Grayscale stencil lithography for patterning multispectral color filters

This document provides supplementary information to "Grayscale stencil lithography for patterning multispectral color ﬁlters". It includes details of fabrication of multispectral ﬁlter arrays, material characterization and numerical simulation of the deposition process.


NUMERICAL SIMULATION OF GRAYSCALE STENCIL LITHOGRAPHY A. Constructing point spread function of deposition
The point spread function (PSF) of each deposition step is the function of deposition time T, substrate tilting angle θ, deposition rate R = 1, mask-substrate distance D ms , source-substrate distance D ss = 52cm and material source diameter d m = 15mm. Deposition at tilted angle will result in annular-shape PSF. The inner and outer radius of the PSF are: r in = D ms tan(θ) − 1 2 d m D ms D ss cos(θ) (S1) r out = D ms tan(θ) + 1 2 d m D ms D ss cos(θ) The total amount of materials deposited inside the annular area is: T × R = T, which results in the thickness surface density ρ of: For deposition at normal incident without tilting, the PSF is circular shape with radius of r = 1 2 d m D ms D ss and thickness surface density of ρ = T/(πr 2 ),The PSF of the single step is then defined by the annular shape with area density PSF(r in , r out , ρ). The total PSF is obtained by combining the PSF of each step.PSF combined = ∑ PSF

B. Convolution between PSF and shadow mask
The shadow masks are defined as 2D binary matrix M, in which 1 represents the open areas allow material passing through while 0 represents the masked areas. The deposition result H, i.e. spatial distribution of deposition thickness, is then calculated by convolution between the PSF combined with M.

SENSITIVITY OF DEPOSITION THICKNESS, SUR-FACE ROUGHNESS AND COLOR TO THE ACCU-RACY OF SUBSTRATE ANGLE CONTROL
Due to the limitation on the manual substrate angle control in the eBeam evaporator we used, the angle accuracy is about 0.1°. Given the pre-determined deposition steps and angles, the accuracy of substrate angle control will affect the outcome, especially the surface roughness. To investigate the effects of angle control error on the deposition thickness and reflective color, we conducted the following simulation analysis. Following the steps and angles for depositions with masksubstrate distance of 10 mm as described in Section 2 and Figure  2, we simulate deposition of 150 nm and 30 nm thicknesses through the stencils shadow mask with 50% and 10% filling ratio. We introduce random error to the actual angle of each step. The real deposition angle θ real = θ target + rand · w, where θ target is the target angle of the step, rand is a random number in (-1°, 1°), w is the error weight representing the significance of the error. We calculated the mean deposition thickness and surface roughness (R a ) as the function of the error weight. The averaged values of 100 different realizations for each error weight are shown in Figure S1. Since the filling ratio of stencil determines the actual amount of materials depositing onto the substrate, the error in angle control does not affect the mean deposition thickness significantly, as shown in Figure S1 (a) and (c). However, the surface roughness increases as the angle error weight increases, which will affect the color uniformity of the actual deposition.
As shown in Figure S1 (b) and (d), the maximum Ra under certain angle realization can be higher than 10 nm, which can significantly affect the thin-film interference. Correspondingly, we simulated the actual colors of depositions with angle errors, through the stencils originally designed for the best-matched red, green and blue colors. The results with certain angle errors are shown in Figure S2. As expected, as the error weight increases, the color uniformity decreases. Interestingly, due to the sensitivities of different colors to the variation in the double TiO 2 layer thickness are different, the color uniformity among the red, green, and blue blocks are different. For example, the green color block shows less sensitivity to the surface roughness, due to the relatively large span of green on the pallet in Figure 3(b). On the other hand, the red and blue blocks show larger sensitivity to the surface roughness. Meanwhile, due to the hexagonal periodic pattern of the stencil, the color non-uniformity also shows a hexagonal periodicity. These results imply the importance of angle control in the grayscale stencil lithography.

FABRICATION DETAILS OF 10-BY-10 COLOR FILTER ARRAYS
A. Design of stencil shadow mask for the 10-by-10 blocks  Figure S3. Figure S3(d) shows an example of the circular arrays in one of the block area to define the filling ratio of 50%. The periodicity of the hexagonal circular array is 0.75 mm. The design of shadow masks were manufactured with stainless-steel PCB stencils by OSH Stencils, with 0.001" fabrication tolerance. The fabricated stencils are shown in Figure S4.

B. Deposition stage for mounting the mask ans substrate
The stencil shadow mask is fixed together with deposition substrate on a custom deposition stage, as shown in Figure S5. The top and bottom TiO 2 shadow masks were clamped by steel frames to prevent warping during deposition. Aluminum spacers from McMaster Inc. were used to control the mask-substrate distance to 10 mm. When doing eBeam deposition, the substrate stage is attached to the rotation head in the eBeam chamber with a magnetic contact, while the substrate and masks face the material source.

C. Details of eBeam evaporation
The depositions were conducted with AJA ATC-E eBeam evaporator with Glancing Angle Deposition Substrate Holder at MIT.Nano. The accuracy of manually controlled stage tilting angle is 0.1°. Ag, Pt, TiO 2 , Au, Ti, Si and Al material target from AJA Inc. were used for deposition. The deposition rate for all materials is fixed at 2Ȧ/s. The stage rotation speed is fixed at 50 rounds per minute for all deposition. Depositions were conducted with the chamber under high vacuum level above 1 × 10 −6 torr. When depositing TiO 2 , the substrate is back sputtered with O 2 to improve the oxygen content. Before and after deposition of layers with spatially variable thickness, the stencil shadow mask was added and removed from the deposition stage. For deposition of other layers, no shadow mask was used.

DISCUSSION ON THE THICKNESS VARIATION ACROSS THE BOUNDARY BETWEEN TWO COLOR REGIONS
Besides the material imperfections that can affect the color quality, which we have discussed in detail in the main text, the reflective color is also determined by the TiO 2 layer thickness in the 2-variable-layer Fabry-Perot type filter. Therefore, the color variation observed in Figure 4(e) near the edge of the two large color "blocks" can originate from two other sources. (1) The algorithm to create the stencil pattern. In this algorithm, due to the finite resolution of the stencil, discretized feature sampling is conducted at the boundary between different "blocks", which caused the fine features of distinct apertures sizes near the boundary, as shown in Figure 4(a) and (b). The deposition thickness at these locations will cause color variation. (2) Due to the deposition strategy, we introduced in Section 2 and Figure 2, the finite lateral size of the PSF and the material flux spreading at the boundary of a "block" will cause the thickness variation and an "outline" around the "block" as shown in Figure 4(c) and (d).
The first source of the edge color variation can be compensated by further developing the color matching and stencil pattern converting algorithm. While the second source can be compensated by improving the stencil resolution and edge aperture design. Here we show how the flux spreading at the boundary affects the deposition thickness to illustrate this origin of edge color variation. For example, we follow the same deposition  steps described in Section 2 and Figure 2, with mask-substrate distance of 10 mm, to deposit two adjoined regions with target deposition thickness of 150 nm and 30 nm through stencils with filling ratio of 50% and 10%, separately. We calculate the thickness profile at the boundary between the two regions, as shown in Figure S6. Due to the flux spreading at the boundary, the thickness at the boundary deviates from the targeted deposition thickness at the central area of the blocks, which results in the color variation. The boundary spread size is on the level of 1.5 mm in this case. The larger the pinhole size, the larger the flux spreading size. Therefore, regions with larger target thickness may have thicker "outline" around the blocks, as shown near the boundary of the bottom region in Figure 4(c) and (e). Even though this variation exists in the current version of stencil design, it could be compensated by improving the stencil resolution and properly designing the filling ratios and aperture patterns near the boundary, which calls for further optimization.  [1]. Optical properties of Ag [2], Pt [3], Al [3], Si [4], Au [2] and Ti [5] used in simulation were obtained from literature. The simulated reflective color was again converted with CIE color matching function under illuminant D65. The evaluation of matching between simulated color and reference colors was done based on the Delta 1994 color difference standards.

A. TiO 2 refractive index
The refractive index of TiO 2 is very sensitive to the deposition condition. Figure S7 shows the measured n of TiO 2 deposited under different conditions. Back sputtering O 2 during eBeam evaporation can help to improve the oxygen content in the deposited layer and increase the refractive index. However, the measured n is still about 0.6 lower than the ordinary TiO 2 crystals in literature [6]. †These authors contributed equally to this work