Large-range lithography misalignment sensing with sub-2-nm accuracy through automatic dual-frequency Moiré fringes analysis

Lithography is the backbone of semiconductor and microelectromechanical system (MEMS) fabrication, where even the slightest deviation on the nanometer scale can ripple through an entire production chain, affecting both yield and reliability. As the push toward smaller device geometries intensifies, multi-exposure lithography has become indispensable for realizing ultra-fine patterning. However, this advancement brings its own complications—chief among them, the precision of alignment and the limited sensing range during overlay correction. These two factors now stand as central obstacles to the continued scaling of modern lithographic systems. Moiré fringe–based alignment techniques have, in many respects, been the preferred choice in the industry. Their appeal lies in their simple optical configuration, high sensitivity, and theoretical ability to achieve sub-nanometer resolution. Nonetheless, two deeply rooted issues constrain their full potential: the periodic aliasing of fringes and the spectral leakage encountered during phase extraction. The first limits the measurable displacement range to only a few micrometers, as the repeating periodicity of the Moiré pattern causes ambiguities once the misalignment exceeds roughly half of the grating period. The second arises during digital phase retrieval, where signal truncation and discrete sampling unavoidably distribute spectral energy into neighboring frequencies. Together, these effects compromise both range and precision, rendering traditional Moiré-based systems unsuitable for the next generation of nanofabrication tools that demand extended dynamic range without sacrificing accuracy. Researchers previously have explored various ways to overcome these limitations such as introducing static interferometric references, hierarchical grating designs, or beat-frequency modulation schemes and while each method brings a measure of improvement, most increase optical complexity or computation time, and few are robust enough for industrial-scale application. More recently, deep-learning-based algorithms have entered the scene, promising adaptive fringe interpretation but requiring extensive datasets and heavy processing power, which limit their practicality in real-time environments. Still, the most persistent challenge remains spectral leakage. In Moiré alignment imaging, the discrete Fourier transformation of non-integer sampled fringes inevitably spreads the spectral power, corrupting phase-unwrapping accuracy precisely where nanometer-level sensitivity is crucial. Containing this leakage without eroding spatial detail continues to be one of the more complex problems in precision lithography metrology. To this account, new research paper published in Optics Express and conducted by Feifan Xu, Jin Zhang, Weishi Li, and led by Professor Haojie Xia from the School of Instrument Science & Opto-electronics Engineering at Hefei University of Technology, The researchers developed two key innovations: a composite dual-frequency alignment mark consisting of upper and lower differential gratings, and an automatic lookup difference table (ALDT) algorithm for absolute misalignment computation. The dual-frequency mark enables interference patterns with extended periodicity, while the ALDT algorithm decodes large displacements unambiguously.

The research team designed a composite alignment mark in which the upper differential gratings (periods P₁ and P₂) functioned as measuring elements, while the lower gratings (P₃ and P₄) served as references. When illuminated by a coherent light source, interference between these grating pairs produced two sets of Moiré fringes—one with period PM₁₂ and the other with PM₃₄. Because these periods differ, the interference generates a dual-frequency pattern whose combined phase evolution encodes a unique mapping of wafer-mask misalignment. This arrangement effectively merges fine and coarse measurements into one optical process, allowing large-range detection without additional alignment marks. To extract accurate displacement data from the captured fringe images, the authors developed the ALDT algorithm. This method converts the offset of dual-frequency fringes into a set of arithmetic progressions, where each pair of upper and lower fringe shifts defines a unique misalignment interval. By establishing a lookup table of these intervals, the system can unambiguously determine the actual offset even when it exceeds the fundamental Moiré period. The result is a non-iterative, absolute measurement capable of spanning a range determined by the least common multiple (LCM) of the grating-derived base units. In practice, this translated to an expansion of the measurable range from 2.6 µm to 120 µm—a nearly 50-fold improvement over conventional systems.

The authors ensured phase accuracy and showed each fringe image processed with a 2D-HSCW prior to applying fast Fourier transform–based phase extraction. This self-convolution window function effectively suppressed spectral leakage that typically arises from non-integer truncation or camera sampling effects. Their simulations using MATLAB validated that the 2D-HSCW achieved unbiased phase estimation, even under significant image truncation. The precision of upper and lower fringe measurements remained within nanometer deviations across all test conditions, with the upper fringes consistently yielding superior accuracy. Then they validated experimentally on custom-fabricated alignment marks etched onto chrome-coated quartz wafers via ion-beam lithography. Using a collimated 530 nm LED source and a high-resolution CMOS camera, the researchers conducted step-displacement tests on a vibration-isolated optical platform. The ALDT algorithm maintained real-time performance, requiring only 0.15 seconds per measurement. Across multiple experimental runs, the system achieved sub-2-nm accuracy, with maximum errors below 2 nm and mean absolute errors under 1.54 nm.

In conclusion, the development reported by Professor Haojie Xia’s team represents a decisive step toward unifying high-precision and large-range lithography alignment within a single optical framework. Indeed, with the two-dimensional Hanning self-convolution window, the new system achieves sub-2-nm accuracy across a 120 µm range, offering a unified, real-time solution to lithography alignment challenges. The combination of composite dual-frequency Moiré marks and the ALDT algorithm resolves a long-standing tradeoff between measurement range and accuracy—a problem that has limited Moiré-based systems for decades. The researchers successfully established an elegant numerical scheme that bypasses periodic aliasing, allowing misalignment to be decoded uniquely across an extended range by interleaving the arithmetic intervals of two fringe sets,. This mathematical structure transforms what was once a relative measurement into an absolute one, delivering stability that is essential for the sub-nanometer domain. It is worth mentioning the role of the 2D-HSCW and by the authors addressing spectral leakage at the source rather than through post-hoc correction, they ensured the integrity of phase information even when imaging conditions deviate from ideal assumptions. The new method’s ability to achieve real-time processing while preserving nanometer accuracy demonstrates its suitability for in situ industrial integration. The fact that such precision was maintained across 120 µm of range marks a fundamental shift in how alignment sensors can be engineered for advanced semiconductor production. Beyond lithography, the framework opens new opportunities in precision metrology, MEMS calibration, optical displacement sensing, and nanoscale assembly. Any system requiring accurate relative position tracking—such as wafer bonding, deformable mirror alignment, or nanoscale robotics—can benefit from this dual-frequency Moiré strategy. Its algorithmic architecture, based on modular arithmetic and difference lookup, can also be adapted for three-dimensional positioning or even integrated with machine learning for self-correcting calibration. The implications extend further into manufacturing efficiency. Eliminating the need for separate coarse alignment steps simplifies the optical head design and shortens process cycles, reducing cost and complexity. As fabrication nodes approach the angstrom scale, where overlay tolerances become comparable to atomic dimensions, techniques capable of sub-2-nm reproducibility are indispensable. Professor Haojie Xia and colleagues approach therefore satisfies current industrial needs and also anticipates future requirements for ultra-dense integrated circuit production.