Mathematical analyses of inverse scatterometry

Emmanuel M. Drege; Rayan M. Al-Assaad; Dale M. Byrne

doi:10.1117/12.473453

16 July 2002 Mathematical analyses of inverse scatterometry

Emmanuel M. Drege, Rayan M. Al-Assaad, Dale M. Byrne

Proceedings Volume 4689, Metrology, Inspection, and Process Control for Microlithography XVI; (2002) https://doi.org/10.1117/12.473453
Event: SPIE's 27th Annual International Symposium on Microlithography, 2002, Santa Clara, California, United States

Abstract

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.

Citation Download Citation

Emmanuel M. Drege, Rayan M. Al-Assaad, and Dale M. Byrne "Mathematical analyses of inverse scatterometry", Proc. SPIE 4689, Metrology, Inspection, and Process Control for Microlithography XVI, (16 July 2002); https://doi.org/10.1117/12.473453

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