Characterization of the Inverse Problem in Critical Dimension Measurement of Diffraction Gratings

In this paper, the inverse problem of extracting critical dimensions of the grating is defined, using data obtained by ellipsometric spectrometry. We give an overview of theoretical models describing diffraction gratings and their interactions with incident light, with a special emphasis on the coupled-wave method. A method for mapping the output space (points on Poincaré’s sphere defined by the ellipsometric angles for each wavelength) to the input space (grating dimensions) is presented, where samples of the output space are picked equidistantly. Using this method, distribution of the measurement precision for a given type of experimental setup is established, and tested on examples from a set of permalloy gratings