Robust surface reconstruction by design-guided SEM photometric stereo

We present a novel approach that addresses the blind reconstruction problem in scanning electron microscope (SEM) photometric stereo for complicated semiconductor patterns to be measured. In our previous work, we developed a bootstrapping de-shadowing and selfcalibration (BDS) method, which automatically calibrates the parameter of the gradient measurement formulas and resolves shadowing errors for estimating an accurate threedimensional (3D) shape and underlying shadowless images. Experimental results on 3D surface reconstruction demonstrated the significance of the BDS method for simple shapes, such as an isolated line pattern. However, we found that complicated shapes, such as lineand-space (L&S) and multilayered patterns, produce deformed and inaccurate measurement results. This problem is due to brightness fluctuations in the SEM images, which are mainly caused by the energy fluctuations of the primary electron beam, variations in the electronic expanse inside a specimen, and electrical charging of specimens. Despite these being essential difficulties encountered in SEM photometric stereo, it is difficult to model accurately all the complicated physical phenomena of electronic behavior. We improved the robustness of the surface reconstruction in order to deal with these practical difficulties with complicated shapes. Here, design data are useful clues as to the pattern layout and layer information of integrated semiconductors. We used the design data as a guide of the measured shape and incorporated a geometrical constraint term to evaluate the difference between the measured and designed shapes into the objective function of the BDS method. Because the true shape does not necessarily correspond to the designed one, we use an iterative scheme to develop proper guide patterns and a 3D surface that provides both a less distorted and more accurate 3D shape after convergence. Extensive experiments on real image data demonstrate the robustness and effectiveness of our method.