2.1.

Thin-Film Deposition

The Ge and ${\mathrm{BaF}}_2$ layers were deposited under high vacuum ($<{10}^{-6}\mathrm{mbar}$), 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 ${\mathrm{BaF}}_2$ 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 $\ge 100°\mathrm{C}$, the temperature variation could readily be controlled within a tolerance of $\pm 5°\mathrm{C}$. 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 $1.5\pm 0.1Å/\mathrm{s}$ 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 ${\mathrm{BaF}}_2$ thin-films was performed at a deposition rate of $5\pm 0.2Å/\mathrm{s}$, 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 ${\mathrm{BaF}}_2$ 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 ${\mathrm{BaF}}_2$ thin-films. An exemplar of temperature profiles for ${\mathrm{BaF}}_2$ thin-films deposited at 50°C (red) and 100°C (blue) is shown in Fig. 2.

Fig. 2

Substrate temperature profiles for Ge and ${\mathrm{BaF}}_2$ thin-films deposited at 50°C and 100°C. The dashed lines represent the substrate heating and cooling periods before and after the thin-film deposition periods represented by the solid lines.

A significant challenge during the deposition of the relatively thick Ge and ${\mathrm{BaF}}_2$ thin-films of the order of $1\mu \mathrm{m}$ 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 ${\mathrm{BaF}}_2$ layers and to prevent any spitting or streaming. The issue of boat failure was not observed during the deposition of ${\mathrm{BaF}}_2$ films. However, a sudden failure of the quartz crystal microbalance was observed regularly during ${\mathrm{BaF}}_2$ 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.

2.2.

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 $\alpha$– and $\beta$– series, respectively. The $\alpha$– series DBRs consisted of $\lambda /4$-thick $\mathrm{Ge}/{\mathrm{BaF}}_2/\mathrm{Ge}$ layers deposited on an Si substrate coated with a $\lambda /4$-thick ${\mathrm{BaF}}_2$ spacer layer, whereas the, $\beta$– series DBRs consisted of $\lambda /4$-thick Ge/Air/Ge layers. The intermediate ${\mathrm{BaF}}_2$ mirror layer existing in $\alpha$– series DBRs was replaced with an air-gap in $\beta$– series 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 ($\beta$– 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 $\alpha$– and $\beta$– series DBRs is shown in Fig. 3.

Fig. 3

The DBR fabrication process. Thicknesses are not to scale. (a) Deposition of a $\lambda /4$-thick low refractive index ${\mathrm{BaF}}_2$ spacer layer on Si substrate; (b) deposition of first high refractive index Ge layer. In the case of $\alpha$ – series DBRs; (c)–(d) deposition of $\lambda /4$-thick low and high refractive index ${\mathrm{BaF}}_2$ and Ge layers. In the case of $\beta$ – series DBRs: (e) spinning and hard-baking of PMMA A9 sacrificial layer and deposition of the second quarter-wavelength thick Ge thin film on top of PMMA A9; (f)–(g) patterning of etching holes through the top Ge layer using an AZ2035 photoresist mask, and dry release of air-gap DBRs via the removal of PMMA layer in the ${\mathrm{O}}_2$ plasma.

2.3.

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 $\lambda /4$-thick Ge and ${\mathrm{BaF}}_2$ films of targeted center LW of $10\mu \mathrm{m}$ were deposited on $100\mu \mathrm{m}$ 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 $100\text{-}\mu \mathrm{m}$ thin Si substrates before and after deposition. The same tool was later used to perform flatness measurement over the free-standing membranes of fabricated $\beta$– series 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 ${\mathrm{BaF}}_2$ layers to investigate the refractive index and extinction coefficient in the IR region, which were then compared with past studies.^31,32 Finally, the ${\mathrm{BaF}}_2$ 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 $35\mu \mathrm{m}\times 35\mu \mathrm{m}$. The optical transfer matrix method (OpenFilters⁵¹) 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 ${\mathrm{BaF}}_2$ being used in the model.

Cross-sectional analysis of DBRs was performed using an FEI Helios Nanolab ultra high-resolution 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.

3.1.

Thin-Film Stress

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 ${\mathrm{BaF}}_2$ 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 $\lambda /4$ 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 ($<100\mathrm{MPa}$) can be achieved when the deposition was initiated and maintained at 150°C, as shown in Fig. 4. On the other hand, ${\mathrm{BaF}}_2$ 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).

Fig. 4

Residual stress in thermally deposited Ge and ${\mathrm{BaF}}_2$ $\lambda /4$-thick films as a function of initial deposition temperature. Thin-film stress was calculated using Stoney’s formula by measuring the thin film stress-induced substrate curvature.

3.2.

Characterization of Optical Parameters: Refractive Index and Extinction Coefficient

Ge and ${\mathrm{BaF}}_2$ 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.^29–32,53 The optical properties of ${\mathrm{BaF}}_2$ were extracted from the transmission response of a $2.6\text{-}\mu \mathrm{m}$ thick layer of ${\mathrm{BaF}}_2$ deposited on a silicon substrate. This was recorded for wavelengths from 1.2 to $12\mu \mathrm{m}$ and analysed with the Cauchy dispersion model using general-purpose software (NKDMatl⁵⁴) to extract the $n$- and $k$-values. The recorded transmission spectrum was found to adequately match the Cauchy dispersion model for wavelengths up to $5.5\mu \mathrm{m}$; however, the quality of the fit was reduced for wavelengths longer than $5.5\mu \mathrm{m}$. Therefore, we used the extracted $n$- and $k$-values only for wavelengths below $5.5\mu \mathrm{m}$, which are indicated in Figs. 5(a) and 5(b) as magenta open diamond symbols. For the purpose of comparison, Fig. 5(a) includes $n$-values obtained by Querry,³² as indicated by the red solid line; whereas $k$-values reported were zero and are not represented on the log scale in Fig. 5(b). We have measured $n$-values of 1.37 for ${\mathrm{BaF}}_2$ and $k$-values of near-zero, which compares favourably with the measurements of Querry, where the $n$-values were found to range from 1.47 to 1.36 with a $k$-value of zero over the wavelength range 0.6 to $12.2\mu \mathrm{m}$. Based on this favourable agreement between our measurement and previous literature for wavelengths below $5.5\mu \mathrm{m}$, our measured $n$- and $k$-values were linearly extrapolated into the LWIR region, as indicated in Figs. 5(a) and 5(b) with magenta dashed lines. This will be discussed later in the paper with a comparison to the data derived from the characterised DBR performance, which is indicated in Fig. 5(b) as blue open square symbols. Ge and Si $n$- and $k$-values used in this study are also shown in Fig. 5.^29,53,55

Fig. 5

Measured (a) refractive index ($n$), and (b) extinction coefficient ($k$) of ${\mathrm{BaF}}_2$ thin-films and their comparison with previous studies. The $n$- and $k$-values in this study (indicated as “extracted”) were measured from the transmission of a $2.6\text{-}\mu \mathrm{m}$ thick ${\mathrm{BaF}}_2$ layer, which was fitted with the Cauchy dispersion model only for wavelengths shorter than $5.5\mu \mathrm{m}$. Stimulated by a favourable agreement with prior literature (Querry³²) the $n$- and $k$-values were linearly projected beyond $5.5\mu \mathrm{m}$ into the LWIR region for wavelengths up to $12\mu \mathrm{m}$ and are indicated by dashed lines. The reported $k$-values for ${\mathrm{BaF}}_2$ were zero and are not represented on the log scale in (b). The ${\mathrm{BaF}}_2$ $k$-values indicated as “derived” were obtained in order to achieve agreement between the measured and simulated reflectance spectra of ${\alpha }_{LW}$ by adjusting the $k$-values during fitting iterations. The $n$- and $k$-values of Si, Ge, and ${\mathrm{BaF}}_2$ used in this study have been taken from Refs. 2930.31.–32, 53, and 55.

3.3.

Structural Characterization of DBRs

Extensive characterization was performed to investigate the layered structures formed by sequential depositions of Ge and ${\mathrm{BaF}}_2$ $\lambda /4$-thick films to form the DBRs. Figure 6(a) shows the cross-sectional scanning electron micrograph of an exemplar ${\alpha }_{LW}$ 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 ${\mathrm{BaF}}_2$ 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 ${\alpha }_{MW}$ and ${\alpha }_{LW}$ DBRs. In the case of $\beta$–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 $\beta$–series DBRs to show similar characteristics.

Fig. 6

FIB-SEM cross-section of ${\alpha }_{LW}$, elemental mapping, and compositional analysis. The roughness in (a) on the top surface has been induced by the cross-section preparation process of the FIB method and is not representative of the actual as-fabricated thin-film surface roughness. Colour legend of the mapped elements is common to all elemental maps presented in (b)–(f). (g) Compositional analysis describing the weight (%) of each element present within the field of view. Images (b)–(f) are post-processed for better visualisation, and original images are provided in the appendix (see Fig. 13).

3.4.

Membrane Flatness Profiles

Figure 7(a) shows an optical microscopic image of a released $500\mu \mathrm{m}\times 500\mu \mathrm{m}$ ${\beta }_{LW}$ – series 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 ${\beta }_{LW}$ – series 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 ${\beta }_{LW}$ – series 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 $\alpha$– series DBRs for similar line scan lengths. Since there are no suspended layers, it can be inferred that any bowing reported for the $\alpha$– DBRs is mainly due to substrate deformation arising from film stress. The required level of flatness, in the range of $<20\mathrm{nm}$, was achieved for both $\alpha$– and $\beta$– series DBRs and indicates that negligible performance degradation is expected since 20 nm of bowing is significantly below the required $\lambda /20$ optical condition at the center wavelength by more than two orders of magnitude.

Fig. 7

(a) Micrograph of a dry released $500\mu \mathrm{m}\times 500\mu \mathrm{m}$ air-gap DBR. The edge profile has been drawn, and the colour of the unreleased area has been lightened to delineate the released area from the unreleased area. The dashed diagonal line AA’ is indicative of the position in which the membrane flatness measurements were performed. (b) Line-scans taken diagonally over the optical surface of ${\beta }_{LW}$ – series DBRs, indicating concave-upwards bowing of 10–20 nm was observed across the surface of fabricated LWIR DBRs. Profiles were measured for all device sizes using a Zygo Newview 6 K white light optical surface profiler. The rectangular area indicated by the dotted line in (b) is magnified vertically in the inset of (b).

3.5.

DBR Reflectance Spectra

Figure 8 shows both simulated and measured reflectance of $\alpha$– and $\beta$– series DBRs for single-point [Figs. 8(a) and 8(b)] and spatially distributed (multi-point) measurements [Fig. 8(c)]. 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 $\alpha$– and $\beta$– series 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 $\beta$– series DBRs [see Fig. 8(c)]. A measurement spot size of approximately $35\mu \mathrm{m}\times 35\mu \mathrm{m}$ 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 $500\mu \mathrm{m}\times 500\mu \mathrm{m}$ sized $\beta$– series sample in Fig. 8(c). The left side of Fig. 8(a) shows that the peak reflectance value measured for ${\alpha }_{MW}$ (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 $5\mu \mathrm{m}$). 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 $\alpha$– series DBRs, inter-layer bowing was not of concern, and there was little motivation to perform spatially distributed measurements.

Fig. 8

Measured and simulated reflectance spectra for (a) $\alpha$– and (b) $\beta$– series DBRs for single-point measurements at the DBR center, and (c) diagonally distributed (multi-point) reflectance spectra measurements over the suspended square area of a $500\mu \mathrm{m}\times 500\mu \mathrm{m}$ $\beta$– series DBR. The left and right sides of the figure show the data obtained for the MWIR and LWIR bands, respectively, using different $\alpha$– and $\beta$– series DBR structures with thin-films of optical thicknesses appropriate for either MWIR or LWIR bands. The measurements in (b) have been performed at the center points of the $200\mu \mathrm{m}\times 200\mu \mathrm{m}$, $500\mu \mathrm{m}\times 500\mu \mathrm{m}$ and $1\mathrm{mm}\times 1\mathrm{mm}$ sized $\beta$– series DBRs. 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 $2.6\mu \mathrm{m}$ thick ${\mathrm{BaF}}_2$ 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 “$k$-derived”) that were adjusted during the fitting iteration in order to achieve favourable agreement between measured and simulated reflectance spectra of ${\alpha }_{LW}$ (red solid lines).

The measured reflectance spectrum for ${\alpha }_{LW}$ [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 $10.2\mu \mathrm{m}$. However, a notable drop in the measured reflectance was observed for longer wavelengths, which can be associated with increased absorption in the ${\mathrm{BaF}}_2$ layer for wavelengths beyond $10.2\mu \mathrm{m}$, resulting in a drop in the reflectance of ${\alpha }_{LW}$ to a value close to 75% at $12\mu \mathrm{m}$. For wavelengths below $10.2\mu \mathrm{m}$, good agreement was obtained between simulation [black dashed line in Fig. 8(a)] and experiment using the $n$- and $k$-values measured for wavelengths below $5.5\mu \mathrm{m}$ and linearly extrapolating into the LWIR region (see Fig. 5). However, for simulations to match the measured data beyond $10\mu \mathrm{m}$, the ${\mathrm{BaF}}_2$ extinction coefficient needed to progressively increase with wavelength, reaching a value of close to 1 as wavelength approaches $12\mu \mathrm{m}$ (refer to data in Fig. 5(b) indicated as “${\mathrm{BaF}}_2$ – derived”). The corresponding agreement between measurement and simulation can be observed in Fig. 8(a) by a comparison of data measured for ${\alpha }_{LW}$ with the OpenFilters simulation (red solid line) employing the derived values of $k$.

The observed decrease in the measured reflectance of ${\alpha }_{LW}$ for longer wavelengths could be related to the growth method of the ${\mathrm{BaF}}_2$ thin-films, which may result in higher absorption in ${\mathrm{BaF}}_2$ for wavelengths beyond $10.2\mu \mathrm{m}$ in comparison to crystalline bulk ${\mathrm{BaF}}_2$³² that can provide $>70\%$ transmission for wavelengths up to $11\mu \mathrm{m}$. It is also important to note that the ${\mathrm{BaF}}_2$ spacer layer experiences a longer heat treatment in comparison to the ${\mathrm{BaF}}_2$ 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 ${\mathrm{BaF}}_2$ layer. Therefore, we anticipate the potential for process improvements that could lead to higher reflectance of ${\alpha }_{LW}$ beyond $10.2\mu \mathrm{m}$ 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 ${\beta }_{MW}$ 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 $500\mu \mathrm{m}\times 500\mu \mathrm{m}$ sized $\beta$– series samples, an array of $6\times 6$ 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 $500\mu \mathrm{m}\times 500\mu \mathrm{m}$ sized ${\beta }_{MW}$ 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 $n$- and $k$-values extracted from the transmission response of a $2.6\mu \mathrm{m}$ thick ${\mathrm{BaF}}_2$ 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 ${\beta }_{MW}$ 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 ${\beta }_{LW}$ 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 $10\mu \mathrm{m}$. These measured reflectance characteristics of ${\beta }_{LW}$ compare favourably with the simulated reflectance values [represented by the red solid line on the right-hand side of Fig. 8(b)] obtained using the derived $k$-values for ${\mathrm{BaF}}_2$ 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 ($12\mu \mathrm{m}$), a similar reflectance spectrum was obtained via simulation using $n$- and $k$-values of ${\mathrm{BaF}}_2$ 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 ${\beta }_{LW}$ remain high, it is reasonable to attribute the drop in measured reflectance of ${\alpha }_{LW}$ as being solely due to the extra layer of ${\mathrm{BaF}}_2$ centrally located within the ${\alpha }_{LW}$ DBR, which is not present in ${\beta }_{LW}$ DBRs.

Similar to ${\beta }_{MW}$, spatially distributed (multi-point) measurements were performed over the entire optical area of ${\beta }_{LW}$. Exemplars of reflectance measurements for three different spots along the diagonal of the $500\mu \mathrm{m}\times 500\mu \mathrm{m}$ sized ${\beta }_{LW}$ are shown on the right-hand side of Fig. 8(c). For each measured ${\beta }_{LW}$ 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 ${\beta }_{LW}$ 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 $\ge 35\%$ 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

Table 2

Comparison of results presented in this work with prior literature reports on surface micromachined DBRs in the MWIR and LWIR bands.

Summarizing the characteristics shown in Fig. 8, it can be stated that highly reflective $\beta$– series 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, $\alpha$ – series 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 $\alpha$– series DBRs in the LWIR band observed for wavelengths longer than $10.2\mu \mathrm{m}$ 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, $\alpha$– series 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.