Lithography is a key technology in integrated circuit manufacturing. Before each exposure, the mask must be precisely aligned with the pattern formed by the previous lithography to ensure minimal positional error between different layers. The alignment process is jointly completed by the alignment system of the lithography machine and the alignment marks on the wafer, which directly affects the chip overlay accuracy and production yield. The continuous reduction of feature size leads to higher requirements for alignment accuracy, and the alignment marks are prone to asymmetric deformation due to process influence, resulting in alignment position deviation. The asymmetry of marks is an important factor affecting alignment accuracy, and selecting alignment marks with good process adaptability in advance is the key to ensuring alignment accuracy. Therefore, by establishing a simulation evaluation model for alignment marks, the variation laws of alignment position deviation (APD) and wafer quality (WQ) with deformation size, groove depth, and duty cycle are analyzed for marks that undergo asymmetric deformation at different positions. The principle of selecting marks based on process adaptability is also given, which provides support and reference for the design optimization of alignment marks and the evaluation of alignment accuracy.

At advanced nodes, due to the alignment mark period to incident wavelength ratio being less than 10, the grating is in a resonance region with a complex diffraction behavior, and an accurate model is established using a rigorous coupled wave analysis. For asymmetric deformation alignment marks, the rigorous coupled wave analysis alone cannot accurately construct their surface shape function, and it is necessary to use a joint layer approximation method to divide them into several layers with equal thickness. When there are enough layers of division, each layer can be approximated as a rectangular structure. At this time, the rectangular grating of each layer can be calculated separately, and the reflection coefficient and diffraction efficiency can be solved by combining the boundary conditions of each layer. Then, using the reflection coefficients of positive and negative diffraction beams, the APD is calculated.

Using APD and WQ of the alignment mark as evaluation parameters, the appropriate number of layers for the mark is determined. First, the variation of APD and WQ with deformation amount, groove depth, and duty cycle under different asymmetric deformation conditions is analyzed. The simulation results of changing the magnitude of deformation indicate that the absolute value of APD is positively correlated with the magnitude of deformation, and the sensitivity of APD measured at different wavelengths and polarization states to changes in deformation varies. Under the same amount of deformation, when asymmetric deformation occurs at the top, the APD changes the most and the sensitivity is the highest, followed by that at the bottom, and that at the sidewall is the smallest (Figs. 8-10). Second, the simulation results of changing the groove depth show that when the groove depth is 1/2 of the incident wavelength, the WQ curve shows a valley with a value close to 0, and the APD shows a jumping extremum. In contrast, when the groove depth is 1/4 of the incident wavelength, a peak appears in the WQ curve and there is no fluctuation in APD (Fig. 11). Third, the simulation results of changing the duty cycle show that when the duty cycle of the alignment mark is selected around 0.5, the APD value is lower and the WQ is larger (Fig. 12).

In this study, a method is proposed for calculating APD using positive and negative diffraction order reflection coefficients based on the principle of self-referencing interference. APD and WQ are used as evaluation parameters to analyze the variation of APD and WQ with deformation amount, groove depth, and duty cycle under different positions of asymmetric deformation. When asymmetric deformation occurs at the sidewall, the APD is least affected by the deformation amount and the sensitivity is the lowest, followed by that at the bottom, and that at the top is the highest. When the asymmetric mark is at the sidewall, the APD is least affected by the duty cycle and the sensitivity is the lowest, followed by that at the top, and that at the bottom is the highest. When asymmetric deformation occurs at the top, bottom, or any position on the sidewall, the APD is not significantly affected by the depth of the groove. Therefore, the APD at different positions is influenced by parameters such as deformation amount, groove depth, duty cycle, etc., and changes with the different positions of deformation, while WQ is less affected by the position of deformation and the magnitude of deformation. The alignment system of the lithography machine needs to be configured with multiple measurement wavelengths to avoid the measurement signals with extreme APD values and improve the process adaptability of groove depth. When the duty cycle is selected around 0.5, the APD value is low and the WQ is large. The methods and the simulation results proposed in this article provide support and reference for the design optimization of alignment marks and the evaluation of alignment accuracy.