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Viscoelastic behavior of polishing pad: Effects on edge roll-off during silicon wafer polishing
Precision Engineering 62 (2020) 30–39
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Viscoelastic behavior of polishing pad: Effects on edge roll-off during silicon wafer polishing Urara Satake *, Sena Harada, Toshiyuki Enomoto Department of Mechanical Engineering, Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka, 565-0871, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Polishing Silicon wafer Flatness Edge roll-off Polishing pad Viscoelasticity
In semiconductor device fabrication, surface flatness of silicon wafers has a significant impact on the chip yield. Hence, there is a strong demand to prevent the deterioration in surface flatness near the wafer edge due to edge roll-off during polishing. In the present study, we investigate the viscoelastic behavior of polishing pads and its effects on the uniformity of material removal distribution near the wafer edge. On the basis of the findings, we propose polishing conditions required to improve surface flatness near the wafer edge. The double-sided pol ishing experiments performed using silicon wafers reveal that the proposed polishing conditions effectively reduce edge roll-off.
1. Introduction In semiconductor industry, there are stringent requirements for higher integration density of circuits in order to improve the perfor mance of semiconductor devices. Thickness uniformity of the silicon wafers that serve as the substrates of the semiconductor devices can affect the capability of several device processing steps. The variation of wafer thickness is included in the depth-of-focus budget of lithography process [1] and also affects uniformity of film thickness in CMP process [2]. Surface flatness of the wafers, therefore, is tightly specified both on the global scale and on the individual chip-site scale [3]. SEMI standards include specifications for surface flatness of wafers described by global metrics such as GBIR (Global Backside Ideal focal plane Range) as well as local metrics such as SFQR (Site Front side least sQuare focal plane Range) [4]. In the manufacturing of the most advanced devices, the global flatness across an entire wafer and the chip-site flatness must be < 100 and < 20 nm, respectively. However, surface flatness in the peripheral region of a wafer is seriously deteriorated because of edge roll-off (ERO) during polishing, which is the final stage of wafer fabrication. In the typical polishing process of wafers, double-sided polishing (DSP) and single-sided pol ishing are applied in the order. Surface of a wafer is mirrored in DSP and then finished extremely smoothly in single-sided polishing. Both global flatness and site flatness of a wafer are dominantly affected by perfor mances of DSP process [3]. Surface flatness near the wafer edge is also strongly affected by ERO during DSP. Since large ERO brings about
significant chip yield loss in the semiconductor device manufacturing, it is strongly required to reduce ERO [5] in DSP process. Aiming to achieve good surface flatness near the wafer edge, a number of studies have investigated how ERO is affected by polishing process parameters, such as properties of a polishing pad [6–12], pre-polished surface profile of a wafer [7,13], and specifications of a wafer chuck including a holder and a retainer ring [14,15]. In our pre vious study [6,7], effect of thickness, Poisson’s ratio, and anisotropy of Young’s modulus of a polishing pad on ERO has been investigated. On the basis of the investigation, we have revealed that a polishing pad having small thickness, large Poisson’s ratio, and highly anisotropic Young’s modulus can reduce ERO effectively. We have also found that ERO can be reduced under polishing conditions with a small settlement of a wafer into a polishing pad, that is, applying low polishing pressure and using a hard polishing pad result in less ERO [7]. Viscoelastic properties of polishing pads are commonly believed to be a critical parameter to ERO. Hence, compression recovery rate, which characterizes the viscoelastic behavior of materials, is widely used as an indicator for evaluation of polishing pads. However, only elastic prop erties of a polishing pad have been considered in our previous investi gation [6,7]. Several analytical studies [8–12] have indicated that the material removal distribution near the wafer edge depends on the viscoelastic property of a polishing pad; however, the causal relation ship remains unclear. In this study, we investigate how the viscoelastic behavior of pol ishing pads affects the material removal distribution near the wafer edge
* Corresponding author. E-mail address: [email protected] (U. Satake). https://doi.org/10.1016/j.precisioneng.2019.11.005 Received 17 August 2019; Received in revised form 25 September 2019; Accepted 16 October 2019 Available online 9 November 2019 0141-6359/© 2019 Elsevier Inc. All rights reserved.
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Fig. 2. Silicon wafer geometry in the peripheral region.
Fig. 1. Typical time-deformation curve of a polishing pad obtained via indentation creep test.
Table 1 Geometric and material properties of wafer model and polishing pad model used in FEA of single-sided polishing.
in order to reveal the causal relationship between the viscoelastic property of a polishing pad and ERO. On the basis of the results, we propose polishing conditions required to reduce ERO. We also evaluate the corresponding polishing performance of the proposed conditions in double-sided polishing experiments on silicon wafers.
Length mm Wafer 14 Polishing pad Pad 50 A Pad 50 B Pad 50 C
2. Effects of viscoelastic behavior of a polishing pad on ERO ERO results from much more material removal in the peripheral region than that in the other region on the wafer surface during pol ishing. Preston’s equation [16], which is commonly used to estimate the material removal rate during polishing, indicates that the material removal distribution on the wafer surface is proportional to the contact stress distribution between the wafer and the polishing pad. Polishing pads commonly used in the polishing process of silicon wafers typically exhibit viscoelastic behavior including creep deforma tion, creep recovery, and stress relaxation. Fig. 1 shows a timedeformation curve of the commercial nonwoven type polishing pad (Nitta Haas Inc., SUBA 840) obtained via indentation creep test, in which a cylindrical indenter was indented into the surface of the pol ishing pad at a constant pressure. The polishing pad deformed instan taneously once subjected to pressure, and the instantaneous elastic deformation was followed by the time-dependent increase in deforma tion, which is known as creep. The contact stress distribution between the wafer and the polishing pad during polishing can be obtained through the analytical solutions of the contact problem between a rigid cylindrical punch and a viscoelastic layer. When a rigid cylindrical punch is indented into a viscoelastic layer and slides at a constant speed over the boundary of the layer, the contact stress distribution between the punch and the viscoelastic layer has the following features according to the viscoelastic theory [17–19]:
Thickness mm
Poisson’s ratio
Young’s modulus MPa
Viscosity coefficient a
b
0.4
0.3
193000
–
–
0.8
0.3
2.8
21.7
13.2
0.8
0.3
2.8
10.8
13.2
0.8
0.3
2.8
1.2
13.2
rounded shape in the chamfer area (Fig. 2) effectively reduces the degree of stress concentration near the edge. In addition, we have found that the shape of a wafer in the chamfer area becomes more rounded as polishing progressed under the polishing conditions with a small settlement of the wafer into the polishing pad. Thus, it has been concluded that reduction in the wafer settlement into the polishing pad during polishing results in less ERO. Using those findings as the theoretical basis, we investigate effects of the viscoelastic property of a polishing pad on the wafer set tlement into the polishing pad during polishing in Section 4. 3. Effects on the contact stress concentration near the wafer edge In this section, we investigate how the viscoelastic property of a polishing pad affects the degree of stress concentration near the wafer edge. In the previous studies [6], we have found that Young’s modulus, namely, the instantaneous elastic property of a polishing pad does not affect the contact stress distribution between a wafer and a polishing pad. Whereas, the contact stress distribution can be affected by the viscoelastic property, specifically, stress relaxation property of a pol ishing pad according to the viscoelastic theory [17–19], as mentioned in Section 2. Thus, we investigate the relationship between the stress relaxation property of the polishing pad and the degree of stress con centration near the edge. Finite element analysis (FEA) was conducted under plane strain conditions via the commercial FEA software (MSC Software Corp., Marc 2018). We modeled single-sided polishing process, where a wafer is indented into a polishing pad with polishing pressure applied to the top surface of the wafer uniformly and simultaneously slides at a constant speed on the polishing pad surface. The geometric properties and the material properties of the wafer model and the pol ishing pad model are listed in Table 1. The wafer model having a much shorter length than the typical wafer was applied to reduce calculation time. We modeled three types of polishing pads (Pads A–C) having different stress relaxation property. Fig. 3 shows the time-deformation
� There occurs stress concentration near the edge of the contact area. � The contact stress distribution is asymmetric in a section parallel to the sliding direction of the punch because of the stress relaxation behavior of the viscoelastic layer. The singular stresses near the edge of the contact area result in significantly greater material removal near the wafer edge during pol ishing. Therefore, ERO is affected by the degree of stress concentration near the wafer edge. Our previous studies [6,7] have revealed that the degree of stress concentration near the wafer edge depends on properties of a polishing pad such as thickness, Poisson’s ratio, and anisotropy of Young’s modulus. In Section 3, we discuss effects of the viscoelastic property of a polishing pad on the degree of stress concentration near the wafer edge. In the previous work [7], we have also revealed that a wafer with the 31
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Fig. 3. Time-deformation curves of polishing pad models used in FEA.
Fig. 5. Measured time-deformation curves of polishing pads used in the singlesided polishing experiments. Table 2 Single-sided polishing conditions. Single-sided polishing machine (Lapmaster SFT Corp., LP-15F) Workpiece Diameter Polishing pad Diameter Slurry Abrasive particle size Concentration Supply rate Polishing pressure Rotation speed of workpiece Rotation speed of polishing pad
Single crystal silicon wafer 125 mm Nonwoven type 420 mm Colloidal silica (Fujimi Inc., GLANZOX-1302) 35 nm 0.9 wt% 25 mL/min 13.8 kPa 0 rpm 40 rpm
Fig. 4. Calculated contact stress distribution between the wafer and the pol ishing pad.
curves of Pads A–C, which were obtained via FEA of the indentation creep test. Pad A has the highest creep deformability, followed in order by Pad B, and Pad C. Considering that the retardation time, which characterizes the creep behavior, has a correlation with the relaxation time, which characterizes the stress relaxation behavior, Pad A can perform the largest stress relaxation, followed in order by Pad B, and Pad C. Fig. 4 shows the contact stress distribution between the wafer and the polishing pad calculated via FEA of the single-sided polishing. The contact stress was concentrated at the wafer edge, and a noticeable asymmetry was observed in the contact stress distribution. The degree of
Fig. 6. Surface profiles near the wafer edge after single-sided polishing. 32
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stress concentration was evaluated for each wafer edge by the difference between the normalized peak stress value and the normalized stress value at a distance of 0.7 mm from the periphery of the wafer. The de gree of stress concentration near the leading edge was higher than that near the trailing edge in every case. It can be seen that there was a larger difference in the degree of stress concentration between near the leading edge and near the trailing edge when a polishing pad has higher ability for stress relaxation. To verify the effects of the stress relaxation property of the polishing pad on ERO experimentally, single-sided polishing experiments were performed on silicon wafers. We prepared three types of nonwoven type polishing pads (Pads D–F) and evaluated their stress relaxation prop erties via the indentation creep tests using the indentation measurement apparatus [7]. A cylindrical indenter was indented into the surface of the polishing pad at a constant pressure (100 kPa) for 0.25 s. As shown in the measured time-deformation curve of each polishing pad (Fig. 5), Pad D had the highest creep deformability, followed in order by Pad E, and Pad F. These results indicate that Pad D can perform the largest stress relaxation, followed in order by Pad E, and Pad F. Table 2 lists the single-sided polishing conditions. To examine the difference in ERO between near the leading edge and near the trailing edge of the wafer, the wafer was not rotated during polishing unlike a typical polishing process. Fig. 6 shows the surface profiles near the wafer edge after polishing, which were measured with the stylus type surface roughness tester (Kosaka Laboratory Ltd., SE3500). ERO was evaluated by defining the roll-off amount (ROA) as the vertical displacement from the level line to the measured wafer profile at a distance of 1 mm from the periphery of the wafer. Consistent with the above analytical investigation, ERO near the leading edge were larger than that near the trailing edge in every case. There was a larger difference in ERO between near the leading edge and near the trailing edge when using a polishing pad having higher ability for stress relaxation, which is also in agreement with the above analytical findings. In a typical polishing process, material removal is circumferentially averaged on a wafer surface because of the wafer rotation; therefore, ERO is also circumferentially averaged on a wafer. In each of the above FEA results for Pad A, Pad B, and Pad C (Fig. 4), the average degree of stress concentration near the leading edge and near the trailing edge was 2.03, 1.99, and 1.96, respectively. The results indicate that the average degree of stress concentration near the leading edge and near the trailing edge depends little on the stress relaxation properties of the polishing pad. We concluded that while the stress relaxation behavior of the polishing pad affects the material removal distribution near the wafer edge, ERO negligibly depends on the stress relaxation properties of the polishing pad under the typical polishing conditions in which the wafer rotate during polishing. Whereas, the average ROA at the leading edge and at the trailing edge was distinctly different for each polishing pad in the above experimental results (Fig. 6); the average ROA for Pad D, Pad E, and Pad F was 550 nm, 190 nm, and 170 nm, respectively. The results are believed to be due to the difference in the wafer settlement into the polishing pad during polishing, which affects ERO as explained in Sec tion 2.
Fig. 7. Schematic of a sliding wafer on a polishing pad during polishing.
4. Effects on the wafer settlement into the polishing pad
Fig. 8. Calculation of "estimated deformation".
4.1. Determinants of the wafer settlement into the polishing pad
polishing pad is indented by the sliding wafer during polishing. A certain position "P" on the polishing pad is subjected to a constant load from being passed by the leading edge of the wafer (at time tL) until being passed by the trailing edge of the wafer (at time tT). The total defor mation of the polishing pad at the position "P" at time t* (tL < t* < tT) can be estimated as the sum of the instantaneous elastic deformation occurred at time tL and the accumulated creep deformation over the duration of loading, that is, the period from time tL to time t*.
As mentioned in Section 2, our previous studies [7] have revealed that ERO can be effectively reduced under the polishing conditions with a small settlement of the wafer into the polishing pad. In this section, we investigate how the viscoelastic property of a polishing pad affects the wafer settlement into the polishing pad during polishing. The wafer settlement is determined by the deformation of the pol ishing pad occurred under the wafer. As illustrated in Fig. 7, the 33
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Fig. 9. "Actual wafer settlement" calculated via FEA vs. the average of "esti mated deformation" of all positions (P1–P29).
The loading period at the position "P" up to time t* varies according to the distance between the position "P" and the leading edge of the wafer; the loading period is shorter as the position "P" is closer to the leading edge. Therefore, the total deformation of the polishing pad estimated as the sum of the instantaneous elastic deformation and the accumulated creep deformation (referred to as "estimated deformation") also varies depending on the position "P", whereas the wafer settlement into the polishing pad during polishing (referred to as "actual wafer settlement") is quite uniform because of high rigidity of the wafer. Thus, we investigate the relation between "actual wafer settlement" and "estimated deformation" at each position on the polishing pad under the wafer. First, FEA of the single-sided polishing was conducted under the analytical conditions listed in Table 1 to calculate "actual wafer settle ment" for the five types of polishing pads having different viscoelastic properties (Pads G–K). In the analysis for Pad H, we applied three levels of sliding speed of the wafer (110 mm/s, 440 mm/s, and 1100 mm/s), which affects the loading period at each position on the polishing pad. Next, we calculated "estimated deformation" at each position on the polishing pad under the wafer in the above FEA model (P1–P29 illus trated in Fig. 8(a)). As mentioned above, "estimated deformation" at each position can be calculated from the loading period at each position and the deformability, that is, time-deformation curve of the polishing pad. The loading period at each position was calculated from the sliding speed of the wafer and the distance between each position and the leading edge of the wafer. The time-deformation curves of Pads G–K are shown in Fig. 8(b), which were obtained via FEA of the indentation creep test. Fig. 8(c) plots the calculated "estimated deformation" at each position and the average of "estimated deformation" of all positions. "Actual wafer settlement" calculated via FEA was compared with the average of "estimated deformation" of all positions in Fig. 9. These re sults suggest that "actual wafer settlement" corresponded to the average of "estimated deformation". It was concluded that the wafer settlement into the polishing pad during polishing can be estimated from the deformability, that is, time-deformation curve of the polishing pad and the loading period at each position on the polishing pad under the wafer. The loading period at each position is determined by the polishing conditions such as diameter of a wafer and sliding speed of a wafer.
Fig. 10. Double-sided polishing process.
undoubtedly have low deformability; however, the usage of them can contribute to deterioration of surface quality of wafers, such as forma tion of micro-scratch. To reduce ERO without problems due to excessive hardness of the polishing pads, we consider the polishing conditions required to reduce the wafer settlement into the polishing pad. In a previous work [7], we have proposed the polishing conditions to reduce ERO in the single-sided polishing process. Surface flatness of the wafer, however, is dominantly affected by performances of the DSP process [3], which is followed by the single-sided polishing process in the wafer manufacturing. Each position on the polishing pad is repeatedly loaded by the wafer whenever the wafer slides on that position during polishing; that is, each position on the polishing pad is subjected to repeated loading/unloading cycles. On the basis of the viscoelastic theory, creep deformability of a viscoelastic body is dependent on the loading history under the repeated loading/unloading cycles, which suggests that the creep deformability of the polishing pad depends on the cyclic loading conditions during polishing. Thus, we investigate how the time-deformation curve of the polishing pad is affected by the cyclic loading conditions, that is, the combination of the loading periods and the unloading periods. In a typical DSP process (Fig. 10), several wafers are polished simultaneously between the upper polishing pad and the lower polishing pad. Each wafer is placed in the hole of the carrier as a workpiece holder, which rotates while revolving around the center of the polishing pad. The hole is located at the eccentric position of the carrier; hence the wafer moves both in the circumferential direction and in the radial di rection on the polishing pad. Because of this wafer movement, each
4.2. Deformability of the polishing pad during polishing As described in Section 4.1, there are two determinants of the wafer settlement into the polishing pad during polishing: the deformability of the polishing pad and the loading period at each position on the pol ishing pad under the wafer. Polishing pads made of hard materials 34
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Table 3 Double-sided polishing conditions for repeated indentation creep tests. Diameter of inner gear Diameter of carrier Diameter of workpiece Eccentric distance between carrier center and workpiece center Number of carriers per batch Number of workpieces per carrier Initial angle of carrier hole (see Fig. 10(b))
Rotation speed of carriersa Orbital speed of carriersa Rotation speed of upper polishing pada Rotation speed of lower polishing pada
Fig. 11. Indentation measurement apparatus [7].
a
400 mm 525 mm 300 mm 88 mm 5 1 ϕ1: 0 deg ϕ2: 0 deg ϕ3: 0 deg ϕ4: 0 deg ϕ5: 0 deg DSP Condition A
DSP Condition B
2.1 rpm 10.7 rpm 5 rpm 15 rpm
10.1 rpm 5.3 rpm 5 rpm 15 rpm
The clockwise direction is negative when viewed from above the machine.
Fig. 12. Cyclic loading conditions for repeated indentation creep tests.
Fig. 13. Measured time-deformation curve of the polishing pad.
position on the polishing pad is subjected to the cyclic loading in which both the loading period and the unloading period can vary with each cycle. In addition, the position in the inner or outer area on the polishing pad can often be subjected to the cyclic loading with significantly long unloading periods. To investigate the effects of cyclic loading conditions on a timedeformation curve of a polishing pad, we conducted the repeated indentation creep tests for the commercial nonwoven type polishing pad (Nitta Haas Inc., SUBA 840) using the on-machine indentation mea surement apparatus (Fig. 11) [7]. The apparatus can measure the
displacement of the surface of a polishing pad indented repeatedly under a set cyclic loading condition with set pressure by cylindrical indenter. The driving device of the indenter consists of a voice-coil motor (NEO MAX Co. Ltd., X-1743), which accurately controls the high-frequency setting pressure. In the repeated indentation creep tests in this study, the polishing pad was subjected to multiple loading/unloading cycles with the pres sure kept constant (100 kPa) over the loading period. We applied the two different cyclic loading conditions (Condition A and B) described in Fig. 12(a) and Fig. 12(b). The loading/unloading cycles of Conditions A 35
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loading/unloading cycle, the following behavior of the polishing pad was observed (Fig. 13(c)): The polishing pad deformed instantaneously once subjected to a load, and creep deformation was accumulated over the loading period. The elastic deformation disappeared instantaneously once the load was removed, and part of the creep deformation recovered during the unloading period. At the end of the cycle, the residual deformation was observed. As shown in Fig. 14, we confirmed that no residual deformation was present when the polishing pad underwent the extremely long unloading period. The result indicates that no plastic deformation occurred in the polishing pad; in other words, the observed residual deformation arose from the creep deformation which has not been recovered because of short unloading period. First, we investigated the effects of the loading history on the creep deformability of the polishing pad, which is defined as the creep increment within a given loading period (Fig. 15(a)). Fig. 15(b) plots the creep increment within the first 0.4 s of a loading period in each cycle under Condition B, which indicates that the creep deformability of the polishing pad varied every cycle. This result follows the Boltzmann’s superposition principle [20], which states that each loading/unloading independently contributes to the deformation of a viscoelastic body under the repeated loading/unloading cycles. It means that the creep increment during the loading period in a certain cycle is affected by the recovery behavior in every previous cycle (Fig. 16(b)). The larger the effects of the recovery behavior in the previous cycles are, the more effectively the creep deformability of the polishing pad is reduced. Therefore, the creep deformability of the polishing pad is effectively reduced when the load is applied soon after the preceding load is removed, that is, when the unloading period is short (Fig. 16(c)). Next, the effects of the loading history on the instantaneous deformability of the polishing pad were examined. As shown in Fig. 13 (a) and (b), the instantaneous deformability of the polishing pad also varied every cycle, which is not observed in the behavior of typical viscoelastic materials. We plotted the instantaneous elastic deformation in each cycle against the residual deformation in the preceding cycle with the best fitting straight line in Fig. 17. There was an evidently negative correlation; specifically, the instantaneous elastic deformation in each cycle was directly proportional to the residual deformation in the preceding cycle. The proportional constant negligibly depended on the cyclic loading conditions. We concluded that the instantaneous deformability of the polishing pad is effectively reduced when the re sidual deformation is large in the preceding cycle, that is, when the unloading period is relatively short compared to the loading period. On the basis of the above investigation, we established the consti tutive model for polishing pads to represent the relation between cyclic loading conditions and a time-deformation curve of a polishing pad. It is empirically clear that the polishing pads exhibit nonlinear viscoelastic behavior; that is, the stress-strain relation of the polishing pad is dependent on the strain range. Thus, we modified the Schapery’s constitutive model [21,22] based on the principles of irreversible ther modynamics, which has so far been widely used to characterize the nonlinear viscoelastic behavior of materials. On the basis of the above findings, the constant term in the Schapery’s constitutive equation, which represents the instantaneous elastic deformation, was substituted by a first-degree polynomial function of the residual deformation in the preceding cycle. To verify the proposed constitutive model, the calculated timedeformation curves via the proposed constitutive equation were compared with the measured ones via the repeated indentation creep tests for the commercial nonwoven type polishing pad (Nitta Haas Inc., SUBA 840) under the four different cyclic loading conditions (Condi tions A–D shown in Fig. 12). The loading/unloading cycles of Conditions C and D occur at Positions A and B (Fig. 10(b)), respectively, on the lower polishing pad under the DSP Condition B listed in Table 3. Prior to the verification, the material parameters in the proposed constitutive equation were identified via the repeated indentation creep tests under the two different cyclic loading conditions. For better
Fig. 14. Measured time-deformation curve under cyclic loading with extremely long unloading period.
Fig. 15. Change in creep deformability of a polishing pad.
and B occur at Positions A and B (Fig. 10(b)), respectively, on the lower polishing pad under DSP Condition A listed in Table 3. As mentioned above, both the loading period and the unloading period vary with each cycle in both Conditions A and B, and Condition B, which occurs in the inner area on the polishing pad, has significantly long unloading periods. Fig. 13 shows the measured time-deformation curves. During a 36
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Fig. 16. Effects of loading history on the creep deformability of a polishing pad.
with each cycle. The material parameters to obtain the calculated timedeformation curves that best fit the measured ones were identified by using the least squares method. The calculated time-deformation curves via the proposed constitu tive equation with the identified material parameters were compared with the measured ones in Fig. 18. Fig. 19 plots the instantaneous elastic deformation and the creep deformation in a calculated and a measured time-deformation curve in the last cycle. The calculated results were in good agreement with the measured ones under every cyclic loading conditions, which confirmed that the proposed constitutive equation can calculate the time-deformation curve of the polishing pad under a given DSP conditions. Combining the findings in Section 4.1 and the proposed constitutive equation above enables us to calculate the wafer settlement into the polishing pad from a given DSP conditions. 5. Polishing conditions required to reduce the wafer settlement On the basis of the investigation in Section 4, the following cyclic loading conditions effectively reduce the wafer settlement into the polishing pad, resulting in less ERO:
Fig. 17. Relation between the instantaneous elastic deformation in each cycle and the residual deformation in the preceding cycle.
� The loading period is short, which can reduce the total accumulation of the creep deformation during that loading period. � The unloading period is short, which can reduce the creep deform ability of the polishing pad.
identification of the material parameters especially related to the creep behavior and the creep recovery behavior, the identification tests were conducted under the cyclic loading conditions with long loading periods (loading period: 1.25 s, unloading period: 0.25 s) and those with long unloading periods (loading period: 0.25 s, unloading period: 1.25 s), where both of the loading period and the unloading period do not vary 37
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Table 4 Double-sided polishing conditions for polishing experiments. Polishing machine
Double-sided polishing machine (Hamai Co., Ltd., 9BF)
Diameter of inner gear Workpiece Diameter Thickness Carrier Diameter Thickness Polishing pad
178 mm Single crystal silicon wafer 125 mm 525 μm Glass epoxy resin type 232 mm 400 μm Nonwoven type (Nitta Haas Inc., SUBA840) Colloidal silica (Fujimi Inc., GLANZOX-1302) 35 nm 0.9 wt% 5.2 L/min 36.25 mm
Slurry Abrasive particle size Concentration Supply rate Eccentric distance between carrier center and workpiece center Number of workpieces per carrier Polishing pressure
Number of carriers per batch Initial angle of carrier hole (see Fig. 10(b))
Rotation speed of carriersa Orbital speed of carriersa Rotation speed of upper polishing pada Rotation speed of lower polishing pada a
Fig. 18. Verification of the proposed constitutive equation.
1 13.8 kPa DSP Condition C
DSP Condition D
5 ϕ1: 0 deg ϕ2: 20 deg ϕ3: 40 deg ϕ4: 60 deg ϕ5: 80 deg 4.1 rpm 5.2 rpm 6.6 rpm 20.0 rpm
3 ϕ1: 0 deg ϕ2: 0 deg ϕ3: 0 deg 4.1 rpm 5.2 rpm 4.0 rpm 12.0 rpm
The clockwise direction is negative when viewed from above the machine.
The larger the relative sliding speed of the wafer against the pol ishing pad, the shorter the loading period at each position on the pol ishing pad is. The unloading period at each position on the polishing pad can be reduced by increasing the total number of wafers and setting the trajectories of the wafers to be close to each other. Both the trajectory and the relative sliding speed of each wafer can be provided as desired by setting the appropriate DSP conditions. DSP conditions required to provide the above approaches can be considered on the basis of the kinematics. In concrete, the trajectory of a wafer can be calculated kinematically by using rotation speed of carriers, orbital speed of carriers, diameter of an inner gear, diameter of a carrier, diameter of a wafer, eccentric distance between carrier center, and initial arrangement of a wafer on the polishing pad, that is, initial angles of a carrier hole (ϕ1–ϕ5 shown in Fig. 10(b)). We also calculate the relative sliding speed of a wafer against a polishing pad based on the kinematics by using rotation speed of carriers, orbital speed of carriers, rotation speed of a polishing pad, diameter of an inner gear, diameter of a carrier, diameter of a wafer, and eccentric distance between carrier center. On the basis of the above kinematical relationship, we can consider better DSP conditions and specifications of polishing machine corresponding to each proposed approach. To verify the effectiveness of the proposed approaches in reducing ERO, DSP experiments were conducted under the DSP conditions listed in Table 4. DSP Condition C was set to reduce the wafer settlement into the lower polishing pad by applying the above three approaches, and DSP Condition D was set as reference. Under DSP Condition C, more wafers are polished simultaneously, and there is the larger difference between the orbital speed of the carriers and the rotation speed of the lower polishing pad, leading to larger sliding speed of the wafers relative to the lower polishing pad. In addition, all wafers move along the same path on the lower polishing pad because of the appropriate initial arrangement of the wafers. On the basis of the findings in Section 4, the wafer settlement into the
Fig. 19. Instantaneous elastic deformation and creep deformation in a calcu lated and a measured time-def.
� The unloading period is relatively short compared to the loading period, which can reduce the instantaneous deformability of the polishing pad. The cyclic loading conditions at each position on the polishing pad is determined by the total number of wafers polished simultaneously, the trajectory of each wafer on the polishing pad, and the sliding speed of each wafer relative to the polishing pad. The above effective cyclic loading conditions can be provided by the following approaches: � Increase the total number of wafers � Set the trajectories of the wafers to be close to each other � Increase the relative sliding speed of the wafers 38
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conditions in which the wafer rotate during polishing. Next, we inves tigated the effects of the viscoelastic behavior of polishing pads on wafer settlement into a polishing pad during polishing, which affects ERO. The relation between viscoelastic property of a polishing pad and wafer settlement were revealed. Furthermore, we established the constitutive model for polishing pads considering the effects of polishing conditions on the viscoelastic behavior of a polishing pad during polishing. On the basis of the investigation, we proposed polishing conditions required to reduce wafer settlement, resulting in reduction in ERO. The results of DSP experiments on silicon wafers confirmed that the proposed polish ing conditions can effectively reduce ERO. References [1] Tony L, Schmitz, Angela D, Davies, Chris, Evans, Robert E, Parks. Silicon wafer thickness variation measurements using the national institute of standards and technology infrared interferometer. Opt Eng 2003;42/8:2281–90. [2] Pradeep, Vukkadala, Kevin T, Turner, Jaydeep K, Sinha. Impact of wafer geometry on CMP for advanced nodes. J Electrochem Soc 2011;158/10:1002–9. [3] T€ onshoff HK, Schmieden Wv, Inasaki I, K€ onig W, Spur G. Abrasive machining of silicon. Ann. CIRP 1990;39/2:621–35. [4] SEMI (semiconductor equipment and materials international), SEMI M49, SEMI Standards. [5] Byrne G, Mullany B, Young P. The effect of pad wear on the chemical mechanical polishing of silicon wafers. Ann. CIRP 1999;48/1:143–6. [6] Enomoto T, Satake U, Miyake T, Tabata N. A newly developed polishing pad for achieving high surface flatness without edge roll off. CIRP Ann - Manuf Technol 2011;60:371–4. [7] Satake U, Enomoto T, Obayashi Y, Sugihara T. Reducing edge roll-off during polishing of substrates. Precis Eng 2018;51:97–102. [8] Guanghui Fu, Abhijit Chandra. A model for wafer scale variation of material removal rate in chemical mechanical polishing based on viscoelastic pad deformation. J Electron Mater 2002;31/10:1066–73. [9] Miyake T, Enomoto T, Hirose K. The edge roll off generation mechanism in polishing by considering the viscoelasticity of polishing pads. Proc ASME Int Manuf Sci Eng Conf 2009;2009:1. MSEC2009. [10] Hashimoto Y, Suzuki N, Hino R, Shamoto E. Dynamic finite element analysis of contact stress in CMP process. J Jpn Soc Precis Eng 2011;77/5:513–9. [11] Suzuki N, Asaba M, Hashimoto Y, Shamoto E. Identification of nonlinear viscoelasticity of polishing pad using an on-machine compression tester. In: Proceedings of ICPT 2012 - international conference on planarization/CMP technology; 2012. [12] Hashimoto Y, Suzuki N, Asaba M, Hino R, Shamoto E. Elasto hydrodynamic lubrication analysis of CMP process with consideration of micro asperity contact of polishing pad. J Jpn Soc Precis Eng 2013;79/1:73–80. [13] Fukuda A, Fukuda T, Fukunaga A, Tsujimura M. Influence of wafer edge geometry on removal rate profile in chemical mechanical polishing: wafer edge roll-off and notch. Jpn J Appl Phys 2012;51(5):05EF01. [14] Ship-Peng L, Yeou-Yih L, Jen-Ching H. Analysis of retaining ring using finite element simulation in chemical mechanical polishing process. Int J Adv Manuf Technol 2007;34:547–55. [15] Suzuki N, Hashimoto Y, Yasuda H, Yamaki S, Mochizuki Y. Prediction of polishing pressure distribution in CMP process with airbag type wafer carrier. CIRP Ann. 2017;66/1:329–32. [16] Preston FW. The theory and design of plate glass polishing machines. J Soc Glass Technol 1927;11:214–56. [17] Mark AV. The uniform motion of rectangular and parabolic punches in a viscoelastic layer. J Appl Math Mech 2008;72/4:492–8. [18] Alexandrov VM, Mark AV. Constant velocity motion of a strip die on the boundary of a viscoelastic base. Mech Solids 2009;44/1:114–21. [19] Stepanov F, Torskaya EV. Modeling of sliding of a smooth indenter over a viscoelastic layer coupled with a rigid base. Mech Solids 2018;53/1:60–7. [20] Christensen RM. Theory of viscoelasticity. Academic Press; 1971. [21] Schapery RA. On a thermodynamic constitutive theory and its application to various nonlinear materials. Thermoinelasticity; 1970. p. 259–85. [22] Schapery RA. Nonlinear viscoelastic solids. Int J Solids Struct 2000;37:359–66.
Fig. 20. Calculated wafer settlement and measured surface profiles near the wafer edge.
lower polishing pad was calculated under each DSP conditions. Fig. 20 (a) shows the changes in the average of calculated settlement of all wafers with time. The time average during 100 s under DSP Conditions C and D were 30 μm and 37 μm, respectively. These results indicate that DSP Condition C can effectively reduce the wafer settlement into the lower polishing pad. As shown in the measured profiles of lower surface near the wafer edge after polishing (Fig. 20(b)), DSP Condition C resulted in less ERO compared to DSP Condition D. The average ROA of all wafers after polishing under Conditions C and D were 370 nm and 450 nm, respec tively. The results confirmed the effectiveness of the proposed ap proaches in reducing ERO. 6. Conclusions To improve surface flatness near the wafer edge during silicon wafer polishing, effects of the viscoelastic behavior of polishing pads on ERO were investigated. First, we investigated the effects of the viscoelastic behavior of polishing pads on contact stress concentration occurred at the wafer edge, resulting in ERO. On the basis of the analytical and experimental investigation, we found that ERO negligibly depends on the viscoelastic property of the polishing pad under the typical polishing
39
Contents lists available at ScienceDirect
Precision Engineering journal homepage: http://www.elsevier.com/locate/precision
Viscoelastic behavior of polishing pad: Effects on edge roll-off during silicon wafer polishing Urara Satake *, Sena Harada, Toshiyuki Enomoto Department of Mechanical Engineering, Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka, 565-0871, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Polishing Silicon wafer Flatness Edge roll-off Polishing pad Viscoelasticity
In semiconductor device fabrication, surface flatness of silicon wafers has a significant impact on the chip yield. Hence, there is a strong demand to prevent the deterioration in surface flatness near the wafer edge due to edge roll-off during polishing. In the present study, we investigate the viscoelastic behavior of polishing pads and its effects on the uniformity of material removal distribution near the wafer edge. On the basis of the findings, we propose polishing conditions required to improve surface flatness near the wafer edge. The double-sided pol ishing experiments performed using silicon wafers reveal that the proposed polishing conditions effectively reduce edge roll-off.
1. Introduction In semiconductor industry, there are stringent requirements for higher integration density of circuits in order to improve the perfor mance of semiconductor devices. Thickness uniformity of the silicon wafers that serve as the substrates of the semiconductor devices can affect the capability of several device processing steps. The variation of wafer thickness is included in the depth-of-focus budget of lithography process [1] and also affects uniformity of film thickness in CMP process [2]. Surface flatness of the wafers, therefore, is tightly specified both on the global scale and on the individual chip-site scale [3]. SEMI standards include specifications for surface flatness of wafers described by global metrics such as GBIR (Global Backside Ideal focal plane Range) as well as local metrics such as SFQR (Site Front side least sQuare focal plane Range) [4]. In the manufacturing of the most advanced devices, the global flatness across an entire wafer and the chip-site flatness must be < 100 and < 20 nm, respectively. However, surface flatness in the peripheral region of a wafer is seriously deteriorated because of edge roll-off (ERO) during polishing, which is the final stage of wafer fabrication. In the typical polishing process of wafers, double-sided polishing (DSP) and single-sided pol ishing are applied in the order. Surface of a wafer is mirrored in DSP and then finished extremely smoothly in single-sided polishing. Both global flatness and site flatness of a wafer are dominantly affected by perfor mances of DSP process [3]. Surface flatness near the wafer edge is also strongly affected by ERO during DSP. Since large ERO brings about
significant chip yield loss in the semiconductor device manufacturing, it is strongly required to reduce ERO [5] in DSP process. Aiming to achieve good surface flatness near the wafer edge, a number of studies have investigated how ERO is affected by polishing process parameters, such as properties of a polishing pad [6–12], pre-polished surface profile of a wafer [7,13], and specifications of a wafer chuck including a holder and a retainer ring [14,15]. In our pre vious study [6,7], effect of thickness, Poisson’s ratio, and anisotropy of Young’s modulus of a polishing pad on ERO has been investigated. On the basis of the investigation, we have revealed that a polishing pad having small thickness, large Poisson’s ratio, and highly anisotropic Young’s modulus can reduce ERO effectively. We have also found that ERO can be reduced under polishing conditions with a small settlement of a wafer into a polishing pad, that is, applying low polishing pressure and using a hard polishing pad result in less ERO [7]. Viscoelastic properties of polishing pads are commonly believed to be a critical parameter to ERO. Hence, compression recovery rate, which characterizes the viscoelastic behavior of materials, is widely used as an indicator for evaluation of polishing pads. However, only elastic prop erties of a polishing pad have been considered in our previous investi gation [6,7]. Several analytical studies [8–12] have indicated that the material removal distribution near the wafer edge depends on the viscoelastic property of a polishing pad; however, the causal relation ship remains unclear. In this study, we investigate how the viscoelastic behavior of pol ishing pads affects the material removal distribution near the wafer edge
* Corresponding author. E-mail address: [email protected] (U. Satake). https://doi.org/10.1016/j.precisioneng.2019.11.005 Received 17 August 2019; Received in revised form 25 September 2019; Accepted 16 October 2019 Available online 9 November 2019 0141-6359/© 2019 Elsevier Inc. All rights reserved.
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Fig. 2. Silicon wafer geometry in the peripheral region.
Fig. 1. Typical time-deformation curve of a polishing pad obtained via indentation creep test.
Table 1 Geometric and material properties of wafer model and polishing pad model used in FEA of single-sided polishing.
in order to reveal the causal relationship between the viscoelastic property of a polishing pad and ERO. On the basis of the results, we propose polishing conditions required to reduce ERO. We also evaluate the corresponding polishing performance of the proposed conditions in double-sided polishing experiments on silicon wafers.
Length mm Wafer 14 Polishing pad Pad 50 A Pad 50 B Pad 50 C
2. Effects of viscoelastic behavior of a polishing pad on ERO ERO results from much more material removal in the peripheral region than that in the other region on the wafer surface during pol ishing. Preston’s equation [16], which is commonly used to estimate the material removal rate during polishing, indicates that the material removal distribution on the wafer surface is proportional to the contact stress distribution between the wafer and the polishing pad. Polishing pads commonly used in the polishing process of silicon wafers typically exhibit viscoelastic behavior including creep deforma tion, creep recovery, and stress relaxation. Fig. 1 shows a timedeformation curve of the commercial nonwoven type polishing pad (Nitta Haas Inc., SUBA 840) obtained via indentation creep test, in which a cylindrical indenter was indented into the surface of the pol ishing pad at a constant pressure. The polishing pad deformed instan taneously once subjected to pressure, and the instantaneous elastic deformation was followed by the time-dependent increase in deforma tion, which is known as creep. The contact stress distribution between the wafer and the polishing pad during polishing can be obtained through the analytical solutions of the contact problem between a rigid cylindrical punch and a viscoelastic layer. When a rigid cylindrical punch is indented into a viscoelastic layer and slides at a constant speed over the boundary of the layer, the contact stress distribution between the punch and the viscoelastic layer has the following features according to the viscoelastic theory [17–19]:
Thickness mm
Poisson’s ratio
Young’s modulus MPa
Viscosity coefficient a
b
0.4
0.3
193000
–
–
0.8
0.3
2.8
21.7
13.2
0.8
0.3
2.8
10.8
13.2
0.8
0.3
2.8
1.2
13.2
rounded shape in the chamfer area (Fig. 2) effectively reduces the degree of stress concentration near the edge. In addition, we have found that the shape of a wafer in the chamfer area becomes more rounded as polishing progressed under the polishing conditions with a small settlement of the wafer into the polishing pad. Thus, it has been concluded that reduction in the wafer settlement into the polishing pad during polishing results in less ERO. Using those findings as the theoretical basis, we investigate effects of the viscoelastic property of a polishing pad on the wafer set tlement into the polishing pad during polishing in Section 4. 3. Effects on the contact stress concentration near the wafer edge In this section, we investigate how the viscoelastic property of a polishing pad affects the degree of stress concentration near the wafer edge. In the previous studies [6], we have found that Young’s modulus, namely, the instantaneous elastic property of a polishing pad does not affect the contact stress distribution between a wafer and a polishing pad. Whereas, the contact stress distribution can be affected by the viscoelastic property, specifically, stress relaxation property of a pol ishing pad according to the viscoelastic theory [17–19], as mentioned in Section 2. Thus, we investigate the relationship between the stress relaxation property of the polishing pad and the degree of stress con centration near the edge. Finite element analysis (FEA) was conducted under plane strain conditions via the commercial FEA software (MSC Software Corp., Marc 2018). We modeled single-sided polishing process, where a wafer is indented into a polishing pad with polishing pressure applied to the top surface of the wafer uniformly and simultaneously slides at a constant speed on the polishing pad surface. The geometric properties and the material properties of the wafer model and the pol ishing pad model are listed in Table 1. The wafer model having a much shorter length than the typical wafer was applied to reduce calculation time. We modeled three types of polishing pads (Pads A–C) having different stress relaxation property. Fig. 3 shows the time-deformation
� There occurs stress concentration near the edge of the contact area. � The contact stress distribution is asymmetric in a section parallel to the sliding direction of the punch because of the stress relaxation behavior of the viscoelastic layer. The singular stresses near the edge of the contact area result in significantly greater material removal near the wafer edge during pol ishing. Therefore, ERO is affected by the degree of stress concentration near the wafer edge. Our previous studies [6,7] have revealed that the degree of stress concentration near the wafer edge depends on properties of a polishing pad such as thickness, Poisson’s ratio, and anisotropy of Young’s modulus. In Section 3, we discuss effects of the viscoelastic property of a polishing pad on the degree of stress concentration near the wafer edge. In the previous work [7], we have also revealed that a wafer with the 31
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Fig. 3. Time-deformation curves of polishing pad models used in FEA.
Fig. 5. Measured time-deformation curves of polishing pads used in the singlesided polishing experiments. Table 2 Single-sided polishing conditions. Single-sided polishing machine (Lapmaster SFT Corp., LP-15F) Workpiece Diameter Polishing pad Diameter Slurry Abrasive particle size Concentration Supply rate Polishing pressure Rotation speed of workpiece Rotation speed of polishing pad
Single crystal silicon wafer 125 mm Nonwoven type 420 mm Colloidal silica (Fujimi Inc., GLANZOX-1302) 35 nm 0.9 wt% 25 mL/min 13.8 kPa 0 rpm 40 rpm
Fig. 4. Calculated contact stress distribution between the wafer and the pol ishing pad.
curves of Pads A–C, which were obtained via FEA of the indentation creep test. Pad A has the highest creep deformability, followed in order by Pad B, and Pad C. Considering that the retardation time, which characterizes the creep behavior, has a correlation with the relaxation time, which characterizes the stress relaxation behavior, Pad A can perform the largest stress relaxation, followed in order by Pad B, and Pad C. Fig. 4 shows the contact stress distribution between the wafer and the polishing pad calculated via FEA of the single-sided polishing. The contact stress was concentrated at the wafer edge, and a noticeable asymmetry was observed in the contact stress distribution. The degree of
Fig. 6. Surface profiles near the wafer edge after single-sided polishing. 32
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stress concentration was evaluated for each wafer edge by the difference between the normalized peak stress value and the normalized stress value at a distance of 0.7 mm from the periphery of the wafer. The de gree of stress concentration near the leading edge was higher than that near the trailing edge in every case. It can be seen that there was a larger difference in the degree of stress concentration between near the leading edge and near the trailing edge when a polishing pad has higher ability for stress relaxation. To verify the effects of the stress relaxation property of the polishing pad on ERO experimentally, single-sided polishing experiments were performed on silicon wafers. We prepared three types of nonwoven type polishing pads (Pads D–F) and evaluated their stress relaxation prop erties via the indentation creep tests using the indentation measurement apparatus [7]. A cylindrical indenter was indented into the surface of the polishing pad at a constant pressure (100 kPa) for 0.25 s. As shown in the measured time-deformation curve of each polishing pad (Fig. 5), Pad D had the highest creep deformability, followed in order by Pad E, and Pad F. These results indicate that Pad D can perform the largest stress relaxation, followed in order by Pad E, and Pad F. Table 2 lists the single-sided polishing conditions. To examine the difference in ERO between near the leading edge and near the trailing edge of the wafer, the wafer was not rotated during polishing unlike a typical polishing process. Fig. 6 shows the surface profiles near the wafer edge after polishing, which were measured with the stylus type surface roughness tester (Kosaka Laboratory Ltd., SE3500). ERO was evaluated by defining the roll-off amount (ROA) as the vertical displacement from the level line to the measured wafer profile at a distance of 1 mm from the periphery of the wafer. Consistent with the above analytical investigation, ERO near the leading edge were larger than that near the trailing edge in every case. There was a larger difference in ERO between near the leading edge and near the trailing edge when using a polishing pad having higher ability for stress relaxation, which is also in agreement with the above analytical findings. In a typical polishing process, material removal is circumferentially averaged on a wafer surface because of the wafer rotation; therefore, ERO is also circumferentially averaged on a wafer. In each of the above FEA results for Pad A, Pad B, and Pad C (Fig. 4), the average degree of stress concentration near the leading edge and near the trailing edge was 2.03, 1.99, and 1.96, respectively. The results indicate that the average degree of stress concentration near the leading edge and near the trailing edge depends little on the stress relaxation properties of the polishing pad. We concluded that while the stress relaxation behavior of the polishing pad affects the material removal distribution near the wafer edge, ERO negligibly depends on the stress relaxation properties of the polishing pad under the typical polishing conditions in which the wafer rotate during polishing. Whereas, the average ROA at the leading edge and at the trailing edge was distinctly different for each polishing pad in the above experimental results (Fig. 6); the average ROA for Pad D, Pad E, and Pad F was 550 nm, 190 nm, and 170 nm, respectively. The results are believed to be due to the difference in the wafer settlement into the polishing pad during polishing, which affects ERO as explained in Sec tion 2.
Fig. 7. Schematic of a sliding wafer on a polishing pad during polishing.
4. Effects on the wafer settlement into the polishing pad
Fig. 8. Calculation of "estimated deformation".
4.1. Determinants of the wafer settlement into the polishing pad
polishing pad is indented by the sliding wafer during polishing. A certain position "P" on the polishing pad is subjected to a constant load from being passed by the leading edge of the wafer (at time tL) until being passed by the trailing edge of the wafer (at time tT). The total defor mation of the polishing pad at the position "P" at time t* (tL < t* < tT) can be estimated as the sum of the instantaneous elastic deformation occurred at time tL and the accumulated creep deformation over the duration of loading, that is, the period from time tL to time t*.
As mentioned in Section 2, our previous studies [7] have revealed that ERO can be effectively reduced under the polishing conditions with a small settlement of the wafer into the polishing pad. In this section, we investigate how the viscoelastic property of a polishing pad affects the wafer settlement into the polishing pad during polishing. The wafer settlement is determined by the deformation of the pol ishing pad occurred under the wafer. As illustrated in Fig. 7, the 33
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Fig. 9. "Actual wafer settlement" calculated via FEA vs. the average of "esti mated deformation" of all positions (P1–P29).
The loading period at the position "P" up to time t* varies according to the distance between the position "P" and the leading edge of the wafer; the loading period is shorter as the position "P" is closer to the leading edge. Therefore, the total deformation of the polishing pad estimated as the sum of the instantaneous elastic deformation and the accumulated creep deformation (referred to as "estimated deformation") also varies depending on the position "P", whereas the wafer settlement into the polishing pad during polishing (referred to as "actual wafer settlement") is quite uniform because of high rigidity of the wafer. Thus, we investigate the relation between "actual wafer settlement" and "estimated deformation" at each position on the polishing pad under the wafer. First, FEA of the single-sided polishing was conducted under the analytical conditions listed in Table 1 to calculate "actual wafer settle ment" for the five types of polishing pads having different viscoelastic properties (Pads G–K). In the analysis for Pad H, we applied three levels of sliding speed of the wafer (110 mm/s, 440 mm/s, and 1100 mm/s), which affects the loading period at each position on the polishing pad. Next, we calculated "estimated deformation" at each position on the polishing pad under the wafer in the above FEA model (P1–P29 illus trated in Fig. 8(a)). As mentioned above, "estimated deformation" at each position can be calculated from the loading period at each position and the deformability, that is, time-deformation curve of the polishing pad. The loading period at each position was calculated from the sliding speed of the wafer and the distance between each position and the leading edge of the wafer. The time-deformation curves of Pads G–K are shown in Fig. 8(b), which were obtained via FEA of the indentation creep test. Fig. 8(c) plots the calculated "estimated deformation" at each position and the average of "estimated deformation" of all positions. "Actual wafer settlement" calculated via FEA was compared with the average of "estimated deformation" of all positions in Fig. 9. These re sults suggest that "actual wafer settlement" corresponded to the average of "estimated deformation". It was concluded that the wafer settlement into the polishing pad during polishing can be estimated from the deformability, that is, time-deformation curve of the polishing pad and the loading period at each position on the polishing pad under the wafer. The loading period at each position is determined by the polishing conditions such as diameter of a wafer and sliding speed of a wafer.
Fig. 10. Double-sided polishing process.
undoubtedly have low deformability; however, the usage of them can contribute to deterioration of surface quality of wafers, such as forma tion of micro-scratch. To reduce ERO without problems due to excessive hardness of the polishing pads, we consider the polishing conditions required to reduce the wafer settlement into the polishing pad. In a previous work [7], we have proposed the polishing conditions to reduce ERO in the single-sided polishing process. Surface flatness of the wafer, however, is dominantly affected by performances of the DSP process [3], which is followed by the single-sided polishing process in the wafer manufacturing. Each position on the polishing pad is repeatedly loaded by the wafer whenever the wafer slides on that position during polishing; that is, each position on the polishing pad is subjected to repeated loading/unloading cycles. On the basis of the viscoelastic theory, creep deformability of a viscoelastic body is dependent on the loading history under the repeated loading/unloading cycles, which suggests that the creep deformability of the polishing pad depends on the cyclic loading conditions during polishing. Thus, we investigate how the time-deformation curve of the polishing pad is affected by the cyclic loading conditions, that is, the combination of the loading periods and the unloading periods. In a typical DSP process (Fig. 10), several wafers are polished simultaneously between the upper polishing pad and the lower polishing pad. Each wafer is placed in the hole of the carrier as a workpiece holder, which rotates while revolving around the center of the polishing pad. The hole is located at the eccentric position of the carrier; hence the wafer moves both in the circumferential direction and in the radial di rection on the polishing pad. Because of this wafer movement, each
4.2. Deformability of the polishing pad during polishing As described in Section 4.1, there are two determinants of the wafer settlement into the polishing pad during polishing: the deformability of the polishing pad and the loading period at each position on the pol ishing pad under the wafer. Polishing pads made of hard materials 34
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Table 3 Double-sided polishing conditions for repeated indentation creep tests. Diameter of inner gear Diameter of carrier Diameter of workpiece Eccentric distance between carrier center and workpiece center Number of carriers per batch Number of workpieces per carrier Initial angle of carrier hole (see Fig. 10(b))
Rotation speed of carriersa Orbital speed of carriersa Rotation speed of upper polishing pada Rotation speed of lower polishing pada
Fig. 11. Indentation measurement apparatus [7].
a
400 mm 525 mm 300 mm 88 mm 5 1 ϕ1: 0 deg ϕ2: 0 deg ϕ3: 0 deg ϕ4: 0 deg ϕ5: 0 deg DSP Condition A
DSP Condition B
2.1 rpm 10.7 rpm 5 rpm 15 rpm
10.1 rpm 5.3 rpm 5 rpm 15 rpm
The clockwise direction is negative when viewed from above the machine.
Fig. 12. Cyclic loading conditions for repeated indentation creep tests.
Fig. 13. Measured time-deformation curve of the polishing pad.
position on the polishing pad is subjected to the cyclic loading in which both the loading period and the unloading period can vary with each cycle. In addition, the position in the inner or outer area on the polishing pad can often be subjected to the cyclic loading with significantly long unloading periods. To investigate the effects of cyclic loading conditions on a timedeformation curve of a polishing pad, we conducted the repeated indentation creep tests for the commercial nonwoven type polishing pad (Nitta Haas Inc., SUBA 840) using the on-machine indentation mea surement apparatus (Fig. 11) [7]. The apparatus can measure the
displacement of the surface of a polishing pad indented repeatedly under a set cyclic loading condition with set pressure by cylindrical indenter. The driving device of the indenter consists of a voice-coil motor (NEO MAX Co. Ltd., X-1743), which accurately controls the high-frequency setting pressure. In the repeated indentation creep tests in this study, the polishing pad was subjected to multiple loading/unloading cycles with the pres sure kept constant (100 kPa) over the loading period. We applied the two different cyclic loading conditions (Condition A and B) described in Fig. 12(a) and Fig. 12(b). The loading/unloading cycles of Conditions A 35
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loading/unloading cycle, the following behavior of the polishing pad was observed (Fig. 13(c)): The polishing pad deformed instantaneously once subjected to a load, and creep deformation was accumulated over the loading period. The elastic deformation disappeared instantaneously once the load was removed, and part of the creep deformation recovered during the unloading period. At the end of the cycle, the residual deformation was observed. As shown in Fig. 14, we confirmed that no residual deformation was present when the polishing pad underwent the extremely long unloading period. The result indicates that no plastic deformation occurred in the polishing pad; in other words, the observed residual deformation arose from the creep deformation which has not been recovered because of short unloading period. First, we investigated the effects of the loading history on the creep deformability of the polishing pad, which is defined as the creep increment within a given loading period (Fig. 15(a)). Fig. 15(b) plots the creep increment within the first 0.4 s of a loading period in each cycle under Condition B, which indicates that the creep deformability of the polishing pad varied every cycle. This result follows the Boltzmann’s superposition principle [20], which states that each loading/unloading independently contributes to the deformation of a viscoelastic body under the repeated loading/unloading cycles. It means that the creep increment during the loading period in a certain cycle is affected by the recovery behavior in every previous cycle (Fig. 16(b)). The larger the effects of the recovery behavior in the previous cycles are, the more effectively the creep deformability of the polishing pad is reduced. Therefore, the creep deformability of the polishing pad is effectively reduced when the load is applied soon after the preceding load is removed, that is, when the unloading period is short (Fig. 16(c)). Next, the effects of the loading history on the instantaneous deformability of the polishing pad were examined. As shown in Fig. 13 (a) and (b), the instantaneous deformability of the polishing pad also varied every cycle, which is not observed in the behavior of typical viscoelastic materials. We plotted the instantaneous elastic deformation in each cycle against the residual deformation in the preceding cycle with the best fitting straight line in Fig. 17. There was an evidently negative correlation; specifically, the instantaneous elastic deformation in each cycle was directly proportional to the residual deformation in the preceding cycle. The proportional constant negligibly depended on the cyclic loading conditions. We concluded that the instantaneous deformability of the polishing pad is effectively reduced when the re sidual deformation is large in the preceding cycle, that is, when the unloading period is relatively short compared to the loading period. On the basis of the above investigation, we established the consti tutive model for polishing pads to represent the relation between cyclic loading conditions and a time-deformation curve of a polishing pad. It is empirically clear that the polishing pads exhibit nonlinear viscoelastic behavior; that is, the stress-strain relation of the polishing pad is dependent on the strain range. Thus, we modified the Schapery’s constitutive model [21,22] based on the principles of irreversible ther modynamics, which has so far been widely used to characterize the nonlinear viscoelastic behavior of materials. On the basis of the above findings, the constant term in the Schapery’s constitutive equation, which represents the instantaneous elastic deformation, was substituted by a first-degree polynomial function of the residual deformation in the preceding cycle. To verify the proposed constitutive model, the calculated timedeformation curves via the proposed constitutive equation were compared with the measured ones via the repeated indentation creep tests for the commercial nonwoven type polishing pad (Nitta Haas Inc., SUBA 840) under the four different cyclic loading conditions (Condi tions A–D shown in Fig. 12). The loading/unloading cycles of Conditions C and D occur at Positions A and B (Fig. 10(b)), respectively, on the lower polishing pad under the DSP Condition B listed in Table 3. Prior to the verification, the material parameters in the proposed constitutive equation were identified via the repeated indentation creep tests under the two different cyclic loading conditions. For better
Fig. 14. Measured time-deformation curve under cyclic loading with extremely long unloading period.
Fig. 15. Change in creep deformability of a polishing pad.
and B occur at Positions A and B (Fig. 10(b)), respectively, on the lower polishing pad under DSP Condition A listed in Table 3. As mentioned above, both the loading period and the unloading period vary with each cycle in both Conditions A and B, and Condition B, which occurs in the inner area on the polishing pad, has significantly long unloading periods. Fig. 13 shows the measured time-deformation curves. During a 36
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Fig. 16. Effects of loading history on the creep deformability of a polishing pad.
with each cycle. The material parameters to obtain the calculated timedeformation curves that best fit the measured ones were identified by using the least squares method. The calculated time-deformation curves via the proposed constitu tive equation with the identified material parameters were compared with the measured ones in Fig. 18. Fig. 19 plots the instantaneous elastic deformation and the creep deformation in a calculated and a measured time-deformation curve in the last cycle. The calculated results were in good agreement with the measured ones under every cyclic loading conditions, which confirmed that the proposed constitutive equation can calculate the time-deformation curve of the polishing pad under a given DSP conditions. Combining the findings in Section 4.1 and the proposed constitutive equation above enables us to calculate the wafer settlement into the polishing pad from a given DSP conditions. 5. Polishing conditions required to reduce the wafer settlement On the basis of the investigation in Section 4, the following cyclic loading conditions effectively reduce the wafer settlement into the polishing pad, resulting in less ERO:
Fig. 17. Relation between the instantaneous elastic deformation in each cycle and the residual deformation in the preceding cycle.
� The loading period is short, which can reduce the total accumulation of the creep deformation during that loading period. � The unloading period is short, which can reduce the creep deform ability of the polishing pad.
identification of the material parameters especially related to the creep behavior and the creep recovery behavior, the identification tests were conducted under the cyclic loading conditions with long loading periods (loading period: 1.25 s, unloading period: 0.25 s) and those with long unloading periods (loading period: 0.25 s, unloading period: 1.25 s), where both of the loading period and the unloading period do not vary 37
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Table 4 Double-sided polishing conditions for polishing experiments. Polishing machine
Double-sided polishing machine (Hamai Co., Ltd., 9BF)
Diameter of inner gear Workpiece Diameter Thickness Carrier Diameter Thickness Polishing pad
178 mm Single crystal silicon wafer 125 mm 525 μm Glass epoxy resin type 232 mm 400 μm Nonwoven type (Nitta Haas Inc., SUBA840) Colloidal silica (Fujimi Inc., GLANZOX-1302) 35 nm 0.9 wt% 5.2 L/min 36.25 mm
Slurry Abrasive particle size Concentration Supply rate Eccentric distance between carrier center and workpiece center Number of workpieces per carrier Polishing pressure
Number of carriers per batch Initial angle of carrier hole (see Fig. 10(b))
Rotation speed of carriersa Orbital speed of carriersa Rotation speed of upper polishing pada Rotation speed of lower polishing pada a
Fig. 18. Verification of the proposed constitutive equation.
1 13.8 kPa DSP Condition C
DSP Condition D
5 ϕ1: 0 deg ϕ2: 20 deg ϕ3: 40 deg ϕ4: 60 deg ϕ5: 80 deg 4.1 rpm 5.2 rpm 6.6 rpm 20.0 rpm
3 ϕ1: 0 deg ϕ2: 0 deg ϕ3: 0 deg 4.1 rpm 5.2 rpm 4.0 rpm 12.0 rpm
The clockwise direction is negative when viewed from above the machine.
The larger the relative sliding speed of the wafer against the pol ishing pad, the shorter the loading period at each position on the pol ishing pad is. The unloading period at each position on the polishing pad can be reduced by increasing the total number of wafers and setting the trajectories of the wafers to be close to each other. Both the trajectory and the relative sliding speed of each wafer can be provided as desired by setting the appropriate DSP conditions. DSP conditions required to provide the above approaches can be considered on the basis of the kinematics. In concrete, the trajectory of a wafer can be calculated kinematically by using rotation speed of carriers, orbital speed of carriers, diameter of an inner gear, diameter of a carrier, diameter of a wafer, eccentric distance between carrier center, and initial arrangement of a wafer on the polishing pad, that is, initial angles of a carrier hole (ϕ1–ϕ5 shown in Fig. 10(b)). We also calculate the relative sliding speed of a wafer against a polishing pad based on the kinematics by using rotation speed of carriers, orbital speed of carriers, rotation speed of a polishing pad, diameter of an inner gear, diameter of a carrier, diameter of a wafer, and eccentric distance between carrier center. On the basis of the above kinematical relationship, we can consider better DSP conditions and specifications of polishing machine corresponding to each proposed approach. To verify the effectiveness of the proposed approaches in reducing ERO, DSP experiments were conducted under the DSP conditions listed in Table 4. DSP Condition C was set to reduce the wafer settlement into the lower polishing pad by applying the above three approaches, and DSP Condition D was set as reference. Under DSP Condition C, more wafers are polished simultaneously, and there is the larger difference between the orbital speed of the carriers and the rotation speed of the lower polishing pad, leading to larger sliding speed of the wafers relative to the lower polishing pad. In addition, all wafers move along the same path on the lower polishing pad because of the appropriate initial arrangement of the wafers. On the basis of the findings in Section 4, the wafer settlement into the
Fig. 19. Instantaneous elastic deformation and creep deformation in a calcu lated and a measured time-def.
� The unloading period is relatively short compared to the loading period, which can reduce the instantaneous deformability of the polishing pad. The cyclic loading conditions at each position on the polishing pad is determined by the total number of wafers polished simultaneously, the trajectory of each wafer on the polishing pad, and the sliding speed of each wafer relative to the polishing pad. The above effective cyclic loading conditions can be provided by the following approaches: � Increase the total number of wafers � Set the trajectories of the wafers to be close to each other � Increase the relative sliding speed of the wafers 38
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Precision Engineering 62 (2020) 30–39
conditions in which the wafer rotate during polishing. Next, we inves tigated the effects of the viscoelastic behavior of polishing pads on wafer settlement into a polishing pad during polishing, which affects ERO. The relation between viscoelastic property of a polishing pad and wafer settlement were revealed. Furthermore, we established the constitutive model for polishing pads considering the effects of polishing conditions on the viscoelastic behavior of a polishing pad during polishing. On the basis of the investigation, we proposed polishing conditions required to reduce wafer settlement, resulting in reduction in ERO. The results of DSP experiments on silicon wafers confirmed that the proposed polish ing conditions can effectively reduce ERO. References [1] Tony L, Schmitz, Angela D, Davies, Chris, Evans, Robert E, Parks. Silicon wafer thickness variation measurements using the national institute of standards and technology infrared interferometer. Opt Eng 2003;42/8:2281–90. [2] Pradeep, Vukkadala, Kevin T, Turner, Jaydeep K, Sinha. Impact of wafer geometry on CMP for advanced nodes. J Electrochem Soc 2011;158/10:1002–9. [3] T€ onshoff HK, Schmieden Wv, Inasaki I, K€ onig W, Spur G. Abrasive machining of silicon. Ann. CIRP 1990;39/2:621–35. [4] SEMI (semiconductor equipment and materials international), SEMI M49, SEMI Standards. [5] Byrne G, Mullany B, Young P. The effect of pad wear on the chemical mechanical polishing of silicon wafers. Ann. CIRP 1999;48/1:143–6. [6] Enomoto T, Satake U, Miyake T, Tabata N. A newly developed polishing pad for achieving high surface flatness without edge roll off. CIRP Ann - Manuf Technol 2011;60:371–4. [7] Satake U, Enomoto T, Obayashi Y, Sugihara T. Reducing edge roll-off during polishing of substrates. Precis Eng 2018;51:97–102. [8] Guanghui Fu, Abhijit Chandra. A model for wafer scale variation of material removal rate in chemical mechanical polishing based on viscoelastic pad deformation. J Electron Mater 2002;31/10:1066–73. [9] Miyake T, Enomoto T, Hirose K. The edge roll off generation mechanism in polishing by considering the viscoelasticity of polishing pads. Proc ASME Int Manuf Sci Eng Conf 2009;2009:1. MSEC2009. [10] Hashimoto Y, Suzuki N, Hino R, Shamoto E. Dynamic finite element analysis of contact stress in CMP process. J Jpn Soc Precis Eng 2011;77/5:513–9. [11] Suzuki N, Asaba M, Hashimoto Y, Shamoto E. Identification of nonlinear viscoelasticity of polishing pad using an on-machine compression tester. In: Proceedings of ICPT 2012 - international conference on planarization/CMP technology; 2012. [12] Hashimoto Y, Suzuki N, Asaba M, Hino R, Shamoto E. Elasto hydrodynamic lubrication analysis of CMP process with consideration of micro asperity contact of polishing pad. J Jpn Soc Precis Eng 2013;79/1:73–80. [13] Fukuda A, Fukuda T, Fukunaga A, Tsujimura M. Influence of wafer edge geometry on removal rate profile in chemical mechanical polishing: wafer edge roll-off and notch. Jpn J Appl Phys 2012;51(5):05EF01. [14] Ship-Peng L, Yeou-Yih L, Jen-Ching H. Analysis of retaining ring using finite element simulation in chemical mechanical polishing process. Int J Adv Manuf Technol 2007;34:547–55. [15] Suzuki N, Hashimoto Y, Yasuda H, Yamaki S, Mochizuki Y. Prediction of polishing pressure distribution in CMP process with airbag type wafer carrier. CIRP Ann. 2017;66/1:329–32. [16] Preston FW. The theory and design of plate glass polishing machines. J Soc Glass Technol 1927;11:214–56. [17] Mark AV. The uniform motion of rectangular and parabolic punches in a viscoelastic layer. J Appl Math Mech 2008;72/4:492–8. [18] Alexandrov VM, Mark AV. Constant velocity motion of a strip die on the boundary of a viscoelastic base. Mech Solids 2009;44/1:114–21. [19] Stepanov F, Torskaya EV. Modeling of sliding of a smooth indenter over a viscoelastic layer coupled with a rigid base. Mech Solids 2018;53/1:60–7. [20] Christensen RM. Theory of viscoelasticity. Academic Press; 1971. [21] Schapery RA. On a thermodynamic constitutive theory and its application to various nonlinear materials. Thermoinelasticity; 1970. p. 259–85. [22] Schapery RA. Nonlinear viscoelastic solids. Int J Solids Struct 2000;37:359–66.
Fig. 20. Calculated wafer settlement and measured surface profiles near the wafer edge.
lower polishing pad was calculated under each DSP conditions. Fig. 20 (a) shows the changes in the average of calculated settlement of all wafers with time. The time average during 100 s under DSP Conditions C and D were 30 μm and 37 μm, respectively. These results indicate that DSP Condition C can effectively reduce the wafer settlement into the lower polishing pad. As shown in the measured profiles of lower surface near the wafer edge after polishing (Fig. 20(b)), DSP Condition C resulted in less ERO compared to DSP Condition D. The average ROA of all wafers after polishing under Conditions C and D were 370 nm and 450 nm, respec tively. The results confirmed the effectiveness of the proposed ap proaches in reducing ERO. 6. Conclusions To improve surface flatness near the wafer edge during silicon wafer polishing, effects of the viscoelastic behavior of polishing pads on ERO were investigated. First, we investigated the effects of the viscoelastic behavior of polishing pads on contact stress concentration occurred at the wafer edge, resulting in ERO. On the basis of the analytical and experimental investigation, we found that ERO negligibly depends on the viscoelastic property of the polishing pad under the typical polishing
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