White light interferometry, as an effective non-destructive method, is widely employed for measuring characteristic parameters of microstructures. Among these microstructures, the rectangular grating is a typical periodic step structure and has extensive utilization in precision machining due to its diverse materialization properties based on surface morphology characteristic parameters. However, when the groove depth of the grating is smaller than the coherence length of the adopted light source, the batwing effect occurs near or at the edge of the step in the sample under measurement. ISO series 25178 provides a standard morphology for calculating the characteristic parameters of groove depth and linewidth through three-dimensional surface morphology analysis, which necessitates determining the position of the step edge. The batwing effect poses challenges to precisely locating the step edge position and may result in a false representation of information near the edge of the step discontinuity. We propose a new algorithm for determining the characteristic parameters of rectangular gratings by utilizing the distribution difference of the coherence signals between the upper and lower surfaces, thus avoiding the traditional method of extracting step edge position from three-dimensional surface morphology. The introduced algorithm demonstrates excellent measurement accuracy, high repeatability, and exceptional robustness in calculating the desired characteristic parameters of rectangular gratings.

We propose an algorithm for precise positioning of the step edge in rectangular gratings based on the distribution difference of the coherence peak among different sampling points. The algorithm is designed to improve the detection efficiency of characteristic parameters by incorporating parallel processing techniques. Firstly, during vertical scanning, the coherence signals undergo modulation. Simultaneously, the contrast information is obtained by the gravity method to extract the center of gravity position of the modulation envelope across all sampling points within the field of view. Then, the peak of the contrast envelope is calculated to further accentuate the discrepancy between the upper and lower surfaces of the rectangular grating. By identifying these surfaces, we acquire the step position information, which allows to generate the mask matrix and determine the linewidth values. To obtain the groove depth, we combine the mask matrix and three-dimensional surface morphology of the rectangular grating. Meanwhile, we extend the application of the "W/3" guideline specifically for the rectangular grating structure to mitigate the influence of the batwing effect on depth measurements. Additionally, we incorporate the Stoilov algorithm to calculate the contrast information during the vertical scanning, enabling simultaneous determination of the step edge position and three-dimensional surface morphology. This parallel processing approach enhances the efficiency and accuracy of the algorithm. Generally, our algorithm provides an effective means for precisely positioning the step edge in rectangular gratings, while considering the influence of the batwing effect on depth measurements.

Experiments are conducted via a self-developed white light interferometry system to evaluate the feasibility and accuracy of the proposed method. Two rectangular gratings with different characteristic parameters are selected as measurement samples. The first sample calibrated by Physikalisch-Technische Bundesanstalt (PTB) has a groove depth of 189.6 nm±1.0 nm and a linewidth of 6 μm. The second sample certified by VLSI standards traceable to the National Institute of Standards and Technology (NIST) has a groove depth of 90.5 nm±2.8 nm and a linewidth of 50 μm. Ten repeatability measurements are performed in the same area of each sample based on the proposed algorithm. For the first sample, the average depth value is determined to be 188.97 nm with a relative error of 0.33% [Fig. 8(a)]. The average linewidth value is measured to be 6.12 μm with a relative error of 2% [Fig. 8(b)]. Similarly, for the second sample, the average depth value is 90.10 nm with a relative error of 0.40% [Fig. 8(c)]. The average linewidth value is determined to be 99.04 μm with a relative error of 0.96% [Fig. 8(d)]. These measurement results demonstrate the accuracy and effectiveness of the algorithm. Furthermore, the standard deviation of the ten repeatability measurement results is analyzed to assess the algorithm stability. The small standard deviation confirms the consistent and reliable performance of the proposed method. Additionally, the influence of error terms during the experiment on the measurement results is investigated. Specifically, variations in sample placement tilt angle, interference fringe numbers, and interference fringe direction are examined. The results indicate that these error terms exert minimal effect on the measurements, highlighting the robustness of the proposed algorithm. In general, the experimental results validate the feasibility and accuracy of the algorithm in accurately determining the groove depth and linewidth of rectangular gratings. The algorithm exhibits stability and robustness and becomes a reliable tool for precise metrology in surface morphology measurements.

We present a new approach for accurately measuring the characteristic parameters of rectangular gratings under the batwing effect. Unlike conventional calibration methods, our method focuses on the distribution difference of coherence signals between the upper and lower surfaces of the grating. This approach addresses the limitations of ISO series 25178 in accurately measuring the characteristic parameters in the presence of the batwing effect. To validate this method, we conduct simulations of interferograms during the vertical scanning based on linear system theory. By analyzing the modulation envelope of these interferograms, we can precisely detect the step edge position and distinguish the upper and lower surfaces of the grating sample. Finally, by applying ISO standards, we accurately measure the characteristic parameters of the rectangular grating. Experimental results using two rectangular gratings with different groove depths and linewidths demonstrate the repeatability and robustness of our method. The implementation of the "W/3" guideline in measuring rectangular gratings is significantly improved to accurately measure the characteristic parameters. Importantly, our method features high efficiency, high precision, and fine repeatability without requiring any physical upgrades to the instrument. Considering the ongoing trend towards miniaturization of rectangular gratings, our method has broader applications.