Abstract
Overlay control is of vital importance to good device performances in semiconductor manufacturing. In this work, the differential Mueller matrix calculus is introduced to investigate the Mueller matrices of double-patterned gratings with overlay displacements, which helps to reveal six elementary optical properties hidden in the Mueller matrices. We find and demonstrate that, among these six elementary optical properties, the linear birefringence and dichroism, LB' and LD', along the ± 45° axes show a linear response to the overlay displacement and are zero when the overlay displacement is absent at any conical mounting. Although the elements from the two 2 × 2 off-diagonal blocks of the Mueller matrix have a similar property to LB' and LD', as reported in the literature, we demonstrate that it is only valid at a special conical mounting with the plane of incidence parallel to grating lines. The better property of LB' and LD' than the Mueller matrix elements of the off-diagonal blocks in the presence of overlay displacement verifies them to be a more robust indicator for the diffraction-based overlay metrology.
Highlights
The unceasing requirement of small semiconductor device features drives the development of many new optical lithography techniques, of which double patterning or multi-patterning lithography has emerged as a promising enhancement technique to reduce the critical dimension (CD) in the pattern on a wafer [1,2,3]
Most of current overlay measurement techniques, such as the normal incidence spectroscopic reflectometry (NISR) [6], the angle-resolved scatterometry [7, 8], the phase-structured illumination technique [9], and the Mueller matrix ellipsometry (MME) [10,11,12], arise from the optical scatterometry, termed as the optical critical dimension (OCD) metrology, which has been developed for the measurement of CD in semiconductor manufacturing [13]
Considering the fact that the off-diagonal block elements of the Mueller matrix will not be zero even when the azimuthal angle φ has a minor offset from 0° or 90° in the case of δ = 0, we want to further examine whether or not we could achieve good measurement results using γ m13 based on the principal component (PC) weighting approach at the azimuthal configurations that slightly deviate from 90°
Summary
The unceasing requirement of small semiconductor device features drives the development of many new optical lithography techniques, of which double patterning or multi-patterning lithography has emerged as a promising enhancement technique to reduce the critical dimension (CD) in the pattern on a wafer [1,2,3]. Most of current overlay measurement techniques, such as the normal incidence spectroscopic reflectometry (NISR) [6], the angle-resolved scatterometry [7, 8], the phase-structured illumination technique [9], and the Mueller matrix ellipsometry (MME) [10,11,12], arise from the optical scatterometry, termed as the optical critical dimension (OCD) metrology, which has been developed for the measurement of CD in semiconductor manufacturing [13] For this reason, the data analysis methods that have been developed for OCD metrology could be naturally applied for overlay metrology. The simulation results demonstrated that the linear birefringence or dichroism along the ± 45° axes was a more robust overlay indicator than the off-diagonal block elements of the Mueller matrix for the DBO metrology
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