Moiré interferometry with high alignment resolution in proximity lithographic process Shaolin Zhou,1,4 Song Hu,2 Yongqi Fu,3,* Xiangmin Xu,1 and Jun Yang4 1
School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510640, China 2
State Key Laboratory of Optical Technologies for Microfabrication, Institute of Optics & Electronics, Chinese Academy of Sciences, Chengdu 610209, China
3
School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China 4
Department of Mechanical and Materials Engineering, Western University (The University of Western Ontario), London, Ontario, N6A 5B9, Canada *Corresponding author: [email protected] Received 22 October 2013; revised 13 January 2014; accepted 15 January 2014; posted 16 January 2014 (Doc. ID 199841); published 7 February 2014
Moiré interferometry is widely used as the precise metrology in many science and engineering fields. The schemes of moirés-based interferometry adopting diffraction gratings are presented in this paper for applications in a proximity lithographic system such as wafer-mask alignment, the in-plane twist angle adjustment, and tilts remediation. For the sake of adjustment of lateral offset as well as the tilt and inplane twist angle, schemes of the m; −m and m; 0 moiré interferometry are explored, respectively. Fundamental derivation of the moiré interferometry and schemes for related applications are provided. Three pairs of gratings with close periods are fabricated to form the composite grating. And experiments are performed to confirm the moiré interferometry for related applications in our proximity lithographic system. Experimental results indicate that unaligned lateral offset is detectable with resolution at the nanometer level, and the tilt and in-plane twist angle between wafer and mask could be manually decreased down to the scope of 10−3 and 10−4 rad, respectively. © 2014 Optical Society of America OCIS codes: (220.3740) Lithography; (120.3940) Metrology; (120.3180) Interferometry; (050.1950) Diffraction gratings. http://dx.doi.org/10.1364/AO.53.000951
1. Introduction
Interferometry has always been among the most widely used techniques of precise metrology for a great variety of applications, e.g., laser or digital electronic speckle interferometry [1,2], profilometry and surface measurement [3,4], computerized interferometric measurement [5], moiré interferometry for strain analysis [6], interferometric imaging and microscopy [7] or lithography [8], and holography and wavefront test [9] etc. Particularly, in a typical photolithographic system (the stepper or mask 1559-128X/14/050951-09$15.00/0 © 2014 Optical Society of America
aligner that operates in a projective or proximity way of exposure), interferometry-based precise metrology and control are usually intensively employed to guarantee the well-defined resolution and high quality of ultimate micro/nano structures for fabrication of electronic and optoelectronic devices in many fields, such as master or mold fabrication in soft lithography [10–12], surface prototyping for labon-a-chip (LOC) devices [13,14], micro- or nanofabrication for optical components [15], and photonic crystals [16]. Further, the interferometric techniques adopting diffraction grating are more frequently applied and incorporated in several subsystems of mask aligner or stepper-like wafer-mask alignment and leveling, 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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mounting and test, objective focusing, etc. Flanders proposed an interferometric alignment technique by detection of intensity of two symmetric interfering beams diffracted by two gratings with the same period on wafer and mask for x-ray lithography [17]. The heterodyne interferometric method that associates displacement with the phase change of a beat signal produced by two-frequency laser beams diffracted from gratings on wafer and mask was proposed by Itoh et al. [18] and by Suzuki and Une [19] for alignment of an x-ray stepper. Uchida et al. explored a moiré interference alignment technique for a proximity lithographic system using a moiré intensity signal produced by cyclic interlaced shift between overlapped gratings with the same period [20]. Similar schemes was also utilized in the ASML TTL and ATHENA alignment sensor for optical projection printing systems, in which only one pair of the 1st or higher symmetric diffraction orders from one grating on a wafer are captured to propagate through another grating on mask to generate the cyclic moiré intensity signal [21–23]. Recently, an interferometric spatial phase imaging method was proposed for precise alignment and position control for zone-platearray lithography or scanning probe lithography by Moon et al. [24–26]. All of these methods tend to take full advantages of high sensitivity of diffractioninduced interferometry. However, the intensity based or heterodyne interferometric schemes almost suffer from the same challenge of relatively lower robustness due to signal fluctuations or susceptibility caused by wafer-mask gap variation, photoresist layer, and so on. Overall, the interferometric spatial phase imaging scheme that embeds unaligned offset into the spatial phase of interference fringe pattern obtains higher alignment accuracy than other intensity-based schemes and shows better performances in the balancing factors of accuracy, complexity, and robustness than other techniques, whereas the checkerboard grating involved in the process still induces more challenges in structural fabrication and duration as well as higher complexity. For sake of higher robustness than those intensitybased or heterodyne interferometric schemes, and simultaneous taking into account adequate balance between accuracy and complexity, the route of moiré analogous interferometry is proposed and deeply explored in this paper. The versatility of this scheme facilitates not only accurate displacement adjustment but also angle calibration for processes of wafer-mask alignment and focusing and leveling in the proximity lithographic systems. Signal fluctuations or susceptibility can be avoided by reflecting both the displacement and angle variations into phase distribution of a moiré fringe pattern, which combines the advantages of interferometry with intrinsic high accuracy and the convenient fringe pattern processing with the ability of pattern analysis to ensure high robustness. First, detailed analyses are provided with respect to the principle and mechanism of presented moiré interferometric 952
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schemes, in which how the wafer-mask unaligned offset, tilt, or parallelism, and the in-plane twist angle are then directly denoted by the phase distribution of fringe patterns generated by diffractions of superposed gratings as well as reflections from a wafer surface is derived at length. Then three types of composite grating formed by different pairs of diffraction gratings with close periods are designed and fabricated and ultimately employed in the experiments to validate the schemes of moiré interferometry for our mask aligner. Finally, related experimental results during the wafer-mask alignment process, especially the tilt remediation and twist angle adjustment, as well as the involved moiré interferometry and equal-thickness interferometry, are discussed systematically. The mechanism of the moiré interferometry is summarized in Section 2, and schemes involved in the alignment process are introduced in Section 3. In Section 4, related experimental results and corresponding analyses are presented. 2. Fundamental A. m; −m Moiré Interferometry
Multidiffractions usually occur at the surfaces of two superposed gratings to create a series of diffracted waves that overlap together to form certain irregular distribution. The diffracted wave that undergoes the mth diffraction at the first grating and the nth diffraction at the second grating is termed as the m; n order. Here, all symmetrical orders, like the m; −m and −m; m m 1; 2; 3… orders, of two gratings with close periods, are adopted to create a low-frequency distribution in the presented moiré interferometry for the purpose of alignment during lithography process. As shown in Fig. 1, at the incidence of a planar wave, all symmetrically diffracted orders from two gratings G1 and G2 can be selectively collected (through the spatial filter) and projected onto the CCD surface, where the moiré interferometric field is formed and recorded. Taking into account any two symmetrically diffracted waves m; −m and −m; m, the complex amplitude Em;−m and E−m;m at the rear surface of G2 can be expressed as
Fig. 1. Schematic of m; −m moiré interferometry for wafer-mask alignment.
sin θm;−m x ; Am;−m exp i2π λ
(1)
sin θ−m;m E−m;m A−m;m exp i2π x ; λ
(2)
Em;−m
where, Am;−m and A−m;m , θm;−m and θ−m;m denote the amplitude and diffraction angles of two symmetric orders, respectively. For simplicity, the initial phases are neglected, and two symmetric orders are assumed to have the same amplitude under ideal conditions, namely A−m;m Am;−m. According to the diffraction equations of two gratings, the diffraction angle θm;−m of m; −m order can be readily derived, namely sin θm;−m mλf 1 − f 2 , where f 1 1∕P1 , f 2 1∕P2 , and P1 , P2 are the periods of G1 and G2 , respectively (assuming P2 > P1 ). Obviously, closer periods of two gratings lead to a smaller diffraction angle θm;−m and thus more resolvable interference fringes with a bigger period. Therefore, two gratings with close periods are chosen to limit the divergence of all symmetric orders within a small range to ensure that as more high orders as possible can be captured, so that overlap of all symmetrical orders (plus the zero order) gives rise to the ultimate moiré interference field by summation of all symmetric pairs, namely X Em;−m E−m;m E E0;0 m
A0;0 2
X Am;−m cos2πmjf 1 − f 2 jx:
(3)
m
where E is the complex amplitude of all symmetric waves diffracted by G1 and G2 . Apparently, for limited numbers of symmetric orders, series in Eq. (3) converge to a periodic distribution with the spatial frequency of f 1 − f 2, which turns out to be very low when two gratings are chosen to have approximate periods. As a result, spatially highly resolvable fringes with low frequency or a large period are produced and shift cyclically along with the continual lateral shift between two gratings. High sensitivity can be obtained due to the fact that one cycle of a later shift of 1∕f 1 P1 between two gratings would induce one significantly magnified cycle of fringe shift of 1∕f 1 − f 2 [27]. In other words, any lateral offset Δx between G1 and G2 that directly changes the optical path difference (OPD) and thus the phase difference of two symmetric diffraction orders is therefore reflected into a distinct phase shift of fringes in such a way of interferometry, and a similar relationship between lateral offset and the phase shift can be seen from the m; 0 moiré interferometry in the next section. B.
higher symmetric orders to be collected. Considering this, we employed another pair of orders that undergo zero diffraction at either of the superposed gratings and the same order diffraction at the other one, namely the 0; m and m; 0m 1; 2; 3… order pairs. Because all the 0; m and m; 0 order pairs have similar diffraction angles and thus a tiny included angle in between for gratings with close periods, they facilitate a similar interferometric scheme for wafer-mask alignment, which is termed as the m; 0 interferometry, shown in Fig. 2. Similarly, the complex amplitude of 0; m and m; 0 can be derived, and their interference intensity I m is expressed as I m I 1m I 2m p 2π sin θ1m − sin θ2m x ; 2 I 1m I 2m cos λ
(4)
where the initial phase difference is also neglected, and I 1m and I 2m , θ1m , and θ2m are the intensity and diffraction angles of the 0; m and m; 0 order, respectively. As can be seen in Fig. 2, it is obvious that any gap variation or lateral shift between G1 and G2 change the OPD and thus lead to a cyclic phase shift of the interference field (fringes). Considering the effect of gap variation and lateral displacement of certain grating (e.g., G1 ) to the phase shift along with the diffraction equations of two gratings, the intensity I m can be also derived as p I m I 1m I 2m 2 I 1m I 2m cos2πf 1 − f 2 x Δφ; (5) where, f 1 1∕P1 , f 2 1∕P2 and P1 ; P2 are the periods of grating G1 and G2 , and the phase variation Δφ can be written as 1 1∕ cos θ1m ΔG : Δφ 2π mf 1 Δx λ
(6)
Hereinto, Δx and ΔG is the lateral displacement and gap variation between G1 and G2 , respectively.
m; 0 Moiré Interferometry
Although m; 0 and −m; 0 are another series of symmetric diffraction orders, the divergence and included angle in-between are usually too large for
Fig. 2. Schematic of the 0; m and m; 0 moiré interferometry. 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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Apparently, the m; 0 interferometry is able to monitor the gap vibration and lateral shift simultaneously with high accuracy due to the fact that diffractions by two gratings with close periods give rise to much resolvable low-frequency-sensitive moiré fringes in fundamentally a similar way as m; −m moiré interferometry. Practically, either the gap variation or the lateral shift needs to be kept unchanged when the other one is under detection using this m; 0 interferometry. 3. Application Schemes
Usually, alignment also involves adequate adjustments that should be undertaken to remedy any tilt and in-plane twist angle existing between wafer and mask, prior to the elimination of unaligned offset. We discuss how the aforementioned moiré interferometry aids in performing tilt remediation and in-plane twist angle adjustment during the whole process of wafer-mask alignment in this section. A.
Tilt Remediation: Wafer-Mask Leveling
Shown in Fig. 3, the m; 0 moiré interferometry for tilt remediation is realized in a reflective way. At the incidence of a collimated laser beam reflected by the splitter and reflector, the same order B1 and B2 (usually the 1st diffraction) of gratings G1 and G2 with close periods diffract back with approximate angles at the surface of G2, with either B1 or B2 equivalent to the Littrow angle, such that both beams could be collected by a low NA and long work distance lens to generate the interference field to be recorded by a CCD. In order to avoid the effect of lateral shift to phase variation in the 0; m and m; 0 interferometry, both gratings are placed on a mask in order to monitor the gap change between wafer and mask independently. In such a way, any gap changes within a certain range can be directly and solely associated with the OPD change between B1 and B2 as well as the phase shift of ultimate interference field according to Eq. (6). Noticeably, tilt remediation is supposed to be carried out first to guarantee the parallelism between
Fig. 3. Scheme of m; 0 and 0; m moiré interferometry for wafer-mask alignment plus tilt remediation and twist adjustment. 954
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the wafer and mask, prior to further gap adjustment and alignment in our scheme. Since one of the interfering beams (B1 in Fig. 3) is reflected back by the wafer surface after diffraction, any tilts between the wafer and mask plane directly induce beam deflection and change in the phase distribution of the ultimate interference field. As is shown in the schematic in Fig. 4, when tilt of the wafer causes beam B1 to deflect to B01 , the fringe vector F that denotes the spatial frequency and direction of original interference field (fringes) is forced to deflect to F 0 , which denotes the varied phase distribution. For simplicity, the overall tilt can be decomposed into the cross-section component in the ZOX plane, and the longitudinal section component in ZOY plane. As long as the wafer is tilted in the longitudinal section and cross section by certain small angles, δφ and δθ, respectively, the beam B1 reflected from wafer is deflected by 2δφ and 2δθ, accordingly. So according to the geometrics of vectors, shown in Fig. 4, tiltmodulated interference field denoted by the deflected vector F 0 can be readily derived as p I I 1 I 2 2 I 1 I 2 cosF 0 · X φ0 ;
(7)
where 2π tanθ1 2δθ p F λ 1 tan2 θ1 2δθ tan2 2δφ 0
tan 2δφ − sin θ2 ; p 2 1 tan θ1 2δθ tan2 2δφ
(8)
is the wave vector of the interference field to denote spatial frequency and direction of fringe distribution, and X x; y denotes the coordinates in the XOY plane (also the grating surface plane). According to results in Eqs. (7) and (8), tilt between wafer and mask influence the phase distribution of interference field by changing the amplitude and direction of interference wave vector. Specifically, because tilts in both sections are usual tiny, tilt term δθ in the cross section mainly induces a frequency shift, and tilt term δφ in the longitudinal section mainly contributes to fringe deflection, according to Eq. (8).
Fig. 4. Schematic of beam deflection induced by wafer tilt and corresponding change of the phase distribution (fringe vector) of interference field.
within a certain limited range, and the m; 0 moiré interferometry needs to be further employed for fine adjustment. This process is discussed along with the experimental results in Section 4. C.
Fig. 5. Equal-thickness interference caused by tilted wafer with regard to the mask at a small gap.
B.
Equal-Thickness Interference
At the same time, the existence of tilt between wafer and mask also leads to a similar phenomenon of equal thickness interference, caused by waferreflected and back-diffracted orders within a certain range of gap: an alternative for tilt remediation. Shown in Fig. 5, when gratings G1 and G2 are illuminated by a planar wave that is incident at the 1st order Littrow angle of G1, diffractions take place on both sides of gratings. The 1st order that propagates through is reflected back by the wafer surface to overlap with the back-diffracted first order at the surface of either grating. Only when certain tilt exists between wafer and mask to induce certain angle the two orders (B1 and B01 or B2 and B02 in Fig. 6), cyclic constructive and deconstructive interference that occurs at the grating surface can be observed. As a result, any tilt can be monitored in a similar way by the phase distribution of equalthickness fringes: the direction and frequency. According to geometrics in Fig. 5 and interference theory, increased tilt leads to bigger interference angle and denser equal-thickness fringes with higher frequency, and the wave vector of fringes can be used to denote the amount of tilts δθ and δφ in both sections in a similar way as the moiré interferometry discussed in a previous section. However, the equalthickness interference is used in a qualitative way to coarsely adjust the tilt at a small gap, which varies
Fig. 6. Scheme of m; −m moiré interferometry arranged in a reflective way for in-plane twist angle adjustment and subsequent wafer-mask alignment.
Twist Angle Adjustment and Alignment
When the wafer and mask are adjusted to be parallel with each other at an adequate gap for proximity exposure, in-plane twist angle adjustment is the final step to be completed right before alignment. Although the m; 0 interferometry is also applicable for twist angle adjustment, the m; −m moiré interferometry tends to be more advantageous because the interference of symmetric orders is insusceptible to gap fluctuation during the subsequent alignment process to eliminate the unaligned offset. And the m; −m moiré interferometry is realized in a reflective way similar to that of the tilt remediation. The differences between the schemes of twist angle adjustment and tilt remediation lie in the incident angle of illumination and arrangement of gratings. The collimated laser beam is split and reflected to be perpendicularly incident on two superposed composite gratings, as shown in Fig. 6. The symmetric orders that diffract back with small angles are collected by a lens with low NA and long work distance, so as to form the final m; −m moiré interference fringes on CCD plane, usually generated by the orders of 1; −1 and −1; 1 from the gratings with period at magnitude of microns scale. In order to double the effect of the twisted angle to the phase shift of corresponding interference fringes (field), one couple of composite gratings are designed to be composed of four sets of gratings with close periods of P1 and P2 and arranged in an opposite sequence on the wafer and mask. As a result, the twist angle is monitored and adjusted by the mechanism that any amounts of in-plane rotation between two composite gratings would induce reverse deflection to four sets of fringes in a similar way as the tilt remediation scheme. As the fringe frequency remains almost unchanged within a small range of rotation, the in-plane twist angle is then solely associated with the fringe deflection. This easy-toimplement technique can be applicable in a qualitatively way in that it is verified to be able to manually remedy the in-plane twist angle within the scope of 10−4 rad. The fundamental derivation and performance of twist angle adjustment is discussed at length previously [28], which is briefly cited here for good context and a comparison of various moiré interferometric schemes in wafer-mask alignment. According to analyses in Section 1, phase deviation between two corresponding sets of fringes can be used for unaligned offset detection in subsequent wafer-mask alignment after twist angle adjustment. The alignment sensitivity is also doubled by the composite grating due to the fact that any lateral offset induces reverse phase shift as well as doubled phase deviation between two corresponding sets of fringes. Detailed analysis of the moiré effect and 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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Fig. 7. Composite grating with left and right part arranged as (a) G1 and (b) G2 shown in Fig. 3.
related mechanism of the interferometric alignment based on superposed gratings is described in previous study [27], related results of which are also briefly cited here for integrity of context and comparison in discussion in Section 4. 4. Results and Discussion
To confirm the validity of moiré interferometry and its application in alignment process of our proximity lithographic system, an alignment system was built, and related experiments were performed according to schemes in Section 2. A 633 nm laser beam, an 8× lens with long work distance of 110 mm and a WAT902H CCD with pixel width of 8.3 μm are used for schemes in our experimental system. For tilt remediation in wafer-mask leveling, gratings with close periods of P1 1 μm and P2 1.1 μm were fabricated by means of x-ray lithography. Furthermore, in order to double the effects of tilts δθ and δφ in both sections to frequency shift and deflection of interference fringes, a composite grating that is formed by four sets of gratings with close periods, P1 and P2 , in a similar way as the ones for twist angle adjustment is adopted, as shown in Fig. 7. In such a way, two sets of interference fringes occur at the surface of G2, with the upper set of
fringes generated by back diffraction from the upper-right grating (with period P2 ) and the waferreflected diffraction from the upper-left grating (with period P1 ), also see Fig. 3, and the bottom set of fringes generated by diffraction from the bottomright grating (with period P1 ) and the bottom-left grating (with the period P2 ) in an opposite sequence as the upper one. Results of several states of tilt remediation are shown in Figs. 8 and 9. The patterns are split into two parts, with the left part induced by equal-thickness interference and the right part caused by moiré interference that occurs at the surface of G2. When tilts exist in both sections, the equal-thickness fringes distribute along an arbitrary direction, and two split sets of fringes on the right part become reversely deflected with different frequencies, as shown in Fig. 8(a). When tilt in the longitudinal section is almost eliminated to leave only the cross section component, the equal thickness fringes become horizontally distributed, and the other two sets of fringes in the right part extend longitudinally along the same direction and only differ in frequencies, as shown in Fig. 8(b). Similarly, when tilt only exists in longitudinal section, the equalthickness fringes then are then vertically distributed and the other two sets of fringes tend to be reversely deflected with almost the same frequency, as shown in Fig. 8(c). When tilts in both sections are ideally remedied, the equal-thickness fringes disappear (with infinite period) and the other two sets of fringes become in absolute agreement with each other, as shown in Fig. 9(b). Hereinto only the orders of (1, 0) and (0, 1) are diffracted and collected to participate the moiré interferometry in our scheme. Figure 9(a) shows result of the (0, 0) order background with no interference when the two diffraction orders are filtered. According to Eqs. (7) and (8), the wave vector of upper and bottom fringes in the right part can be derived as F 0up
2π tanθ1 2δθ p λ 1 tan2 θ1 2δθ tan2 2δφ tan 2δφ − sin θ2 ; p ; (9) 1 tan2 θ1 2δθ tan2 2δφ
Fig. 8. Results of fringe distribution of moiré interference and equal-thickness interference that correspond to tilts existing in (a) both sections, (b) cross section, (c) longitudinal section, respectively. 956
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Fig. 9. Results recorded (a) without, and (b) with participation of the (1, 0) and (0, 1) diffraction orders.
F 0bottom
2π tanθ2 2δθ ; sin θ1 − p λ 1 tan2 θ2 2δθ tan2 2δφ tan 2δφ (10) − p : 1 tan2 θ2 2δθ tan2 2δφ
Apparently, shown in Eqs. (9) and (10), tilts in both sections δθ and δφ) lead to opposite frequency variations and deflections between the upper and bottom part of fringes. The frequency and angle deviation Δf , Δθ can be readily derived as Δf
2δθ · cos θ1 cos θ2 ; λ
cos θ1 tan 2δφ sin θ1 − sin θ2 cos θ2 tan 2δφ : a tan sin θ1 − sin θ2
(11)
Δθ ≈ a tan
(12)
As a result, the amount and direction of tilts in two sections can be coarsely indicated by the equal-thickness fringes in a qualitative way and then quantitatively remedied by the other two sets of fringes with variable frequencies and deflection as well as doubled sensitivity by utilization of the composite gratings. For in-plane twist angle adjustment and further alignment, two composite gratings on both wafer
and mask, arranged in opposite sequence in Fig. 6, are also similar as the one for tilt remediation. Three pairs of gratings with close periods of P1 4 μm, P2 4.4 μm; P1 6 μm, P2 8 μm; and P1 8 μm, P2 10 μm are adopted to form the composite grating, respectively. Other than the 1; −1 moiré interferometry, experiments using the (1, 0) moiré interferometry are also performed for both the in-plane twist angle adjustment and alignment. In either case, fringes become cyclically blurred and clear due to the Talbot effect induced by gap variation between two composite gratings, and clearly resolvable fringes can only be observed at a series of gaps that equal to the Talbot distance and integer times of Talbot distance, see results of gratings with periods of P1 4 μm, P2 4.4 μm, as shown in Fig. 10. Therefore, fringe patterns recorded at gaps of integer times of Talbot distance are used to adjust the inplane twist angle and unaligned offset. Figure 11 show results of the 1; −1 interferometry of gratings with periods of P1 6 μm, P2 8 μm, where half part of the four-quadrant fringe pattern is intercepted. Results in Fig. 12 show the process of inplane twist angle being gradually remedied by the (1, 0) moiré interferometry using gratings with periods of P1 8 μm and P2 10 μm. These results confirm that tilt remediation could be achieved with preserved angular resolution of better than 10−3 rad and sensitivity in twist angle adjustment is attainable at the level of 10−4 rad even in a manual performance. After twist angle remediation, unaligned offset is denoted and adjusted by the phase difference of two sets of fringes with doubled sensitivity. Figure 13 shows stepwise changed phase differences caused by gradually increased offset in the 1; −1 moiré interferometry of alignment using gratings with periods of P1 8 μm, P2 10 μm, and the step of offset is about one-eighth of the average period of two grating. Thus alignment sensitivity δx is directly associated with and determined by the phase resolution δφ of fringe pattern processing, namely, according to Eq. (3), δx
δφ P1 P2 · : 2π P1 P2
(13)
Fig. 10. Results of the 1; −1 moiré interferometry: (a) the background with 1; −1 and −1; 1 orders filtered. (b) Obscure fringe pattern recorded at an arbitrary gap of non-Talbot distance. (c) Clear one recorded at the gap of Talbot distance. 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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periods of P1 4 μm and P2 4.4 μm is higher than that of all other pairs. 5. Summary
Fig. 11. Results of twist angle adjustment and alignment using gratings with periods of P1 6 μm, P2 8 μm, where (a) certain in-plane twist angle exist, (b) twist angle remedied with certain unaligned offset, and (c) aligned with offset almost eliminated.
For gratings with periods P1 8 μm, P2 10 μm, phase resolution is readily attainable at the level of 10−2, so the alignment sensitivity around 7 nm can be obtained. In addition, it is apparent to notice the period of fringes generated by gratings with periods of P1 6 μm, P2 8 μm is much smaller than that of the other two pairs of gratings. According to Eqs. (3) and (5), periods of fringes generated by gratings with periods of P1 4 μm and P2 4.4 μm, P1 6 μm and P2 8 μm, and P1 8 μm and P2 10 μm can be derived as 44, 24, and 40 μm, respectively, in both the 1; −1 and m; 0 moiré interferometry. Ultimately, for constant phase resolution, gratings with smaller periods that are closer to each other lead to higher alignment sensitivity. Thus alignment sensitivity of gratings with
Schemes of moiré interferometry presented in this paper are employed as the precise metrology for angle and displacement adjustment in alignment of a proximity lithographic system. Basically, the presented m; −m interferometry is performed in an on-axis way that utilizes symmetric orders with approximate angles diffracted from gratings with close periods, while the m; 0 interferometry is performed in a similar but off-axis way. In principle, the lateral offset and angle derivation (tilt and the inplane twist angle) can be directly associated with phase distribution of fringes generated in both cases of interferometry. However, our derivation indicates that the m; 0 moiré interferometry turns out to be more appropriate and efficient for tilt remediation, in which tilts in both the cross and longitudinal section can be qualitatively eliminated first by the equalthickness interference fringes and then precisely remedied according to the deflections and frequencies of the m; 0 interference fringes. Moreover, both schemes are fundamentally applicable for the in-plane twist angle adjustment and alignment after tilt remediation, but the on-axis m; −m moiré interferometry is more robust to gap variation for unaligned offset detection due to the symmetry of optical path of diffraction orders. To confirm the validity of our schemes, three pairs of gratings with close periods are adopted for the purpose of individually composing three types of composite grating, and related experiments are carried out. Results indicate that schemes of moiré interferometry presented in this paper facilitate all offset and angle
Fig. 12. Process of in-plane twist angle remediation by the (0, 1) and (1, 0) interference fringes from (a) certain twist angle to (b) the state of adequately adjusted and (c) ideally adjusted.
Fig. 13. Stepwise increased offset leads to two parts of fringes with varied phase differences of (a) 0, (b) π∕2, (c) π, (d) 3π∕2. 958
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adjustments in an accurate and easy-to-control process, by which tilt and in-plane twist angle are readily remedied down to the scope of 10−3 and 10−4 rad, and ultimate alignment resolution at the nanometer level is attainable. We acknowledge financial support from the Fundamental Research Funds for the Central Universities of South China University of Technology (2012ZM 0026). References 1. M. Iskander, “Optical measurement of strain and stress,” in Modelling with Transparent Soils SE - 4 (Springer, 2010), pp. 27–44. 2. D. J. Chen and F. P. Chiang, “Computer-aided speckle interferometry using spectral amplitude fringes,” Appl. Opt. 32, 225–236 (1993). 3. P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993). 4. J. Schwider and L. Zhou, “Dispersive interferometric profilometer,” Opt. Lett. 19, 995–997 (1994). 5. J. C. Wyant, “Computerized interferometric surface measurements,” Appl. Opt. 52, 1–8 (2013). 6. C. A. Walker, “Moiré interferometry for strain analysis,” Opt. Lasers Eng. 8, 213–262 (1988). 7. Y. Kuznetsova, A. Neumann, and S. R. Brueck, “Imaging interferometric microscopy: approaching the linear systems limits of optical resolution,” Opt. Express 15, 6651–6663 (2007). 8. X. Chen and S. R. Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt. Lett. 24, 124–126 (1999). 9. J. C. Wyant and V. P. Bennett, “Using computer generated holograms to test aspheric wavefronts,” Appl. Opt. 11, 2833–2839 (1972). 10. J.-H. Lee, C.-H. Kim, Y.-S. Kim, K.-M. Ho, K. Constant, W. Leung, and C.-H. Oh, “Diffracted moiré fringes as analysis and alignment tools for multilayer fabrication in soft lithography,” Appl. Phys. Lett. 86, 204101 (2005). 11. J. C. Love, D. B. Wolfe, H. O. Jacobs, and G. M. Whitesides, “Microscope projection photolithography for rapid prototyping of masters with micron-scale features for use in soft lithography,” Langmuir 17, 6005–6012 (2001). 12. G. M. Whitesides, E. Ostuni, S. Takayama, X. Jiang, and D. E. Ingber, “Soft lithography in biology and biochemistry,” Annu. Rev. Biomed. Eng. 3, 335–373 (2001). 13. T. Scharnweber, R. Truckenmüller, A. M. Schneider, A. Welle, M. Reinhardt, and S. Giselbrecht, “Rapid prototyping of
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microstructures in polydimethylsiloxane (PDMS) by direct UV-lithography,” Lab Chip 11, 1368–1371 (2011). W. Chen, R. H. W. Lam, and J. Fu, “Photolithographic surface micromachining of polydimethylsiloxane (PDMS),” Lab Chip 12, 391–395 (2012). Y. Zhang, N. Gao, and C. Xie, “Using circular Dammann gratings to produce impulse optic vortex rings,” Appl. Phys. Lett. 100, 041107 (2012). P. Yao, G. J. Schneider, B. Miao, D. W. Prather, E. D. Wetzel, and D. J. O’Brien, “Fabrication of three-dimensional photonic crystals with multilayer photolithography,” Proc. SPIE 5720, 27–35 (2005). D. C. Flanders and H. I. Smith, “A new interferometric alignment technique,” Appl. Phys. Lett. 31, 426–428 (1977). J. Itoh, T. Kanayama, N. Atoda, and K. Hoh, “An alignment system for synchrotron radiation x‐ray lithography,” J. Vac. Sci. Technol. B 6, 409–412 (1988). M. Suzuki and A. Une, “An optical-heterodyne alignment technique for quarter-micron x-ray lithography,” J. Vac. Sci. Technol. B 7, 1971–1976 (1989). Y. Uchida, S. Hattori, and T. Nomura, “An automatic mask alignment system using moire interference,” J. Vac. Sci. Technol. B 5, 244–247 (1987). G. Bouwhuis and S. Wittekoek, “Automatic alignment system for optical projection printing,” IEEE Trans. Electron Devices ED-26, 723–728 (1979). R. Navarro and S. Keij, “Extended ATHENA alignment performance and application for the 100-nm technology node,” Proc. SPIE 4344, 682–694 (2001). G. Pugh and M. Giorgi, “Evaluation of ASML ATHENA alignment system on Intel front-end processes,” Proc. SPIE 4689, 286–294 (2002). R. Menon, E. E. Moon, M. K. Mondol, F. J. Castaño, and H. I. Smith, “Scanning-spatial-phase alignment for zone-platearray lithography,” J. Vac. Sci. Technol. B 22, 3382–3385 (2004). E. E. Moon, L. Chen, P. N. Everett, M. K. Mondol, and H. I. Smith, “Interferometric-spatial-phase imaging for six-axis mask control,” J. Vac. Sci. Technol. B 21, 3112–3115 (2003). E. E. Moona and H. I. Smith, “Nanometer-precision pattern registration for scanning-probe lithographies using interferometric-spatial-phase imaging,” J. Vac. Sci. Technol. B 24, 3083–3087 (2006). S. Zhou, Y. Fu, X. Tang, S. Hu, W. Chen, and Y. Yang, “Fourierbased analysis of moiré fringe patterns of superposed gratings in alignment of nanolithography,” Opt. Express 16, 7869–7880 (2008). S. Zhou, C. Xie, Y. Yang, S. Hu, X. Xu, and J. Yang, “Moirébased phase imaging for sensing and adjustment of in-plane twist angle,” Photonics Technol. Lett. IEEE 25, 1847–1850 (2013).
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School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510640, China 2
State Key Laboratory of Optical Technologies for Microfabrication, Institute of Optics & Electronics, Chinese Academy of Sciences, Chengdu 610209, China
3
School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China 4
Department of Mechanical and Materials Engineering, Western University (The University of Western Ontario), London, Ontario, N6A 5B9, Canada *Corresponding author: [email protected] Received 22 October 2013; revised 13 January 2014; accepted 15 January 2014; posted 16 January 2014 (Doc. ID 199841); published 7 February 2014
Moiré interferometry is widely used as the precise metrology in many science and engineering fields. The schemes of moirés-based interferometry adopting diffraction gratings are presented in this paper for applications in a proximity lithographic system such as wafer-mask alignment, the in-plane twist angle adjustment, and tilts remediation. For the sake of adjustment of lateral offset as well as the tilt and inplane twist angle, schemes of the m; −m and m; 0 moiré interferometry are explored, respectively. Fundamental derivation of the moiré interferometry and schemes for related applications are provided. Three pairs of gratings with close periods are fabricated to form the composite grating. And experiments are performed to confirm the moiré interferometry for related applications in our proximity lithographic system. Experimental results indicate that unaligned lateral offset is detectable with resolution at the nanometer level, and the tilt and in-plane twist angle between wafer and mask could be manually decreased down to the scope of 10−3 and 10−4 rad, respectively. © 2014 Optical Society of America OCIS codes: (220.3740) Lithography; (120.3940) Metrology; (120.3180) Interferometry; (050.1950) Diffraction gratings. http://dx.doi.org/10.1364/AO.53.000951
1. Introduction
Interferometry has always been among the most widely used techniques of precise metrology for a great variety of applications, e.g., laser or digital electronic speckle interferometry [1,2], profilometry and surface measurement [3,4], computerized interferometric measurement [5], moiré interferometry for strain analysis [6], interferometric imaging and microscopy [7] or lithography [8], and holography and wavefront test [9] etc. Particularly, in a typical photolithographic system (the stepper or mask 1559-128X/14/050951-09$15.00/0 © 2014 Optical Society of America
aligner that operates in a projective or proximity way of exposure), interferometry-based precise metrology and control are usually intensively employed to guarantee the well-defined resolution and high quality of ultimate micro/nano structures for fabrication of electronic and optoelectronic devices in many fields, such as master or mold fabrication in soft lithography [10–12], surface prototyping for labon-a-chip (LOC) devices [13,14], micro- or nanofabrication for optical components [15], and photonic crystals [16]. Further, the interferometric techniques adopting diffraction grating are more frequently applied and incorporated in several subsystems of mask aligner or stepper-like wafer-mask alignment and leveling, 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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mounting and test, objective focusing, etc. Flanders proposed an interferometric alignment technique by detection of intensity of two symmetric interfering beams diffracted by two gratings with the same period on wafer and mask for x-ray lithography [17]. The heterodyne interferometric method that associates displacement with the phase change of a beat signal produced by two-frequency laser beams diffracted from gratings on wafer and mask was proposed by Itoh et al. [18] and by Suzuki and Une [19] for alignment of an x-ray stepper. Uchida et al. explored a moiré interference alignment technique for a proximity lithographic system using a moiré intensity signal produced by cyclic interlaced shift between overlapped gratings with the same period [20]. Similar schemes was also utilized in the ASML TTL and ATHENA alignment sensor for optical projection printing systems, in which only one pair of the 1st or higher symmetric diffraction orders from one grating on a wafer are captured to propagate through another grating on mask to generate the cyclic moiré intensity signal [21–23]. Recently, an interferometric spatial phase imaging method was proposed for precise alignment and position control for zone-platearray lithography or scanning probe lithography by Moon et al. [24–26]. All of these methods tend to take full advantages of high sensitivity of diffractioninduced interferometry. However, the intensity based or heterodyne interferometric schemes almost suffer from the same challenge of relatively lower robustness due to signal fluctuations or susceptibility caused by wafer-mask gap variation, photoresist layer, and so on. Overall, the interferometric spatial phase imaging scheme that embeds unaligned offset into the spatial phase of interference fringe pattern obtains higher alignment accuracy than other intensity-based schemes and shows better performances in the balancing factors of accuracy, complexity, and robustness than other techniques, whereas the checkerboard grating involved in the process still induces more challenges in structural fabrication and duration as well as higher complexity. For sake of higher robustness than those intensitybased or heterodyne interferometric schemes, and simultaneous taking into account adequate balance between accuracy and complexity, the route of moiré analogous interferometry is proposed and deeply explored in this paper. The versatility of this scheme facilitates not only accurate displacement adjustment but also angle calibration for processes of wafer-mask alignment and focusing and leveling in the proximity lithographic systems. Signal fluctuations or susceptibility can be avoided by reflecting both the displacement and angle variations into phase distribution of a moiré fringe pattern, which combines the advantages of interferometry with intrinsic high accuracy and the convenient fringe pattern processing with the ability of pattern analysis to ensure high robustness. First, detailed analyses are provided with respect to the principle and mechanism of presented moiré interferometric 952
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schemes, in which how the wafer-mask unaligned offset, tilt, or parallelism, and the in-plane twist angle are then directly denoted by the phase distribution of fringe patterns generated by diffractions of superposed gratings as well as reflections from a wafer surface is derived at length. Then three types of composite grating formed by different pairs of diffraction gratings with close periods are designed and fabricated and ultimately employed in the experiments to validate the schemes of moiré interferometry for our mask aligner. Finally, related experimental results during the wafer-mask alignment process, especially the tilt remediation and twist angle adjustment, as well as the involved moiré interferometry and equal-thickness interferometry, are discussed systematically. The mechanism of the moiré interferometry is summarized in Section 2, and schemes involved in the alignment process are introduced in Section 3. In Section 4, related experimental results and corresponding analyses are presented. 2. Fundamental A. m; −m Moiré Interferometry
Multidiffractions usually occur at the surfaces of two superposed gratings to create a series of diffracted waves that overlap together to form certain irregular distribution. The diffracted wave that undergoes the mth diffraction at the first grating and the nth diffraction at the second grating is termed as the m; n order. Here, all symmetrical orders, like the m; −m and −m; m m 1; 2; 3… orders, of two gratings with close periods, are adopted to create a low-frequency distribution in the presented moiré interferometry for the purpose of alignment during lithography process. As shown in Fig. 1, at the incidence of a planar wave, all symmetrically diffracted orders from two gratings G1 and G2 can be selectively collected (through the spatial filter) and projected onto the CCD surface, where the moiré interferometric field is formed and recorded. Taking into account any two symmetrically diffracted waves m; −m and −m; m, the complex amplitude Em;−m and E−m;m at the rear surface of G2 can be expressed as
Fig. 1. Schematic of m; −m moiré interferometry for wafer-mask alignment.
sin θm;−m x ; Am;−m exp i2π λ
(1)
sin θ−m;m E−m;m A−m;m exp i2π x ; λ
(2)
Em;−m
where, Am;−m and A−m;m , θm;−m and θ−m;m denote the amplitude and diffraction angles of two symmetric orders, respectively. For simplicity, the initial phases are neglected, and two symmetric orders are assumed to have the same amplitude under ideal conditions, namely A−m;m Am;−m. According to the diffraction equations of two gratings, the diffraction angle θm;−m of m; −m order can be readily derived, namely sin θm;−m mλf 1 − f 2 , where f 1 1∕P1 , f 2 1∕P2 , and P1 , P2 are the periods of G1 and G2 , respectively (assuming P2 > P1 ). Obviously, closer periods of two gratings lead to a smaller diffraction angle θm;−m and thus more resolvable interference fringes with a bigger period. Therefore, two gratings with close periods are chosen to limit the divergence of all symmetric orders within a small range to ensure that as more high orders as possible can be captured, so that overlap of all symmetrical orders (plus the zero order) gives rise to the ultimate moiré interference field by summation of all symmetric pairs, namely X Em;−m E−m;m E E0;0 m
A0;0 2
X Am;−m cos2πmjf 1 − f 2 jx:
(3)
m
where E is the complex amplitude of all symmetric waves diffracted by G1 and G2 . Apparently, for limited numbers of symmetric orders, series in Eq. (3) converge to a periodic distribution with the spatial frequency of f 1 − f 2, which turns out to be very low when two gratings are chosen to have approximate periods. As a result, spatially highly resolvable fringes with low frequency or a large period are produced and shift cyclically along with the continual lateral shift between two gratings. High sensitivity can be obtained due to the fact that one cycle of a later shift of 1∕f 1 P1 between two gratings would induce one significantly magnified cycle of fringe shift of 1∕f 1 − f 2 [27]. In other words, any lateral offset Δx between G1 and G2 that directly changes the optical path difference (OPD) and thus the phase difference of two symmetric diffraction orders is therefore reflected into a distinct phase shift of fringes in such a way of interferometry, and a similar relationship between lateral offset and the phase shift can be seen from the m; 0 moiré interferometry in the next section. B.
higher symmetric orders to be collected. Considering this, we employed another pair of orders that undergo zero diffraction at either of the superposed gratings and the same order diffraction at the other one, namely the 0; m and m; 0m 1; 2; 3… order pairs. Because all the 0; m and m; 0 order pairs have similar diffraction angles and thus a tiny included angle in between for gratings with close periods, they facilitate a similar interferometric scheme for wafer-mask alignment, which is termed as the m; 0 interferometry, shown in Fig. 2. Similarly, the complex amplitude of 0; m and m; 0 can be derived, and their interference intensity I m is expressed as I m I 1m I 2m p 2π sin θ1m − sin θ2m x ; 2 I 1m I 2m cos λ
(4)
where the initial phase difference is also neglected, and I 1m and I 2m , θ1m , and θ2m are the intensity and diffraction angles of the 0; m and m; 0 order, respectively. As can be seen in Fig. 2, it is obvious that any gap variation or lateral shift between G1 and G2 change the OPD and thus lead to a cyclic phase shift of the interference field (fringes). Considering the effect of gap variation and lateral displacement of certain grating (e.g., G1 ) to the phase shift along with the diffraction equations of two gratings, the intensity I m can be also derived as p I m I 1m I 2m 2 I 1m I 2m cos2πf 1 − f 2 x Δφ; (5) where, f 1 1∕P1 , f 2 1∕P2 and P1 ; P2 are the periods of grating G1 and G2 , and the phase variation Δφ can be written as 1 1∕ cos θ1m ΔG : Δφ 2π mf 1 Δx λ
(6)
Hereinto, Δx and ΔG is the lateral displacement and gap variation between G1 and G2 , respectively.
m; 0 Moiré Interferometry
Although m; 0 and −m; 0 are another series of symmetric diffraction orders, the divergence and included angle in-between are usually too large for
Fig. 2. Schematic of the 0; m and m; 0 moiré interferometry. 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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Apparently, the m; 0 interferometry is able to monitor the gap vibration and lateral shift simultaneously with high accuracy due to the fact that diffractions by two gratings with close periods give rise to much resolvable low-frequency-sensitive moiré fringes in fundamentally a similar way as m; −m moiré interferometry. Practically, either the gap variation or the lateral shift needs to be kept unchanged when the other one is under detection using this m; 0 interferometry. 3. Application Schemes
Usually, alignment also involves adequate adjustments that should be undertaken to remedy any tilt and in-plane twist angle existing between wafer and mask, prior to the elimination of unaligned offset. We discuss how the aforementioned moiré interferometry aids in performing tilt remediation and in-plane twist angle adjustment during the whole process of wafer-mask alignment in this section. A.
Tilt Remediation: Wafer-Mask Leveling
Shown in Fig. 3, the m; 0 moiré interferometry for tilt remediation is realized in a reflective way. At the incidence of a collimated laser beam reflected by the splitter and reflector, the same order B1 and B2 (usually the 1st diffraction) of gratings G1 and G2 with close periods diffract back with approximate angles at the surface of G2, with either B1 or B2 equivalent to the Littrow angle, such that both beams could be collected by a low NA and long work distance lens to generate the interference field to be recorded by a CCD. In order to avoid the effect of lateral shift to phase variation in the 0; m and m; 0 interferometry, both gratings are placed on a mask in order to monitor the gap change between wafer and mask independently. In such a way, any gap changes within a certain range can be directly and solely associated with the OPD change between B1 and B2 as well as the phase shift of ultimate interference field according to Eq. (6). Noticeably, tilt remediation is supposed to be carried out first to guarantee the parallelism between
Fig. 3. Scheme of m; 0 and 0; m moiré interferometry for wafer-mask alignment plus tilt remediation and twist adjustment. 954
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the wafer and mask, prior to further gap adjustment and alignment in our scheme. Since one of the interfering beams (B1 in Fig. 3) is reflected back by the wafer surface after diffraction, any tilts between the wafer and mask plane directly induce beam deflection and change in the phase distribution of the ultimate interference field. As is shown in the schematic in Fig. 4, when tilt of the wafer causes beam B1 to deflect to B01 , the fringe vector F that denotes the spatial frequency and direction of original interference field (fringes) is forced to deflect to F 0 , which denotes the varied phase distribution. For simplicity, the overall tilt can be decomposed into the cross-section component in the ZOX plane, and the longitudinal section component in ZOY plane. As long as the wafer is tilted in the longitudinal section and cross section by certain small angles, δφ and δθ, respectively, the beam B1 reflected from wafer is deflected by 2δφ and 2δθ, accordingly. So according to the geometrics of vectors, shown in Fig. 4, tiltmodulated interference field denoted by the deflected vector F 0 can be readily derived as p I I 1 I 2 2 I 1 I 2 cosF 0 · X φ0 ;
(7)
where 2π tanθ1 2δθ p F λ 1 tan2 θ1 2δθ tan2 2δφ 0
tan 2δφ − sin θ2 ; p 2 1 tan θ1 2δθ tan2 2δφ
(8)
is the wave vector of the interference field to denote spatial frequency and direction of fringe distribution, and X x; y denotes the coordinates in the XOY plane (also the grating surface plane). According to results in Eqs. (7) and (8), tilt between wafer and mask influence the phase distribution of interference field by changing the amplitude and direction of interference wave vector. Specifically, because tilts in both sections are usual tiny, tilt term δθ in the cross section mainly induces a frequency shift, and tilt term δφ in the longitudinal section mainly contributes to fringe deflection, according to Eq. (8).
Fig. 4. Schematic of beam deflection induced by wafer tilt and corresponding change of the phase distribution (fringe vector) of interference field.
within a certain limited range, and the m; 0 moiré interferometry needs to be further employed for fine adjustment. This process is discussed along with the experimental results in Section 4. C.
Fig. 5. Equal-thickness interference caused by tilted wafer with regard to the mask at a small gap.
B.
Equal-Thickness Interference
At the same time, the existence of tilt between wafer and mask also leads to a similar phenomenon of equal thickness interference, caused by waferreflected and back-diffracted orders within a certain range of gap: an alternative for tilt remediation. Shown in Fig. 5, when gratings G1 and G2 are illuminated by a planar wave that is incident at the 1st order Littrow angle of G1, diffractions take place on both sides of gratings. The 1st order that propagates through is reflected back by the wafer surface to overlap with the back-diffracted first order at the surface of either grating. Only when certain tilt exists between wafer and mask to induce certain angle the two orders (B1 and B01 or B2 and B02 in Fig. 6), cyclic constructive and deconstructive interference that occurs at the grating surface can be observed. As a result, any tilt can be monitored in a similar way by the phase distribution of equalthickness fringes: the direction and frequency. According to geometrics in Fig. 5 and interference theory, increased tilt leads to bigger interference angle and denser equal-thickness fringes with higher frequency, and the wave vector of fringes can be used to denote the amount of tilts δθ and δφ in both sections in a similar way as the moiré interferometry discussed in a previous section. However, the equalthickness interference is used in a qualitative way to coarsely adjust the tilt at a small gap, which varies
Fig. 6. Scheme of m; −m moiré interferometry arranged in a reflective way for in-plane twist angle adjustment and subsequent wafer-mask alignment.
Twist Angle Adjustment and Alignment
When the wafer and mask are adjusted to be parallel with each other at an adequate gap for proximity exposure, in-plane twist angle adjustment is the final step to be completed right before alignment. Although the m; 0 interferometry is also applicable for twist angle adjustment, the m; −m moiré interferometry tends to be more advantageous because the interference of symmetric orders is insusceptible to gap fluctuation during the subsequent alignment process to eliminate the unaligned offset. And the m; −m moiré interferometry is realized in a reflective way similar to that of the tilt remediation. The differences between the schemes of twist angle adjustment and tilt remediation lie in the incident angle of illumination and arrangement of gratings. The collimated laser beam is split and reflected to be perpendicularly incident on two superposed composite gratings, as shown in Fig. 6. The symmetric orders that diffract back with small angles are collected by a lens with low NA and long work distance, so as to form the final m; −m moiré interference fringes on CCD plane, usually generated by the orders of 1; −1 and −1; 1 from the gratings with period at magnitude of microns scale. In order to double the effect of the twisted angle to the phase shift of corresponding interference fringes (field), one couple of composite gratings are designed to be composed of four sets of gratings with close periods of P1 and P2 and arranged in an opposite sequence on the wafer and mask. As a result, the twist angle is monitored and adjusted by the mechanism that any amounts of in-plane rotation between two composite gratings would induce reverse deflection to four sets of fringes in a similar way as the tilt remediation scheme. As the fringe frequency remains almost unchanged within a small range of rotation, the in-plane twist angle is then solely associated with the fringe deflection. This easy-toimplement technique can be applicable in a qualitatively way in that it is verified to be able to manually remedy the in-plane twist angle within the scope of 10−4 rad. The fundamental derivation and performance of twist angle adjustment is discussed at length previously [28], which is briefly cited here for good context and a comparison of various moiré interferometric schemes in wafer-mask alignment. According to analyses in Section 1, phase deviation between two corresponding sets of fringes can be used for unaligned offset detection in subsequent wafer-mask alignment after twist angle adjustment. The alignment sensitivity is also doubled by the composite grating due to the fact that any lateral offset induces reverse phase shift as well as doubled phase deviation between two corresponding sets of fringes. Detailed analysis of the moiré effect and 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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Fig. 7. Composite grating with left and right part arranged as (a) G1 and (b) G2 shown in Fig. 3.
related mechanism of the interferometric alignment based on superposed gratings is described in previous study [27], related results of which are also briefly cited here for integrity of context and comparison in discussion in Section 4. 4. Results and Discussion
To confirm the validity of moiré interferometry and its application in alignment process of our proximity lithographic system, an alignment system was built, and related experiments were performed according to schemes in Section 2. A 633 nm laser beam, an 8× lens with long work distance of 110 mm and a WAT902H CCD with pixel width of 8.3 μm are used for schemes in our experimental system. For tilt remediation in wafer-mask leveling, gratings with close periods of P1 1 μm and P2 1.1 μm were fabricated by means of x-ray lithography. Furthermore, in order to double the effects of tilts δθ and δφ in both sections to frequency shift and deflection of interference fringes, a composite grating that is formed by four sets of gratings with close periods, P1 and P2 , in a similar way as the ones for twist angle adjustment is adopted, as shown in Fig. 7. In such a way, two sets of interference fringes occur at the surface of G2, with the upper set of
fringes generated by back diffraction from the upper-right grating (with period P2 ) and the waferreflected diffraction from the upper-left grating (with period P1 ), also see Fig. 3, and the bottom set of fringes generated by diffraction from the bottomright grating (with period P1 ) and the bottom-left grating (with the period P2 ) in an opposite sequence as the upper one. Results of several states of tilt remediation are shown in Figs. 8 and 9. The patterns are split into two parts, with the left part induced by equal-thickness interference and the right part caused by moiré interference that occurs at the surface of G2. When tilts exist in both sections, the equal-thickness fringes distribute along an arbitrary direction, and two split sets of fringes on the right part become reversely deflected with different frequencies, as shown in Fig. 8(a). When tilt in the longitudinal section is almost eliminated to leave only the cross section component, the equal thickness fringes become horizontally distributed, and the other two sets of fringes in the right part extend longitudinally along the same direction and only differ in frequencies, as shown in Fig. 8(b). Similarly, when tilt only exists in longitudinal section, the equalthickness fringes then are then vertically distributed and the other two sets of fringes tend to be reversely deflected with almost the same frequency, as shown in Fig. 8(c). When tilts in both sections are ideally remedied, the equal-thickness fringes disappear (with infinite period) and the other two sets of fringes become in absolute agreement with each other, as shown in Fig. 9(b). Hereinto only the orders of (1, 0) and (0, 1) are diffracted and collected to participate the moiré interferometry in our scheme. Figure 9(a) shows result of the (0, 0) order background with no interference when the two diffraction orders are filtered. According to Eqs. (7) and (8), the wave vector of upper and bottom fringes in the right part can be derived as F 0up
2π tanθ1 2δθ p λ 1 tan2 θ1 2δθ tan2 2δφ tan 2δφ − sin θ2 ; p ; (9) 1 tan2 θ1 2δθ tan2 2δφ
Fig. 8. Results of fringe distribution of moiré interference and equal-thickness interference that correspond to tilts existing in (a) both sections, (b) cross section, (c) longitudinal section, respectively. 956
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Fig. 9. Results recorded (a) without, and (b) with participation of the (1, 0) and (0, 1) diffraction orders.
F 0bottom
2π tanθ2 2δθ ; sin θ1 − p λ 1 tan2 θ2 2δθ tan2 2δφ tan 2δφ (10) − p : 1 tan2 θ2 2δθ tan2 2δφ
Apparently, shown in Eqs. (9) and (10), tilts in both sections δθ and δφ) lead to opposite frequency variations and deflections between the upper and bottom part of fringes. The frequency and angle deviation Δf , Δθ can be readily derived as Δf
2δθ · cos θ1 cos θ2 ; λ
cos θ1 tan 2δφ sin θ1 − sin θ2 cos θ2 tan 2δφ : a tan sin θ1 − sin θ2
(11)
Δθ ≈ a tan
(12)
As a result, the amount and direction of tilts in two sections can be coarsely indicated by the equal-thickness fringes in a qualitative way and then quantitatively remedied by the other two sets of fringes with variable frequencies and deflection as well as doubled sensitivity by utilization of the composite gratings. For in-plane twist angle adjustment and further alignment, two composite gratings on both wafer
and mask, arranged in opposite sequence in Fig. 6, are also similar as the one for tilt remediation. Three pairs of gratings with close periods of P1 4 μm, P2 4.4 μm; P1 6 μm, P2 8 μm; and P1 8 μm, P2 10 μm are adopted to form the composite grating, respectively. Other than the 1; −1 moiré interferometry, experiments using the (1, 0) moiré interferometry are also performed for both the in-plane twist angle adjustment and alignment. In either case, fringes become cyclically blurred and clear due to the Talbot effect induced by gap variation between two composite gratings, and clearly resolvable fringes can only be observed at a series of gaps that equal to the Talbot distance and integer times of Talbot distance, see results of gratings with periods of P1 4 μm, P2 4.4 μm, as shown in Fig. 10. Therefore, fringe patterns recorded at gaps of integer times of Talbot distance are used to adjust the inplane twist angle and unaligned offset. Figure 11 show results of the 1; −1 interferometry of gratings with periods of P1 6 μm, P2 8 μm, where half part of the four-quadrant fringe pattern is intercepted. Results in Fig. 12 show the process of inplane twist angle being gradually remedied by the (1, 0) moiré interferometry using gratings with periods of P1 8 μm and P2 10 μm. These results confirm that tilt remediation could be achieved with preserved angular resolution of better than 10−3 rad and sensitivity in twist angle adjustment is attainable at the level of 10−4 rad even in a manual performance. After twist angle remediation, unaligned offset is denoted and adjusted by the phase difference of two sets of fringes with doubled sensitivity. Figure 13 shows stepwise changed phase differences caused by gradually increased offset in the 1; −1 moiré interferometry of alignment using gratings with periods of P1 8 μm, P2 10 μm, and the step of offset is about one-eighth of the average period of two grating. Thus alignment sensitivity δx is directly associated with and determined by the phase resolution δφ of fringe pattern processing, namely, according to Eq. (3), δx
δφ P1 P2 · : 2π P1 P2
(13)
Fig. 10. Results of the 1; −1 moiré interferometry: (a) the background with 1; −1 and −1; 1 orders filtered. (b) Obscure fringe pattern recorded at an arbitrary gap of non-Talbot distance. (c) Clear one recorded at the gap of Talbot distance. 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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periods of P1 4 μm and P2 4.4 μm is higher than that of all other pairs. 5. Summary
Fig. 11. Results of twist angle adjustment and alignment using gratings with periods of P1 6 μm, P2 8 μm, where (a) certain in-plane twist angle exist, (b) twist angle remedied with certain unaligned offset, and (c) aligned with offset almost eliminated.
For gratings with periods P1 8 μm, P2 10 μm, phase resolution is readily attainable at the level of 10−2, so the alignment sensitivity around 7 nm can be obtained. In addition, it is apparent to notice the period of fringes generated by gratings with periods of P1 6 μm, P2 8 μm is much smaller than that of the other two pairs of gratings. According to Eqs. (3) and (5), periods of fringes generated by gratings with periods of P1 4 μm and P2 4.4 μm, P1 6 μm and P2 8 μm, and P1 8 μm and P2 10 μm can be derived as 44, 24, and 40 μm, respectively, in both the 1; −1 and m; 0 moiré interferometry. Ultimately, for constant phase resolution, gratings with smaller periods that are closer to each other lead to higher alignment sensitivity. Thus alignment sensitivity of gratings with
Schemes of moiré interferometry presented in this paper are employed as the precise metrology for angle and displacement adjustment in alignment of a proximity lithographic system. Basically, the presented m; −m interferometry is performed in an on-axis way that utilizes symmetric orders with approximate angles diffracted from gratings with close periods, while the m; 0 interferometry is performed in a similar but off-axis way. In principle, the lateral offset and angle derivation (tilt and the inplane twist angle) can be directly associated with phase distribution of fringes generated in both cases of interferometry. However, our derivation indicates that the m; 0 moiré interferometry turns out to be more appropriate and efficient for tilt remediation, in which tilts in both the cross and longitudinal section can be qualitatively eliminated first by the equalthickness interference fringes and then precisely remedied according to the deflections and frequencies of the m; 0 interference fringes. Moreover, both schemes are fundamentally applicable for the in-plane twist angle adjustment and alignment after tilt remediation, but the on-axis m; −m moiré interferometry is more robust to gap variation for unaligned offset detection due to the symmetry of optical path of diffraction orders. To confirm the validity of our schemes, three pairs of gratings with close periods are adopted for the purpose of individually composing three types of composite grating, and related experiments are carried out. Results indicate that schemes of moiré interferometry presented in this paper facilitate all offset and angle
Fig. 12. Process of in-plane twist angle remediation by the (0, 1) and (1, 0) interference fringes from (a) certain twist angle to (b) the state of adequately adjusted and (c) ideally adjusted.
Fig. 13. Stepwise increased offset leads to two parts of fringes with varied phase differences of (a) 0, (b) π∕2, (c) π, (d) 3π∕2. 958
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