Three-dimensional image correction of tilted samples through coordinate transformation

In scanned probe measurements of micrometer- or nanometer-scale lines, it is nearly impossible to maintain the sample in a perfectly level position, and even a small amount of tilt can contribute to the accuracy of the result of the measure such as linewidth or step height. The current practice in image processing to deal with this problem is to conduct a line-by-line analysis to find the best fit of the substrate profile and subtract this background from all data points, thus describing 3D plane turns as a series of lines and processing them in succession in the x- or y-direction. In this paper a coordinate transformation method is proposed. The new coordinate system can be established on the basis of the inclined angle of the sample as well as the translation of three axes between the old coordinate system and the new coordinate system. The method can mathematically derive and hence correct all tilts around the x-, y- and z-axes and produce a leveled image simultaneously. Feature dimensions such as width, height, sidewall angle and pitch are calculated on the basis of simulated images using the coordinate transformation method and other methods. The result shows the advantage of the proposed method.