## Abstract

We explore an easy-to-implement moiré-based measurement scheme for the mask-wafer misalignment in nanoimprint lithography. By introducing the beat signal of moiré fringes, the measurement range increase by dozens or even hundreds of times, while the measurement accuracy doesn’t get affected and still kept in nanoscale. Moreover, the alignment signal, collected throughout the whole imprint process, is independent of the wafer-mask gap and beam fluctuation, which makes it very suitable for the misalignment measurement in NIL. The experiment shows that sub-10 nm alignment could be obtained within a measurement range of 500µm, which is expected to be improved after the parameter optimization.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Nanoimprint lithography (NIL) [1], by virus of the ultra-high resolution and low cost, becomes an attractive technique applied in many disciplines where nanostructures are needed, e.g. micro-sensors, micro-optics, photonic crystals, and quantum devices. Thereinto, the integrated circuits (ICs) manufacturing is considered as the most potential application. However, the high resolution alone is not enough for IC manufacturing; the corresponding overlay alignment accuracy must be achieved. In general, the lithography techniques have a very strict demand on the overlay alignment accuracy, typically only 1/5∼1/4 of the minimum feature size, namely the alignment accuracy for NIL needs to reach nanoscale. Actually, some excellent works [2–10], represented by the optical alignment methods, have been devoted to the measurement with high-sensitivity and high-accuracy. Despite these methods perform well in the process of lithography, they are easily affected by the mask-wafer gap and beam fluctuation. Different from that in proximity lithography, the alignment in NIL is performed while bringing the mask in contact with the wafer on the wafer and imprint into it. Therefore, the alignment scheme in the NIL must be independent of the wafer-mask gap, for avoiding the influence caused by the gap change during the imprint process. Herein, the recently proposed moiré-pattern-based alignment methods [11–18] attempt to solve this problem.

The linear moiré fringes, with its inherent high-sensitivity, is widely used for the above misalignment measurement. But owing to the influence of periodicity, the measurement range of linear moiré fringe is limited within a small range. Hence, some alignment methods have to adopt the specially-designed marks [11–20] for the pre-alignment, as a necessary supplement to linear gratings. In spite of the validity of these approaches, there is still a lack of sufficient progress to inherently increase the measure performance of linear moiré fringes, inevitably leading to some deficiencies:

- • The inextricable influence of pre-alignment on the final measure accuracy
- • The inconvenient two-step alignment process
- • The unbreakable restriction from imaging system.

## 2. Alignment principle

As illustrated in Fig. 1(a), the wafer alignment mark consists of three sets of linear gratings: one set of linear grating *G _{wa}* with a period of

*P*for measurement and two sets of linear gratings

_{wa}*G*and

_{r1}*G*respectively with periods of

_{r2}*P*and

_{r1}*P*for reference. Correspondingly, the mask alignment mark is composed of two sets of linear gratings

_{r2}*G*and

_{ma1}*G*with periods of

_{ma2}*P*and

_{ma1}*P*and two transparent areas, as shown in Fig. 1(b). Specifically,

_{ma2}*P*and

_{ma1}*P*are closely equal to

_{ma2}*P*plus additional terms $\Delta {P_1}\; and\; \Delta {P_2}\; ({ > 0} )$, i.e., ${P_{ma1}} = {P_{wa}} + \Delta {P_1}$ and ${P_{ma2}} = {P_{wa}} + \Delta {P_2}$.

_{wa}When uniform incident light passes through the superposed linear gratings, e.g. *G _{wa}* and

*G*(or

_{ma1}*G*and

_{wa}*G*), the Moiré fringe could be formed due to interference of diffraction waves, as shown in Fig. 1(c). The periods of formed moiré fringes

_{ma2}*P*and

_{m1}*P*could be written as:

_{m2}*P*and

_{m1}*P*, are much larger than the original measurement grating period

_{m2}*P*, whose magnification factors are as below: ${M_1} = {P_{ma1}}/({{P_{ma1}} - {P_{wa}}} )\; $, ${M_2} = {P_{ma2}}/({{P_{ma2}} - {P_{wa}}} )$. By virtue of the magnification effect of moiré fringes, the tiny relative displacement between the mask and wafer could be accurately measured. Assuming that the relative displacement of mask is $\varDelta$

_{wa}*x*, as shown in Fig. 1(c), the intensity distributions of corresponding moiré fringes could be quantitatively expressed as

*G*and

_{r1}*G*are used for comparison with the moiré fringes to obtain the phase differences, so their periods are set to equal to the periods of corresponding moiré fringes, i.e. ${P_{r1}} = {P_{m1}} = {P_{ma1}}{P_{wa}}/({{P_{ma1}} - {P_{wa}}} )$ and ${P_{r2}} = {P_{m2}} = {P_{ma2}}{P_{wa}}/({{P_{ma2}} - {P_{wa}}} )$

_{r2}*.*In such cases, the intensity distributions of their corresponding reference gratings

*G*and

_{r1}*G*could be written as where $a({x,y} )$ and $b({x,y} )$ respectively denote the background intensity and the amplitude of moiré fringe. The above four equations could be divided into two parts: the moiré fringes formed by

_{r1}*G*and

_{wa}*G*and its corresponding reference grating

_{ma1}*G*; the moiré fringes formed by

_{r1}*G*and

_{wa}*G*and its corresponding reference grating

_{ma2}*G*, any of which is able to be used for the nanoscale misalignment measurement. Further analysis indicates that, the relationships between the phase differences ($\Delta {{\varphi }_1}$ and $\Delta {{\varphi }_2}$) and the relative displacement ($\varDelta$

_{r2}*x*) could be written as where ${{\varphi }_{m1}} = 2\pi ({x + \Delta x} )/{P_{wa}} - 2\pi x/{P_{ma1}}$ and ${{\varphi }_{m2}} = 2\pi ({x + \Delta x} )/{P_{wa}} - 2\pi x/{P_{ma2}}$ are respectively the spatial phases of the moiré fringes, ${{\varphi }_{r1}} = 2\pi ({1/{P_{wa}} - 1/{P_{ma1}}} )({x + \Delta x} )$ and ${{\varphi }_{r2}} = 2\pi ({1/{P_{wa}} - 1/{P_{ma2}}} )({x + \Delta x} )$ are respectively the spatial phases of their reference gratings

*G*and

_{r1}*G*. The relative misalignment Δ

_{r2}*x*could be induced from the Eq. (7) or Eq. (8) as following: or where

*n*is an integer. In term of the general alignment method with linear moiré fringes, the phase difference $\Delta {{\varphi }_1}$ (or $\Delta {{\varphi }_2}$) falls below the range of one period, i.e.

*n = 0*, resulting to a limited measurement range no larger than

*P*or

_{ma1}*P*. Herein, we try to introduce a nonzero

_{ma2}*n*into alignment measurement, which could effectively expand the phase difference to several periods and further achieve a large alignment range. By coupling Eq. (9) and Eq. (10), the period parameter

*n*could be extracted and written as

*P*and

_{ma1}*P*are design values and could be plugged into without measuring, the Δ

_{ma2}*φ*and Δ

_{1}*φ*are measuring values and could be achieved from Eqs. (7) and (8) after phase extraction. Plugging the period parameter

_{2}*n*into Eq. (9) or Eq. (10), the offset $\varDelta$

*x*could be solved out. Meanwhile, the expression of measurement range $\Delta {x_{range}}$ could be deduced as

## 3. Design and fabrication of alignment mark

The aim of optimal design is to expand the measurement range as far as possible provided that the measurement accuracy is kept within nanoscale. According to Eq. (12), the measurement range is proportional to the *P _{ma1}* and

*P*, and inversely proportional to their difference, which seems that the gratings

_{ma2}*G*and

_{ma1}*G*with large periods and slight difference are helpful to expand the range. But according to Eqs. (7) and (8), the overlarge periods of

_{ma2}*G*and

_{ma1}*G*bring in a big challenge of phase extraction if the measurement accuracy is required to remain within the nanoscale. Thus, we suggest the two values are not more than 10μ

_{ma2}*m*, and with a difference less than 0.5μ

*m*. The periods of moiré fringes

*P*and

_{m1}*P*, according to Eqs. (1) and (2), are determined by the values of

_{m2}*P*and

_{wa}*P*, whose magnification factors (

_{ma1}(or P_{ma2})*M*and

_{1}*M*should be controlled within a proper range, because a huge magnification factor results in that the number of captured moiré fringes is insufficient for analysis while a tiny one results in that the moiré fringes are insensitive to the offset Δ

_{2})*x*. Empirically, the range of magnification factor is 5 to 20, which need to be adjusted based on the real system. Meanwhile, since the periods of reference gratings

*P*and

_{r1}*P*are respectively equal to periods of their corresponding moiré fringes

_{r2}*P*and

_{m1}*P*, another design requirement for

_{m2}*P*is to ensure that the

_{wa}*P*and

_{m1}*P*are integers, which brings in the convenience of calculation and fabrication. In term of the overall size of alignment mark in this scheme, the length of mark along the measuring direction should be less than the measurement range Δ

_{m2}*x*in order to avoid the huge error caused by the count confusion of beat signal. Given all this, we propose one group of alignment marks (with the same size of

_{range}*910×800*μ

*m*) for experiment, whose grating periods are respectively

^{2}*P*μ

_{ma1}=9.5*m*,

*P*μ

_{ma2}=9.6*m*,

*P*μ

_{wa}=9*m*,

*P*μ

_{r1}=171*m*and

*P*μ

_{r2}=144*m*, corresponding to a measurement range of

*912*μ

*m*. These alignment marks are drawn with a commercial software (Tanner EDA L-edit) and the drawings are shown in Fig. 2(a). Considering the grating periods in the experiment are very close, we commission a professional manufacturing team to fabricate it with an electron-beam lithography tool (Raith 150 Turnkey system), and the local SEM (scanning electron microscope) images are depicted in Fig. 2(b). These alignment marks are used for the one-dimensional misalignment measurement along x-direction to prove its validity. As for the two-dimensional measurement, it could be realized by combining two groups of mutually orthogonal marks: one for measurement in x-direction; the other one for measurement in y-direction.

## 4. Experiment and discussion

The experimental setup is shown in Fig. 3. The wafer alignment mark is mounted on a manual XY stage (*100 mm* travel range, resolution *1* μ*m*), while the mask alignment mark is mounted on a piezomotor-drived Q-522 Q-Motion miniature linear stage (*6.5 mm* travel range, resolution *4 nm*). The miniature linear stage is connected with a computer, and used for the control of relative displacement between the mask and wafer. The illuminating beam through the collimation system from a LED source (630∼*632.5 nm*, *5 mW* output power) is employed for the alignment illumination, which is diffracted by the mask and wafer alignment marks, and then imaged by a *8×* objective lens, forming moiré fringes collected by a CCD camera (*VA-47MC-M/C 7*, resolution *8856×5280 px*, pixel size *5.5 × 5.5* μ*m ^{2}*).

In the course of alignment in NIL, the gap distance between the mask and wafer changes within a reasonable range of several micrometers, meaning the computed results calculated from images captured at different position should keep the same. Actually, the moiré fringes, as shown in Fig. 4, become in-focus and out-of-focus with the variation of gap distances because of the Talbot effect, and further analyses indicate that this phenomenon is periodical and related to the grating periods and illuminating wavelength. Because the period of linear grating *G _{wa}* is constant, when the mask-wafer gap is adjusted to be at a certain integer times of Talbot distances, the clear moiré fringe pattern could be captured by the CCD camera. If the miniature linear stage then performs a rightward movement with a distance of $\varDelta$

*x*, the moiré fringes exhibit the same leftward movements at different speeds while the image of reference gratings keep stationary, as shown in Fig. 5, which is agree well with the theoretical prediction described in Sec. 2.

As a critical process, the algorithm implementation scheme is described as following:

**Step_1:**To improve the precision of phase extraction algorithm [5,20,21], the captured patterns are cut with integral number of moiré fringe period as much as possible. For the two moiré patterns with different periods, it doesn't matter that their truncated lengths are not equal, but is important to guarantee that their initial truncated points are the same, as shown in Figs. 6(a) and 6(b).**Step_2:**The truncated moiré patterns are filtered and processed by the 2D-FFT (fast Fourier transform) phase extraction algorithm, during which the fourth-order Hamming window is adopted for better results. After that, the wrapped phase distribution patterns could be achieved, as shown in Fig. 6(c).**Step_3:**After the phase unwrapping algorithm [20–22] is performed on the wrapped phase distribution patterns, the phase distribution curves could be obtained, as shown in Fig. 6(d). They are then processed by the linear fitting algorithm to get the phase values, which could be plugged into Eqs. (7) and (8) to get the phase differences Δ*φ*and Δ_{1}*φ*._{2}

In order to verify the accuracy of the proposed method, 6 groups of experiments with different experimental parameters are performed to calculate the maximum, mean errors and standard deviation, whose corresponding results are shown in Fig. 7. The experimental results indicated that the maximal errors in each experiment are all less than *6 nm*, and the corresponding mean errors and standard deviations are respectively less than *5.61* and *0.028 nm*. Since there are no explicit coarse and fine alignment marks in the proposed method, the results are entirely relying on the analysis of phase distributions, which is susceptible to the environmental noise and data processing algorithm. Figure 8 displays the gray distribution curves along with the red-dot and blue-dot lines in captured pattern, both of which are mixed with a lot of random noise from the illuminating and imaging systems.

Another noteworthy aspect is the influence of signal length on the accuracy of phase extraction. For a better explanation, an experiment is performed with different truncated moiré patterns on the condition of perfect alignment, i.e. $\varDelta$*x = *0μ*m*, whose results are revealed in Fig. 9. It could be seen that, the absolute error is about *0.004 rad* when the signal length is integer multiple of the fringe period, but up to *0.3 rad* if the ratio of signal length to fringe period is non-integer. Obviously, the length of truncated signal exerts an important impact on the accuracy of phase extraction, further on the accuracy of alignment, which could be explained by the spectrum leakage and partly weakened by introducing special window functions. Additionally, according to the Eq. (12), the measurement range is totally determined by the grating periods *P _{12}* and

*P*, and independent of the maximum field of view (FOV) of observation lens. This inference is proved in our experiment, and provides us an effective path to extend the measurement range by only selecting the proper gratings with large periods and subtle difference. Thus, a part of the captured moiré pattern is enough for us to obtain the results, which avoids the limitation of device size and makes the measuring system simple and efficient in practical use.

_{22}## 5. Conclusion

In summary, we propose a controllable and easy-to-implement measurement scheme for the mask-wafer misalignment in NIL. Compared with the classical moiré-based alignment methods, this scheme has a nano-scale measurement capacity within a submillimeter-scale range, which ensures the high accuracy and meanwhile expands the range almost hundred-fold. By virtue of the insensitivity to the mask-wafer gap and beam fluctuation, the misalignment information could remain achievable and available throughout and after the whole imprint process, making this proposed method suitable for the misalignment measurement in NIL. Through further optimization, this high-precision large-range moiré-based alignment approach could also be extended to other photolithography techniques like proximity, X-ray and projection lithographies, and other application fields like the positioning in CNC, laser-cutting and water-jet-cutting machines.

## Disclosures

The authors declare no conflicts of interest.

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