Surface Reconstruction From Microscopic Images in Optical Lithography

Abstract

We propose a shape-from-shading method to reconstruct surfaces of silicon wafers from images of printed circuits taken with scanning electron microscope. Our method combines the physical model of the optical acquisition system with prior knowledge about the shapes of the patterns in the circuit. The reconstruction of the surface is formulated as an optimization problem with a combined criterion based on the irradiance equation and a shape prior that constrains the shape of the surface to agree with the expected shape of the pattern. To account for the variability of the manufacturing process, the model allows a non-linear elastic deformation between the expected patterns and the reconstructed surface. Our method provides two outputs: a reconstructed surface and a deformation field. The reconstructed surface is derived from the shading observed in the images and the prior knowledge about circuit patterns, which results in a shape-from-shading technique stable and robust to noise. The deformation field produces a mapping between the expected shape and the reconstructed surface, which provides a measure of deviation between the models and the real manufacturing process.

Computational Fluid Dynamics Modeling and Online Monitoring of Aerosol Jet Printing Process

“…26(b) and 26(c)) using calibrated stereo cameras (located off the testbed), and analyzed to extract the height of the structure based on the differences in perspective. Stereo-photometry has been implemented in literature [61,62]. This method has advantages of a large standoff distance and is more robust to rough or irregular depositions.…”

Direct Variational Perspective Shape from Shading with Cartesian Depth Parametrisation

“…where Ψ is the Charbonnier function [13] Ψ (s 2 ) = 2λ 2 1 + s 2 λ 2 (15) with contrast parameter λ . Such higher-order smoothness terms have already been successfully applied in the context of perspective SfS parametrised in terms of the radial depth [29], orthographic SfS [49], image denoising [31], optical lithography [21] and motion estimation [18]. Finally, the use of the confidence function c in the data term allows to exclude unreliable image regions which have been identified a priori, e.g.…”