1. INTRODUCTION

The push to miniaturize bulky optical elements to go from 3D forms into 2D forms has driven the development of flat optics and metasurfaces [1] for applications in optical filtering and wave front manipulation [2,3]. Optical multilayer structures have been applied widely as spectral filters [4–7] and diffractive elements [8,9] with a small form factor, in which the thickness variation within the layer structure offers the key customizability. In spectral filters, structures of various layer thicknesses support tunable optical modes, which results in the customizable transmission or reflection. Furthermore, as shown in Fig. 1(a), pairing arrays of color filters with photodetectors increasingly draws attention as a promising solution to acquire spatially resolved hyperspectral information in a single snapshot [10]. For this purpose, planar thin film filters by means of Bragg stacks or Fabry–Perot cavities [11] outperform color pigments [12], optical gratings [13], and metasurfaces [14] due to their wavelength tunability, small footprint requirements for dispersion, and high efficiency. Metal–dielectric–metal-type optical cavities have been applied widely as reflective or transmissive color filters [15,16], with high customizability by adjusting the dielectric layer thickness. The minimized differences regarding the required physical stack configuration along with a highly variable spectral function makes it a promising candidate for multispectral color filter arrays. However, the major challenge for the application lies in the manufacturing complexity of multilayer structures with different materials and 2D patterning of arrays with spatially variable layer thicknesses responsible for the individual filtering spectrum.

 

Fig. 1. (a) Example of optical multilayer structures as customizable filter arrays by spatially varying the middle layer thickness, which can be applied for multispectral or hyperspectral sensing. (b) Schematic of conventional lithography method to generate spatially varying deposition thickness by iterative patterning through multiple photoresist masks. (c) Schematic of the proposed grayscale stencil lithography that can generate patterns of spatially varying deposition thickness with single shadow mask. Details of the deposition strategy and results are discussed in Sections 2 and 3.

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The conventional method to create thin film patterns with spatial thickness variation usually utilize patterned photoresists as the shadow mask to define open areas for each material deposition or etching step [17,18], as shown in Fig. 1(b). The material thickness generated by each iteration is fixed among all of the open areas. By repeated deposition through multiple photoresist hard masks, the pattern of thin films with spatial thickness variation can be created. Notwithstanding the low manufacturing efficiency and hurdles involved with the pattern alignment, lithography, and lift-off, the final number of achievable wavelength bands for color filtering applications is also limited by the number of iteration cycles used [14]. Recently, a grayscale lithography technique has been applied to overcome the aforementioned obstacles [11,19,20]. The development rate of photoresists used for grayscale lithography is sensitive to the exposure dose. As a result, the spatial control of photoresist thickness after development could be achieved by adjusting the dose over the patterning area. Grayscale lithography has been applied to generate Fabry–Perot-type optical stacks by using the resist either directly as the dielectric layer or as the etching mask to transfer the thickness profile onto the underneath dielectric substrate. In the first scenario, despite the improved patterning efficiency and resolution of grayscale lithography, the choice of low-index photoresists limits the design space of optical properties for the dielectric layer. Alternatively, using the grayscale patterned photoresist as etching masks enables a wider choice of materials. However, the need for etching will further increase the manufacturing complexity and cost. Therefore, a manufacturing technology that can efficiently generate customizable spatial thickness variation without limited material choices is needed, which can allow us to find the structural and material design for multispectral color filters with fewer manufacturing requirements and better filtering performance.

In this paper, we propose grayscale stencil lithography for customizable spatially thickness-variable eBeam material deposition without the iterative patterning process, as shown in Fig. 1(c). Stencil lithography utilizes steady or movable shadow masks, usually made of semiconductors or metals, with apertures defining the open areas for material deposition [21–23]. The features of resistless-ness and reusability of the stencil shadow mask make it favorable for fabricating micro/nano electro-mechanical systems. In conventional stencil lithography, the transferred deposition pattern has a fixed thickness over the patterns defined directly by the apertures on the shadow mask [21]. We develop a grayscale version of stencil lithography by utilizing the filling ratio of aperture arrays on the customized stencil to define the total amount of deposited materials over certain areas on the substrate. Meanwhile, we design strategies to optimize the point spread function (PSF) of the deposition. Therefore, the materials passing through the shadow mask can be evenly deposited onto the areas defined by the aperture arrays and results in a prescribed spatial thickness profile with a single and reusable shadow mask. This technique allows us to efficiently customize the material stacks for color filtering applications. Even though the current lateral patterning resolution is limited by the commercial stencil used in the paper, the size and periodicity of the apertures can approach micro- to nano-meter scale with advanced machining or milling technologies [24,25], and we foresee great application potentials of the proposed method for micro/nano-scale fabrication.

Further, we demonstrate a proof-of-concept reflective multispectral color filter array with two thickness-variable layers fabricated with grayscale stencil lithography. This offers a broader design space to achieve a wide reflection spectrum on the CIE color space since we are no longer limited to the use of a photoresist as one of the optical layers as in grayscale lithography [11,19,20]. This is done by extending conventional stencil lithography from a binary version [21,22] into a grayscale version so that optically favorable high-index materials can be deposited with arbitrary thickness across a wafer scale. We also introduce improvements on the material design side, by showing how to extend conventional metal–dielectric–metal stacks [15,16] into a double cavity or a more advanced stack (as shown later with a Si-containing stack) to capture a large 2D region of the CIE plot with a 2D or even just 1D variation in the stack thickness. We further investigate the dependence of optical performance and reproducibility on the quality control of deposition and materials. The stack designed with a single thickness-variable layer of Si achieves a wide reflective color span with a thinner total thickness and less dependency on the material’s deposition quality.

2. GRAYSCALE STENCIL LITHOGRAPHY

The grayscale stencil lithography process can be seen as an analogue to optical imaging through arrays of pinhole cameras with finite apertures. The ejection of materials in the eBeam pockets is analogous to the “light” coming from the “source,” which passes through the holes on the shadow masks to finally cast the “image” onto the deposition substrate with spatially variable thickness “intensity.” We define the thickness distribution of the deposition through an infinitely small hole on the shadow mask as the PSF, which is determined by the depositing strategy described below. The convolution between arrays of apertures with finite size on the shadow mask with the PSF determines the image of customizable 2D patterns of spatial thickness variation. We designed shadow mask patterns using circular apertures on hexagonal arrays and sent them to OSH Stencils for commercial laser cutting onto a 3 mil (76 µm) thick metal stencil. The periodicity and size of the holes determine the spatially customizable filling ratio, which controls the local amount of materials that can be deposited onto the substrate. During deposition, the stencil is mounted onto holders with spacers to create a specific distance between the shadow mask and substrate. In order to reduce the surface roughness of material deposited through the discrete stencil apertures, we chose a PSF with a Gaussian-shaped distribution and a lateral dimension larger than the periodicity of the apertures on the shadow mask. This is because the overlap between depositions through adjacent similarly sized apertures will help to homogenize the deposition rate behind this group of apertures. Theoretically, how the materials spread through an infinitely small hole on the shadow mask can be controlled by the shape factor of the source, so that the Gaussian-shaped PSF and the deposition with spatial thickness variation can be achieved within a single step. This can be done by customizing the angular profile of material ejected from the eBeam pockets. Williams and others demonstrated an attempt of this manner to fabricate layered structures with linear thickness variation along only a single spatial direction [26] using rather complex deposition instrumentation, which is not feasible for most common eBeam evaporators. Due to the limitation on continuously adjusting the material ejection profile, we need to divide the deposition into multiple steps with the substrate tilted at specific angles while rotating the substrate along the deposition. The combination of circular PSFs defined by each step results in the digitized Gaussian-shaped PSF, in which the PSFs of individual steps are just adjoining. Finally, by performing a convolution between the PSF and the shadow mask, we can predict the 2D spatial variation of the resultant patterned deposition. (See Supplement 1 for the details of numerical simulation of deposition results.) Further, we would like to point out that this idea can be applied to material deposition methods other than eBeam evaporation, e.g.,  physical vapor deposition, as long as the material’s flux travels in straight lines. However, the effects of the target source shape factor in different deposition methods need to be considered when modeling the PSF. The sharp emission point in the eBeam evaporator simplifies our modeling.

 

Fig. 2. (a) The deposition process used combines four substrate tilting angles and deposition time, each of which gives a different PSF of the deposited material. Examples of how the PSF arises is shown for one particular point in the dot-raster shadow mask. The combined PSF results in the digitized Gaussian-shaped PSF designed to have a span $D$ larger than the periodicity of apertures on the stencil shadow mask. The convolution between the combined PSF and the shadow mask is the predicted deposition thickness. (b) Simulated deposition thickness and surface roughness (${{\rm{R}}_{\rm{a}}}$) as functions of stencil’s filling ratio, following the procedures shown in (a). (c) Simulated ${{\rm{R}}_{\rm{a}}}$ at fixed deposition dose of 42 (arbitrary unit) and various filling ratios and mask–substrate distances. The numbers denote the minimum required deposition steps to achieve a combined PSF with lateral dimension larger than 0.75 mm.

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For example, Fig. 2(a) shows one specific strategy of a four-step deposition with substrates tilted at $\theta = 0^\circ$, 1.7°, 3.3°, and 5.0°, and deposition times $T$ of 2.7, 14.8, 15.6, and 8.9 (arbitrary unit) at some constant deposition rate. The PSF of an individual step and combined PSF were simulated based on our eBeam evaporator equipment, where the simulation parameters include material source diameter (15 mm), source–substrate distance (52 cm), and mask–substrate distance (10 mm), which results in the Gaussian-shaped PSF with lateral dimension $D$ of 1.01 mm. The convolution between the combined PSF and a shadow mask with apertures of various filling ratios arranged in a ${3} \times { 3}$ block array results in the deposition of block patterns with spatial thickness variation. As shown in Fig. 2(b), simulations with filling ratios ranging from 0% to 50% show that the deposition thickness is linearly proportional to the filling ratio, while the arithmetic averaged surface roughness (${{\rm{R}}_{\rm{a}}}$) at each filling ratio is small. In the simulated range, the maximum ${{\rm{R}}_{\rm{a}}}$ of the aforementioned strategy is 0.22 (A.U.) at a filling ratio of 36.4% with targeted deposition thickness of 16.1 (A.U.). We can foresee that a sub-2 nm ${{\rm{R}}_{\rm{a}}}$ can be achieved in deposition thicknesses ranging from 0 to 150 nm for color filter applications described in the following sections.

A sufficiently wide combined PSF is required to reduce the deposition surface roughness caused by the unevenly overlapped material flux through adjacent apertures on the shadow mask. Since we cannot continuously customize the material ejection profile from the eBeam pocket in our equipment, we have to discretize the analog PSF into multiple deposition steps to achieve the digitized Gaussian PSF shown in Fig. 2(a). The trade-off between the fabrication complexity, i.e., number of deposition steps, and the surface roughness is discussed in Fig. 2(c). The number of required deposition steps is defined as the minimum steps needed to have the lateral dimension $D$ of the combined PSF larger than the periodicity of the apertures on the shadow mask (0.75 mm). Since the source–substrate distance is practically fixed in a deposition chamber, the required number of deposition steps is the function of only mask–substrate distance. In Fig. 2(c), we plot the ${{\rm{R}}_{\rm{a}}}$ of deposition with various filling ratios and mask–substrate distances, with a fixed total amount of deposition dose of 42 (A.U.). The numbers on the plot indicate the required deposition steps. With increasing mask–substrate distance, the number of required deposition steps decreases, since the contributing width of the circular PSF from each deposition step expands. For mask–substrate distance ranging from 5 to 17 mm, the surface roughness is small, as shown in the bottom panel of Fig. 2(c). However, when increasing the mask–substrate distance to beyond 17 mm, the surface roughness increases dramatically because the two-level digitized PSF then deviates a lot from the perfect Gaussian-like profile required to homogenize the deposition profile beyond the shadow mask. The maximum ${{\rm{R}}_{\rm{a}}}$ can be as large as 20 nm for a targeted deposition thickness of 150 nm. For actual depositions demonstrated in the following sections, the mask–substrate distance is chosen to be 10 mm to balance the fabrication complexity, control accuracy of tilting angles (about 0.1°), and surface roughness. (See Supplement 1 for more discussion on the sensitivity of deposition outcomes to the accuracy of angle control.) A more precisely controlled deposition, e.g.,  PSF with a hexagonal lateral shape, can help to further minimize the surface roughness. However, it requires computer-numerical control of the substrate rotation motor and the deposition tilting angle, which are beyond the customizability of the eBeam evaporator we used. Also, we would like to point out that other treatments including substrate temperature control can further reduce surface roughness caused by island effects or surface diffusion, which are neglected in our modeling.

 

Fig. 3. (a) Schematic of the multilayer stack structure of ${\rm{TiO}}_{2}/{\rm{Pt}}/{\rm{TiO}}_{2}/{\rm{Ag}}$ on Si substrate. The top and bottom ${\rm{TiO}}_{2}$ layers have variable thicknesses from 0 to 150 nm. (b) Simulated reflective colors of the stack structure by varying the top and bottom ${\rm{TiO}}_{2}$ layer thicknesses, under illuminant D65. The cross marks denote the closest matching with representative colors of red, green, blue, cyan, magenta, yellow, black, and white. (c) Simulated spectral absorption profiles in the stack structures with configurations matching with red, green, and blue colors. The thicknesses of bottom and top ${\rm{TiO}}_{2}$ layers (${t_{\rm{b}}}$, ${t_{\rm{t}}}$) are (138 nm, 36 nm), (78 nm, 70 nm), and (98 nm, 128 nm), separately. (d) Experimental deposition results of stacks with block patterns of variable reflective colors. The scale bar is 2 cm. (e) Comparison between experimental and simulated reflection spectra of stacks with targeted bottom and top ${\rm{TiO}}_{2}$ layer thicknesses of (133 nm, 33 nm), (100 nm, 133 nm), and (83 nm, 66 nm), corresponding to red, green, and blue curves, separately. (f) Reflective color span on the CIE plot. The closed black dashed line shows the simulated envelope of achievable color span by the stack structure. The open circular dots show the measured reflective colors on the ${10 } \times { 10}$ blocks in (d). The inserted plot shows the zoom-in color trajectories of stacks with 33 nm and 100 nm top ${\rm{TiO}}_{2}$ layers, while the spline curves with arrows show the direction of bottom ${\rm{TiO}}_{2}$ layer increment.

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3. RESULTS AND DISCUSSION

A. Two-Variable-Layer Multispectral Color Filter Arrays

The grayscale stencil lithography method allows material deposition of customizable 2D patterns with spatial thickness variation. In the following section, we apply the method to fabricate multispectral reflective color filter arrays with two layers of variable thicknesses to achieve a broad span of the color spectrum. The configuration of the multilayer stack structure is shown in Fig. 3(a), which contains ${\rm{TiO}}_{2}/{\rm{Pt}}/{\rm{TiO}}_{2}/{\rm{Ag}}$ on Si substrate. The thickness of Pt and Ag layers are fixed at 15 nm and 40 nm, separately, whereas the thicknesses of the top and bottom ${\rm{TiO}}_{2}$ layers vary from 0 to 150 nm. The stack structure acts as a lossy double optical cavity. The Ag bottom reflection layer is thick enough to prevent light penetration into the Si substrate. Light is absorbed mainly by the middle Pt layer. Different configurations of the top and bottom ${\rm{TiO}}_{2}$ layer thicknesses result in the variation of the spectral absorption profile by the Pt layer across the visible range to give rise to multispectral reflective colors. As shown in Fig. 3(b), the achievable colors are simulated by solving the reflection spectrum of the stack structure with variable top and bottom ${\rm{TiO}}_{2}$ layers at a step of 2 nm. The cross marks on the plot denote the layer configurations of the closest color matching with the representative colors of red, green, blue, cyan, magenta, yellow, black, and white. In Fig. 3(c), the spatial distribution of absorbed spectral energy inside the stack structure, i.e., spectral absorption profile, of configurations matching with the red, green, and blue colors is plotted. The thickness axis denotes the position inside the stack, from bottom to top. The high absorption region is located in the middle Pt layer. By varying the top and bottom ${\rm{TiO}}_{2}$ layer thicknesses, the electric field distribution in the stack is altered, resulting in the variation of the spectral absorption profile. Different from conventional lossless Fabry–Perot cavities in which destructive interference causes color filtering, the reflected color here is determined by the spectrum of the least absorbed wavelengths by the middle thin metal layer.

The designed multispectral reflective filter array is fabricated with the grayscale stencil lithography method. The deposition follows the same steps and angles as in Section 2 and Fig. 2. (See Supplement 1 for details of the shadow mask assembly.) Stencil shadow masks for depositing the top and bottom ${\rm{TiO}}_{2}$ layers are designed with ${10} \times {10}$ blocks of varying aperture filling ratios linearly spanning from 0% to 50%. A bottom mask with block holes is placed on top of the substrate through the process to confine the deposition in the areas defined by the blocks. During the deposition, we need to use each of the two stencil shadow masks only once for each of the two ${\rm{TiO}}_{2}$ layers. Compared with the conventional lithography-and-lift-off process [12,17,18], which needs $N$ times of iterative lithography and deposition with different photoresist patterns to generate $N$ different thicknesses, our grayscale stencil lithography method significantly reduces the fabrication complexity. The deposition result is shown in Fig. 3(d), with arrows indicating the directions of linearly increasing top and bottom ${\rm{TiO}}_{2}$ layer thicknesses. A white LED light source is illuminated on to the sample and generates vivid colors properly reproducing the simulation predictions in Fig. 3(b). Currently, the spatial resolution of the color patches deposited by this method is limited by the stencil resolution since the material flux has to be deliberately expanded and overlapped (see the Supplement 1 discussion on the flux spreading at the boundaries) to uniformly cover the block region behind apertures. The resolution limit of deposited features is determined by the size of these regions, which is in turn determined by the aperture spacing on the stencil. Further advancements in stencil manufacturing and deposition control will improve the fabrication resolution.

Simulated and measured reflection spectra of configurations matching with red, green, and blue reflective colors in real depositions are shown in Fig. 3(e). Different from the conventional metal–dielectric–metal structure with single and sharp light absorption peaks [5,27], the double cavity with two variable high-index dielectric layers generates multiple spectral absorption peaks with relatively wide bandwidth in the visible range [28], which expands the span of the reflective color spectrum. The simulated envelope of reflective colors achieved with the current stack configuration is shown as the dashed line in Fig. 3(f). We can see that the current design has better color coverage for red and blue compared to green, which is due mainly to the wide bandwidth of reflection peaks located in the green region. The thickness of the middle metal layer plays a crucial role in determining the color span [5], which will be discussed in later sections. The measured colors on the fabricated sample are shown as the circular dots located inside the envelope in Fig. 3(f). Due to the finite number of top and bottom ${\rm{TiO}}_{2}$ layer thickness combinations, the measured colors are a discrete sampling within the area inside the envelops. The inserted zoom-in plot shows the color trace on the CIE chart of stacks with 33 and 100 nm top ${\rm{TiO}}_{2}$ layers. The spine curves and arrows show the evolution of reflective colors with increasing the bottom ${\rm{TiO}}_{2}$ layer from 0 to 150 nm. Even though the color trajectories are similar, the stack with the 100 nm top ${\rm{TiO}}_{2}$ layer has a wider reflection bandwidth, which causes the trajectory to be closer to the white center. Meanwhile, we would like to point out that the design of this stack is not optimized regarding color space coverage due to our limited searching in materials and structural parameters. Another design with improved CIE coverage but more complex material combinations will be shown in the following section.

Furthermore, we demonstrate that the grayscale stencil lithography method can be applied to deposit arbitrary 2D patterns. As shown in Fig. 4, an “MIT Dome” pattern on silicon substrate was deposited following the same aforementioned stack configuration. The stencil shadow masks to deposit the top and bottom ${\rm{TiO}}_{2}$ layers are shown in Figs. 4(a) and 4(b). The simulated deposition thickness is shown in Figs. 4(c) and 4(d). The final deposition result is shown in Fig. 4(e). It is obvious that there is an irregular non-uniform color mismatch on the pattern, which may be caused by issues related to the degradation of ${\rm{TiO}}_{2}$’s refractive index due to oxygen deficiency [29,30] and non-uniform deposition thickness across the wafer substrate. More details will be discussed in the following sections. Besides the material imperfection, the flux spreading at the boundaries between different color regions can also cause thickness and color variations at the boundaries between different color regions. (See the Supplement 1 discussion on the flux spreading at the boundaries.)

 

Fig. 4. (a), (b) Schematic of masks used for top and bottom ${\rm{TiO}}_{2}$ layer depositions of the “MIT Dome” pattern. (c), (d) Simulated deposition thickness with spatial thickness variation following the strategy in Fig. 2(a). (e) Deposition results on Si substrate cut from 152.4 mm wafer. All scale bars are 2 cm.

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To investigate the relation between the reflective color span and the thickness of the middle Pt layer, we compared the numerical simulation of the reflection spectrum and color palettes of stacks with middle Pt layers of 5, 15, and 30 nm, as shown in Fig. 5(a). When reducing the Pt layer thickness to 5 nm, the absorption by the metal layer decreases, which causes the shrinkage of the color span as noted by the dashed envelope on the CIE chart. Meanwhile, with the 5 nm Pt layer, the stack structure approaches the configuration with only ${\rm{TiO}}_{2}$ and Ag layers. As a result, the inserted palette plot shows less dependence on the individual top and bottom ${\rm{TiO}}_{2}$ layer thicknesses, but stronger dependence on the summation of two ${\rm{TiO}}_{2}$ layer thicknesses. On the other hand, increasing the Pt layer thickness increases the reflection by the Pt layer, and reduces the amount of light that can be coupled into the bottom ${\rm{TiO}}_{2}$ layer. Therefore, the achievable color spectrum shrinks significantly to the white center on the CIE chart; meanwhile, the palette shows less sensitivity to the bottom ${\rm{TiO}}_{2}$ layer thickness. Figure 5(b) shows the simulated reflection spectrum of stack configurations with 5, 15, and 30 nm Pt layers. When the middle Pt layer is 15 nm, the three configurations correspond to the closest matches with red, green, and blue colors. Similar to a simple metal–dielectric–metal structure, increasing the Pt layer thickness enhances the light confinement in the Pt/bottom ${\rm{TiO}}_{2}/{\rm{Ag}}$ layers and sharpens the spectral absorption profile. Along with the effects of complex round-trip phase shifting in the Pt and ${\rm{TiO}}_{2}$ layers, increasing the Pt layer thickness causes the shifting and broadening of the reflection spectrum. In summary, the middle Pt layer thickness determines the trade-off between the light that can be coupled into the Pt/bottom ${\rm{TiO}}_{2}/{\rm{Ag}}$ layers and the amount of light that can be absorbed by the Pt layer. It further determines the achievable reflective color span and the sensitivity against adjusting the top and bottom ${\rm{TiO}}_{2}$ layers. Based on the aforementioned consideration, we chose 15 nm as the Pt layer thickness for previous sample deposition.

 

Fig. 5. (a) Color span and tunability of stacks with middle Pt layers of 5 nm, 15 nm, and 30 nm. The dashed lines in the CIE chart denote the simulated envelope of achievable reflective colors by the stack. The inserted plots show the simulated palettes of stacks with various Pt layer thicknesses, which follow the same coordinates in Fig. 3(b). (b) Simulated reflection spectra of stacks with various Pt thicknesses. The bottom and top ${\rm{TiO}}_{2}$ layer thicknesses are (138 nm, 36 nm), (98 nm, 128 nm), and (78 nm, 70 nm), separately, corresponding to the best matching with red, green, and blue colors with 15 nm Pt layer. (c) Required total thickness of ${\rm{TiO}}_{2}$ layers for matching the six representative colors, as the function of index degradation in ${\rm{TiO}}_{2}$. (d) Evaluation of color matching scores for the six representative colors, as the function of index degradation in ${\rm{TiO}}_{2}$.

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Another crucial parameter that affects the reflective color is the complex refractive index of the materials in the multilayer structure. Ag and Pt are relatively stable through the eBeam deposition process. However, the refractive index of ${\rm{TiO}}_{2}$ is very sensitive to the oxygen content and deposition condition. Oxygen deficiency can cause a lower $n$ of ${\rm{TiO}}_{2}$. The measured real-part refractive index of ${\rm{TiO}}_{2}$ is about 0.6 less than the fitting of ordinary ${\rm{TiO}}_{2}$ crystals in literature [31]. (See Supplement 1 for details of material characterization.) In order to investigate the effects of the refractive index differences on the reflective color, we simulated the color palettes of the same stacks with varying top and bottom ${\rm{TiO}}_{2}$ layers from 0 to 150 nm at a step of 5 nm. The $n$ of ${\rm{TiO}}_{2}$ is modeled by the fitting equation of DeVore [31], with an additional $\delta$ term to quantify the degradation of it:

B. One-Variable-Layer Multispectral Reflective Color Filters

For the two-variable-layer stack, in order to achieve a broad range of colors, the combined thickness of the ${\rm{TiO}}_{2}$ is quite thick at up to 300 nm in total. However, the coverage of the reflective spectrum in the green and cyan regions is still not optimum. Also, as discussed in the previous section, ${\rm{TiO}}_{2}$ is also susceptible to sub-stoichiometric deposition, which results in the degradation of the refractive index. The combined factors of the great thickness and the imperfection of the deposited ${\rm{TiO}}_{2}$ means that the reproducibility of the structural color can be quite unreliable.

In order to reduce the dependence on the material’s quality of the variable thickness layers and further reduce the total stack thickness to achieve a rainbow reflective spectrum, we searched for a stack limited to just one variable layer. This was found to be feasible using Si as the variable layer, since Si has a more predictable refractive index than ${\rm{TiO}}_2$ under eBeam deposition. Although the results were generated from a random search, we can understand why Si emerged as the best candidate, as it has a high refractive index and a corresponding low absorption coefficient in the visible spectrum. With a more predictable refractive index, a smaller stack height, and a reduction in the variable layers from two to one, this Si-containing stack will allow us to test the optical limits of color reproduction using grayscale lithography while eliminating physical imperfections that deteriorate and blur the color reproduction.

 

Fig. 6. (a) Schematic of stack structures with single Si variable layer for generating rainbow reflective color spectrum. (b) Simulated spectral absorption profiles for stacks with Si layers of 59 nm, 34 nm, and 18 nm, separately, corresponding to best matching of red, green, and blue colors. (c) Schematic of rotation stencil deposition to generate a radial-varying reflective color pattern. The stencil shadow mask with radial-varying filling ratios can convert a uniform material flux to linearly increased flux along the radial direction. The scale bar is 3 cm. (d) Simulated and measured reflective colors generated by stacks with single thickness-variable layer. The black line and arrow denote simulated reflective color of our stack when the thickness of Si varies from 0 to 100 nm. The black dots are the experimental measured color of the same stack with the Si layer thickness varying from 0 to 75 nm. The observed range of color is much greater than other thin film stacks, such as the Ge on Au stack from Kats and others with a 0 to 30 nm Ge layer [7].

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The configuration of the stack with one variable layer thickness is shown in Fig. 6(a), which includes complex multilayers of 18 nm ${\rm{TiO}}_{2}/7\;{\rm{nm}}$ Ti/8 nm Au/25 nm ${\rm{TiO}}_{2}/8\;{\rm{nm}}$ Ag/Thickness variable layer of Si from 0 to 75 nm/30 nm Al on Si substrate. This stack shares a mechanism similar to the two-variable-layer design to generate reflective structural color. Figure 6(b) plots the spectral absorption profile of the configurations matching best with the red, green, and blue colors. The Si layer thicknesses for the three configurations are 59, 34, and 18 nm, respectively. Meanwhile, the required total stack thickness is less than 180 nm. The absorption takes place mainly in the top Ti and Au metal layers. This stack generates broader and stronger spectral absorption bands, which results in a sharpened reflection spectrum, especially for the green color. We validated this stack design with a second form of “grayscale” stencil lithography. A shadow mask was custom-designed with apertures shown in Fig. 6(c), which can convert a uniform material deposition flux in the eBeam chamber into a linearly varying flux in the radial direction. During deposition, the shadow mask is separated from the substrate and rotates relative to the substrate. The effective filling ratio of the open area on the shadow mask is designed to be linearly dependent on the radial position. The use of a filling ratio to influence the deposition flux is essentially the same methodology as used in the 2D grayscale stencil lithography. For this rotating shadow mask, we benefit from a simpler mask design and fabrication, but sacrifice one degree of freedom since we can vary the filling ratio only radially instead of over a 2D space. This mask allows fast verification of reflective properties of a designed optical stack with a single variable layer. The generated circular-symmetric color pattern is shown in Fig. 6(c), where the linearly increasing flux of Si material corresponds to a color variation along the radial direction. After deposition, different parts of the wafers were observed with an ellipsometer to capture the reflected spectrum. The simulated and measured evolution of reflective colors is shown in Fig. 6(d). This time, the stack could cover more green and cyan color spaces compared to the previous design. The color space coverage is improved compared to previous studies [7] and comparable to recent state of the art [19]. Meanwhile, the saturation of the observed colors lies close to the simulated colors, showing a low sensitivity of reproduced colors to the material deposition imperfection. The remaining mismatch can probably be explained by sub-stoichiometric deposition in the ${\rm{TiO}}_{2}$ layers or natural oxidation in reactive metals such as the Ti and Al surfaces used in this stack. Due to the infinite design space for multilayer stack configurations, the optimum stack design is hard to define since it depends on a compromise between the reproduction accuracy of any required colors and the fabrication complex of the multilayer stack.

4. CONCLUSION AND OUTLOOK

In summary, we developed a new type of grayscale stencil lithography method to deposit 2D patterns with spatial thickness variation, which improves manufacturing efficiency and removes material limitation compared to conventional iterative lithography-and-lift-off approaches and grayscale lithography methods. We demonstrated the deposition strategy to generate spatial thickness variation with a single stencil shadow mask; meanwhile, the surface roughness can be reduced to less than 2 nm for a deposition thickness of 150 nm. Then, this approach was utilized for a proof-of-concept application to create multispectral reflective color filter arrays with two thickness-varying ${\rm{TiO}}_{2}$ layers, which produced a wide range of structural color in the visible range. The mechanism of reflective filtering in the lossy Fabry–Perot-type stack structure was studied by investigating the effects of the metal absorbing layer thickness and the degradation of ${\rm{TiO}}_{2}$ layers’ refractive index on the achievable color range and quality. We showed that by tuning the Pt layer thickness, the trade-off between the color span and customizability could be balanced.

Further, another stack design was proposed to overcome the limitations of using ${\rm{TiO}}_{2}$ as the variable layer, whose required thickness and index degradation may reduce the deposition reproducibility and reliability. A single variable thickness of Si was applied in the alternative stack configuration, which shows a rainbow reflective spectrum, thinner overall thickness, and less sensitivity to deposition imperfection. Even though the physical design of Fabry–Perot-type cavities is not new, this improved design implies that more complicated combinations of materials may deserve a deeper searching to further optimize optical multilayers as color filters.

The grayscale stencil lithography method demonstrated shows great potential for micro/nano fabrications due to its features of customizable 2D patterning with spatial thickness variation and the freedom of applicable materials for deposition. Manufacturing and processing technologies developed for nano stencil lithography [24,25] can be applied directly to further improve the patterning resolution of the grayscale stencil lithography technique. As the aperture size becomes smaller, the effects of material clogging and mask thickening during the deposition need to be considered, which is neglected in the current work due to the larger size of apertures compared to the deposition thickness. Meanwhile, methods to prevent aperture clogging with self-assembled molecules on the shadow mask are also appealing [24]. Despite those challenges, the customizability brought by grayscale stencil lithography is beneficial for applications beyond color filtering. It can potentially replace the current design principles of flat optics, which are limited by the conventional spatially fixed depositions. By using this technique, it would be possible to fabricate flat Fresnel/Kino-like lens [33] or microlens arrays [34]. We also foresee a broad application of it in active and tunable filter arrays [35], and flat diffractive optical elements [36]. Meanwhile, the gentler technological curve of this method is favorable for labs without access to heavily booked eBeam lithography machines in exploring the field of flat optics.