Introduction

The demand for nanometer-level precision positioning technology in industrial fields is rapidly increasing, especially in fields such as semiconductor manufacturing1, nanoengineering2, and large-scale optical systems3. As micro-scale device sizes decrease, the manufacturing process faces growing challenges in maintaining metrological accuracy4. Nanometer-level positioning technology has become one of the key technologies in modern industrial production and scientific research5. For instance, in the chip manufacturing process, nanometer-level positioning accuracy is crucial for the precision of micro/nano structure fabrication6. Positioning accuracy not only governs pattern placement precision but also critically influences feature sizes, enabling more compact chip architectures and enhanced performance. Additionally, reliable nanometer-level positioning system minimizes errors during the manufacturing process, which contributes to higher production efficiency and significantly reduces waste, leading to improved manufacturing level7,8.

Planar optical microstructures possess the inherent capability to encode spatial information, making them fundamental to high-precision measurement and positioning technologies9,10,11. With this principle, grating-based measurement technology has gradually become an important tool in high-precision measurement and positioning due to its unique advantages, including high accuracy, multi-degree-of-freedom capabilities, and compact structure12,13,14. However, most existing grating-based measurement schemes employ incremental encoding methods. Although these methods can precisely measure relative displacement, they lack the capability for absolute position marking15. This means that if the system loses its initial reference point, it cannot be recovered, and the measurement process must be restarted. Addressing these constraints is critical for deployment in complex or highly dynamic operational scenarios16,17. To overcome the limitations of incremental grating measurement, a kind of cross-scale structure known as a hybrid grating was proposed, which combined incremental grating and absolute marks18. This combination enables high-precision displacement measurements while ensuring the system consistently maintains a known absolute position, thereby significantly enhancing the stability and reliability of the measurement system, particularly in complex or dynamic environments.

The hybrid grating, which is the most crucial component to realize absolute measurement, adopts a planar segmented layout, with two regions: a reflective incremental encoding region and a transmissive absolute encoding region, enabling simultaneous incremental displacement measurement and absolute position marking within the same device19. The incremental encoding region generates displacement signals through phase modulation of light via subwavelength periodic nanostructures, while the absolute encoding region employs a mask-modulated intensity distribution to establish positional markers. These complementary encoding strategies exhibit distinct dimensional requirements: the incremental encoding region necessitates submicron-scale features to achieve nanometer-level positioning resolution, while the absolute markers employ microscale-to-millimeter-scale structures to enable robust position discrimination and optimal error-resetting intervals. The functional regions have distinct structural characteristics and must maintain consistent directional vectors among structures to ensure system precision. Therefore, the fabrication of hybrid grating was a challenge in nanoengineering20,21,22. Although techniques such as laser direct writing and electron beam lithography can achieve high-precision cross-scale patterns generation, their high costs, low processing speeds, and limitations on processing area make them unsuitable for realizing the design of the current hybrid gratings23,24,25,26. Laser interference lithography is a technique for fabricating periodic patterns27,28. Offering advantages such as large processing areas, high efficiency, and cost-effectiveness29,30. However, it has limitations when applied to the fabrication of nonperiodic patterns31. This is mainly due to the inherent tendency of interference fields to produce highly regular, periodic structures32,33. Breaking this regularity requires complex modulation of phase, amplitude, or polarization, which is technically challenging to implement with stability and precision. In addition, nonperiodic patterns are more sensitive to wavefront errors and process variations, leading to issues such as pattern distortion, local exposure nonuniformity, and narrow process windows34. Therefore, a single lithography technique alone cannot adequately meet the fabrication requirements for hybrid cross-scale structures35,36,37.

To address this challenge, hybrid lithography techniques that integrate multiple patterning approaches have been developed38. These methods typically combine maskless techniques, such as electron beam lithography (EBL) and direct laser writing (DLW), with mask-based processes, such as photolithography and nanoimprint lithography (NIL)39. This integration enables both the flexible generation of localized high-resolution features and the large-area replication necessary for scalable production. Among them, EBL-based hybrid lithography provides sub-10 nm resolution, making it suitable for patterning of fine structures. However, its inherently low throughput, high equipment cost, and complex process flow limit its applicability to large-scale manufacturing. DLW-based combinations offer design flexibility and low cost compared to EBL but are constrained by limited resolution and scan speed, which makes them inadequate for the rapid fabrication of nanoscale feature structures40,41. Photolithography, owing to its mature process, high throughput, and low per-unit cost, has been widely employed for rapid patterning of large-area base structures, offering excellent scalability for mass production. Although the initial equipment investment is relatively high, it achieves superior cost-effectiveness in high-volume manufacturing. In comparison, nanoimprint lithography (NIL) provides higher patterning resolution and enables the fabrication of fine micro/nanostructures. However, NIL still faces engineering challenges such as mold degradation and cumulative imprinting errors, making it more suitable for small-batch production and research-oriented applications. In addition, most hybrid lithography approaches require different types of photoresists or operate under different exposure wavelengths. Their alignment procedures are typically conducted across multiple layers, which makes it difficult to achieve complex cross-scale patterning within a single structural layer, limiting their versatility in certain applications42,43,44.

In this work, we present a hybrid lithography approach to address the fabrication challenges of cross-scale hybrid structures for nanolevel positioning. Firstly, the positioning principles of the hybrid grating are briefly introduced. Then, a complete fabrication process is proposed, including substrate preparation, lithography, region-specific thin film deposition, and etching. The cross-scale patterns are generated by multi-step mask-interference lithography, and alignment marks on the mask are utilized to ensure the alignment of the directional vectors of lines between different regions. Finally, the fabricated devices, featuring an 11 mm reflective incremental encoding region and transmissive absolute encoding regions with three distinct feature sizes, were thoroughly characterized. The deployment of a hybrid grating enabled sub-nanometer accuracy across a 3000-micron measurement span. The results validate the effectiveness of this process in achieving high-precision cross-scale structure fabrication.

Results and discussion

The nanolevel absolute positioning of cross-scale hybrid structures

Figure 1a shows the structures of the hybrid grating used for multi-degree-of-freedom absolute displacement measurement. According to the different feature sizes of the patterns, they are labeled as the structures I–III, which represent absolute encoding with different positioning accuracies, and the structure IV, which represents periodic 2-dimensional (2D) crossed array structures. Structures I–III adopt a transmission design and work in conjunction with the front mask plate to obtain zero-position pulse signals.

Fig. 1: Schematic of the hybrid grating and its working principle for absolute nanometer-scale positioning.
figure 1

a The schematic of a hybrid grating designed for absolute measurement. b Correct interregional relationship: parallel. c Incorrect interregional relationship: non-parallel. d Signals generated by the hybrid grating and front mask. The signals I–IV correspond to the signals generated by structures I–IV in (a), respectively. e The principle of absolute nanolevel positioning by pulse peak marker and signal subdivision

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According to the angular spectrum propagation theory, as a transparent window, the absolute encoding structure has the modulation function:

$$t(x)=\mathop{\sum }\limits_{i=1}^{n}{a}_{i}\times {{rect}}\left(\frac{x-i\times b}{b}\right),\,0\le x\le 3L$$
(1)

where ai represents the modulation coefficient of each structure, b is the width of the mask region, rect is the rectangular window function, and L is the width of a group of codes.

Due to the relative positioning difference between the mask plate and the hybrid grating, the beam is divided into two cases: transmission and reflection, namely:

$${\rm{f}}(x)=\left\{\begin{array}{c}1,0\le x\le L\\ 1-t(x),L\le x\le 2L\\ 1,2L\le x\le 3L\end{array}\right.$$
(2)

Therefore, the light intensity distribution modulated by the hybrid grating is given by:

$${I}_{1}({x}_{0},h)=I(x,h)\cdot f(x+{x}_{0}),\,0\le {x}_{0}\le 2L,\,0\le x\le 2L$$
(3)

where h and x0 represent the vertical distance and the relative horizontal displacement between the mask and the hybrid grating.

The generated signals are illustrated in Fig. 1d. From the Eq. (3), it can be seen that when the zero-position markers of the mask plate and the hybrid grating coincide, the light passing through the zero-position markers of the mask and the hybrid grating is at its maximum, while the reflected light intensity received is at its minimum. Therefore, when the mask plate and the hybrid grating are displaced relative to each other, the reflected light signal received by the photodetector is a negative pulse signal. During the displacement process, this serves as the zero-position signal, enabling coarse displacement information acquisition and zero-position determination.

Structure IV is a periodic 2D-crossed array that diffracts the incident light. The 0th-order and 1st-order diffracted light interfere with reference light, generating sinusoidal variations that depend on the grating position. The period of sine wave signals is relative to the period of the 2D-crossed array and determines the positioning accuracy and measurement resolution45. The consistency of its surface profile determines the system error for nanometer-level positioning. These functional structures are located on the same plane but at different positions in space, effectively avoiding interference between functional regions while simplifying the complexity of signal processing. The combination of transmission and reflection structures facilitates the separation design of the hybrid grating and the reading head. The light signals feedback from different functional regions need to ensure that they propagate along a predetermined path and polarization state so that the signal can be accurately obtained by the reading head. Therefore, the directional vectors of the lines in different regions should be aligned.

The design of the mask

A mask with alignment markers, as illustrated in Fig. 2, was designed and fabricated to ensure precise alignment with the grating line directions and enable high-precision fabrication of the encoding region. The central region of the hybrid grating is a 2-dimensional grating with a period of 1 micron and a line width of several hundred nanometers. Mask lithography is unable to achieve the fabrication at this line width, so interference lithography is used to generate the patterns. Since the mask is made from chromium-coated quartz glass, there is a flatness error in its surface profile. The reflected light from the two interfaces of the mask will undergo parallel plate interference, which affects the energy distribution of the exposure interference field and degrades the uniformity of the generated patterns. Therefore, during the fabrication of the mask, the glass in the middle region is removed. Additionally, alignment marks in x and y directions are fabricated on the mask. As illustrated in Fig. 2b, the line directions of AMx and AMy are perpendicular to each other, and the alignment marks are formed by scanning in the same direction as the lines in the encoding region, as Fig. 2c shows.

Fig. 2: The design of the mask with alignment marks.
figure 2

a The schematic of the mask with alignment marks. b The direction relationship between AMx and AMy. c The direction relationship between AM and the patterns of the encoding area

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The fabrication method of cross-scale transmissive and reflective structures

The complete fabrication process is illustrated in Fig. 3a. First, quartz glass was selected as the substrate due to its optical transparency, which is essential for the final transmissive structure. A 100 nm thick chromium (Cr) film was uniformly deposited on the quartz surface to serve as a light-shielding layer and subsequent etch mask. Next, a 500 nm thick photoresist layer (AZ1500) was spin-coated onto the Cr-coated substrate to fabricate the desired microstructure pattern. The photoresist was then exposed using a combination of proximity mask lithography and laser interference lithography, which enables the generation of non-periodic structures and periodic 2D cross-array structures. This hybrid lithography step is critical for ensuring accurate pattern definition over a large area. The exposure consists of three steps, during which a photomask with alignment marks is employed to generate non-periodic structures and achieve pattern alignment between different regions. Following development, a 30 nm thick silver (Ag) film was deposited across the 2D cross-array. The Ag layer enhances the diffraction efficiency and damage threshold of the structure, particularly. After deposition, the exposed Cr areas were removed using inductively coupled plasma (ICP) etching, transferring the photoresist pattern into the Cr film. This step created openings in the Cr layer, which form the encoding region. Finally, the residual photoresist was removed, completing the fabrication process and yielding a hybrid structure that integrates a transmissive absolute encoding region with a 2D grating composed of a Cr–photoresist–Ag multilayer configuration.

Fig. 3: The fabrication process of the hybrid grating.
figure 3

a The whole process of the device, including coating, lithography, and etching. b Exposure process. Exposure I: block the region designated for grating fabrication and expose the code area. Exposure II: change the blocking to expose the 1-dimensional grating. Exposure III: rotate the substrate by 90° and generate 2-dimensional grating patterns. CCD images are used to align the patterns. PR photoresist, S substrate, BLA blocking A, BLB blocking B

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The formation of cross-scale patterns is the most critical step. According to the above structure, the required composite structures consist of different scales and types of structures. Structures I and II are transmissive regions with a line width of millimeters. Structure III is a transmissive region with a line width of tens of microns. Structure IV is a reflective region with a line width of submicron. Moreover, the structures must ensure the consistency of their directional vectors. Figure 1b, c shows the correct and incorrect interregional relationship. Considering the resolution limitations of proximity lithography and the challenges of laser interference lithography in fabricating non-periodic structures at the micron scale, we employed a combined processing strategy of mask lithography and laser interference lithography.

Structure IV was fabricated by interference lithography, while other areas were generated using mask lithography. The exposure optical path is a split-amplitude dual-beam configuration, and the 2D cross grating is created through a double-exposure process, which is shown in Fig. 3b. During the lithography process, it is crucial to ensure the precise alignment of the structures’ directional vectors to prevent aberration errors caused by misalignment. Therefore, we introduced high-precision, multi-degree-of-freedom optical path adjustment devices into the exposure optical path to control the direction of the exposure interference fringes. Additionally, dynamic light field control technology was introduced during the fabrication process to enhance the quality of the periodic structure fabrication46.

The observation and alignment of patterns’ orientation

To observe the situation of the exposure interference field, alignment marks are arranged at the substrate S, which are gratings with period of twice the interference period g of the two beams I1 and I2, as the Fig. 3b shows. According to the wave vector matching condition of grating diffraction, the relationship among the wave vector of incident and diffracted light kin and kout and the grating vector G is:

$${{\bf{k}}}_{{\rm{out}}}-{{\bf{k}}}_{{\rm{in}}}=m{\bf{G}},\,m=0,\pm 1,\pm 2,\cdots$$
(4)

The scale form is the grating equation:

$${{g}}_{\rm{ref}}(\sin \alpha +\,\sin \theta )=m\lambda ,\,m=0,\pm 1,\pm 2,\cdots$$
(5)

where gref is the period of alignment marks, m is the diffraction order, θ is the incident angle, and α is the diffraction angle. When considering only the case where the incident light I1 and I2, diffracted light, and the grating vector of the alignment mark are coplanar, the diffracted light I1,1,−1 and I2,+1 propagate along the normal direction of the reference plane, and the superposition of them generates a uniform optical field.

In practice, alignment marks always have fabrication errors. Actually, the period of the alignment marks is gref = 2 g + ϵ, causing changes in the propagation directions of I1,−1 and I2,+1 and form interference fringes on the CCD camera plane with the period of p:

$${p}=\frac{{g}\cdot {{g}}_{{\rm{ref}}}}{|\varepsilon |}$$
(6)

Since ϵ is a negligible quantity, the magnitude of p is significantly greater than that of g. Consequently, the reference interference fringes become macroscopically observable and the direction of that is related to the grating vector of the alignment mark.

In Fig. 3b, the direction of alignment marks and exposure fringes is consistent. According to the initial and real-time CCD image, fluctuations in the phase difference can be observed, which influence the quality of patterns and the accuracy of directional error observation. Thus, it was dynamically controlled by adjusting the optical path difference between I1 and I2, which is called fringe locking technology. As Fig. 3b illustrates, when the alignment marks rotate around the z-axis, the wave vectors of I1,−1 and I2,+1 gain positive and negative y-component, respectively. Thus, the wave vector difference between them gains a y-component, causing the interference fringes of the two beams to tilt on the CCD camera plane. The patterns can be aligned by observing the reference images and adjusting the directions of S. After the x-directional lines were recorded in the photoresist, the substrate was rotated 90° using the rotation stage. The reference fringes generated by the y-direction alignment marks were then monitored to determine the new orientation. Subsequently, the alignment procedure was repeated, and a second exposure was performed to generate the cross-array structure.

Experimental

Optical setup

The photolithography optical path for processing the photoresist patterns of the hybrid grating is illustrated in Fig. 4. The He–Cd laser beam, with a wavelength (λ) of 441.6 nm, is first split by a polarizing beam splitter (PBS), then expanded using spatial filters SF1 and SF2. A half-wave plate WP1 is used to adjust the intensity ratio between beams. The half-wave plate WP2 is used to match the polarization direction of the two beams. After expanding, Beam1 and Beam2 are collimated by Lens1 and Lens2 and reflected by Mirror3 and Mirror4 at an angle θ. Two beams overlap and interfere, forming an interference field with a period of g:

$$g=\frac{\lambda }{2sin(\theta )}$$
(7)
Fig. 4: The optical setup.
figure 4

a The schematic of the optical setup. b The physical image of the optical setup

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The reference interference lights generated by the alignment marks on the mask are recorded by the CCD. The substrate is fixed on a rotation stage to adjust the direction of the substrate. Mirror4 is fixed on a piezoelectric mount for fine-tuning the beam direction.

Exposure process

The 3-step exposure process is illustrated in Fig. 3b. Exposure I: Non-periodic encoding patterns are fabricated through selective beam occlusion (Beam1 or Beam2) combined with mask-modulated single-wavefront exposure. To suppress interference artifacts induced by mask surface irregularities, the mask must be tightly adhered to the substrate, with a refractive index-matching liquid filling the gap to reduce abrupt refractive index transitions at the interface. During this step, regions designated for periodic microstructures remain protected by specialized shielding components Blocking A. Exposure II: Blocking A and B are used to protect the cross-scale structures while leaving only the reference markers exposed. The reference fringes captured by the CCD camera are used to adjust the fringe orientation within the exposure field. The piezo-mounted Mirror4 is finely adjusted to align the reference fringes along the Y-axis. Blocking A is then removed, and the central region is exposed using a fringe-locking technique. Exposure III: The substrate is rotated to approximately 90°. Blocking A and B are used again to protect the cross-scale structures. The reference fringes are observed, and coarse adjustments are made using the rotation stage, followed by fine adjustments via the piezo-mounted mirror to ensure the reference fringe orientation matches that in Exposure II. Once the alignment is completed, fringe locking and exposure are performed. Finally, the substrate is removed for development, post-baking, microscopic inspection, and other subsequent processes.

The characteristics of the cross-scale hybrid structure

Figure 5 presents a comprehensive characterization and functional demonstration of the hybrid grating fabricated following the process outlined in Fig. 3. A photograph of the completed hybrid grating is shown in Fig. 5a. To evaluate the uniformity and repeatability of the proposed method over large areas, we performed systematic characterization of multiple batches of fabricated hybrid grating samples. Firstly, atomic force microscopy (AFM) was employed to evaluate the fabrication quality of the two-dimensional grating regions, specifically characterizing the profile and structural depth. As shown in Fig. 5b–i, two representative samples were selected, and four different regions on each sample (corresponding to areas I–IV in Fig. 5a) were measured. The AFM images exhibited highly regular and periodic structures, indicating that the method enables the fabrication of large-area periodic structures with excellent structural uniformity. To further examine batch-to-batch consistency, we analyzed four independently fabricated samples by extracting cross-sectional profiles along both X and Y directions from their AFM images, as shown in Fig. 5m. The resulting profiles demonstrate periodicity and high contour consistency in both directions across all samples, validating the reproducibility of the fabrication process across different batches. Groove depth uniformity was also assessed through statistical analysis. For each of the four samples, five representative regions were selected, and the average peak-to-valley depth of multiple structure units within each region was calculated. The statistical results, summarized in Fig. 5n, show high consistency in groove depth across samples, further confirming the fabrication precision of the proposed method. Microscope images of the encoding region after etching is shown in Fig. 5k, l. A set of structures was randomly selected for width measurements, confirming that the fabrication results closely match the design specifications. Utilizing the hybrid grating, we acquired pulse peak signals and incremental interference signals, as Fig. 5j illustrates. The measurement datum can be determined by combining the pulse peak signals and the incremental interference signals. These results confirm the practical significance of the fabricated hybrid grating for applications in absolute positioning systems. With the use of the hybrid grating, we achieve a measurement resolution better than 1 nm and a repeatability within ±0.4 nm. In comparison, state-of-the-art commercial absolute linear encoders, such as the product series of Renishaw and Heidenhain, typically offer system accuracies on the order of ±1 μm with interpolation errors in the range of 20–40 nm47,48. The proposed hybrid grating therefore provides a substantial improvement in both resolution and repeatability, making it highly suitable for ultra-precise positioning and metrology applications.

Fig. 5: Characterization results of the hybrid grating.
figure 5

a Photography of a hybrid grating. b–i The AFM images of 2 hybrid gratings in regions I–IV. j The nanolevel absolute positioning signals obtained using a hybrid grating. k, l Microscopic photo of the encoding structure (The data in the figure was obtained using the microscope’s built-in scale tool). m Cross-sectional views of 4 samples in the 2D grating region. n Trench depth at sampling points (4 samples)

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The overall alignment accuracy relies on two critical components: the monitoring of reference fringes and the angular control of the exposure beam. For fringe monitoring, two primary sources of error are (1) the fabrication precision of the reference alignment marks and (2) the detection accuracy of the CCD camera. Imperfections in the reference mark fabrication—such as periodicity errors, directional deviations, or low pattern contrast—may result in blurred or distorted reference fringes, thereby reducing the clarity and reliability of the reference signals. On the detection side, limitations in CCD resolution, noise interference, and optical aberrations may cause fringe image degradation or geometric distortion, thereby directly impacting the accuracy of the alignment adjustment. To decrease these errors, we employ high-contrast, precisely fabricated reference marks, select a high-resolution and low-noise CCD camera, and optimize the optical detection path. In addition, image processing techniques such as noise filtering and edge enhancement are applied to improve fringe recognition and localization accuracy. Quantitative evaluation demonstrates that, after image processing, the average SNR of the fringe images increases from 8.33 dB to 10.54 dB, and the standard deviation of the extracted fringe inclination angles decreases from 6.95° to 3.47°, indicating improved fringe stability and recognition consistency. The second key aspect is the adjustment of the exposure beam, which governs the direction of the interference field and thus the orientation of the fabricated pattern. In our system, a piezoelectric mirror mount is used to achieve high-precision control of the beam’s incident angle. The angular adjustment resolution of this mount is 0.7 μrad, ensuring that the directional alignment error between different pattern regions remains within 0.7 μrad.

Conclusion

In this study, we propose a fabrication technique for hybrid cross-scale structures designed for nanolevel absolute positioning. High-quality cross-scale patterns were successfully generated through hybrid lithography, and the direction consistency was ensured with the use of alignment marks. The hybrid grating integrates reflective periodic structures and a transmissive non-periodic structure, simultaneously providing incremental signal and absolute position marking. To match the precision, the designed hybrid grating incorporates subwavelength periodic structures and millimeter and micrometer-scale non-periodic structures, and the different regions of that should be in a consistent direction. Since a single lithography method has limitations in patterning, we employ a combination of mask lithography and interference lithography in a three-step process to fabricate the patterns. To observe the distribution direction of the interference field and ensure the directional consistency of the two regions’ structures, alignment marks are embedded in the mask. This approach for photoresist patterns fabrication is efficient, cost-effective, and reliable, overcoming the limitations of other methods in fabricating large-area composite micro/nano structures.

The realization of the hybrid grating forms the foundation for absolute measurement, enabling nanometer-level precision and high stability measurements. Furthermore, the cross-scale hybrid structure fabrication method can be applied to the processing of other optical devices, providing valuable insights for fabricating complex optical devices in various application scenarios.

Although the proposed method demonstrates promising performance in terms of structural stability and process repeatability, several key challenges remain when extending it to large-area fabrication and industrial-scale production. First, the fabricated performance of interference lithography relies on the coherence and wavefront uniformity of the light source. As the exposure area increases, the required size of the collimating optics also grows, making the system more vulnerable to optical aberrations and environmental vibrations. These factors can compromise the stability and uniformity of the interference fringes, leading to reduced patterning consistency across large areas. In the experimental system presented in this work, the aperture of the collimating optics is 100 mm, enabling a highly uniform exposure area of approximately 40–50 mm in a single exposure. However, a zone-by-zone stitching exposure strategy combined with a global alignment strategy can be employed to further expand the fabrication area44,49. Second, the mask’s pattern fidelity tends to degrade over repeated use, which negatively affects the quality of alignment fringes and hinders precise alignment between structural regions. Furthermore, scale-up introduces increased processing time, system complexity, and yield control difficulties, all of which impose constraints on mass production. To address these issues, it is essential to maintain the quality of the photoresist mask, especially the alignment in complex patterns, and to optimize process parameters such as coating thickness, exposure dose, and etching duration. Sustained improvements in optical system design, multi-step alignment accuracy, and high-uniformity processing solutions will be necessary to achieve reliable and scalable large-area structures fabrication.