Scatterometry is an optical technique that has been studied and tested in recent years in semiconductor fabrication metrology for critical dimensions. Previous work presented an iterative linearized method to retrieve surface-relief profile parameters from reflectance measurements upon diffraction. With the iterative linear solution model in this work, rigorous models are developed to represent the random and deterministic or offset errors in scatterometric measurements. The propagation of different types of error from the measurement data to the profile parameter estimates is then presented. The improvement in solution accuracies is then demonstrated with theoretical and experimental data by adjusting for the offset errors. In a companion paper (in process) an improved optimization method is presented to account for unknown offset errors in the measurements based on the offset error model.
Comparative study of the relaxation behavior at very low frequencies of acrylate polymers with pendant 1,3dioxane rings in their structureThe profile shape and the flow behavior of polymer nanoscale gratings made by a thermal nanoimprint process are precisely examined using visible light angular scatterometry. Nanoimprinted poly͑methyl methacrylate͒ ͑PMMA͒ lines with 60-800 nm width, 100-200 nm height, and varied residual thicknesses of 70-400 nm have been investigated using this optical approach, and insightful observations are made regarding residual stress buildup during thermal nanoimprint. In addition, a nonlinear profile model has been developed for scatterometry to monitor the "melting" behavior of PMMA gratings under annealing around its glass transition temperature. The polymer nanostructures were found to relax primarily at high stress regions.
Optical scatterometry has been proven to be a useful tool for the inspection and assessment of lithographic processes. The characteristic signature of the scattergram provides information about the surface relief profile and can be rapidly and non-invasively acquired. Currently, attention is being focused on the inversion of scatterometric data to determine the surface profile of the relief structure. To overcome the highly non-linear relationship between the properties of the diffracting structure and the diffraction measurements, we present a linearized solution based on a least-squared refinement method. This approach relies on the reliability of lithographic processes, which allows us to determine the departures of structural key parameters from a set of expected design values. This linearized inversion, as shown by the mathematical formalism, is independent of the scatterometric measurement configuration. Hence it can be applied whether, for example, the incident angle or wavelength of the light is varied to acquire either irradiance of phase information. This is validated in this paper by various examples handling the retrieval of three geometrical parameters (groove depth, line width, and sidewall angle) from reflectance data simulated using the rigorous coupled-wave theory (RCWT) for both angular and wavelength scans. An additional benefit of the proposed linearized solution is the ability to examine mathematically the significance of measurement errors. An analytical propagation of error is presented, connecting measurement noise to the soughed parameter precisions and uncertainties. We applied this formalism to the cases mentioned above, where we simulated the retrieval of three parameters from measurements containing various levels of noise. This studies allows us to draw preliminary conclusions on the sensitivity of scatterometry with respect to the number and types of structural parameters to be retrieved, but also to the technique employed to gather the measurements.
Visible light angular scatterometry is applied to characterize the geometry and physical properties of sub-100-nm-wide polymer gratings fabricated using nanoimprint lithography and electron beam lithography. Measurement sensitivities to small variations in linewidth and slope angle were evaluated theoretically, which suggests that TM polarized incident light offers improved sensitivity for the measurements of sub-45-nm critical dimensions ͑CDs͒. A variable angle scatterometer using a red laser is built, and measurement results of various polymethylmethacrylate ͑PMMA͒ gratings with sub-100-nm CDs reveals good accuracies and fit well to the scanning electron microscopy ͑SEM͒ measurements. In addition to geometry and dimension measurements, new functionality is implemented in the modeling to characterize polymer residue thickness, polymer flow dynamics, and evidence of stress in the nanoimprinted polymer gratings. Scatterometry is also applied to detect possible undercut line profiles resulting from electron beam lithography. The results promote using this low-cost and noninvasive technique to characterize polymer nanostructures as well as understand and control the underlying lithographic processes. © 2008 Society of Photo-Optical Instrumentation Engineers.
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