Electrostatically Tuned Optical Filters Based on Hybrid Plasmonic-Dielectric Thin Films for Hyperspectral Imaging

micromachines

Article Electrostatically Tuned Optical Filters Based on Hybrid Plasmonic-Dielectric Thin Films for Hyperspectral Imaging

Ahmed Abdelghfar 1,*, Mohamed A. Mousa 1 , Bassant M. Fouad 1 , Ahmed H. Saad 1, Noha Anous 2 and Noha Gaber 1,*

1 Center for Nanotechnology, Zewail City of Science and Technology, October Gardens, Giza 12578, Egypt; [email protected] (M.A.M.); [email protected] (B.M.F.); [email protected] (A.H.S.) 2 Faculty of Engineering, Ain-Shams University, 1 Elsarayat St., Abbassia, Cairo 11517, Egypt; [email protected] * Correspondence: [email protected] (A.A.); [email protected] (N.G.)

Abstract: Hyperspectral imaging has a wide range of uses, from medical diagnostics to crop monitoring; however, conventional hyperspectral imaging systems are relatively slow, bulky, and rather costly. In this paper, we present an inexpensive, compact tunable optical filter for hyperspectral applications. The filter is based on a Fabry-Pérot interferometer utilizing hybrid metallic-dielectric mirrors and actuated using a MEMS electrostatic actuator. The optical filter is designed using the transfer matrix method; then, the results were verified by an electromagnetic wave simulator. The actuator is based on a ring-shaped parallel plate capacitor and is designed using COMSOL Multiphysics. An

actuation displacement of 170 nm was used, which is the required distance to tune the filter over the whole visible range (400–700 nm). There are two designs proposed for the optical filter: the first

Citation: Abdelghfar, A.; Mousa, was optimized to provide maximum transmission and the other is optimized to have minimum M.A.; Fouad, B.M.; Saad, A.H.; full-width-half-maximum (FWHM) value. The first design has a maximum transmission percentage Anous, N.; Gaber, N. Electrostatically of 94.45% and a minimum transmission of 86.34%; while the minimum FWHM design had an average Tuned Optical Filters Based on FWHM value of 7.267 nm. The results showed improvements over the current commercial filters Hybrid Plasmonic-Dielectric Thin both in transmission and in bandwidth. Films for Hyperspectral Imaging. Micromachines 2021, 12, 767. https:// Keywords: tunable optical filter; visible range filters; hyperspectral imaging; plasmonic filters; doi.org/10.3390/mi12070767 MEMS tunable filters; electrostatic actuators

Academic Editor: Niall Tait

Received: 30 April 2021 1. Introduction Accepted: 25 June 2021 Since the development of hyperspectral imaging, the technology has proven to be use- Published: 29 June 2021 ful in many applications. Hyperspectral imaging techniques capture a three-dimensional cube containing spectral-spatial information about the scanned object. This cube is some- Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in times also called the hypercube [1]. The cube is formed by imaging the spatial dimensions published maps and institutional affil- at different spectral bands, forming a contiguous spectrum of spatial-spectral information iations. about the scanned object. This captures spectral information that cannot be acquired by a color camera alone [2,3]. Such information enables the detection and classification of material properties throughout its spectral fingerprint [4]. This allows hyperspectral imaging to be utilized in many applications such as medical diagnostics [1,5], food and water quality check [6,7], agriculture crop monitoring [8,9], archaeology [10,11], and astronomy [12,13]. Copyright: © 2021 by the authors. Despite the potential utilities, commercial hyperspectral cameras are expensive and are Licensee MDPI, Basel, Switzerland. relatively large. As a result, the spread of hyperspectral imagers is limited [2]. This article is an open access article distributed under the terms and Hyperspectral imaging systems are classified according to their spectral range, acquisi- conditions of the Creative Commons tion mode, type of detector, and spectral filtering technology [1]. Traditional hyperspectral Attribution (CC BY) license (https:// imagers either scan the spectral bands or the spatial dimension of the hypercube. These creativecommons.org/licenses/by/ methods are relatively slow due to the filters used and the sensitive moving parts required, 4.0/). which adds complexity to the system. The snapshot method, on the other hand, enables

Micromachines 2021, 12, 767. https://doi.org/10.3390/mi12070767 https://www.mdpi.com/journal/micromachines Micromachines 2021, 12, 767 2 of 14

the system to capture a full hypercube in one shot. However, there is a compromise in the form of a lower spatial resolution to allow for a better spectral resolution. This is because, in a snapshot hyperspectral camera, pixels consist of a number of sub-pixels, each with a spectral filter applied [2]. This, in turn, increases the pixel size; hence, there is a decrease in the spatial resolution and an increase in the spectral resolution. The key component in any hyperspectral system is the spectral filtering technique utilized [14]. Almost all specifications of the system are dependent on the selected spectral filtering technology. Hyperspectral imaging systems can employ various methods, such as filter wheels [15,16], prisms [17,18], gratings [19], and tunable optical filters [20–23]. Tunable optical filters offer an acceptable bandwidth and switching time without the compromise of the special resolution. They can be based on different principles of operation, such as acousto-optic tunable filter (AOTF) and liquid-crystal tunable filter (LCTF). Each technology has its own advantages and disadvantages. For example, AOTFs offer a rapid wavelength tunability; however, they suffer from a very low transmission percentage. LCTFs, on the other hand, offer a wide tuning range, but they have low scanning speed along with low transmission percentage [24]. Cutting-edge LCTFs currently available in the market have a maximum transmission that does not exceed 70%, with a full-width-half-maximum (FWHM) of 35 nm. Other available designs are optimized to have a narrow FWHM value of 10 nm; however, this impacts the transmission percentage value, reducing it to less than 50% at its maximum [25]. Fabry-Pérot interferometers demonstrate optical filtering performance, enabling them to be used as tunable filters. Those interferometers consist of two partially reflective mirrors facing each other, separated by a gap. The mirrors’ reflectivity, along with the gap’s thickness and material, define the filtering behavior of the structure. Highly reflective mirrors are required for narrow bandwidth filter, although they must have low attenuation so as to not reduce the filter’s transmission, which renders metallic mirrors not particularly suitable. Multilayer-dielectric mirrors are ideal for that, although they require many bilayers and, therefore many fabrication steps. Employing one thin plasmonic layer with a few dielectric layers can offer a good compromise. Several types of material have been utilized in the separating gap [26]. In order to tune the optical filter, either the gap’s thickness or refractive index (RI) is changed to control the central wavelength of the filter’s transmission band. Varying the gap’s thickness is more practical, because it simply requires an actuator, not a supply of different materials, or special materials of electrically controlled properties to change the RI. Micro-electro-mechanical systems (MEMS) actuators are devices that convert electrical signals into motion, typically within micrometer range. They offer precise and reliable movement, a compact size, and the potential for mass production which in turn lowers the overall price. Electrostatic MEMS actuators utilize the electrostatic force resulting from applying different voltage values to two electrodes placed close to each other [27]. Such actuators are perfect for the design in hand as they offer a nanometer precision which is translated into a high wavelength tunability accuracy for the tunable filter [28]. Electrostatic actuation also does not interfere with the optical functionality of the filter, because the actuator could be designed separated from the filter layers. Such actuators also do not produce heat or parasitic effects that may affect the filter’s operation. Therefore, electrostatic MEMS actuators are suitable method of actuation for such filters. In this paper, we present electrostatically actuated tunable filters for hyperspectral imaging systems. The optical filters are based on hybrid plasmonic-dielectric thin films. The filters were designed, using MATLAB from The MathWorks, Inc., a MATLAB code based on the transfer matrix method developed in-house, subsequently, the results were verified by electromagnetic wave numerical simulations using COMSOL. The actuator was designed analytically, and then miniaturized versions were simulated electromechanically on COMSOL Multiphysics for verification. Micromachines 2021, 12, x FOR PEER REVIEW 3 of 14

Micromachines 2021, 12, 767 3 of 14 2. Device Design One of the main advantages of the proposed device that it is a stand-alone chip that can2. be Device placed Design in front of an ordinary monochromatic camera to turn it into a hyperspectral imagingOne one. of the Figure main advantages 1 shows ofa schematic the proposed of device the designed that it is a stand-alonefilter. As shown chip that in the figure, thecan MEMS be placed chip in frontconsi ofsts an of ordinary two glass monochromatic wafers bonded camera together, to turn it into holding a hyperspectral the circular mirrors formingimaging a one. Fabry Figure-Pérot1 shows filter, a schematic along with of the the designed actuating filter. electrodes As shown informing the figure, an electrostatic parallelthe MEMS plate chip capacitor. consists of The two glasselectrodes wafers bondedare chosen together, to be holding from the indium circular tin mirrors oxide (ITO) [28], forming a Fabry-Pérot filter, along with the actuating electrodes forming an electrostatic aluparallelminum plate [29] capacitor. or silver The [30] electrodes due to are their chosen electric to be fromconductivity indium tin and oxide adhesion (ITO) [28], to glass substrate.aluminum A diaphragm [29] or silver is [ 30realized] due to theirby wetly electric etching conductivity a circular and adhesion trench to in glass the sub- upper wafer to reducestrate. its A diaphragmthickness ismaking realized it by easy wetly to etchingmove. aThis circular forms trench a suspension in the upper system wafer to that contains thereduce movable its thickness mirror making of the it filter, easy to and move. the This movable forms a electrode suspension of system the actuator. that contains The lower wa- the movable mirror of the filter, and the movable electrode of the actuator. The lower wafer fer contains the fixed mirror and the fixed electrode. The mirrors are deposited in the mid- contains the fixed mirror and the fixed electrode. The mirrors are deposited in the middle dlearea area of theof the two two wafers wafers on the on inner the facesinner to faces form to the form filter, the while filter, the electrodeswhile the are electrodes of are of ringring shapes shapes surrounding them. them. This This design design allows allows decoupling decoupling of the actuation-controlling of the actuation-controlling electrodeselectrodes from from thethe filter filter mirrors; mirrors; hence, hence, controls controls the tuning the tuning gap is controlledgap is controlled without without in- terferinginterfering with with the the optical optical filter filter operation. operation.

Figure 1. Schematic representation of the MEMS chip. Figure 1. Schematic representation of the MEMS chip. 2.1. Filter Design 2.1. FilterIn this Design section, the operation principle of the optical filter is discussed, along with the design criteria for hyperspectral imaging applications. As mentioned earlier, the filter is basedIn onthis a Fabry-Psection,érot the interferometer operation principle and actuated of usingthe optical an electrostatic filter is MEMS discussed, actuator. along with the designFabry-P criteriaérot resonators for hyperspectral are based on interferenceimaging applications. between the incident As mentioned light on it andearlier, the the filter is basedlight reflectedon a Fabry multiple-Pérot times interferometer inside the resonator. and actuated The distance using between an electrostatic the two reflecting MEMS actuator. Fabrymirrors-Pérot defines resonators the resonator are performance based on interference and hence the centralbetween wavelength the incident of the Fabry-light on it and the Pérot filter. The transmission profile of a typical Fabry-Pérot filter is described by the light reflected multiple times inside the resonator. The distance between the two reflecting following relation: d = λ(2mπ + φa + φb)/2πngap mirrors defines the resonator performance and hence the central wavelength of the Fabry- Pérot filter. The transmissionT = profile1 − r2 /of 1a+ typicalr2 − 2rcos Fabryδ -Pérot filter is described(1) by the following relation: 푑 = 휆(2푚휋 + 휙푎 + 휙푏)/2휋푛푔푎푝 where, r is the mirror’s reflection coefficient, and δ is the total phase. The maximum 2 2 transmission occurs when δ = φprop푇 =−((1φa−+푟φb))/=(12+mπ푟, where− 2푟푐표푠φprop훿) = 4πngapd is the (1) propagation phase shift, φa and φb are the phase shift due to reflection from the two mirrors where,respectively, 푟 is thed is themirror’s mirror’s reflection gap thickness, coefficient, and ngap is theand gap’s 훿 is material the total RI. To phase. determine The maximum transmissionthe cavity thickness occurs required when 훿 for= a 휙 certain푝푟표푝 − central(휙푎 + wavelength,휙푏) = 2푚휋 we, where apply the휙푝푟표푝 previous= 4휋푛푔푎푝푑 is the propagation phase shift, 휙푎 and 휙푏 are the phase shift due to reflection from the two mirrors respectively, 푑 is the mirror’s gap thickness, and 푛푔푎푝 is the gap’s material RI. To determine the cavity thickness required for a certain central wavelength, we apply the previous phase condition, and rearrange to find the cavity thickness; which results in the relation 푑 = 휆(2푚휋 + 휙푎 + 휙푏)/2휋푛푔푎푝 [31]. The FWHM of the Fabry-Pérot filter is an

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phase condition, and rearrange to find the cavity thickness; which results in the relation d = λ(2mπ + φa + φb)/2πngap [31]. The FWHM of the Fabry-Pérot filter is an important parameter, as it measures how narrow the spectral line of the filter is. For normal incidence, it can be determined by the following equation: √ 2 FWHM = (1 − r)λ /2π rngapd (2)

For the oblique incidence, the gap thickness is replaced by the effective gap thickness de f f = d/cos θ where θ is the angle of incidence [32]. As shown by the previous equations, the mirror’s reflectivity greatly affects the filtering performance of the interferometer; therefore, the mirrors’ design is an important factor to consider in the design process. Several designs have been presented for mirrors; such as, dielectric mirrors, metallic reflective mirrors and hybrid designs [28,33]. Dielectric materials exhibit low attenuation properties; which enables the addition of a large number of layers without dramatically affecting the transmission percentage which enables achieving narrow bandwidths. These narrow bandwidths are achieved by adding more layers, because adding more layers introduces more restrictions on which frequencies meet the conditions of constructive interference; and hence, sharp band-pass filters with high transmission filters are produced. However, dielectric mirrors require a large number of layers to achieve that narrow bandwidth, which therefore requires many fabrication steps. Beside the fabrication cost resulting from that, it also renders the process more prone to fabrication discrepancies in material properties and in layers’ thicknesses [34,35]. The large number of fabrication steps adds complexity to the filter’s implementation and sets it at a higher price point. Metallic mirrors, on the contrary, exhibit high attenuation due to the absorption nature of the metallic layer used. This results in lower transmission percentage values at the pass band of the filter. However, one metal layer is enough to form a metallic mirror, which removes the complexities involved in the fabrication of the dielectric layer and lowers the cost of the filter. The bandwidth of the metallic mirrors is determined by the nature of the metal used. The range of light the metal reflects is determined by the atomic structure of the material, as described by Drude-Lorentz model. For instance, silver bandwidth covers the entire visible range along with part of the infra-red range. Combining both metallic and dielectric layers in the mirror design allows the filter to have both advantages. Using one thin metal layer-of just few nanometers thickness to not cause high attenuation-along with just few dielectric layers, produces a mirror with high performance in terms of the narrow bandwidth, high transmission percentage and sharp line filter, without requiring many fabrication steps. The filter presented in this paper consists of two partially reflective mirrors facing each other. Each mirror is a glass substrate with hybrid dielectric-plasmonic thin films deposited on it, as shown in Figure2. Only three layers for each mirror are sufficient: two dielectric layers, and one thin metallic layer. This design is chosen to have both dielectric layers and metallic layers deposited on each other to add more degrees of freedom in the design process, and compensate for the draw backs of the metallic mirrors. All the materials chosen in this design have extremely low extinction coefficients in the visible range to prevent attenuation due to material absorption, along with good adhesion to each other and to the substrate. For the dielectric layers, two materials are chosen: one has to have a high RI, while the other has to have a low RI. For applications in the visible light range, silicon dioxide (SiO2) and titanium dioxide (TiO2) are commonly used [35]. Both materials have a nearly zero extinction coefficient in the visible range (400–700 nm), and have a sufficiently different refractive index values: TiO2 is the high-RI material that has an average value of 2.17, according to Sarkar et al. [36], and SiO2 is the low-RI material with a value of around 1.46 according to Malitson [37]. For both materials, the RI dependence on the wavelength is taken into consideration in the model. In the visible range, silver (Ag) has a low extinction coefficient; therefore, it has a low absorption in this band, which translates to a high transmission in the filter performance. In addition, silver has good adhesion to the used materials [35]. Therefore, the metallic layer in this design is chosen to Micromachines 2021, 12, 767 5 of 14

Micromachines 2021, 12, x FOR PEER REVIEW 5 of 14 be silver. The ﬁlter is symmetrical: both mirrors have the same number of layers, and each layer in each mirror has the same material and thickness.

FigureFigure 2. Schematic2. Schematic representation representation of the ﬁlter’sof the layers.filter’s layers.

TheThe thickness thickness of the of layers the layers defines defines the filter’s the performance. filter’s performance. Hyperspectral Hyperspectral imaging imaging requiresrequires the the optical optical filter filter to reach to reach the maximum the maximum transmission transmission possible in possible order to harvest in order to harvest the maximum power from the specified spectral band. Furthermore, the spectral band needsthe maximum to be as well-defined power from as possible. the specified Hence, spectral the bandwidth band. needsFurthermore, to be as narrow the spectral band asneeds possible, to be in orderas well to- enabledefined the as separation possible. between Hence, a higherthe bandwidth number of needs bands, to which be as narrow as increasespossible, the in spectral order resolution.to enable Thethe rejectionseparation band between must cover a higher the whole number operation of bandbands, which in- ofcreases the filter the and spectral the camera resolution. sensor used. The rejection The presented band structure must cover has some the whole degrees operation of band freedomof the filter in the and design; the camera therefore, sensor we will used. present The two presented designs for structure tunable hyperspectralhas some degrees of free- imaging filters: one is optimized for maximum transmission, and the other is optimized for dom in the design; therefore, we will present two designs for tunable hyperspectral imag- minimum FWHM. Optimization is performed using a MATLAB code developed in-house anding based filters: on theone transfer is optimized matrix method, for maximum then verified transmission, by electromagnetic and wavethe other numerical is optimized for simulationsminimum by FWHM. COMSOL. Optimization The resulting is valuesperformed of the using layer thicknesses a MATLAB are code summarized developed in-house inand Table based1. on the transfer matrix method, then verified by electromagnetic wave numerical simulations by COMSOL. The resulting values of the layer thicknesses are summa- Table 1. Optimized layers’ thicknesses for filters structure targeting maximum transmission and minimumrized in FWHM. Table 1.

Table 1.Layer Optimized layers’ Maximum thicknesses Transmission for filters Filter structure Minimumtargeting FWHM maximum Filter transmission and

minimumTiO2 Layer FWHM. 43 nm 63 nm SiO2 Layer 25 nm 50 nm Ag LayerLayer Maximum 20 nm Transmission Filter 40Minimum nm FWHM Filter Variable AirTiO Gap2 Layer (150 nm–320 nm)43 nm (150 nm–320 nm) 63 nm SiO2 Layer 25 nm 50 nm The depositionAg Layer of thin films initiates intrinsic20 and nmthermal stresses in the wafer40 due nm to latticeVariable mismatch Air the Gap difference in thermal(150 coefficient. nm–320 nm) Hence, such effects(150 must nm– be320 nm) considered in the design process. Deposition of thin film of TiO2 on glass substrate using The deposition of thin films initiates intrinsic and thermal stresses in the wafer due to lattice mismatch the difference in thermal coefficient. Hence, such effects must be considered in the design process. Deposition of thin film of TiO2 on glass substrate using electron beam evaporation causes tensile residual stress in the order of 170 MPa [38]. While deposition of thin film of SiO2 on a thin film of TiO2 causes a compression stress in the same order to form [39,40]. Deposition of silver on the other hand causes a tensile stress in the order of 18 Pa which gives a radius of curvature in the range of thousands of kilometers according to Stoney’s equation [38]. Therefore, carefully designing the stresses in the films during the fabrication process will result in an almost perfect plan filter.

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electron beam evaporation causes tensile residual stress in the order of 170 MPa [38]. While Fabry-Pérot filtersdeposition are known of thin to film be of dep SiO2endenton a thin on film the of angle TiO2 causes of incidence; a compression therefore, stress in the for real life imagingsame applications order to form will [39 dictate,40]. Deposition the filter of silverto be on inserted the other in hand an causesoptical a tensilesystem stress in the order of 18 Pa which gives a radius of curvature in the range of thousands of kilometers that allow rays collection, and collimate them on the filter. Such systems have been pre- according to Stoney’s equation [38]. Therefore, carefully designing the stresses in the films sented earlier in theduring literature the fabrication [40]. Some process systems will result allow in anfor almost a field perfect of view plan filter.of 30 degrees [41]. Fabry-Pérot filters are known to be dependent on the angle of incidence; therefore, for real life imaging applications will dictate the filter to be inserted in an optical system that 2.2. Actuator Design allow rays collection, and collimate them on the filter. Such systems have been presented earlier in the literature [40]. Some systems allow for a field of view of 30 degrees [41]. The tunable air gap in the filter is controlled by an electrostatic actuator. As indicated by the name, the actuator2.2. Actuator uses Design electrostatic force to bend the diaphragm and thus move the upper mirror closer Theto the tunable bottom air gap mirror. in the filter The is actuator controlled consists by an electrostatic of two parallel actuator. Asplate indicated by the name, the actuator uses electrostatic force to bend the diaphragm and thus move electrodes, which are perfect suited for Fabry-Pérot filter structures because they have the the upper mirror closer to the bottom mirror. The actuator consists of two parallel plate same simple structure.electrodes, As shown which in are Figure perfect suited3, the for actuator Fabry-Pé isrot added filter structures as a pair because of parallel they have the plates around the mirrors.same simple For structure. an electrostatic As shown parallel in Figure 3 plate, the actuator actuator, is added at displacement as a pair of parallel value 푥, the drivingplates voltage around is given the mirrors. by the For following an electrostatic relation: parallel plate actuator, at displacement value x, the driving voltage is given by the following relation: 2 푉 = √2푘푥(푔푎푐푡 −q푥) /휀퐴푎푐푡 (3) 2 V = 2kx(gact − x) /εAact (3) where 푘 is the diaphragm spring constant, 푔푎푐푡 is the initial gap of the actuator (at zero applied voltage), 휀 whereis the permittivityk is the diaphragm of the spring material constant, betweengact is the the two initial electrodes gap of the actuatorand 퐴푎푐푡 (at zero is the actuator electrodeapplied area. voltage), The actuatorε is the permittivity is controlled of the by material applying between a DC the twovoltage electrodes across and Aact is the actuator electrode area. The actuator is controlled by applying a DC voltage across the two electrodes. The actuator is allowed to move by only one-third of the initial gap. If the two electrodes. The actuator is allowed to move by only one-third of the initial gap. If the voltage is increasedthe voltage to exceed is increased this distance, to exceed the this movable distance, the plate movable may plate stick may to stickthe fixed to the fixed one and become immovable.one and become This immovable.phenomenon This is phenomenon known as ispull known-in, asand pull-in, the voltage and the voltage limit limit is called the pull-in voltageis called the[28 pull-in]. voltage [28].

Figure 3.Figure Cross 3. sectionalCross sectional view view of the of the MEMS MEMS actuated actuated ﬁlter, filter, with with the dimensionsthe dimensions indicated. indicated.

As indicated by theAs dimensions indicated by in the Figure dimensions 3, the in Figurefilter 3is, thedesigned ﬁlter is designed to be in to the be inmilli the millimeterme- scale, and it should be operated at appropriate voltages. The upper substrate has a thickness ter scale, and it shouldof 0.6 be mm operated and a diameter at appropriate of 12 mm, whilevoltages. the lower The substrateupper substrate has the same has diameter a thickness of 0.6 mmbut and a thicknessa diameter of 1 mm.of 12 Themm, mirror while diameter the lower is determined substrate to has be 3.033 the mmsame and the diameter but a thicknesselectrodes’ of 1 mm. width The and mirror the initial diameter gap between is determined them is 0.365 to mm be and 3.033 660 mm nm respectively and the electrodes’ widthfor and acceptable the initial voltage gap value between of actuation. them is The 0.365 diaphragm mm and has 660 a minimal nm respec- thickness of 30 µm, but its thickness increases due to the circular nature of the trench wetly etched in tively for acceptable voltage value of actuation. The diaphragm has a minimal thickness the wafer. The design is initially determined by the previous analytical formula, then it of 30 µm, but its thicknessis to be optimizedincreases using due COMSOLto the circular Multiphysics. nature However, of the trench simulating wetly the etched actual design in the wafer. The designby linked is initially mechanical determined and electrostatic by the modules previous in theanalytical millimeter formula, scale is notthen successful it is to be optimized using COMSOL Multiphysics. However, simulating the actual design by linked mechanical and electrostatic modules in the millimeter scale is not successful due to the computational power needed. Therefore, the design is scaled down by factors from 1/1000 to 16/1000. All the design dimensions are changed accordingly except the mirrors gap and the actuator gap to keep the filter functionality intact. Only the mechanical simulation could be done with real dimensions, which is important to get the diaphragm spring constant. As the structure is circularly symmetric, only one-quarter of it can be simulated and symmetry plans can be put to depict the complete circular shape. This helps saving the computational power and time. The cross section of the structure – depicted in Figure 3 is drawn in 2D, then revolved by 90° to realize one-quarter of the 3D

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due to the computational power needed. Therefore, the design is scaled down by factors from 1/1000 to 16/1000. All the design dimensions are changed accordingly except the mirrors gap and the actuator gap to keep the ﬁlter functionality intact. Only the mechanical simulation could be done with real dimensions, which is important to get the diaphragm spring constant. As the structure is circularly symmetric, only one-quarter of it can be simulated and symmetry plans can be put to depict the complete circular shape. This helps saving the computational power and time. The cross section of the structure –depicted in Figure3 is drawn in 2D, then revolved by 90◦ to realize one-quarter of the 3D structure. For all the simulations, normal automatic mesh is applied, and stationary study is used. The boundary condition used is applying a ﬁxed constraint on the two substrates perimeters and on the below surface of the lower substrate. For the electromagnetic simulation, the actuation voltage and ground boundary conditions are applied on the electrodes. While in the mechanical simulation done in the real dimensions to get the spring constant of the diaphragm, a force is applied to its center equivalent to the expected electrostatic force between the electrodes if they could be simulated in these large dimensions. This applied force F moves the movable structure downwards by a certain distance x, then Hooke’s law (F = −kx) is used to get the stiffness k. A graph is plotted between the applied force and displacement, then the spring constant is obtained as the negative of the slope of the obtained straight line.

3. Results and Discussion For evaluating the filter optical performance, the transmission curves are generated using the transfer matrix, method then verified using the COMSOL electromagnetic waves module. Normal incidence is assumed for all filter curves, and the transmission range of interest is the visible wavelength range. Based on the transmission curves generated, the required parameters for evaluating a filter for usability in hyperspectral imaging applications are obtained. These parameters are: the maximum transmission percentage, FWHM of the spectral pass band, the change in FWHM with the wavelength, and the linearity of the scanned wavelength with the tuned gap. For the actuator, the main design parameters obtained were the tuning range, diaphragm stiffness, and maximum and minimum required voltage for actuation. As mentioned earlier, a model that describes the actuator with scaled-down dimensions are developed, so all the previous parameters changes are studied by considering the scaling factor.

3.1. Filter Design Results As mentioned earlier, two designs are presented: one is optimized to have as maximum transmission as possible with rather acceptable FWHM values, and the other is optimized for the minimum FWHM values possible with acceptable transmission values. The acceptable range for each value is determined from the available filter specifications in the market [25]. Figure4a shows the transmission spectra of the design optimized for maximum transmission. As shown, the filter exhibits the highest transmission at the longest wavelength in the band with a value of 94.45%, and a minimum transmission at the violet color with value of 86.34%. The FWHM of this design is rather quite high for hyperspectral filters, it has an average FWHM value of 56.933 nm. Both the transmission percentage and the FWHM increase as the wavelength increases. The change of the FWHM values over the entire tunability gap is 27 nm; it starts at 38 nm at 417 nm then it gradually increases to reach its maximum at 758 nm with a value of 56 nm. Figure4b shows the change of the peak wavelength with tuning the air gap. As shown, the resonance wavelength changes linearly with the gap value. Micromachines 2021, 12, x FOR PEER REVIEW 8 of 14

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(a) (b)

Figure 4. Results generated(a )by MATLAB code for the design optimized for maximum transmission:(b) (a) Transmission spectra of the filter at different air gap values; (b) Resonance wavelength versus the tuned air gap thickness of the filter. FigureFigure 4.4. ResultsResults generatedgenerated byby MATLABMATLAB codecode forfor thethe designdesign optimizedoptimized forfor maximummaximum transmission:transmission: ((aa)) TransmissionTransmission spectraspectra ofof thethe filterfilter at at different different air airFilters gap gap values; values; based ( b( bon)) Resonance Resonance Fabry-Perot wavelength wavelength interferometers versus versus the the exhibit tuned tuned air aira secondary gap gap thickness thickness peak of of the thebehavior. filter. filter. The spectral distance between the two peaks is determined by the mirrors’ reflectivity and the gap valuesFiltersFilters. basedThebased filter onon Fabry-PerotisFabry designed-Perot to interferometersinterferometers have one peak exhibitexhibit in the spectral aa secondarysecondary range peakpeak from behavior.behavior. 400–700 Thenm.The spectralThespectral range distancedistance could be betweenbetween extended thethe totwotwo 400 peakspeaks–750 isnm;is determineddetermined however, byaby secondary thethe mirrors’mirrors’ peak reflectivityreflectivity shows up andand at the400the gapnmgap when values.values tuning. TheThe filterfilter the isfilteris designeddesigned to 750 totonm. havehave Such oneone a peakparasitic in the peak spectral has a range signal from to noise 400–700400– 700ratio nmnm. of. The5.278The rangerange for the could maximum be be extended extended transmission to to 400 400–750– design750 nm; nm; in however, Figure however, 4 a.a Ifsecondary a the secondary application peak peak shows does shows notup upallowat 400 at 400fornm such nmwhen when noise, tuning tuning a blocking the the filter filter filter to to750 must 750 nm. nm. be Such used Such a to aparasitic parasiticensure effectivepeak peak has has spectral a a signal signal filtering. to noise ratioratio ofof 5.2785.278For forfor thethe maximumdesignmaximum optimized transmissiontransmission to achieve designdesign the inin sharpest FigureFigure4 a.4 resonancea. If If the the application application peaks, the does does transmiss not not allow allowion for such noise, a blocking filter must be used to ensure effective spectral filtering. spectrafor such are noise, shown a blocking in Figure filter 5a. mustThe filter be used covers to ensure the whole effective visible spectral range filtering.from 400 nm up For the design optimized to achieve the sharpest resonance peaks, the transmission to 750For nm. the The design transmission optimized behavior to achieve of this the filter sharpest is not resonance linear. It has peaks, a minimum the transmiss valueion at spectra are shown in Figure5a. The filter covers the whole visible range from 400 nm up to thespectra 552 nmare wavelengthshown in Figure with 5transmissiona. The filter coversvalue of the 34.14%, whole andvisible a maximum range from transmission 400 nm up 750 nm. The transmission behavior of this filter is not linear. It has a minimum value at the valueto 750 at nm. the The red transmission color with transmission behavior of valuethis filter of 64.95%. is not linear. The FWHM It has a values minimum have value an av- at 552 nm wavelength with transmission value of 34.14%, and a maximum transmission value eragethe 552 of nm7.267 wavelength nm, which with is lower transmission than the narrowvalue of bandwidth 34.14%, and filters a maximum offered in transmission the market at the red color with transmission value of 64.95%. The FWHM values have an average of [25,value42 ].at Like the redthe colormaximum with transmissiontransmission valuefilter, oftuning 64.95%. the The air FWHMgap thickness values changeshave an theav- 7.267 nm, which is lower than the narrow bandwidth filters offered in the market [25,42]. resonanceerage of 7.267 wavelength nm, which linearly is lower as shownthan the in narrow Figure bandwidth5b. filters offered in the market Like[25,42 the]. Like maximum the maximum transmission transmission filter, tuning filter, the tuning air gap the thickness air gap changesthickness the changes resonance the wavelengthresonance wavelength linearly as shownlinearly in as Figure shown5b. in Figure 5b.

(a) (b)

Figure 5. Results generated( bya) MATLAB code for the design optimized for minimum FWHM:(b) (a) Transmission spectra of the ﬁlter at different air gap values; (b) Resonance wavelength versus the tuned air gap thickness of the ﬁlter.

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Figure 5. Results generated by MATLAB code for the design optimized for minimum FWHM: (a) Transmission spectra of the filter at different air gap values; (b) Resonance wavelength versus the tuned air gap thickness of the filter.

3.2. Filter Results Verification To verify the results generated in the design process by the MATLAB code, the filter structure is studied by COMSOL numerical simulations under the same illumination and incidence conditions. The Electromagnetic Waves, Frequency Domain interface, found Micromachines 2021, 12, 767 9 of 14 under the Wave Optics module, is used in this study. This interface uses Helmholtz equations to solve for the time-harmonic electromagnetic field distributions [43]. Two-dimen- sional3.2. Filter model Results Verificationis used, which solves in the modeled two-dimensional structure and as- sumesTo verifythat the results third generated dimension in the is design infinite. process To by save the MATLABcomputational code, the filtertime and power, the widthstructure of is the studied device by COMSOL is chosen numerical to be simulations 10 µm, which under the is same large illumination enough andto not function as a waveguideincidence conditions. and small The Electromagneticenough to avoid Waves, meshing Frequency problems. Domain interface, The thicknesses found of the filter under the Wave Optics module, is used in this study. This interface uses Helmholtz layersequations are to as solve in Table for the 1. time-harmonic However, substrates electromagnetic thicknesses field distributions are set [43to]. be Two- large enough not to functiondimensional as model layers isused, and which small solves enough in the modelednot to cause two-dimensional meshing structure and computation and al issues, whichassumes is that 300 the nm. third Materials dimension isare infinite. set to To be save matching computational the one time used and power, in MATLAB the code in the designwidth of process. the device This is chosen simulation to be 10 couldµm, which be enhanced is large enough to match to not the function actual as adevice by increas- waveguide and small enough to avoid meshing problems. The thicknesses of the filter inglayers the are substrate as in Table 1thicknesses. However, substrates and the thicknesses width value, are set toand be large extend enough it into not to three-dimensional model;function ashowever, layers and the small simulation enough not toperformed cause meshing and and parameters computational chosen issues, matched which the analytical andis 300 transfer nm. Materials matrix are calculated set to be matching results, the onewhich used indicated in MATLAB that code they in the are design still sufficient to de- scribeprocess. the This real simulation device could behavior. be enhanced to match the actual device by increasing the substrate thicknesses and the width value, and extend it into three-dimensional model; however,Figure the simulation6 shows performedthe results and ob parameterstained from chosen the matched two-dimensional the analytical and model in COMSOL comparedtransfer matrix to calculatedthe results results, generated which indicated by the that MATLAB they are still code sufficient used toin describe the design process. All thethe realspectrum device behavior. has been simulated and compared; however, five curves only was chosen to Figure6 shows the results obtained from the two-dimensional model in COMSOL display.compared Results to the results are generatedmatching by each the MATLAB other, with code useda maximum in the design error process. of 2.32% All at gap value of 308the spectrumnm, and has an been average simulated error and of compared; 0.7302% however, from all five the curves spectra only was of chosenthe different to gap values; whichdisplay. proves Results are the matching reliability each of other, the with results a maximum achieved error by of 2.32%the MATLAB at gap value code. of As illustrated in308 Figure nm, and 7 an, at average the resonan error of 0.7302%ce wavelength, from all the the spectra electric of the field different resonates gap values; inside the cavity of which proves the reliability of the results achieved by the MATLAB code. As illustrated in theFigure filter7, at and the resonance builds up wavelength, to have themaximum electric field value. resonates inside the cavity of the filter and builds up to have maximum value.

FigureFigure 6. 6.Comparing Comparing the transmission the transmission spectra of spectra the ﬁlter of optimized the filter for optimized maximum transmission for maximum at transmission at different gap values obtained from COMSOL and MATLAB. different gap values obtained from COMSOL and MATLAB.

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Figure 7. Electric field distribution in the filter with gap value of 260 nm at resonance wavelength of 625 nm.

The filter is also simulated with the introduction of lateral inhomogeneity in the thicknesses of the deposited films. Assuming a change of 10% in each layer, the worst

cases is where the change of 10% of all the layer’s thickness occur [35]. This case is simu- FigureFigure 7. Electric7. Electric field field distribution distribution in the in filter the filter with gapwith value gap ofvalue 260 nmof 260 at resonancenm at resonance wavelength wavelength of 625 nm. latedof 625and nm compared. to the homogeneous design results. The inhomogeneity is assumed to be a liner change acrossThe filter the is width also simulated of the withfilter the to introductionbe at its minimum of lateral inhomogeneityat the middle in and the its maximumThe filter at isthethicknesses also edges. simulated of As the shown deposited with the in films. introduction Figure Assuming 8, a of few a lateral change spikes inhomogeneity of 10% that in eachdoes layer, innot the the disturb worst cases the thicknesses of theis wheredeposited the change films. ofAssuming 10% of all thea change layer’s of thickness 10% in occur each [35layer,]. This the case worst is simulated and general peak shape are found as an effect of the layer’s inhomogeneity, and the central cases is where thecompared change toof the10% homogeneous of all the layer’s design thickness results. Theoccur inhomogeneity [35]. This case is is assumed simu- to be a liner wavelengthlated and comparedis shiftedchange to to acrossthe a smallerhomogeneous the width wavelengths’ of thedesign filter results. to values. be at The its minimum Forinhomogeneity the simulated at the middle is assumed values and its maximumthe max- imumto be error a liner is changearoundat the across edges.1.9%. the AsThis width shown shift of inthe could Figure filter 8 beto, a be fewtreated at spikes its minimum by that proper does at not thecalibration disturbmiddle the and of general the fabri- peak catedits filter.maximum at shapethe edges. are found As shown as an effectin Figure of the 8, layer’s a few inhomogeneity,spikes that does and not the disturb central the wavelength is shifted to a smaller wavelengths’ values. For the simulated values the maximum error is general peak shape are found as an effect of the layer’s inhomogeneity, and the central around 1.9%. This shift could be treated by proper calibration of the fabricated filter. wavelength is shifted to a smaller wavelengths’ values. For the simulated values the maximum error is around 1.9%. This shift could be treated by proper calibration of the fabricated filter.

Figure 8.FigureComparing 8. Comparing the transmission the transmission spectra of the spectra ﬁlter optimizedof the filter for optimized maximum for transmission maximum with transmission and without lateral in homogeneityFigurewith 8. inand Comparing the without layers’ thicknesses.lateral the intransmission homogeneity inspectra the layers’ of the thicknesses. filter optimized for maximum transmission with and without lateral in homogeneity in the layers’ thicknesses.

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3.3. Actuator Design Results 3.3. Actuator Design Results As seen in the optical design, the actuator should move the mirror from a gap of 150 nmAs to aseen gap in of the 320 optical nm. This design, is could the actuator be achieved should by move applying the certainmirror from minimum a gap andof 150 maximumnm to a gap voltages of 320 on nm. the This actuator is could plate. be These achieved values by areapplying needed certain to be determined,minimum and along max- withimum diaphragm voltages stiffness. on the actuator The structure plate. isThese designed values to haveare needed dimensions to be atdetermined, the millimeter along scalewith as diaphragm described in stiffness. Section 2.2 The. Therefore, structure simulatingis designed the to wholehave dimensions structure at at the the millimeter millimeter scalescale is notas described possible duein Section to the computational2.2. Therefore, powersimulating required. the whole To overcome structure this at the issue, millime- the designter scale is scaled is not downpossible to due the micrometerto the computational scale, as mentionedpower required. earlier, To with overcome down-scaling this issue, factors.the design Then is results scaled are down extrapolated to the micrometer to the original scale, as design mentioned scale. earlier, Only the with mechanical down-scal- performanceing factors. could Then beresults verified are extrapolated by COMSOL to at the the original millimeter design scale scale. to determine Only the the mechanical actual valueperformance of the diaphragm could be stiffness verifiedk by. The COMSOL voltage at required the millimeter for actuation, scale to on determine the other hand,the actual is notvalue possible of the to diaphragm be calculated stiffness using 푘 COMSOL. The voltage at this required scale, soforit actuation, is calculated on the analytically other hand, andis comparednot possible to to the be extrapolated calculated using model. COMSOL at this scale, so it is calculated analytically andUsing compared this approach, to the extrapolated the relation model. between the scaling factor X and the diaphragm stiffnessUsink isg found this approach, to be linear, the as relation shown inbetween Figure9 thea, so scaling it is safe factor to fit 푋 it withand the a first diaphragm order polynomialstiffness 푘 equation, is found which to be islinear, found as to shown be: in Figure 9a, so it is safe to fit it with a first order polynomial equation, which is found to be: Diaphragm Stiffness = 88 X − 0.00832 (4) Diaphragm Stiffness = 88 푋 − 0.00832 (4) X where,where, is푋 theis the scaling scaling down down factor. factor. The The minimum minimum and and maximum maximum voltages voltages required required for for actuation verses the scaling down factor are as shown in Figure9b. As illustrated, the actuation verses the scaling down factor are as shown in Figure 9b. As illustrated, the relation is not quite linear, therefore they are fitted with the following formulas relation is not quite linear, therefore they are fitted with the following formulas −0.48 Minimum푀푖푛푖푚푢푚 Actuation 퐴푐푡푢푎푡푖표푛 Voltage 푉표푙푡푎푔푒= 7.6=( 7007.6 X(700) 푋)−0.48 (5)(5)

− −0.527 Maximum푀푎푥푖푚푢푚 Actuation 퐴푐푡푢푎푡푖표푛 Voltage 푉표푙푡푎푔푒= 15.7= 15(700.7 X(700) 0.527푋) (6)(6)

(a) (b)

FigureFigure 9. Actuator9. Actuator performance performance at at different different scaling scaling factors factors obtained obtained by by COMSOL: COMSOL: (a) ( Diaphragma) Diaphragm stiffness stiffness at differentat different scalingscaling factors.; factors.; (b) ( Minimumb) Minimum and and maximum maximum required required actuation actuation voltage voltage at differentat different scaling scaling ratios. ratios.

ToTo validate validate the the model, model, the the diaphragm diaphragm stiffness stiffness is is calculated calculated atat thethe millimeter scale (X (Xvalue value of 1) usingusing COMSOLCOMSOL mechanicalmechanical model,model, and and compared compared with with the the predicted predicted value value fromfrom the the extrapolated extrapolated formulas. formulas. The The predicted predicted value value from from the the extrapolated extrapolated data data is 88 is N/m88 N/m andand the the calculated calculated value value using using COMSOL COMSO isL 87.48is 87.48 N/m, N/m, Figure Figure 10 10shows shows the the mechanical mechanical simulationsimulation results results from from COMSOL COMSOL mechanicalmechanical module. The The minimum minimum and and maximum maximum volt- voltagesages for for actuation actuation are are calculated calculated analytically usingusing equationequation 3 3 and and from from the the extrapolated extrapolated formulas.formulas. The The analytically analytically calculated calculated results results are are 0.308 0.308 V andV and 0.466 0.466 V forV for the the minimum minimum and and maximummaximum voltages voltages respectively; respectively; while while the extrapolatedthe extrapolated results results are 0.327 are V0.327 as the V minimumas the mini-

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voltage and 0.497 V as the maximum voltage. Indeed, these values are a little different mum voltage and 0.497 V as the maximum voltage. Indeed, these values are a little differ- from those obtained analytically, but this is expected due to the fringes capacitance that is ent from those obtained analytically, but this is expected due to the fringes capacitance not accounted in the analytical model. The stated empirical formulas might also be useful that is not accounted in the analytical model. The stated empirical formulas might also be for the predication of an intermediate design values if needed. useful for the predication of an intermediate design values if needed.

Figure 10. Upper substrate displacement at the original design scale (scaling factor 1) in the me- Figure 10. Upper substrate displacement at the original design scale (scaling factor 1) in the mechani- chanical model. cal model.

4.4. Conclusions Conclusions AA tunabletunable opticaloptical filterfilter has been designed designed and and optimized optimized for for hyperspectral hyperspectral imaging imag- ingapplications. applications. The Thepresented presented filter filter is based is based on Fabry on Fabry-P-Pérot interferometer,érot interferometer, utilizing utilizing hybrid hybridplasmonic plasmonic-dielectric-dielectric thin film thin mirrors, film mirrors, and actuated and actuated using an using electrostatic an electrostatic MEMS actuator. MEMS actuator.Two optical Two filter optical designs filter have designs been have illustrated: been illustrated: one was optimized one was optimized to have maximum to have maximumtransmission, transmission, and the other and was the otheroptimized was optimized to have a tominimum have a minimum FWHM valu FWHMe. The value. filter Theoptimized filter optimized for maximum for maximum transmission, transmission, presented presented transmission transmission rates up rates to up 94.45% to 94.45% with withand and average average FWHM FWHM value value of 56.933 of 56.933 nm; nm;whereas, whereas, the filter the filter optimized optimized for a for minimum a mini- mumFWHM FWHM value value offers offers a transmission a transmission up to up 64.95% to 64.95% with withan average an average FWHM FWHM value value of 7.267 of 7.267nm. These nm. These vales, vales, to the tobest the of best our ofknowledge, our knowledge, exceeds exceeds the designs the designs available available in the market. in the market.The designs The designswere attained were attained by modeling by modeling the multilayers the multilayers by the transfer by the transfermatrix method matrix , method,and verified and verifiedby numerical by numerical modeling. modeling. Both methods Both methods demonstrated demonstrated similar similar performance, performance,with error with less error than less 2.32%. than The 2.32%. actuator The actuator was designed was designed and verified and by verified analytical by analytical modeling modelingand by extrapolating and by extrapolating the values the from values scaled from-down scaled-down COMSOL COMSOL models. It models. offered It an offered actua- antion actuation range of range 170 nm, of 170 which nm, enabled which enabled tuning tuningof the filter’s of the filter’sgap to gapscan to the scan entire the entirevisible visiblerange (400 range–700 (400–700 nm) by nm)varying by varyingthe applied the voltage applied between voltage 0.327 between and 0.497 0.327 V. and The 0.497 design V. Thecould design be scaled could up be or scaled down up based or down on the based desired on the application. desired application. The fabrication The fabricationprocess has processbeen started has been by the started thin films’ by the deposition; thin films’ then, deposition; it will be then, followed it will by be the followed complete by struc- the completeture fabrication structure and fabrication characterization. and characterization.

AuthorAuthor Contributions: Contributions: Conceptualization, A.A., A.A., N.A. N.A. and and N.G.; N.G.; methodology, methodology, A.A., A.A., N.A. N.A. and N.G.; and N.G.;COMSOL COMSOL actuator actuator simulations, simulations, M.A.M. M.A.M. and B.M.F.; and B.M.F.; Matlab Matlab analysis, analysis, A.A.; A.A.;COMSOL COMSOL optical optical simu- simulationslations and andcomparison comparison with withMatlab, Matlab, A.H.S.; A.H.S.; literature literature and market and market survey, survey, A.A.; writing A.A.; writing——original originaldraft preparation, draft preparation, A.A.; writing A.A.;— writing—reviewreview and editing, and N.G. editing, and N.G.N.A.; and supervision, N.A.; supervision, N.G.; project N.G.; ad- projectministration, administration, N.G.; funding N.G.; acquisition, funding acquisition, N.G. All authors N.G. All hav authorse read have and readagreed and to agreedthe published to the publishedversion of version the manuscript. of the manuscript. Funding:Funding:This This work work has has been been funded funded by by The The Science Science and and Technology Technology Development Development Fund Fund (STDF), (STDF), Egypt,Egypt, grant grant number number 33356. 33356. InstitutionalInstitutional Review Review Board Board Statement: Statement:Not Not applicable. applicable. InformedInformed Consent Consent Statement: Statement:Not Not applicable. applicable.

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Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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