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Subsurface crack damage in silicon wafers induced by resin bonded diamond wire sawing
Materials Science in Semiconductor Processing 57 (2017) 147–156
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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Subsurface crack damage in silicon wafers induced by resin bonded diamond wire sawing
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Tengyun Liua, Peiqi Gea,b, , Wenbo Bia,b, Yufei Gaoa,b a b
School of Mechanical Engineering, Shandong University, Jinan 250061, China Key Laboratory of High-Efficiency and Clean Mechanical Manufacture at Shandong University, Ministry of Education, Jinan 250061, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Resin bonded diamond wire saw Silicon wafer Subsurface crack damage
In order to optimize the process of wire sawing, this work studied the subsurface crack damage in silicon wafers induced by resin bonded diamond wire sawing using theoretical and experimental methods. A novel mathematical relationship between subsurface crack damage depth and processing parameters was established according to the indentation fracture mechanics. Sawing experiment using resin bonded diamond wire saw was performed on a wire saw machine. The validity of the proposed model was conducted by comparing with the experimental results. At last, the influences of processing parameters on subsurface damage depth were discussed. Results indicate that the median cracks are mainly oblique cracks which generate the subsurface crack damage. On the diamond wire saw cross section, the abrasives with the position angle 78° between abrasive position and vertical direction generate the largest subsurface damage depth. Furthermore, abrasives, generating the subsurface damage, tend away from the bottom of diamond wire with the increase of wire speed or decreases with the increase of feed rate. However, the wire speed and feed rate have opposite effects on the subsurface crack damage depth. In addition, the subsurface crack damage depth is unchanged when the ratio of feed rate and wire speed does not change.
1. Introduction Wire sawing is the first step in silicon ingot processing, which accounts for a large proportion of the total cost of silicon wafer manufacturing. To reduce the cost of wire sawing, resin bonded diamond wire saw is developed and considered as a novel slicing technique. Compared with slurry wire saw, the resin bonded diamond wire saw has the advantages of higher cutting efficiency, lower machining cost, and higher cutting quality. However, subsurface damage (SSD) is unavoidable during wire sawing, including microcrack, amorphous layer, residual stress, dislocation, and other types of damage. Hed et al. [1] first developed the subsurface damage model for optical material as shown in Fig. 1, which was often used in the studies of subsurface damage for silicon wafers induced by wire sawing. SSD may impact on the function of silicon wafer in three major aspects: mechanical property, optical property, and electronic property. SSD deteriorates the mechanical property of silicon wafer, reduces the fracture strength, provides sites for light-absorbing contaminants to reside, causes atoms at or near fracture surfaces to be more easily ionizable (by changing the chemical or electronic environment), and/or modulates locally the electromagnetic field [2]. Therefore, the SSD
⁎
must be eliminated in order to improve the property of silicon wafer. The material removal mechanisms for slurry wire saw and fixed diamond wire saw are dissimilar, which results in the different types of subsurface crack damage in silicon wafers sawn by these two techniques. Funke et al. [3] observed the crack damage in silicon wafers sawn by slurry wire saw. They found out that the distribution of crack location was random. Moreover, these crack depths decreased gradually along the direction from wire inlet to wire outlet. However, Würzner et al. [4] revealed that cracks distributed along the direction of sawing grooves and appeared periodically in silicon wafers sawn by fixed diamond wire saw. A further difference found by Möller [5] was that the amorphous layer appeared locally on the wafer surface sawn by fixed diamond wire saw. Kang et al. [6] compared the subsurface crack damage depth of these two kinds of silicon wafers. They inferred that the quality of silicon wafer sawn by fixed diamond wire saw was superior to that sawn by slurry wire saw. Furthermore, the subsurface crack depth induced by slurry wire sawing was larger than that induced by fixed diamond wire sawing. In addition, Watanabe et al. [7] showed the similar conclusion via experiment and argued that the resin bonded diamond wire saw was suited for the fabrication of ultra-thin silicon wafers.
Corresponding author at: School of Mechanical Engineering, Shandong University, Jinan 250061, China. E-mail addresses: [email protected] (T. Liu), [email protected] (P. Ge), [email protected] (W. Bi), [email protected] (Y. Gao).
http://dx.doi.org/10.1016/j.mssp.2016.10.021 Received 19 May 2016; Received in revised form 18 September 2016; Accepted 12 October 2016 1369-8001/ © 2016 Elsevier Ltd. All rights reserved.
Materials Science in Semiconductor Processing 57 (2017) 147–156
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Fig. 1. Schematic of subsurface damage for optical material [1].
2. Model of subsurface crack depth
Many factors influence the subsurface crack damage depth during wire sawing, such as the feed rate of the workpiece, wire speed, slicing orientation, abrasive size, etc. Sopori et al. [8] researched the effects of various processing parameters on the subsurface damage. They found out that the subsurface crack depth mainly depended on the feed rate, wire speed and abrasive size. Würzner et al. [4] investigated the effect of wire speed on the surface damage for silicon wafers sawn by fixed diamond wire saw. Their results indicated that the maximum crack length decreased when wire speed increased. Teomete [9] found out that the subsurface crack depth increased with the increase of feed rate, and increased as the wire speed decreased. However, it was unchanged when the feed rate and wire speed increased or decreased proportionally. These conclusions show that a smaller subsurface crack damage depth and a higher material removal rate can be obtained through increasing feed rate and wire speed proportionally. A large number of empirical and semi-empirical relationships between subsurface crack damage depth and surface roughness have been established according to the experimental results of machining optical materials. Preston [10] firstly found out that the subsurface crack damage depth was two or three times of the surface roughness for ground surface. After that, Lambropoulos et al. [11] obtained a linear relationship with a proportional coefficient between subsurface crack depth and surface roughness. Gao et al. [12] developed a nonlinear theoretical model for these two machining damages according to the Lambropoulos's model. However, it is still difficult to predict the crack damage depth directly when processing parameters are known using the above method. Hence, a novel mathematical relationship between subsurface crack damage depth and processing parameters was proposed on the basis of indentation fracture mechanics in this paper. The validity of this model was conducted by comparing with the experimental results obtained through the bonded interface section technique and SEM. This proposed model can be used to evaluate the subsurface crack damage depth in a quick, accurate and no destructive way, which is benefit to optimize wire sawing process, reduce processing cost, and lower the probability of wafer fracture in latter machining process.
2.1. Crack system in resin bonded diamond wire sawing The process of resin bonded diamond wire sawing is shown in Fig. 2. The wire and workpiece move along two perpendicular directions with the speeds vs and vf respectively. Abrasives, forced normal force P and tangential force Q, make the motion of sliding and plowing on the workpiece surface to achieve the material removal, which is similar to the scratching of moving indenter, as shown in Fig. 3. Brittle fracture behavior is considered as the main way of material removal during wire sawing. Crack is formed by the tensile and shear stress which are the result of interaction between indenter and material during scratching. The moving indentation usually involves two primary cracks: lateral crack and median crack. There are normal force P and tangential force Q acting on the sharp indenter which taper angle is 2α. A plastic zone and crack system will emerge when the normal force exceeds a certain value. The indentation is surrounded by a nearly hemispherical plastic zone under which contains median crack and lateral crack propagating toward to subsurface and surface respectively. In the following analysis, the depth of median crack is defined as the subsurface damage depth (SSD). Experimental results of scratching process indicate that the lateral crack depth is approximately to the plastic zone size. According to the study of Lambropoulos et al. [13], the lateral crack depth can be expressed as the size of the plastic zone:
Cli = bi = 0.43(sin α )1/2 (cos α )1/3(
E 1/2 P 1/2 ) ( ) H H
(1)
where Cli is the lateral crack depth; bi is the plastic zone size; α is the half taper angle of indenter; E is the elastic modulus of single crystal silicon; H is the hardness of single crystal silicon; P is the normal force on diamond abrasive. According to the study of Lawn et al. [14], the theoretical depth of median crack can be expressed as:
Fig. 2. Resin bonded diamond wire sawing.
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Fig. 3. Crack system in scratching motion. 2/3 ⎡⎡ ⎛ ⎞1/2 ⎤ P ⎤ XeM 2/3 E ⎥ ⎢ ⎥ ⎢ Cmi = (1 + M ) × (cot α ) ⎜ ⎟ ⎢⎢⎣ ⎝ H ⎠ ⎥⎦ KIC ⎥⎦ Xr ⎣
XeM
damage depth is obtained through subtracting the effective radius of wire R from the maximum projection length of the line OBi projecting along the direction OA. Hence, the subsurface crack damage depth (SSD) is obtained by:
(2)
M
where and Xr are indentation coefficients of the elastic stress field and plastic stress field, which are 0.032 and 0.026 respectively. KIC is the fracture toughness of single crystal silicon.
SSD = max [OBi sin θi − R]
(3)
where R is the effective radius of diamond wire which is the sum of abrasive size and radius of core wire; θi is the position angle of abrasive. The length of line OBi is given by:
2.2. Subsurface crack damage depth
OBi = R + Cmi
Abrasives distribute randomly on one arbitrary wire cross section, as shown in Fig. 4. Based on the study of Chung C, abrasives on the bottom of the wire cross section mainly contribute to the material removal. Yet, the abrasives on the two sides are used to generate the wafer surface [15]. Abrasives in ductile cutting mode are neglected because there is no crack generated. Median cracks appear when the material removal mode of abrasives is brittle cutting mode. Some of these median cracks, generated under the bottom of kerf, may be removed later, while others may penetrate into the sliced surface forming subsurface damage. Under this condition, the whole kerf surface is considered, which is regarded as semicircle, as shown in Fig. 4. Therefore, the median crack depth is considered as the subsurface damage depth. The subsurface crack damage depth is abbreviated as SSD in the latter. In Fig. 4, the origin point O is set on the center of wire; the position angle of abrasive on wire cross section is θi; and the blue dashed line is defined as the sliced surface of silicon wafers. The subsurface crack
(4)
When the indention depth of abrasive is hi, the needed normal force is:
P=
1 πHhi2(tan α )2 2
(5)
Hence the median crack depth Eq. (2) is rewritten to: 2/3 1 2 2 ⎡⎡ ⎛ E ⎞1/2 ⎤ πHhi (tan α ) ⎤⎥ XM Cmi = ⎢⎢(1 + eM ) × (cot α )2/3⎜ ⎟ ⎥ 2 ⎥ ⎢⎢⎣ ⎝ H ⎠ ⎥⎦ KIC Xr ⎦ ⎣
(6)
Eq. (6) can be simplified to:
Cmi = χhi4/3
(7)
where χ is a proportionality coefficient relating to material property and indenter shape, that is:
Fig. 4. Subsurface crack damage in wafers during wire sawing. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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T. Liu et al. 2/3 1 2 ⎡⎡ ⎛ E ⎞1/2 ⎤ πH (tan α ) ⎤⎥ XM χ = ⎢⎢(1 + eM ) × (cot α )2/3⎜ ⎟ ⎥ 2 ⎥ ⎢⎢⎣ ⎝ H ⎠ ⎥⎦ KIC Xr ⎦ ⎣
range of 57–90° plays a dominated role on the subsurface crack damage compared to the abrasives in the position angle range of 0– 57°. The value of function f(θi) reaches maximum when the position angle of abrasive is 78°, indicating that the deepest subsurface crack damage is caused by the abrasives with this position angle. It is worth noting that the variable θi is assumed as a continuous variable. The length of wire used slicing is extremely large compared with the abrasive size in practice. Even though there is no abrasive on the ith wire cross section with position angle θi, an abrasive grit will be located on the (i+k)th wire cross section with the same position angle. Therefore, this assumption is reasonable.
(8)
Therefore, the SSD is described by combining the Eqs. (3) and (7):
SSD = max [(R + χhi 2/3)sin θi − R]
(9)
The SSD can be regarded as a maximum value of one function with the variable θi which is:
f (θi ) = (R + χhi 2/3)sin θi − R
(10)
The indentation depth of abrasives is obtained according to the study of Gao and Ge [16]:
⎡ ⎤4/9 10−27/8(0.3KIC )1/2 H3/8vf ⎢ hi = cos θi ⎥ ⎢⎣ 0.43π 3/4ε 5/8αnα03/8(tan α )23/12(sin α )1/2E7/8Nsvs ⎥⎦
3. Experiment 3.1. Experimental setup
(11) The experiment was performed on a reciprocating diamond wire saw machine which type is WXD170. Its principle is shown in Fig. 6. This machine is a kind of single-wire sawing setup, including one wire spool, one tension wheel, one idler, and two work idler wheels. The resin bonded diamond wire with length 100 m was twined around the spool, and both ends were fixed to the two sides of the spool. The wire was tensioned by the tension wheel and three idler wheels, and drove by the wire spool which made a mixing movement concluding a reciprocal motion and an axial motion according to a certain transmission ratio. The workpiece fixed to the workbench was fed along the direction that is perpendicular to the wire moving direction. The technique index of this machine is given in Table 1. The diameter of the resin bonded diamond wire saw used in this experiment is 120 µm. The abrasive size is in the range of 8–16 µm. The morphology of this kind of wire saw is shown in Fig. 7. The density of abrasive on this wire was obtained through SEM picture, which is about 450 grits/mm2.
where ε is the tangential load coefficient, ε=1.1; αn is an indentation coefficient relating to the grit shape, αn=0.12; α0 is a dimensionless constant relating to the penetrator shape, and for Vickers hardness penetrator α0=2; α is the half tape angle of abrasive; KIC is the fracture toughness of single crystal silicon; H is the hardness of single crystal silicon; vf is the feed rate; E is the elasticity modulus of single crystal silicon; Ns is the dynamic effective abrasives; vs is the wire speed. Therefore, the Eq. (11) can be simplified to:
hi = γ (
vf vs
4
cos θi )9
(12)
where γ is the proportionality coefficient related to material property and indenter shape. Combining Eqs. (10) and (12), the function f(θi) with the variable θi is:
f (θi ) = [R + χγ (
vf vs
8
cos θi )27 ] sin θi − R XeM
(13)
M
and Xr are 0.032 and 0.026 respectively; the Generally, the half tip angle of abrasive α is 50°; the elasticity modulus of silicon is E=183 GPa; the hardness of silicon H=10 GPa; the fracture toughness of silicon is KIC=0.82 MPa m1/2; The parameters from Ref. [16] were applied to preliminary analysis. The outer radius of diamond wire is R=140 µm. The density of abrasives on wire is Ns=396/mm2. The feed rate vf is 5 µm/s, and the wire speed is 2 m/s respectively. The curve of the function f(θi) is shown in Fig. 5 with the change of variable θi whose interval is [0,90°]. From Fig. 5, it can be seen that the value of function f(θi) firstly increases then decreases with the increase of position angle θi. Abrasives on different positions of wire cross section have different effects on the subsurface crack damage. Abrasives in the position angle
3.2. Processing parameters The feed rate is usually in the range of 6–9 µm/s during slurry wire sawing in industry. While in this experiment, the maximum feed rate and wire speed were taken 12.5 µm/s and 1.5 m/s respectively for the stationary of slicing process under the consideration of the device parameters. 5 groups of slicing experiments were done according to the processing parameters in Table 2. The direction 〈001〉 of the workpiece was selected as the slicing direction on the basis of the optimum cleavage direction of (100) silicon wafer. The wire tension was 10 N considering the vibration and strength of wire. Water was used as the coolant.
Fig. 5. The variation curve of f(θi) with position angle θi.
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Fig. 6. The principle of the reciprocating diamond wire saw machine.
Table 1 Technique index of the reciprocating diamond wire saw machine. Length of wire (m)
Diameter of wire (mm)
Wire speed (m/s)
Feed rate (mm/min)
Wire tension (MPa)
20–200
0.2–0.6
0–3
0.005–18
0–0.6
Fig. 7. The morphology of resin bonded diamond wire saw.
Table 2 Processing parameters used in experiment. No.
Wire speed (m/s)
Feed rate (μm/s)
1 2 3 4 5
0.8 1.0 1.0 1.2 1.5
6.25 8.33 12.5 12.5 12.5
tightly, as shown in Fig. 8. After slicing, the acetone was used to melt the adhesive, following of which the two samples were separated. Then, they were cleaned with deionized water in ultrasonic cleaners at least 10 min. At last the polished surface was used to SEM examination. The average value of five subsurface crack damage depths measured on different positions of the polished surface was considered as the final damage depth for each slicing.
3.3. The measurement of subsurface crack damage depth In this paper, the bonded interface sectioning technique was used to evaluate the subsurface crack damage according to the study of Agarwal and Rao [17]. According to this method, two (100) wafers, 50 mm in diameter and 3 mm in thickness, were used. Both specimens had one polished surface which was bonded together with adhesive. Then, one clump weight was applied in order to push them together 151
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Fig. 8. The procedure of the experiment. (a) Fist step: bonding two wafers. (b) The second step: diamond wire sawing. (c) The third step: SSD depth measurement.
4. Results and discussion
the median crack to be inclined to extend this plane.
4.1. Morphology of subsurface damage
4.2. Comparison of theoretical and experimental results
The morphology of subsurface crack damage can be seen clearly in Fig. 9. The chipping and crack are the primary damage by using the bonded interface sectioning technique to evaluate the subsurface damage. From these figures, it is found that the median cracks are oblique crack. Besides that, some lateral cracks do not extend to the sliced surface, leading to crack criss-crossing, as shown in Fig. 9(b). In this experiment, we used the (100) silicon wafers as slicing sample. The anisotropy of silicon and the force condition on abrasive can be adopted to explain the oblique cracks. The moving abrasives are exerted the normal force and tangential force during wire sawing. These forces change the stress field in front and back of moving abrasives, altering the length and direction for median crack propagation. On the other hand, the optimum cleavage plane of silicon induces
The same processing parameters to experimental parameters are taken for theoretical calculation. Besides that, the material parameters of silicon were taken according to the (100) silicon wafer. The diameter of wire is 120 µm; the density of abrasives on wire is 450 grits per square millimeter; and the half tip angle of abrasive is 50°. The experimental and theoretical results of the subsurface crack damage (SSD) depths are shown in Table 3. These two results are comparable from Table 3 and the error is reasonable, demonstrating the validity of the proposed model. The experimental results are smaller than the theoretical results because the median cracks are oblique cracks in practice which is not considered in the model. The maximum relative error is 11.6% which could be considered as reasonable, indicating the validity of this established model.
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Fig. 9. The morphology of subsurface damage of sliced wafer. (a) The median crack and chipping. (b) The lateral crack and chipping. (c) The median crack and half penny chipping.
moves down integrally with the increase of wire speed, that is to say the maximum value of function f(θi) has a lowering trend. But the variable value θi for maximum of function values is unchanged. Besides, the down trend of function f(θi) becomes slowly with the increase of wire speed. The position angle θi of abrasive affecting the subsurface crack damage increases with the increase of wire speed. From Fig. 11, it can be seen that the SSD has the same variation trend to the function f(θi) with the increase of wire speed. During wire sawing, the crack propagation depends on the normal force and tangential force applied to the abrasives. The smaller force is, the
4.3. Influence of processing parameters on subsurface crack damage depth The main factors influencing subsurface crack damage depth are wire speed and feed rate during wire sawing. In this paper, the effects of these two factors are analyzed by the function f(θi). Ten wire speeds from 1 m/s to 10 m/s were taken. The feed rate was kept at 5 µm/s, and other parameters were kept unchanged. Under this condition, the changes of function f(θi) and the subsurface crack damage depth (SSD) are shown in Figs. 10 and 11. The function f(θi) 153
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Table 3 Results of SSD depths from theoretical model and experiment. No.
Wire speed vs (m/s)
Feed rate vf (μm/ s)
Theoretical SSD (μm)
Experimental SSD (μm)
Relative error
1 2 3 4 5
0.8 1.0 1.0 1.2 1.5
6.25 8.33 12.5 12.5 12.5
28.7 29.3 33.4 31.5 29.3
26.48 26.82 29.53 27.95 27.39
7.7% 8.5% 11.6% 11.3% 6.5%
Fig. 10. The different curves for f(θi) with various wire speeds.
Fig. 11. The change of SSD with wire speed.
subsurface crack damage decreases with the increase of feed rate. The mode of material removal for diamond abrasives changes with the change of processing parameters. Based on the study of Chung and Le [18], increasing wire speed or decreasing feed rate increases significantly the number of ductile cutting abrasives, which generates smoother slicing surface and shallower subsurface crack damage. But a larger wire speed causes excessive vibration of wire, which results in deteriorating the wafer surface. Increasing the feed rate will increase the cutting force and the material removal rate. Based on the proposed model, increasing or decreasing feed rate and wire speed proportionally will not affect the SSD in theory. From the experimental results and theoretical results, as shown in Fig. 14, increasing the feed rate and wire speed proportional has less effect on the SSD depth. That is to say,
smaller indentation depth and SSD will get. The number of abrasives taking part in removing material increases in unit time with the increase of wire speed. This results in the reduction of the normal force and SSD. Analyzing the effect of feed rate on the SSD in the same way, ten feed rates were taken from 1 µm/s to 10 µm/s, and the wire speed was taken 2 m/s. The cures of function f(θi) and the SSD with different feed rates are shown in Fig. 12 and 13 respectively. It can be seen that, the feed rate has an opposite effect compares with wire speed. The SSD increases with the increasing the feed rate, and the function f(θi) has the similar trend with the SSD. Increasing feed rate will increase the normal force and lead to a larger indention depth and median crack depth. Furthermore, the position angle θi of abrasive affecting the 154
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Fig. 12. The different curves for f(θi) with various feed rates.
Fig. 13. The change of SSD with feed rate.
Fig. 14. The change of SSD depth with the ratio of feed rate and wire speed.
it is possible to increase the processing efficiency and keep the smaller SSD depth simultaneously, which is very beneficial during diamond wire sawing.
5. Conclusion In this paper, the subsurface crack damage depth for single crystal silicon wafers sawn with resin bonded diamond wire saw was studied in 155
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[2] D.W. Camp, M.R. Kozlowski, et al., Subsurface damage and polishing compound affect the 355-nm laser damage threshold of fused silica surfaces, Laser-Induced Damage in Optical Materials International Society for Optics and Photonics, 1998, pp. 356–364 [3] C. Funke, O. Sciurova, O. Kiriyenko, H.J. Möller, Surface damage from multi-wire sawing and mechanical properties of silicon wafers, in: Proceedings of the 20th European Photovoltaic Solar Energy Conference, 2005, pp. 6–10. [4] S. Würzner, A. Falke, R. Buchwald, H.J. Möller, Determination of the impact of the wire velocity on the surface damage of diamond wire sawn silicon wafers, Energy Procedia 77 (2015) 881–890. [5] H.J. Möller, Wafering of silicon, Semicond. Semimet. 92 (2015) 63–109. [6] R.K. Kang, Y.F. Zeng, S. Gao, Z.G. Dong, D.M. Guo, Surface layer damage of silicon wafers sliced by wire saw process, Adv. Mater. Res. 797 (2013) 685–690. [7] N. Watanabe, Y. Kondo, D. Ide, T. Matsuki, H. Takato, I. Sakata, Characterization of polycrystalline silicon wafers for solar cells sliced with novel fixed-abrasive wire, Prog. Photovolt.: Res. Appl. 18 (7) (2010) 485–490. [8] B. Sopori, P. Basnyat, S. Devayajanam, et al., Analyses of diamond wire sawn wafers: effect of various cutting parameters, in: Proceedings of the 42th IEEE Photovoltaic Specialists Conference (PVSC), 2015, pp. 1–6. [9] E. Teomete, Wire saw process-induced surface damage characterization, Arab. J. Sci. Eng. 38 (5) (2013) 1209–1215. [10] F.W. Preston, The structure of abraded glass surfaces, Trans. Opt. Soc. 23 (3) (1922) 141–164. [11] J.C. Lambropoulos, S.D. Jacobs, B. Gillman, F. Yang, J. Ruckman, Subsurface damage in microgrinding optical glasses, LLE Rev. 73 (1997) 45–49. [12] Y.F. Gao, P.Q. Ge, S.J. Li, Investigation of subsurface damage depth of single crystal silicon in electroplated wire saw slicing, Key Eng. Mater. 416 (2009) 306–310. [13] J.C. Lambropoulos, S.D. Jacobs, J. Ruckman, Material removal mechanisms from grinding to polishing, Ceram. Trans. 102 (1999) 113–128. [14] B.R. Lawn, A.G. Evans, D.B. Marshall, Elastic/plastic indentation damage in ceramics: the median/radial crack system, J. Am. Ceram. Soc. 63 (9–10) (1980) 574–581. [15] C.H. Chung, Generation of diamond wire sliced wafer surface based on the distribution of diamond grits, Int. J. Precis. Eng. Manuf. 15 (5) (2014) 789–796. [16] Y.F. Gao, P.Q. Ge, Analysis of grit cut depth in fixed-abrasive diamond wire saw slicing single crystal silicon, Solid State Phenom. 175 (2011) 72–76. [17] S. Agarwal, P.V. Rao, Experimental investigation of surface/subsurface damage formation and material removal mechanisms in SiC grinding, Int. J. Mach. Tool Manuf. 48 (6) (2008) 698–710. [18] C.H. Chung, V.N. Le, Depth of cut per abrasive in fixed diamond wire sawing, Int. J. Manuf. Technol. 80 (5–8) (2015) 1337–1346.
theory and experiment. A novel mathematical relationship between the subsurface crack damage depth and processing parameters was proposed on the basis of indentation fracture mechanics. The validity of this proposed model was proved by the bonded interface sectioning technique. This model can be used to predict the subsurface crack damage depth and optimize the processing parameters. The detailed conclusions are as follows: (1) The position of abrasive which generates the largest subsurface crack damage depth is unchanged when the parameters of wire are decided. Furthermore, the minimum angle of abrasive position larger than that the abrasives have effect on the subsurface crack damage increases with the increase of wire speed and decreases with the increase of feed rate. (2) The median cracks are mainly oblique crack. Some lateral cracks do not extend to sliced wafer surface and become one type of damage with median crack. (3) The proposed mathematical model is comparable with the experimental results. The maximum relative error is 11.6% which could be considered reasonable. (4) Feed rate and wire speed have different effects on the subsurface crack damage depth. The damage depth will decrease with the increase of wire speed and decrease of the feed rate. Increasing proportionally the feed rate and wire speed will lead to a larger material removal rate with the subsurface crack damage depth unchanged. Acknowledgement This work is supported by Shandong Provincial Natural Science Foundation of China (ZR2014EEM034) and National Natural Science Foundation of China (Nos. 51075240 and 51205234). References [1] P.P. Hed, D.F. Edwards, J.B. Davis, Subsurface Damage in Optical Materials: Origin, Measurement and Removal, Lawrence Livermore National Laboratory (LLNL) Report, 1989, pp. 1–17
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Subsurface crack damage in silicon wafers induced by resin bonded diamond wire sawing
crossmark
⁎
Tengyun Liua, Peiqi Gea,b, , Wenbo Bia,b, Yufei Gaoa,b a b
School of Mechanical Engineering, Shandong University, Jinan 250061, China Key Laboratory of High-Efficiency and Clean Mechanical Manufacture at Shandong University, Ministry of Education, Jinan 250061, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Resin bonded diamond wire saw Silicon wafer Subsurface crack damage
In order to optimize the process of wire sawing, this work studied the subsurface crack damage in silicon wafers induced by resin bonded diamond wire sawing using theoretical and experimental methods. A novel mathematical relationship between subsurface crack damage depth and processing parameters was established according to the indentation fracture mechanics. Sawing experiment using resin bonded diamond wire saw was performed on a wire saw machine. The validity of the proposed model was conducted by comparing with the experimental results. At last, the influences of processing parameters on subsurface damage depth were discussed. Results indicate that the median cracks are mainly oblique cracks which generate the subsurface crack damage. On the diamond wire saw cross section, the abrasives with the position angle 78° between abrasive position and vertical direction generate the largest subsurface damage depth. Furthermore, abrasives, generating the subsurface damage, tend away from the bottom of diamond wire with the increase of wire speed or decreases with the increase of feed rate. However, the wire speed and feed rate have opposite effects on the subsurface crack damage depth. In addition, the subsurface crack damage depth is unchanged when the ratio of feed rate and wire speed does not change.
1. Introduction Wire sawing is the first step in silicon ingot processing, which accounts for a large proportion of the total cost of silicon wafer manufacturing. To reduce the cost of wire sawing, resin bonded diamond wire saw is developed and considered as a novel slicing technique. Compared with slurry wire saw, the resin bonded diamond wire saw has the advantages of higher cutting efficiency, lower machining cost, and higher cutting quality. However, subsurface damage (SSD) is unavoidable during wire sawing, including microcrack, amorphous layer, residual stress, dislocation, and other types of damage. Hed et al. [1] first developed the subsurface damage model for optical material as shown in Fig. 1, which was often used in the studies of subsurface damage for silicon wafers induced by wire sawing. SSD may impact on the function of silicon wafer in three major aspects: mechanical property, optical property, and electronic property. SSD deteriorates the mechanical property of silicon wafer, reduces the fracture strength, provides sites for light-absorbing contaminants to reside, causes atoms at or near fracture surfaces to be more easily ionizable (by changing the chemical or electronic environment), and/or modulates locally the electromagnetic field [2]. Therefore, the SSD
⁎
must be eliminated in order to improve the property of silicon wafer. The material removal mechanisms for slurry wire saw and fixed diamond wire saw are dissimilar, which results in the different types of subsurface crack damage in silicon wafers sawn by these two techniques. Funke et al. [3] observed the crack damage in silicon wafers sawn by slurry wire saw. They found out that the distribution of crack location was random. Moreover, these crack depths decreased gradually along the direction from wire inlet to wire outlet. However, Würzner et al. [4] revealed that cracks distributed along the direction of sawing grooves and appeared periodically in silicon wafers sawn by fixed diamond wire saw. A further difference found by Möller [5] was that the amorphous layer appeared locally on the wafer surface sawn by fixed diamond wire saw. Kang et al. [6] compared the subsurface crack damage depth of these two kinds of silicon wafers. They inferred that the quality of silicon wafer sawn by fixed diamond wire saw was superior to that sawn by slurry wire saw. Furthermore, the subsurface crack depth induced by slurry wire sawing was larger than that induced by fixed diamond wire sawing. In addition, Watanabe et al. [7] showed the similar conclusion via experiment and argued that the resin bonded diamond wire saw was suited for the fabrication of ultra-thin silicon wafers.
Corresponding author at: School of Mechanical Engineering, Shandong University, Jinan 250061, China. E-mail addresses: [email protected] (T. Liu), [email protected] (P. Ge), [email protected] (W. Bi), [email protected] (Y. Gao).
http://dx.doi.org/10.1016/j.mssp.2016.10.021 Received 19 May 2016; Received in revised form 18 September 2016; Accepted 12 October 2016 1369-8001/ © 2016 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic of subsurface damage for optical material [1].
2. Model of subsurface crack depth
Many factors influence the subsurface crack damage depth during wire sawing, such as the feed rate of the workpiece, wire speed, slicing orientation, abrasive size, etc. Sopori et al. [8] researched the effects of various processing parameters on the subsurface damage. They found out that the subsurface crack depth mainly depended on the feed rate, wire speed and abrasive size. Würzner et al. [4] investigated the effect of wire speed on the surface damage for silicon wafers sawn by fixed diamond wire saw. Their results indicated that the maximum crack length decreased when wire speed increased. Teomete [9] found out that the subsurface crack depth increased with the increase of feed rate, and increased as the wire speed decreased. However, it was unchanged when the feed rate and wire speed increased or decreased proportionally. These conclusions show that a smaller subsurface crack damage depth and a higher material removal rate can be obtained through increasing feed rate and wire speed proportionally. A large number of empirical and semi-empirical relationships between subsurface crack damage depth and surface roughness have been established according to the experimental results of machining optical materials. Preston [10] firstly found out that the subsurface crack damage depth was two or three times of the surface roughness for ground surface. After that, Lambropoulos et al. [11] obtained a linear relationship with a proportional coefficient between subsurface crack depth and surface roughness. Gao et al. [12] developed a nonlinear theoretical model for these two machining damages according to the Lambropoulos's model. However, it is still difficult to predict the crack damage depth directly when processing parameters are known using the above method. Hence, a novel mathematical relationship between subsurface crack damage depth and processing parameters was proposed on the basis of indentation fracture mechanics in this paper. The validity of this model was conducted by comparing with the experimental results obtained through the bonded interface section technique and SEM. This proposed model can be used to evaluate the subsurface crack damage depth in a quick, accurate and no destructive way, which is benefit to optimize wire sawing process, reduce processing cost, and lower the probability of wafer fracture in latter machining process.
2.1. Crack system in resin bonded diamond wire sawing The process of resin bonded diamond wire sawing is shown in Fig. 2. The wire and workpiece move along two perpendicular directions with the speeds vs and vf respectively. Abrasives, forced normal force P and tangential force Q, make the motion of sliding and plowing on the workpiece surface to achieve the material removal, which is similar to the scratching of moving indenter, as shown in Fig. 3. Brittle fracture behavior is considered as the main way of material removal during wire sawing. Crack is formed by the tensile and shear stress which are the result of interaction between indenter and material during scratching. The moving indentation usually involves two primary cracks: lateral crack and median crack. There are normal force P and tangential force Q acting on the sharp indenter which taper angle is 2α. A plastic zone and crack system will emerge when the normal force exceeds a certain value. The indentation is surrounded by a nearly hemispherical plastic zone under which contains median crack and lateral crack propagating toward to subsurface and surface respectively. In the following analysis, the depth of median crack is defined as the subsurface damage depth (SSD). Experimental results of scratching process indicate that the lateral crack depth is approximately to the plastic zone size. According to the study of Lambropoulos et al. [13], the lateral crack depth can be expressed as the size of the plastic zone:
Cli = bi = 0.43(sin α )1/2 (cos α )1/3(
E 1/2 P 1/2 ) ( ) H H
(1)
where Cli is the lateral crack depth; bi is the plastic zone size; α is the half taper angle of indenter; E is the elastic modulus of single crystal silicon; H is the hardness of single crystal silicon; P is the normal force on diamond abrasive. According to the study of Lawn et al. [14], the theoretical depth of median crack can be expressed as:
Fig. 2. Resin bonded diamond wire sawing.
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Fig. 3. Crack system in scratching motion. 2/3 ⎡⎡ ⎛ ⎞1/2 ⎤ P ⎤ XeM 2/3 E ⎥ ⎢ ⎥ ⎢ Cmi = (1 + M ) × (cot α ) ⎜ ⎟ ⎢⎢⎣ ⎝ H ⎠ ⎥⎦ KIC ⎥⎦ Xr ⎣
XeM
damage depth is obtained through subtracting the effective radius of wire R from the maximum projection length of the line OBi projecting along the direction OA. Hence, the subsurface crack damage depth (SSD) is obtained by:
(2)
M
where and Xr are indentation coefficients of the elastic stress field and plastic stress field, which are 0.032 and 0.026 respectively. KIC is the fracture toughness of single crystal silicon.
SSD = max [OBi sin θi − R]
(3)
where R is the effective radius of diamond wire which is the sum of abrasive size and radius of core wire; θi is the position angle of abrasive. The length of line OBi is given by:
2.2. Subsurface crack damage depth
OBi = R + Cmi
Abrasives distribute randomly on one arbitrary wire cross section, as shown in Fig. 4. Based on the study of Chung C, abrasives on the bottom of the wire cross section mainly contribute to the material removal. Yet, the abrasives on the two sides are used to generate the wafer surface [15]. Abrasives in ductile cutting mode are neglected because there is no crack generated. Median cracks appear when the material removal mode of abrasives is brittle cutting mode. Some of these median cracks, generated under the bottom of kerf, may be removed later, while others may penetrate into the sliced surface forming subsurface damage. Under this condition, the whole kerf surface is considered, which is regarded as semicircle, as shown in Fig. 4. Therefore, the median crack depth is considered as the subsurface damage depth. The subsurface crack damage depth is abbreviated as SSD in the latter. In Fig. 4, the origin point O is set on the center of wire; the position angle of abrasive on wire cross section is θi; and the blue dashed line is defined as the sliced surface of silicon wafers. The subsurface crack
(4)
When the indention depth of abrasive is hi, the needed normal force is:
P=
1 πHhi2(tan α )2 2
(5)
Hence the median crack depth Eq. (2) is rewritten to: 2/3 1 2 2 ⎡⎡ ⎛ E ⎞1/2 ⎤ πHhi (tan α ) ⎤⎥ XM Cmi = ⎢⎢(1 + eM ) × (cot α )2/3⎜ ⎟ ⎥ 2 ⎥ ⎢⎢⎣ ⎝ H ⎠ ⎥⎦ KIC Xr ⎦ ⎣
(6)
Eq. (6) can be simplified to:
Cmi = χhi4/3
(7)
where χ is a proportionality coefficient relating to material property and indenter shape, that is:
Fig. 4. Subsurface crack damage in wafers during wire sawing. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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T. Liu et al. 2/3 1 2 ⎡⎡ ⎛ E ⎞1/2 ⎤ πH (tan α ) ⎤⎥ XM χ = ⎢⎢(1 + eM ) × (cot α )2/3⎜ ⎟ ⎥ 2 ⎥ ⎢⎢⎣ ⎝ H ⎠ ⎥⎦ KIC Xr ⎦ ⎣
range of 57–90° plays a dominated role on the subsurface crack damage compared to the abrasives in the position angle range of 0– 57°. The value of function f(θi) reaches maximum when the position angle of abrasive is 78°, indicating that the deepest subsurface crack damage is caused by the abrasives with this position angle. It is worth noting that the variable θi is assumed as a continuous variable. The length of wire used slicing is extremely large compared with the abrasive size in practice. Even though there is no abrasive on the ith wire cross section with position angle θi, an abrasive grit will be located on the (i+k)th wire cross section with the same position angle. Therefore, this assumption is reasonable.
(8)
Therefore, the SSD is described by combining the Eqs. (3) and (7):
SSD = max [(R + χhi 2/3)sin θi − R]
(9)
The SSD can be regarded as a maximum value of one function with the variable θi which is:
f (θi ) = (R + χhi 2/3)sin θi − R
(10)
The indentation depth of abrasives is obtained according to the study of Gao and Ge [16]:
⎡ ⎤4/9 10−27/8(0.3KIC )1/2 H3/8vf ⎢ hi = cos θi ⎥ ⎢⎣ 0.43π 3/4ε 5/8αnα03/8(tan α )23/12(sin α )1/2E7/8Nsvs ⎥⎦
3. Experiment 3.1. Experimental setup
(11) The experiment was performed on a reciprocating diamond wire saw machine which type is WXD170. Its principle is shown in Fig. 6. This machine is a kind of single-wire sawing setup, including one wire spool, one tension wheel, one idler, and two work idler wheels. The resin bonded diamond wire with length 100 m was twined around the spool, and both ends were fixed to the two sides of the spool. The wire was tensioned by the tension wheel and three idler wheels, and drove by the wire spool which made a mixing movement concluding a reciprocal motion and an axial motion according to a certain transmission ratio. The workpiece fixed to the workbench was fed along the direction that is perpendicular to the wire moving direction. The technique index of this machine is given in Table 1. The diameter of the resin bonded diamond wire saw used in this experiment is 120 µm. The abrasive size is in the range of 8–16 µm. The morphology of this kind of wire saw is shown in Fig. 7. The density of abrasive on this wire was obtained through SEM picture, which is about 450 grits/mm2.
where ε is the tangential load coefficient, ε=1.1; αn is an indentation coefficient relating to the grit shape, αn=0.12; α0 is a dimensionless constant relating to the penetrator shape, and for Vickers hardness penetrator α0=2; α is the half tape angle of abrasive; KIC is the fracture toughness of single crystal silicon; H is the hardness of single crystal silicon; vf is the feed rate; E is the elasticity modulus of single crystal silicon; Ns is the dynamic effective abrasives; vs is the wire speed. Therefore, the Eq. (11) can be simplified to:
hi = γ (
vf vs
4
cos θi )9
(12)
where γ is the proportionality coefficient related to material property and indenter shape. Combining Eqs. (10) and (12), the function f(θi) with the variable θi is:
f (θi ) = [R + χγ (
vf vs
8
cos θi )27 ] sin θi − R XeM
(13)
M
and Xr are 0.032 and 0.026 respectively; the Generally, the half tip angle of abrasive α is 50°; the elasticity modulus of silicon is E=183 GPa; the hardness of silicon H=10 GPa; the fracture toughness of silicon is KIC=0.82 MPa m1/2; The parameters from Ref. [16] were applied to preliminary analysis. The outer radius of diamond wire is R=140 µm. The density of abrasives on wire is Ns=396/mm2. The feed rate vf is 5 µm/s, and the wire speed is 2 m/s respectively. The curve of the function f(θi) is shown in Fig. 5 with the change of variable θi whose interval is [0,90°]. From Fig. 5, it can be seen that the value of function f(θi) firstly increases then decreases with the increase of position angle θi. Abrasives on different positions of wire cross section have different effects on the subsurface crack damage. Abrasives in the position angle
3.2. Processing parameters The feed rate is usually in the range of 6–9 µm/s during slurry wire sawing in industry. While in this experiment, the maximum feed rate and wire speed were taken 12.5 µm/s and 1.5 m/s respectively for the stationary of slicing process under the consideration of the device parameters. 5 groups of slicing experiments were done according to the processing parameters in Table 2. The direction 〈001〉 of the workpiece was selected as the slicing direction on the basis of the optimum cleavage direction of (100) silicon wafer. The wire tension was 10 N considering the vibration and strength of wire. Water was used as the coolant.
Fig. 5. The variation curve of f(θi) with position angle θi.
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Fig. 6. The principle of the reciprocating diamond wire saw machine.
Table 1 Technique index of the reciprocating diamond wire saw machine. Length of wire (m)
Diameter of wire (mm)
Wire speed (m/s)
Feed rate (mm/min)
Wire tension (MPa)
20–200
0.2–0.6
0–3
0.005–18
0–0.6
Fig. 7. The morphology of resin bonded diamond wire saw.
Table 2 Processing parameters used in experiment. No.
Wire speed (m/s)
Feed rate (μm/s)
1 2 3 4 5
0.8 1.0 1.0 1.2 1.5
6.25 8.33 12.5 12.5 12.5
tightly, as shown in Fig. 8. After slicing, the acetone was used to melt the adhesive, following of which the two samples were separated. Then, they were cleaned with deionized water in ultrasonic cleaners at least 10 min. At last the polished surface was used to SEM examination. The average value of five subsurface crack damage depths measured on different positions of the polished surface was considered as the final damage depth for each slicing.
3.3. The measurement of subsurface crack damage depth In this paper, the bonded interface sectioning technique was used to evaluate the subsurface crack damage according to the study of Agarwal and Rao [17]. According to this method, two (100) wafers, 50 mm in diameter and 3 mm in thickness, were used. Both specimens had one polished surface which was bonded together with adhesive. Then, one clump weight was applied in order to push them together 151
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Fig. 8. The procedure of the experiment. (a) Fist step: bonding two wafers. (b) The second step: diamond wire sawing. (c) The third step: SSD depth measurement.
4. Results and discussion
the median crack to be inclined to extend this plane.
4.1. Morphology of subsurface damage
4.2. Comparison of theoretical and experimental results
The morphology of subsurface crack damage can be seen clearly in Fig. 9. The chipping and crack are the primary damage by using the bonded interface sectioning technique to evaluate the subsurface damage. From these figures, it is found that the median cracks are oblique crack. Besides that, some lateral cracks do not extend to the sliced surface, leading to crack criss-crossing, as shown in Fig. 9(b). In this experiment, we used the (100) silicon wafers as slicing sample. The anisotropy of silicon and the force condition on abrasive can be adopted to explain the oblique cracks. The moving abrasives are exerted the normal force and tangential force during wire sawing. These forces change the stress field in front and back of moving abrasives, altering the length and direction for median crack propagation. On the other hand, the optimum cleavage plane of silicon induces
The same processing parameters to experimental parameters are taken for theoretical calculation. Besides that, the material parameters of silicon were taken according to the (100) silicon wafer. The diameter of wire is 120 µm; the density of abrasives on wire is 450 grits per square millimeter; and the half tip angle of abrasive is 50°. The experimental and theoretical results of the subsurface crack damage (SSD) depths are shown in Table 3. These two results are comparable from Table 3 and the error is reasonable, demonstrating the validity of the proposed model. The experimental results are smaller than the theoretical results because the median cracks are oblique cracks in practice which is not considered in the model. The maximum relative error is 11.6% which could be considered as reasonable, indicating the validity of this established model.
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Fig. 9. The morphology of subsurface damage of sliced wafer. (a) The median crack and chipping. (b) The lateral crack and chipping. (c) The median crack and half penny chipping.
moves down integrally with the increase of wire speed, that is to say the maximum value of function f(θi) has a lowering trend. But the variable value θi for maximum of function values is unchanged. Besides, the down trend of function f(θi) becomes slowly with the increase of wire speed. The position angle θi of abrasive affecting the subsurface crack damage increases with the increase of wire speed. From Fig. 11, it can be seen that the SSD has the same variation trend to the function f(θi) with the increase of wire speed. During wire sawing, the crack propagation depends on the normal force and tangential force applied to the abrasives. The smaller force is, the
4.3. Influence of processing parameters on subsurface crack damage depth The main factors influencing subsurface crack damage depth are wire speed and feed rate during wire sawing. In this paper, the effects of these two factors are analyzed by the function f(θi). Ten wire speeds from 1 m/s to 10 m/s were taken. The feed rate was kept at 5 µm/s, and other parameters were kept unchanged. Under this condition, the changes of function f(θi) and the subsurface crack damage depth (SSD) are shown in Figs. 10 and 11. The function f(θi) 153
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Table 3 Results of SSD depths from theoretical model and experiment. No.
Wire speed vs (m/s)
Feed rate vf (μm/ s)
Theoretical SSD (μm)
Experimental SSD (μm)
Relative error
1 2 3 4 5
0.8 1.0 1.0 1.2 1.5
6.25 8.33 12.5 12.5 12.5
28.7 29.3 33.4 31.5 29.3
26.48 26.82 29.53 27.95 27.39
7.7% 8.5% 11.6% 11.3% 6.5%
Fig. 10. The different curves for f(θi) with various wire speeds.
Fig. 11. The change of SSD with wire speed.
subsurface crack damage decreases with the increase of feed rate. The mode of material removal for diamond abrasives changes with the change of processing parameters. Based on the study of Chung and Le [18], increasing wire speed or decreasing feed rate increases significantly the number of ductile cutting abrasives, which generates smoother slicing surface and shallower subsurface crack damage. But a larger wire speed causes excessive vibration of wire, which results in deteriorating the wafer surface. Increasing the feed rate will increase the cutting force and the material removal rate. Based on the proposed model, increasing or decreasing feed rate and wire speed proportionally will not affect the SSD in theory. From the experimental results and theoretical results, as shown in Fig. 14, increasing the feed rate and wire speed proportional has less effect on the SSD depth. That is to say,
smaller indentation depth and SSD will get. The number of abrasives taking part in removing material increases in unit time with the increase of wire speed. This results in the reduction of the normal force and SSD. Analyzing the effect of feed rate on the SSD in the same way, ten feed rates were taken from 1 µm/s to 10 µm/s, and the wire speed was taken 2 m/s. The cures of function f(θi) and the SSD with different feed rates are shown in Fig. 12 and 13 respectively. It can be seen that, the feed rate has an opposite effect compares with wire speed. The SSD increases with the increasing the feed rate, and the function f(θi) has the similar trend with the SSD. Increasing feed rate will increase the normal force and lead to a larger indention depth and median crack depth. Furthermore, the position angle θi of abrasive affecting the 154
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Fig. 12. The different curves for f(θi) with various feed rates.
Fig. 13. The change of SSD with feed rate.
Fig. 14. The change of SSD depth with the ratio of feed rate and wire speed.
it is possible to increase the processing efficiency and keep the smaller SSD depth simultaneously, which is very beneficial during diamond wire sawing.
5. Conclusion In this paper, the subsurface crack damage depth for single crystal silicon wafers sawn with resin bonded diamond wire saw was studied in 155
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[2] D.W. Camp, M.R. Kozlowski, et al., Subsurface damage and polishing compound affect the 355-nm laser damage threshold of fused silica surfaces, Laser-Induced Damage in Optical Materials International Society for Optics and Photonics, 1998, pp. 356–364 [3] C. Funke, O. Sciurova, O. Kiriyenko, H.J. Möller, Surface damage from multi-wire sawing and mechanical properties of silicon wafers, in: Proceedings of the 20th European Photovoltaic Solar Energy Conference, 2005, pp. 6–10. [4] S. Würzner, A. Falke, R. Buchwald, H.J. Möller, Determination of the impact of the wire velocity on the surface damage of diamond wire sawn silicon wafers, Energy Procedia 77 (2015) 881–890. [5] H.J. Möller, Wafering of silicon, Semicond. Semimet. 92 (2015) 63–109. [6] R.K. Kang, Y.F. Zeng, S. Gao, Z.G. Dong, D.M. Guo, Surface layer damage of silicon wafers sliced by wire saw process, Adv. Mater. Res. 797 (2013) 685–690. [7] N. Watanabe, Y. Kondo, D. Ide, T. Matsuki, H. Takato, I. Sakata, Characterization of polycrystalline silicon wafers for solar cells sliced with novel fixed-abrasive wire, Prog. Photovolt.: Res. Appl. 18 (7) (2010) 485–490. [8] B. Sopori, P. Basnyat, S. Devayajanam, et al., Analyses of diamond wire sawn wafers: effect of various cutting parameters, in: Proceedings of the 42th IEEE Photovoltaic Specialists Conference (PVSC), 2015, pp. 1–6. [9] E. Teomete, Wire saw process-induced surface damage characterization, Arab. J. Sci. Eng. 38 (5) (2013) 1209–1215. [10] F.W. Preston, The structure of abraded glass surfaces, Trans. Opt. Soc. 23 (3) (1922) 141–164. [11] J.C. Lambropoulos, S.D. Jacobs, B. Gillman, F. Yang, J. Ruckman, Subsurface damage in microgrinding optical glasses, LLE Rev. 73 (1997) 45–49. [12] Y.F. Gao, P.Q. Ge, S.J. Li, Investigation of subsurface damage depth of single crystal silicon in electroplated wire saw slicing, Key Eng. Mater. 416 (2009) 306–310. [13] J.C. Lambropoulos, S.D. Jacobs, J. Ruckman, Material removal mechanisms from grinding to polishing, Ceram. Trans. 102 (1999) 113–128. [14] B.R. Lawn, A.G. Evans, D.B. Marshall, Elastic/plastic indentation damage in ceramics: the median/radial crack system, J. Am. Ceram. Soc. 63 (9–10) (1980) 574–581. [15] C.H. Chung, Generation of diamond wire sliced wafer surface based on the distribution of diamond grits, Int. J. Precis. Eng. Manuf. 15 (5) (2014) 789–796. [16] Y.F. Gao, P.Q. Ge, Analysis of grit cut depth in fixed-abrasive diamond wire saw slicing single crystal silicon, Solid State Phenom. 175 (2011) 72–76. [17] S. Agarwal, P.V. Rao, Experimental investigation of surface/subsurface damage formation and material removal mechanisms in SiC grinding, Int. J. Mach. Tool Manuf. 48 (6) (2008) 698–710. [18] C.H. Chung, V.N. Le, Depth of cut per abrasive in fixed diamond wire sawing, Int. J. Manuf. Technol. 80 (5–8) (2015) 1337–1346.
theory and experiment. A novel mathematical relationship between the subsurface crack damage depth and processing parameters was proposed on the basis of indentation fracture mechanics. The validity of this proposed model was proved by the bonded interface sectioning technique. This model can be used to predict the subsurface crack damage depth and optimize the processing parameters. The detailed conclusions are as follows: (1) The position of abrasive which generates the largest subsurface crack damage depth is unchanged when the parameters of wire are decided. Furthermore, the minimum angle of abrasive position larger than that the abrasives have effect on the subsurface crack damage increases with the increase of wire speed and decreases with the increase of feed rate. (2) The median cracks are mainly oblique crack. Some lateral cracks do not extend to sliced wafer surface and become one type of damage with median crack. (3) The proposed mathematical model is comparable with the experimental results. The maximum relative error is 11.6% which could be considered reasonable. (4) Feed rate and wire speed have different effects on the subsurface crack damage depth. The damage depth will decrease with the increase of wire speed and decrease of the feed rate. Increasing proportionally the feed rate and wire speed will lead to a larger material removal rate with the subsurface crack damage depth unchanged. Acknowledgement This work is supported by Shandong Provincial Natural Science Foundation of China (ZR2014EEM034) and National Natural Science Foundation of China (Nos. 51075240 and 51205234). References [1] P.P. Hed, D.F. Edwards, J.B. Davis, Subsurface Damage in Optical Materials: Origin, Measurement and Removal, Lawrence Livermore National Laboratory (LLNL) Report, 1989, pp. 1–17
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