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It has been shown in literature that cross-shaped holes arrays can be made insensitive to polarization at normal incidence, and can even feature good stability for off-normal incidence. In this work we look for the optimal design rules to obtain high spectral stability conditions in the visible for those structures, through a complete review of all geometrical parameters using CMOS-compatible materials. Rigorous Coupled Wave Analysis (RCWA) simulations have been used to identify the most-impacting parameters and to determine typical ranges allowing for the realization of low-color errors image sensors whatever the light incidence. It appears that the two main parameters are the ratio of the arm width to the arm length of the crosses and the distance between crosses, which both have to be low to ensure stable responses of the filters. We demonstrate the results with CIE chromaticity diagrams reporting the responses of a RGB filter designed with the established rules under various illumination conditions.
© 2013 Optical Society of America
1. Introduction
Color filtering is an essential step of the image capture process. The scene light is decomposed into elementary colors (generally red, green and blue) which are each distributed onto pixels, traditionally organized in Bayer matrix. One obtains afterwards, by photo-conversion, an electrical signal for each primary color on all locations of the respective pixels over the photodetectors matrix. For the last 15 years, color filters based on nanostructured metallic filters have been widely studied. They are known to have quite interesting filtering properties since Ebbesen et al. linked the extraordinary optical transmission observed in sub-wavelength structures to plasmon resonances [1], contradicting the previous theory on light diffraction by small holes [2]. Nowadays, the physical origin of this phenomenon is rather well understood [3–5]. Surface plasmons are propagating oscillations of the metallic free-electrons gas that results from a coupling between the impinging electromagnetic wave and the metal surface, which can be obtained by structuring the metallic layer. The use of hole-array structures allows the exploitation of this phenomenon to convert back these surface waves into photons at resonance on the opposite surface. The corresponding wavelength is linked to characteristic dimensions of the metallic patterns. This last feature makes metallic filters particularly interesting compared to color resists (sequentially deposited) [6] since all color filters can be realized in one single lithographic step. Indeed filter spectral characteristics can be adjusted pixel by pixel all over the whole matrix by varying only the dimensions of holes and array and not the metal thickness. Furthermore, such filters can feature a satisfying IR rejection and thus do not require the use of an external infrared filter. While this paper focuses on image sensing applications, plasmons are also intensely investigated in several other fields such as high-resolution photolithography [7], bio-sensing [8] or silicon photonics [9]. Many types of structures have been studied, in one dimension first with slits [10–12], then in two dimensions with basic holes shapes – squares [13, 14], rectangles [15–18], circles [16–19], triangles [19], crosses [20–22] - and different kinds of arrays – square or hexagonal [23].
Although all of these nanostructured filters show interesting results for filtering, they can present a high dependency with respect to polarization and incident angle, which is harmful for imaging or light sensor applications. Whereas most works focus only on the polar incident angle, we show that 2D arrays may also be sensitive to azimuthal angle, even for low polar angles, which has never been reported to our knowledge. In imaging or light sensor applications, light is generally unpolarized (or arbitrarily polarized) and can impinge the filters matrix within a significant range of polar and azimuthal angles, which implies that nanostructured metallic filters must be as stable as possible regarding these three parameters in order to have a uniform spectral response of each color pixels on the sensor, whatever their localization. Recently, it has been shown that holes with a cross-shape in gold layer exhibit a good tolerance towards polar incident angles up to 60° with no peaks shift [21] and that it is possible to reduce their sensitivity to polarization even at non-normal incidence [24].
Furthermore, among the metals featuring plasmonic properties in the visible range, noble metals such as Ag or Au have shown the best results in terms of transmission and color purity [25, 26]. However, these metals currently have the major disadvantage to be undesirable in industrial clean rooms, as they are contaminants in CMOS front-end fabrication lines. Many authors are now taking into account these industrial concerns in their work, which demonstrates a growing interest from industries to transfer plasmonic devices in CMOS environment [12, 19, 27–29]. Thus, the present requirements of microelectronics fabs regarding material contamination led us to focus our study on CMOS-compatible device.
In this work we look for the stability conditions with respect to polarization and incident angles for cruciform holes patterns made in an Aluminum film through Rigorous Coupled Wave Analysis (RCWA) computations. This aims to evaluate their potential to be used in image sensors made of fully compatible CMOS material. The study is organized around accurate geometrical criteria and their impact on crosses properties. The right conditions and parameters ranges being extracted from computations results, an illustration of performance is drawn on chromaticity diagrams for RGB filters designed with the established rules.
2. Model representation
The simulations of the nanostructured filters are performed using an in-house RCWA method [30], well-suited to electromagnetic issues with infinite periodic arrays. The results presented in this paper are obtained with 8-harmonics calculations. The studied metallic filters consist in metallic films of Aluminum perforated by a square array of cross-shaped holes filled with silica. The array and crosses geometries are studied with different a/P ratios (where a is the arm length of crosses and P the period of the array) and shape factors (defined as the ratio of the arm width b by the arm length a of crosses), as shown in Fig. 1. The period P is considered the same in the x- and y-axis of the array to avoid polarization dependency in normal incidence. This paper aims to precise which are the relevant geometrical parameters impacting the angular stability and polarization sensitivity of cruciform-hole filters, and to explain their role in order to propose optimized designs with highly stable responses. We first report the influence of the metal thickness, then the impact of the crosses size through the a/P ratio and the shape factor sf = b/a, and finally the role of the distance d between crosses.
Fig. 1 (a) Scheme of a typical nanostructured metallic filter with an Al layer of thickness hm, filled and surrounded with SiO2. (b) Top view of the filter array, with a period P and crosses of arm length a and arm width b.
The global stability of the structure is evaluated through the stability of the response of the filter when it is illuminated with different angles of polar incidence θ, under both TM and TE polarizations, and finally with different azimuths φ, all defined in Fig. 1. In TE (resp. TM) polarizations the electric (resp. magnetic) fields are perpendicular to the incidence plane. For instance for a null azimuthal angle, the electric field E is along the y-axis, and the magnetic field H is in the (xz) plane. The sensitivity to azimuth of such structures has not raised much interest up to now. Yet, it may have detrimental effects depending on the type of optical application, and should ideally be suppressed. This article attempts to evaluate and possibly to limit its impact. Note that the values of polar incident angles considered further are equivalent angles in air as if we had a significant but finite thickness of SiO2 above the filter.
The metal chosen for the following calculations is Al, as Cu has a significant absorption below 600nm, making blue and green colors nearly impossible to obtain with this metal. The general knowledge about Al deposition and etching processes is widely profitable compared to noble materials. Obviously, the material used for the superstrate, the substrate and the holes filling has to be well-known and compliant with industrial fab environment too. The same dielectric is used in the holes and all around the metallic layer, to get an improved transmission efficiency of the filters [31]. SiO2 and Si3N4 are common dielectric materials in microelectronics industry, thus they entirely fill the aforementioned required properties. SiO2 has been preferred for computations since its low refractive index leads to plasmonic filters with lower absorbance in the visible region and less metallic losses [32], ensuring slightly higher transmissions. For the simulations presented here, the refractive index of SiO2 is set to 1.46 which is a common value for PECVD-grown silica (Plasma Enhanced Chemical Vapor Deposition) and the absorption is neglected (k = 0). The indexes variations of Al as a function of the wavelength are extracted from Palik reference [33]. The superstrate and the substrate are both considered infinite in the simulations.
3. Simulation results
3.1 Effect of metal thickness
The first parameter studied is the thickness of the metallic layer. An array of cruciform holes in an Al film filled with SiO2 has been simulated for various thicknesses ranging from 25nm to 300nm. The spectral response is monitored for different polar angles of incidence θ and azimuths φ, and for different polarizations TM and TE.
The spectra presented in Figs. 2(a)-2(b) and Figs. 2(c)-2(d) correspond to a representative filter with P = 150nm, a/P = 0.8, b/a = 0.6 and d = 30nm, for a low (50nm) and a high (200nm) values of thickness, and for two azimuths φ = 0° and φ = 45° respectively. At first glance, no obvious improvement of angular stability is noticed going from thin metallic films to thicker layers, although a faster decrease of the transmission can be observed at hm = 200nm when the polar angle of incidence is increased. Going deeper into analysis, one can notice that for φ = 0° it is mainly the TM polarization which is sensitive to polar incident angle, which confirms the experimental observations in [24], whereas for φ = 45° it is the TE polarization.
Fig. 2 Spectral responses of filters (P = 150nm, a/P = 0.8, b/a = 0.6, and thus d = 30nm) under two different polarizations and with different incidence angles for (a) φ = 0° and (b) φ = 45° with hm = 50nm. Spectral responses for (c) φ = 0° and (d) φ = 45° with hm = 200nm.
Figure 3(a) and Fig. 3(b) show the resonance wavelength shift due to the incident angle for the average response calculated from TE and TM polarizations responses, and for φ = 0° and φ = 45° respectively. At normal incidence, it can be seen the resonance is significantly red-shifted for low values of thickness as hm = 25nm or hm = 50nm. It results from a coupling between modes on the two opposite surfaces that can only occur for low thicknesses, defined in literature as inferior to three times the skin depth of the metal [34]. This is in agreement with our simulations since the skin depth of Al in the visible range is around 12nm. Moreover, the graphs reveal that thin metal layers exhibit larger resonance shifts for high incident angle, and that thicker ones (above 150nm) can limit the sensitivity of the filter to illumination conditions.
Fig. 3 Resonance peak position as a function of the incident angle for increasing metal thicknesses at (a) φ = 0° and (b) φ = 45° calculated for the average response between TE and TM polarizations responses. (P = 150nm, a/P = 0.8, b/a = 0.6, and thus d = 30nm).
Metal thickness can thus be used to tune the stability of cross-hole filters, which becomes very good for a thickness superior to 150nm. However, there is a trade-off to do between stability, transmission and rejection quality, depending on the desired application. Indeed, thick metallic layers will lead to high-rejection and more stable filters but with limited transmission, whereas thinner ones will give filters with high transmission but poor rejection and worst stability. The Al thickness is set to 75nm for the following investigations to have both acceptable transmission and rejection when scanning the other geometrical parameters.
3.2. Effect of the ratio a/P
This part focuses on the size of the crosses relatively to the period of the array: the arm length of crosses is varied keeping b/a, the metal thickness hm and the period P constant. The spectral responses of filters are studied for different a/P ratios under TM and TE polarizations, with different polar angles of incidence θ and for two azimuths φ.
Figures 4(a)-4(b) and Figs. 4(c)-4(d) represent the spectral stability for a low-a/P filter (0.53) and for a high-a/P one (0.8), for φ = 0° and φ = 45° respectively. For the calculations, a metal thickness hm = 75nm, a period P = 150nm and a constant shape factor b/a = 0.6 are considered. Whatever the azimuth, the a/P ratio has no significant impact on stability towards incident angle, but is rather linked to rejection and transmission efficiency. Getting high values of a/P broadens the peak, increases the transmission (because of the increase of the aperture area) but deteriorates the rejection of filters. Figure 5(a) and Fig. 5(b) show, for the average polarization response, that increasing a/P leads to a significant shift of the resonance wavelength at normal incidence as it is mainly dependent on the arm length of crosses [21]. Otherwise, no evolution regarding angular and polarization stability is observed between low and high-a/P filters.
Fig. 4 Spectral responses of filters (hm = 75nm, P = 150nm, b/a = 0.6) under two different polarizations and with different incidence angles for (a) φ = 0° and (b) for φ = 45° with a/P = 0.53. Spectral responses for (c) φ = 0° and (d) φ = 45° with a/P = 0.8.
Fig. 5 Resonance peak position as a function of the incident angle for increasing a/P ratios at (a) φ = 0° and (b) φ = 45° calculated for average polarization.
There is thus no restrictive condition on the a/P ratio to design stable filters. However, there will still be a compromise when designing the nanostructures between the selectivity of the filters and their transmission efficiency. a/P has been set to 0.8 to provide sufficient transmission and rejection for the following studies.
3.3 Effect of the ratio b/a
For given period P and a/P ratio, crosses can still be designed with different shapes according to the arm width b. These shapes can be represented by a geometrical parameter that we defined earlier as the shape factor b/a. The spectra stabilities under azimuth and polar incident angles are studied for both TM and TE polarizations for b/a ranging from 0.2 to 0.8.
As an illustration, we show in Fig. 6 the responses of three plasmonic filters with the same metal thickness hm = 75nm, period P = 150nm, ratio a/P = 0.8, and thus spacing d = 30nm, but with different shape factors, b/a = 0.4, b/a = 0.6 and b/a = 0.8 for φ = 0° (see Fig. 6(a), 6(b) and 6(c) respectively) and φ = 45° (see Fig. 6(d), 6(e) and 6(f) respectively).
Fig. 6 Spectral responses of filters (P = 150nm, hm = 75nm, a/P = 0.8 and thus d = 30nm) under two different polarizations and with different polar incident angles for (a) b/a = 0.4 and φ = 0°. (b) b/a = 0.6 and φ = 0°. (c) b/a = 0.8 and φ = 0°. (d) b/a = 0.4 and φ = 45°. (e) b/a = 0.6 and φ = 45°. (f) b/a = 0.8 and φ = 45°.
The results show that the shape factor widely governs the behavior of such filters in their spectral sensitivity to incident angles and polarization of the incident light. A large shape factor induces low stability for non-normal light incidence, together with a high sensitivity to polarization. The quasi-symmetric behavior of TE and TM polarizations at azimuths φ = 0° and φ = 45° respectively for b/a = 0.6 and b/a = 0.8 is still noticed, but it is not observed for the smallest shape factor (see Fig. 6(a) and Fig. 6(d)), where the differences between the two polarizations are barely visible, and the sensitivity with respect to polar incident angle, as well as to azimuth, is very significantly reduced.
This behavior demonstrates that the stability with respect to polar and azimuthal incident angles is directly linked to the shape factor of crosses. Our computation results show that the condition of stability can be reached for values of shape factor inferior to 0.5. This property of cross-shaped-hole array makes metallic filters particularly interesting for light sensors and displays applications. Indeed, it allows the realization of optical device without loss of transmission, but also without any color shift, for a wide range of angles, whatever the polarization of the source.
Normalized electric field maps on top surface of the metallic layer are shown on Fig. 7 for the two extreme b/a ratios 0.4 and 0.8 at the resonant wavelengths λ = 475nm and λ = 330nm respectively, and for normal incidence and TE polarization. TM polarization response can be derived by a 90° rotation. For the smallest shape factor, it can be seen that the electric field is highly localized in the internal corners of the crosses. This potentially explains the stability of small-shape-factor crosses, owing to the well-known high stability of localized resonances [24, 35]. The largest shape factor has a totally different type of resonance, the electric field being mainly located on two opposite long edges of the crosses, and not as localized as in the previous case. This could explain the loss of the response stability of crosses arrays when the shape factor is increased. At last, it can be noticed that the resonance of large-b/a crosses get similar to that of square/rectangular holes [36], the remaining little internal angles having no specific impact on the resonance mode.
Fig. 7 Electric field norm |(E)| on top surface of the metallic filter (P = 150nm, hm = 75nm, a/P = 0.8 and thus d = 30nm), for normal incidence and TE polarization and for (a) b/a = 0.4 and λ = 475nm. (b) b/a = 0.8 and λ = 330nm .
3.4 Intercrosses distance
Finally, we focus on the spacing between crosses and its impact on stability towards polar and azimuthal incident angles. The parameter studied is d, the shape of crosses being kept constant. Simulations were performed for d ranging from 20nm to 150nm.
Figure 8 shows the impact of increasing intercrosses distance on the filter angular response. The metal thickness hm = 75nm, arm length a = 120nm and shape factor b/a = 0.6 are kept constant. Each graph shows the angular stability for both TM and TE polarizations, Figs. 8(a)-8(c) representing crosses arrays with the closest distance between crosses of respectively d = 20nm, d = 50nm, d = 100nm, for an azimuth φ = 0°. As it can be seen, close crosses result in a rather angularly stable filter, while slight shifts and transmission losses can be noticed for d = 50nm, and even stronger deteriorations of the stability are observed for d = 100nm. This implies that near-crosses arrays allow for better angular and polarization stabilities. For the smallest spacing d = 20nm, the evolution with increasing azimuths (φ = 0°, φ = 22.5° and φ = 45°) is also presented in Figs. 9(a)-9(c). When φ = 22.5°, the responses of TE and TM polarizations are very similar and their deterioration with θ is slightly less important than their worst stability case (φ = 0° for TM and φ = 45° for TE).
Fig. 8 Spectral responses of filters (hm = 75nm, a = 120nm, b/a = 0.6) for both TM and TE polarizations at different polar incident angles for φ = 0° and (a) d = 20nm. (b) d = 50nm. (c) d = 100nm.
Fig. 9 Spectral responses of a filter (hm = 75nm, a = 120nm, b/a = 0.6) with d = 20nm for both TM and TE polarizations at different polar incident angles and for (a) φ = 0°. (b) φ = 22.5°. (c) φ = 45°.
In order to get further into the analysis, we drew in Fig. 10 the transmission peak resonant wavelength as a function of the polar angle with mean polarization, for different values of the spacing d between adjacent crosses, and for different azimuths. The difference of behavior between a low shape factor (sf = 0.4) and a high shape factor (sf = 0.6) is also reported on the graphs. Structures all have a metal thickness hm = 75nm and an arm length a = 120nm. Globally, one can first notice that for normal incidence, a low shape factor leads to less wavelength dispersion as a function of d than high shape factor, which confirms that it is globally less sensitive to period, and therefore more related to localized resonance. For φ = 0°, the low shape factor filter is stable regarding the polar incident angle only for low intercrosses distance d whereas the high shape factor filter is unstable even for low d, and this instability worsens for high d. However, filters gain progressively in stability and are less sensitive to d going from φ = 0° to φ = 22.5°, then from φ = 22.5° to φ = 45°.
Fig. 10 Evolution of the resonance peak shift induced with the polar incident angle θ with mean polarization for different intercrosses distance d, and for different azimuths and two distinct shape factors b/a = 0.4 and b/a = 0.6. Filter dimensions are: hm = 75nm and a = 120nm.
This behavior may be explained as follows: when crosses are very close to each other (low d), surface plasmon polaritons (SPPs) can hardly propagate along the metal surface because metal becomes almost discontinuous, and then the localized character of resonances is predominant. These localized surface plasmons (LSPs) are nearly insensitive to light properties and incidence [24, 35], which explains the high stability of the filter whatever the angle of incidence and the azimuth. On the other hand, when crosses get farther from each other, it widens the “corridors” between crosses in which the SPPs are progressively able to propagate. For high values of intercrosses distance, the SPPs, which are sensitive to light incidence, become predominant and explain the deterioration of the filters stability. The coexistence of these two types of resonance and their predominance as a function of the spacing between patterns have already been highlighted for square holes [37], rectangular holes [15] and also cross-hole arrays [22], but their respective impact on the angular and polarization sensitivity had not been clearly demonstrated yet. Moreover, a more significant degradation of the stability is observed at φ = 0° than at φ = 22.5° and φ = 45°. This is explained by the fact that the SPPs propagation is facilitated in the direction of the aperture between two adjacent crosses, corresponding to both x and y-axis in the case of a square array. When the illumination gets farther from φ = 0°, the stability of the filter progressively improves until reaching its maximum at φ = 45°, where the SPPs propagation are hindered by the dielectric holes on the way, thus limiting their impact to the benefit of LSPs (see Fig. 11).
Fig. 11 Impact of localized resonances (purple areas) and SPPs (arrows) depending on the intercrosses distance d and azimuth φ.
We note that even when crosses are close to each other, a worse stability is observed for high shape factors than for lower ones. This confirms that the shape factor is the main criterion of stability for cross-shaped filters. It can be thus concluded from these simulations that realizing a structure with crosses close to each other is preferable to make a highly stable filter, nearly independent of the incident angle or polarization.
4. Application to CIE diagrams with highly stable plasmonic filters
The stability of filters obtained with previously described conditions can be illustrated drawing CIE chromaticity diagrams.
Three color filters have been designed with the same metal thickness, to allow for an easy potential technological realization. The thickness is set to 50nm to favor the transmission efficiency, and allow for the realization of small shape factor crosses with low etching aspect ratios. We designed filters with a period P = 150nm for the blue one, P = 150nm for the green one, and P = 250nm for the red one. a/P is set under 0.8 to provide sufficient transmission efficiency. The shape factors for the three color filers are inferior to 0.5 to ensure a satisfying stability: b/a = 0.4 for blue, b/a = 0.25 for green, and b/a = 0.3 for red filter. All of these parameters ensure also low intercrosses distance.
In Fig. 12 are represented the spectra of these RGB filters for normal incidence. Foremost, it can be noticed that producing pure colors with plasmonic filters may be hard, especially for green and red filters. Then, the red, green and blue filters were simulated under both TM and TE polarizations, for all possible azimuths and for polar incident angles up to 60°. The chromatic components of each spectral response are extracted and reported on three chromaticity diagrams, each taking into account variations of polar incident angle on three different ranges with increasing severity: θЄ[0°,15°], θЄ[0°,30°] and θЄ[0°,60°].
Fig. 12 (a) Example of RGB filters at normal incidence using small-shape-factor cruciform holes arrays. Blue filter: P = 150nm, hm = 50nm, a/P = 0.6, sf = 0.4. Green filter: P = 150nm, hm = 50nm, a/P = 0.7, sf = 0.25. Red filter: P = 250nm, hm = 50nm, a/P = 0.6, sf = 0.3. (b) CIE diagram representing the color variations of each R,G and B filters when simulated with TM or TE polarizations, with all possible azimuth values and for θЄ[0°,15°] range. (c) for θЄ[0°,30°]. (d) for θЄ[0°,60].
The blue and the green filters are extremely stable even at high incidence angles, up to 60° in this study, whereas the stability decreases when the filter wavelength gets closer to red, especially beyond 30° of polar incidence. The difficulty to obtain good color purities and stability for red color is due to the absorption of Al which becomes even more important for wavelengths above 700nm, thus deteriorating optical properties of the resonance.
5. Conclusion
In this work, we have demonstrated highly stable RGB filters with cross-shaped-hole arrays by identifying the main geometrical parameters impacting the angular stability and the sensitivity to polarization, which are to first-order the shape factor, defined as the ratio between the arm width and the arm length of crosses, and to second-order the spacing between crosses. Both have to be low to favor LSP resonances and thus to ensure the robustness of filters responses, with b/a inferior to 0.5 and d inferior to 75nm. We showed also that the filter robustness has a non-negligible dependence towards incident azimuthal angle. Filters robustness is weak for azimuths 0° and 90° (directions of the crosses arms) and is maximum for φ = 45°, where the SPPs propagation is limited. The metal thickness can possibly be increased above 150nm to improve filters stability, but the impact will be low and will be at the expense of the transmission efficiency.
Such stability properties can be used for wide angle light sensors, or for low color-error image sensors or displays with wide-angle and uniform response on each pixel on the matrix, whatever the polarization and incidence of light.
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