thermal annealing [23–27], phase 4.0/). change materials [28], laser pumping [29–31], liquid crystal [32,33], flexible materials [34],

Nanomaterials 2021, 11, 598. https://doi.org/10.3390/nano11030598 https://www.mdpi.com/journal/nanomaterials Nanomaterials 2021, 11, 598 2 of 10

and micro-electro-mechanical systems (MEMS) technique [35–40]. In these tuning approaches, MEMS-based metamaterials exhibit good linearity and large tuning range, which are preferable to phase change and flexible materials that highly rely on the nonlinear properties of nature materials. Furthermore, metamaterials are also used in biosensing applications. The surface plasmonic metamaterial sensors pave the way to next-generation biological and chemical sensors for high-throughput, label-free, and multianalyte sensing applications [41,42]. The principle of surface plasmonic metamaterial for biosensing application is the resonant wavelength of absorption spectra shift by changing the medium refraction index. The metamaterial-based sensors are encapsulated and integrated with microfluidic chips to detect the biomolecules [43]. Such surface plasmonic metamaterial-based biosensors also suffer the same limitations of low sensitivity and selectivity [44]. In this study, we propose four designs of tunable split-disk metamaterial (SDM) absorbers. For a convenient description, SDM with one, two, three, and four splits are named SDM-1, SDM-2, SDM-3, and SDM-4, respectively. They are composed of a bottom Au mirror layer anchored on Si substrate and a suspended SDM nanostructure. These four SDMs are investigated first to determine the optimized geometrical parameters including split length and width. These four SDMs are reconfigurable and exhibit different active and flexible tunability in absorption intensity and resonance. Moreover, the resonances of the four SDMs can be tuned by changing the gap between the top SDM nanostructures and bottom Au mirror layers. When these SDMs are exposed to different environment ambients, they show high sensitivities with a high correlation coefficient of 0.9999. They are suitable for the use of gas sensors and biosensors.

2. Designs and Methods The schematic drawing of proposed SDM is illustrated in Figure1. It is composed of a bottom Au mirror layer anchored on Si substrate and a suspended SDM nanostructure. Four SDM configurations are periodic split-disks with one (SDM-1), two (SDM-2), three (SDM-3), and four (SDM-4) splits. The geometrical denotations are split length (ai) and split width (bi) as shown in Figure1a, disk diameter ( d), disk period (P), and the gap between bottom Au mirror layer and top SDM nanostructures (zi) as shown in Figure1b, where i varies from 1 to 4 to represent SDM-1 to SDM-4, respectively. Herein, the P, d values, and thickness of Au layers are kept constant as 1.5 × 1.5 µm2, 1.0 µm, and 100 nm, respectively. The top SDM is suspended and supported by using a membrane composed of an Si/Si3N4 bilayer using residual stress induced electrothermal actuators (ETAs). As the structures are released, the initial stress between the Si and Si3N4 layers makes the cantilever deform out-of-plane and bend upward. By applying a direct current (DC) bias voltage on these residual stress-induced ETAs, the electrothermal attraction force is induced between the released cantilevers. Meanwhile, the out-of-plane bilayer cantilever will be bent downward to the substrate owing to such electrothermal attraction force. Therefore, the SDM can be tuned vertically by actuating the ETAs to change the z value between the top SDM and bottom mirror layer. When exposed on an electromagnetic wave, the absorber can generate the collective oscillation of free electrons on account of the metal-insulator-metal (MIM) structure [45,46], resulting in the absorption of incident electromagnetic energy. To numerically calculate the optical properties of SDM devices, the Lumerical so- lution’s software finite difference time-domain (FDTD) solutions were employed in the full-field plane electromagnetic wave. Owing to the Si and Si3N4 bilayer with a very low absorption coefficient at the IR wavelength range, the influence of the electromagnetic wave propagation of the SDM can be ignored. The permittivity value of the Au material at the IR wavelength range is calculated according to the Drude-Lorentz model [47,48]. The propagation direction of the incident IR wave is set to be perpendicular to the x–y plane. The periodic boundary conditions are applied in the x- and y-axis direction, while the perfectly matched layer (PML) boundary conditions are assumed in the z-axis direction. The reflection (R) and the transmission (T) of the incident IR wave are calculated by spectra Nanomaterials 2021, 11, x FOR PEER REVIEW 3 of 11

Nanomaterials 2021, 11, 598 3 of 10 The periodic boundary conditions are applied in the x- and y-axis direction, while the perfectly matched layer (PML) boundary conditions are assumed in the z-axis direction. The reflection (R) and the transmission (T) of the incident IR wave are calculated by spec- monitorstra monitors set below set below and aboveand above the devices, the devices, respectively. respectively. The correspondingThe corresponding absorption absorption (A) is(A deﬁned) is defined as A as= 1A− = T1 −− TR −. R Since. Since the the transmission transmission of of incident incident electromagnetic electromagnetic light light is is blockedblocked by by the the bottom bottom Au Au mirror mirror layer, layer, the the absorption absorption can can be simply be simply obtained obtained by A by= 1A− = R1 .− ItR apparently. It apparently means means that that high high absorption absorption is earned is earned from from low low reﬂection. reflection.

FigureFigure 1. 1.(a ()a Schematic) Schematic drawing drawing of of four four types types of of split-disk split-disk metamaterials metamaterials (SDMs). (SDMs). They They are are (i) SDM-1,(i) SDM- 1, (ii) SDM-2, (iii) SDM-3 and (iv) SDM-4, respectively. (b) The cross-sectional view of SDM. (ii) SDM-2, (iii) SDM-3 and (iv) SDM-4, respectively. (b) The cross-sectional view of SDM.

3. ResultsTo numerically and Discussion calculate the optical properties of SDM devices, the Lumerical solu- tion’sFigure software2 shows finite the difference absorption time-domain spectra of four(FDTD) SDMs solutions with different were employeda values, in the where full- zfieldand bplanevalues electromagnetic are kept constant wave. as zThe= 100 permittivity nm, and b value= 200 of nm, Au respectively. material at SDM-1the IR wave- and length range is calculated according to the Drude-Lorentz model [47,48]. The propagation SDM-3 exhibit dual-resonance characteristics, which are denoted as ω1 and ω2 as shown in Figuredirection2a,c, of while the incident SDM-2 and IR wave SDM-4 is showset to onlybe perpendicular single-resonance to the as x–y shown plane. in Figure The periodic2b,d, boundary conditions are applied in the x- and y-axis direction, while the perfectly respectively. It is obvious to observe that ω2 is the main resonance for SDM-1 and SDM-3 sincematched they layer exhibit (PML) the identical boundary tuning conditions characteristic are assumed of SDM-2 in the andz-axis SDM-4. direction. By changingThe reflec- ationvalues (R) fromand the 100 transmission nm to 500 nm (T for) of SDM-1incident and IR SDM-2wave are and calculated from 100 by nm spectra to 400 monitors nm for SDM-3set below and and SDM-4, above the the main devices, absorption respectively. resonances The are corresponding red-shifted from absorption the wavelengths (A) is de- offined 2.76 µasm A to = 4.091 − Tµ m,− R 2.78. Sinceµm the to 4.38transmissionµm, 2.65 µofm incident to 3.32 µelectromagneticm, and 2.70 µm light to 3.56 is µblockedm for SDM-1,by the SDM-2,bottom SDM-3,Au mirror and layer, SDM-4, the respectively. absorption Whilecan be the simply absorption obtained intensities by A = increase 1 − R. It toapparently 99.8%, 75.5%, means 52.5%, that andhigh 47.8%absorption for SDM-1, is earned SDM-2, from SDM-3,low reflection. and SDM-4, respectively. It is worth noting that the main resonances disappear when a = 500 nm for SDM-2 and a3.= 400Results nm forand SDM-3 Discussion and SDM-4 because of the enlarged splits contacting each other and then separatingFigure 2 shows the disks. the absorption spectra of four SDMs with different a values, where z andFigure b values3 shows are kept the absorption constant as spectra z = 100 of fournm, SDMsand b with= 200 different nm, respectively.b values, where SDM-1z and and aSDM-3values areexhibit kept constantdual-resonance as z = 100 charac nm, andteristics,a = 300 which nm. Theare absorptiondenoted as resonances ω1 and ω2of asω shown1 are blue-shiftedin Figure 2a,c, by increasing while SDM-2b values and for SDM-4 SDM-1 show and SDM-3 only single-resonance as shown in Figure as3 a,c,shown respectively. in Figure µ µ The2b,d, tuning respectively. ranges are It 230is obvious nm from to theobserve wavelength that ω2 ofis 1.80the mainm to resonance2.03 m for for SDM-1 SDM-1 and and fromSDM-3 the wavelengthsince they exhibit of 2.23 µ them to identical 2.46 µm fortuning SDM-3, characteristic while the main of SDM-2 absorption and resonancesSDM-4. By ofchanging the four SDMsa values are from red-shifted 100 nm by to increasing 500 nm for the SDM-1b values and from SDM-2100 nmandto from 300 nm100 andnm to then 400 blue-shiftednm for SDM-3 by increasing and SDM-4, the theb values main fromabsorption 300 nm resonances to 500 nm. are The red-shifted tuning ranges from of thethe mainwave- absorptionlengths of resonances2.76 µm to are 4.09 80 µm, nm, 2.78 210 nm,µm 160to 4.38 nm, µm, and 2.65150 nmµm forto 3.32 SDM-1, µm, SDM-2, and 2.70 SDM-3, µm to and3.56 SDM-4, µm for respectively. SDM-1, SDM-2, The SDM-3, main resonances and SDM-4, disappear respectively. when bWhile= 400 the nm absorption for SDM-3 inten- and SDM-4sities increase since the to disks 99.8%, are 75.5%, separated. 52.5%, Therefore, and 47.8% the shiftsfor SDM-1, of the mainSDM-2, absorption SDM-3, resonancesand SDM-4, arerespectively. dominated byIt isa valuesworth innoting the ranges that the of 1330 main nm resonances, 1600 nm, disappear 670 nm, and when 860 nm a = for500 SDM-1, nm for SDM-2, SDM-3, and SDM-4, respectively, and gradually enlarge the absorption intensities, while the shifts of the main absorption resonances are minor by changing b values.

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Nanomaterials 2021, 11, 598 SDM-2 and a = 400 nm for SDM-3 and SDM-4 because of the enlarged splits contacting4 of10 each other and then separating the disks.

Nanomaterials 2021, 11, x FOR PEER REVIEW 5 of 11 FigureFigure 2. 2.AbsorptionAbsorption spectra spectra of of(a) (SDM-1,a) SDM-1, (b) (SDM-2,b) SDM-2, (c) (SDM-3,c) SDM-3, and and (d) (SDM-4d) SDM-4 with with different different a values,a values, where where z andz and b valuesb values are arekept kept constant constant as z as = 100z = 100nm, nm, and and b = 200b = 200nm,nm, respectively. respectively.

Figure 3 shows the absorption spectra of four SDMs with different b values, where z and a values are kept constant as z = 100 nm, and a = 300 nm. The absorption resonances of ω1 are blue-shifted by increasing b values for SDM-1 and SDM-3 as shown in Figure 3a,c, respectively. The tuning ranges are 230 nm from the wavelength of 1.80 µm to 2.03 µm for SDM-1 and from the wavelength of 2.23 µm to 2.46 µm for SDM-3, while the main absorption resonances of the four SDMs are red-shifted by increasing the b values from 100 nm to 300 nm and then blue-shifted by increasing the b values from 300 nm to 500 nm. The tuning ranges of the main absorption resonances are 80 nm, 210 nm, 160 nm, and 150 nm for SDM-1, SDM-2, SDM-3, and SDM-4, respectively. The main resonances disappear when b = 400 nm for SDM-3 and SDM-4 since the disks are separated. Therefore, the shifts of the main absorption resonances are dominated by a values in the ranges of 1330 nm, 1600 nm, 670 nm, and 860 nm for SDM-1, SDM-2, SDM-3, and SDM-4, respectively, and gradually enlarge the absorption intensities, while the shifts of the main absorption resonances are minor by changing b values.

FigureFigure 3. 3.AbsorptionAbsorption spectra spectra of of(a) ( aSDM-1,) SDM-1, (b) ( bSDM-2,) SDM-2, (c) (SDM-3,c) SDM-3, and and (d) (SDM-4d) SDM-4 with with different different b values,b values, where where z andz and a valuesa values are arekept kept constant constant as z as =100z =100 nm, nm, and and a = a300= 300nm, nm, respectively. respectively.

ToTo test test the the SDMs’ SDMs’ possession possession of of active active tunability, tunability, the the top top SDM SDM nanostructures nanostructures are are suspendedsuspended and and connected connected to to the the ME MEMSMS actuators actuators for for the the changing changing z valuesz values of of the the SDMs. SDMs. FigureFigure 44 shows shows the the absorption absorption spec spectratra of of four SDMs with differentdifferent z values, where aa andand b b values are kept constant as a = 300 300 nm, nm, and and bb == 200 200 nm. nm. The The gaps gaps could could be be actively actively tuned tuned byby using using electrostatic electrostatic or orelec electrothermaltrothermal forces. forces. TheThe maximum maximum absorption absorption intensities intensities of the of mainthe mainresonances resonances are 99.9%, are 99.9%, 82.8%, 82.8%, 91.5%, 91.5%, and 85.8% and 85.8%at the atwavelengths the wavelengths of 3.42 of µm, 3.42 3.82µm, µm,3.82 3.56µm µm,, 3.56 andµm, 3.80 and µm 3.80 forµm SDM-1 for SDM-1 (Figure (Figure 4a),4 a),SDM-2 SDM-2 (Figure (Figure 4b),4b), SDM-3 SDM-3 (Figure ( Figure 4c),4c ), andand SDM-4 SDM-4 (Figure (Figure 4d),4d), respectively. respectively. The The z zvaluesvalues are are 50 50 nm. nm. Under Under these these conditions, conditions, SDM-1 exhibits perfect absorption up to 99.9%, indicating its potential application as a high-efficient absorber. By changing the z value from 50 nm to 200 nm, the absorption resonances of the SDMs are blue-shifted in the range of 320 nm. In addition, the absorption intensities could be attenuated and the spectra bandwidths become broader. This indicates the proposed SDMs could be explored for variable optical attenuator (VOA) application.

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SDM-1 exhibits perfect absorption up to 99.9%, indicating its potential application as a high-efﬁcient absorber. By changing the z value from 50 nm to 200 nm, the absorption resonances of the SDMs are blue-shifted in the range of 320 nm. In addition, the absorption Nanomaterials 2021, 11, x FOR PEER REVIEW 6 of 11 intensities could be attenuated and the spectra bandwidths become broader. This indicates the proposed SDMs could be explored for variable optical attenuator (VOA) application.

FigureFigure 4. Absorption 4. Absorption spectra spectra of (a) ofSDM-1, (a) SDM-1, (b) SDM-2, (b) SDM-2, (c) SDM-3, (c) and SDM-3, (d) SDM-4 and ( dwith) SDM-4 different with z different z values,values, where where a anda and b valuesb values are kept are constant kept constant as a = 300 as nm,a = 300and nm,b = 200 and nm,b = respectively. 200 nm, respectively.

ToTo further further prove prove the proposed the proposed SDMs SDMs for sensing for sensing applications, applications, the four SDMs the four were SDMs were designeddesigned to be to exposed be exposed to ambient to ambient environments environments with different with different refraction refraction indexes (n indexesi) to (n ) to demonstrate the high-efficient and high-sensitive sensor applications. Figure 5 shows the i demonstrate the high-efficient and high-sensitive sensor applications. Figure5 shows the absorption spectra of the SDMs by changing the surrounding refraction index from 1.0 to 1.4,absorption where the z spectra, a, and b of values the SDMs are kept by constant changing as z the = 50 surrounding nm, a = 300 nm, refraction and b = 200 index nm, from 1.0 to respectively.1.4, where theSDM-1z, a ,shows and b valuesthe absorption are kept resonances constant asarez =red-shifted 50 nm, a =from 300 nm,the wave- and b = 200 nm, lengthrespectively. of 2.04 µm SDM-1 to 2.83 shows µm and the from absorption the wavelength resonances of 3.42 are µm red-shifted to 4.74 µm from forthe ω1 and wavelength of ω22.04, respectively,µm to 2.83 byµ mincreasing and from the the n1wavelength value from 1.0 of 3.42to 1.4µ mas toshown 4.74 µinm Figure for ω 15a.and Theω 2ab-, respectively, sorptionby increasing intensities the aren1 valuestable at from 99.9%. 1.0 toAs1.4 shown as shown in Figure in Figure 5b, the5 a.absorption The absorption resonances intensities are arestable red-shifted at 99.9%. from As the shown wavelength in Figure of 3.815b, µm the to absorption 5.29 µm for resonancesSDM-2 by increasing are red-shifted the n2 from the value,wavelength while the of 3.81absorptionµm to 5.29intensitiesµm for increase SDM-2 minorly by increasing from the82.8%n2 tovalue, 89.5%. while SDM-3 the absorption showsintensities the absorption increase resonances minorly from are 82.8%red-shifted to 89.5%. from SDM-3the wavelength shows the of absorption2.54 µm to 3.46 resonances are µmred-shifted and from the from wavelength the wavelength of 3.56 µm of 2.54to 4.89µm µm to for 3.46 ω1 µandm andω2, respectively, from the wavelength by increas- of 3.56 µm ing the n3 value as shown in Figure 5c. The absorption intensities increase gradually from to 4.89 µm for ω1 and ω2, respectively, by increasing the n3 value as shown in Figure5c. The 64.9% to 75.3% and from 91.4% to 95.4% for ω1 and ω2, respectively. As for SDM-4, the absorption intensities increase gradually from 64.9% to 75.3% and from 91.4% to 95.4% for absorption resonances are red-shifted from the wavelength of 3.80 µm to 5.24 µm by in- ω1 and ω2, respectively. As for SDM-4, the absorption resonances are red-shifted from the creasing the n4 value, while absorption intensities increase minorly from 85.8% to 91.1% aswavelength shown in Figure of 3.80 5d.µ mThe to four 5.24 SDMsµm by exhibi increasingt refraction the nindex-sensitive4 value, while features absorption that intensities indicateincrease that minorly absorption from 85.8%resonanc toes 91.1% are asred-shifted shown in by Figure increasing5d. The ni four values. SDMs It can exhibit be refraction explainedindex-sensitive that the features relative that permittivity indicate thatof the absorption surrounding resonances insulator are layer red-shifted changed, by increasing resultingni values. in the It can change be explained of resonant that frequency the relative [17]. permittivity of the surrounding insulator layer changed, resulting in the change of resonant frequency [17]. To further evaluate the sensitivity (S) and ﬁgure of merit (FOM) of SDM-based sensors, they can be deﬁned as follows [49].

∆λ S S = , FOM = (1) ∆n FWHM where ∆λ is the resonance shift caused by a refraction index change (∆n) and FWHM is the full width at half maximum (FWHM) of resonance. Figure6 shows the relationships of reso-

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nances and ni values of the SDMs. The fitting trends are highly linear, with a correlation coefficient of 0.9999. The S and FOM values are calculated at main resonances. The four SDMs exhibit high sensitivity of 3312 nm/RIU, 3362 nm/RIU, 3342 nm/RIU, and 3567 nm/RIU as shown in Figure6a–d, respectively. These results are better than those reported in this wavelength range [50–53], where the maximum sensitivity is only 1060 nm/RIU. The maximum FOM values are 13.25, 15.28, 20.89, and 17.8 for SDM-1, SDM-2, SDM-3, and SDM-4, respectively. These results indicate the proposed SDM absorbers are suitable to be used as high-efficient and high-sensitive gas sensors and biosensors, since the refraction Nanomaterials 2021, 11, x FOR PEER REVIEW 7 of 11 index of the ambient environment could be calculated by the change in the absorption resonances, which is related to the type of gas and bio-molecules.

FigureFigure 5. Absorption 5. Absorption spectra spectra of (a) SDM-1, of (a) ( SDM-1,b) SDM-2, (b (c)) SDM-2, SDM-3, and (c) SDM-3,(d) SDM-4 and exposed (d) SDM-4 to ambient exposed to ambient environmentsenvironments with with different different refraction refraction indexes, indexes, where z, where a, and bz ,valuesa, and areb values kept constant are kept as z constant = 50 as z = 50 nm, Nanomaterials 2021, 11, x FOR PEER REVIEWnm, a = 300 nm, and b = 200 nm, respectively. 8 of 11 a = 300 nm, and b = 200 nm, respectively. To further evaluate the sensitivity (S) and figure of merit (FOM) of SDM-based sensors, they can be defined as follows [49]. ∆𝜆 𝑆 𝑆 , 𝐹𝑂𝑀 (1) ∆𝑛 𝐹𝑊𝐻𝑀 where Δλ is the resonance shift caused by a refraction index change (Δn) and FWHM is the full width at half maximum (FWHM) of resonance. Figure 6 shows the relationships of resonances and ni values of the SDMs. The fitting trends are highly linear, with a correlation coefficient of 0.9999. The S and FOM values are calculated at main resonances. The four SDMs exhibit high sensitivity of 3312 nm/RIU, 3362 nm/RIU, 3342 nm/RIU, and 3567 nm/RIU as shown in Figure 6a–d, respectively. These results are better than those reported in this wavelength range [50–53], where the maximum sensitivity is only 1060 nm/RIU. The maximum FOM values are 13.25, 15.28, 20.89, and 17.8 for SDM-1, SDM-2, SDM-3, and SDM-4, respectively. These results indicate the proposed SDM absorbers are suitable to be used as high-efficient and high-sensitive gas sensors and biosensors, since the refraction index of the ambient environment could be calculated by the change in the absorption resonances, which is related to the type of gas and bio-molecules.

FigureFigure 6. The 6. Therelationships relationships of resonances of resonances and n values and of (na) valuesSDM-1, ( ofb) (SDM-2,a) SDM-1, (c) SDM-3, (b) SDM-2, and (d) (c) SDM-3, and SDM-4,(d) SDM-4, respectively. respectively.

To Tobetter better understand understand the coupling the coupling effects wi effectsthin SDMs, within the SDMs,corresponding the corresponding electric electric (E) field and magnetic (H) field distributions of SDMs are plotted in Figure 7 and 8, re- (E) ﬁeld and magnetic (H) ﬁeld distributions of SDMs are plotted in Figures7 and8, spectively, where the n, z, a, and b values are kept constant as n = 1.0, z = 50 nm, a = 300 nm, and b = 200 nm, respectively. In the main resonances, E-field energies are focused on the edges of disks and insulator layers as shown in Figures 7b,c,e,f while H-field energies are confined in insulator layers right below the center of the disks as shown in Figures 8b,c,e,f. The electromagnetic energies are confined within the top SDM nanostructures and bottom Au mirror layers, and the observed field energy around the edge of the SDMs are electric dipole resonances. The electrical vectors of the up and down sides of the top of the SDM, and left and right parts of the insulator layers are opposite, respectively, resulting in a strong magnetic response. The combination of strong local magnetic response and electric dipole resonances cause the enhanced absorption. The physical mechanism could be explained by an LC oscillator circuit excited by an external electromagnetic field. The equivalent circuit model of MIM nanostructures are inductances, resistances, and capacitors, which is equivalent to an LC oscillator circuit. According to the Drude-Lorentz model [17], the resonant frequency can be expressed by

1 𝐶 𝑧 𝑓 (2) 2𝜋𝐿𝐶 2𝜋𝑙𝜀 𝑤

where Le = μ0l2/t and Ce = ε0εcwt/z are the equivalent inductance and capacitance determined by SDM cells, c0 is the light velocity in vacuum, εc is the relative permittivity of the materials within the SDM, w is the metallic width, z is the gap width, l is the size of the circuit model (i.e., a and b), and t is the metallic thickness. For ω1, the E- and H-field energies are focused nearby or below the edge of the top of the SDM for SDM-1 as shown in Figure 7a and Figure 8a, respectively, while the E- and H-field energies are confined near the splits for SDM-3 as shown in Figure 7d and Figure 8d, respectively. This demonstrates that absorption resonances ω1 are caused by the coupling effects within the top of the SDM nanostructures.

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respectively, where the n, z, a, and b values are kept constant as n = 1.0, z = 50 nm, a =300 nm, and b = 200 nm, respectively. In the main resonances, E-field energies are focused on the edges of disks and insulator layers as shown in Figure7b,c,e,f while H-field energies are confined in insulator layers right below the center of the disks as shown in Figure8b,c,e,f. The electromagnetic energies are confined within the top SDM nanostructures and bottom Au mirror layers, and the observed field energy around the edge of the SDMs are electric dipole resonances. The electrical vectors of the up and down sides of the top of the SDM, and left and right parts of the insulator layers are opposite, respectively, resulting in a strong magnetic response. The combination of strong local magnetic response and electric dipole resonances cause the enhanced absorption. The physical mechanism could be explained by an LC oscillator circuit excited by an external electromagnetic field. The equivalent circuit model of MIM nanostructures are inductances, resistances, and capacitors, which is equivalent to an LC oscillator circuit. According to the Drude-Lorentz model [17], the resonant frequency can be expressed by r 1 C0 z fLC = √ = √ (2) 2π LeCe 2πl εc w

where Le = µ0l2/t and Ce = ε0εcwt/z are the equivalent inductance and capacitance determined by SDM cells, C0 is the light velocity in vacuum, εc is the relative permittivity of the materials within the SDM, w is the metallic width, z is the gap width, l is the size of the circuit model (i.e., a and b), and t is the metallic thickness. For ω1, the E- and H-field energies are focused nearby or below the edge of the top of the SDM for SDM-1 as shown in Figures 7a and8a, respectively, while the E- and H-field energies are confined near the splits for SDM-3 as shown Nanomaterials 2021, 11, x FOR PEER REVIEW 9 of 11 in Figures7d and8d, respectively. This demonstrates that absorption resonances ω1 are caused by the coupling effects within the top of the SDM nanostructures.

Figure 7. E-field distributions of SDM-1 monitored at (a) ω1 and (b) ω2 resonances, SDM-2 monitored at (c) ω resonance, Figure 7. E-ﬁeld distributions of SDM-1 monitored at (a) ω1 and (b) ω2 resonances, SDM-2 monitored at (c) ω resonance, SDM-3 monitored at (d) ω1 and (e) ω2 resonances, and SDM-4 monitored at (f) ω resonance, respectively. SDM-3 monitored at (d) ω1 and (e) ω2 resonances, and SDM-4 monitored at (f) ω resonance, respectively.

Figure 8. H-field distributions of SDM-1 monitored at (a) ω1 and (b) ω2 resonances, SDM-2 monitored at (c)ω resonance, SDM-3 monitored at (d) ω1 and (e) ω2 resonances, and SDM-4 monitored at (f) ω resonance, respectively.

4. Conclusions In conclusion: we propose four tunable SDM absorbers. By tailoring the geometrical dimensions, the absorption spectra could be tuned within a “molecule fingerprint” wavelength range, which indicates the potential application as multi-gases sensors and biosensors. Furthermore, the absorption intensities decrease by increasing the gap between the SDMs and bottom Au mirror layer. To demonstrate that the proposed SDM devices could be applied as high-sensitive sensors, the SDM devices were exposed to ambient environments with different refraction indexes. The four SDMs exhibit high sensitivity of 3312 nm/RIU, 3362 nm/RIU, 3342 nm/RIU, and 3567 nm/RIU for SDM-1, SDM-2, SDM-3, and SDM-4, respectively. The corresponding FOM are 13.25, 15.28, 20.89, and 17.8 for SDM-1, SDM-2, SDM-3, and SDM-4, respectively. The correlation coefficient is 0.9999. The tuning

Nanomaterials 2021, 11, x FOR PEER REVIEW 9 of 11

Nanomaterials 2021, 11, 598 8 of 10 Figure 7. E-field distributions of SDM-1 monitored at (a) ω1 and (b) ω2 resonances, SDM-2 monitored at (c) ω resonance, SDM-3 monitored at (d) ω1 and (e) ω2 resonances, and SDM-4 monitored at (f) ω resonance, respectively.

Figure 8. H-field distributions of SDM-1 monitored at (a) ω1 and (b) ω2 resonances, SDM-2 monitored at (c)ω resonance, Figure 8. H-field distributions of SDM-1 monitored at (a) ω1 and (b) ω2 resonances, SDM-2 monitored at (c) ω resonance, SDM-3 monitored at (d) ω1 and (e) ω2 resonances, and SDM-4 monitored at (f) ω resonance, respectively. SDM-3 monitored at (d) ω1 and (e) ω2 resonances, and SDM-4 monitored at (f) ω resonance, respectively. 4. Conclusions 4. ConclusionsIn conclusion: we propose four tunable SDM absorbers. By tailoring the geometrical dimensions,In conclusion: the absorption we propose spectra four could tunable be tuned SDM within absorbers. a “molecule By tailoring fingerprint” the geometri- wave- callength dimensions, range, which the indicates absorption the spectra potential could application be tuned as within multi-gases a “molecule sensors fingerprint”and biosen- wavelengthsors. Furthermore, range, the which absorption indicates intensitie the potentials decrease application by increasing as multi-gases the gap sensorsbetween and the biosensors.SDMs and bottom Furthermore, Au mirror the absorption layer. To demo intensitiesnstrate decrease that the by proposed increasing SDM the devices gap between could thebe applied SDMs and as high-sensitive bottom Au mirror sensors, layer. the ToSDM demonstrate devices were that exposed the proposed to ambient SDM environ- devices couldments bewith applied different as high-sensitive refraction indexes. sensors, The the four SDM SDMs devices exhibit were high exposed sensitivity to ambient of 3312 environmentsnm/RIU, 3362 withnm/RIU, different 3342 refractionnm/RIU, and indexes. 3567 Thenm/RIU four SDMsfor SDM-1, exhibit SDM-2, high sensitivity SDM-3, and of 3312SDM-4, nm/RIU, respectively. 3362 nm/RIU, The corresponding 3342 nm/RIU, FOM and are 3567 13.25, nm/RIU 15.28, for20.89, SDM-1, and 17.8 SDM-2, for SDM-1, SDM-3, andSDM-2, SDM-4, SDM-3, respectively. and SDM-4, The respectively. corresponding The co FOMrrelation are 13.25, coefficient 15.28, is 20.89, 0.9999. and The 17.8 tuning for SDM-1, SDM-2, SDM-3, and SDM-4, respectively. The correlation coefficient is 0.9999. The tuning range of resonance is within the range of a “molecule fingerprint”, allowing the SDM devices to be used for the identification of molecules. These results open an avenue to their application as high-efficient multi-gas sensors and biosensors, switches, VOAs, and so on.

Author Contributions: Conceptualization, Y.Z. and Y.-S.L.; methodology, Y.Z. and Y.-S.L.; software, Y.Z.; validation, Y.Z. and Y.-S.L.; investigation, Y.Z., P.L., and Y.-S.L.; resources, Y.-S.L.; data curation, Y.Z. and Y.-S.L.; writing—original draft preparation, Y.Z. and Y.-S.L.; writing—review and editing, Y.Z., P.L., and Y.-S.L.; supervision, Y.-S.L.; project administration, Y.-S.L.; funding acquisition, Y.-S.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the financial support from the National Key Research and Development Program of China (2019YFA0705004). Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest.

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