Grayscale-to-Color: Scalable Fabrication of Custom Multispectral Filter Arrays

Snapshot multispectral image (MSI) sensors have been proposed as a key enabler for a plethora of multispectral imaging applications, from diagnostic medical imaging to remote sensing. With each application requiring a different set, and number, of spectral bands, the absence of a scalable, cost-effective manufacturing solution for custom multispectral filter arrays (MSFAs) has prevented widespread MSI adoption. Despite recent nanophotonic-based efforts, such as plasmonic or high-index metasurface arrays, large-area MSFA manufacturing still consists of many-layer dielectric (Fabry–Perot) stacks, requiring separate complex lithography steps for each spectral band and multiple material compositions for each. It is an expensive, cumbersome, and inflexible undertaking, but yields optimal optical performance. Here, we demonstrate a manufacturing process that enables cost-effective wafer-level fabrication of custom MSFAs in a single lithographic step, maintaining high efficiencies (∼75%) and narrow line widths (∼25 nm) across the visible to near-infrared. By merging grayscale (analog) lithography with metal–insulator–metal (MIM) Fabry–Perot cavities, whereby exposure dose controls cavity thickness, we demonstrate simplified fabrication of MSFAs up to N-wavelength bands. The concept is first proven using low-volume electron beam lithography, followed by the demonstration of large-volume UV mask-based photolithography with MSFAs produced at the wafer level. Our framework provides an attractive alternative to conventional MSFA manufacture and metasurface-based spectral filters by reducing both fabrication complexity and cost of these intricate optical devices, while increasing customizability.


Addition of an encapsulation layer
Depositing an inert capping layer on top of the MIM stack provides chemical and mechanical durability, preventing oxidation and increasing rigidity. A material such as MgF 2 (similar to quartz) provides these qualities. It is relatively inert, mechanically rigid, optically transparent and moreover, relatively straightforward to deposit post-metallization of the second mirror. Supplementary Figure 2 shows the simulation of the transmission of the Ag (26 nm)-MIM stack (125 nm insulator) as a function of MgF 2 encapsulation layer thickness (0-50 nm). A dispersive material model 7 is used for its refractive index. It is observed the transmission peak slightly shifts to longer wavelengths with increasing MgF 2 thickness and increases a small amount. The FWHM also gradually increases. We therefore conclude that the encapsulation layer provides negligible degradation in transmission characteristics, and if anything, slightly improves them. S3

Angle dependency
In imaging optics, a high F-number (numerical aperture ~ 0) typically implies parallel rays incident on the sensor array, while a low F-number implies the rays arrive at an angle (numerical aperture > 0). For multi-layered MSFAs, the spectral response is often a function of incidence angle, which in combination with polarization angle, affects the transmission characteristics of the filter. Figure 8 shows FDTD simulations (Bloch boundary conditions and angled source using BFAST conditions) of the MIM structure under orthogonal incident polarizations (TE and TM) for varying angles of incidence up to 60º. For conventional CMOS image sensors, the chief ray angle (CRA) -broadly defining the cone of angles incident upon the center top of the pixel -can be up to  30 (with the larger angles, e.g. 30, more commonplace in smartphone sensors). It can be observed that, between 0 -30º incident angle, the peak spectral position varies from ~590-578 nm (Δλ ~ 12 nm) for TM and from ~590 -565 nm (Δλ ~ 25 nm) for TE. The transmission intensity remains relatively constant (~85%) across these angles. The FWHM (~36 nm at 0º, for TM and TE) narrows slightly by ~5 nm for TE, and for TM widens by ~15 nm (at 30º). Beyond 30º, the spectral shift increases more significantly, especially for TE-polarization.

Supplementary
For interference filters in general, there is typically a blue-shift of the resonant peak arising from a phase-shift reduction in the dielectric layer for larger angles. 8 For interference based optical filters, there are methods to compensate for such a spectral shift, including: in-plane nanostructuring; incorporation of additional dielectric layers; and addition of microlens arrays. 8,9 Conversely, for the relatively thin (<200 nm thick) Ag-MIM filters here, that only support first-order FP-type modes, the angular dependency is somewhat reduced compared to thicker structures with a high number of alternating index layers. The small vertical-to-lateral aspect ratio of the MIM pixels result in relatively small angle dependency. S4

Dose variation
As described in the main manuscript, the effect of exposure dose and correct choice of development time (and developer) controls the final thickness of the remaining resist (insulator) in a MIM cavity, hence controlling the center position of the transmission spectra. To demonstrate this, Supplementary Figure 3 shows the transmission spectra of a set of 5 µm pixels which vary in exposure dose across three different development times. It can be observed-both quantitatively in (a) and visually in (b)-that for a constant dose range (0.1-0.7 Cm -2 here) the position of the peak blue-shifts with increasing development time. As the developer is selectively removing resist that has not been sufficiently cross-linked (due to MaN-series photoresist being negative tone), a longer development time results in more resist being removed, hence thinner cavity and shorter wavelength mode. This is further illustrated in Supplementary Figure 5, which shows a rectangular array with transmission wavelength across the visible spectrum and respective SEM micrograph.

Proximity effect
In EBL, the proximity effect is the unwanted exposure of regions adjacent to the pattern being exposed due to electron scattering events in the resist. The proximity effect can be lessened through the translation of the grayscale MSFA approach to larger batch processing i.e. photolithography. However, for this work (in which EBL is utilized) as the density of features increases, the proximity effect is more pronounced. In this work, each filter pixel has its center wavelength defined by a specific exposure dose. As a result of the proximity effect, the total dose applied to a specific region (pixel) is additionally dependent on the dose applied to surrounding pixels. 10,11 The proximity effect can be observed by comparing the patterning of isolated pixels (i.e. arrays with non-exposed spacing between pixels) to dense arrays; the dose required to achieve a specific wavelength (resist thickness) is lower in dense arrays than it is in isolated regions. Supplementary Figure 6 (a) shows an optical micrograph (transmission) of the dose test array, in which the regions (1) and (2) are arrays of equally sized pixels which both also equally increase in exposure dose (from ~0.17-0.52 Cm -2 ; 10s development time), but with 'isolated' and 'dense' configurations respectively. It is observed that the arrays in (2) are highly red shifted in transmission indicating a larger thickness in remaining resist and thus greater accumulated exposure dose. This is due to the unwanted cumulative adjacent exposure from the neighboring pixels. Supplementary Figure 6 (b) is an additional example of the effect: a 1951 USAF resolution target, in which each element of the line triplets is given a different exposure dose. The final thickness/filtered wavelength is a function of spatial position within the rectangle as the averaged dose density is larger at the center of the rectangle than it is in the corner/edges. S5 The impact of the proximity effect in a Bayer filter array was investigated by examining the transmission characteristics of a 3-channel RGB array as a function of position from the edge of the array (Supplementary Figure 7). The center wavelength of the transmission peak (in both green and blue pixels) appears to remain relatively constant following a sharp change approximately 50-100 µm from the edges. This is likely due to the cumulative dose density remaining approximately constant for pixels away from the edge of the array, a consequence of the periodic array pattern. A simple empirical correction adopted for this work was to 'over pattern' each MSFA, such that the area of interest (image sensor area) is >100 µm from the edge of the MSFA pattern. This approach also demands reducing the dose profile to compensate for increased cumulative exposure in the central region. It would also be possible to perform Monte Carlo electron scattering simulations for each pattern to optimize the dose patterns and avoid this empirical correction, however, the commercial software to perform these simulations was not available for this study.

Resist thermal reflow
Thermal reflow is a fabrication processing technique that involves the thermal treatment of a photoresist (post-development) such that the resist is brought to a temperature ≳ glass transition temperature. 12 By doing so, the resist 'reflows', fully or partially depending on the temperature and time, which can be used to smooth the resist. The technique, for example, can be used to turn staircase-like 3D-pattens to 3D slopes, 12 or to fabricate microlens arrays. In this work, shown with several examples in Supplementary Figure 21, we used thermal reflow to smooth the resist surface post-development, but pre-second metal mirror deposition, to flatten/smooth the second mirror surface, narrowing the FWHM and boosting transmission efficiency.

Variability in optical performance across array
The intra-and inter-chip variability of the optical characteristics of fabricated MSFAs is shown in Supplementary Figure 10 and Supplementary Figure 11. For each MSFA, a range of unit cells were chosen at random across the array (but at least 100µm from the border of the array due to the proximity effect issue described in Section 2.2) and the filter spectra were recorded and analyzed using an optical microscope. Supplementary Figure 10 shows the variability in peak wavelength across different pixels for RGB MSFAs (i.e. Bayer mosaics) for three different processing recipes corresponding to three differently processed separate chips (listed below, Recipes 1-3). (a) and (b) are of two different dose (D) profiles for the 3-channels. For each 'recipe' (described in the caption), spectra of four randomly positioned unit cells were analyzed (4x 3-channels = 12 points) i.e. 4 transmission spectra per channel (wavelength band). Figure 11 shows box plots of the optical transmission characteristics of a range of MSFA geometries fabricated across three different chips (i.e. the three different recipes from Supplementary Figure 10). These include 2 x 3-channel designs (RGB1 and RGB2), RGB+1, and 3x different 3x3 mosaics (each with a varying dose profile range). The three different recipes correspond to the following processing conditions:
It can be observed from both figures that the variation in optical performance characteristics is minimal within each respective array. For example, the respective channel peak wavelength shift S6 is typically ≲5nm across the arrays and different recipes (Supplementary Figure 11b). Moreover, it can be concluded from these results that the addition of baking steps to the standard protocol enhances the peak transmission. As shown in Supplementary Figure 11 (a) adding a postdevelopment bake (Recipe 3) increases the peak-transmission up to ~80%. The FWHM is also improved (Supplementary Figure 11c) through adding additional thermal treatment; decreasing to ~50 nm in comparison to the standard protocol.

Pixel resolution dose tests
In the main manuscript, we use 11µm x 11µm pixel dimensions, primarily due to limitations with the experimental image sensor setup, however, these length scales can be easily reduced. To demonstrate such scalabilty, we fabricated arrays where exposure dose is varied linearly, with pixel sizes range from: 5.5 µm down to 460 nm (Supplementary Figure 12) Note, 460 nm is not the upmost limit to resolution but for this pixel dimension, the range of lateral-to-vertical aspect ratios of ~9:1 (e.g. ~450 nm:50 nm) to ~9:4 (e.g. ~ 450 nm:200 nm) meaning that they exhibit low aspect ratios and are mechanically stable, hence we suspect the resolution can extend beyond what is demonstrated here. In addition, Supplementary Figure 13 shows a series of angled SEM micrographs of 1 µm and 500 nm pixels showing the surface morphology, and their uniformity at these size scales.

Materials considerations for CMOS processing
Even though SU-8 is a thermally and chemically stable photoresist, a longer-term solution would be to use glass (SiO 2 ), which could be achieved using the grayscale resist as an etching mask for a reactive ion etching step (see Supplementary Figure 22). The use of thin-film Ag similarly provides a potential challenge in the form of long term chemical stability. By encapsulating Ag with chemically inert and optically transparent thin films, such as silicon oxide, this issue is lessened. However, a more comprehensive approach would be to replace the Ag with alternating high-low index all-dielectric mirrors operating with a cut-off wavelength of ~400 nm, thus passing the visible-NIR. These mirrors typically require a minimum of 3 thin-film layers 13 and can be deposited easily within a reactive sputtering or e-beam evaporation step (akin to the metallic mirrors here).  (1) and (2) -are the same size but vary in spacing. In (2) the proximity effect causes the final pixel thickness to be greater than in (1) due to the additional exposure from adjacent pixels. In (b), the proximity effect is highlighted in a USAF 1951 resolution target in which each element (in the line triplet) is given a different dose (hence different final wavelength). However, due to the increased 'dose density' in the center of the rectangle compared to the corners/edges, the final thickness and hence wavelength is different. A homogenous transformation matrix (T), incorporating a rotation by an arbitrary angle followed by a linear translation, is applied to the raw image (c), to account for the misalignment of the MSFA to the image sensor. This transformed matrix is then multiplied by a MSFA matrix (with N-bands), (d), which decomposes the 2D-intensity matrix into N x 2D matrices (one for each wavelength band). The mapping of filter pixel to image sensor is then taken into account in the MSFA matrix. This matrix is then reduced in size by a factor of 5 in each dimension (through bilinear interpolation). Finally, each channel is interpolated (d) by a pixel specific filter kernel (akin to Bayer filter demosaicing) to estimate the missing pixels between actual data. The output (g) is then N x 2D matrices: one for each wavelength band. Supplementary Figure S19. Transmission spectra as a function of exposure dose in MSFA mosaic. Four separate wafers processed with similar dose matrices (represented on the y-axis) but different processing parameters: PEB 65°C for 2min: development of (a) 30s, (b) 1min, (c) 2min; and PEB 95°C for 2 min: development of (d) 1 min. PEB strongly related to final resist (insulator) due to governing degree of cross linkage. Transmission spectra obtained using optical characterization setup in Suppl.