Asymmetric fluid-structure dynamics in nanoscale imprint lithography

λE IE R0E R1Film withRefractive Index nAirFilmSubstrateFigure 4.1 Interference effectGap sensing is based on the periodicity of the reflectivity spectrum, asseen in equation 4.2. Since the spectral reflectivity is periodic in wavenumber,for 400 ~ 800 nm. Fourier analysis can be used to perform a spectraldecomposition. The calculation of the thickness of an optical thin film is trivialonce this information is obtained. The thickness of a film can be computed asdiMagFFT= [4.3]2 nwn∆wnwhere i FFT is the index of the FFT maximum and n wn is the wavenumber averagedindex of refraction. The ratio of sampled points in the wavenumber spectrumtaken at even intervals over a spectral range,d∆wn1=λmin1−λmax, to the number ofpoints in the FFT is defined as the magnification factor, Mag [Colburn 2001].This method can measure film thickness down to about 350 nm based on awavenumber averaged refractive index of 1.5 and has been demonstrated to be ingood agreement with spectral ellipsometry and profilometry. For films below 350nm, Inflection-Maximum-Minimum Analysis (IMMA) is used to compute thefilm thickness. The reader is referred to Chapter 8 of Colburn’s dissertation formore detailed information the theoretical background of FFT-based spectralreflectometry. This gap sensing system is under development for Dissolution55