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This paper aims to deal with a four-quadrant gratings alignment method benefiting from phase demodulation for proximity lithography, which combines the advantages of interferometry with image processing. Both the mask alignment mark and the wafer alignment mark consist of four sets of gratings, which bring the convenience and simplification of realization for coarse alignment and fine alignment. Four sets of moiré fringes created by superposing the mask alignment mark and the wafer alignment mark are highly sensitive to the misalignment between them. And the misalignment can be easily determined through demodulating the phase of moiré fringe without any external reference. Especially, the period and phase distribution of moiré fringes are unaffected by the gap between the mask and the wafer, not excepting the wavelength of alignment illumination. Disturbance from the illumination can also be negligible, which enhances the technological adaptability. The experimental results bear out the feasibility and rationality of our designed approach.
©2013 Optical Society of America
1. Introduction
The progress in semiconductor manufacturing is to reduce the feature size that constitutes of ICs designs [1,2]. Smaller features allow for faster and more advanced ICs that consume less power and can be produced at lower cost [2]. The shrink in features is derived by photolithography, which has become the main semiconductor manufacturing tool. The lithographic manufacturing process of an IC consists of approximately 30 cycles [3]. Each layer defines a specific layer. The relative positioning (overlay) among different layers in lithographic technologies like X-ray lithography and nanoimprinting lithography, is extremely important. It determines the final performance of the device such as microprocessor, memory [3]. The current feature size has been extended to tens of nanometers, which requires alignment accuracy in order of nanometer. Traditionally, alignment techniques mainly fall into three sorts:
- • The intensity-based detection method that measures the critical intensity values of diffracted beams.
In X-ray lithography, for example, Flanders et.al [6] reported an alignment scheme with detectivity of misalignment about 10nm according to balancing the interference of laser diffracted by matched gratings on the mask and the wafer. Subsequently, Fay et.al [7] proposed similar scheme using linear zone-plate as the alignment mark, obtaining the aligned position by means of detecting the maximal or relative intensity of two diffracted beams from a narrow dotted grating on a wafer.
- • The phase-based signal detection method that measures the phase of a beat signal from two diffracted beams of slightly different periods.
Kanayama et. al [8] and Une et. al [9] presented a dual-frequency laser heterodyne alignment technique in X-ray lithography based on beat signal associated with the wafer displacement. The detectivity of misalignment was 5nm.
However, the accuracy of the geometric imaging method is always limited because it depends heavily upon simple image process such as detecting and extracting features of alignment mark. The gap between the mask and the wafer prevents the two marks from being clearly imaging simultaneously, thus a highly accurate alignment cannot be easily realized in proximity lithography. And the intensity-based or phase-based methods undergo these problems of high complexity and beam fluctuation caused by the wafer process such as the resist layer.
Since the discovery of moiré phenomenon in 1874 by L.Raleigh [10], subsequently it gradually becomes an attractive technique in many fields such as displacement and angle measurement, shape and strain measurement and profile measurement etc [11–17]. In recent years, optical alignment methods based on moiré fringe with typical applications for nanoimprint lithography and X-ray lithography have attracted wide attention and research activity [18–27]. Several types of moiré fringes created by only overlapping two elongated circular gratings, radial gratings, and Fresnel zone plates etc. simply and directly are used for the measurement of in-pane displacement [11, 13–15], which however are not suitable to directly identify the difference between perfect alignment and small misalignment moiré fringes within sub-period without any external reference. Many achievements have been obtained using dual-grating moiré fringes in Refs [21–28]. However, only two gratings used for fine alignment is not convenient and appears not completely reasonable. The phase analysis method using “average rows” or “columns” in these literatures [22–24] might be not reliable unless the relative angular displacement between the mask and the wafer is eliminated to zero [27,28].
To address above shortages, our group proposes a modified moiré fringe alignment method for proximity lithography through designing a novel alignment mark. This method takes full advantage of the phase values of all pixels in moiré fringe patterns, which can overcome many problems of previously proposed alignment methods and gratings. The noise and distortion induced by wafer process can be eliminated by image processing [27,28]. Experimental results are given to verify the feasibility of this scheme in Sec.4.
2. Alignment principle
The mask alignment mark and the wafer alignment mark are illustrated in Figs. 1(a) -1(b), respectively. Both of them are composed of four sets of line gratings. The second and fourth quadrants of the mask alignment mark have the period P1, while the remaining quadrants have the period P2. P2 is closely equal to P1 plus an additional term ΔP (>0), that is, P2 = ΔP + P1. Similarly, the wafer alignment mark consists of the same four sets of line gratings but complimentary placement. During the alignment between the mask and the wafer, moiré fringes can be formed since the alignment marks on the mask and the wafer with different periods of four quadrants are superposed each other under uniform illumination, as shown in Figs. 1(c)-1(d) (The original gratings were removed). Here, the four sets of moiré fringes have the same period
It is much larger than P1 and P2, hence magnifying the original gratings period by the factor of about P2/(P2-P1) [20,21,27]. The magnification effect of moiré fringe can be used to measure a minute relative linear displacement between the mask and the wafer with accuracy in nanometer scale. Assuming that Δx and ΔX are respectively referred to an actual misalignment and a moiré fringe displacement along x-direction, Δy and ΔY are respectively referred to an actual misalignment and a moiré fringe displacement along y-direction. For the alignment marks, an actual displacement can be magnified by a factorWhere Pa = 2 × P1P2/(P1 + P2) represents the average period of gratings P1 and P2 [21,27]. The factor of 2 in Eq. (2) enhances the measurement sensitivity in that the moiré fringes between the two rows move periodically in opposite directions. Furthermore, a relative linear displacement between the mask and the wafer will induce a periodical shift in spatial phase of moiré fringes, and thus can be obtained by the phase demodulation of moiré fringes for accurate alignment.
Fig. 1 Alignment marks and moiré fringes: (a) the mask alignment mark; (b) the wafer alignment mark; (c) moiré fringes pattern with misalignment by Δx(≠0). A shift of Δx in x-direction will lead to a moiré shift between the two rows of moiré fringes, the moiré fringe patterns in the first and third of quadrants move leftward, while the others move rightward; (d) moiré fringes pattern with perfect alignment in x-direction. In (a)-(b), the shaped “+” is used for coarse alignment. In (c)-(d), the original gratings were removed.
As shown in Fig. 1(c), the mask and the wafer are misaligned by certain relative linear displacement Δx, while Fig. 1(d) shows that the mask and the wafer are aligned perfectly. The first and second row of moiré fringe in Figs. 1(c)-1(d) can be complementarily adopted as phase analysis, making the practical application simple and convenient. Taking the first row of moiré fringe as an example, the intensity distributions in the upper and lower sets of moiré fringes can be respectively expressed as
where A(x,y) represents the background intensity in the image, which is insensitive to the change in phase; and B(x,y) represents the amplitude of moiré fringe and is sensitive to the phase change. The coordinates (x,y) denote the position in moiré fringe pattern. According to Eqs. (3)-(4), the phase difference between two sets of moiré fringe iswhere δupp = 2π[(x + Δx)/P1-x/P2] and δlow = 2π[x/P1-(x-Δx)/P2] are respectively the spatial average phase of the upper and the lower sets of moiré fringes. Since grating periods P1, P2 are known, the relative linear displacement can be determined by3. Design and fabrication of alignment mark
Figure 2 shows the alignment marks we 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 2(a) is the whole layout, which consists of four sets of different alignment marks like Fig. 2(b), respectively located on the four corners of Fig. 2(a). The periods of gratings starting 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 displacement measurement of x-direction, while the lower two sets of alignment marks with grating line along x-direction are used for the displacement measurement in y-direction. The coarse alignment can be achieved through the shaped “+” with line width 20μm as shown in Figs. 1(b)-1(c). Figure 2(c) illustrates a composition image of four local SEM (scanning electron microscope) images with magnification of 1.5E3. The drawing of partial enlargement in Figs. 2(d)-2(e) is magnified 6E3 times. The single grating is of size 500µm × 500µm.
Fig. 2 The designed alignment mark: (a) the whole alignment mark; (b) one of the alignment marks in (a); (c) a composition image of four local SEM images with magnification of 1.5E3 ;(d) local SEM image of single alignment mark with magnification of 6E3 ;(e) another local SEM image of single alignment mark with magnification of 6E3.
4. Experimental results and discussion
In order to verify the feasibility of the proposed alignment method above, an experiment is performed. The experimental setup is shown in Fig. 3(a) . It consists of several parts, including an alignment illumination source, a diaphragm, a collimation lens, the mask alignment mark and the wafer alignment mark, a piezoelectric translator (PZT, the resolution and stroke are respectively 2nm (closed loop) and 100μm), an imaging part (including an image collection card) and a computer etc., all of which function in cooperation to achieve the alignment measurement between the mask and the wafer. An alignment illumination source with 635.2nm wavelength and 5mW output power, along with a collimating lens provide a uniform and collimated light. The light beams illuminate onto the mask alignment mark and the wafer alignment, where the moiré fringes can be produced and collected through the CCD imaging system. The pixel number and pitch of CCD (WAT902H2, China) are 768 × 576 pixels and 8.4μm × 9.6μm, respectively. The local length and magnification of the imaging lens are respectively 110 mm and 8 × . And the computer with signal process software is used to demodulate the phase of moiré fringe pattern and the measurement result can be obtained. Periods of alignment marks in our experiments are respectively 4μm (P1) and 4.4μm (P2), 6μm (P1) and 8μm (P2) for measurement in x-direction as well as 8μm (P1) and 10μm (P2) for measurement in y-direction, corresponding to magnifications (here, the magnification of the imaging lens is not considered) about 40, 7 and 9 according to Eq. (2). The mask etched with alignment mark is mounted on a manual stage and the wafer etched with alignment mark is fixed on PZT. PZT is connected to a computer, which is used to control the relative displacement between the mask and the wafer. The captured moiré fringes patterns are processed using 2-Dimensional Fast Fourier Transform (2-D FFT) to obtain the relative linear displacement. In experimental setup, several parameters can be adjustable: the focal lengths of imaging lens and size of diaphragm, the distance between the mask and the wafer, switching among different alignment mark pairs. The system is carefully adjusted to achieve a uniform illumination and a clear moiré fringe pattern on the CCD imaging system. The mask alignment mark and the wafer alignment mark are adjusted to be parallel by a PZT through previously proposed approach [27,28], and the gap between the wafer and the mask approximately is within tens of micrometers. During the experiment, it is found that the contrast of moiré fringe varies periodically with the gap between the mask and the wafer. This phenomenon relates to the sizes of the gratings P1, P2 and grating self-imaging due to Tabor effect. Parts of moiré fringes with contrasts changed from 0.9953 to 0.1172 are shown in Fig. 4 . In spite of the changed contrasts, the calculated results indicate that the periods of moiré fringe in Figs. 4(a)-4(e) remain the same with 38pixels. These intensity curves on the left of Fig. 4 show that coordinate positions of along the x–direction are all consistent. All analyses above indicate the insensitivity of period and the phase distributions of moiré fringe to the gap. Equation (1) also hints that the period of moiré fringe is independent of the wavelength of alignment illumination. Disturbance from the illumination can be therefore negligible, which enhances the technological adaptability.
Fig. 3 (a) the experimental setup. The mask alignment mark and the wafer alignment mark are shown in the upper right corner; (b) the captured moiré fringe pattern for fine alignment in x-direction. The analyzed area (the first row) is included in red box. The second row of moiré fringes can be considered as a complementary analyzed area.
Fig. 4 The analytical results: effects of the gaps changed from 10μm to 20μm on the phase and period of moiré fringes with grating periods 8μm and 10μm are shown from (a) to (b). Parts of moiré fringes, corresponding intensities, contrasts and periods are respectively given from the left to right column.
The coarse alignment is performed using the shaped “+” on the center of alignment marks shown in Figs. 1(a)-1(b) and Figs. 2(b)-2(c). Before fine alignment, the coarse alignment is achieved through manual stages with accuracy better than 2μm to make the misalignment into the range of fine alignment. The process of coarse alignment is shown in Fig. 5 . Followed by the fine alignment, from which the relative linear displacement between the mask and the wafer can be obtained by the proposed method in Sec.2.
Fig. 5 The coarse alignment process: (a) the misaligned pattern both in x- and y-directions; (b) the misaligned pattern only in x–direction; (c) the misaligned pattern only in y-direction; (d) the aligned pattern both in x- and y-directions.
During fine alignment, a clear moiré fringe pattern can be imaged on the CCD imaging system at many different positions by adjusting the gap, which meets well with the requirement of proximity lithography alignment. PZT is used to perform the input step distance to the wafer. In the first group of experiment for alignment in x-direction, the mask alignment mark consists of gratings P2 (4.4μm) and P1 (4μm) while the wafer alignment mark consists of complementary gratings P1 (4μm) and P 2(4.4μm). For the alignment in y-direction, the second and third groups of experiment are developed. In the second one, the mask alignment mark consists of gratings P2 (8μm) and P1 (6μm) while the wafer alignment mark consists of gratings P1 (6μm) and P2 (8μm). In the third one, the mask alignment mark consists of gratings P2 (10μm) and P1 (8μm) while the wafer alignment mark consists of gratings P1 (8μm) and P2 (10μm). For three groups of experiments, the input step distances 0.1μm and 0.2μm are adopted, respectively.
The experimental moiré fringes of Fig. 6 show two situations of movement in fringes which are respectively indicated by solid-red arrows and dotted-red arrows. The movement directions in the first and third, second and fourth quadrants are consistent, respectively. Therefore, the cross-reference moiré fringe sets in A and B can be both used to calculate the relative linear displacement with opposite signs. This design can be considered more convenient and simpler than the case of two gratings [21–28] for practical fine alignment for phase analysis. The experimental phenomenon agrees well with our theoretical prediction described in Sec. 2.
Fig. 6 The schematic of moiré fringe movement direction during fine alignment. Moiré fringe sets A and B can be used to calculate the relative linear displacement between the mask and the wafer. Solid-red and dotted-red arrows respectively represent two movement situations of moiré fringe when the wafer alignment mark moves respectively leftward and rightward.
For improvement of the accuracy of phase extraction using 2D-FFT [27,28], the captured patterns are as far as possibly cut with integral number of moiré fringe period, which are respectively shown in Figs. 8(a)-8(b). And the corresponding experimental results are given in Fig. 7 . The experimental results of the first group are shown in Figs. 7(a)-7(b). For the input step of 0.1μm and 20 repeated measurements, the standard deviation of error, the mean error and the maximal error are respectively 2.432nm, 3.767nm and 7.800nm. In contrast, the standard deviation of error, the mean error and the maximal error are respectively 3.518nm, 4.995nm and 11.400nm when the input step is 0.2μm. Figures 7(c)-7(d) are respectively the experimental results of the second group. In Fig. 7(c) with input step 0.1μm, the standard deviation of error, the mean error and the maximal error are respectively 5.302nm, 6.738nm and 18.700nm. Compared with the case of Fig. 7(c), Fig. 7(d) shows the result of input step 0.2μm that the standard deviation of error, the mean error and the maximal error are respectively 6.786nm, 12.780nm and 22.000nm. The similar analyzed results of the third group are also given in Figs. 7(e)-7(f).
Fig. 7 Measured error vs. input linear displacement: (a) the input step is 0.1μm with grating period 4μm and 4.4μm; (b) the input step is 0.2μm with grating period 4μm and 4.4μm; (c) the input step is 0.1μm with grating period 6μm and 8μm; (d) the input step is 0.2μm with grating period 6μm and 8μm;(e) the input step is 0.1μm with grating period 8μm and10μm; (f) the input step is 0.2μm with grating period 8μm and10μm. Both (a) and (b) are the measured results for x-direction, while (c)-(f) for y-direction.
The results indicate that the error with nanometer scale for linear displacement measurement can be experimentally achieved by our proposed method. The measured linear displacement is linearly dependent upon the input linear displacement. According to the analyzed results shown in Fig. 7, the maximal error is less than 15nm, the mean error is not greater than 5nm and the standard error is less than 4nm in x-direction. While in y-direction, the mean error does not exceed 15nm, whereas the standard error is not greater than 10nm. Errors are mainly from environmental disturbance, the limitation of phase extraction algorithm, the fabrication error of alignment marks and noises, etc. Especially, the PZT with absolution of 2nm will also limit the accuracy of our method in experiment. The gray distribution curves with noises along the red-dot line in Figs. 8(a) -8(b) are respectively given in Figs. 8(c)-8(d). It can be found that the noises are at random distributed, which will affect the accuracy of phase extraction [21, 27]. Additionally, the accuracy of phase extraction using FFT is essentially needed to be noted. Figure 9 shows the results on condition that the moiré fringe pattern has a size of 512 pixels × 512pixels and P1 = 4 pixels, P2 = αP1. The number of moiré fringe varies with α, whose effects on the phase extraction accuracy should be considered. Assuming that the intensity distribution of moiré fringe is described as follows
Where the theoretical phase isWhen the number of moiré fringe in a given image is an integer, the absolute and relative error of the extracted phase with respect to α are respectively shown in Figs. 9(a)-9(b). One can obviously be seen from Fig. 9(a) that the absolute error is extremely small with magnitude of 10−13 rad. And the relative error also maintains magnitude of 10−12. It appears that the error is independent of α (or the number of moiré fringe). Comparatively, the absolute error shown in Figs. 9(c)-9(d) is much less that the number of moiré fringe is not an integer. The error fluctuates little with different values of α, corresponding to varied numbers of moiré fringe in a given image. Therefore, whether the number of moiré fringe in a given pattern is or not an integer will have a significant impact on the accuracy of phase extraction, further on the accuracy of alignment.Fig. 8 The analyzed moiré fringes: (a) moiré fringe pattern with grating periods 4μm and 4.4μm; (b) moiré fringe pattern with grating periods 8μm and 10μm; (c) intensity distribution as a function of location along the red-dot line shown in (a); (d) intensity distribution as a function of location along the red-dot line shown in (b).
Fig. 9 The phase extraction error analysis using 2-D FFT. The image size is 512 × 512 pixels, P1 = 4pixles, P2 = αP1. (a) and (b) respectively represent the absolute error and relative error in the case of the number of moiré fringe being not an integer; (c) and (d) represent the absolute error and relative error in the case of the number of moiré fringe being an integer.
5. Conclusion
In this paper, a novel designed four-quadrant gratings based alignment scheme employing the phase of moiré fringes is presented, which is highly accurate and reliable due to making full use of phase values in whole moiré fringe pattern. The insensitivity of the period and phase distribution of moiré fringes to the gap between the mask and the wafer as well as the wavelength of alignment illumination has been experimentally verified and discussed. The exhaustive experimental process has been developed, and the main error source and uncertainty are also detailedly analyzed. The experimental results prove that the measurement error with 10nm below can be achieved, which is expected to be applied in practical proximity lithography and other applications like NC (Numerical Control) machine tool positioning.
Acknowledgments
The authors thank Min Zhong, Yan Tang and Minyong Chen for their helpful assistance during experiment and discussion in writing this paper. This work was supported by Program for the National Science Foundation of China (Grant No. 61204114).
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