Stress on the roller system

When the substrate and the mask in the roller system are moving, constant stress is being applied on the substrate, which might affect the light distribution in the PR layer. In this section, we evaluated this stress and the associated photoelastic properties of the PR film. As shown in Figure 29A, the transparent quartz cylinder has a diameter 𝐷 of 150 mm with a thickness of 3 mm. The photomask and photoresist on the PET films are mounted on PDMS cushions with the thickness 𝑇 of ~ 5 mm. The PET film has a thickness of 100 ~ 200 µm and the PR layer has a thickness 𝑡 of 100 nm. The thickness of the PET mask and PR layer is negligible compared to that of PDMS cushions. Therefore, only the deformation of the PDMS cushions are taken into consideration in estimating the stress on the PR layer. Based on the experimental setup, the area of PDMS cushions in contact is 𝐴 = 𝑊 × 𝐿 = 5 mm × 40 mm. The angle of the contact region is 𝜃 = 𝑊 𝜋𝐷⁄ ~ 3.82°, which is quite small. Thus, we can treat the PDMS cushions as flat surfaces during the contact exposure. The PDMS cushions have a Young’s modulus 𝐸 of ~ 1.8 MPa, [70,74] and the deformation in thickness 𝛿𝑇 of the PDMS cushions during the movement of the stage and the cylinder can be estimated to be ~ 1 mm. The strain on the PDMS cushion is ℰ = 𝛿𝑇 𝑇⁄ , and the corresponding stress is 𝜎 = 𝐹 𝐴⁄ , where 𝐹 is the force and 𝐴 is the contact area. According to the

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definition of elastic modulus 𝐸 = 𝜎 ℰ⁄ . The force on the PR layer can be calculate as 𝐹 = 𝐸𝐴𝛿𝑇 𝑇⁄ ~ 72 N and the stress on the sample is 𝜎 = 𝐸𝛿𝑇 𝑇⁄ ~ 3.6 × 105 _Pa.

Figure 29 Stress analyses and photoelasticity of the PR film.

(A) Schematics of the quartz cylinder (B) Thickness independence of the PR layer.

By treating the thin PR layer as an isotropic medium, two-dimensional photoelasticity is applicable and the magnitude of its relative retardation is given by the stress-optic law [75]

𝛥 =2𝜋𝑡

𝜆 𝐶(𝜎1− 𝜎2) (19)

where 𝛥 is the induced retardation, 𝐶 is the stress-optic coefficient, 𝑡 is the PR thickness, 𝜆 is the vacuum wavelength, and 𝜎1 and 𝜎2 are the first and second principal stresses, respectively. The

exact value of the stress-optic coefficient of the PR film used in the experiment is not reported to the best of our knowledge, thus the typical value of polystyrene (PS) 𝐶 ~ 1×10-10 _Pa-1 _{[76] is used}

for the estimation of the photoelasticity. In fact, the stress-optic coefficients of polymer films including PS, polycarbonate (PC) and cyclo olefin copolymer (COC) are quite similar. Hence the index change of the film due to the stress can be estimated as 𝛿𝑛 = 𝐶 ∙ 𝜎 ~ 3.6×10-5_{, which is}

negligible compared to the refractive index of PR 𝑛𝑃𝑅 ~ 1.69. As shown in Figure 29B, when the

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Since the Al film in the lithography system has losses, the quality factor (Q-factor) of the waveguide mode is low, therefore providing higher tolerance for the index change. The induced retardation due to the stress can be calculated as 𝛥 = 2𝜋𝑡𝐶𝜎 𝜆⁄ ~ 5.6×10-5 _{rad across the whole}

resist layer, which is far less than 𝜋/2. Because of the weak PR thickness dependence, this tiny phase retardation should not affect the interference of light. Therefore, we conclude that despite of the constant stress from the roller during the exposure, the light distribution in the PR remains unchanged and uniform.

2.6.4 Results and discussions

Continuous nano-scale patterns are successfully produced using our plasmonic roller system, as shown in Figure 30. The photomask mounted on PDMS in the PRL is illustrated in Figure 30A, and the SEM image of the pattern is shown in Figure 30C. The patterns are composed of parallel lines with the linewidth around 50 nm on PR with thickness of 100 nm, which is comparable to the result of waveguide lithography system discussed in Chapter 2. Since the mask is currently made by EBL, the scale of the patterns is 2 mm ×1 mm, the corresponding photo of the mask and resist under microscope is shown Figure 30B and D, respectively. If larger pattern is desired, the width can be readily extended by increasing the size of the mask and laser beam. However, the length of the final pattern is determined by the motion of the motorized stage.

In this preliminary work, we used the photomask on PET made by EBL; however, the mask can also be made by nanoimprint lithography or photolithography to achieve an Al grating over a larger area. Plasmonic photo roll lithography is possible with custom-built equipment to print large-scale patterns continuously with high-speed. Larger pattern size is possible as hardware upgrades. If larger pattern is desired, the width can be readily extended (might up to several meters) by

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increasing the size of the mask and laser beam. The length of the pattern is can be controlled determined by the motion of the motorized stage (might up to kilometer). With further optimization, such systems can find their have practical applications in the large-scale production of electronics and photonics, such as integrated circuits, solar panels as well as LCDs, etc.

Figure 30 Experimental results made by the plasmonic roller system.

(A) Photo of the PET mask mounted on the quartz cylinder (B) Periodic pattern on the PET mask under microscope. The scale of the mask is 2 mm × 1 mm. (C) SEM images of the nanoscale pattern in PR with thickness of 100 nm. (D) Photo of the resist pattern under microscope.