Asymmetric fluid-structure dynamics in nanoscale imprint lithography

directly applicable to in situ gap sensing in SFIL. Some of these methods requireprecise angular sweeps such as the X-ray method described by Sakurai and Iida.Others can be quite computationally complex, requiring comparisons betweenexperimental and theoretical waveforms, which are stored in a database for aparticular film with known optical properties such as the index of refraction. Thissearch for matching waveforms can be time-consuming. In this research, a realtimegap sensing method that can potentially measure thin films down to 50 nmhas been applied to measure the gap between the template and the substrateduring the squeezing process. This chapter attempts to provide the background inthe optical theory necessary to understand the basis for this innovative tool.4.2 ANALYSIS OF SPECTRAL REFLECTIVITYWhen an optical flat is placed in near contact with another optically flatsurface, dark and bright bands will be formed. These bands are known asinterference fringes, caused by constructive (bright bands) and destructiveinterference (dark bands) of light, and their shape gives a visual representation ofthe flatness and parallelism of the surface being tested. The parallelism andthickness of the gap is indicated by the amount of curvature and spacing betweenthe interference fringes. Straight, parallel, and evenly spaced interference fringesindicate that the two flat surfaces are parallel along one axis. Spectralreflectometry relies on this constructive-destructive interference property of light.For optically thin films in the visible wavelength range, the oscillations inthe reflectivity are periodic in wavenumber (k = 2π/λ) such as shown the by theequation for the reflectivity of a single optical thin film53