All-Dielectric Color Filter with Ultra-Narrowed Linewidth

micromachines

Article All-Dielectric Color Filter with Ultra-Narrowed Linewidth

Kai Xu 1, Yanlong Meng 1,2,* , Shufen Chen 2, Yi Li 1, Zhijun Wu 3 and Shangzhong Jin 1

1 College of Optical and Electronic Technology, China Jiliang University, Hangzhou 310018, China; [email protected] (K.X.); [email protected] (Y.L.); [email protected] (S.J.) 2 Key Laboratory for Organic Electronics and Information Displays and Jiangsu Key Laboratory for Biosensors, Institute of Advanced Materials (IAM), Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), Nanjing University of Posts and Telecommunications (NUPT), 9 Wenyuan Road, Nanjing 210023, China; [email protected] 3 Fujian Key Laboratory of Light Propagation and Transformation, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; [email protected] * Correspondence: [email protected]; Tel.: +86-571-87676264

Abstract: In this paper, a transmissive color filter with an ultra-narrow full width at half of the maximum is proposed. Exploiting a material with a high index of refraction and an extremely low extinction coefficient in the visible range allows the quality factor of the filter to be improved. Three

groups of GaP/SiO2 pairs are used to form a Distributed Brag reﬂector in a symmetrical Fabry-Pérot cavity. A band-pass ﬁlter which is composed of ZnS/SiO2 pairs is also introduced to further promote the purity of the transmissive spectrum. The investigation manifests that a series of tuned spectrum with an ultra-narrow full width at half of the maximum in the full visible range can be obtained

by adjusting the thickness of the SiO2 interlayer. The full width at half of the maximum of the transmissive spectrum can reach 2.35 nm. Simultaneously, the transmissive efﬁciency in the full

visible range can keep as high as 0.75. Our research provides a feasible and cost-effective way for realizing ﬁlters with ultra-narrowed linewidth.

Citation: Xu, K.; Meng, Y.; Chen, S.; Li, Y.; Wu, Z.; Jin, S. All-Dielectric Keywords: color filter; ultra-narrow linewidth; distributed Bragg reflection (DBR) Color Filter with Ultra-Narrowed Linewidth. Micromachines 2021, 12, 241. https://doi.org/10.3390/ mi12030241 1. Introduction Color filter is a kind of optical device which plays a significant role in many industrial Academic Editor: Patrice Salzenstein fields, such as spectroscopy instruments, imaging sensors, and displays [1–4]. The precision and sensibility of many optical systems used in those fields are mainly decided by such Received: 17 January 2021 an optical device. Generally, there are two types of optical filters: reflective filter and Accepted: 24 February 2021 transmissive filter [5]. Usually, the reflective filter is realized by a perfect absorber, of which Published: 27 February 2021 the filtered wavelengths are fully absorbed. As a result, its function is embodied in the reflective characteristic. On the contrary, the filtering function of a transmissive filter is Publisher’s Note: MDPI stays neutral obtained by permitting the required wavelengths to pass through. In comparison with with regard to jurisdictional claims in the reflective filter, the transmissive filter is proper to be used in displays, charge-coupled published maps and institutional affil- devices, and hyperspectral imaging. With respect to the transmissive filter, the quality iations. factor or the full width at half of the maximum (FWHM) of the transmissive spectrum is a principal characteristic if we want a filter with high accuracy and resolution [3]. In addition, the efficiency of the filter is also an important characteristic that should be considered. That is because a higher transmittance means a better energy use of incident light, which will be Copyright: © 2021 by the authors. beneficial to reduce the dissipation of power and obtain a high intensity of the signal in Licensee MDPI, Basel, Switzerland. optical systems using these filters. This article is an open access article Up to now, there have been many reports on filters realized by surface plasmons [6–11], distributed under the terms and Fabry–Pérot (FP) microcavities [12–21], grating guided-mode resonance [22–28], and Mie conditions of the Creative Commons scattering [29–35]. However, high quality-factor filters realized by surface plasmons or Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ Mie scattering always involve in many sophisticated nanostructures, such as nanohole 4.0/). array metal films [10,36], metal grating [23,37], and nanoparticle arrays. In comparison,

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array metal films [10,36], metal grating [23,37], and nanoparticle arrays. In comparison, the FP cavity based on multilayered thin films presents many advantages, such as easy to the FP cavity based on multilayered thin films presents many advantages, such as easy to bebe fabricated, fabricated, facilitating facilitating large-scale large-scale producti production.on. In In recent recent years, years, there there have have been been a a large numbernumber of of reports reports on on the the design design of of filters filters base basedd on on the the FP FP cavity cavity [16,20,21,38–41]. [16,20,21,38–41 ].Using Using a dielectrica dielectric layer layer sandwiched sandwiched by by two two metallic metallic layers layers to to form form an an FP FP cavity cavity is is a a convenient way,way, which is also also named named as as metal-dielectric-metal metal-dielectric-metal (MDM) (MDM) structure. structure. However, However, the the strong strong absorptionabsorption of of metallic metallic layers layers limits limits the the quality quality factor factor [39]. [39]. To To further further improve improve the the quality quality factorfactor of of such such structure, structure, a a distributed distributed Bragg Bragg reflection reflection (DBR) (DBR) is is a a preferable candidate to to substitutesubstitute the the metallic metallic reflective reflective mirror. mirror. Sinc Sincee the the DBR DBR structure structure is fabricated by various dielectricdielectric layers, layers, the the absorption absorption in in metallic metallic layers layers can can be beavoided. avoided. So far, So there far, there are still are few still reportsfew reports on filters on filters with withextremely extremely narrow narrow FWHM FWHM (<10 nm) (<10 in nm) the in visible the visible range range with a with rela- a tivelyrelatively simple simple DBR DBR structure. structure. InIn this this paper, paper, we we propose propose a a transmission filter filter structure structure based based on on an an FP FP cavity. cavity. The The reflectivereflective mirror mirror is is composed composed of of GaP/SiO GaP/SiO2 etalon.2 etalon. As a As direct a direct bandgap bandgap semiconductor semiconductor ma- terialmaterial with with a bandgap a bandgap of 2.26 of 2.26eV, GaP eV, GaP has hasa high a high refractive refractive index index in the in visible the visible range range and canand also can be also prepared be prepared by low-temperature by low-temperature atomic layer atomic deposition layer deposition technology technology or chemical or vaporchemical deposition vapor deposition technology, technology, which is which compatible is compatible with other with thin-film other thin-film deposition deposition pro- cessingprocessing [42]. [42 In]. addition, In addition, the the absorption absorption coefficient coefficient is isclose close to to zero zero when when the the wavelength wavelength isis longer longer than than 470 nm. A multilayer composed ofof ZnS/SiOZnS/SiO22 pairspairs is is used used as as a band-pass filterfilter to to improve improve the the quality quality of of the the spectrum. spectrum. Since Since the the materials materials used used have have relatively relatively small small absorptionabsorption in in the the visible visible range, range, it it is is expect expecteded to to obtain obtain a a smaller smaller FWHM FWHM through through structural structural design.design. This This research research not not only only contributes contributes to to the the preparation preparation of of large-area, large-area, high-resolution high-resolution transmissivetransmissive filters filters but but also also helps helps expand expand the the application range of high-refractive-index semiconductorsemiconductor materials materials in in the the optical optical field. field.

2.2. Simulation Simulation Models Models TheThe simulated simulated structure structure in in this this paper paper is is shown shown in Figure 11.. TheThe lightlight incidentsincidents fromfrom thethe top top of of the the device device and and outputs outputs from from a a glass glass su substrate.bstrate. As As shown shown in in Figure Figure 11,, the device’s structurestructure can can be be divided divided into into two two components components—a—a symmetrical symmetrical FP FP cavity cavity and and a a band-pass band-pass filter. The FP cavity is realized by two DBRs and a SiO interlayer. The DBR consists of filter. The FP cavity is realized by two DBRs and a SiO2 interlayer. The DBR consists of several groups of GaP/SiO pairs. The thicknesses of GaP and SiO in each group and several groups of GaP/SiO2 pairs.2 The thicknesses of GaP and SiO2 in2 each group and the numberthe number of groups of groups have have been been optimized optimized for obtaining for obtaining a transmissive a transmissive spectrum spectrum with with an an ultra-narrow FWHM and high intensity. The ZnS/SiO2 multilayer is set on top of the ultra-narrow FWHM and high intensity. The ZnS/SiO2 multilayer is set on top of the cavity cavity as a band-pass filter for the purpose of improving the purity of the transmissive as a band-pass filter for the purpose of improving the purity of the transmissive spectrum. spectrum. The refractive indices and extinction coefficients of various materials used in the The refractive indices and extinction coefficients of various materials used in the simula- simulation are shown in Figure2. All the data are quoted from other reports [43–45]. tion are shown in Figure 2. All the data are quoted from other reports [43–45].

FigureFigure 1. 1. StructuralStructural diagram diagram of of the the device device used used in in simulation. simulation.

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FigureFigure 2.2. RefractiveRefractive indicesindices andand extinctionextinction coefﬁcientscoefficients ofof materialsmaterials usedused inin simulation.simulation.

AA finite-differencefinite-difference time-domaintime-domain (FDTD)(FDTD) simulationsimulation was performedperformed by usingusing com-com- mercialmercial software (Version (Version 8.24, 8.24, Ansys Ansys Lumerica Lumerical,l, Inc, Inc, Vancouver, Vancouver, BC, BC, Canada). Canada). In the In sim- the simulation,ulation, a plane a plane electromagnetic electromagnetic (EM) (EM) wave wave was used was usedas an asexcitation an excitation source. source. The intensity The in- tensityof the electric of the electricfield was field set was to 1, set and to the 1, andincident the incident direction direction was the was z backward. the z backward. The bound- The boundaryary condition condition in the inz-direction the z-direction and other and otherdirections directions were wereperfect perfect match match layer layer (PML) (PML) and and periodic boundary conditions, respectively. In order to simulate the performance of periodic boundary conditions, respectively. In order to simulate the performance of the the device in different polarization states, two polarization, i.e., transverse magnetic (TM), device in different polarization states, two polarization, i.e., transverse magnetic (TM), transverse electric (TE) modes, were used. In TM and TE modes, the polarization directions transverse electric (TE) modes, were used. In TM and TE modes, the polarization direc- of the electric field were set to parallel to and perpendicular to the plane of incidence. A tions of the electric field were set to parallel to and perpendicular to the plane of incidence. Broadband Fixed Angle Source Technique (BFAST) was used to simulate the transmissive A Broadband Fixed Angle Source Technique (BFAST) was used to simulate the transmis- spectra of the device as the incidence of the wide-band EM wave is oblique. A monitor of sive spectra of the device as the incidence of the wide-band EM wave is oblique. A monitor electric field power was located on the opposite side of the device to test the transmittance. of electric field power was located on the opposite side of the device to test the transmit- In addition, a 2D electric field monitor was placed parallel to the incident plane to test the tance. In addition, a 2D electric field monitor was placed parallel to the incident plane to distribution of the electric field in each layer. test the distribution of the electric field in each layer. 3. Results and Discussion 3.1.3. Results Optimization and Discussion of the FP Cavity 3.1. OptimizationAs a principal of componentthe FP Cavity of the device, the FP cavity without a band-pass filter was optimizedAs a principal firstly. The component main purpose of the of thedevice, optimization the FP cavity is to generatewithout a kindband-pass of transmissive filter was spectrum,optimized which firstly. possesses The main an purp ultra-narrowose of the FWHMoptimization and high is to transmittance generate a kind simultaneously. of transmis- Itsive is wellspectrum, known which that the possesses spectral an FWHM ultra-narrow is determined FWHM by and the high reflectivity transmittance of the reflective simulta- ends,neously. the It refractive is well known index, that and the thicknessspectral FWHM of the interlayeris determined [46]. by Its the expression reflectivity is shown of the asreflective follows: ends, the refractive index, and the thickness of the interlayer [46]. Its expression −c ln(R R ) is shown as follows: FWHM = 1 2 (1) 4πnd −cRRln( ) where R1 and R2 are the reflectivitiesFWHM of the= reflective12 ends, c is the velocity of electro-(1) magnetic waves in vacuum, n is the refractive index4πnd of the interlay, and d is the physical thickness of the SiO2 interlayer. According to the equation, it is clear that the FWHM can where R1 and R2 are the reflectivities of the reflective ends, c is the velocity of electromag- be narrowed by increasing the reflectivities of the two DBRs in the proposed structure, netic waves in vacuum, n is the refractive index of the interlay, and d is the physical thick- the refractive index, and the thickness of the intermediate dielectric layer. Accordingly, ness of the SiO2 interlayer. According to the equation, it is clear that the FWHM can be the thicknesses of each layer and the number of GaP/SiO groups in the DBR will be the narrowed by increasing the reflectivities of the two DBRs2 in the proposed structure, the critical parameters, which should be optimized firstly. refractive index, and the thickness of the intermediate dielectric layer. Accordingly, the In the beginning, the number of GaP/SiO2 groups is set to three. The thickness of thicknesses of each layer and the number of GaP/SiO2 groups in the DBR will be the critical each layer in the DBR is optimized by the Particle Swarm optimization method [47,48], parameters, which should be optimized firstly. which has been a mature module of the software. The aim of optimization is that the In the beginning, the number of GaP/SiO2 groups is set to three. The thickness of each mean reflectance at the interface between the SiO interlayer and the DBR reaches the layer in the DBR is optimized by the Particle Swarm2 optimization method [47,48], which highest value. According to the result of optimization, the thicknesses of GaP and SiO2

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Micromachines 2021, 12has, 241 been a mature module of the software. The aim of optimization is that the mean re- 4 of 12 flectance at the interface between the SiO2 interlayer and the DBR reaches the highest value. According to the result of optimization, the thicknesses of GaP and SiO2 in a single etalon are fixedin a to single 38 nm etalon and 100 are nm, fixed respective to 38 nmly. and In order 100 nm, to illustrate respectively. the result In order of opti- to illustrate the mization clearly,result the of reflective optimization spectra clearly, of th thee DBRs reflective with spectra different of thicknesses the DBRs with of GaP different and thicknesses SiO2 are plotted in Figure 3. It can be seen from Figure 3a that the DBR with 38 nm-thick of GaP and SiO2 are plotted in Figure3. It can be seen from Figure3a that the DBR with GaP and 100 nm-thick SiO2 shows a better reflection in the range from 450 nm to 750 nm, 38 nm-thick GaP and 100 nm-thick SiO2 shows a better reflection in the range from 450 nm which coversto the 750 visible nm, which range coversexactly, the than visible other range DBRs. exactly, The reflectance than other of DBRs. the optimized The reflectance of the DBR reflectoroptimized is higher DBRthan reflector0.8 in the is full higher range. than Especially 0.8 in the in full the range. range Especiallyfrom 460 nm in theto range from 680 nm, the mean460 nm reflectance to 680 nm, surpasses the mean 0.9. reflectance Once the thicknesses surpasses 0.9.of GaP Once and the SiO thicknesses2 are fixed, of GaP and the number of GaP/SiO2 pairs can be determined facilely. It is obvious in Figure 3a that SiO2 are fixed, the number of GaP/SiO2 pairs can be determined facilely. It is obvious in the reflectanceFigure of the3a thatDBR the reflector reflectance becomes of the hi DBRgher reflectorand higher, becomes even close higher to and 1.0 higher,in the even close 2 range from 450to 1.0 nm in to the 750 range nm, as from the 450 number nm to of 750 Gap/SiO nm, as pairs the number increases. of Gap/SiOAccording2 pairs to increases. such a result,According it seems that to such the more a result, numbers it seems of thatGap/SiO the more2 pairs numbers the DBR of has, Gap/SiO the better2 pairs the DBR performancehas, the FP the cavity better possesses. performance However, the FP the cavity mean possesses. reflectance However, of the DBR the ismean not the reflectance of only factor thatthe should DBR is be not considered. the only factor Subseq thatuently, should the be transmissive considered. spectrum Subsequently, of the the FP transmissive cavity with spectrum170 nm-thick of the SiO FP2 cavityinterlayer with is 170 simulated nm-thick and SiO 2plottedinterlayer in Figure is simulated 3b. It andis plotted in straightforwardFigure that3b. the It isintensity straightforward of the tran thatsmissive the intensity spectrum of the at transmissivethe center wavelength, spectrum at the center i.e., the resonantwavelength, wavelength i.e., theof the resonant FP cavi wavelengthty, decreases of thedramatically FP cavity, as decreases the number dramatically of as the groups increases.number As ofshown groups in increases. the inset Asin Fi showngure 3b, in thethe inset transmission in Figure 3atb, 520 the transmissionnm almost at 520 nm vanishes whenalmost the vanishesnumber of when GaP/SiO the number2 pairs reaches of GaP/SiO five.2 Inpairs another reaches aspect, five. Inthe another more aspect, the GaP/SiO2 pairsmore will GaP/SiO lead to a2 morepairs complicated will lead to afabrication more complicated processing fabrication and higher processing cost un- and higher doubtedly. Accordingly,cost undoubtedly. three groups Accordingly, of GaP/SiO three2 groups in the DBR of GaP/SiO are the2 bestin the choice DBR for are the the best choice device. for the device.

Figure 3. ReflectiveFigure spectra 3. Reflective (a) of thespectra distributed (a) of the Bragg distributed reflection Bragg (DBR) reflecti reflectorson (DBR) with reflectors various structuralwith various parameters and structural parameters and transmissive spectra (b) of the Fabry–Pérot (FP) cavity with different transmissive spectra (b) of the Fabry–Pérot (FP) cavity with different numbers of GaP/SiO2 pairs. The inset of the left chart is an enlargementnumbers of the of transmissive GaP/SiO2 pairs. spectra The at inset the centerof the left wavelengths. chart is an enlargement of the transmissive spectra at the center wavelengths. Once the structural parameters of the DBR are fixed, the resonant wavelength of the Once the structural parameters of the DBR are fixed, the resonant wavelength of the FP cavity is determined only by the physical thickness of the SiO2 interlayer. The resonant FP cavity is determinedwavelength only of the by FP the cavity physical can thickness be expressed of the as SiO follows2 interlayer. [46]: The resonant wavelength of the FP cavity can be expressed as follows [46]: λλ= mλm = 2dn(λ) (2) mdn()m 2 (2)

where d is the thickness of SiO2, n(λ) is the refractive index of SiO2, m is the eigenmode where d is the thickness of SiO2, n(λ ) is the refractive index of SiO2, m is the order, and λ stands for the resonant wavelength of mth eigenmode. Figure4 shows λ m eigenmode order,the evolution and m of stands the transmissive for the resonant spectrum wavelength as thethickness of mth eigenmode. of the intermediate Figure dielectric 4 shows the layerevolution SiO2 ofchanges. the transmissive It is obvious spec thattrum three as ultra-narrowthe thickness bright of the bands intermediate appear in sequence, dielectric layerwhich SiO represent2 changes. three It is obvious different that orders three of resonanceultra-narrow mode, bright as the bands thickness appear of in SiO 2 increases sequence, whichfrom represent 50 nm to 300three nm. different The peak orders of the of resonance spectrum atmode, the resonant as the thickness wavelength of presents a SiO2 increasesredshift from 50 ranging nm to 300 from nm. 420 The nm peak to 700of the nm spectrum as the thickness at the resonant of SiO 2wavelengthincreases. That means three primary colors for displays can be obtained easily via such a structure.

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presents a redshift ranging from 420 nm to 700 nm as the thickness of SiO2 increases. That means three primary colors for displays can be obtained easily via such a structure. According to Equation (1), it can be known that the resonant wavelength of the eigenmode in a high order will present a narrower FWHM than that in low order when the interlayer of the FP cavity is fixed to a certain thickness. However, the high order in- Micromachines 2021, 12, x FOR PEER REVIEW 5 of 12 dicates that the photons will travel in multiple rounds in the cavity before exiting from the other side. That will lead to a decay of the transmissive spectrum once loss exists in the dielectric layers [46]. As a result, using the resonant wavelength of an eigenmode in a presents a redshift ranging from 420 nm to 700 nm as the thickness of SiO2 increases. That Micromachines 2021, 12, 241 higher-order to pursuit a narrower FWHM is not a suitable scheme for realizing a5 filter of 12 meanswith high three efficiency. primary Incolors this paper,for displays we choose can be the obtained 1st order easily eigenmode via such to a realizestructure. the function Accordingof the FP cavity. to Equation (1), it can be known that the resonant wavelength of the eigenmode in a high order will present a narrower FWHM than that in low order when the interlayer of the FP cavity is fixed to a certain thickness. However, the high order indicates that the photons will travel in multiple rounds in the cavity before exiting from the other side. That will lead to a decay of the transmissive spectrum once loss exists in the dielectric layers [46]. As a result, using the resonant wavelength of an eigenmode in a higher-order to pursuit a narrower FWHM is not a suitable scheme for realizing a filter with high efficiency. In this paper, we choose the 1st order eigenmode to realize the function of the FP cavity.

Figure 4. EvolutionEvolution of of the the transmissive transmissive spectrum spectrum of ofthe the FP FPcavity cavity as the as thethickness thickness of interlayer of interlayer changes.

AccordingIn order to analyze to Equation the characteristics (1), it can be of known the FP thatcavity the further, resonant we wavelengthextracted the oftrans- the eigenmodemissive spectra in a highof the order cavity will with present various a narrower thicknesses FWHM of the than SiO that2 interlayer in low order (see Figure when the 5). interlayerIt is straightforward of the FP cavity that isthe fixed center to a waveleng certain thickness.th shifts However,from blue the range high to order red range indicates se- thatquentially the photons along with will travelthe increment in multiple of the rounds thickness in the of cavity SiO2. beforeWhen the exiting thickness from theincreases other side.from That128 nm will to lead 248 tonm, a decaythe center of the wavelength transmissive shifts spectrum from 465 once nm loss to 636 exists nm. in The the dielectricvariation Figurelayersrange [4.of46 Evolution the]. As transmissive a result, of the using transmissive spectrum the resonant spectrum almost wavelength cove of thrse FP the cavity of visible an eigenmodeas the range. thickness The in a detailedof higher-order interlayer data toof changes.pursuitthe transmissive a narrower spectra FWHM are is notlisted a suitable in Table scheme 1. As forshown realizing in the a filtertable, with the highFWHMs efficiency. of all Inspectra this paper, are less we than choose 10 thenm. 1st In orderparticular, eigenmode the FWHMs to realize of thespectra function corresponding of the FP cavity. to the centerIn wavelengthsorder order to to analyze analyze at 465 the the nm, characteristics characteristics 520 nm, and of 620 th ofe thenmFP cavityreach FP cavity further,6.46 nm, further, we 2.05 extracted wenm, extracted and the 5.35 trans- nm, the missivetransmissiverespectively. spectra Meanwhile, spectra of the ofcavity the the with cavitytransmittances various with variousthicknesses can reach thicknesses of0.756, the SiO0.822, of2 interlayer the and SiO 0.902,2 interlayer (see respectively. Figure (see 5). ItFigure is straightforward5). It is straightforward that the center that the waveleng center wavelengthth shifts from shifts blue from range blue to red range range to red se- quentiallyrange sequentially along with along the withincrement the increment of the thickness of the thickness of SiO2. When of SiO the2. When thickness the thicknessincreases fromincreases 128 nm from to 128 248 nmnm, to the 248 center nm, thewavelength center wavelength shifts from shifts 465 nm from to 465 636 nm nm. to The 636 variation nm. The rangevariation of the range transmissive of the transmissive spectrum spectrum almost cove almostrs the covers visible the range. visible The range. detailed The detailed data of thedata transmissive of the transmissive spectra spectra are listed are listedin Table in Table1. As1 .shown As shown in the in thetable, table, the theFWHMs FWHMs of ofall spectraall spectra are areless less than than 10 10nm. nm. InIn particular, particular, the the FWHMs FWHMs of of spectra spectra corresponding corresponding to the center wavelengths at at 465 465 nm, nm, 520 nm, and 620 nm reach 6.46 nm, 2.05 nm, and 5.35 nm, respectively. Meanwhile, the transmittances can can reach reach 0.756, 0.756, 0.822, 0.822, and and 0.902, 0.902, respectively. respectively.

Figure 5. Transmissive spectra of FP cavity with different thicknesses of interlayer.

Figure 5. Transmissive spectra of FP cavity withwith different thicknesses ofof interlayer.interlayer.

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Table 1. The spectral data of the FP cavities with various thicknesses of SiO2 interlayer.

Thickness of SiO2 Center Wavelength Maximum Transmit- FWHM (nm) (nm)Table 1. The spectral(nm) data of the FP cavities withtance various thicknesses of SiO2 interlayer. 128 465 Center Wavelength0.756 Maximum6.46 Thickness of SiO (nm) FWHM (nm) 144 2484 (nm)0.833 Transmittance3.11 156 128500 4650.841 0.7563.02 6.46 170 144520 4840.822 0.8332.05 3.11 186 156545 5000.889 0.8412.97 3.02 170 520 0.822 2.05 196 561 0.867 2.93 186 545 0.889 2.97 206 196576 5610.856 0.8672.59 2.93 216 206590 5760.847 0.8562.82 2.59 234 216620 5900.902 0.8475.35 2.82 248 234636 6200.911 0.9026.45 5.35 248 636 0.911 6.45

3.2. Optimization of the Band-Pass Filter 3.2. Optimization of the Band-Pass Filter To improve the quality of the spectrum further, we introduce a band-pass filter on top of the FP cavityTo to improve stop the the light, quality of wh ofich the the spectrum wavelength further, is right we introduceconsistent awith band-pass the filter on top of the FP cavity to stop the light, of which the wavelength is right consistent with superfluous resonant wavelength, pass through. The structural parameters of the band- the superfluous resonant wavelength, pass through. The structural parameters of the pass filter, which is composed of ZnS/SiO2 pairs, are optimized by utilizing a similar way band-pass filter, which is composed of ZnS/SiO pairs, are optimized by utilizing a similar to that used in the optimization of the FP cavity. 2 way to that used in the optimization of the FP cavity. The transmissive spectra of ZnS/SiO2 pairs with different thicknesses and number of The transmissive spectra of ZnS/SiO pairs with different thicknesses and number pairs are compared in Figure 6. The main purpose for the2 optimization is depressing the of pairs are compared in Figure6. The main purpose for the optimization is depressing spectral transmittance at the two ends of the visible range but allowing high spectral trans- the spectral transmittance at the two ends of the visible range but allowing high spectral mittance in the variation range of the resonant wavelength mentioned in Section 3.1. As transmittance in the variation range of the resonant wavelength mentioned in Section 3.1. shown in Figure 6a, the permitted band of the spectrum shifts to red as the thicknesses of As shown in Figure6a, the permitted band of the spectrum shifts to red as the thicknesses ZnS and SiO2 increase. In comparison with other spectra, the spectrum of the band-pass of ZnS and SiO2 increase. In comparison with other spectra, the spectrum of the band-pass filter with 107 nm-thick ZnS and 107 nm-thick SiO2 presents a permitted band that can filter with 107 nm-thick ZnS and 107 nm-thick SiO2 presents a permitted band that can cover the range from 465 nm to 636 nm. Though increasing the number of ZnS/SiO2 pairs cover the range from 465 nm to 636 nm. Though increasing the number of ZnS/SiO2 is helpful forpairs widening is helpful the bandwidth for widening and the fo bandwidthrming a steep and edge forming (see aFigure steep 6b), edge the (see per- Figure6b), the formance of band-pass filter with four groups of ZnS/SiO2 is sufficient to achieve the aim performance of band-pass filter with four groups of ZnS/SiO2 is sufficient to achieve the of optimization.aim In of order optimization. to illustrate In orderthe results to illustrate of optimization, the results the of transmissive optimization, spectra the transmissive of an integratedspectra device of anare integrated simulated. device are simulated.

Figure 6. Transmissive spectra of the band-pass filters with different thicknesses (a) and numbers (b) of ZnS/SiO pairs. Figure 6. Transmissive spectra of the band-pass filters with different thicknesses (a) and numbers 2 In the left chart, the number of ZnS/SiO2 is fixed to three. In the right chart, both of the thicknesses of ZnS and SiO2 are (b) of ZnS/SiO2 pairs. In the left chart, the number of ZnS/SiO2 is fixed to three. In the right chart, 107 nm. both of the thicknesses of ZnS and SiO2 are 107 nm. Figure7 shows the transmissive spectra of the integrated device. It can be seen Figure 7 shows the transmissive spectra of the integrated device. It can be seen from from the figure that the integrated device obtains an outstanding unimodal spectrum the figure that the integrated device obtains an outstanding unimodal spectrum in the full in the full visible range due to the suppression in the short wavelength range and long- wavelength range. In addition, the integrated device keeps excellent performance. As

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visible range due to the suppression in the short wavelength range and long-wavelength range. In addition, the integrated device keeps excellent performance. As a result, the aFWHMs result, theof the FWHMs transmissive of the transmissivespectra in the spectra visible in range the visible are still range less arethan still 10 lessnm. than The 10FWHMs nm. The at center FWHMs wavelengths at center wavelengths of 465 nm, 520 of 465nm, nm,and 520620 nm,nm are and 6.70 620 nm, nm 2.35 are 6.70nm, nm,and 2.356.91 nm,nm, andrespectively. 6.91 nm, respectively.Although the Although introduction the introductionof ZnS/SiO2 will of ZnS/SiO weaken2 thewill transmit- weaken thetance transmittance slightly, the slightly, transmittance the transmittance of the integrated of the integrateddevice is still device higher is still than higher 0.75 at than various 0.75 atwavelengths. various wavelengths. The transmittances The transmittances reach 0.75, 0.82, reach and 0.75, 0.90 0.82, at 465 and nm, 0.90 520 at 465nm, nm,and 520620 nm,nm, andrespectively. 620 nm,respectively.

FigureFigure 7. TransmissiveTransmissive spectra spectra of of integrated integrated devi devicece with with different different thicknesses thicknesses of ofSiO SiO2 interlayer.2 interlayer. BlackBlack solidsolid lineline representsrepresents thethe transmittancetransmittance curvecurve ofof thethe chosenchosen band-passband-pass ﬁlter.filter.

3.3.3.3. Evaluation ofof thethe Device’sDevice’s PerformancePerformance InIn orderorder to to evaluate evaluate the the chromaticity chromaticity of of the the transmissive transmissive spectrum, spectrum, the the color color coordinate coordi- ofnate the of transmissive the transmissive spectrum spectrum in the in 1931 the Commission1931 Commission Internationale Internationale de L’Eclairage de L'Eclairage (CIE) coordinate(CIE) coordinate system system is calculated is calculated according according to the to CIE-XYZthe CIE-XYZ tristimulus tristimulus value, value, which which is obtainedis obtained from from the the following following expressions: expressions: Z X XkR()x()d= =k R(λλλλ)x(λ)dλ (3)(3)

Z Y YkR()y()d==k R(λλλλ)y(λ)dλ (4)(4) Z Z = k R(λ)z(λ)dλ (5) Z = kR()z()d λλλ (5) where k is the adjustment factor, x, y and z are the optical efficiency functions, and R(λ) is thewhere calculatedkis the spectrum.adjustment The factor, coordinate x, y canand bez calculatedare the optical as follows: efficiency functions, and R()λ is the calculated spectrum. The coordinate can be calculated as follows: X x = (6) X + YX+ Z x = ++ (6) XYZY y = (7) X + Y + Z Y The coordinates of spectra with differenty = center wavelengths are shown in Figure8.(7) It XYZ++ can be seen from the figure that the chromaticities of various transmissive spectra are very closeThe to the coordinates boundary ofof thespectra CIE chart,with different especially ce fornter the wavelengths spectrum with are a shown center wavelengthin Figure 8. ofIt can 465 nm.be seen It indicates from the that figure the that spectrum the chro hasmaticities a high color of various purity. transmissive As the thickness spectra of theare intermediatevery close to layerthe boundary increases, of the the corresponding CIE chart, especially coordinate for varies the spectrum from the regionwith a of center blue towavelength the regions of of465 green, nm. It yellow, indicates and that red the successively. spectrum has As a shown high color in Figure purity.8, mostAs the of thick- the coordinates locate outside the Adobe RGB and sRGB chromatic gamut. That means a larger scale of chromatic gamut can be obtained, and more vivid colors can be reproduced via such filter.

Micromachines 2021, 12, x FOR PEER REVIEW 8 of 12 Micromachines 2021, 12, x FOR PEER REVIEW 8 of 12

ness of the intermediate layer increases, the corresponding coordinate varies from the re- ness of the intermediate layer increases, the corresponding coordinate varies from the region of blue to the regions of green, yellow, and red successively. As shown in Figure 8, gion of blue to the regions of green, yellow, and red successively. As shown in Figure 8, most of the coordinates locate outside the Adobe RGB and sRGB chromatic gamut. That most of the coordinates locate outside the Adobe RGB and sRGB chromatic gamut. That Micromachines 2021, 12, 241 means a larger scale of chromatic gamut can be obtained, and more vivid colors can8 of 12be means a larger scale of chromatic gamut can be obtained, and more vivid colors can be reproduced via such filter. reproduced via such filter.

Figure 8. The chromaticities of transmissive spectra at different wavelengths. The two triangles Figure 8. The chromaticities ofof transmissivetransmissive spectra spectra at at different different wavelengths. wavelengths. The The two two triangles triangles stand stand for the gamut scale of Adobe RGB and sRGB. forstand the for gamut the gamut scale of scale Adobe of Adobe RGB and RGB sRGB. and sRGB. Figure 9 shows the distribution of electric fields in each layer in the integrated device Figure9 9 shows shows thethe distributiondistribution ofof electricelectric fieldsfields in in eacheach layerlayer inin thethe integratedintegrated devicedevice at various wavelengths when the thickness of SiO2 is 170 nm. Correspondingly, the center at various wavelengths when the thickness ofof SiO22 is 170 170 nm. nm. Correspondingly, Correspondingly, thethe centercenter wavelength of the transmissive spectrum is 520 nm. The intensity of the electric field at wavelength of the transmissive spectrum is 520520 nm. The intensity of the electric fieldfield atat 520 nm in the intermediate medium gets to the maximum in comparison with the electric 520 nm in the intermediate medium gets to the maximum in comparison with the electric fields at other wavelengths, such as 460 nm, 600 nm, and 700 nm. The consistency between fieldsfields at other wavelengths, suchsuch asas 460 nm,nm, 600 nm, and 700 nm. The consistency between the wavelength where the electric field in cavity reaches the maximum and the center the wavelength where the electric fieldfield in cavitycavity reachesreaches thethe maximummaximum andand thethe centercenter wavelength of the transmissive spectrum indicates that the FP microcavity plays a deci- wavelength ofof thethe transmissivetransmissive spectrum spectrum indicates indicates that that the the FP FP microcavity microcavity plays plays a decisive a decisive role in the filter device. rolesive inrole the in filter the filter device. device.

FigureFigure 9.9. DistributionDistribution ofof electricelectric fieldfield inin filterfilter atat 460460 nmnm ((aa),), 520520 nmnm ((bb),), 600600 nmnm ((cc),), andand 700700 nmnm ((d).). Figure 9. Distribution of electric field in filter at 460 nm (a), 520 nm (b), 600 nm (c), and 700 nm (d). TheThe thicknessthickness ofof SiOSiO2 interlayerinterlayer inin FPFP cavitycavity isis 170170 nm.nm. The thickness of SiO22 interlayer in FP cavity is 170 nm. According to Equation (1), the ultra-narrow linewidth of the filter is ascribable to the high reflection on the GaP/SiO2 DBR, while the high transmissive efficiency is attributable to the low absorption of the device. Figure 10b shows the absorbed power density in each layer at various wavelengths. It can be seen in Figure 10a that a slight absorption occurs in the GaP layer, which is adjacent to the intermediate layer. Accompany with the diminishing Micromachines 2021, 12, x FOR PEER REVIEW 9 of 12

According to Equation (1), the ultra-narrow linewidth of the filter is ascribable to the Micromachines 2021, 12, 241 high reflection on the GaP/SiO2 DBR, while the high transmissive efficiency is attributable9 of 12 to the low absorption of the device. Figure 10b shows the absorbed power density in each layer at various wavelengths. It can be seen in Figure 10a that a slight absorption occurs in the GaP layer, which is adjacent to the intermediate layer. Accompany with the dimin- ofishing reflectivity of reflectivity at the resonant at the resonant wavelength, waveleng the transmissiveth, the transmissive efficiency efficiency at resonant at resonant wave- λ λ λ lengthwavelength gets to gets a very to higha very value high according value according to the formula to theA( formula) + T( )A( +λ R() + )T( =λ 1.) Figure+ R(λ) 10= d1. showsFigure an10d overall shows absorption an overall of absorption the device of in th thee fulldevice visible in the range. full Itvisible can be range. seen fromIt can the be figureseen from that the absorption figure that in theabsorption full range in isthe very full lowrange except is very for low a strong except peak for a near strong 460 peak nm andnear a 460 small nm absorption and a small peak absorption near 700 nm. peak As near shown 700 in nm.Figure As 10 showna,c, the in strong Figure absorptions 10a,c, the at these wavelengths occur in the top DBR of the FP cavity and the band-pass filter. That strong absorptions at these wavelengths occur in the top DBR of the FP cavity and the is because the GaP and SiO2 layers in the DBR forms some submicrocavities as well as band-pass filter. That is because the GaP and SiO2 layers in the DBR forms some submi- the ZnS and SiO2 layers in the band-pass filter. When the wavelengths of incident light crocavities as well as the ZnS and SiO2 layers in the band-pass filter. When the wave- satisfy the resonant conditions in those submicrocavities, there will be an enhancement of lengths of incident light satisfy the resonant conditions in those submicrocavities, there the electric field in the interlayer. Thus, some discrete absorbing peaks at those resonant will be an enhancement of the electric field in the interlayer. Thus, some discrete absorbing wavelengths will exist in the absorption curve. peaks at those resonant wavelengths will exist in the absorption curve.

FigureFigure 10.10. DistributionDistribution ofof absorptionabsorption power power density density at at 460 460 nm nm ( a(),a), 520 520 nm nm (b (),b), and and 700 700 nm nm (c ()c with) with a

170a 170 nm-thick nm-thick SiO SiO2. Figure2. Figure (d ()d presents) presents the the total total absorption absorption of of the the optical optical ﬁlter. filter.

FigureFigure 1111 showsshows thethe evolutionevolution ofof thethe transmissivetransmissive spectrumspectrum asas thethe angleangle ofof incidenceincidence withwith differentdifferent polarization modes modes increases increases from from 0° 0 ◦toto 50°. 50 ◦An. An evident evident shifting shifting of the of cen- the ◦ centerter wavelength wavelength occurs occurs asas the the angle angle of of incidence incidence is is greater greater than 10°.. The variation almostalmost reachesreaches 5050 nmnm for both of the modes, modes, as as show shownn in in Figure Figure 11, 11 ,suggesting suggesting that that the the device device is issensitive sensitive to tothe the incident incident angle. angle. Another Another import importantant message message from from Figure Figure 11 is 11 that is thatthe evo- the evolutionlution trends trends of ofthe the transmissive transmissive spectra spectra in in TM TM & & TE TE modes modes are are consistent. There isis onlyonly aa differencedifference inin thethe intensitiesintensities ofof thethe transmissivetransmissive spectra.spectra. TheThe similarsimilar evolutionevolution trendstrends inin differentdifferent modesmodes areare attributedattributed toto thethe isotropyisotropy ofof lightlight responseresponse ofof thethe ﬁlmfilm inin thethe x-yx-y plane.plane. The results of the simulation manifest that the ﬁlter based on the proposed structure in this paper presents an excellent performance. Moreover, Gudovskikh, A. S. et al. reported that GaP could be grown on a Si wafer by low-temperature plasma-enhanced atomic layer deposition [42]. As for ZnS and SiO2, all these materials can be deposited by atomic layer deposition according to other researchers’ reports [49,50]. Accordingly, it provides us a feasible way to fabricate the device in the same chamber at one time without breaking down the vacuum. As a result, the device investigated in this paper also has a potential value for a practical application in the future. MicromachinesMicromachines 20212021,, 1212,, 241x FOR PEER REVIEW 1010 of 1212

Figure 11. EvolutionFigure of the 11. transmissive Evolution of spectrum the transmi in TMssive (a spectrum) and TE ( bin) asTM the (a) incident and TE angle(b) as increases.the incident angle increases. 4. Conclusions The results of the simulation manifest that the filter based on the proposed structure In summary, a transmissive filter composed of GaP/SiO2 DBR and ZnS/SiO2 is . simulated.in this paper An presents ultra-narrow an excellent linewidth performance of spectrum in Moreover, the visible Gudovskikh, range is obtained A. S. according et al. re- toported the results that GaP of the could simulation. be grown The on FWHMs a Si wafer of transmission by low-temperature peaks corresponding plasma-enhanced to the centeratomic wavelengthslayer deposition at 465 [42]. nm, As 520 for nm, ZnS and and 620 SiO nm2, all reach these 6.70 materials nm, 2.35 can nm, be anddeposited 6.91 nm, by respectively.atomic layer Becausedeposition the according entire device to other is designed researchers’ based reports on dielectric [49,50]. materials, Accordingly, a very it lowprovides total absorptionus a feasible in way the to visible fabricate range the is device achieved. in the The same transmittance chamber at ofone the time device without can reachbreaking 0.75, down 0.82, the and vacuum. 0.90 at 465 As nm, a result, 520 nm, the anddevice 620 investigated nm. In comparison in this paper with traditional also has a MDMpotential structure, value for the a narrowerpractical linewidthapplication and in higherthe future. transmittance result in more saturated primary colors. Finally, a larger scale of the color gamut can be realized in comparison with4. Conclusions that of Adobe RGB color gamut. Additionally, the device also shows polarization- independentIn summary, characteristics, a transmissive which filter is verycomposed suitable of forGaP/SiO high-resolution2 DBR and imagingZnS/SiO2 systems, is simu- detectors,lated. An ultra-narrow and spectrometers. linewidth of spectrum in the visible range is obtained according to the results of the simulation. The FWHMs of transmission peaks corresponding to the Authorcenter wavelengths Contributions: atSimulation, 465 nm, 520 K.X.; nm, writing—original and 620 nm reach draft preparation, 6.70 nm, 2.35 K.X. nm, and Y.M.;and 6.91 writing— nm, reviewrespectively. and editing, Because S.C., Y.L.,the entire and Z.W.; device S.J. provided is designed the insight based and on useful dielectric information. materials, All authorsa very have read and agreed to the published version of the manuscript. low total absorption in the visible range is achieved. The transmittance of the device can Funding:reach 0.75,This 0.82, work and was 0.90 partially at 465 nm, supported 520 nm, by and the 620 National nm. In Key comparison Research and with Development traditional ProgramMDM structure, (No. 2017YFB0403501), the narrower Sciencelinewidth and and Technology higher transmittance Program Project result of State in more Administration saturated forprimary Market colors. Regulation Finally, (2019MK147). a larger scale The of authors the color also gamut acknowledge can be financial realized support in comparison from the Nationalwith that Major of Adobe Fundamental RGB color Research gamut. Program Additi of Chinaonally, (Grant the No.device 91833306), also shows the National polarization- Natural Scienceindependent Foundation characteristics, of China (Grant which Nos. is 62074083very suitable and 62005131), for high-resolution the Priority Academicimaging systems, Program Development of Jiangsu Higher Education Institutions (Grant No. YX030003). detectors, and spectrometers. Conflicts of Interest: The authors declare no conflict of interest. Author Contributions: Simulation, K.X.; writing—original draft preparation, K.X. and Y.M.; writ- References ing—review and editing, S.C., Y.L., and Z.W.; S.J. provided the insight and useful information. All authors have read and agreed to the published version of the manuscript. 1. 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