We design, fabricate and characterise a narrowband Fabry-Pérot multispectral filter set for the visible range (400–750nm) that is suitable for integration onto complementary-metal oxide-semiconductor image sensors. We reduce the fabrication steps by fixing the physical cavity length and altering the effective optical length instead. Using electron-beam lithography, a sub-wavelength hole array is patterned in a silicon nitride cavity layer, backfilled with poly(methyl methacrylate), and bounded by aluminium mirrors to create 23 filters with full-width half-maximums of 22–46nm. Additionally, for colourmetric reproduction applications, using as few as 10 filters gives a colour difference (CIEDE2000) of 0.072, better than trichromatic filters.
© 2012 OSA
Multispectral imaging systems are increasingly in demand for applications including agricultural monitoring systems , quality control , art conservation  and medical  and scientific imaging . Contemporary multispectral imaging technologies typically exploit dispersion (prisms, gratings) or interference (etalons). Dispersive methods offer fine resolution but are difficult to intergrate with an array of photodetectors so are often best for single point measurements. Interference-based imagers that use filter wheels in front of the camera are too bulky for the smallest satellites and unmanned aerial vehicles and their speed can be limited by their mechanical nature. Faster systems can be made with electronically tuneable filters but the fabrication of multiple filter and polariser stages is not trivial , and multiple exposures are still required as for filter wheels. An emerging approach is the integration of filters directly on top of the image sensor’s pixel array, providing multispectral imaging in a single exposure. For example two multispectral filters were demonstrated at 1500nm using 41 layer photonic crystals , but in the visible range only trichromatic (RGB) filters have been realised . In comparison Fabry-Pérot (FP) filters are much thinner, and so can be expected to have less crosstalk when arrayed.
Conventionally, the passband of a FP filter is determined by the cavity length. Each additional passband that is desired in a planar array of FP filters costs additional fabrication steps. It would be preferable to fix the cavity length and tune the optical length instead. This concept has been validated in , where gold nanoparticles doped a poly(methyl methacrylate) (PMMA) filled cavity to good effect but in an uncontrolled manner. We present here a technique that provides controlled tuning via lithographic means. We select the effective refractive index of each FP cavity by choosing the fill ratio of its two dielectrics. The remainder of the paper describes the design of a full set of narrowband filters for the visible range that is compatible with CMOS image sensors, the fabrication and characterisation of an example set, and an evaluation of the colourimetric imaging performance.
Our FP cavity contains two dielectrics bounded by optically thin aluminium (Al) mirrors. We control the dielectric filling ratio lithographically, by etching holes into a deposited layer of silicon nitride (SiN) and backfilling with PMMA. PMMA is spin castable and hardens on baking. A fully intact upper mirror layer can then be deposited. A further layer of PMMA is spin-cast on top to act as an anti-reflection layer (ARL), both increasing transmission and preventing the mirror oxidising. A schematic of the proposed filter structure is shown in Fig. 1(a), where holes of diameter d and period Λ are etched into the SiN, and assuming planarisation after backfilling. The inverse structure, where the etch leaves SiN pillars, is not shown. Neglecting dispersion, for a fixed physical length cavity comprising two dielectrics of refractive index n1, n2 the maximum tuning range is 1 : n2/n1 where n2 > n1, or 38% for SiN (n2 = 2.05) and PMMA (n1 = 1.49).
We studied the behaviour of the hole structure (fill ratio ) in detail using a commercial finite-difference time-domain (FDTD) tool (Lumerical) to account for the expected dispersion. The effective refractive index (neff) of the cavity was extracted from the calculated transmission spectra and was shown to depend only on the ratio of the hole-size to the period of the hole array and not on the cavity length tSiN, for practical structures of interest to us. The results were well fitted by the average of the second order transverse electric ( ) and transverse magnetic ( ) effective medium theory (EMT) :Fig. 1(b), for a representative range of hole sizes and cavity lengths, with FDTD results as markers and Eq. 1 as lines.
In order to ensure sufficient free spectral range that each filter has only one transmission peak in the visible range, careful selection of the physical cavity length (tSiN) was required, as well as optimisation of the mirror thickness, hole/pillar diameter, array period and ARL thickness. We studied an extensive parameter range using an adapted version of the FDTD tool TEMPEST . Aluminium was modelled by the Drude + 2 critical points model . The chosen design parameters were tSiN=150nm (first resonance) and tSiN=240nm (second resonance) for the long and short wavelength halves of the band respectively, 20nm mirrors and 100nm ARL, Λ=200nm and both pillar and hole structures with 60 ≤ d ≤ 180 nm. The use of two cavity lengths is consistent with the expected maximum tuning range of a single cavity. The transmission of the filters is plotted in Fig. 2. Full-width half-maximums (FWHM) of 13–36nm were achieved corresponding to finesse of 10–30, or mirror reflectivity of 0.7–0.9. The transmission and FWHM is typically better at shorter wavelengths due to dispersion in the aluminium.
We fabricated a subset of the structures in Fig. 1, selecting a single physical cavity length. The bottom Al mirror and the SiN cavity were deposited onto a microscope slide by a Plassys MEB 400S Electron Beam Evaporator and an Oxford Instruments PECVD tool respectively. Spin-coated ZEP520A electron beam (EB) resist was exposed using a Vistec VB6 UHR EWF lithography tool. The holes were etched using CHF3/O2 in a Plasmalab 80 Plus. After resist removal, PMMA was spin-coated as backfill and baked. We did not polish away the slight overfill. The upper Al mirror was deposited. PMMA was spin-coated on top of the whole stack to form the ARL. An array of 6 filter subsets, each with a different mask hole size, was fabricated simultaneously. Different filter passbands were produced in each of the sets by altering the EB dosage (237–2000 μC/cm2) to achieve fine variation of the hole size.
The transmission was measured using a TFProbe MSP300 spectrometer, and is plotted in Fig. 3 for a selection of 23 filters that cover the whole visible range. The insert shows white light transmission microscope images. The measured results are in good agreement with the simulations, with transmission highest and FWHM narrowest at the shorter wavelengths as expected. Quantitatively the measured transmission is 4–13% (8–17% simulated) and the measured FWHM is 22–46nm (13–36nm simulated) both in reasonable agreement with the FDTD simulations in Fig. 2. The reduced transmission compared to a trichromatic dye filter can be compensated for once in use, by opening the aperture of the imaging system’s lens by 2–3 stops. We attribute the small discrepancies to the unexpectedly wide tuning range we demonstrated with this hole-only, single physical cavity length set. We have introduced an external filter (High-pass, λc=525nm) to eliminate any unwanted second resonances for clarity in Fig. 3 although it does not completely block the second resonance in the green of the two longest wavelength filters. Note that a FP filter set using two cavity lengths does not need the additional filter because the unwanted resonances lie outside the visible band. We have already demonstrated that aluminium-based filters can be integrated on a CMOS imager .
A focused ion beam (FIB) was used to mill a hole so that a scanning electron microscope (SEM) could examine the cross-section; see Fig. 4(a). The Al and SiN thickness was uniform across all filters (approximately 15nm and 200nm respectively). The overfill layer thickness varied with hole size as expected (15–90nm) giving a slight red shift. After careful study of the dimensions, overfill, materials and spectrometer set-up, we attribute the widely extended tuning range to the unexpected dispersion in the SiN. In our machine, a significant increase in silicon (Si) content arises if the SiH4 flow rate increases during deposition . The resulting mixture of Si and SiN is more dispersive and lossy than stoichiometric Si3N4. The impact on device performance can be illustrated by estimating the average refractive index of the Si/SiN mixture using zeroth-order EMT. Substituting this index for that of stoichiometric Si3N4 in Eq. 1 and using the T-matrix method  to rapidly calculate the overall transmission, we replicated the measured performance. We plot the measured response of the filter in Fig. 4(b), along with two simulated responses, one using stoichiometric Si3N4, the other the Si-rich SixNy obtained during deposition. We simulated the remainder of the filters using the Si-rich SixNy model and the results are plotted in Fig. 4(c), obtaining transmission between 2–7% and FWHM 22–40nm. The simulated FWHM are in excellent agreement with the measured results (22–46nm) and the reduction in transmission from 4–13% is equivalent to overestimating the Al layer thickness by a few nanometres. This experimental result suggests non-standard materials can be usefully exploited.
The performance of the filters under non-normal incident illumination, as occurs at the pixel-array edges, was investigated by simulation assuming two standard camera configurations. First a telephoto lens (e.g. for surveillance or long-focus microscopy) with ±20° field of view and second, a single lens reflex (SLR) camera objective with up to a ±50° field of view . For sake of space we show the results superimposed in Fig. 4(b) for the stoichiometric Si3N4 case, for incidence at ±0° and ±25°. There is little change for the moderate incidence angle (telephoto lens) but a small blue shift of 11nm at ±25° (SLR lens). An analysis of the Poynting vector of the transmitted light over a plane 200nm below a typical filter shows a maximum variation in angle of 0.01% (0.1%) and in magnitude of 0.03% (0.2%) from the expected direction for illumination incident at an angle of 0° (25°) to the normal. This negligible degree of scattering is consistent with the subwavelength nature of the structure.
In addition to detecting narrow spectral bands, multispectral filters offer improved colour reproduction as measured by the CIEDE2000 formula . We used 24 patches of the Gretag-Macbeth colour checker as training data, then simulated a test of the filter set by multiplying their measured transmission spectra by the spectra of 1269 patches from the Munsell colour book under D65 illumination. For all 23 filters we obtain ΔE2000=0.0474, nearly 60 times better than a representative tricolour filter that achieves 2.711 . We studied the relationship between ΔE2000 and number of filters by using a genetic algorithm to select optimal members of the set. The colour difference linearly increases to 0.072 for 10 filters (0.005/filter), but from 10 to 6 filters the additional colour difference per filter removed increases to 0.070/filter, giving ΔE2000=0.35 for 6 filters.
The fabrication of a set of 23 narrowband filters, with FWHM of 22–46nm, covering the full visible band (400–750nm) has been demonstrated, with better CIEDE2000 colour difference performance than trichromatic filters. The structures use holes etched into the dielectric layer (SiN) of a FP cavity that is then backfilled with a second dielectric (PMMA) to act as a tuning mechanism. The fabrication cost and complexity is reduced compared to varying the physical cavity length alone. We used only CMOS compatible materials to illustrate that our approach is suitable for direct integration onto CMOS image sensors in industrial foundries. The application of such narrowband filters across a sensor array will enable the simultaneous detection of the full visible spectrum at high resolution in a compact system. We expect this approach will enable multispectral imaging in CubeSats and small unmanned aerial vehicles.
This work was supported by the Engineering and Physical Sciences Research Council ( EP/G008329/1). Damien McGrouther operated the FIB milling machine.
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