Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles

Abstract

Diffraction from a periodic structure is sensitive to small changes in the shape of that structure. It is possible to exploit this behavior of the scatter data for accurate, precise, rapid, nondestructive, and in situ measurements of grating structures. We present the use of rigorous coupled-wave theory to generate diffraction profiles to train a partial least-squares (PLS) multivariate calibration routine. The resulting PLS calibration model was applied to experimental diffraction data from gratings in etched bulk silicon to predict etch depths. A single-detector scanning scatterometer was used to measure the scatter from 32-μm-pitch structures illuminated with a He–Ne laser beam. The scatterometer measured the diffraction patterns from grating structures at 14 die locations on each of a set of five wafers. The theoretically based PLS estimator was then used to predict etch depths from scatterometry data obtained from the 70 different grating structures. The etch depth predictions were in excellent agreement with those obtained with a scanning force microscope (i.e., 0.9-μm-deep structures were predicted with an average error of 0.007 μm). This is a significant step toward the solution of the parametric inverse grating diffraction problem: that of quantitative prediction of structure dimensions from the measurement of scatter data.