Main

In the semiconductor microelectronics industry, multiple exposure is increasingly important. Lithography alignment technologies have advanced significantly, evolving from early methods such as bright-field and dark-field alignment to sophisticated techniques such as interferometric and heterodyne holographic alignment. This progression has improved alignment accuracy from the micrometre to the nanometre scale, significantly benefitting the integrated circuit manufacturing industry. Modern high-precision lithography systems primarily use grating diffraction-based spatial filtering and field image processing alignment. These methods, including zone plate, laser interference and Moiré fringe-based alignments, generally achieve accuracies greater than 20 nm. However, as chip stacking and feature size scaling continue, there is an increasing need for even greater alignment accuracy and process stability to maintain yield, performance and reliability in complex, multilayer semiconductor manufacturing. Alignment technology using traditional optical imaging means in multiple exposure is limited by the optical diffraction limit. Overcoming this limitation remains a significant challenge1,2,3. In this work, we demonstrate a method that exploits a physical optical phenomenon—bound states in the continuum (BICs)4,5,6,7,8—to overcome this longstanding limitation.

BIC were first explored in quantum mechanics nearly a century ago. It is only within the past 10 years that their complex physics has been utilized to create sharp resonances, known as quasi-BIC, in a range of photonic systems9,10,11,12,13. This provides new mechanisms and opportunities for research in areas such as nonlinear enhancement14,15,16,17,18, sensitive detection19,20, chiral metasurfaces21,22,23,24, lasers25 and light field control26,27. The fundamental concept of BIC involves the complete decoupling of the resonant mode from all environmental radiation channels. This results in a dark state characterized by an infinite Q factor and zero resonance width. The coupling coefficient can become negligible due to symmetry, particularly when the spatial symmetry of the mode does not align with that of the outgoing radiating waves28,29,30,31. If the radiative losses become non-zero, for example, due to in-plane symmetry breaking, BIC transform into quasi-BIC with a high, yet finite, radiative Q factor32. Typical examples include tilted elliptical cylinders33, crescent shape meta-atoms34, slightly differently sized blocks35, symmetry breaking in the permittivity of the constituent materials36, and so on.

As shown in Fig. 1a, in the multi-exposure system, we have integrated nanostructures with dimensions smaller than the wavelength next to the conventional cross marks commonly used for alignment. Before each mask exposure, we first conduct coarse alignment using conventional cross marks, followed by fine alignment via BIC resonance in adjacent nanopillar arrays. This process is iterated sequentially for all masks in the multi-exposure fabrication. Thus, we can attain alignment accuracy surpassing the diffraction limit by leveraging the relationship between the signal and displacement demonstrated by their BIC characteristics, as illustrated in Fig. 1b,c. From simulation and experimental perspectives, we studied this transition process from BIC to quasi-BIC caused by the out-of-plane asymmetry. The experimental results demonstrate the transition from non-existence to the occurrence of resonance and the transition of the quality factor from larger to smaller as the degree of this asymmetry increases. The presence or absence of BIC resonance and quality factors can be important tools for precise alignment accuracy control.

Fig. 1: Schematic of the future multi-exposure system.
Fig. 1: Schematic of the future multi-exposure system.
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a, Nanostructures with dimensions smaller than the wavelength are integrated with the conventional alignment marks in the multi-exposure system. b, Schematic of the transition process from BIC state to quasi-BIC states governed by out-of-plane asymmetry. c, The transition from non-existence to the occurrence of resonance as displacement appears.

Results

The bilayer meta-device comprises two layers of square SU-8 nanopillar arrays, with a layer of SU-8 film in between. They are bonded to the glass substrate using another layer of SU-8 film. The width of the nanopillars (W) is 300 nm, and the period of the hexagonal lattice is 535 nm; the heights of the nanopillars in the top layer (H1) and the bottom layer (H2) are 550 nm and 410 nm, respectively. The thicknesses of the two films (H3) are both 150 nm. When the nanopillars in the upper and lower layers align, symmetry-protected BIC emerge as a result of the symmetry incompatibility (Fig. 1b). When a specific displacement occurs between the nanopillars in the upper and lower layers, leading to the disruption of out-of-plane symmetry, symmetry-protected BIC undergo a transition into quasi-BIC, resulting in the emergence of a sharp resonance. The heightened sensing sensitivity resulting from the high Q factor of quasi-BIC resonances can be achieved by controlling this displacement. The proposed quasi-BIC meta-device is fabricated through two nanoimprint steps, enabling convenient, rapid, reproducible alignment mark production. Consequently, the exhibited resonance is highly suitable for scalable sensing applications, attributable to two key factors. Such a quick and straightforward process is well suited for execution in chip manufacturing, which requires precise positioning. The following sections will present the simulation, experimental findings and pertinent analytical discussions.

The breaking of out-of-plane symmetry is achieved through the relative displacement (D) between the upper and lower layers of nanopillars. Figure 2 depicts the transmission variation concerning the displacement (D) within the 570–610 nm wavelength range (Supplementary Note 1). It is evident that, as the displacement increases gradually from 0 nm, resonance transitions from absence to presence, accompanied by a gradual reduction in the Q factor. This transition intuitively signifies the shift from BIC to quasi-BIC states near the 590 nm wavelength.

Fig. 2: Simulated transition process from BIC state to quasi-BIC states.
Fig. 2: Simulated transition process from BIC state to quasi-BIC states.
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Transmission map concerning the displacement (D) within the 570–610 nm wavelength range. The full width at half maximum (Δ) of the transmission can be observed to vanish when the displacement (D) is approaching zero.

In the experimental section, we aim to quantify the transition process from BIC to quasi-BIC states, thereby corroborating the simulation outcomes. As a proof of principle, we fabricated several samples, distinguished solely by varying displacements between the top and bottom layers (Supplementary Note 2 and Supplementary Fig. 1). Figure 3a shows the top view of the fabricated double-layer nanopillars, exhibiting a hexagonal arrangement for the top and bottom layer nanopillars. The orientations of the nanopillars were accurately aligned with a rotation angle of 1°. The dimensions of each layer were measured from the cross-sectional view of the double-layer nanopillars, as depicted in Fig. 3b. Specifically, the top layer nanopillars had a height of 550 nm (H1), the intermediate layer had a thickness of 150 nm (H3), the bottom layer nanopillars had a height of 410 nm (H2) and the bottom layer had a thickness of 150 nm (H3). Figure 3c–f displays the double-layer nanopillars with varying displacements (D). These displacements were measured as 0, 30, 40 and 110 nm, respectively. The measured quality factors are near-infinite, 200, 120 and 66, respectively, and the experimental set-up is shown in Supplementary Fig. 2. The experimental transmittance spectra illustrated in Fig. 4a present different implementations of meta-devices, each distinguished by unique out-of-plane symmetries. These spectra exhibit excellent agreement with corresponding numerical simulations (Fig. 4b), capturing a transition from a BIC state to a quasi-BIC state. We also discuss the resolution of the displacements measured from the Q factors from the perspective of the electric dipole (Supplementary Note 4). Although nanoimprint lithography is robust, with minimal errors even after repeated template use, our simulations indicate that such processing errors do not affect the method we propose (Supplementary Fig. 8).

Fig. 3: Micrographs of double-layer nanopillars with varying displacements.
Fig. 3: Micrographs of double-layer nanopillars with varying displacements.
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a, Top view of double-layer nanopillars with a 1° rotation angle between top and bottom nanopillars. b, Cross-sectional view of double-layer nanopillars consisting of 550-nm-tall top layer nanopillars, 150-nm-thick intermediate layer, 410-nm-tall bottom layer nanopillars and a 150-nm-thick bottom layer. c–f, Double-layer nanopillars with displacements (D) of 0 nm (c), 30 nm (d), 40 nm (e) and 110 nm (f).

Fig. 4: Experimental demonstration of the transition of BIC states controlled by the out-of-plane symmetries.
Fig. 4: Experimental demonstration of the transition of BIC states controlled by the out-of-plane symmetries.
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a, Experimental verification of the displacements induced quasi-BIC in the nanoimprint bilayer meta-devices. The out-of-plane asymmetry is created by the displacement between the two layers of the nanoimprint meta-device. We select samples with displacements (D) of 0, 30, 40 and 110 nm, respectively, for experimental measurement. b, The corresponding numerical transmittance spectra of the nanoimprint BIC meta-devices. Discrepancies arise from deviations from nominal fabricated device dimensions and inaccuracies in the ellipsometry data.

Discussion

In conclusion, we propose and demonstrate the activation of out-of-plane symmetry-induced quasi-BIC in nanoimprint bilayer meta-devices distinguished by an asymmetrical displacement between their two metasurfaces. Our experimental analysis of displacement-dependent transmittance spectra identifies resonances around 590 nm wavelength. With increasing displacement distances, the Q factor of these resonances steadily decreases, with measured values ranging from approximately 200 to 66. This phenomenon signifies the transition from BIC states to quasi-BIC states governed by the out-of-plane asymmetry in the nanoimprint bilayer meta-device. The changes in quasi-BIC Q factors clearly reflect the variations in displacement between the upper and lower layers without a diffraction limit in the future multi-exposure optical lithography system used in the advanced semiconductor manufacturing.

The limitations imposed by practical imperfections, such as material absorption, fabrication tolerances and surface roughness, inherently constrain the Q factor from reaching infinite values. To address these challenges, we propose two complementary strategies. First, enhancing fabrication precision can significantly reduce surface roughness, while selecting materials with minimal loss can improve the dissipation Q factor. Second, optimizing the design, such as by reducing the height of the nanostructures, can suppress radiation loss, thereby enhancing the radiation Q factor and the overall Q factor. These approaches collectively aim to mitigate the impact of real-world imperfections and improve the performance of the system. A recent work37 achieved approximately 10 nm overlay accuracy in the x and y directions using interferometric techniques and addressed z-axis alignment. By contrast, our work introduces an innovative method leveraging symmetry-protected BIC to surpass the diffraction limit, based on optical physics. This approach offers a novel method for managing the transition from BIC to quasi-BIC through nanoscale structural displacement, using Q factor changes as an alignment signal. This provides a clear physical mechanism and simplifies signal detection. Moreover, our method integrates seamlessly into semiconductor multi-exposure processes and is compatible with existing photolithography markers, which differs from previous methods1,2,3.