Ge/BaF2 thin-films for surface micromachined mid-wave and long-wave infrared reflectors

Abstract. High performance distributed Bragg reflectors (DBRs) are key elements to achieving high finesse MEMS-based Fabry–Pérot interferometers (FPIs). Suitable mechanical parameters combined with high contrast between the refractive indices of the constituent optical materials are the main requirements. In this paper, Germanium (Ge) and barium fluoride (BaF2) optical thin-films have been investigated for mid-wave infrared (MWIR) and long-wave infrared (LWIR) filter applications. Thin-film deposition and fabrication processes were optimised to achieve mechanical and optical properties that provide flat suspended structures with uniform thickness and maximum reflectivity. Ge-BaF2-Ge 3-layer solid-material DBRs have been fabricated that matched the predicted simulation performance, although a degradation in performance was observed for wavelengths beyond 10  μm that is associated with optical absorption in the BaF2 material. Ge-Air-Ge 3-layer air-gap DBRs, in which air rather than BaF2 served as the low refractive index layer, were realized to exhibit layer flatness at the level of 10 to 20 nm across lateral DBR dimensions of several hundred micrometers. Measured DBR reflectance was found to be ≳90  %   over the entire wavelength range of the MWIR band and for the LWIR band up to a wavelength of 11  μm. Simulations based on the measured DBR reflectance indicates that MEMS-based FPIs are able to achieve a peak transmission of ≳90  %   over the entire MWIR band and up to 10  μm in the LWIR band, with a corresponding spectral passband of ≲50  nm in the MWIR and <80  nm in the LWIR.


Introduction
Fabry-Pérot interferometers (FPIs) provide a spectrometer architecture that is compatible with thin-film surface-micromachined microelectromechanical systems (MEMS). FPIs consist of two mirrors, which in a MEMS implementation generally consist of a pair of distributed Bragg reflectors (DBRs), separated by an optical cavity. The thicknesses of the constituting DBR layers and the separation between the DBRs are selected based on the spectral band of operation. 20,21 Conventional spectrometers use bulky and fragile optics, which makes them non-portable and hinders their suitability for in-field deployment. However, FPIs fabricated using MEMS technology have a small footprint, are mechanically robust, use very little power, and are hence fieldportable. This ability to overcome many of the drawbacks of conventional spectrometers systems 3,20,21 makes them attractive for deployment in platforms requiring low size, weight, and power (SWaP), such as unmanned autonomous vehicles (UAVs), drones, satellites, and mobile phones.
Typically, MEMS-based filters are either implemented using a guided-mode resonance effect or a multiple-beam interference-effect. A study on the guided-mode resonance for the realization of resonant filters has been well presented by the group of Magnusson, [22][23][24] and Ko et al. 24 have recently published a study claiming realization of prototypes. In the latter work, the fabricated devices had a very large die size (width: 26 mm, height: 18 mm) and tuning of the transmission peak was performed mechanically, by an external tuning mechanism resulting in a relatively bulky system. Nevertheless, as a demonstration technology, this approach is useful for benchtop implementations, which do not demand low SWaP or integration on portable platforms.
On the other hand, in a multiple-beam interference approach, multiple beams are captured in a cavity between two mirror plates or DBRs to realize FPIs. In MEMS implementations, DBRs for the FPIs can be fabricated by depositing an alternating sequence of low-absorbing dielectric layers of high-and low-refractive index materials. 25 In this configuration, λ∕4-thick optical films are deposited, where the thickness of each optical layer is equivalent to one quarter of the wavelength for which the DBR is designed. 12,26,27 High reflectivity of the DBRs is assured if there is a high contrast between the refractive indices of the high-and low index materials, which provides a pathway toward the realization of narrowband FPIs. In this paper, germanium (Ge) and barium fluoride ðBaF 2 Þ∕air have been considered as the high and low refractive index materials/media, respectively, for the fabrication of DBRs. The λ∕4-thickness 28 and optical constants [29][30][31][32] for the thin-films required for applications in the technologically important MWIR and LWIR bands are listed in Table 1. Ge thin-films have been previously explored by several research groups 2,12,21,27,[33][34][35][36] to fabricate DBRs in the IR region. In particular, our group at The University of Western Australia 12,21,27,33,34 and InfraTec GmbH 2, 36 have used Ge thin-films as Table 1 Material parameters for the design of MWIR and LWIR DBRs at center wavelengths of 4 and 10 μm, respectively. This table shows the calculated λ∕4-thicknesses for materials, targeted and achieved mirror flatness, and simulated and measured mirror reflectance. Note that the deposited layer thicknesses are within a tolerance of ±5%.  31,32 Air 2500 1 β LW >97 99 >94 99 a a high refractive index material along with low refractive index materials such as SiO x , SiN x , and ZnS for the fabrication of shortwave and longwave IR FPIs. The studies based on SiO x and SiN x are mainly focused in the short wave infrared region since SiO x and SiN x are absorbing in the LWIR spectral band, which renders them unsuitable for the development of narrowband FPIs at LWIR wavelengths. On the other hand, ZnS is non-absorbing in the LWIR region but its refractive index of 2.2 as a low refractive index material combined with Ge is not sufficient to provide a high refractive index contrast (a key component to developing narrowband FPIs). Thus, it is impractical for ZnS-based FPIs to achieve a narrow linewidth (typically ≤1% of the design wavelength as inferred from the following studies 7,12,16,[37][38][39] in the LWIR region for hyperspectral sensing and imaging, although these FPIs would be suitable for multi-spectral sensing and imaging. To fill this gap, we propose BaF 2 as a low refractive index material due to its low refractive index in the LWIR spectral band, 31,32 combined with Ge for the development of narrow-linewidth FPIs in the LWIR spectral band for hyperspectral sensing and imaging applications. Within the MWIR and LWIR spectral bands, the availability of materials with adequate optical and mechanical properties is limited, especially in the LWIR. While BaF 2 thin-films have previously been used for optical coatings, 40,41 the applicability and compatibility of the material with micromachining processes to enable high performance wavelength discrimination in the MWIR and LWIR band has not previously been studied. Although BaF 2 is a highly attractive optical material due to its low refractive index 31,32 in the MWIR and LWIR wavelength ranges and can significantly boost the optical performance of optical MEMS devices, it is not yet a mature technology for micromachining applications from the application point of view. For example, BaF 2 is slightly hygroscopic 42 in nature, and therefore requires process development for adopting it in MEMS fabrication processes, where water is the most commonly used solvent for cleaning the samples. Furthermore, significant challenges associated with the thermal deposition of films that are several micrometers thick must be resolved since such layers are required to achieve the λ∕4-wavelength thickness requirement for filter applications in the LWIR region. Finally, the process compatibility of multilayer Ge∕BaF 2 thick films must be addressed to demonstrate the feasibility of this material combination to enhance the available choices when designing filters for MWIR and LWIR applications. The use of Ge∕BaF 2 stacks in these applications introduce challenges in controlling residual stresses and surface roughness while maintaining the high optical performance expected from BaF 2 layers. Adhesion of these materials between themselves and other commonly used MEMS materials throughout the range of wet and dry etching steps is required during the fabrication of complex MEMS-based structures and must be addressed. In this work, we have thoroughly addressed these challenges, in order to take advantage of the exceptional optical properties of BaF 2 thin-films for optical MEMS applications. For optimal performance, a high level of parallelism between the DBRs is required, typically better than λ∕10 or λ∕20 for MEMS-based optical applications. [43][44][45][46] Our efforts in this work culminate in fabricating layers with mirror parallelism exceeding a level of λ∕200 for the suspended mirror layers. This work provides reliable and reproducible methods to develop high performing surface micromachined DBRs for the MWIR and LWIR wavelength regions using thermally evaporated BaF 2 as a low refractive index material and their suitability in the development of MEMS-based optical FPIs. Throughout this work, Ge thin-films have been used as the high refractive index material and two alternatives for the low refractive index layers have been explored, as schematically shown in Fig. 1(a). We have investigated the use of either BaF 2 thin-films or an air-gap as the low-refractive index media for the DBRs. Figure 1(b) shows the 3D representation of an air-gap DBR. To improve visualization, the top Ge layer is rendered to show the profile of the underlying sacrificial layer. Thin-film deposition conditions have been optimized to yield thin-film layers having low stress, low surface roughness, and excellent optical properties in order to demonstrate solid-material DBRs as well as suspended Ge air-gap DBRs with 200 μm × 200 μm, 500 μm × 500 μm, and 1 mm × 1 mm optical areas toward their subsequent incorporation into FPIS that can be hybridized with either single point IR detectors or focal plane imaging arrays. Lastly, this paper predicts the expected characteristics of FPIs based on the reflectance response of the fabricated DBRs via optical simulations. The fabrication of experimental FPIs is beyond the scope of this paper and will be addressed in future studies.

Thin-Film Deposition
The Ge and BaF 2 layers were deposited under high vacuum (<10 −6 mbar), using a thermal evaporator, with an in-situ thermocouple to monitor the substrate temperature. In order to investigate the impact of substrate temperature on the residual stress of Ge and BaF 2 thin-films, the depositions were initiated at four different substrate temperatures: 25°C, 50°C, 100°C, and 150°C using a substrate heating block. Since a cooling system was not integrated into our system, a rise in substrate temperature was observed during the deposition due to radiative heating from the evaporation source for depositions initiated at temperatures 50°C and below. Therefore, for depositions initiated at temperatures 25°C and 50°C, the substrate temperature was kept within the temperature windows of 25°C to 70°C and 50°C to 70°C, respectively. For depositions initiated at temperatures ≥100°C, the temperature variation could readily be controlled within a tolerance of AE5°C. It is noted that the thin-films were deposited without breaking vacuum either in a single run or by adopting a multi-step deposition technique. Substrate heating was available both before and during the deposition to control the substrate temperature. On completion of the deposition run, the substrate was allowed to cool down to room temperature before opening the chamber.
The deposition of Ge thin-films was performed at a deposition rate of 1.5 AE 0.1 Å∕s in a single continuous run satisfying the above-mentioned conditions. Figure 2 shows exemplar temperature profiles for Ge thin-films deposited at 50°C (green) and 100°C (blue). The dashed lines in Fig. 2 represent the substrate heating and cooling periods before and after the thin-film deposition periods represented by the solid lines. However, deposition of BaF 2 thin-films was performed at a deposition rate of 5 AE 0.2 Å∕s, and a multi-step deposition technique was adopted for depositions initiated at temperatures 25°C and 50°C to achieve the desired thicknesses mentioned in Table 1. Once the substrate temperature reached the maximum limit of the temperature window, the deposition was stopped to allow the temperature to drop to the minimum limit of the temperature window without breaking vacuum. Consequently, the deposition of BaF 2 thin-films was divided into two and four steps of equally distributed thicknesses for MWIR and LWIR DBRs, respectively. Although a multi-step deposition technique was not required for depositions initiated at 100°C and 150°C, to ensure sample-to-sample consistency, the depositions initiated at these temperatures were also performed in steps and provide the same waiting period between each deposition step for the BaF 2 thin-films. An exemplar of temperature profiles for BaF 2 thinfilms deposited at 50°C (red) and 100°C (blue) is shown in Fig. 2.
A significant challenge during the deposition of the relatively thick Ge and BaF 2 thin-films of the order of 1 μm in thickness was the integrity of the evaporation sources and materials for such a prolonged time and the sudden failure of the quartz crystal microbalance 47,48 during deposition due to overheating. Therefore, it becomes critically important to select an evaporation source that is compatible with the deposited material and can survive the long deposition time. In the case of Ge, the issue of boat failure was quite common in the middle of a deposition. Therefore, the deposition of Ge thin-films was performed using two boats in one run by switching between boats. On the other hand, a multi-chamber baffled boxes chimney boat was used to deposit the comparatively thick BaF 2 layers and to prevent any spitting or streaming. The issue of boat failure was not observed during the deposition of BaF 2 films. However, a sudden failure of the quartz crystal microbalance was observed regularly during BaF 2 deposition in a single run due to excessive radiative heat from the evaporation source. The adopted multi-step deposition technique helps to prevent the sudden failure of the quartz crystal microbalance and also provides reasonable control of the thin-film surface roughness.

DBR Fabrication Process
This section presents the fabrication process of DBRs for the MWIR and LWIR wavelength spectral bands. For a better understanding of the fabrication process, the solid-material and air-gap DBRs are categorised as αand βseries, respectively. The αseries DBRs consisted of λ∕4-thick Ge∕BaF 2 ∕Ge layers deposited on an Si substrate coated with a λ∕4-thick BaF 2 spacer layer, whereas the, βseries DBRs consisted of λ∕4-thick Ge/Air/Ge layers. The intermediate BaF 2 mirror layer existing in αseries DBRs was replaced with an airgap in βseries DBRs using surface micromachining techniques. The subscripts MW and LW will be used to represent the mid-wave and long-wave IR bands, respectively. The performance of DBRs, especially those with an internal air-gap (β-series DBRs), will depend on the substrate and on the residual stress of thin-film layers on that substrate since compressive residual stress of thin-films can lead to various deformations such as tilt, bending, and buckling. Through an appropriate control of material residual stress, the degree of tilt and bending in any suspended layers can be minimized to yield good optical quality in the fabricated DBRs. A process flow for the fabrication of αand βseries DBRs is shown in Fig. 3.

2.2.1
Common steps for αand β-DBR's a. A low refractive index λ∕4-thick BaF 2 spacer layer was thermally evaporated on the starting Si-substrates as shown in Fig. 3(a). This low refractive index spacer layer is used to differentiate the high-low-high refractive index 3-layer mirror from the substrate and to improve the optical performance of the mirror. b. As shown in Fig. 3(b), a λ∕4-thickness Ge layer was thermally evaporated onto the BaF 2 spacer layer. For the MWIR and LWIR DBRs, the targeted λ∕4-thicknesses of Ge thinfilms were 250 and 625 nm, respectively.

βseries DBRs
e. For βseries DBRs, a λ∕4-thickness MicroChem Corp. PMMA A9 sacrificial layer was spun at 4000 rpm for MWIR DBRs and at 1250 rpm for LWIR DBRs to realize λ∕4-air cavities for both wavelength ranges, as shown in Fig. 3(e). The PMMA A9 sacrificial layer was soft-baked at 180°C for 2 min, and then the temperature was ramped to 210°C for a total of 15 min to cure it fully. In order to improve the adhesion of PMMA A9, adhesion promoter Brewer Science APX-K1 was spun at 4000 rpm and baked at 130°C for 30 s before spin-depositing the PMMA. The PMMA A9 sacrificial layer was followed by a thermally evaporated λ∕4-thickness Ge layer, as shown in Fig. 3(e). f. Subsequently, for free-standing βseries DBRs, the top Ge layer was patterned with the help of negative photoresist AZ2035 to create perforation holes (6 μm in diameter) in the top Ge layer using CF 4 based plasma etching [see Fig. 3(f)] to facilitate removal (release) of the PMMA sacrificial layer. g. Finally, the negative photoresist and sacrificial layer were removed at the same time in an O 2 plasma in a March PM-600 Barrel Asher for 20 min with 120 W RF power at 1 Torr chamber pressure. After the dry release of the sacrificial layer, the top Ge layer was suspended over the bottom Ge layer forming an air cavity DBR, as shown in Fig. 3(g). At this stage, the βseries DBRs were ready for optical characterization.
The above methods were used to fabricate αseries DBRs, as well as βseries DBRs with various optical areas of 200 μm × 200 μm, 500 μm × 500 μm, and 1 mm × 1 mm. The measured thicknesses of deposited films were all within the targeted value tolerance of AE5%. Where the actual measured thickness of each thin-film is mentioned in the appendix (see Fig. 12).

Measurement and Characterization Techniques
Optical characterization techniques were used to estimate the thin-film stress using a radius of curvature measurements, to extract their optical properties such as refractive index (n) and extinction coefficient (k) from the transmission spectra of thin-films, to determine the flatness of suspended membranes, and to measure optical reflection spectra. The stress of thin-films was measured by applying Stoney's formula. 49,50 To measure the thin-film intrinsic stress, the λ∕4thick Ge and BaF 2 films of targeted center LW of 10 μm were deposited on 100 μm thick silicon substrates. In order to estimate the residual stress of thin-films, a Zygo Newview 6 K white light optical surface profilometer was used to measure the radius of curvature of 100-μm thin Si substrates before and after deposition. The same tool was later used to perform flatness measurement over the free-standing membranes of fabricated βseries DBRs. A Spotlight 200i FT-IR Microscopy System with Spectrum Two by Perkin Elmer was used to measure the transmission response of thin-films and DBR reflectance. Transmission measurements were performed with the FTIR Spectrum Two, and the refractive index (n) and extinction coefficient (k) of the materials were extracted from the transmission response. This study was mainly focused on the less well-known BaF 2 layers to investigate the refractive index and extinction coefficient in the IR region, which were then compared with past studies. 31,32 Finally, the BaF 2 thin-films were incorporated as an alternating layer with Ge thin-films to realize DBRs. The reflectance measurements of the DBRs were performed using the FTIR Microscope, which allows direct measurement of the DBR reflectance. The microscope beam was focused in the center of the DBR, to a measurement spot size of approximately 35 μm × 35 μm. The optical transfer matrix method (OpenFilters 51 ) was used to simulate the reflectance of the multilayer thin-film DBR stack of the fabricated devices, 25,52 with the experimentally determined thicknesses and optical constants of Ge and BaF 2 being used in the model.
Cross-sectional analysis of DBRs was performed using an FEI Helios Nanolab ultra highresolution scanning electron microscope (SEM) equipped with focused ion beam (FIB) technology. The elemental mapping and compositional analysis of thin-films over a FIB-milled cross-section were enabled by energy-dispersive spectroscopy (EDS). This allowed the quality of thin-film interfaces, composition, and their elemental distribution to be determined over the thicknesses of the deposited thin-films. Figure 4 shows the thin-film stress values as a function of the starting deposition temperature calculated from Stoney's formula for the deposited Ge and BaF 2 thin-films. Ge thin-films were found to be characterised by residual tensile stress, which decreased monotonically with increasing substrate temperature. The measured tensile stress for a λ∕4 Ge thin-films was 421 MPa when the deposition started at room temperature. This stress value reduced significantly to 163 MPa when the deposition was initiated at a temperature of 50°C. Our experiments indicate that a manageable level of tensile thin-film stress (<100 MPa) can be achieved when the deposition was initiated and maintained at 150°C, as shown in Fig. 4. On the other hand, BaF 2 exhibits only a relatively small change in stress with deposition temperature, albeit with a change from a tensile to compressive nature, over the entire temperature range investigated (see Fig. 4).

Characterization of Optical Parameters: Refractive Index and Extinction Coefficient
Ge and BaF 2 have been used as the high and low refractive index material, respectively, in DBR fabrication because of their attractive near-zero absorption in the LWIR region as well as their high refractive index contrast. [29][30][31][32]53 The optical properties of BaF 2 were extracted from the transmission response of a 2.6-μm thick layer of BaF 2 deposited on a silicon substrate. This was recorded for wavelengths from 1.2 to 12 μm and analysed with the Cauchy dispersion model using general-purpose software (NKDMatl 54 ) to extract the nand k-values. The recorded transmission spectrum was found to adequately match the Cauchy dispersion model for wavelengths up to 5.5 μm; however, the quality of the fit was reduced for wavelengths longer than 5.5 μm. Therefore, we used the extracted n-  to the data derived from the characterised DBR performance, which is indicated in Fig. 5(b) as blue open square symbols. Ge and Si nand k-values used in this study are also shown in Fig. 5. 29,53,55

Structural Characterization of DBRs
Extensive characterization was performed to investigate the layered structures formed by sequential depositions of Ge and BaF 2 λ∕4-thick films to form the DBRs. Figure 6(a) shows the crosssectional scanning electron micrograph of an exemplar α LW DBR, where the cross-section was prepared for imaging with the help of the FIB technique. It can be observed in Fig. 6(a) that the interface with the Si-substrate is well-defined and that the Ge and BaF 2 thin-films and interfaces are free from delamination and cracks. The degree of roughness that can be noted on the top surface is mainly associated with the cross-section preparation process, which used a highly FIB and is not a true representation of the as-fabricated surface roughness. Figures 6(b)-6(f) show material elemental maps over the cross-section obtained using EDS and further confirm the formation of well-defined thin-film interfaces. During this cross-sectional investigation, a minimal level of oxygen was found to be present (<1.7%) as reported in the compositional analysis shown in Fig. 6(g), which was evenly distributed throughout the films. Importantly, no increase in oxygen was observed neither at the thin-film interfaces nor within the thin films that could plausibly be associated with the cooling breaks during deposition. An overcoating gold layer was used to prevent charging effects during FIB/SEM investigations. These characteristics were observed to be common for both α MW and α LW DBRs. In the case of β-series DBRs cross-sectional analysis was not performed due to the expectation that the suspended membranes would collapse during the FIB cross-section preparation process. Nevertheless, we expect the β-series DBRs to show similar characteristics.

Membrane Flatness Profiles
Figure 7(a) shows an optical microscopic image of a released 500 μm × 500 μm β LWseries DBR. The colour of the inner boundary of the unreleased area has been lightened for clarity. Figure 7(b) shows line-scans taken diagonally over the upper surface of all β LWseries DBRs, as depicted in Fig. 7(a). The inset of Fig. 7(b) shows the same data on a magnified scale.   A concave-upwards bowing of 10 to 20 nm was observed across the total released area in all three sizes of β LWseries DBRs. The bowing within the optical area of the devices is limited to well below 10 nm, indicating very high surface flatness of the top Ge suspended layer taken over several hundred micrometers. Similarly, a high degree of flatness of the order of 5 to 10 nm was observed in the unpatterned αseries DBRs for similar line scan lengths. Since there are no suspended layers, it can be inferred that any bowing reported for the α-DBRs is mainly due to substrate deformation arising from film stress. The required level of flatness, in the range of <20 nm, was achieved for both αand βseries DBRs and indicates that negligible performance degradation is expected since 20 nm of bowing is significantly below the required λ∕20 optical condition at the center wavelength by more than two orders of magnitude.  The simulated reflectance spectra in the MWIR band (solid blue lines) have been obtained using n-and k -values extracted from the measured transmission response of a 2.6 μm thick BaF 2 layer, and for the LWIR region using n-and k -values that were projected linearly into the LWIR region from MWIR obtained data (dashed black lines), or using k -values (see Fig. 5 indicted as "kderived") that were adjusted during the fitting iteration in order to achieve favourable agreement between measured and simulated reflectance spectra of α LW (red solid lines).

DBR Reflectance Spectra
The left and right sides of Fig. 8 show the data obtained for the MWIR and LWIR bands, respectively, originating from the characterization of different αand βseries DBRs designed to operate specifically in the MWIR or LWIR band. The central insets provide the structural cross-sections of the measured devices [see Fig. 8(a) and 8(b)] and the top-view micrograph depicts the spatial position of measurements over the suspended βseries DBRs [see Fig. 8(c)]. A measurement spot size of approximately 35 μm × 35 μm was adopted for the measurements. In the case of single-point measurements, only one measurement at the center of the DBR was performed. On the other hand, in the case of spatially distributed measurements, an array of measurements has been performed covering the entire optical area of the DBR, out of which data for three measurement points are presented for the 500 μm × 500 μm sized βseries sample in Fig. 8(c). The left side of Fig. 8(a) shows that the peak reflectance value measured for α MW (represented by brown open circles) was above 97% and was found to closely match the peak simulated reflectance value of 98.7% (represented by the blue solid line), which was obtained via simulations using experimentally extracted n and k values (see Fig. 5). However, although the simulated reflectance remains above 95% over the entire MWIR band, the measured reflectance values are reduced to nearly 90% for the long wavelength end of the MWIR region (approaching 5 μm). Nevertheless, even with 90% reflectance, these DBRs are viable candidates to produce narrow-band Fabry-Pérot (FP) filters in the MWIR region. Due to the solid structure of αseries DBRs, inter-layer bowing was not of concern, and there was little motivation to perform spatially distributed measurements. The measured reflectance spectrum for α LW [as shown by the yellow open circles on the right-hand side of Fig. 8(a)] was found to be characterised by a peak reflectance value of 97% and to remain above 96% for wavelengths between 8 and 10.2 μm. However, a notable drop in the measured reflectance was observed for longer wavelengths, which can be associated with increased absorption in the BaF 2 layer for wavelengths beyond 10.2 μm, resulting in a drop in the reflectance of α LW to a value close to 75% at 12 μm. For wavelengths below 10.2 μm, good agreement was obtained between simulation [black dashed line in Fig. 8(a)] and experiment using the nand k-values measured for wavelengths below 5.5 μm and linearly extrapolating into the LWIR region (see Fig. 5). However, for simulations to match the measured data beyond 10 μm, the BaF 2 extinction coefficient needed to progressively increase with wavelength, reaching a value of close to 1 as wavelength approaches 12 μm (refer to data in Fig. 5(b) indicated as "BaF 2derived"). The corresponding agreement between measurement and simulation can be observed in Fig. 8(a) by a comparison of data measured for α LW with the OpenFilters simulation (red solid line) employing the derived values of k.
The observed decrease in the measured reflectance of α LW for longer wavelengths could be related to the growth method of the BaF 2 thin-films, which may result in higher absorption in BaF 2 for wavelengths beyond 10.2 μm in comparison to crystalline bulk BaF 2 32 that can provide >70% transmission for wavelengths up to 11 μm. It is also important to note that the BaF 2 spacer layer experiences a longer heat treatment in comparison to the BaF 2 mirror layer sandwiched between the two Ge layers. This can also possibly lead to a change in thin-film morphology and impact the optical characteristics of the BaF 2 layer. Therefore, we anticipate the potential for process improvements that could lead to higher reflectance of α LW beyond 10.2 μm wavelengths; however, this is beyond the scope of the current study.
The left side of Fig. 8(b) shows three measured reflectance spectra for a single point measurement located at the center of each of the square β MW DBRs of different areas and compares them to the simulated reflectance spectra predicted for this cross-sectional structure [depicted in the central inset of Fig. 8(b)]. An overall reflectance of above 94% was measured over the entire MWIR region for all three fabricated sizes. The reflectance measurements were in agreement with each other and were found to closely match the simulated reflectance spectrum where the overall reflectance value was predicted to remain above 97% within the entire MWIR region. Multiple single-point measurements were subsequently performed over the entire optical area to assess the reflectance spectra uniformity and repeatability for every point of observation. In the case of 500 μm × 500 μm sized βseries samples, an array of 6 × 6 equally distributed measurements was used to cover the entire optical area. The left side of Fig. 8(c) shows the measured reflectance spectra obtained at three different locations along the diagonal for a 500 μm × 500 μm sized β MW DBR [as shown in the central inset of Fig. 8(c)]. All three measured spectra compare favourably with the simulated reflectance data, which was obtained by OpenFilters software using the nand k-values extracted from the transmission response of a 2.6 μm thick BaF 2 layer. The measured reflectance was found to remain above 94% over the entire MWIR region for all three measurements, which closely matches the simulated reflectance, which is predicted to remain above 97% for the entire MWIR band. The observed variation in the measured data represents the spread across all spatially distributed measurements spanning the entire optical area, which is confined to within <2%. This observation was found to be common for every spatially distributed point of observation over the entire optical area for all measured β MW samples. As such, the observed uniformity in the spatially measured reflectance spectra can be correlated to the high degree of flatness of the suspended DBR layers.
Similar reflectance results were observed for β LW single point and multiple point measurements. Single point measurements were performed at the center of each of the square DBRs of different areas. As presented on the right-hand side of Fig. 8(b), the measured reflectance value was found to remain above 94% over the entire LWIR region, with a peak reflectance value of 98% at wavelengths around 10 μm. These measured reflectance characteristics of β LW compare favourably with the simulated reflectance values [represented by the red solid line on the righthand side of Fig. 8(b)] obtained using the derived k-values for BaF 2 presented in Fig. 5(b), which are predicted to remain above 97% for the entire LWIR region. Notably, apart from a relatively insignificant difference of <2% near the long wavelength end (12 μm), a similar reflectance spectrum was obtained via simulation using nand k-values of BaF 2 linearly extrapolated into the LWIR region (see Fig. 5), which is represented with a black dashed line on the right side of Fig. 8(b) and is characterised by a peak reflectance of above 99% along with an overall reflectance of more than 98% over the entire LWIR band. Since the reflectance values for all measured and simulated spectra for β LW remain high, it is reasonable to attribute the drop in measured reflectance of α LW as being solely due to the extra layer of BaF 2 centrally located within the α LW DBR, which is not present in β LW DBRs.
Similar to β MW , spatially distributed (multi-point) measurements were performed over the entire optical area of β LW . Exemplars of reflectance measurements for three different spots along the diagonal of the 500 μm × 500 μm sized β LW are shown on the right-hand side of Fig. 8(c). For each measured β LW spectrum the total reflectance was found to remain above 94% over the entire LWIR band, reaching a peak reflectance value of 99%. Furthermore, the spread across all spatially distributed measurements spanning the entire optical area is confined to within <2%. This was found to be common for all measured β LW samples. Again, this high degree of uniformity in the spatially measured reflectance spectra can be correlated to the high degree of flatness of the suspended DBR layers. Table 2 shows a comparison of the reflectance characteristics measured in this work with previously reported studies on surface micromachined DBRs in the MWIR and LWIR regions, along with the materials used to fabricate these DBRs. Prior literature reports peak reflectance values ranging from 90% to 94% in the MWIR region along with reflectance of ≥35% over the entire MWIR band, 25,56 whereas DBRs reported in this work have demonstrated superior peak reflectance of >97% and reflectance over the entire MWIR band surpassing 90%. In the case of LWIR DBRs, the results reported in this work have demonstrated superior or comparable peak reflectance and reflectance over the entire LWIR band of >97.5% and >94%, respectively, whereas peak reflectance and reflectance over the entire LWIR band in prior literature reports were >99% and >90%, respectively. 57 Summarizing the characteristics shown in Fig. 8, it can be stated that highly reflective βseries DBRs have been successfully fabricated for both MWIR and LWIR regions with good agreement between simulation and measurement, which renders them viable candidates for the fabrication of narrow FWHM MWIR and LWIR FP filters. In addition, αseries DBRs were also characterized to be highly reflective in the MWIR band making them suitable for the realization of narrow FWHM MWIR FP filters. However, a sharp drop in the measured reflectance spectra of αseries DBRs in the LWIR band observed for wavelengths longer than 10.2 μm limits their applicability in realizing narrow FWHM FP filters that cover the entire LWIR band. In spite of this, from a fabrication, reproducibility and uniformity point of view, αseries DBRs are preferable since they do not contain any suspended layers and, hence, they are not subject to interlayer variability due to air-gap variations caused by stress imbalance or due to actuation.

Fabry-Pérot Interferometer for Infrared Imaging and Sensing
Based on the reflectance spectra demonstrated by DBRs in the MWIR and LWIR bands, we evaluated the suitability of αand β-DBRs toward the realization of FPIs for hyperspectral sensing and imaging applications. For LWIR FPIs, this suitability is only assessed up to a wavelength of 11 μm due to excessive absorption within the BaF 2 layer beyond this wavelength. The αand β-DBRs were used in three different combinations in an FPI arrangement to achieve a narrow linewidth of less than 30 to 50 nm and 80 to 110 nm in the case of MWIR and LWIR spectral bands, respectively, required for hyperspectral sensing and imaging applications. This involved assessment of the optical performance of (1) a solid-material FPI (αα-FPI) consisting of a solid-material freestanding top DBR (α) and a solid-material fixed bottom DBR (α) on an Si substrate, separated by an air-gap optical cavity [represented on the left-hand side of Fig. 9(a)]; (2) a hybrid FPI (αβ-FPI) consisting of an air-gap freestanding top DBR (β) and a solid-material fixed bottom DBR (α) on an Si substrate, separated by an air-gap optical cavity [see left-hand side of Fig. 9(b)]; (3) an air-gap FPI (ββ-FPI) consisting of an air-gap freestanding top DBR (β) and an air-gap fixed bottom DBR (β) on an Si substrate, separated by an air-gap optical cavity [see left-hand side of Fig. 9(c)]. The simulated optical performance of FPI structures consisting of these three combinations of αand β-DBRs is shown on the right-hand side of Fig. 9. The transmission response plotted logarithmically in dB units is shown in Fig. 10 to present the expected out-of-band rejection performance. It is important to note that these simulation results are valid for imperfection-free FPIs, where fabrication induced variations are not considered, such as surface roughness and parallelism between the top and bottom DBRs. The λ∕4-thicknesses of the thin-films are presented in Table 1. In order to investigate the suitability of αα-, αβand ββ-FPIs, the optical transmission response of the FPIs was modeled for various optical cavity gaps in the MWIR and LWIR bands. In our modeling, a λ∕4-thick BaF 2 layer is present on both sides of a double-side polished <100> oriented 300 μm thick Si substrate. The BaF 2 layer on the front side serves as a spacer layer between the bottom DBR and the silicon substrate, and on the backside serves as an anti-reflection coating to suppress the effect of multiple reflections.  Figures 9 and 10 show exemplar transmission peaks, linewidths, and out-of-band rejection ratio of αα, αβ, and ββ based FPIs in the MWIR and LWIR regions for the designed center wavelengths as well as for the shorter and longer bounds of each wavelength band and are summarized in Fig. 11 for the full spectral band. For the longer wavelength bound where the first order transmission peak is located near a wavelength of 5 and 12 μm for MWIR and LWIR bands, respectively, the second-order transmission peak is located near the shorter wavelength end, which is also shown in Figs. 9 and 10 to indicate the extent of the free spectral range (FSR). Figures 11(a) and 11(b) presents a summary of the predicted peak transmission values and linewidth values, respectively, for the FPI transmission peaks over the full MWIR and LWIR spectral bands. For the case of MWIR FPIs, a peak transmission above 90% for ααand ββ-FPIs and above 87% for αβ-FPIs can be achieved over the entire MWIR band, as depicted for exemplar transmission peaks in Fig. 9 and summarized in Fig. 11(a) for the full spectral band. The transmission peaks for these FPIs are predicted to have a linewidth at the design center wavelength of 4 μm equal to 20 nm, 14 nm, and 11 nm for αα-, αβand ββ-FPIs, respectively, as shown in Fig. 9 and summarized in Fig. 11(b). The linewidth of FPIs was found to broaden by almost a factor of 3 in comparison to the linewidth at the center wavelength for wavelengths near the shorter and longer wavelength bounds of the MWIR band. Linewidth values of 51 and 40 nm, 39 and 28 nm, and 27 and 21 nm are predicted for the shorter and longer wavelength bounds of the MWIR band Fig. 9 Modeled optical transmission of two separate FPIs designed to operate in either the MWIR or LWIR spectral band by incorporating αand βseries DBRs with different optical cavity lengths specific to the MWIR or LWIR spectral bands. Three combinations of DBRs (a) ααpairs, (b) αβpairs and (c) ββpairs were investigated for spectral characteristics of FPIs. The corresponding cross-sectional geometries are presented schematically on the left-hand side and were designed for a center wavelength of 4 μm and 10 μm for MWIR and LWIR spectral bands, respectively. The air-gap optical cavity distance, d , separating the DBR pairs that determine the transmission wavelengths are indicated next to the peaks on the right-hand side. Exemplar FSR for the MWIR band is indicated for d ¼ 2.675 μm for all three DBR combinations as the wavelength separation between the first-and second-order FPI transmission peaks. In the case of LWIR, due to high optical absorption in the BaF 2 mirror layer beyond 10.2 μm, the extent of the LWIR FSR is not shown.  for αα-, αβand ββ-FPIs, respectively. The simulation shows that an FSR of > 2 μm can be achieved for αα-, αβand ββ-FPIs, as shown in Fig. 9. Furthermore, as shown in Fig. 10, the out-of-band rejection characteristics for the design center wavelength of 4 μm are predicted to be >65, >70, and >75 dB for αα-, αβ-, and ββ-FPIs, respectively. This is expected to reduce to ∼20 dB (45 dB), 25 dB (50 dB), and 30 dB (50 dB) for the shorter (longer) wavelength ends of the MWIR band for αα-, αβand ββ-FPIs, respectively.
Similarly, the simulations of αα-, αβ-, and ββ-FPIs for the LWIR region show a peak transmission above 90% for αα-FPIs and above 97% for αβand ββ-FPIs can be achieved for the shorter wavelengths (8 to 10 μm) of the LWIR band. The peak transmission drops to 50% at wavelengths of 10.2 μm, 10.3 μm and 11 μm for αα-, αβand ββ-FPIs, respectively, which restricts the utilization of FPIs over the entire LWIR band. The simulations show that these FPIs have linewidth values equal to the 51, 36, and 29 nm of the center design wavelength of 10 μm for αα-, αβ-, and ββ-FPIs, respectively. The linewidth of the FPIs broadens by up to 1.6 times the linewidth value at the center design wavelength for wavelengths near the short wavelength end of the LWIR band. For wavelengths longer than 10 μm, the peak transmission drops abruptly due to optical absorption in the BaF 2 mirror layer, therefore the extent of the LWIR FSR is not shown. The simulation data presented in Fig. 10 shows that for the design center wavelength of 10 μm, out-of-band rejection ratios of >65, >70, and >75 dB can be achieved for αα-, αβ-, and ββ-FPI designs, respectively. This is expected to reduce to approximately 35, 40, and 45 dB for the shorter end (8 μm) of the LWIR band for αα-, αβ-, and ββ-FPIs, respectively.
The simulated spectral characteristics of FPIs are summarized in Table 3 and, for comparison, a set of optical requirements of FPIs for hyperspectral sensing and imaging applications. Typically, to perform hyperspectral sensing and imaging, it is required to have the peak transmission above 50% and the spectral width below 1% of the design wavelength. In the case of MWIR FPIs, a linewidth of much lower than 1% of the targeted wavelength can be easily achieved for wavelengths between 3.2 and 5 μm using ααand αβpair FPIs and over the entire MWIR spectrum for ββ-FPIs, as shown in Fig. 11(b). The linewidth broadens up to 1.7% (51 nm) and 1.3% (39 nm) of the design wavelength for ααand αβ-FPIs, respectively, while still covering the entire MWIR band. This linewidth over the entire MWIR spectrum is very useful for hyperspectral sensing and imaging applications. For LWIR FPIs, the peak transmission starts to drop abruptly after 10 μm, which limits their operating range in the LWIR region. The simulations show that for αα-, αβ-, and ββ-FPIs, the peak transmission drops to a level below 50% for wavelengths longer than 10.2, 10.3, and 11 μm, respectively [as depicted in Fig. 11(a)], and is associated with absorption phenomena observed in the BaF 2 mirror layer for longer wavelengths. The αα-, αβ-, and ββ-FPIs demonstrated a narrow linewidth of less than 1% of the design wavelength for wavelengths 8 to 10.2 μm, 8 to 10.3 μm, and 8 to 11 μm, respectively, in the LWIR spectral band along with peak transmission above 50%. The FPI simulations based on the optical performance of the DBRs in the MWIR spectrum show that all three combinations of αα-, αβ-, and ββ-FPIs can satisfy the optical requirements needed for hyperspectral sensing and imaging applications across the MWIR band. For the LWIR case, the peak transmission drops abruptly for wavelengths above 10 μm due to absorption losses in the BaF 2 mirror layers, allowing these FPIs to be used only within the shorter wavelength half of the LWIR band (8 to 10 μm) along with the attractive peak transmission of above 90%. This range can be extended up to 10.2, 10.3, and 11 μm with a peak transmission of above 50% for αα-, αβand ββ-FPIs along with linewidth of <1%, as shown in Fig. 11. Hence, we can conclude that αα-, αβand ββ-FPIs can be used for wavelengths in the 8 to 11 μm range based on their structural geometry while maintaining a spectral transmission above 50% and a linewidth below 1%. Additionally, simulation results presented in Figs. 9-11 show that the ββ-FPIs are superior and have more potential to produce narrowband FPIs. However, it is very difficult to fabricate these FPIs due to their complex fabrication process with multiple airgaps. On the other hand, αα-FPIs based on solid-material DBRs are the most practical approach to realize narrowband FPIs from the fabrication point of view since αseries DBRs are not subject to interlayer variability due to air-gap variations caused by stress imbalance or during actuation in a tunable filter FPI configuration.

Summary and Conclusions
The fabrication and optical characterization of Ge and BaF 2 based solid-material and air-gap (α-and βseries) DBRs have been presented in this paper. DBRs with high reflectivity were designed and demonstrated for operation in either the MWIR or LWIR wavelength ranges. In the case of αseries DBRs, a drop in reflectance of the DBRs is noticed toward the long wavelength end of the wavelength range in both the MWIR (3 to 5 μm) and LWIR (8 to 12 μm) spectral bands. The MWIR DBRs demonstrated a moderate drop in the measured reflectance, to 90%, in comparison to the simulated reflectance of 95%. However, for LWIR DBRs, the reflectance drops sharply after 10 μm and reaches 76%, at a wavelength of 12 μm, which limits their applicability in the realization of narrow FWHM Fabry-Pérot filters over the entire LWIR band. On the other hand, βseries DBRs were demonstrated with optical dimensions of 200 μm × 200 μm, 500 μm × 500 μm and 1 mm × 1 mm, and exhibited flatness of the order of 10 to 20 nm over the entire optical area. Single point spectral measurements at the center of devices show good agreement with simulated optical models for both MWIR and LWIR DBRs. The fabricated βseries DBRs have reflectance over 94%, in comparison to the simulated reflectance above 97%. Multiple single point measurements were also performed to evaluate the reflectance spectra uniformity and repeatability for every point of observation over the entire optical area, especially in the case of βseries DBRs and to confirm a high degree of reflectance uniformity over the entire optical area.
The DBR experimental results extend the current MEMS approach toward the fabrication of FPIs for narrow-band hyperspectral sensing and imaging applications. To this end, optical transmission of three different types of solid, hybrid, and air-gap (αα, αβ, and ββ, respectively) FPIs was examined based on three-layer αand βseries DBRs in the MWIR and LWIR spectral bands. Optical modeling indicates that in the case of the MWIR region, the αα-, αβ-, and ββ-FPIs cover 90% of the MWIR spectral band with peak transmission above 90% and spectral width <1% of the targeted wavelength. However, for the LWIR spectral band, the αα-, αβ-, and ββ-FPIs provide an operating range of 8 to 10.2 μm, 8 to 10.3 μm and 8 to 11 μm, respectively, while maintaining the peak transmission above 50%, with a narrow spectral linewidth <1% of the targeted wavelength, which exceeds the optical requirements for hyperspectral imaging applications. Figure 12 provides the actual thicknesses of thermally deposited λ∕4-thick optical thin-films, measured using Dektak 150 surface profiler. Figures 12(a) and 12(b) represent the solidmaterial and air-gap (α-and βseries) DBRs designed in MWIR and LWIR spectral bands, respectively. Figure 13 provides original images of structural characterization of α LW DBR. Figure 13(a) shows the cross-sectional scanning electron micrograph. Figures 13(b)-13(f) shows material elemental maps over the cross-section, and the compositional analysis is shown in Fig. 13(g).