1. Introduction

Electromagnetic (EM) wave absorbers play a pivotal role in a wide range of applications such as bolometers [1], solar thermophotovoltaics [2], thermal imaging [3], sensors [4], EM-shielding [5], thermal camouflaging [6], and optical filters [7]. These optical filters can then be used in color displays [8], light-emitting diodes (LEDs) [9] and decorative photovoltaics [10,11]. All of these applications require either broadband absorbers or single/multiple resonant absorbers, and both of these types of absorbers can be made from nanostructures [12,13] or thin-film multilayers [14,15].

Nanostructured absorbers as color filters can either utilize metal-dielectric-metal (MDM) [16–18] or all-dielectric [19–22] design configurations. All-dielectric color filters provide a single resonance response whose reflectance efficiency is significantly higher as compared to MDM structures. The efficiency is achieved by using low loss nanostructured dielectrics as top layer thus, making it easier to produce additive colors red (R), green (G), and blue (B). However, any other resonance or material response affects the outcome color which is formed by a combination of reflections and transmissions at each wavelength in the visible regime. The all-dielectric color filters suffer from multiple resonances as the dimensions of unit cell elements are increased. Apart from this, the pixel size (minimum number of unit cell elements that mimic the response of periodic boundary conditions for single element in perfectly matched layer-PML boundary conditions) of nanostructured (either MDM or all-dielectric) color filters has to be kept large because the high, single resonance reflectance efficiency of a single unit cell is extremely low. Moreover, the fabrication of nanostructures is time-consuming and costly.

Time and cost-effective alternative is to utilize thin-film multilayers [23,24] in color filtering which circumvent nanofabrication challenges and their pixel size can be tuned as per requirement. Many demonstrations of such multilayer color filters can be found in literature, which shows that they can have several designs based on the number of layers [25,26]. Previously explored trilayer thin film geometries for color filters employed Fabry-Perot (FP) etalons [27,28]. A two-way etalon is also shown [28], which can either be reflection-based or transmission-based and therefore, can cover the cyan-magenta-yellow (CMY) and the RGB color gamut. The devised etalons have the same thickness of thin metal for both top and bottom layers, and the color is usually obtained from the transmission side. This method incurs transmission and reflection losses because both phenomena are simultaneously present. These losses yield lower color purity. Apart from this, most of the etalons previously demonstrated employ more than three layers which is time-consuming and sometimes difficult to realize.

To address these shortcomings, we propose a trilayer design of metal-dielectric-metal (Fig. 1) which offers substantial color purity enhancement. The proposed designs employ metals with a higher melting point on top which also provides enhanced absorption and thermal stability. The major motivation of our proposed designs is that it does not involve any additional layers other than three as compared to previous works [29–32] and FP etalons [27,28], which employ more layers and for Copper (Cu) bottom metal layer, magenta (M) and yellow (Y) colors can be attained with only two layers. In literature, where the same number of layers is employed as the proposed design, the material combinations are different which provide less reflectance/transmission efficiency and low color purity whereas the proposed design achieves highly pure cyan and magenta colors. The design overcomes the limitations of nanostructured color filters by providing lower fabrication cost and time with a tunable pixel size as explained by a comparison provided in Table 1.

 

Fig. 1. Layer description of multilayer color filter showing the thickness of top ultra-thin metal layer d₁ and sandwiched semiconductor layer d₂ and bottom metal layer’s thickness (d₃) is fixed at 100 nm.

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Table 1. Literature survey of the selected research along with their limitations

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An analytical solution of the proposed MDM design is extracted for this type of electromagnetic layered-problem for twelve (12) different material combinations. Moreover, a unique design methodology for realizing such highly efficient color filters using trilayers is discussed in detail in design methodology. The rationale for this design lies in the addition of an ultra-thin metal-layer on top of bilayer that can significantly enhance the color purity, which is the resemblance of the color to its hue, by providing extra control over absorptance. The design achieves high color purity by improving absorption and therefore, realizing negligible reflectance at particular wavelengths where subtractive colors (CMY) can be observed. This technique is applied for a total of twelve (12) combinations and the enhancement in color purity is observed for all of them. For the sake of simplicity, the design methodology of the Silver-Silicon (MS) bilayer towards the Silver (Ag)-Silicon (Si)-Titanium (Ti) (MDM) trilayer is analyzed thoroughly in “Design and Methodology” section. The major motivation of this step-by-step approach is that although a bilayer would be the most suitable option for color filtering, it does not provide much control over the reflectance spectrum. Therefore, an increase in the number of layers is the only option. The same method explained in design methodology can be applied for the rest of the proposed configurations. The acquired color results (based on the thickness of different layers) of all possible combinations are presented in the “Results and Discussion” section. For the proof of concept, the Ag-Si-Ti multilayer design was also fabricated for CMY colors. All the results are carried out for p-polarization except when distinctly specified.

2. Design methodology

Both RGB and CMY sets define the entire color gamut and if one set is attained, the other set can be derived by color mixing. The RGB color model is an additive while CMY is subtractive. The CMY are labeled as such because they are formed by subtraction of one of the RGB colors from white light. This statement implies that (1-red) produces cyan, (1-green) produces magenta and (1-blue) produces yellow. The pure values of the CMY colors can be plotted by converting the RGB values of (0, 255, 255) for Cyan, (255, 0, 255) for Magenta and (255, 255, 0) for Yellow to Yxy values of Commission Internationale de l'Elcairage (CIE) 1931 plot by the help of conversion matrix to get XYZ coordinates (1).

In order to obtain the CMY colors, a resonance is required at particular wavelength such as for magenta, absorptance is required at 517 nm, and the rest of the wavelengths should be adequately reflected [33]. This theory suggests that destructive interference is required at the desired wavelength and at all other wavelengths, constructive interference is needed [34]. In our analysis, we show a formulation for magenta and, the rest of the two colors can be obtained by a similar method (for cyan, two instances of absorptance are required as shown in Fig. 3(b)). The design is initiated by introducing two-layers and is then extended to three layers due to the inability of two-layers to generate high color purity. Only Ag-Si bilayer and Ag-Si-Ti trilayer designs are considered to explain the methodology. The choice of using Si as dielectric layer lies in its higher refractive index. Moreover, in this study, we only need reflectance minima at certain wavelengths and we do not require reflectance maxima for the rest of the wavelengths for high color purity. Therefore, lossy dielectrics can also be employed.

2.1 The two-layer model

An analytical approach is taken to improve the absorption provided by the two layers, i.e., a dielectric layer on top of a metal layer. The initial design of silicon (Si) on top of silver (Ag) is considered. Since the materials under study are dispersive in nature, their values of refractive indices at each wavelength are taken from the handbook of optical constants [35]. The reflectance and thus, in turn, the absorptance, provided by the two-layer design can be calculated using the following formula [36] as the transmission is rendered effectively zero when using a thick metal ground plane.

Since we need reflectance to be zero at 517 nm (or absorptance to be maximum ≈1), the expression (5) infers that partial reflection from the air/Si interface must be equal and opposite in magnitude to the partial reflection from Si/Ag interface plus the phase shift. After calculating the reflectance form Si-Ag interface for a thickness of Si ranging between 1–200 nm, it is observed that the reflectance indeed goes approximately to zero a few times at 517 nm (Fig. 2), but the reflectance also goes to zero at other points (multiple reflection minima), due to destructive interference which is undesired. When the thickness of Si is less than 25 nm, the absorptance is not high enough which is also unwanted.

 

Fig. 2. Two-layer reflection against the variable thickness of silicon. The black vertical line shows 517 nm and horizontal lines show the thickness of Silicon needed to achieve that response.

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2.2 The three-layer model and design rule

As an improvement, one thin layer of metal is proposed to be added on top of the existing semiconductor and metal layers. An analytical approach that extends the two-layer calculation to find the reflectance and absorptance from three layers, is derived in Appendix A and depicted in Fig. A1. The resulting equation for reflectance from a three-layer is described below (Eq. 6).

 

Fig. 3. (a) Reflection plot for a fixed 10 nm thickness of Titanium and 100 nm Ag with variable Si thickness. The black vertical line shows 517 nm and horizontal lines show the thickness of Silicon needed to achieve that response. (b) Reflection curves for pure CMY color filters achieved from Single resonance (SR) and dual resonance (DR) responses with different thicknesses of Silicon and fixed thicknesses for Ag (100 nm) and Ti (10 nm).

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3. Results and discussion

The previously established theory is further backed up by the help of CIE 1931 plots of two-layered and three-layered designs with the same materials as discussed in the previous section. Figure 4(a) shows the CIE plot of two layers with Si thickness ranging from 1–200 nm, and Fig. 4(b) shows the three-layered design with a 10 nm thick Ti layer (200 points, each representing thickness of Si from 1–200 nm). It is evident from Fig. 4(a) and 4(b) that the two layer’s color purity shown in Fig. 4(a) is significantly inferior as compared to color purity offered by three layers shown in Fig. 4(b) as trilayer design touches the pure color values of cyan and magenta.

 

Fig. 4. CIE 1931 plot for (a) Two-layered multilayer structure and (b) Three-layer proposed multilayer structure. The black triangle shows pure CMY values obtained from the conversion matrix.

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The superior performance of the three-layered structure lies in the increase of the absorptance of single resonance (SR) and dual resonance (DR) responses that occur in this multilayer. The dual resonance is needed to obtain pure cyan which occurs at a certain thickness of Si as previously shown in Fig. 3(b). This feature helps the structure to achieve higher color purity as it can also be seen from Fig. 4(b) that almost exact cyan and magenta can be achieved using this arrangement of the Ag-Si-Ti.

 

Fig. 5. Predicted color plot of the surface by changing the angle of multilayer structure (Ag-Si-Ti) under p- (a-d) and s-polarizations (e-h).

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Angle insensitivity of the design was also checked, which shows that the design is angle insensitive up to approximately 60° as shown in Fig. 5. It can be observed from the results that an increase in angle results in shifting of the spectra upward or downward along the y-axis for p- and s-polarizations respectively. For s-polarization, the high-purity color spectrum shifts downwards implying that a small thickness of Ti can achieve desired colors whereas the opposite is true for p-polarization. This phenomenon can be utilized to further decrease the height of the top metal layer.

RGB color plots for different material combinations as discussed in the introduction are provided in Fig. 6, which shows color enhancement as compared to the two-layer design. The results of GaN with Ti as top layer show higher color purity for a large band of thicknesses and is thus, a better option for multilayer color filters (Figs. 6(c), 6(g), and 6(k)). It can be further observed that top and bottom metal layers also have a significant effect on the color filtering of this three-layered multilayer structure. Chromium layer serving as top metal layer squeezes the color band and moves blue and cyan upwards (a higher thickness of top metal layered is required to achieve these colors), but shifts yellow and magenta down which is practically not suitable (Figs. 6(b), 6(d), 6(f), 6(h), 6(j), and 6(l)). Therefore, Titanium is recommended as the top metal layer (Figs. 6(a), 6(c), 6(e), 6(g), 6(i), and 6(k)). For bottom metal layers, Ag (Figs. 6(a)–6(d)) and Al (Figs. 6(i)–6(l)) produce almost identical results except Cu (Figs. 6(e)–6(h)). Copper squeezes the color band as compared to both Ag and Al but on the other hand, it can provide magenta and yellow colors without using the top metal layer.

 

Fig. 6. Predicted color plot of the surface for different material combinations of multilayer color filters. Here (a-d) use Ag as bottom metal layer, (e-h) use Cu and (i-l) use Al. In the case of sandwiched semiconductor layers, (a, b, e, f, i, j) use Si and (c, d, g, h, k, l) GaN. Lastly for top metal layers, (a, c, e, g, i, k) have Ti as top layer whereas (b, d, f, h, j, l) have Cr as a top metal layer.

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In order to compare our results with related works, relative distance ($RD = \sqrt {{{({{C_{PX}} - {C_X}} )}^2} + {{({{C_{PY}} - {C_Y}} )}^2}}$, where C_PX and C_PY are pure color coordinates on CIE plot and C_X and C_Y are the coordinates on CIE plot for particular color achieved by the design) is calculated. Lower the RD, the better the color purity of the design. Our designs of single resonances have RD of 0.0578, 0.0116 and 0.0758 (against CIE coordinates of (0.2217, 0.2710), (0.3276, 0.1636), and (0.4650, 0.4447)) for CMY respectively while dual resonance designs have RD of 0.0136, 0.0509 and 0.0715 (against CIE coordinates of (0.2111, 0.3288), (0.3129, 0.2044), and (0.4118, 0.4341)) for CMY respectively. These values were compared with related literature and ‘tick’ is marked where our design yields better results and ‘cross’ is marked where the results were found to be worse (Table 2).

Table 2. Comparison of RD with related literature. Ag-Si-Ti Single Resonance (SR) and Dual Resonance (DR) designs are compared here with existing literature where curves for CMY were provided. MM represents metamaterial structures that employ nanostructures whereas ML represents multilayer designs.

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It can be seen from the table that our design only produces poor yellow color against Ref. [33] where both SR and DR responses failed to improve the results. The design, however, outperforms other multilayer designs with a greater number of layers and even outperforms other metamaterial designs that use nanostructures. It is also important to mention here that these results are only calculated for Ag-Si-Ti but the Ag-GaN-Ti trilayer is deemed to outperform these results as can be seen in Fig. 6(c), 6(g), and 6(k).

To verify our proposed design, we have fabricated three-multilayer (Ag-Si-Ti) structures for single resonance (SR) based CMY color filtering using the magnetron sputtering system (DaON 1000S). The general setting of 0.006 torrs was maintained while the substrate was given a rotation. For DC excitation, 400 V and 96-100 mA were maintained and for RF excitation forward power of 100 W and return the power of 6-7 W was maintained. A temperature of 400°C was maintained to sputter Si. Time taken to deposit 100 nm of Ag was approximately 3 min and 10-30 secs at the rate of 2.6-2.9 Ǻ/s whereas 10 nm of Ti took approximately 3 min and 15-25 secs at the rate of 0.6-0.8 Ǻ/s for all three devices. The time taken to deposit 30 nm, 40 nm and 50 nm of Si at the rate of 3.7-4.1 Ǻ/s was 1 min and 10 secs, 2 min and 8 secs and 2 min and 55 secs, respectively.

The reflection spectra of all three samples were measured using UV-Visible/Near-Infrared spectrophotometer (Jasco V-770) and their comparison with analytical prediction is shown in Fig. 7(a). The analytical and measured results agree with each other. The images of the samples were taken with a 13-megapixel camera while holding the samples in front of an office window (shown in Fig. 7(b)), which captures reflection images under diffused sunlight. The reflective CMY colors were observed in the respective captured images. The scanning electron microscopy (SEM) images (taken using FEI 450 Nova NanoSEM) of the devices are shown in Figs. 7(c)–7(e). The SR designs were fabricated at slightly higher thicknesses than the forecasted values from analytical calculations to account for the possible sputtering errors in less sophisticated magnetron sputtering. For better accuracy, we recommend using atomic layer deposition (ALD) to deposit an extremely thin layer of silicon.

 

Fig. 7. (a) Analytical and measured reflection curves of single-resonance CMY filters. (b) Fabricated CMY color filters. SEM images of fabricated samples for (c) cyan, (d) magenta and (e) yellow color filters.

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4. Conclusion

In this paper, we have shown a unique analytical methodology to design thin-film multilayer absorbers which can be efficiently employed in color filtering applications. The design uses three thin films of metal-semiconductor-metal, which in our case is Ag-Si-Ti, to achieve high purity of CMY colors. The CMY colors thus obtained, outmatch previously developed thin-film multilayer color filters and are also, to an extent, able to surpass nanostructured based color filters designed for CMY colors. The design is also angle insensitive up to 60° and is predicted to withstand high temperatures due to overlapped top thin metal layers. Similarly, results of different variations of the same design pattern are also shown which have varying materials i.e. different materials for metal-semiconductor-metal layers, and it was observed that all the designs show good color filtering especially Ag-GaN-Ti. The design of Ag-Si-Ti was also fabricated for CMY colors harnessing single resonance colors of Silicon and the measured results were in favor of the analytical calculations.

Appendix A: Derivation of reflection from a three-layered multilayer structure

According to Fig. 8 we have

(8)$${E_{1f}} = {t_{01}}{E_{0f}} + {r_{10}}{E_{1b}}$$

where, E_if/b is Electric-field in medium i traveling forward or backward depending upon the subscript f and b, ${t_{mn}} = \frac{{2{n_m}\cos {\theta _m}}}{{{n_m}\cos {\theta _m} + {n_n}\cos {\theta _n}}}$ and ${t_{mn}} = \frac{{2{n_m}\cos {\theta _m}}}{{{n_n}\cos {\theta _m} - {n_m}\cos {\theta _n}}}$ are transmission coefficients for s- and p-polarization respectively, ${r_{mn}} = \frac{{{n_m}\cos {\theta _m} - {n_n}\cos {\theta _n}}}{{{n_m}\cos {\theta _m} + {n_n}\cos {\theta _n}}}$ and ${r_{mn}} = \frac{{{n_n}\cos {\theta _m} - {n_m}\cos {\theta _n}}}{{{n_n}\cos {\theta _m} + {n_m}\cos {\theta _n}}}$ are the reflection coefficients for s- and p-polarization respectively while n_m is refractive index of medium m, θ_m is angle of incidence, β_m is $\frac{{2\pi }}{\lambda }{n_m}{d_m}\cos {\theta _m}$, λ is wavelength and d_m is thickness of the layer.

 

Fig. 8. Three-layered structure showing three different mediums represented by n1, n2, and n3 with d1 and d2 as the thickness of first and second layer whereas third metal layer is supposed as infinitely thick to avoid transmission.

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Rearranging and applying ${r_{10}} ={-} {r_{01}}$

(9)$${E_{0f}} = \frac{1}{{{t_{01}}}}({{E_{1f}} + {r_{01}}{E_{1b}}} )$$

From Fig. 8 we also have the following relation

(10)$${E_{0b}} = {r_{01}}{E_{0f}} + {t_{10}}{E_{1b}}$$

Rearranging and applying ${t_{10}} = \frac{{1 - r_{01}^2}}{{{t_{01}}}}$

(11)$${E_{0b}} = \frac{1}{{{t_{01}}}}({{r_{01}}{E_{1f}} + {E_{1b}}} )$$

Similarly for other E-fields

(12)$${E_{1f}} = \frac{1}{{{t_{12}}}}({{E_{2f}} + {r_{12}}{E_{2b}}} ){e^{ - i{\beta _1}}}$$

(13)$${E_{1b}} = \frac{1}{{{t_{12}}}}({{r_{12}}{E_{2f}} + {E_{2b}}} ){e^{i{\beta _1}}}$$

(14)$${E_{2f}} = \frac{1}{{{t_{23}}}}{E_{3f}}{e^{ - i{\beta _2}}}$$

(15)$${E_{2b}} = \frac{{{r_{23}}}}{{{t_{23}}}}{E_{3f}}{e^{i{\beta _2}}}$$

Back substitution of (14) and (15) into (12) and (13)

(16)$${E_{1f}} = \frac{{{E_{3f}}}}{{{t_{12}}{t_{23}}}}({{e^{ - i{\beta_2}}} + {r_{12}}{r_{23}}{e^{i{\beta_2}}}} ){e^{ - i{\beta _1}}}$$

(17)$${E_{1b}} = \frac{{{E_{3f}}}}{{{t_{12}}{t_{23}}}}({{r_{12}}{e^{ - i{\beta_2}}} + {r_{23}}{e^{i{\beta_2}}}} ){e^{i{\beta _1}}}$$

Back substitution of (16) and (17) into (9) and (11)

(18)$${E_{0f}} = \frac{{{E_{3f}}}}{{{t_{01}}{t_{12}}{t_{23}}}}({({{e^{ - i{\beta_2}}} + {r_{12}}{r_{23}}{e^{i{\beta_2}}}} ){e^{ - i{\beta_1}}} + {r_{01}}({{r_{12}}{e^{ - i{\beta_2}}} + {r_{23}}{e^{i{\beta_2}}}} ){e^{i{\beta_1}}}} )$$

Rearranging we have

(19)$$T = \frac{{{E_{3f}}}}{{{E_{0f}}}} = \frac{{{t_{01}}{t_{12}}{t_{23}}{e^{i({{\beta_1} + {\beta_2}} )}}}}{{1 + {r_{01}}{r_{12}}{e^{i2{\beta _1}}} + ({{r_{12}} + {r_{01}}{e^{i2{\beta_1}}}} ){r_{23}}{e^{i2{\beta _2}}}}}$$

where,

T = Transmittance

Similarly,

(20)$${E_{0b}} = \frac{{{E_{3f}}}}{{{t_{01}}{t_{12}}{t_{23}}}}({({{r_{01}}{e^{ - i{\beta_2}}} + {r_{01}}{r_{12}}{r_{23}}{e^{i{\beta_2}}}} ){e^{ - i{\beta_1}}} + ({{r_{12}}{e^{ - i{\beta_2}}} + {r_{23}}{e^{i{\beta_2}}}} ){e^{i{\beta_1}}}} )$$

Dividing (20) by (18)

(21)$$R = \frac{{{E_{0b}}}}{{{E_{0f}}}} = \frac{{{r_{01}} + {r_{12}}{e^{i2{\beta _1}}} + ({{r_{01}}{r_{12}} + {e^{i2{\beta_1}}}} ){r_{23}}{e^{i2{\beta _2}}}}}{{1 + {r_{01}}{r_{12}}{e^{i2{\beta _1}}} + ({{r_{12}} + {r_{01}}{e^{i2{\beta_1}}}} ){r_{23}}{e^{i2{\beta _2}}}}}$$

where,

R = Reflectance, and

(22)$$A = 1 - R,$$

where,

A = Absorptance.

Disclosures

The authors declare no conflicts of interest.

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