Kinematic analysis of in situ measurement during chemical mechanical planarization process Hongkai Li, Tongqing Wang, Qian Zhao, Yonggang Meng, and Xinchun Lu
Citation: Review of Scientific Instruments 86, 105118 (2015); doi: 10.1063/1.4934366 View online: http://dx.doi.org/10.1063/1.4934366 View Table of Contents: http://aip.scitation.org/toc/rsi/86/10 Published by the American Institute of Physics
Articles you may be interested in Research on influences of contact force in chemical mechanical polishing (CMP) process AIP Advances 5, 041305 (2014); 10.1063/1.4903700
REVIEW OF SCIENTIFIC INSTRUMENTS 86, 105118 (2015)
Kinematic analysis of in situ measurement during chemical mechanical planarization process Hongkai Li, Tongqing Wang, Qian Zhao, Yonggang Meng, and Xinchun Lua) State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
(Received 4 July 2015; accepted 10 October 2015; published online 27 October 2015) Chemical mechanical planarization (CMP) is the most widely used planarization technique in semiconductor manufacturing presently. With the aid of in situ measurement technology, CMP tools can achieve good performance and stable productivity. However, the in situ measurement has remained unexplored from a kinematic standpoint. The available related resources for the kinematic analysis are very limited due to the complexity and technical secret. In this paper, a comprehensive kinematic analysis of in situ measurement is provided, including the analysis model, the measurement trajectory, and the measurement time of each zone of wafer surface during the practical CMP process. In addition, a lot of numerical calculations are performed to study the influences of main parameters on the measurement trajectory and the measurement velocity variation of the probe during the measurement process. All the efforts are expected to improve the in situ measurement system and promote the advancement in CMP control system. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4934366]
I. INTRODUCTION
Chemical mechanical planarization (CMP) is presently the most widely used planarization technique that can offer excellent both local and global planarity on the wafer surface.1 In the past few years, copper (Cu) has been widely used as metal interconnects, replacing aluminum (Al),2 due to its advantageous characteristics, such as low resistivity.3 Therefore, Cu CMP has been applied in modern integrated circuit (IC) manufacturing.4 During the Cu CMP process,4,5 the Cu removal in the first step normally requires much higher rate, and the remaining flat Cu profile is of primary importance. However, the profile can drift easily due to the CMP process variation.4 To solve this problem, the real-time profile control (RTPC) system has been proposed. The RTPC system is based on the in situ measurement and the multi-zone CMP technique.6,7 As an important part of the RTPC system, in situ measurement can provide the thickness profile of Cu layer in real-time, though it is difficult to perform under the practical condition.8 Without it, the control system cannot compute new multi-zone polishing pressures for achieving the desired thickness profile. Currently, the eddy current method,9,10 which can measure the thickness of metal layer on the wafer surface, has been employed in in situ measurement during the Cu CMP process. Good control effect relies on the accurate feedback. It is necessary to get the actual measurement path under the wafer surface during the CMP process and the measurement time of each zone. However, the in situ measurement has remained unexplored from such a kinematic standpoint. Available resources of the related kinematic analysis are very limited due to the complexity and technical security. In the previous in situ measurement module,11 the hall sensor was used for a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Telephone/fax: + 86 10 6279 7362.
0034-6748/2015/86(10)/105118/9/$30.00
indicating the measurement region, and only when the probe entered and left the measurement region could be known. For more accurate measurement, the control system has to track the measurement path, or position the measurement point (the probe of the eddy current sensor) in real-time. In this paper, a comprehensive kinematic analysis of the in situ measurement has been done, including the measurement trajectory, influences of main parameters on the measurement trajectories, the measurement time of each zone, and the measurement velocity variation during the CMP process. II. MEASUREMENT TRAJECTORY MODEL AND EQUATION A. Trajectory model
The rotary-type CMP tool is the mainstream polisher. It includes a polishing platen to which a pad is attached and a polishing head which holds the wafer and presses it against the pad. The polishing head rotates about its axis and oscillates, and at the same time the polishing platen rotates in the same direction.6,12,13 The probe of the eddy current sensor is embedded in the polishing platen under the pad. The measurement is performed every time the probe passes beneath the wafer. So, three basic motions, which are the rotation of the polishing platen (or probe), the rotation of the polishing head (or wafer), and the oscillation of the polishing head (or wafer), define the relative motion between the wafer and the probe.14 In this paper, the actual measurement process is modeled by simplifying the domain into a two-dimensional area, as shown in Fig. 1. B. Trajectory equation
To describe the in situ measurement trajectory, two coordinate systems are defined, as shown in Fig. 1: a fixed coordinate system denoted as XOY, the origin of which is
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FIG. 2. Measurement range.
x = −e · cos θ 1 + R · cos(θ − θ 1) 1 y1 = e · sin θ 1 + R · sin(θ − θ 1) .
(4)
C. Measurement range
FIG. 1. Schematic of the measurement trajectory model.
located at the platen center, and a rotating coordinate system denoted as X1O1Y1, which is fixed at the center of wafer surface and rotates synchronously with the wafer. In general, the X1-axis makes an angle α with the X-axis, and the angle α is caused by the rotation of the wafer. Assume the probe is located at point P. The coordinate of P in the XOY is (x, y), and its coordinate in the X1O1Y1 is (x 1, y1). The e is the center distance between the platen and the wafer (OO1). Considering the geometric (vector) relationship, it can be concluded that (x 1, y1) and (x, y) have such a relationship as the following equation shows: x = y · sin θ 1 − (e − x) · cos θ 1 1 (1) y1 = y · cos θ 1 + (e − x) · sin θ 1 . In Eq. (1), θ 1 = ωht + θ 10, where ωh is the angular velocity of the polishing head, t is the duration time, and θ 10 is the initial angle between the X1-axis and the X-axis. The moving trajectory of the probe in the XOY can be described as x = R · cos θ (2) y = R · sin θ . In Eq. (2), θ = ω pt + θ 0, where ω p is the angular velocity −−→ of the polishing platen, θ 0 is the initial angle between the OP and the X-axis, and R is the radial distance of the probe to the platen center. Using Eqs. (1) and (2), the trajectory equation of the probe in X1O1Y1 is shown by Eq. (3). And Eq. (3) can be transformed into a simplified equation, as shown by Eq. (4), x = R · sin θ · sin θ 1 − (e − R · cos θ) · cos θ 1 1 y1 = R · sin θ · cos θ 1 + (e − R · cos θ) · sin θ 1 ,
(3)
The area covered by wafer is axisymmetric with respect to the X-axis. During the CMP process, the probe moves in a circle along with the anticlockwise rotation of the polishing platen. In this paper, define that the probe is in the measurement area, only every time the probe passes beneath the wafer surface. And the measurement range is estimated as follows. In Fig. 1, point A is the entry point of the probe, while point B is the exit point. In this section, the measurement range is estimated regardless of the oscillation of the polishing head because the probe moves too fast in practice, compared with the oscillation of the polishing head. Thus, point A is X-axis symmetric with point B. As shown in Fig. 2, assume the angle of ∠O1OB is α. Therefore, ∠AOB = 2α. In ∆BOO1, (OO21 + OB2 − O1B2) 2 × OO1 × OB 2 (e + R2 − R12) = . (5) 2·e·R In Eq. (5), OB = R, O1B = R1, and OO1 = e. In this paper, R is 190 mm and R1 is the radius of the 300 mm wafer, which is 150 mm. During the CMP process, e ranges between 175 mm and 215 mm, due to the oscillation of the polishing head. When e = 175 mm, α = 48.31◦ and ∠AOB = 96.62◦ and when e = 215 mm, α = 42.92◦ and ∠AOB = 85.84◦. Therefore, the actual measurement range is in [85.84◦, 96.62◦]. The CMP control system can use the measurement range as the bounded constraint and can make whether the probe has been in the measurement area possibly, just in case some big exceptional events happen. cos α =
TABLE I. Kinematic parameters. Parameter ωp ωh R e
Value 103 rpm 97 rpm 190 mm 175-215 mm
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FIG. 3. Movement trajectory in X1O1Y1: (a) 0.7 s; (b) 10 s; and (c) 100 s.
FIG. 4. Measurement trajectories under the wafer surface: (a) 10 s and (b) 3 successive trajectories.
FIG. 5. Actual movement trajectory in X1O1Y1: (a) 10 s; (b) 30 s; and (c) 60 s.
III. MEASUREMENT TRAJECTORY CALCULATION
In this paper, all the calculations are for 12-in. (300 mm) wafer and 5-zone polishing head. The main kinematic parameters, which are shown in Table I, are all from the practical process. The trajectory plotting is done using Matlab. First, assume θ 0 = −180◦, θ 10 = 0◦, and e = 175 mm, regardless of the oscillation of the polishing head. Based on the trajectory equation, the movement trajectory of the probe in X1O1Y1 is depicted at the times of 0.7 s, 10 s, and 100 s, as shown in Fig. 3. In Fig. 3, it is obviously observed that movement trajectory gradually covers the available area, and its border is a circle. Using the attained movement trajectory, we can find all the measurement trajectories under the wafer surface, as shown in Fig. 4. In Fig. 4, the measurement trajectories are depicted at the time of 10 s. And 3 successive measurement trajectories are used for explaining how the final distribution of the measurement trajectories forms.
Considering the oscillation of the polishing head, e is a function of time. During the actual CMP process, the oscillation period is 5 s, and the max oscillation distance is 40 mm. In a one-way movement, the average velocity of the polishing head is 16 mm/s, while the linear velocity of the probe is about 2049.4 mm/s (much larger than 16 mm/s). Therefore, the oscillation is generally not taken into consideration. In this paper, e is simplified to a triangle wave, which makes the calculations more accurate and close to the fact. During each cycle, e changes from 175 mm to 215 mm first and then back to 175 mm. With all other parameters unaltered, the actual movement trajectory of the probe in X1O1Y1 is depicted at the times of 10 s, 30 s, and 60 s, as shown in Fig. 5. The corresponding actual measurement trajectories under the wafer surface are shown in Fig. 6. Comparing Fig. 6(a) with Fig. 4(a), it can be concluded that the oscillation of the polishing head influences the trajectory distribution, while each measurement trajectory is still a smooth curve. Because of the oscillation motion, the probe has a chance to pass beneath the wafer center. Based
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FIG. 6. Actual measurement trajectories under the wafer surface: (a) 10 s; (b) 30 s; and (c) 60 s.
FIG. 7. Measurement trajectories with e = 215 mm: (a) 10 s and (b) 3 successive trajectories.
FIG. 8. Measurement trajectories with e = 190 mm: (a) 10 s and (b) 3 successive trajectories.
on the measurement trajectories, we can position the probe during in situ measurement process. IV. INFLUENCES OF MAIN PARAMETERS ON THE MEASUREMENT TRAJECTORIES
In this section, the oscillation of the polishing head is not taken into consideration, just in order to clearly observe the influence of each parameter on the measurement trajectories. A. Study 1: e
Assume e = 215 mm, with other parameters unaltered. The measurement trajectories are depicted at the time of 10 s, as shown in Fig. 7. Comparing Fig. 4 with Fig. 7, it is obviously observed that e determines the minimum distance from the wafer center to the trajectory curve. In Fig. 4, the wafer center is out of each trajectory curve, when e = 175 mm. In Fig. 7, the wafer center is inside each trajectory curve, when e = 215 mm. If e = 190 mm, each trajectory curve can definitely pass through the wafer center, as shown in Fig. 8.
B. Study 2: ωp and ωh
Generally, ω p is not equal to ωh , or ω p is slightly greater than ωh , for good with in wafer uniformity results. If ω p = ωh , the trajectory equation, or Eq. (4), can be transformed into the equation below, as shown by x = −e · cos(ωht + θ 10) + R · cos(θ 0 − θ 10) 1 (6) y1 = e · sin(ωht + θ 10) + R · sin(θ 0 − θ 10) . According to Eq. (6), the movement trajectory in X1O1Y1 is a circle, and angular velocity of the polishing platen only influences the movement speed of the probe. Thus, all measurement trajectories overlap together. Here, assume ω p = ωh = 97 rpm, θ 0 = −180◦, θ 10 = 0◦, and e = 200 mm. The result is shown in Fig. 9. C. Study 3: θ0 and θ10
Based on study 2, keep ω p = ωh = 97 rpm, θ 10 = 0◦, and e = 200 mm unchanged, and, respectively, set θ 0 equal to −90◦, 0◦, and 90◦. The results are shown in Fig. 10.
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FIG. 9. ω p = ω h : (a) movement trajectory and (b) measurement trajectory.
FIG. 10. Measurement trajectory curve with different θ 0: (a) θ 0 = −90◦; (b) θ 0 = 0◦; and (c) θ 0 = 90◦.
FIG. 11. Ideal measurement trajectory: (a) θ 0 = −90◦ and (b) θ 0 = −180◦.
As shown in Fig. 10, θ 0 determines the opening of the measurement trajectory curve, when θ 10 is constant, and vice versa. Generally, it can be concluded that θ 0 − θ 10 is the fundamental factor that impacts the opening of the measurement trajectory curve. V. IDEAL MEASUREMENT TRAJECTORY
The ideal measurement trajectory should be a diameter of the wafer surface. After a lot of calculations and analysis, an ideal measurement trajectory has been attained. When e = R = 190 mm, ω p = 2ωh , θ 0 = −90◦, and θ 10 = 0◦, the trajectory equation can be transformed into the equation below, as shown by x = −190 · cos(ωht) + 190 · cos(ωht − 90◦) 1 y1 = 190 · sin(ωht) + 190 · sin(ωht − 90◦) x 1 = −190 · cos(ωht) + 190 · sin(ωht) ⇒ y1 = 190 · sin(ωht) − 190 · cos(ωht) ⇒ { y1 = x 1.
In Eq. (7), x 21 + y12 ≤ 1502. The measurement trajectory is shown in Fig. 11(a). If θ 0 = −180◦, with other parameters unaltered, the trajectory equation is transformed into the equation, y1 = 0, when x 1 ∈ [−150, 150] mm, as shown in Fig. 11(b). Considering the oscillation of the polishing head, it can be concluded that all the ideal measurement trajectories cover a band area of the wafer surface, and each trajectory curve is similar to a diameter, as shown in Fig. 12. Therefore, the measurement trajectory is a diameter, when e = R and ω p = 2ωh . Under such conditions, each measurement trajectory curve overlaps the previous one. The ideal trajectory equation can be transformed into the equation as shown, ω pt + θ 0 θ 0 − 2 · θ 10 · sin x 1 = −2R sin 2 2 . ω t + θ θ − 2 · θ 10 p 0 0 y1 = 2R sin · cos 2 2
(7)
When
θ 0−2·θ 10 2
, kπ (k ∈ N), y1 = − cot
θ 0−2·θ 10 2
(8)
· x.
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Width interval (mm)
FIG. 12. Ideal measurement trajectories under the condition of oscillation motion.
When
θ 0−2·θ 10 2
= kπ (k ∈ N), x1 = 0 ω t + θ0 . y1 = 2R sin p 2
(9)
VI. ANALYSIS OF THE MEASUREMENT TIME AND THE MEASUREMENT VELOCITY A. Study 1: Measurement time
The wafer surface is divided into 5 zones, corresponding to 5 zones of the polishing head. The radial width interval of each zone is listed in Table II. During the practical CMP process, the wafer center oscillates from 175 mm to 215 mm periodically. When the wafer center is at 175 mm, the range of zone 1 is [139, 211] mm. When the wafer center is at 215 mm, the range of zone 1 is [179, 251] mm. Therefore, the probe can always pass through zone 1 and all the zones of the wafer surface can be measured in situ. Using the measurement trajectories as shown in Fig. 6, randomly select 3 measurement trajectories, respectively, in [0, 10] s, [10, 30] s, and [30, 60] s. Totally get 9 measurement trajectories, as shown in Fig. 13. According to the calculations, it shows that the measurement time of each zone is not constant, and its fluctuation is small. The average measurement time of each zone is shown
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
0-36
36-93
93-133
133-146
146-150
in Table III. And the measurement time ratio of zones 1-5 is 1.0:1.69:1.23:0.40:0.126, while the width ratio of zones 1-5 is 1.0:1.58:1.11:0.36:0.11. More generally, we calculated the measurement time of each zone within 60 s (103 times measurements). The calculation results and related statistics are shown in Fig. 14 and Table IV. In Fig. 14, each measurement time curve is symmetric with respect to N = 52. Here, N means n-th measurement. Furthermore, the measurement time fluctuation of zone 1 is the biggest, which can reach to 9.85%, while the measurement time fluctuation of zone 2 (with the biggest width) is the smallest (2.45%), as shown in Table IV. The measurement time fluctuations of other zones are less than 3.6%. Therefore, it is concluded that the measurement time of zone 1 is most sensitive to the oscillation of the polishing head. The measurement time ratio of zones 1-5 is 1.0:1.76:1.25:0.415:0.129. On average, the measurement time of each zone has a certain linear relationship with its radial width, because the oscillation of the polishing head is slow and small. However, the measurement time of each zone is quite small during the practical CMP process (the maximum is less than 0.061 s). If we simply use the width ratio of zones 1-5 to divide the thickness profile (signal) into different zones, the result is less accurate. Based on the position of the probe, the control system can decide when to read the signal data and to which zone the measurement data belong. After subsequent data processing, the thickness of each zone and the difference value between adjacent zones can be obtained. B. Study 2: Measurement velocity
To further study the measurement time fluctuation of each zone, we calculated the relative velocity variation of the probe. In Fig. 15, (a) shows the relative velocity variation in the X1O1Y1 and (b) shows the relative velocity variation under the wafer surface (defined as the measurement velocity) in 60 s. In the macroscopic view, it shows that the relative velocity of the probe varies periodically, which is similar to the triangle wave, and the period is 5 s, which just equals to the oscillation period of the polishing head. However, the results show that
FIG. 13. Measurement trajectories in (a) [0, 10] s; (b) [10, 30] s; and (c) [30, 60] s.
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the measurement velocity variation during each measurement is not monotonic. As shown in Fig. 16, the measurement velocity always increases first and then decreases during each measurement. And the phenomenon exists during the whole in situ measurement process (60 s), even when the variation happens at crest or trough of Fig. 15(b). It is worth noting that the measurement velocity increases more at the rising stage, while it decreases more at the falling stage.
VII. EXPERIMENT AND RESULTS
The CMP tool is shown in Fig. 17. In this paper, several experiments were done to test the calculations above. During the experiment, deionized water (DIW) was used instead of slurry. Therefore, no copper was almost removed. In Fig. 18,
(a) shows the change in distance between the sensor probe and the platen center during the CMP process and (b) shows the original measurement signal synchronously. Based on the trajectory equation, the distance was calculated with the actual rotation angle of the polishing head, the actual oscillation distance of the polishing head, and the actual rotation angle of the polishing platen, which were all read in real time. Generally, the variation of environmental parameters could result in the small drift of measurement signal during the in situ measurement process. Thus, the control system used difference value between the measurement signal and its reference value (when the probe leaves the measurement area) for calculating the thickness of the copper layer on the wafer
TABLE IV. Statistical results of the measurement time. Zone 1 Zone 2 Zone 3 Zone 4
TABLE III. The average measurement time of each zone.
Time (s)
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
0.0338
0.0572
0.0417
0.0137
0.004 27
Average (s) Standard deviation (s) Maximum (s) Minimum (s) Standard deviation/average (%)
0.0325 0.0032 0.0354 0.0242 9.85
0.0572 0.0014 0.0608 0.0558 2.45
FIG. 14. Measurement time of each zone: (a) zone 1; (b) zone 2; (c) zone 3; (d) zone 4; and (e) zone 5.
FIG. 15. Relative velocity variation: (a) in X1O1Y1 and (b) under the wafer surface.
0.0406 0.0012 0.0429 0.0392 2.96
0.013 5 0.000 43 0.014 4 0.012 9 3.19
Zone 5 0.004 2 0.000 15 0.004 5 0.004 3.57
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FIG. 16. Measurement velocity variation: (a) during each measurement and (b) at crest.
FIG. 17. CMP tool.
FIG. 19. Distribution of 3481 measurement points.
FIG. 18. In situ measurement process: (a) distance between the probe and the platen and (b) original measurement signal.
FIG. 20. The in situ measurement trajectory.
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FIG. 21. Measurement result of a Cu profile: (a) measurement signal and (b) actual thickness profile.
surface, and there existed a positive linear relationship between the signal amplitude and the thickness in a certain range. As shown in Fig. 18, the Cu profile was measured, only when the distance between the probe and the platen center was less than 150 mm. When the distance was more than 150 mm, the measurement ended and the amplitude of the original measurement signal kept its reference value (1 V). It was also noted that in situ conditioning could interfere with the measurement signal during the CMP process, which could cause the erroneous judgement on Cu thickness. However, the control system could reject this part of the measurement signal with the aid of the real-time measurement point tracking. After the experiment, a four-point probe meter (Four Dimensions, Inc., US) was used to measure the thickness of the Cu layer on the wafer surface. In this paper, the thickness values of 3481 points distributed evenly on the whole surface were obtained, and the distribution of the measurement points was shown in Fig. 19. In Fig. 19, the x-direction diameter was vertical to the notch, while the x-direction (X1) was parallel to the notch during actual in situ measurement process. Based on the distribution of the measurement points and the actual in situ measurement trajectory, we compared the in situ measurement signal with the actual thickness values of its corresponding (or nearest) points. Here, we took 59 measurement points in each profile, because there were 30 circles in the distribution of 3841 measurement points (the wafer center was the first circle). Take a Cu profile during the CMP process, for example, and its in situ measurement trajectory is shown in Fig. 20. In Fig. 21, the 30th sampling point is the wafer center. The original measurement signal is basically consistent with the thickness profile. Therefore, it was concluded that the trajectory model and equation could properly describe the in situ measurement trajectory during the actual CMP process. VIII. CONCLUSION
In this paper, we modeled the in situ measurement process and established the actual measurement trajectory equation. Based on the practical CMP parameters, we calculated the measurement trajectory and the measurement time of each zone of the wafer surface during the CMP process. According to the calculations, the kinematic parameters had a significant influence on the measurement trajectory, and each parameter played a distinct role. In addition, the measurement time in each zone was not constant, when the polishing head oscillated. And the measurement velocity of the probe varied
periodically, and it always first increased and then decreased during each measurement. During the experiments, DIW was used instead of slurry. According to the experiment results, the trajectory model and equation could properly describe the in situ measurement trajectory during the actual CMP process. ACKNOWLEDGMENTS
The authors greatly appreciate the financial support of the Science Fund for Creative Research Groups (No. 51321092), National Natural Science Foundation of China (Nos. 51205226 and 91323302), and National Basic Research Program of China (No. 2015CB057203). 1P. B. Zantye, “Process reliability and integration issues in chemical mechan-
ical planarization,” Department of Mechanical Engineering (University of South Florida, 2005). 2S. P. Murarka, I. V. Verner, and R. J. Gutman, Copper-Fundamental Mechanisms for Microelectronic Applications (John Wiley & Sons, Inc.„ NY, 2000), p. 337. 3Y. Ein-Eli and D. Starosvetsky, “Review on copper chemical-mechanical polishing (CMP) and post-CMP cleaning in ultra large system integrated (ULSI)—An electrochemical perspective,” Electrochim. Acta 52, 1825–1838 (2007). 4C. X. Tan et al., “Application of real-time Cu thickness profile control in Cu CMP,” ECS Trans. 44, 553–557 (2012). 5M. Krishnan and J. W. Nalaskowski, “Chemical mechanical planarization: Slurry chemistry, materials, and mechanisms,” Chem. Rev. 110, 178–204 (2010). 6T. Wang and X. Lu, “Numerical and experimental investigation on multi-zone chemical mechanical planarization,” Microelectron. Eng. 88, 3327–3332 (2011). 7S. J. Shiu, C. C. Yu, and S. H. Shen, J. Vac. Sci. Technol., B 22(4), 1679–1687 (2004). 8H. Hocheng and Y. L. Huang, “A comprehensive review of endpoint detection in chemical mechanical planarization for deep-submicron integrated circuits manufacturing,” Int. J. Mater. Prod. Technol. 18(4-6), 469–486 (2003). 9Y. Wuliang and A. J. Peyton, “Thickness measurement of metallic plates with an electromagnetic sensor using phase signature analysis,” IEEE Trans. Instrum. Meas. 57(8), 1803–1807 (2008). 10Y. Wuliang, A. J. Peyton, and S. J. Dickinson, “Simultaneous measurement of distance and thickness of a thin metal plate with an electromagnetic sensor using a simplified model,” IEEE Trans. Instrum. Meas. 53(4), 1335–1338 (2004). 11L. Hongkai et al., “A reliable control system for measurement on film thickness in copper chemical mechanical planarization system,” Rev. Sci. Instrum. 84(12), 125101 (2013). 12Y. Moon, “Mechanical aspects of the material removal mechanism in chemical mechanical polishing (CMP),” Department of Mechanical Engineering (University of California, Berkeley, 1999). 13M. R. Oliver, Chemical Mechanical Planarization of Semiconductor Materials (Springer, 2004). 14D. W. Zhao et al., “Kinematic optimization for chemical mechanical polishing based on statistical analysis of particle trajectories,” IEEE Trans. Semicond. Manuf. 26(4), 556–563 (2013).
Citation: Review of Scientific Instruments 86, 105118 (2015); doi: 10.1063/1.4934366 View online: http://dx.doi.org/10.1063/1.4934366 View Table of Contents: http://aip.scitation.org/toc/rsi/86/10 Published by the American Institute of Physics
Articles you may be interested in Research on influences of contact force in chemical mechanical polishing (CMP) process AIP Advances 5, 041305 (2014); 10.1063/1.4903700
REVIEW OF SCIENTIFIC INSTRUMENTS 86, 105118 (2015)
Kinematic analysis of in situ measurement during chemical mechanical planarization process Hongkai Li, Tongqing Wang, Qian Zhao, Yonggang Meng, and Xinchun Lua) State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
(Received 4 July 2015; accepted 10 October 2015; published online 27 October 2015) Chemical mechanical planarization (CMP) is the most widely used planarization technique in semiconductor manufacturing presently. With the aid of in situ measurement technology, CMP tools can achieve good performance and stable productivity. However, the in situ measurement has remained unexplored from a kinematic standpoint. The available related resources for the kinematic analysis are very limited due to the complexity and technical secret. In this paper, a comprehensive kinematic analysis of in situ measurement is provided, including the analysis model, the measurement trajectory, and the measurement time of each zone of wafer surface during the practical CMP process. In addition, a lot of numerical calculations are performed to study the influences of main parameters on the measurement trajectory and the measurement velocity variation of the probe during the measurement process. All the efforts are expected to improve the in situ measurement system and promote the advancement in CMP control system. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4934366]
I. INTRODUCTION
Chemical mechanical planarization (CMP) is presently the most widely used planarization technique that can offer excellent both local and global planarity on the wafer surface.1 In the past few years, copper (Cu) has been widely used as metal interconnects, replacing aluminum (Al),2 due to its advantageous characteristics, such as low resistivity.3 Therefore, Cu CMP has been applied in modern integrated circuit (IC) manufacturing.4 During the Cu CMP process,4,5 the Cu removal in the first step normally requires much higher rate, and the remaining flat Cu profile is of primary importance. However, the profile can drift easily due to the CMP process variation.4 To solve this problem, the real-time profile control (RTPC) system has been proposed. The RTPC system is based on the in situ measurement and the multi-zone CMP technique.6,7 As an important part of the RTPC system, in situ measurement can provide the thickness profile of Cu layer in real-time, though it is difficult to perform under the practical condition.8 Without it, the control system cannot compute new multi-zone polishing pressures for achieving the desired thickness profile. Currently, the eddy current method,9,10 which can measure the thickness of metal layer on the wafer surface, has been employed in in situ measurement during the Cu CMP process. Good control effect relies on the accurate feedback. It is necessary to get the actual measurement path under the wafer surface during the CMP process and the measurement time of each zone. However, the in situ measurement has remained unexplored from such a kinematic standpoint. Available resources of the related kinematic analysis are very limited due to the complexity and technical security. In the previous in situ measurement module,11 the hall sensor was used for a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Telephone/fax: + 86 10 6279 7362.
0034-6748/2015/86(10)/105118/9/$30.00
indicating the measurement region, and only when the probe entered and left the measurement region could be known. For more accurate measurement, the control system has to track the measurement path, or position the measurement point (the probe of the eddy current sensor) in real-time. In this paper, a comprehensive kinematic analysis of the in situ measurement has been done, including the measurement trajectory, influences of main parameters on the measurement trajectories, the measurement time of each zone, and the measurement velocity variation during the CMP process. II. MEASUREMENT TRAJECTORY MODEL AND EQUATION A. Trajectory model
The rotary-type CMP tool is the mainstream polisher. It includes a polishing platen to which a pad is attached and a polishing head which holds the wafer and presses it against the pad. The polishing head rotates about its axis and oscillates, and at the same time the polishing platen rotates in the same direction.6,12,13 The probe of the eddy current sensor is embedded in the polishing platen under the pad. The measurement is performed every time the probe passes beneath the wafer. So, three basic motions, which are the rotation of the polishing platen (or probe), the rotation of the polishing head (or wafer), and the oscillation of the polishing head (or wafer), define the relative motion between the wafer and the probe.14 In this paper, the actual measurement process is modeled by simplifying the domain into a two-dimensional area, as shown in Fig. 1. B. Trajectory equation
To describe the in situ measurement trajectory, two coordinate systems are defined, as shown in Fig. 1: a fixed coordinate system denoted as XOY, the origin of which is
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FIG. 2. Measurement range.
x = −e · cos θ 1 + R · cos(θ − θ 1) 1 y1 = e · sin θ 1 + R · sin(θ − θ 1) .
(4)
C. Measurement range
FIG. 1. Schematic of the measurement trajectory model.
located at the platen center, and a rotating coordinate system denoted as X1O1Y1, which is fixed at the center of wafer surface and rotates synchronously with the wafer. In general, the X1-axis makes an angle α with the X-axis, and the angle α is caused by the rotation of the wafer. Assume the probe is located at point P. The coordinate of P in the XOY is (x, y), and its coordinate in the X1O1Y1 is (x 1, y1). The e is the center distance between the platen and the wafer (OO1). Considering the geometric (vector) relationship, it can be concluded that (x 1, y1) and (x, y) have such a relationship as the following equation shows: x = y · sin θ 1 − (e − x) · cos θ 1 1 (1) y1 = y · cos θ 1 + (e − x) · sin θ 1 . In Eq. (1), θ 1 = ωht + θ 10, where ωh is the angular velocity of the polishing head, t is the duration time, and θ 10 is the initial angle between the X1-axis and the X-axis. The moving trajectory of the probe in the XOY can be described as x = R · cos θ (2) y = R · sin θ . In Eq. (2), θ = ω pt + θ 0, where ω p is the angular velocity −−→ of the polishing platen, θ 0 is the initial angle between the OP and the X-axis, and R is the radial distance of the probe to the platen center. Using Eqs. (1) and (2), the trajectory equation of the probe in X1O1Y1 is shown by Eq. (3). And Eq. (3) can be transformed into a simplified equation, as shown by Eq. (4), x = R · sin θ · sin θ 1 − (e − R · cos θ) · cos θ 1 1 y1 = R · sin θ · cos θ 1 + (e − R · cos θ) · sin θ 1 ,
(3)
The area covered by wafer is axisymmetric with respect to the X-axis. During the CMP process, the probe moves in a circle along with the anticlockwise rotation of the polishing platen. In this paper, define that the probe is in the measurement area, only every time the probe passes beneath the wafer surface. And the measurement range is estimated as follows. In Fig. 1, point A is the entry point of the probe, while point B is the exit point. In this section, the measurement range is estimated regardless of the oscillation of the polishing head because the probe moves too fast in practice, compared with the oscillation of the polishing head. Thus, point A is X-axis symmetric with point B. As shown in Fig. 2, assume the angle of ∠O1OB is α. Therefore, ∠AOB = 2α. In ∆BOO1, (OO21 + OB2 − O1B2) 2 × OO1 × OB 2 (e + R2 − R12) = . (5) 2·e·R In Eq. (5), OB = R, O1B = R1, and OO1 = e. In this paper, R is 190 mm and R1 is the radius of the 300 mm wafer, which is 150 mm. During the CMP process, e ranges between 175 mm and 215 mm, due to the oscillation of the polishing head. When e = 175 mm, α = 48.31◦ and ∠AOB = 96.62◦ and when e = 215 mm, α = 42.92◦ and ∠AOB = 85.84◦. Therefore, the actual measurement range is in [85.84◦, 96.62◦]. The CMP control system can use the measurement range as the bounded constraint and can make whether the probe has been in the measurement area possibly, just in case some big exceptional events happen. cos α =
TABLE I. Kinematic parameters. Parameter ωp ωh R e
Value 103 rpm 97 rpm 190 mm 175-215 mm
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FIG. 3. Movement trajectory in X1O1Y1: (a) 0.7 s; (b) 10 s; and (c) 100 s.
FIG. 4. Measurement trajectories under the wafer surface: (a) 10 s and (b) 3 successive trajectories.
FIG. 5. Actual movement trajectory in X1O1Y1: (a) 10 s; (b) 30 s; and (c) 60 s.
III. MEASUREMENT TRAJECTORY CALCULATION
In this paper, all the calculations are for 12-in. (300 mm) wafer and 5-zone polishing head. The main kinematic parameters, which are shown in Table I, are all from the practical process. The trajectory plotting is done using Matlab. First, assume θ 0 = −180◦, θ 10 = 0◦, and e = 175 mm, regardless of the oscillation of the polishing head. Based on the trajectory equation, the movement trajectory of the probe in X1O1Y1 is depicted at the times of 0.7 s, 10 s, and 100 s, as shown in Fig. 3. In Fig. 3, it is obviously observed that movement trajectory gradually covers the available area, and its border is a circle. Using the attained movement trajectory, we can find all the measurement trajectories under the wafer surface, as shown in Fig. 4. In Fig. 4, the measurement trajectories are depicted at the time of 10 s. And 3 successive measurement trajectories are used for explaining how the final distribution of the measurement trajectories forms.
Considering the oscillation of the polishing head, e is a function of time. During the actual CMP process, the oscillation period is 5 s, and the max oscillation distance is 40 mm. In a one-way movement, the average velocity of the polishing head is 16 mm/s, while the linear velocity of the probe is about 2049.4 mm/s (much larger than 16 mm/s). Therefore, the oscillation is generally not taken into consideration. In this paper, e is simplified to a triangle wave, which makes the calculations more accurate and close to the fact. During each cycle, e changes from 175 mm to 215 mm first and then back to 175 mm. With all other parameters unaltered, the actual movement trajectory of the probe in X1O1Y1 is depicted at the times of 10 s, 30 s, and 60 s, as shown in Fig. 5. The corresponding actual measurement trajectories under the wafer surface are shown in Fig. 6. Comparing Fig. 6(a) with Fig. 4(a), it can be concluded that the oscillation of the polishing head influences the trajectory distribution, while each measurement trajectory is still a smooth curve. Because of the oscillation motion, the probe has a chance to pass beneath the wafer center. Based
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FIG. 6. Actual measurement trajectories under the wafer surface: (a) 10 s; (b) 30 s; and (c) 60 s.
FIG. 7. Measurement trajectories with e = 215 mm: (a) 10 s and (b) 3 successive trajectories.
FIG. 8. Measurement trajectories with e = 190 mm: (a) 10 s and (b) 3 successive trajectories.
on the measurement trajectories, we can position the probe during in situ measurement process. IV. INFLUENCES OF MAIN PARAMETERS ON THE MEASUREMENT TRAJECTORIES
In this section, the oscillation of the polishing head is not taken into consideration, just in order to clearly observe the influence of each parameter on the measurement trajectories. A. Study 1: e
Assume e = 215 mm, with other parameters unaltered. The measurement trajectories are depicted at the time of 10 s, as shown in Fig. 7. Comparing Fig. 4 with Fig. 7, it is obviously observed that e determines the minimum distance from the wafer center to the trajectory curve. In Fig. 4, the wafer center is out of each trajectory curve, when e = 175 mm. In Fig. 7, the wafer center is inside each trajectory curve, when e = 215 mm. If e = 190 mm, each trajectory curve can definitely pass through the wafer center, as shown in Fig. 8.
B. Study 2: ωp and ωh
Generally, ω p is not equal to ωh , or ω p is slightly greater than ωh , for good with in wafer uniformity results. If ω p = ωh , the trajectory equation, or Eq. (4), can be transformed into the equation below, as shown by x = −e · cos(ωht + θ 10) + R · cos(θ 0 − θ 10) 1 (6) y1 = e · sin(ωht + θ 10) + R · sin(θ 0 − θ 10) . According to Eq. (6), the movement trajectory in X1O1Y1 is a circle, and angular velocity of the polishing platen only influences the movement speed of the probe. Thus, all measurement trajectories overlap together. Here, assume ω p = ωh = 97 rpm, θ 0 = −180◦, θ 10 = 0◦, and e = 200 mm. The result is shown in Fig. 9. C. Study 3: θ0 and θ10
Based on study 2, keep ω p = ωh = 97 rpm, θ 10 = 0◦, and e = 200 mm unchanged, and, respectively, set θ 0 equal to −90◦, 0◦, and 90◦. The results are shown in Fig. 10.
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FIG. 9. ω p = ω h : (a) movement trajectory and (b) measurement trajectory.
FIG. 10. Measurement trajectory curve with different θ 0: (a) θ 0 = −90◦; (b) θ 0 = 0◦; and (c) θ 0 = 90◦.
FIG. 11. Ideal measurement trajectory: (a) θ 0 = −90◦ and (b) θ 0 = −180◦.
As shown in Fig. 10, θ 0 determines the opening of the measurement trajectory curve, when θ 10 is constant, and vice versa. Generally, it can be concluded that θ 0 − θ 10 is the fundamental factor that impacts the opening of the measurement trajectory curve. V. IDEAL MEASUREMENT TRAJECTORY
The ideal measurement trajectory should be a diameter of the wafer surface. After a lot of calculations and analysis, an ideal measurement trajectory has been attained. When e = R = 190 mm, ω p = 2ωh , θ 0 = −90◦, and θ 10 = 0◦, the trajectory equation can be transformed into the equation below, as shown by x = −190 · cos(ωht) + 190 · cos(ωht − 90◦) 1 y1 = 190 · sin(ωht) + 190 · sin(ωht − 90◦) x 1 = −190 · cos(ωht) + 190 · sin(ωht) ⇒ y1 = 190 · sin(ωht) − 190 · cos(ωht) ⇒ { y1 = x 1.
In Eq. (7), x 21 + y12 ≤ 1502. The measurement trajectory is shown in Fig. 11(a). If θ 0 = −180◦, with other parameters unaltered, the trajectory equation is transformed into the equation, y1 = 0, when x 1 ∈ [−150, 150] mm, as shown in Fig. 11(b). Considering the oscillation of the polishing head, it can be concluded that all the ideal measurement trajectories cover a band area of the wafer surface, and each trajectory curve is similar to a diameter, as shown in Fig. 12. Therefore, the measurement trajectory is a diameter, when e = R and ω p = 2ωh . Under such conditions, each measurement trajectory curve overlaps the previous one. The ideal trajectory equation can be transformed into the equation as shown, ω pt + θ 0 θ 0 − 2 · θ 10 · sin x 1 = −2R sin 2 2 . ω t + θ θ − 2 · θ 10 p 0 0 y1 = 2R sin · cos 2 2
(7)
When
θ 0−2·θ 10 2
, kπ (k ∈ N), y1 = − cot
θ 0−2·θ 10 2
(8)
· x.
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Width interval (mm)
FIG. 12. Ideal measurement trajectories under the condition of oscillation motion.
When
θ 0−2·θ 10 2
= kπ (k ∈ N), x1 = 0 ω t + θ0 . y1 = 2R sin p 2
(9)
VI. ANALYSIS OF THE MEASUREMENT TIME AND THE MEASUREMENT VELOCITY A. Study 1: Measurement time
The wafer surface is divided into 5 zones, corresponding to 5 zones of the polishing head. The radial width interval of each zone is listed in Table II. During the practical CMP process, the wafer center oscillates from 175 mm to 215 mm periodically. When the wafer center is at 175 mm, the range of zone 1 is [139, 211] mm. When the wafer center is at 215 mm, the range of zone 1 is [179, 251] mm. Therefore, the probe can always pass through zone 1 and all the zones of the wafer surface can be measured in situ. Using the measurement trajectories as shown in Fig. 6, randomly select 3 measurement trajectories, respectively, in [0, 10] s, [10, 30] s, and [30, 60] s. Totally get 9 measurement trajectories, as shown in Fig. 13. According to the calculations, it shows that the measurement time of each zone is not constant, and its fluctuation is small. The average measurement time of each zone is shown
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
0-36
36-93
93-133
133-146
146-150
in Table III. And the measurement time ratio of zones 1-5 is 1.0:1.69:1.23:0.40:0.126, while the width ratio of zones 1-5 is 1.0:1.58:1.11:0.36:0.11. More generally, we calculated the measurement time of each zone within 60 s (103 times measurements). The calculation results and related statistics are shown in Fig. 14 and Table IV. In Fig. 14, each measurement time curve is symmetric with respect to N = 52. Here, N means n-th measurement. Furthermore, the measurement time fluctuation of zone 1 is the biggest, which can reach to 9.85%, while the measurement time fluctuation of zone 2 (with the biggest width) is the smallest (2.45%), as shown in Table IV. The measurement time fluctuations of other zones are less than 3.6%. Therefore, it is concluded that the measurement time of zone 1 is most sensitive to the oscillation of the polishing head. The measurement time ratio of zones 1-5 is 1.0:1.76:1.25:0.415:0.129. On average, the measurement time of each zone has a certain linear relationship with its radial width, because the oscillation of the polishing head is slow and small. However, the measurement time of each zone is quite small during the practical CMP process (the maximum is less than 0.061 s). If we simply use the width ratio of zones 1-5 to divide the thickness profile (signal) into different zones, the result is less accurate. Based on the position of the probe, the control system can decide when to read the signal data and to which zone the measurement data belong. After subsequent data processing, the thickness of each zone and the difference value between adjacent zones can be obtained. B. Study 2: Measurement velocity
To further study the measurement time fluctuation of each zone, we calculated the relative velocity variation of the probe. In Fig. 15, (a) shows the relative velocity variation in the X1O1Y1 and (b) shows the relative velocity variation under the wafer surface (defined as the measurement velocity) in 60 s. In the macroscopic view, it shows that the relative velocity of the probe varies periodically, which is similar to the triangle wave, and the period is 5 s, which just equals to the oscillation period of the polishing head. However, the results show that
FIG. 13. Measurement trajectories in (a) [0, 10] s; (b) [10, 30] s; and (c) [30, 60] s.
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the measurement velocity variation during each measurement is not monotonic. As shown in Fig. 16, the measurement velocity always increases first and then decreases during each measurement. And the phenomenon exists during the whole in situ measurement process (60 s), even when the variation happens at crest or trough of Fig. 15(b). It is worth noting that the measurement velocity increases more at the rising stage, while it decreases more at the falling stage.
VII. EXPERIMENT AND RESULTS
The CMP tool is shown in Fig. 17. In this paper, several experiments were done to test the calculations above. During the experiment, deionized water (DIW) was used instead of slurry. Therefore, no copper was almost removed. In Fig. 18,
(a) shows the change in distance between the sensor probe and the platen center during the CMP process and (b) shows the original measurement signal synchronously. Based on the trajectory equation, the distance was calculated with the actual rotation angle of the polishing head, the actual oscillation distance of the polishing head, and the actual rotation angle of the polishing platen, which were all read in real time. Generally, the variation of environmental parameters could result in the small drift of measurement signal during the in situ measurement process. Thus, the control system used difference value between the measurement signal and its reference value (when the probe leaves the measurement area) for calculating the thickness of the copper layer on the wafer
TABLE IV. Statistical results of the measurement time. Zone 1 Zone 2 Zone 3 Zone 4
TABLE III. The average measurement time of each zone.
Time (s)
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
0.0338
0.0572
0.0417
0.0137
0.004 27
Average (s) Standard deviation (s) Maximum (s) Minimum (s) Standard deviation/average (%)
0.0325 0.0032 0.0354 0.0242 9.85
0.0572 0.0014 0.0608 0.0558 2.45
FIG. 14. Measurement time of each zone: (a) zone 1; (b) zone 2; (c) zone 3; (d) zone 4; and (e) zone 5.
FIG. 15. Relative velocity variation: (a) in X1O1Y1 and (b) under the wafer surface.
0.0406 0.0012 0.0429 0.0392 2.96
0.013 5 0.000 43 0.014 4 0.012 9 3.19
Zone 5 0.004 2 0.000 15 0.004 5 0.004 3.57
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FIG. 16. Measurement velocity variation: (a) during each measurement and (b) at crest.
FIG. 17. CMP tool.
FIG. 19. Distribution of 3481 measurement points.
FIG. 18. In situ measurement process: (a) distance between the probe and the platen and (b) original measurement signal.
FIG. 20. The in situ measurement trajectory.
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FIG. 21. Measurement result of a Cu profile: (a) measurement signal and (b) actual thickness profile.
surface, and there existed a positive linear relationship between the signal amplitude and the thickness in a certain range. As shown in Fig. 18, the Cu profile was measured, only when the distance between the probe and the platen center was less than 150 mm. When the distance was more than 150 mm, the measurement ended and the amplitude of the original measurement signal kept its reference value (1 V). It was also noted that in situ conditioning could interfere with the measurement signal during the CMP process, which could cause the erroneous judgement on Cu thickness. However, the control system could reject this part of the measurement signal with the aid of the real-time measurement point tracking. After the experiment, a four-point probe meter (Four Dimensions, Inc., US) was used to measure the thickness of the Cu layer on the wafer surface. In this paper, the thickness values of 3481 points distributed evenly on the whole surface were obtained, and the distribution of the measurement points was shown in Fig. 19. In Fig. 19, the x-direction diameter was vertical to the notch, while the x-direction (X1) was parallel to the notch during actual in situ measurement process. Based on the distribution of the measurement points and the actual in situ measurement trajectory, we compared the in situ measurement signal with the actual thickness values of its corresponding (or nearest) points. Here, we took 59 measurement points in each profile, because there were 30 circles in the distribution of 3841 measurement points (the wafer center was the first circle). Take a Cu profile during the CMP process, for example, and its in situ measurement trajectory is shown in Fig. 20. In Fig. 21, the 30th sampling point is the wafer center. The original measurement signal is basically consistent with the thickness profile. Therefore, it was concluded that the trajectory model and equation could properly describe the in situ measurement trajectory during the actual CMP process. VIII. CONCLUSION
In this paper, we modeled the in situ measurement process and established the actual measurement trajectory equation. Based on the practical CMP parameters, we calculated the measurement trajectory and the measurement time of each zone of the wafer surface during the CMP process. According to the calculations, the kinematic parameters had a significant influence on the measurement trajectory, and each parameter played a distinct role. In addition, the measurement time in each zone was not constant, when the polishing head oscillated. And the measurement velocity of the probe varied
periodically, and it always first increased and then decreased during each measurement. During the experiments, DIW was used instead of slurry. According to the experiment results, the trajectory model and equation could properly describe the in situ measurement trajectory during the actual CMP process. ACKNOWLEDGMENTS
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