Compact Multilayer Film Structure for Angle Insensitive Color Filtering

Here we report a compact multilayer film structure for angle robust color filtering, which is verified by theoretical calculations and experiment results. The introduction of the amorphous silicon in the proposed unsymmetrical resonant cavity greatly reduces the angular sensitivity of the filters, which is confirmed by the analysis of the phase shift within the structure. The temperature of the substrate during the deposition is expressly investigated to obtain the best optical performance with high peak reflectance and good angle insensitive color filtering by compromising the refractive index of dielectric layer and the surface roughness of the multilayer film. And the outlayer of the structure, worked as the anti-reflection layer, have an enormous impact on the filtering performance. This method, described in this paper, can have enormous potential for diverse applications in display, colorful decoration, anti-counterfeiting and so forth.

The design rules to obtain the thickness of the film stack 1 In the proposed structure, as shown in Fig. S1, the thick silver is chosen to provide high reflectivity while 2 ultra-thin chrome with the intrinsic property n≈k is selected as a partial reflection mirror and the 3 absorptive layer. The amorphous silicon layer is a phase matching layer to induce the highest reflectance 4 at specific wavelength whose optical thickness determines the wavelength of peak reflectance. The outer 5 TiO2 film is an effective anti-reflection layer for chrome film to reduce the reflection further and improve 6 the color saturation. 7 8 Figure S1 | Schematic of the proposed reflective color filter 9 In the simplified model of Air|Cr|a-Si|Ag|Glass, the refractive index of the incident medium and the 10 exit medium are n0 and ns while the optical constant and the thickness of Cr, a-Si, and Ag are set as follow 11 in Table S1: 12 The thickness d is much smaller than the wavelength ( 0 d   ), therefore δ approaches to zero and 1 cosδ, sinδ can be expanded by Taylor's series. The matrix M can be thereby simplified by ignoring high 2 order components as shown in the right part of Eq. (S2): Suppose the effective admittance of film stack a-Si|Ag|Glass is Z=X+iY and the characteristic 5 matrix of film stack a-Si|Ag|Glass is Therefore, the equivalent admittance of film stack Cr|a-Si|Ag|Glass is The reflectance of the whole structure Air|Cr|a-Si|Ag|Glass can be calculated:  2 Based on this principle, the structure is optimized and designed for RGB colors. Taking an example 3 of the green filter, λ0=520nm, n1=3.48, k'=3.32, m=1, the thickness of a-Si is calculated, D=130nm. The 4 reflectance is shown in Figure S2 with the calculated thickness of a-Si. The peak reflectance wavelength 5 shows a shift about 15nm from the desired wavelength, which can be attributed to the approximation of

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In addition, the thickness of TiO2 is determined by λ'/4nTiO2 to realize the anti-reflection at the 12 blocking wavelength region, where λ' is the specific wavelength in the blocking region and nTiO2 is the 13 refractive index of TiO2. The thickness of chrome is no more than 30nm to pass the visible light into the 14 following film stack to obtain the desired reflection.

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In short, the design rule is an effective way to get the rough thickness of every layer. Based on these 16 initial parameters, the properties of the color filter can be further optimized to obtain the accurate 17 thickness of each layer using commercial optical coating software.
1 Figure S4 | The CIE 1931 chromaticity coordinates of the three primary color filters 2 for the unpolarized light at the incidence angles of 0°,15°,30°,40°,50° corresponding 3 to the measured results in Figure 2(a-c).

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On the basis of these measured reflectance spectrums, the chromaticity coordinates at various angles of 5 incidence are calculated and marked in Figure S4. A standard illuminant E is adopted in the color 6 difference calculation, which has constant spectral power distributions over the whole visible spectrum.

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Though the chromaticity coordinates make a small movement with angle of incidence, the reflected 8 specular color makes little change for all the fabricated RGB devices. Compared with the green color 9 filter, the blue and red ones present a much higher saturation because of the efficient suppression at the 10 blocking region and the narrower bandwidth.