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Imaging resolution of complementary metal oxide semiconductor (CMOS) image sensor (CIS) keeps increasing to approximately 7k × 4k. As a result, the pixel size shrinks down to sub-2μm, which greatly increases the spatial optical crosstalk. Recently, plasmonic color filter was proposed as an alternative to conventional colorant pigmented ones. However, there is little work on its size effect and the spatial optical crosstalk in a model of CIS. By numerical simulation, we investigate the size effect of nanocross array plasmonic color filters and analyze the spatial optical crosstalk of each pixel in a Bayer array of a CIS with a pixel size of 1μm. It is found that the small pixel size deteriorates the filtering performance of nanocross color filters and induces substantial spatial color crosstalk. By integrating the plasmonic filters in the low Metal layer in standard CMOS process, the crosstalk reduces significantly, which is compatible to pigmented filters in a state-of-the-art backside illumination CIS.
© 2015 Optical Society of America
1. Introduction
Conventional colorant pigmented color filters in CMOS image sensors (CIS) are chemically and thermally instable, as well as need multistep aligned lithography processes for Red (R), Green (G) and Blue (B) pixels in a Bayer array configuration [1]. As the resolution of CIS keeps increasing, the dimensions of the pixels rapidly decrease down to sub-2μm [2,3], where crosstalk turns to be a serious problem. In general, the pigmented color filters with a thickness of approximately 1μm are fabricated on top of the CIS at a distance of 2-10μm away from the underneath photodiodes, and therefore significant spatial optical crosstalk occurs for the ultrasmall pixels. Inspired by natural color filters, like the wings of Morpho butterflies [4], structural color filters have been recently proposed, where the filtering response is based on the interaction between light and nanostructures instead of the materials properties [5–9]. For CIS application, structural color filters show advantages such as chemical and thermal stability, single-step patterning process (except vertical cavity filters), thin and spectral engineering capability, although they currently suffer from the relatively low efficiency, fabrication difficulties and possible angular sensitivity. Fabry-Perot (FP) resonant color filters based on Metal-Insulator-Metal (MIM) structures were integrated to a CIS with 1.75μm pixels pitch by STMicroelectronics [2]. As FP resonance wavelengths depend on the cavity lengths, aligned multistep lithography processes have to be applied for the MIM resonator color filters. Recently, the pixels were reduced to 1.43μm by using dielectric bar as a color splitter and the light intensity at each pixel was enhanced by 1.85 times compared to the conventional pigmented color filter in the Bayer array. Although Panasonic Corporation has demonstrated a CIS based on this, the large spectrum crosstalk with about 200nm full width at half maximum (FWHM) and optical crosstalk limit its performance [3]. Metallic nanohole array were found to support selective extraordinary transmission [10]. It has been widely investigated as color filters [11–14], which can tune the filtering response via modifying the lateral dimensions and therefore be processed in a single lithography step. Atwater et al placed glass based aluminum nanohole array color filters on top of a CIS with 5.6μm × 5.6μm pixels and demonstrated a colorful imaging function [15]. Chen et al patterned Aluminum nanohole array plasmonic color filters directly on top of the pixel array of CISs and demonstrated the potential imaging function by measuring the photocurrent response from separated pixels as expected [16,17]. All these CISs have the plasmonic color filters on the top surface. Actually, the plasmonic color filters can be integrated in the Metal layers in the standard CMOS process as mentioned in [16,18]. As a result, the spatial optical crosstalk can be greatly reduced due to the small vertical gap between the filters in the Metal layers and the underneath photodiodes. Although the crosstalk of pigmented filters in CISs has been extensively studied [19–22], no quantitative crosstalk investigation especially the spatial optical crosstalk of plasmonic color filters in CISs has been reported so far. Furthermore, the size effect of plasmonic color filters have been investigated for glass substrate [12,23], but not fully evaluated especially in a CIS model.
In this paper, we investigate the optical properties of nanocross color filters in a CIS configuration including the size effect and spatial optical crosstalk by numerical simulation. The limited size of the pixels is found to degenerate the transmission and the color purity of the nanocross color filters, especially in an oblique incidence. Furthermore, we demonstrated that the spatial optical crosstalk can be greatly reduced by integrating these filters in the Metal layers close to the photodiodes. These research results are instructive for the application of structural color filters in both CIS and display.
2. Angle-insensitive plasmonic color filters
Extraordinary transmission through metallic nanohole array provides the function as bandpass filters. The color filters can be fabricated in one lithography step to show different colors in contrast to pigmented filters requiring multiple aligned lithography steps. Furthermore, the filters have wonderful spectral engineering ability due to the structure based color filtering response. The disadvantages of the nanohole array filters are the fabrication difficulty for the feature size down to sub-100nm and the filtering efficiency is much lower than the pigmented ones. Although there are debates on the physical mechanisms, surface plasmon resonance (SPR) and localized SPR (LSPR) are believed to play an important role [24,25]. Generally, the transmissive peaks of plasmonic nanohole color filters based on SPR can be estimated as
where k|| is the in-plane wave vector magnitude and φ is the azimuthal angle of incident light, ax and ay are the lattice dimensions, i and j are the scattering orders of the array. εm and εd are the permittivities for the metal and dielectric medium respectively. As shown by Eq. (1), the peak wavelength is sensitive to the incident angle. This angular dependence has to be suppressed in both imaging and display applications in order to minimize the optical crosstalk. Different from SPR, LSPR is usually insensitive to the incident angle [26–28]. For example, nanocross array has demonstrated angle-independent spectral filtering properties in near infrared and visible due to strong LSPR [26,27,29]. Here we construct RGB filters by silica covered nanocross array in a square lattice in an aluminum film on glass as shown in Fig. 1 and investigate the oblique angle filtering responses. Lumerical FDTD Solution was used to calculate the transmission spectra. Non-uniform meshes were chosen with a minimum mesh size of 5nm. The refractive index of SiO2 is 1.45. θ is the incident angle. Al is used as the metal material with its dielectric constant from Ref [30]. As shown in Fig. 1, at normal incidence R, G, B filters have transmissions of 25%(B), 22.7%(G), 17.5%(R) and FWHMs of 120nm(B), 135nm(G), 160nm(R), respectively. Generally the f-number of the common camera ranges from 1.8 to 16, the corresponding incident angle is less than 17 degree [15]. The f-number is defined as the ratio of focal length (F) to aperture diameter (D). The aperture angle for a given f-number is equal to θ = 2arctan(D/2F). With the increasing incident angleup to 20°, there is no apparent shift of the polarization averaged transmission peaks and no apparent variation of the peak transmission. For larger incidence angle, there is redshift of the transmission peak together with the decreasing peak transmission. The red filter even shows an extra transmission peak at the short wavelength end for > 30° incidence due to the SPR at the Al and SiO2 interface at TM polarization (magnetic field perpendicular to the incidence plane) [23]. The angular spectral filtering responses of the nanocross array filters are acceptable in the following analysis of spatial optical crosstalk in a CIS integrated with the nanocross color filters. It should note that the degradation of the redfilter at large oblique incident angles (>30°) in imaging systems like the cameras of smartphones may have effect on the following crosstalk analysis.
Fig. 1 (a) Schematic of the nanocross array filter, hm = 200nm, ht = 200nm. Polarization averaged transmission spectra of (b) blue filters, p = 150nm, a = 120nm, b = 48nm, (c) green filters, p = 180nm, a = 140nm, b = 50nm, (d) red filters, p = 230nm, a = 180nm, b = 40nm at incident angle of 0-50°.
3. Size effect of nanocross array filters
Most work on structural color filters including plasmonic ones are based on the infinite array, where periodicity has important effect on the filtering response. As shown in Eq. (1), the SPR wavelength is in proportion to the period. In a finite array with the lateral scale less than the propagation length of surface plasmon wave, the transmission rapidly decreases [31]. Although LSPR is localized, the coupling between two adjacent nanoparticles affect the optical property [26]. As a result, it is expected that the nanocross array color filters integrated in a limit size pixel show size effect that has to be considered in the CIS application. Red color filter with the largest period is used to estimate the size effect of the nanocross array filter. Total-field Scattered-field (TFSF) Sources are used to maintain plane wave morphology when Perfectly Matched Layer (PML) boundary condition is applied to terminate the calculation window [32]. Transmission spectra of different numbers of nanocrosses are calculated for a fixed filling-ratio of approximately 0.22 as shown in Fig. 2. The transmission peak wavelength has little variation and the peak transmission tends to be saturated with the increasing number of the nanocrosses. The peak transmission of the infinite structure and 9 nanocrosses array are 21% and 17% respectively. In the following crosstalk analysis in pixel array, 9 nanocrosses for red filters are chosen.
Fig. 2 The size effect of a red color filters (p = 280nm, a = 200nm, b = 50nm) consisting of different numbers of nanocrosses at normal incidence. The black line is for the periodic array. 4, 9, 16, 36, 81and 100 nanocrosses occupy 0.6 × 0.6, 0.89 × 0.89, 1.18 × 1.18, 1.8 × 1.8, 2.66 × 2.66 and 2.96 × 2.96μm2, respectively.
4. Spatial optical crosstalk in CIS integrated with nanocross array filters
Figure 3 shows the schematic of a CIS, which consists of silicon substrate with photodiode, SiN anti-reflection layer, dielectric layer and metal layer for simplicity. In commercial CISs, the thickness and the position of each layer have certain values and depend on different semiconductor foundries. Here we choose some typical values to investigate the general physics. The pixel size is chosen to be 1μm and the RGB nanocross color filters are constructed into a Bayer array in the Metal layer on pixels for colorful imaging. Pigmented color filters on top of the CIS are also calculated for comparison. Microlens array is not included in this model to get a direct relation between the incident angle and the spatial optical crosstalk. In real case, the microlens may have a lateral shift to the pixels underneath for compensation of the difference of incident angle between pixels [20]. As shown in Fig. 3(a), there are two G, one B and one R filters in each 2 × 2 Bayer cell. It should be noted that when the polarized light obliquely incidents on the structure, the transmission spectra of G and G1 pixels are different. As a result, we distinguish them as G and G1. In order to investigate spatial optical crosstalk of each pixel separately, we calculate the transmission of each pixels Ti (TB, TR, TG, TG1) with only one nanocross array filter above itself but the other three pixels are covered with metal shields in a cell. The light flux in the other thee pixels due to the crosstalk are also recorded, for example the case shown in Fig. 3(a), the light flux in the R pixel is defined as CBR, which means the crosstalk flux from B pixel to R pixel. The crosstalk of each pixel can be calculated as Eqs. (2)-(5).
Because the CIS structure is different from that on glass in Fig. 1, the dimensions of the RGB filters are slightly modified. The corresponding parameters are: for Blue filter, we set p = 150nm, a = 110nm, b = 50nm; for Green filter, we set p = 200nm, a = 140nm, b = 60nm; for Red filter, we set p = 280nm, a = 200nm, b = 50nm. For 1μm × 1μm pixel size, 3 × 3 cross periods for red filter are filled, 5 × 5 for green filter, 6 × 6 for blue filter. In all the following calculation, the optical crosstalk and the colors are the average results of TE and TM polarization incidence.Fig. 3 (a) Schematic of the model used to calculate spatial optical crosstalk on CIS, (b) XZ cross-section diagram. The refractive index of SiN is 2. θ is the incident angle.
Figure 4(a) illustrates the calculated transmission spectra Ti with only one R/G/B filter placed on the i pixel. In this case, there is no crosstalk from the other three pixels, but only size effect is included. The spectra are used to calculate the RGB colors as shown in the chromaticity coordinates in CIE 1931 [33] chromaticity diagram (Fig. 4(b)) ignoring the effect of luminance. These results are used for reference in the following spatial optical crosstalk analysis. Figure 5 shows the polarization averaged transmissive spectra of integrated filters at various incident angles. It can be seen that the resonant wavelength does not vary with incident angle, which is desirable in CIS. The relatively low transmission is due to the size effect and metal absorption loss. We calculate the spatial optical crosstalk as shown in Table 1 in a CIS referring to the Eqs. (2)-(5). At h = 2μm, the nanocross color filters have significant spatial optical crosstalk (>20%) at 17 degree incidence, which distorts the filtering colors. However, the spatial optical crosstalk of the nanocross color filters can be greatly suppressed by 5-10 times via bringing them closer to the photodiodes at h = 0.5μm, which can be achieved in practice by integrating them into the Metal layer in standard CMOS process. In this case, most crosstalks are below 20% at 17 degree incidence. For comparison, the spatial optical crosstalks at 17 degree for the pigmented filters on top at h = 2μm (in CMOS process with more than 3 Metal layers the value is even larger) and h = 0.5μm are also calculated. Though at h = 2μm, most crosstalk are above 20% and some are even more than 100%, the optical crosstalk can be similarly reduced by 5-10 times at h = 0.5μm. Figure 6(a)-(f) are the simulated electric field distributions of green and red pixels in the XZ plane at 520nm wavelength for 0 degree and 17 degree incidence with varying h. It is clear that spatial optical crosstalk is prominent at oblique incidence. For the nanocross color filters, larger h induces larger crosstalk due to the longer oblique light propagation distance and thereforesmall gap successfully suppresses the spatial optical crosstalk. The pigmented filters at h = 2μm are calculated for comparison, where obvious spatial crosstalk between neighboring pixels are observed as well.
Fig. 4 (a) Normalized crosstalk-free transmission spectra of integrated RGB filters in a Bayer array CIS with 1μm × 1μm pixels at h = 0.5μm for normal incidence. (b) Calculated color of RGB from the normalized spectra and the chromaticity coordinates of RGB in CIE 1931 chromaticity diagram.
Fig. 5 Polarization averaged transmission of nanocross array (a) blue, (b) green, (c) red color filters in a Bayer array CIS for various incident angles. The pixel size is 1μm × 1μm and the filters are at h = 0.5μm. Each transmission is calculated with the other three pixels covered with metal shields.
Table 1. The spatial optical crosstalk of nanocross color filters and pigmented color filters with 0 and 17 degree incidence at different h = 0.5μm and 2μm for a CIS with 1μm × 1μm pixels. The thickness of the pigmented filters is 600nm.
Fig. 6 (a)-(f) is the simulated electric field distribution of green and red pixels in the XZ plane at 520nm wavelength. (a)-(b) and (d)-(e) are results for 0° and 17° incidence of nanocross color filters, respectively. (c) and (f) are results of pigmented color filter for 0° and 17° incidence. (a) and (d) are for h = 0.5μm, (b), (c), (e) and (f) are at h = 2μm. Silicon photodiode is at the z = 0 plane.
In order to obtain a visual understanding of the spatial optical crosstalk, pixel colors are calculated using the recorded spectra with either nanocross color filters or pigmented filters. The results are shown in Fig. 7. The color of the left two columns are nanocross filters, and the right two columns are pigmented filters. For normal incidence, both the nanocross filters and the pigmented filters regardless of size effect show good colors as shown in Figs. 7(f) and 7(m), which are different due to the different filtering response and should be used as reference colors for nanocross filters and pigmented filters, respectively. When the pixel size shrinks to 2μm, RGB color still can be recognized at normal incidence as shown in Fig. 7(e) and 7(i), where slight color variation can be observed. However, obvious color distortion appears when the pixel size shrinks to 1μm × 1μm at h = 2μm as shown in Fig. 7(c) and 7(j). For oblique incidence, the distortion is even worse in Fig. 7(d) and 7(k). Advanced crosstalk suppression techniques like light guide and backside illumination (BSI) have to be used in the state-of-the-art CISs to ensure the imaging quality. Alternatively, by integrating nanocross color filters in the Metal layer close to the photodiodes (h = 0.5μm), color distortion can be substantially reduced as shown in Fig. 7(a), where the red and blue colors are greatly improved compared to Fig. 7(c). Even for 17° incidence, the colors show substantial improvement. Please Note, regarding the BSI technique and recent development of the front-side illumination (FSI) technique [34,35], the pigmented filters can also be integrated close to the diodes, which substantially reduces the optical crosstalk. Placing at the same distance from the diodes at h = 0.5μm, the pigmented filters also show good color as shown in Fig. 7(h)-7(i). For both techniques, the close distance between diodes and the filters greatly reduce the optical color crosstalk. The easy integration of the nanocross filters to the exsiting Metal Connection layers may fit better for the standard CIS processes.
Fig. 7 The calculated colors of R, G and B pixels in CIS using both nanocross filters (a)-(f) and pigmented color filters (h)-(m). (a)-(d) and (h)-(k) are for 1μm × 1μm pixels. (e) and (l) are for 2μm × 2μm pixels. (a), (b), (h) and (i) are at h = 0.5μm. (c)-(e) and (j)-(l) are at h = 2μm. (f) and (m) are the reference colors of periodic nanocrosses filters and individual pigmented filters regardless of crosstalk.
5. Conclusion
We have discussed the angle insensitivity, size effect and spatial optical crosstalk of plasmonic color filters integrated in CISs by numerical simulation. It is found that nanocross array can provide angle-robust (<20°) selective transmission but the limited size of the nanocross array in a pixel down to 1μm × 1μm reduces the transmission due to the size effect. With the resolution of CISs keeps improving, it is significant to reduce the color distortion. The spatial optical crosstalk is found to be suppressed by 5-10 times by integrating plasmonic color filters in the Metal layers close to the photodiode. Structure color techniques like plasmonic filters in this paper are potential candidates. However, the subwavelength structures utilized in plasmonic color filters require nano-lithography at higher cost. In the meantime, the filtering efficiencies of the current plasmonic color filters are much lower than the pigment techniques due to the parasitic plasmonic losses. More work has to be carried out for practical applications.
Acknowledgment
This work is supported by the grants from the National Natural Science Foundation of China (No. 11274344), Suzhou Science and Technology Development Program Foundation (No. ZXG201425), the Royal Society Newton Advanced Fellowship and and the Opened Fund of the State Key Laboratory on Integrated Optoelectronics (No. IOSKL2013KF01).
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