With the continuous reduction of process nodes in integrated circuit manufacturing, the accuracy requirements for overlay measurements have become increasingly stringent. As optical overlay measurement technology advances, evaluating the robustness of overlay marks and selecting appropriate measurement conditions are essential. When the overlay mark’s pitch is smaller than the incident wavelength, an off-axis aperture and lens must be used during the measurement process to achieve tilted light incidence and obtain diffraction information. The rigorous coupled-wave analysis (RCWA) method analyzes diffraction signals under a single incidence condition. In this paper, we propose a method for calculating the diffraction efficiency of gratings under converging light based on the principle of angle-resolved scattering measurement. This method combines pupil sampling and the RCWA, allowing for the calculation of diffraction signals from resonant domain gratings whose periods are close to the incident wavelength. A model for optical characteristics in overlay measurement is established using this method. Key parameters of overlay marks with different structures, such as diffraction efficiency (D_E), measuring sensitivity (K), and stack sensitivity (S_S), are calculated for various incident light wavelengths and polarization states. In addition, the relationship between these parameters and overlay measurement errors is investigated, offering valuable insights for the design and optimization of overlay marks.

In this paper, we propose a method for calculating the diffraction efficiency of gratings under convergent light, combining pupil sampling with RCWA to obtain the ±1st-order diffraction efficiency of overlay marks (Fig. 2). The pupil is sampled in polar coordinates, and the incident angle, conical angle, and polarization angle at each sampling point are calculated. The diffraction signals of the grating, illuminated by incident light at specific positions, are computed using RCWA. Finally, the overall diffraction efficiency of the overlay mark under all incident light conditions is obtained by weighted averaging. A model for the optical characteristics of overlay measurement is established based on this method. Key parameters for a sample overlay mark (Fig. 7) are calculated for different incident light wavelengths and polarization states (Table 2). Based on the simulation results, appropriate measurement conditions are selected to achieve higher accuracy in overlay measurements. The relationship between the overlay performance parameters and overlay measurement errors is also further investigated.

The simulation results for D_E, K, and S_S under different measurement conditions (Fig. 8) reveal that overlay performance parameters depend on the mark structure, incident wavelength, polarization state, and other factors. For the example overlay mark (Fig. 7), considering the relative importance of key performance parameters, the optimal measurement conditions are, an LOL structure, incident light wavelengths ranging from 660 to 710 nm, and TE polarization. Comparing the performance parameters (K and S_S) and overlay measurement error (δOVL) under different conditions (Fig. 10), it is evident that δOVL shows several peaks when the incident light wavelengths are 480 nm and 600 nm, corresponding to values of K and S_S approaching 0. Variation curves of the ±1st-order diffraction intensity difference with overlay, ranging from -40 nm to 40 nm, are simulated for incident light wavelengths of 480 nm and 600 nm. The Pearson correlation coefficient is used to evaluate the linearity of the simulation curves. The results indicate that when the Pearson correlation coefficient between the ±1st-order diffraction intensity difference and overlay error is relatively low, and the DBO linear measurement conditions are not met, leading to significant measurement errors. To ensure high-precision measurements, wavelengths that cause large errors should be avoided by referencing the overlay simulation curve during actual measurements.

Based on the principle of angle-resolved scattering measurement, we propose a method to calculate the diffraction efficiency of gratings using joint pupil sampling and RCWA under converging light irradiation, addressing the simulation requirements for overlay marks with a pitch close to the wavelength of incident light. An optical characteristic model for overlay measurement, which calculates key parameters for overlay marks, is established using this method. We offer principles for selecting optimal configuration conditions to achieve high-precision overlay measurement. A simulation case illustrates the application of these principles. We conclude that to avoid significant overlay measurement errors, measurement conditions should be chosen where K and S_S do not approach 0, as the variation curves of the ±1st-order diffraction intensity difference with overlay exhibit apparent nonlinearity under such conditions. The method and simulation analysis presented in this paper offer theoretical support and practical references for the design and optimization of overlay marks.