Abstract

We explore the feasibility of a controllable and easy-to-implement moiré-based composite circular-line gratings imaging scheme for optical alignment in proximity lithography. One circular grating and four line gratings located on both the mask alignment mark and wafer alignment mark are used to realize the coarse alignment and fine alignment respectively. The fundamental derivation of coarse alignment employing circular gratings and fine alignment employing line gratings are given. Any displacement of misalignment that occurs at the surface of two overlapped gratings can be sensed and determined through subsequent fringe phase analysis without the influence of the gap between the mask and the wafer or wafer process. The design and manufacture process of the alignment marks are presented. The experimental results validate and demonstrate the feasibility of the proposed approach.

© 2015 Optical Society of America

1. Introduction

Progress in nanotechnology is essential to promote the production of faster computers and high-density data storage. This progress is fueled by the downscaling of integrated circuit (IC) technology, which was predicted a few decades ago by Gordon Moore [1, 2]. The shrink of feature size is promoted by photolithography, which is the most promising and critical technique for IC manufacture. The device fabrication typically requires a number of dissimilar processes of overlay and each of them requires its own lithographic pattern to be exposed [3]. To ensure a correctly functioning device each new pattern must be aligned with the preceeding patterns, and the final performance of the device is even determined by such alignment process. Therefore, alignment accuracy needs to attain nanometer level to meet the requirement of the current feature size. Traditionally, alignment is mainly realized through two categories of approaches:

Alignment point detection method searches the best point, i.e. the optimally aligned point, through moving and comparing the alignment marks relative to each other, such as the linear zone-plate intensity alignment [4], the diffraction gratings laser interferometer alignment [5, 6], the diffraction gratings moiré intensity alignment [7].Those methods have the high sensitivity in aliment process, but their alignment signals are easily affected by the gap between mask and wafer and wafer process, e.g. the resist layer.

Alignment offset detection method detects the offset/deviation between alignment marks which located on each different layers, such as the geometric imaging alignment [8, 9], the laser heterodyne interferometer alignment [10] and the moiré fringe image alignment technique [11–14]. The geometric imaging alignment method is usually unable to clearly capture the overlapped alignment marks simultaneously due to the gap between mask and wafer, so its accuracy is ultimately limited. The laser heterodyne interferometer alignment method can realize high accuracy free from any influences from the gap and wafer process, but the alignment system has to face the problem of high complexity.

Moiré fringe is widely used in many fields such as displacement, shape and strain measurement etc. In recent years, the moiré fringe scheme applied to the optical alignment for proximity lithography has attracted more and more attentions. Especially, the dual-grating based moiré fringe method [15–22], which combined the inherent high detectivity of the interferometric measurement with the conveniences of fringe pattern processing, is quite advantageous for wafer-mask alignment. However, the periodicity and differential motion of dual-grating moiré fringe require the linear-grating marks to be pre-aligned within certain extent, namely the accuracy of coarse alignment must be no more than the half average period of the line gratings. The four-quadrant gratings alignment method was subsequently adopted to use the shaped “+” that acts as the borderline of the line-gratings to perform coarse alignment [21], but the same principle as geometric imaging alignment limits the scope and accuracy of coarse alignment, even affects the final accuracy of total alignment process.

To address the issues above, our group proposes an improved moiré fringe alignment method for proximity lithography through novel design of the alignment marks on both wafer and mask. This method is advantageous to complete the whole alignment process with high accuracy, automation and low complexity. The influence from gap between mask and wafer and the overlay process can be fundamentally relieved and even eliminated by subsequent fringe pattern analysis. The analytical and experimental results are given to verify the feasibility and rationality.

2. Alignment theory

2.1 Coarse alignment

Two circular gratings with close periods T1 and T2 shown in Figs. 1(a)-1(b) respectively are used as marks for coarse alignment. When superposition of two marks occurs in the alignment process, fringe patterns alike as that shown in Figs. 1(c)-1(d) are induced by interference ofdiffraction waves and can be recorded by CCD through the lens. The fringe pattern shown in Fig. 2(c) indicates that the wafer and mask are misaligned by a certain offset ∆x, while the fringe pattern shown in Fig. 1(d) indicates that the wafer and mask are completely aligned, i.e. no existing offset. Generally, the intensity of the each fringe pattern shown in Figs. 1(c)-1(d) can be expressed as

I1(x,y)=a(x,y)+b(x,y)cos(2π(f1(x+Δx)2+(y+Δy)2f2x2+y2))
I2(x,y)=a(x,y)+b(x,y)cos(2π(f1x2+y2f2x2+y2))
Where I1(x, y) and I2(x, y) are recorded intensities corresponding to the misaligned and aligned status, a(x, y) and b(x, y) denote the background intensity and the amplitude modulation of fringes respectively. The coordinates (x, y) denotes pixel of the fringe pattern and f1 = 1/T1 and f2 = 1/T2 are the spatial frequencies of the two gratings respectively, ∆x and ∆y are the relative offsets between two grating marks along x axis and y axis respectively. The relative offsets between the two grating marks are then directly monitored by the phase distribution of the moiré fringe pattern. Considering the circular features of the gratings and fringes, the coordinates system of coarse alignment scheme is transformed from Cartesian coordinates system to Polar coordinates system for convenient phase extraction. Figure 2 shows therelation between two group circular grating marks defined by Polar coordinates system, where O and O1 are the central points of grating marks located on the mask and wafer respectively, ε=(Δx)2+(Δy)2and φ related to misalignment offsets ∆x and ∆y closely are the module and angle of central point O1 relative to the central point O;ρ=(x)2+(y)2 and θ are the module and angle of any point of both grating marks relative to the central point O. Then the phase in Eq. (1) can be transformed and simplified as Eq. (3) and Eq. (4). Equation (4) means that the moiré fringe phase Φ (ρ, θ) is a group sinusoidal varied with ρ and θ, and the amplitude A = 2πf1ε and the phase delay φ of each sinusoidal are fixed once the relative offset between O1 and O is determined. The misalignment offsets ∆x and ∆y can be acquired by Eqs. (5) and (6) respectively.

 

Fig. 1 The two group circular grating marker and the corresponding fringe: (a) the mask alignment grating maker; (b) the wafer alignment grating marker; (c) the fringe distribution of misalignment; (d) the fringe distribution if alignment.

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Fig. 2 The relation between two group circular grating markers in polar coordinates system.

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Φ(ρ,θ)=2π(f1(ρcosθ+εcosφ)2+(ρsinθ+εsinφ)2f2ρ)
Φ(ρ,θ)=2π(f1f2)ρ+2πf1εcos(θφ)
Δx=εcosφ
Δy=εsinφ

2.2 Fine alignment

The fine alignment is realized through two grating marks illustrated in Figs. 3(a)-3(b) respectively. Both of them are composed of two sets of line gratings. The upper part of the mask alignment grating mark have the micron-level periods T1, while the lower part have the periods T2 which is close to T1. Similarly, the wafer alignment grating mark consists of the same two sets of line gratings but arranged in opposite sequence. When superposition of two marks occurs during the alignment process, any relative offsets between wafer and masks cause opposite variations (displacement) for both the upper and lower set of fringes. Figure 3(c) shows the whole fringe pattern when the wafer and mask are misaligned by certain offset ∆x, and Fig. 3(d) shows the whole fringe pattern when the wafer and mask are completely aligned [10]. Similar to the coarse alignment, the intensity of the upper and lower set of fringes in Figs. 3(c)-3(d) can be simplified and expressed as

Iupper(x,y)=a(x,y)+b(x,y)cos[2πf1(x+Δx)2πf2x]
Ilower(x,y)=a(x,y)+b(x,y)cos[2πf1x2πf2(xΔx)]
Where Iupper(x, y) and Ilower(x, y) are recorded intensities corresponding to misaligned and aligned state, ∆x is the relative offset between two grating marks along x axis. Comparing Eq. (7) to Eq. (8), it is obvious that when wafer and mask are completely aligned, two sets of fringes are synchronously ‘in phase’, namely, the phase difference of two sets of fringes becomes zero or integer multiple of due to the periodicity of the sinusoidal function. However, when they are misaligned by certain offset ∆x, the phase distribution of two sets of fringes deviates from each other, hence the relative phase deviation to each other is approximately doubled to some extent, namely,
ΔΦ=Φ1(x,y)Φ2(x,y)=2π(f1+f2)Δx
Where Φ1(x,y) = 2πf1(x + ∆x)- 2πf2x and Φ2(x,y) = 2πf1(x)- 2πf2(x-∆x) are the spatial phase of upper and lower sets of fringes respectively. Since the spatial frequencies f1 and f2 of two gratings are predetermined, the offset ∆x between wafer and mask that depends on the phase difference Φ of two sets of fringe patterns can be computed by Eq. (10).

 

Fig. 3 The two group grating marker and the corresponding fringe: (a) the mask aligment grating maker; (b) the wafer alignment grating marker; (c) the fringe distribution of unalignment; (d) the fringe distribution of alignment.

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Δx=ΔΦT1T22π|T1+T2|

3. Alignment marks fabrication

Figure 4 shows the alignment marks that were designed by software L-edit (A software using for VLSI design), which were fabricated by Institute of Microelectronics of Chinese Academy of Sciences (Beijing, China). Figure 4(a) is the whole layout of the designed five sets of composite mark, which consists of one circular alignment mark alike that shown in Fig. 4(b) and the other four sets of composite line-gratings shown in Fig. 4(c), which respectively located in the central and four corners of Fig. 4(a). The periods of circular gratings are 4μm and 4.4μm for coarse alignment. The periods of line gratings from the upper left to the bottom left are respectively 2μm and 2.2μm, 4μm and 4.4μm, 6μm and 8μm, 8μm and 10μm, which are corresponding to different periods and sensitivities of moiré fringes. The upper two sets of alignment marks with grating line along y-direction are used for the offset measurement of x-direction, while the lower two sets of alignment marks with grating line along x-direction are used for the offset measurement in y-direction. Figure 4(d) illustrates the local SEM (scanning electron microscope) image of circular gratings with magnification of 1.5E3 times. Figure 4(e) illustrates the local SEM (scanning electron microscope) image of line gratings with magnification of 6E3 times. The overall size of each single grating is 500µm × 500µm.

 

Fig. 4 The designed alignment mark: (a) the whole alignment mark; (b)the circular alignment marks in (a); (c) the upper left alignment marks in (a); (d) local SEM image of single circular alignment mark with magnification of 1.5E3;(e) local SEM image of line alignment mark with magnification of 6E3.

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4. Experiment and discussion

The experiment is performed to verify the feasibility of the proposed method. Figure 5(a) shows the experiment setup based on projection alignment. An alignment illumination source with wavelength of 635.2nm and 1mW output power, along with a diaphragm provide a uniform and collimated light. The light beams were adjusted to illuminate the mask alignment mark and the wafer alignment mark that are located on the piezoelectric translator (PZT, the resolution and stroke are respectively 2nm (closed loop) and 100μm) which control by computer; and the moiré fringes can be produced and collected through the CCD imaging system (with an image collection card). The pixel number and pitch of CCD (WAT902H2, Japan) are 768 × 576 pixels and 8.4μm × 9.6μm, respectively. The magnification and work distance of the imaging lens are respectively 8 × and 110 mm. The moiré fringes are post-processed and analyzed to acquire the measurement results finally.

 

Fig. 5 (a) the experiment setup; (b) the captured moiré fringe pattern for coarse alignment (c) the captured moiré fringe pattern for fine alignment with 4 μ m and 4.4μm gratings.

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Figures 5(b)-5(c) show the circular moiré fringes produced by circular grating alignment marks for coarse alignment and the line moiré fringes produced by the composite line grating alignment marks with the period of 4μm and 4.4μm (rotated by 90° clockwise for convenience of image processing) for fine alignment respectively. Considering the periodicity and differential motion of the upper and lower sets of moiré fringe in fine alignment, the precision of coarse alignment is required to locate in the half average period of line moiré fringe. The phase demodulation approach [19] proposed previously is then used to process Fig. 5(b). Figure 6(a) shows the wrapped phase by Park’s phase unwrapping method [23] and Fig. 6(d) shows the unwrapped phase within Polar coordinates system, where the horizontal axis and vertical axis denote the angle θ and the phase Φ(ρ, θ) respectively. The amplitude A and phase delay φ are 12.004 and 1° respectively. According to the Eq. (5) and Eq. (6), the ∆x and ∆y are 1.9102T1 and 0.0333T1. Figure 6(b) shows the fringe pattern after moving the wafer alignment mark 2T1 (8μm) along x axis by PZT. It is almost ideal aligned through observation of human eye. Figure 6(c) and 6(e) show the wrapped phase and unwrapped phase in Polar coordinates system respectively through applying the same phase demodulation and phase unwrapping methods. The amplitude A, phase delay φ, ∆x and ∆y are 0.7216, 178°, −0.1147T1 and 0.004T1 respectively. It is obvious that the moved offset along x axis is 2.0249T1 from the proposed coarse alignment method. The offset is 0.0249T1 (90 nm) and the proposed method meets the requirement of falling into the scope of fine alignment completely.

 

Fig. 6 The coarse alignment process: (a) the wrapped phase after process for Fig. 5(b) ; (b) the fringe pattern after moving 2T1 along x axis; (c) the wrapped phase after process for (b); (d)the unwrapped phase of (a) in polar coordinate system; (e) the unwrapped phase of (c) in polar coordinate system.

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With regard to the process of fine alignment, the previously proposed phase demodulation approach [17] is applied to Fig. 5(c).The wrapped phase and the unwrapped phase are shown in Figs. 7(a)-7(b). According to the Eq. (6), the offset between the mask alignment mark and wafer alignment mark is 0.1766μm. After moving 0.1μm along x axis by PZT, the line fringe pattern is shown in Fig. 7(c). The related wrapped phase and unwrapped phase are shown in Figs. 7(d)-7(e) respectively, and the displacement is 0.0720μm. Comparing the offsets of two fringe pattern, the relative offset is 0.1046μm, so the deviation of the proposed fine alignment method is at the nanometer scale of 4.6nm.

 

Fig. 7 The fine alignment process: (a) the wrapped phase after process for Fig. 5(c); (b)the unwrapped phase of (a); (c) the fringe pattern after moving 0.1μm along x axis; (d) the wrapped phase after process for (c);(e) the unwrapped phase of (d).

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In order to verify the precision of the proposed method, 10 repeated measurements in the experiment are performed to calculate the mean error and standard deviation. In the process of coarse alignment, 4μm and 4.4μm circular gratings are used with the minimal step of 1μm by PZT. Figure 8 shows the measured error results, and the mean error and standard deviation are −13.8nm and 74.31nm respectively. In the process of fine alignment, all of the four groups ofgratings with different periods were used during the repeated measurements, i.e. the 2μm and 2.2μm gratings with the minimal step of 0.02μm, 4μm and 4.4μm gratings with the minimal step of 0.05μm, 6μm and 8μm gratings with the minimal step of 0.5μm, 8μm and 10μm gratings with the minimal step of 0.1μm. Figures 9(a)-9(d) show the measure error results respectively, and the mean errors and standard deviations of each group are shown in Table 1. The results indicated that the error at tens of nanometer scale for coarse alignment and with nanometer scale for fine alignment can be experimentally achieved through the proposed method. It can also be found that all the standard deviations of each group gratings are less than 10 nm with the proposed fine alignment method from Table 1; and the standard deviation also decrease along with the decreasing of grating period. So the alignment accuracy with sub-nanometer scale can be acquired by using the lower period gratings in the whole alignment process.

 

Fig. 8 Measured error related to input step displacement in coarse alignment.

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Fig. 9 Measured error related to input step displacement in coarse alignment: (a) the input step is 0.02μm with grating period 2μm and 2.2μm; (b) the input step is 0.05μm with grating period 4μm and 4.4μm; (c) the input step is 1μm with grating period 6μm and 8μm; (d) the input step is 0.2μm with grating period 8μm and 10μm.

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Tables Icon

Table 1. The mean errors and standard deviations of each group grating (nm).

The errors are mainly from the fabrication error of alignment marks, image acquisition, the limitation of phase extraction algorithm, the error of PZT and the environmental disturbance etc. Firstly, the fabrication error of alignment marks will impact the diffraction efficiency of the gratings, and further affect the quality of the final moiré fringe. Secondly, this method acquires the misaligned offset through fringe image processing, and the image acquisition need to truncate the signal into different pixels of digital image in the process of sampling. When the period of moiré fringe image and the sampling period couldn’t satisfy the conditions of integer multiple, the truncate error will be introduced into subsequent phase analysis, which limits the precision of phase extraction ultimately. Thirdly, 10 repeated measurements are based the stepping of the PZT, the error of PZT itself may cause the cumulative error and affect the alignment accuracy. Finally, the whole experiment is completed on a common optical table; the environmental disturbance may also affect PZT and induce the stochastic error in the course of wafer movement inevitably.

5. Conclusion

An accurate and reliable scheme for optical alignment of proximity lithography is proposed using the composite circular-line gratings and the phase analysis of moiré fringes. The feasibility of coarse alignment employing circular gratings and fine alignment employing the composite line gratings have been explored and verified. The marks fabrication and experiments of wafer-mask alignment have been fully demonstrated. The accuracy and error sources are also analyzed at length. The analytical and experimental results indicate that the alignment accuracy with nanometer scale even sub-nanometer scale can be experimentally attained for proximity lithography.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant No. 61307063 and No. 61405060), the Doctor Foundation of Southwest University of Science and Technology of China (Grant No. 12zx7128) and the Open Foundation of Robot Technology Used for Special Environment Key Laboratory of Sichuan Province (Grant No. 13zxtk08), by the Central Universities of South China University of Technology under Grant 2015 ZZ030, and by the Opening Project of State Key laboratory of Polymer Materials Engineering (Sichuan University) under Grant 2015-4-28.

References and links

1. M. C. Leibovici, G. M. Burrow, and T. K. Gaylord, “Pattern-integrated interference lithography: prospects for nano- and microelectronics,” Opt. Express 20(21), 23643–23652 (2012). [CrossRef]   [PubMed]  

2. B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011). [CrossRef]   [PubMed]  

3. C. Rawlings, U. Duerig, J. Hedrick, D. Coady, and A. Knoll, “Nanometer control of the markerless overlay process using thermal scanning proble lithography,” in Proceeding of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, 2014), pp. 1670–1675.

4. H. Zhou, M. Feldman, and R. Bass, “Subnanometer alignment system for x-ray lithography,” J. Vac. Sci. Technol. B 12(6), 3261–3264 (1994). [CrossRef]  

5. D. C. Flanders, H. I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31(7), 426–428 (1977). [CrossRef]  

6. M. Nelson, J. L. Kreuzer, and G. Gallatin, “Design and test of a through-the-mask alignment sensor for a vertical stage X-ray aligner,” J. Vac. Sci. Technol. B 12(6), 3251–3255 (1994). [CrossRef]  

7. H. Furuhashi, M. Uchida, Y. Uchida, and V. T. Chitnis, “Rough alignment system using moire gratings for lithography,” Proc. SPIE 4417, 568–575 (2001). [CrossRef]  

8. M. Gruber, D. Hagedorn, and W. Eckert, “Precise and simple optical alignment method for double-sided lithography,” Appl. Opt. 40(28), 5052–5055 (2001). [CrossRef]   [PubMed]  

9. L. Jiang and M. Feldman, “Accurate alignment technique for nanoimprint lithography,” Proc. SPIE 5752, 429–437 (2005). [CrossRef]  

10. T. Kanayama, J. Itoh, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation X-ray lithography,” J. Vac. Sci. Technol. B 6(1), 409–412 (1988). [CrossRef]  

11. K. S. Yen and M. M. Ratnam, “Simultaneous measurement of 3-D displacement components from circular moiré fringes: an experimental approach,” Opt. Lasers Eng. 50(6), 887–899 (2012). [CrossRef]  

12. K. S. Yen and M. M. Ratnam, “In-plane displacement sensing from circular gratings moiré fringes using graphic analysis approach,” Sensor Rev. 31(4), 358–367 (2011). [CrossRef]  

13. Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011). [CrossRef]  

14. N. Li, W. Wu, and S. Y. Chou, “Sub-20-nm alignment in nanoimprint lithography using moiré fringe,” Nano Lett. 6(11), 2626–2629 (2006). [CrossRef]   [PubMed]  

15. S. Zhou, Y. Fu, X. Tang, S. Hu, W. Chen, and Y. Yang, “Fourier-based analysis of moiré fringe patterns of superposed gratings in alignment of nanolithography,” Opt. Express 16(11), 7869–7880 (2008). [CrossRef]   [PubMed]  

16. S. Zhou, Y. Yang, L. Zhao, and S. Hu, “Tilt-modulated spatial phase imaging method for wafer-mask leveling in proximity lithography,” Opt. Lett. 35(18), 3132–3134 (2010). [CrossRef]   [PubMed]  

17. F. Xu, S. Hu, and S. Zhou, “Fringe pattern analysis for optical alignment in nanolithography using 2-D Fourier transforms,” Opt. Eng. 50(8), 088001 (2011). [CrossRef]  

18. J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012). [CrossRef]  

19. F. Xu, S. Hu, Y. Yang, J. L. Li, and L. L. Li, “Single closed fringe pattern phase demodulation in alignment of nanolithography,” Optik (Stuttg.) 124(9), 818–823 (2013). [CrossRef]  

20. J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013). [CrossRef]  

21. J. Zhu, S. Hu, J. Yu, S. Zhou, Y. Tang, M. Zhong, L. Zhao, M. Chen, L. Li, Y. He, and W. Jiang, “Four-quadrant gratings moiré fringe alignment measurement in proximity lithography,” Opt. Express 21(3), 3463–3473 (2013). [CrossRef]   [PubMed]  

22. S. Zhou, S. Hu, Y. Fu, X. Xu, and J. Yang, “Moiré interferometry with high alignment resolution in proximity lithographic process,” Appl. Opt. 53(5), 951–959 (2014). [CrossRef]   [PubMed]  

23. Y. C. Park and S. W. Kim, “Determination of two-dimensional planar displacement by moiré fringes of concentric-circle gratings,” Appl. Opt. 33(22), 5171–5176 (1994). [CrossRef]   [PubMed]  

References

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  1. M. C. Leibovici, G. M. Burrow, and T. K. Gaylord, “Pattern-integrated interference lithography: prospects for nano- and microelectronics,” Opt. Express 20(21), 23643–23652 (2012).
    [Crossref] [PubMed]
  2. B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011).
    [Crossref] [PubMed]
  3. C. Rawlings, U. Duerig, J. Hedrick, D. Coady, and A. Knoll, “Nanometer control of the markerless overlay process using thermal scanning proble lithography,” in Proceeding of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, 2014), pp. 1670–1675.
  4. H. Zhou, M. Feldman, and R. Bass, “Subnanometer alignment system for x-ray lithography,” J. Vac. Sci. Technol. B 12(6), 3261–3264 (1994).
    [Crossref]
  5. D. C. Flanders, H. I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31(7), 426–428 (1977).
    [Crossref]
  6. M. Nelson, J. L. Kreuzer, and G. Gallatin, “Design and test of a through-the-mask alignment sensor for a vertical stage X-ray aligner,” J. Vac. Sci. Technol. B 12(6), 3251–3255 (1994).
    [Crossref]
  7. H. Furuhashi, M. Uchida, Y. Uchida, and V. T. Chitnis, “Rough alignment system using moire gratings for lithography,” Proc. SPIE 4417, 568–575 (2001).
    [Crossref]
  8. M. Gruber, D. Hagedorn, and W. Eckert, “Precise and simple optical alignment method for double-sided lithography,” Appl. Opt. 40(28), 5052–5055 (2001).
    [Crossref] [PubMed]
  9. L. Jiang and M. Feldman, “Accurate alignment technique for nanoimprint lithography,” Proc. SPIE 5752, 429–437 (2005).
    [Crossref]
  10. T. Kanayama, J. Itoh, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation X-ray lithography,” J. Vac. Sci. Technol. B 6(1), 409–412 (1988).
    [Crossref]
  11. K. S. Yen and M. M. Ratnam, “Simultaneous measurement of 3-D displacement components from circular moiré fringes: an experimental approach,” Opt. Lasers Eng. 50(6), 887–899 (2012).
    [Crossref]
  12. K. S. Yen and M. M. Ratnam, “In-plane displacement sensing from circular gratings moiré fringes using graphic analysis approach,” Sensor Rev. 31(4), 358–367 (2011).
    [Crossref]
  13. Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
    [Crossref]
  14. N. Li, W. Wu, and S. Y. Chou, “Sub-20-nm alignment in nanoimprint lithography using moiré fringe,” Nano Lett. 6(11), 2626–2629 (2006).
    [Crossref] [PubMed]
  15. S. Zhou, Y. Fu, X. Tang, S. Hu, W. Chen, and Y. Yang, “Fourier-based analysis of moiré fringe patterns of superposed gratings in alignment of nanolithography,” Opt. Express 16(11), 7869–7880 (2008).
    [Crossref] [PubMed]
  16. S. Zhou, Y. Yang, L. Zhao, and S. Hu, “Tilt-modulated spatial phase imaging method for wafer-mask leveling in proximity lithography,” Opt. Lett. 35(18), 3132–3134 (2010).
    [Crossref] [PubMed]
  17. F. Xu, S. Hu, and S. Zhou, “Fringe pattern analysis for optical alignment in nanolithography using 2-D Fourier transforms,” Opt. Eng. 50(8), 088001 (2011).
    [Crossref]
  18. J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
    [Crossref]
  19. F. Xu, S. Hu, Y. Yang, J. L. Li, and L. L. Li, “Single closed fringe pattern phase demodulation in alignment of nanolithography,” Optik (Stuttg.) 124(9), 818–823 (2013).
    [Crossref]
  20. J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
    [Crossref]
  21. J. Zhu, S. Hu, J. Yu, S. Zhou, Y. Tang, M. Zhong, L. Zhao, M. Chen, L. Li, Y. He, and W. Jiang, “Four-quadrant gratings moiré fringe alignment measurement in proximity lithography,” Opt. Express 21(3), 3463–3473 (2013).
    [Crossref] [PubMed]
  22. S. Zhou, S. Hu, Y. Fu, X. Xu, and J. Yang, “Moiré interferometry with high alignment resolution in proximity lithographic process,” Appl. Opt. 53(5), 951–959 (2014).
    [Crossref] [PubMed]
  23. Y. C. Park and S. W. Kim, “Determination of two-dimensional planar displacement by moiré fringes of concentric-circle gratings,” Appl. Opt. 33(22), 5171–5176 (1994).
    [Crossref] [PubMed]

2014 (1)

2013 (3)

F. Xu, S. Hu, Y. Yang, J. L. Li, and L. L. Li, “Single closed fringe pattern phase demodulation in alignment of nanolithography,” Optik (Stuttg.) 124(9), 818–823 (2013).
[Crossref]

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

J. Zhu, S. Hu, J. Yu, S. Zhou, Y. Tang, M. Zhong, L. Zhao, M. Chen, L. Li, Y. He, and W. Jiang, “Four-quadrant gratings moiré fringe alignment measurement in proximity lithography,” Opt. Express 21(3), 3463–3473 (2013).
[Crossref] [PubMed]

2012 (3)

J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

M. C. Leibovici, G. M. Burrow, and T. K. Gaylord, “Pattern-integrated interference lithography: prospects for nano- and microelectronics,” Opt. Express 20(21), 23643–23652 (2012).
[Crossref] [PubMed]

K. S. Yen and M. M. Ratnam, “Simultaneous measurement of 3-D displacement components from circular moiré fringes: an experimental approach,” Opt. Lasers Eng. 50(6), 887–899 (2012).
[Crossref]

2011 (4)

K. S. Yen and M. M. Ratnam, “In-plane displacement sensing from circular gratings moiré fringes using graphic analysis approach,” Sensor Rev. 31(4), 358–367 (2011).
[Crossref]

Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
[Crossref]

F. Xu, S. Hu, and S. Zhou, “Fringe pattern analysis for optical alignment in nanolithography using 2-D Fourier transforms,” Opt. Eng. 50(8), 088001 (2011).
[Crossref]

B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (1)

2006 (1)

N. Li, W. Wu, and S. Y. Chou, “Sub-20-nm alignment in nanoimprint lithography using moiré fringe,” Nano Lett. 6(11), 2626–2629 (2006).
[Crossref] [PubMed]

2005 (1)

L. Jiang and M. Feldman, “Accurate alignment technique for nanoimprint lithography,” Proc. SPIE 5752, 429–437 (2005).
[Crossref]

2001 (2)

H. Furuhashi, M. Uchida, Y. Uchida, and V. T. Chitnis, “Rough alignment system using moire gratings for lithography,” Proc. SPIE 4417, 568–575 (2001).
[Crossref]

M. Gruber, D. Hagedorn, and W. Eckert, “Precise and simple optical alignment method for double-sided lithography,” Appl. Opt. 40(28), 5052–5055 (2001).
[Crossref] [PubMed]

1994 (3)

H. Zhou, M. Feldman, and R. Bass, “Subnanometer alignment system for x-ray lithography,” J. Vac. Sci. Technol. B 12(6), 3261–3264 (1994).
[Crossref]

M. Nelson, J. L. Kreuzer, and G. Gallatin, “Design and test of a through-the-mask alignment sensor for a vertical stage X-ray aligner,” J. Vac. Sci. Technol. B 12(6), 3251–3255 (1994).
[Crossref]

Y. C. Park and S. W. Kim, “Determination of two-dimensional planar displacement by moiré fringes of concentric-circle gratings,” Appl. Opt. 33(22), 5171–5176 (1994).
[Crossref] [PubMed]

1988 (1)

T. Kanayama, J. Itoh, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation X-ray lithography,” J. Vac. Sci. Technol. B 6(1), 409–412 (1988).
[Crossref]

1977 (1)

D. C. Flanders, H. I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31(7), 426–428 (1977).
[Crossref]

Atoda, N.

T. Kanayama, J. Itoh, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation X-ray lithography,” J. Vac. Sci. Technol. B 6(1), 409–412 (1988).
[Crossref]

Austin, S.

D. C. Flanders, H. I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31(7), 426–428 (1977).
[Crossref]

Bass, R.

H. Zhou, M. Feldman, and R. Bass, “Subnanometer alignment system for x-ray lithography,” J. Vac. Sci. Technol. B 12(6), 3261–3264 (1994).
[Crossref]

Burrow, G. M.

Chen, M.

Chen, W.

Chitnis, V. T.

H. Furuhashi, M. Uchida, Y. Uchida, and V. T. Chitnis, “Rough alignment system using moire gratings for lithography,” Proc. SPIE 4417, 568–575 (2001).
[Crossref]

Chou, S. Y.

N. Li, W. Wu, and S. Y. Chou, “Sub-20-nm alignment in nanoimprint lithography using moiré fringe,” Nano Lett. 6(11), 2626–2629 (2006).
[Crossref] [PubMed]

Coady, D.

C. Rawlings, U. Duerig, J. Hedrick, D. Coady, and A. Knoll, “Nanometer control of the markerless overlay process using thermal scanning proble lithography,” in Proceeding of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, 2014), pp. 1670–1675.

David, C.

B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011).
[Crossref] [PubMed]

Ding, Y. C.

J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Duerig, U.

C. Rawlings, U. Duerig, J. Hedrick, D. Coady, and A. Knoll, “Nanometer control of the markerless overlay process using thermal scanning proble lithography,” in Proceeding of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, 2014), pp. 1670–1675.

Eckert, W.

Ekinci, Y.

B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011).
[Crossref] [PubMed]

Feldman, M.

L. Jiang and M. Feldman, “Accurate alignment technique for nanoimprint lithography,” Proc. SPIE 5752, 429–437 (2005).
[Crossref]

H. Zhou, M. Feldman, and R. Bass, “Subnanometer alignment system for x-ray lithography,” J. Vac. Sci. Technol. B 12(6), 3261–3264 (1994).
[Crossref]

Flanders, D. C.

D. C. Flanders, H. I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31(7), 426–428 (1977).
[Crossref]

Fu, Y.

Fujigaki, M.

Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
[Crossref]

Furuhashi, H.

H. Furuhashi, M. Uchida, Y. Uchida, and V. T. Chitnis, “Rough alignment system using moire gratings for lithography,” Proc. SPIE 4417, 568–575 (2001).
[Crossref]

Gallatin, G.

M. Nelson, J. L. Kreuzer, and G. Gallatin, “Design and test of a through-the-mask alignment sensor for a vertical stage X-ray aligner,” J. Vac. Sci. Technol. B 12(6), 3251–3255 (1994).
[Crossref]

Gaylord, T. K.

Gruber, M.

Hagedorn, D.

Hanada, R.

Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
[Crossref]

He, Y.

J. Zhu, S. Hu, J. Yu, S. Zhou, Y. Tang, M. Zhong, L. Zhao, M. Chen, L. Li, Y. He, and W. Jiang, “Four-quadrant gratings moiré fringe alignment measurement in proximity lithography,” Opt. Express 21(3), 3463–3473 (2013).
[Crossref] [PubMed]

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

Hedrick, J.

C. Rawlings, U. Duerig, J. Hedrick, D. Coady, and A. Knoll, “Nanometer control of the markerless overlay process using thermal scanning proble lithography,” in Proceeding of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, 2014), pp. 1670–1675.

Hoh, K.

T. Kanayama, J. Itoh, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation X-ray lithography,” J. Vac. Sci. Technol. B 6(1), 409–412 (1988).
[Crossref]

Hu, S.

Itoh, J.

T. Kanayama, J. Itoh, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation X-ray lithography,” J. Vac. Sci. Technol. B 6(1), 409–412 (1988).
[Crossref]

Jiang, L.

L. Jiang and M. Feldman, “Accurate alignment technique for nanoimprint lithography,” Proc. SPIE 5752, 429–437 (2005).
[Crossref]

Jiang, W.

Kanayama, T.

T. Kanayama, J. Itoh, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation X-ray lithography,” J. Vac. Sci. Technol. B 6(1), 409–412 (1988).
[Crossref]

Kim, S. W.

Kirk, E.

B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011).
[Crossref] [PubMed]

Knoll, A.

C. Rawlings, U. Duerig, J. Hedrick, D. Coady, and A. Knoll, “Nanometer control of the markerless overlay process using thermal scanning proble lithography,” in Proceeding of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, 2014), pp. 1670–1675.

Kreuzer, J. L.

M. Nelson, J. L. Kreuzer, and G. Gallatin, “Design and test of a through-the-mask alignment sensor for a vertical stage X-ray aligner,” J. Vac. Sci. Technol. B 12(6), 3251–3255 (1994).
[Crossref]

Langner, A.

B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011).
[Crossref] [PubMed]

Leibovici, M. C.

Li, J. L.

F. Xu, S. Hu, Y. Yang, J. L. Li, and L. L. Li, “Single closed fringe pattern phase demodulation in alignment of nanolithography,” Optik (Stuttg.) 124(9), 818–823 (2013).
[Crossref]

Li, L.

Li, L. L.

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

F. Xu, S. Hu, Y. Yang, J. L. Li, and L. L. Li, “Single closed fringe pattern phase demodulation in alignment of nanolithography,” Optik (Stuttg.) 124(9), 818–823 (2013).
[Crossref]

Li, N.

N. Li, W. Wu, and S. Y. Chou, “Sub-20-nm alignment in nanoimprint lithography using moiré fringe,” Nano Lett. 6(11), 2626–2629 (2006).
[Crossref] [PubMed]

Li, X.

J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Liu, H. Z.

J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Masaya, A.

Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
[Crossref]

Morimoto, Y.

Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
[Crossref]

Nelson, M.

M. Nelson, J. L. Kreuzer, and G. Gallatin, “Design and test of a through-the-mask alignment sensor for a vertical stage X-ray aligner,” J. Vac. Sci. Technol. B 12(6), 3251–3255 (1994).
[Crossref]

Päivänranta, B.

B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011).
[Crossref] [PubMed]

Park, Y. C.

Ratnam, M. M.

K. S. Yen and M. M. Ratnam, “Simultaneous measurement of 3-D displacement components from circular moiré fringes: an experimental approach,” Opt. Lasers Eng. 50(6), 887–899 (2012).
[Crossref]

K. S. Yen and M. M. Ratnam, “In-plane displacement sensing from circular gratings moiré fringes using graphic analysis approach,” Sensor Rev. 31(4), 358–367 (2011).
[Crossref]

Rawlings, C.

C. Rawlings, U. Duerig, J. Hedrick, D. Coady, and A. Knoll, “Nanometer control of the markerless overlay process using thermal scanning proble lithography,” in Proceeding of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, 2014), pp. 1670–1675.

Seto, H.

Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
[Crossref]

Shao, J. Y.

J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Shimo, K.

Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
[Crossref]

Smith, H. I.

D. C. Flanders, H. I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31(7), 426–428 (1977).
[Crossref]

Tang, X.

Tang, Y.

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

J. Zhu, S. Hu, J. Yu, S. Zhou, Y. Tang, M. Zhong, L. Zhao, M. Chen, L. Li, Y. He, and W. Jiang, “Four-quadrant gratings moiré fringe alignment measurement in proximity lithography,” Opt. Express 21(3), 3463–3473 (2013).
[Crossref] [PubMed]

Tian, H. M.

J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Uchida, M.

H. Furuhashi, M. Uchida, Y. Uchida, and V. T. Chitnis, “Rough alignment system using moire gratings for lithography,” Proc. SPIE 4417, 568–575 (2001).
[Crossref]

Uchida, Y.

H. Furuhashi, M. Uchida, Y. Uchida, and V. T. Chitnis, “Rough alignment system using moire gratings for lithography,” Proc. SPIE 4417, 568–575 (2001).
[Crossref]

Wu, W.

N. Li, W. Wu, and S. Y. Chou, “Sub-20-nm alignment in nanoimprint lithography using moiré fringe,” Nano Lett. 6(11), 2626–2629 (2006).
[Crossref] [PubMed]

Xu, F.

F. Xu, S. Hu, Y. Yang, J. L. Li, and L. L. Li, “Single closed fringe pattern phase demodulation in alignment of nanolithography,” Optik (Stuttg.) 124(9), 818–823 (2013).
[Crossref]

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

F. Xu, S. Hu, and S. Zhou, “Fringe pattern analysis for optical alignment in nanolithography using 2-D Fourier transforms,” Opt. Eng. 50(8), 088001 (2011).
[Crossref]

Xu, X.

Yang, J.

Yang, Y.

Yen, K. S.

K. S. Yen and M. M. Ratnam, “Simultaneous measurement of 3-D displacement components from circular moiré fringes: an experimental approach,” Opt. Lasers Eng. 50(6), 887–899 (2012).
[Crossref]

K. S. Yen and M. M. Ratnam, “In-plane displacement sensing from circular gratings moiré fringes using graphic analysis approach,” Sensor Rev. 31(4), 358–367 (2011).
[Crossref]

Yu, J.

Yu, J. S.

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

Zhao, L.

Zhong, M.

Zhou, H.

H. Zhou, M. Feldman, and R. Bass, “Subnanometer alignment system for x-ray lithography,” J. Vac. Sci. Technol. B 12(6), 3261–3264 (1994).
[Crossref]

Zhou, S.

Zhou, S. L.

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

Zhu, J.

Zhu, J. P.

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

D. C. Flanders, H. I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31(7), 426–428 (1977).
[Crossref]

J. Vac. Sci. Technol. B (3)

M. Nelson, J. L. Kreuzer, and G. Gallatin, “Design and test of a through-the-mask alignment sensor for a vertical stage X-ray aligner,” J. Vac. Sci. Technol. B 12(6), 3251–3255 (1994).
[Crossref]

H. Zhou, M. Feldman, and R. Bass, “Subnanometer alignment system for x-ray lithography,” J. Vac. Sci. Technol. B 12(6), 3261–3264 (1994).
[Crossref]

T. Kanayama, J. Itoh, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation X-ray lithography,” J. Vac. Sci. Technol. B 6(1), 409–412 (1988).
[Crossref]

Nano Lett. (1)

N. Li, W. Wu, and S. Y. Chou, “Sub-20-nm alignment in nanoimprint lithography using moiré fringe,” Nano Lett. 6(11), 2626–2629 (2006).
[Crossref] [PubMed]

Nanotechnology (1)

B. Päivänranta, A. Langner, E. Kirk, C. David, and Y. Ekinci, “Sub-10 nm patterning using EUV interference lithography,” Nanotechnology 22(37), 375302 (2011).
[Crossref] [PubMed]

Opt. Eng. (1)

F. Xu, S. Hu, and S. Zhou, “Fringe pattern analysis for optical alignment in nanolithography using 2-D Fourier transforms,” Opt. Eng. 50(8), 088001 (2011).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

J. Y. Shao, Y. C. Ding, H. M. Tian, X. Li, and H. Z. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Opt. Lasers Eng. (2)

J. P. Zhu, S. Hu, J. S. Yu, Y. Tang, F. Xu, Y. He, S. L. Zhou, and L. L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Lasers Eng. 51(4), 371–381 (2013).
[Crossref]

K. S. Yen and M. M. Ratnam, “Simultaneous measurement of 3-D displacement components from circular moiré fringes: an experimental approach,” Opt. Lasers Eng. 50(6), 887–899 (2012).
[Crossref]

Opt. Lett. (1)

Optik (Stuttg.) (1)

F. Xu, S. Hu, Y. Yang, J. L. Li, and L. L. Li, “Single closed fringe pattern phase demodulation in alignment of nanolithography,” Optik (Stuttg.) 124(9), 818–823 (2013).
[Crossref]

Proc. SPIE (2)

H. Furuhashi, M. Uchida, Y. Uchida, and V. T. Chitnis, “Rough alignment system using moire gratings for lithography,” Proc. SPIE 4417, 568–575 (2001).
[Crossref]

L. Jiang and M. Feldman, “Accurate alignment technique for nanoimprint lithography,” Proc. SPIE 5752, 429–437 (2005).
[Crossref]

SAE Int J. Masetr Manuf. (1)

Y. Morimoto, M. Fujigaki, A. Masaya, K. Shimo, R. Hanada, and H. Seto, “Shape and strain measurement of rotating tire by sampling moiré fringes method,” SAE Int J. Masetr Manuf. 4(1), 1107–1113 (2011).
[Crossref]

Sensor Rev. (1)

K. S. Yen and M. M. Ratnam, “In-plane displacement sensing from circular gratings moiré fringes using graphic analysis approach,” Sensor Rev. 31(4), 358–367 (2011).
[Crossref]

Other (1)

C. Rawlings, U. Duerig, J. Hedrick, D. Coady, and A. Knoll, “Nanometer control of the markerless overlay process using thermal scanning proble lithography,” in Proceeding of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, 2014), pp. 1670–1675.

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Figures (9)

Fig. 1
Fig. 1 The two group circular grating marker and the corresponding fringe: (a) the mask alignment grating maker; (b) the wafer alignment grating marker; (c) the fringe distribution of misalignment; (d) the fringe distribution if alignment.
Fig. 2
Fig. 2 The relation between two group circular grating markers in polar coordinates system.
Fig. 3
Fig. 3 The two group grating marker and the corresponding fringe: (a) the mask aligment grating maker; (b) the wafer alignment grating marker; (c) the fringe distribution of unalignment; (d) the fringe distribution of alignment.
Fig. 4
Fig. 4 The designed alignment mark: (a) the whole alignment mark; (b)the circular alignment marks in (a); (c) the upper left alignment marks in (a); (d) local SEM image of single circular alignment mark with magnification of 1.5E3;(e) local SEM image of line alignment mark with magnification of 6E3.
Fig. 5
Fig. 5 (a) the experiment setup; (b) the captured moiré fringe pattern for coarse alignment (c) the captured moiré fringe pattern for fine alignment with 4 μ m and 4.4μm gratings.
Fig. 6
Fig. 6 The coarse alignment process: (a) the wrapped phase after process for Fig. 5(b) ; (b) the fringe pattern after moving 2T1 along x axis; (c) the wrapped phase after process for (b); (d)the unwrapped phase of (a) in polar coordinate system; (e) the unwrapped phase of (c) in polar coordinate system.
Fig. 7
Fig. 7 The fine alignment process: (a) the wrapped phase after process for Fig. 5(c); (b)the unwrapped phase of (a); (c) the fringe pattern after moving 0.1μm along x axis; (d) the wrapped phase after process for (c);(e) the unwrapped phase of (d).
Fig. 8
Fig. 8 Measured error related to input step displacement in coarse alignment.
Fig. 9
Fig. 9 Measured error related to input step displacement in coarse alignment: (a) the input step is 0.02μm with grating period 2μm and 2.2μm; (b) the input step is 0.05μm with grating period 4μm and 4.4μm; (c) the input step is 1μm with grating period 6μm and 8μm; (d) the input step is 0.2μm with grating period 8μm and 10μm.

Tables (1)

Tables Icon

Table 1 The mean errors and standard deviations of each group grating (nm).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

I 1 (x,y)=a(x,y)+b(x,y)cos( 2π( f 1 (x+Δx) 2 + (y+Δy) 2 f 2 x 2 + y 2 ) )
I 2 (x,y)=a(x,y)+b(x,y)cos( 2π( f 1 x 2 + y 2 f 2 x 2 + y 2 ) )
Φ(ρ,θ)=2π( f 1 (ρcosθ+εcosφ) 2 + (ρsinθ+εsinφ) 2 f 2 ρ )
Φ(ρ,θ)=2π( f 1 f 2 )ρ+2π f 1 εcos(θφ)
Δx=εcosφ
Δy=εsinφ
I upper (x,y)=a(x,y)+b(x,y)cos[2π f 1 (x+Δx)2π f 2 x]
I lower (x,y)=a(x,y)+b(x,y)cos[2π f 1 x2π f 2 (xΔx)]
ΔΦ= Φ 1 (x,y) Φ 2 (x,y)=2π( f 1 + f 2 )Δx
Δx= ΔΦ T 1 T 2 2π| T 1 + T 2 |

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