As the manufacturing process is more integrated, in the field of metrology, there is an increasing demand for method to monitor local dispersion of measurement value that can trace randomly generated week points in the chip. Since it is difficult to obtain local dispersion with an optical method where the relatively large spot compared to the size of the target structure, many attempts have been made to use other method such as scanning electron microscopy (SEM). It is clear that SEM is suitable for obtaining local dispersion thanks to its high resolution, but it is difficult to obtain thickness information because only contrast data is included in the image. From these demands, a method using gray level (GL) index of the SEM image to estimate the depth of the target pattern has been proposed. However, because it is an index that simply correlates the GL value to the depth without considering pattern geometry, it follows different trends depending on the design rule and dispersion of the critical dimension (CD) and depth. In order to overcome this inhomogeneity of the GL index, in this study, we propose 3D GL index considering the field of view (FOV) of secondary electron (SE) emission according to the 3D geometry of the pattern. We apply effective FOV derived from SE emission function estimated by Lambertian distribution and CD and depth of the pattern to conventional GL index. As a result of applying it to the polysilicon hole pattern and comparing it with the vertical-SEM depth measurement, unlike the existing index, 3D GL index shows a clear linear trend with high correlation R2 of 0.781 regardless of design rule and dimension variation. In that it can more accurately and robustly respond to process variation, the proposed 3D GL index can increase the utilization of the depth monitoring method using SEM image.
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