Interprocess control of critical dimensions in production of MEMS
The most common technology for controlling the critical dimensions of MEMS is optical inspection. Manual optical inspection requires a lot of time and involves risks associated with the errors of production operators . The market of optical instruments offers sufficiently developed solutions for controlling the geometric parameters of topological structures (for example, [3, 4]), but in many cases such devices have a very high price. In this article, we describe the technique of automated processing of images obtained with the help of an automated optical system. The cost of such a solution does not exceed 13 thousand euros, and the system meets all the requirements of inspection of MEMS geometry. The developed technique allows to determine with the required accuracy the critical dimensions of hundreds of chips located on a 100 mm silicon or glass wafer. A complete optical inspection of one wafer together with image processing takes less than 10 minutes, and the same operation on manual equipment requires several hours with unstable accuracy in determining critical dimensions due to subjective (by eye) evaluation of the boundary of the measured structure by the operator.
DESCRIPTION OF METHOD
In the framework of automation of production and improvement of quality control of processes, Mapper LLC developed a script in the ImageJ macro language  for processing optical images of chips on a wafer and determining the critical dimensions of specified structures. Script analyzes images, collects data about geometric dimensions in a separate file, and then checks them for compliance with customer requirements. Further, this information is used when deciding whether to send the wafer to the next production stage or for recycling. In comparison with the manual control procedure, the automatic method allows to increase the productivity, as well as to exclude the human factor from control.
The development and testing of the script was carried out on a series of images obtained with the help of the automated optical system used by Mapper. The scheme of this optical system is shown in Fig.1. The 100 mm wafers are placed in turn on the motorized table. Images are taken with the specified focus. The movement control of the table is performed on the basis of the capturing protocol in such a way as to obtain images of the entire surface of interest. During processing of the captured images, the frames are automatically stitched into a general image of the surface of the element. The resulting stitched image is fed to the script input to obtain data on the critical parameters of the surface structures.
The generated image has a high resolution, so that its size in RAM can reach several gigabytes. Because the image processing algorithm is also resource-intensive, only selected significant areas of the stitched image are allocated and processed for saving memory. Thanks to this, a gain in the speed of computation without loss of accuracy is achieved. Since the accuracy of recognizing the boundaries of microstructures is determined by the pixel size, optical systems with a higher resolution will provide greater accuracy of the final result.
In addition to the image, the script loads a configuration file with the analysis settings and provides the resulting file with critical parameters of the structures and their statistical distribution. The advantage of this approach is that not only a single image, but also a whole series of images of a certain type can be input. The script is able to automatically detect inconsistencies in the size of structures, based on the technical requirements of the customer. The correctness of the loaded configuration file is also determined automatically by the script and it promptly warns the user in case the download was made incorrectly.
The efficiency and accuracy of the algorithm were verified by double-blind testing. Image analysis begins with the user indicating a reference position in the image. Using it, the algorithm calculates the optimal distance between the structures and compensates for the deviations in the corners that appeared due to inaccurate loading of the wafer into the optical system. In addition, starting from the reference position, the algorithm segments the image of the wafer with a certain step (due to its large size), highlighting the boundaries of the structures, and finds their parameters. At the moment when the image is fully processed according to the settings, the script finishes.
The central software algorithm is based on the Deriche's boundary method , which, in turn, was created on the basis of the corresponding Canny method . In comparison with the implementation of other methods, the advantage of the Deriche's algorithm is a high degree of both localization of the boundaries and noise suppression. In addition, the Deriche's method is convenient from the point of view of the presence of only one parameter (α) controlling the relation between localization and noise reduction: its decrease leads to a deterioration of the localization and an improvement in the signal-to-noise ratio and vice versa, which was confirmed in the further study.
To determine the optimum value of the parameter α, a series of experiments was carried out at the boundaries of structures complicated by boundary defects. Analysis of the test images was carried out for four values of the parameter α: 4; 2; 1; 0.5. For each value of α along the segment that intersects both the structure boundary and the defect, intensity charts were plotted (Fig.2). The defect is not part of the structure and should not be defined as its boundary. To determine the optimality, the criterion "one boundary – one response" was used.
Fig.2a shows the original image with a change in intensity at the boundary of the structure and the defect adjacent to it. For α = 4 (Fig.2b), the algorithm does not work optimally, since for one boundary there are at once three equivalent responses: from the boundary itself, as well as from the left and right sides of the defect. At α = 2 (Fig.2c), there are no significant changes in the intensity plot, but one can see the effect of suppressing the response from the defect boundaries.
The value α = 1 recommended in  (Fig.2d) shows a significant improvement in the determination of the structure boundary: the difference in intensity between the boundary and the defect becomes noticeably larger. However, in the course of the study it was revealed that α = 0.5 (Fig.2e) makes this difference even more noticeable without significant damage to the localization of the boundary. The conducted experiments also testify to the superiority of using the value α = 0.5, showing that at α = 1 suppression of some of the deepest and largest defects is not sufficient to achieve the optimality criterion, which makes it impossible to correctly determine the critical dimensions of the structure.
The resulting software, thanks to the segmentation of the image and the use of the Deriche's method with a matched optimal value of α = 0.5 is capable of processing an image of 2 gigabytes in about 2 minutes. The algorithm effectively identifies the necessary boundaries and separates them from the boundaries of defects, finding the critical dimensions of microstructures. It also implements the processing of a series of images, monitoring of measured parameters during the counting process, monitoring of user errors when downloading the recipe, and outputting the results to a separate file with statistical processing.
The article presents a set of image processing algorithms implemented in the ImageJ macro language. With their help, the interprocess control of the geometric dimensions of MEMS elements at the Mapper factory is automated. The results of the study of the Deriche's boundary detection algorithm allowed us to determine the optimal value of the parameter α. To improve the flexibility of the algorithms and the ability to use them for different geometries of the products, special configuration files were developed and the possibility of their creation with user settings was provided.
Although the script was designed to control the parameters of only certain wafers, the algorithms allow a significant expansion of its functionality in the future. The implementation of the software at Mapper's production allowed to exclude the influence of the human factor on the measurement processes and to shorten the time for monitoring both individual wafers and their batches. ■