Schematic of a roll-to-roll nanoimprint lithography setup showing a roller of radius R with patterned template, a rigid substrate, and a UV source. UV curable imprint material is ink-jetted as droplets on the substrate which forms a patterned resist layer after UV-curing.
Our model for the R2RNIL shows the roller with radius R and the substrate, both moving with a speed uo . (a) The inset shows the imprint droplets of radius rd with distance d between them. (b) A further simplified view of the process. The figure shows the droplets move in the positive x direction along with the roller and the substrate. The droplets merge at x = xm to form a continuous resist layer of thickness hf . The patterned imprint layer peels off from the roller at x = xp . The minimum gap between the roller and substrate is ho at x = 0.
(a) Schematic diagram showing merging of droplets to the continuous film of imprint material. (i) A continuous film of imprint material and the droplets I, II, and III. (ii) Droplet I coming in contact with the roller as it moves forward. (iii) Droplet I about to merge with the film. (iv) Droplet I completely merges into the film and droplet II merges next. (b) An enlarged view of (a) (iii) showing the position of droplets at the point of merging x = xm . The shape of droplet at x = x 1 can be approximated to be cylindrical. The droplet at x = x 2 is a part of the continuous film and completely conformed to the shape of the roller.
The figure shows the final resist peeling off from the roller as the tensile energy in the resist balances the surface energy due to adhesion in the contact region. (a) hf > ho and (b) hf < ho . For hf < ho , there is no compression zone in the resist layer and the total strain is only due to the tensile zone.
The imprint material behaves as a viscoelastic fluid as it is cured by the UV source. After complete curing, the imprint material can be modeled as an elastic solid. The figure also shows the boundary conditions governing the flow.
The plot showing the point of merging of the droplets xm as a function of hf /ho for different values of R and h o at uo = 1 m/min. The inset shows the plot between non-dimensionalized x m and non-dimensionalized hf . (▼), ho = 1 μm; (▪), ho = 100 nm; (●), ho = 10 nm; (—), R = 2 cm; (---), R = 1 cm.
The plot showing the point of peel-off of the resist from the roller xp as a function of hf /ho for different values of R and ho at uo = 1 m/min. Theinset shows the plot between non-dimensionalized xp and non-dimensionalized hf . (▼), ho = 1 μm; (▪), ho = 100 nm; (●), ho = 10 nm; (—), R = 2 cm; (---), R = 1 cm.
The plot showing the exposure time of the resist layer t as a function ofhf /ho for different values of R and ho at uo = 1 m/min. The inset shows the plot between non-dimensionalized t and non-dimensionalized hf . (♦), ho = 10 μm; (▼), ho = 1 μm; (▪), ho = 100 nm; (—), R = 2 cm; (---), R = 1 cm.
The pressure profile in the viscoelastic regime of the resist layer as a function of distance x for ho = 100 nm, R = 1 cm, uo = 1 m/min, and different values of ho.
The pressure in the elastic region of the resist layer from x = 0 to x = xp for uo = 1 m/min, ho = 1 μm. A positive pressure implies a compressive force, while a negative pressure implies tensile strain in the resist layer. (▼), hf /ho = 0.9; (●), hf /ho = 1.8; (—), R = 2 cm; (---), R = 1 cm.
The force per unit width on the substrate as function of ho at uo = 1 m/min for different values of R and hf /ho . (—), hf /ho = 1.1; (---), hf /ho = 0.98.
The shear force per unit width (fs ) on the substrate as function of ho at uo = 1 m/min for R = 1 cm and different values of hf /ho .
The torque per unit width (T) on the roller as function of ho at uo = 1 m/min for R = 1 cm and different values of hf /ho .
Estimated minimum UV intensity, I (W/cm2) required for curing.
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