With the development of semiconductor technology, the critical dimensions of electronic devices in today’s integrated circuit manufacturing continue to shrink, and the devices are gradually transitioning from traditional planar transistor structures to complex three-dimensional (3D) architectures. While enhancing the performance of logic and memory chips, these changes also pose more measurement challenges. For instance, it is necessary to measure more structural parameters and smaller critical dimensions. Throughout the chip manufacturing process, it is crucial to conduct in-line measurements on the critical dimensions of various two-dimensional (2D) orthogonal grating structures to accurately characterize their structural shapes, thereby ensuring the processing quality. Grazing-incidence small-angle X-ray scattering (GISAXS) is a metrology technique capable of probing structural features on the order of 1-100 nm and providing average topographic information over a large surface area. It enables high-resolution and nondestructive measurements and has the potential to address metrology challenges in semiconductor at future nodes. However, traditional GISAXS methods are mainly employed for measuring the critical dimensions of line gratings. When it comes to 2D orthogonal gratings, traditional GISAXS methods require the gratings to rotate gradually from 0° to 90° during measurement, which results in long measurement time. Therefore, there is still a lack of good solutions to 2D orthogonal grating measurement in GISAXS.

We propose a method to measure the critical dimensions of 2D orthogonal gratings with GISAXS. By analyzing the distribution of Bragg rods in the reciprocal space, a model for locating Bragg peaks of 2D orthogonal gratings at arbitrary incidence and rotation angles is built. Based on this model, the intensity of Bragg peaks can be accurately extracted and rapidly simulated, which helps obtain the reciprocal space information from GISAXS images at different rotation angles. To verify the validity of the proposed model, we perform a simulated GISAXS measurement for 2D orthogonal gratings. The 2D orthogonal grating nanostructure is modeled as five stacked frustums, with different critical dimensions and center offsets in the x and y directions and various parameter values at different heights. A total of 101 GISAXS patterns of this 2D orthogonal grating are generated within the rotation range from 0° to 10°. By employing the derived model of Bragg peaks in GISAXS, the intensity from both high-order and low-order Bragg peaks can be extracted from the simulated pattern at each rotation angle. Meanwhile, the loss function is employed to evaluate the discrepancy between reference data and simulated data of 2D orthogonal gratings with different parameters. Additionally, the differential evolutionary algorithm is adopted to solve the inverse problem of reconstructing the in-depth profiles of 2D orthogonal grating nanostructures.

As shown in Fig. 4(b), when the rotation angle φ=0°, high-order and low-order Bragg peaks are distributed on separate arcs in the GISAXS pattern. As the sample rotates, the arcs deviate in the same direction. Using the localization model, the positions of Bragg peaks at different rotation angles of the 2D orthogonal grating can be precisely determined to quickly extract the corresponding intensity data from the GISAXS patterns. The intensity distribution of different Bragg orders is shown in Fig. 5. These scattered intensity modulations reflect the 3D structural characteristics of the 2D orthogonal grating, which can be reconstructed by analyzing these signal profiles and performing an optimization process. The ranges of the optimization parameters are listed in Table 2 and initial parameter values are randomly generated. To achieve the inverse parameter solution, we incorporate both the data of high-order Bragg peaks (m=-1) and low-order Bragg peaks (m=0) into the optimization process. As shown in Fig. 6, the in-depth profiles of the 2D orthogonal grating nanostructure are successfully reconstructed. Simulation results demonstrate that this method can accurately measure the critical dimensions and center offsets at different heights of 2D orthogonal grating nanostructures and significantly reduce the range of required rotational scanning angles.

We propose a method for measuring the critical dimensions of 2D orthogonal gratings using GISAXS. A theoretical model for locating the Bragg peaks at arbitrary incident angles and rotation angles is built, which contributes to the analysis and extraction of reciprocal space information from GISAXS patterns. Our method makes full use of the position and intensity information from both the high-order and low-order Bragg peaks during the optimization process to solve the scattering inverse problem. Simulation results demonstrate that the critical dimensions and center offset parameters of the 2D orthogonal grating are successfully characterized. Compared to traditional methods, the proposed method requires no additional prior information, and a narrow range of rotation scans is enough to obtain sufficient information and thus accurately reconstruct the in-depth profiles of the complex 2D orthogonal grating nanostructure. This promotes the application of GISAXS in the measurement of 2D orthogonal gratings, which will lay a foundation for further development of GISAXS in semiconductor measurements.