- Email: [email protected]
Study on the subsurface microcrack damage depth in electroplated diamond wire saw slicing SiC crystal
Author’s Accepted Manuscript Study on the Subsurface Microcrack Damage Depth in Electroplated Diamond Wire Saw Slicing SiC Crystal Yufei Gao, Yang Chen, Peiqi Ge, Lei Zhang, Wenbo Bi www.elsevier.com/locate/ceri
PII: DOI: Reference:
S0272-8842(18)32553-7 https://doi.org/10.1016/j.ceramint.2018.09.088 CERI19487
To appear in: Ceramics International Received date: 23 July 2018 Revised date: 3 September 2018 Accepted date: 10 September 2018 Cite this article as: Yufei Gao, Yang Chen, Peiqi Ge, Lei Zhang and Wenbo Bi, Study on the Subsurface Microcrack Damage Depth in Electroplated Diamond Wire Saw Slicing SiC Crystal, Ceramics International, https://doi.org/10.1016/j.ceramint.2018.09.088 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Study on the Subsurface Microcrack Damage Depth in Electroplated Diamond Wire Saw Slicing SiC Crystal Yufei GAOa,b*, Yang CHENa,b, Peiqi GEa,b, Lei ZHANGa,b, Wenbo BIa,b a
School of Mechanical Engineering, Shandong University, Jinan 250061, China
b
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, China
*
Corresponding author.
Email addresses: [email protected] (Y.F. Gao).
Abstract: At present, the fixed-abrasive wire saw machining technology is widely used in the slicing process of SiC single crystal. And the subsurface microcrack damage depth of wire sawn SiC wafer is an important quality control parameter. In this paper, experimental and numerical analysis of the subsurface microcrack damage depth of single-crystal SiC in wire sawing is presented. A finite element model (FEM) which was used for simulation and calculation of subsurface microcrack damage depth in wire saw slicing SiC crystal wafer was established. The variations of maximum
principal stress and stress change rate of sawn crystal and slice in wire sawing were analyzed, and the validity of the FEM was verified by sawing experiment. Further, microcrack damage depths under different ingot feed speeds and wire speeds were predicted and the influence of process parameters on microcrack damage depth was discussed. Research results show that the microcrack damage depth values of simulation are lower than the experimental measurement, but with a consistent change trend of a relative error is less than 15.92%. The subsurface microcrack damage depths of sawn wafer decrease with the increase of wire speed and decrease of feed speed. The research results can be helpful to develop precision and high quality slicing technology of SiC single crystal. Keywords: SiC crystal; wire saw slicing; microcrack damage depth; finite element simulation
1 Introduction Silicon carbide (SiC) single crystal is an important material for production of high-temperature, high-frequency, anti-radiation, high-power electronic devices, especially in extreme conditions and harsh environments, and the characteristics of SiC devices are far better than the Si devices and GaAs devices[1-3]. In general, the machining process of SiC single crystal mainly includes wire sawing, grinding, lapping, and polishing, and wafer cutting is the
first and a key machining procedure that directly affects on subsequent machining cost, and therefore there are some studies focusing on the wire saw slicing SiC single crystal. Hardin et al. [1] and Huang et al. [2] analyzed the influences of process parameters on SiC wafer surface quality and sawing force using different electroplated diamond wire saw and process parameters respectively. Wang et al. theoretically proposed a force model in diamond wire sawing of SiC crystal [3,4]. Li et al. carried out an experimental study of wire saw machining single crystal SiC with ultrasonic vibration and developed an empirical mode for predicting the sliced surface roughness [5]. In respect to the processing characteristics of material ductile regime removal, Pang et al. presented an experimental investigation and finite element analysis of indentation in single-crystal 6H silicon carbide [6], and Xiao et al. studied the mechanism of ductile deformation in ductile regime machining of 6H SiC by employing MD simulations [7]. In the previous studies, there are few studies on subsurface damage of SiC single crystal in fixed abrasive wire saw slicing. During the wire saw slicing SiC single crystal, the material is mostly removed by the brittle mode that can inevitably produce microcrack damage in the slice subsurface [1]. The subsurface microcrack damage not only reduces the slice mechanical strength, but also affects the subsequent process and production cost, which is an important index to evaluate the quality of processing. And sawing process is the key to control the microcrack damage depth of the slice. Therefore, there is great significance to study the depth of microcrack damage in wire saw machining for optimizing the technological parameters and guiding subsequent process. At present, threre are methods of theoretical and experimental analysis for studying subsurface damage depth of machining brittle materials. The theoretical relationship between the subsurface microcrack damage depth and the surface roughness of the processed material has been researched based on the theory of indentation fracture mechanics [8,9]. Wurzner et al. presented that a faster wire speed would leads to lower crack depth in diamond wire sawing multicrystalline silicon wafers [10]. Wang et al. thought the wire saw process can be regarded as quasi-static when analyzing subsurface cracks, according to his analysis results of the influence of wire speed on subsurface cracks inside single crystal SiC[11]. Many studies have found that the material removal of single-crystal SiC was dominated by brittle fracture in fixed diamond
wire sawing[1,2,12], therefore, the primary subsurface damage form is microcrack damage which can be reflected as chipping damage and observed by using the bonded interface sectioning technique (BIST)[13-16]. And the BIST is a simple method which is usually used for observing subsurface microcrack damage depth of brittle material in grinding or wire sawing [13-16]. Establishing the relationship between the sawing process parameters and microcrack damage depth will be an effective guidance for obtaining high-quality wafer. The finite element analysis method which can quickly and nondestructively calculate and analyze the stress distribution in machining brittle materials, can be applied to the prediction of microcrack damage depth. In this paper, experimental and finite element analysis of the subsurface microcrack damage depth of single-crystal SiC in diamond wire sawing is presented. The slicing experiment was conducted using an electroplated diamond wire saw, and the BIST was used to examine the subsurface microcrack damage depth of sawn SiC crystal specimens. A FEM for analysis of the microcrack damage depth in wire sawing SiC single crystal was established, based on the constitutive model of material brittle fracture. The changes of maximum principal stress and stress change rate related to subsurface microcrack depth have been analyzed. The microcrack damage depth has been simulated and calculated, and compared with the experimental results. Furthermore, the relationship between the sawing process parameters and the microcrack damage depth of SiC wafers has been analyzed. The research results can be helpful to further understand the distribution and change of sawing stress field in the slicing SiC crystal process and predict microcrack damage depth by using the finite element simulation model. which can provide an important theoretical value for developing of precision and high quality slicing technology of SiC single crystal.
2 Experiment on Measuring Microcrack Damage Depth of Wire Sawn SiC Wafer 2.1 Sample Preparation The wire sawing-induced subsurface microcrack damage depth was observed and measured by employing the BIST and scanning electron microscope (SEM). In this measurement, two specimens with same dimension were first prepared, one surface of each specimen was polished with surface roughness is less than 10 nm. Then polished surfaces with same dimensionare
bonded together by using an adhesive and applying pressure subsequently, which makes the two specimens like an ingot. The two specimens used in wire sawing experiment are 4H-SiC single crystal with length×width×height as 20 mm×10 mm×5 mm, and the two planes of 20 mm×10 mm were bonded after polished. The cutting direction of the wire saw along the newly formed surface by splicing two planes of 5 mm×10 mm. The specimens are separated after finishing the slicing experiment, and prepared for SEM examination after cleaned by ultrasonic. The process of sample preparation is shown in Fig.1. Polished Surfaces
Pressure
Sliced Surface Microcrack damage depth
Bonded
Pressure
20mm 5mm 10mm
wire saw
Sliced Surface
Polished Surface
vs vw
Sliced Surfaces
Step 2
Step 1
Step3
Fig. 1 The process of sample preparation: step 1: bonding two specimens, step 2: wire sawing, and step 3: SEM examination the subsurface microcrack damage depth. 2.2 Experimental Apparatus and Processing Parameters The diamond wire saw apparatus used in machining experiments is shown in Fig.2. The diamond wire is wrapped around the wire spool and moves when the wire spool is turning, the ingot feeds perpendicularly to the wire move direction to achieve sawing. The wire speed of this wire saw machine can be adjusted by stepless speed regulation between 0 and 3 m/s, and the minimal feed speed of ingot can be 0.015 mm/min. Diamond Wire
Wire spool
(a)
Diamond wire Wire move direction Tension wheel
Nozzle Feed direction
Work idler wheel
Idler
Ingot
Wire spool
(b) Fig. 2 Wire saw apparatus: (a) appearance, (b) schematic. The electroplated diamond wire saw with outer diameter is 0.4 mm is used in the experiment, and the abrasives size on the wire surface is 30~40 μm. The ingot feed speed is set as 0.05 mm /min, and the wire speed is set as 0.5 m/s, 0.75 m/s, 1.0 m/s, 1.5 m/s, 2.0 m/s and 3 m/s respectively. Tap water is used as a coolant.
3 Brittle Cracking Criterion of SiC Single Crystal in Wire Saw Slicing During the wire saw slicing of SiC single crystal, the microcracks in the cutting layer are constantly initiating and propagating to form the brittle swarf and realize the brittle fracture removal of materials. So the Brittle-Cracking-Model of the finite element analysis software ABAQUS has been selected as the material constitutive model of the SiC single crystal to simulate the discontinuous brittle fracture characteristics of material in wire sawing. Through the failure and removal of the elements in the FEM, the microcrack propagation depth is simulated numerically, so as to achieve the purpose of calculating the microcrack damage depth. The Brittle-Cracking-Model uses the Rankine criterion that means when the maximum principal stress of the material exceeds the damage stress, the microcracks will initiate and extend along the normal direction of the crack surface. Fracture energy (Gf) which refers to the energy consumption required for cracking per unit area is selected as the crack initiation criterion of SiC crystal material. According to the fracture energy cracking criterion and characteristics of brittle mode cutting in wire sawing SiC single crystal process, the fracture energy critical value GIf of I type crack (Opening crack model) has been chosen as the cracking
criterion, which is used to define the relationship between the subsequent cracking stress and strain, as shown in Eqs. 1 to Eqs. 3. Gf
(1)
G If
1 2 G If K IC2 E
(2)
u
G f du
(3)
0
Where, —Poisson ratio; E —Young's modulus (MPa);
K IC —Fracture toughness
( Mpa mm )； —Maximum principal stress (Mpa)； u —Node point strain Value (mm).
4 Finite Element Model of Wire Sawing SiC Single Crystal 4.1 Process of Wire Sawing Simulation Analysis Fig.3 shows the finite element simulation process, and the finite element analysis model of wire sawing SiC crystal was established by using ABAQUS software. 4H-SiC was used as the simulation material and the sawing trajectory is along the (0001) crystal plane of SiC crystal. Creating a 3D wire sawing modle Preprocessing Defining material properties FEM solving Meshing n=n+1 Setting analysis steps Y Setting geometric and load boundary
Setting “brittle cracking model” Constitutive model
The node n of the unit Gf
N STATUS=1
G If
Total failure node number n=N
N
Unit reserved
Y STATUS=0
Unit deleted
Fig. 3 Finite element simulation process of wire sawing SiC crystal
4.2 Finite Element Model Fig.4 shows the schematic and FEM of wire saw cutting SiC single crystal. According to the support and location in the actual sawing process of SiC single crystal, the crystal planes ABCO, DEFG and COGF are applied to the fixed constraint, and the SiC crystal slice is represented as HIJK-LMUV in FEM. The crystal size was set as 10 mm 10 mm 10 mm, and the (0001) crystal plane was chosen as the sawed surface, the sawed slice thickness was 0.4 mm and the two kerfs were set with 0.4 mm width to simulate the process of two wires sawing simultaneously to get one slice. Meshing model used the eight-node linear hexahedral uncoordinate element C3D8I. The finer structured meshing was used on the slice and kerf, and the scanning meshing was used in other parts of the crystal. The mesh independence was also verified by changing the mesh size and numbers on the basis of verification of grid convergence. The mesh numbers of 51243、67658、81204 and 92361 are calculated respectively. The analysis results show the maximum stress values are 2.002 MPa and 2.015 Mpa respectively when adopting mesh numbers of 81204 and 92361, which means the calculation results are very close. The final mesh number of the model is selected as 81204 based
on the comprehensive consideration of computational efficiency and accuracy.
(a)
Kerf Sliced wafer
(b) Fig. 4 The schematic (a) and finite element model (b) of wire sawing SiC crystal wafer
4H-SiC which belongs to hexagonal crystal system was chosen in FEM analyse in this paper, and the material parameters of SiC crystal are shown in table 1[17]. Table 1 Material parameters of the SiC crystal Material parameters
Value
Density /g·cm-3
3.21
Hardness(Knoop)/ GPa
28.8±3.5
volume modulus /Pa
22×1010
Poisson's ratio
0.142
Material parameters Thermal conductivity /W/(cm·K) Fracture toughness /MPa·m1/2 Young modulus / GPa Thermal expansion coefficient /(×10-6·K-1)
Value 3.7 4.6 340～420 4.3
4.3 Sawing Force Analysis and Applied to the Finite Element Model Fig.5 shows the force model of the section view of diamond wire sawing SiC crystal. The wire is tightly pressed on the crystal in the cutting process under the action of the normal sawing force, and the contact area of the wire and the crystal can be considered as a long and narrow circular arc. Where vc and vw represents the wire speed and the crystal feed speed, respectively. FN is defined as the total normal sawing force loading to the crystal whose direction is vertical to the kerf, and FT is the total tangential sawing force whose direction is consistent with the
moving direction of the wire saw；FNθ is the distributed normal force and FTθ is the distributed tangential force at the positions of the θ angles, respectively. Then the total normal sawing force FN and the tangential sawing force FT can be calculated by using Eq. 4 [3].
FN 1.0322 vw 0.9355 vs 0.8785 0.0423 D l 0.9355 0.8785 0.0423 vs D l FT 0.6224 vw
(4)
where ρ is the abrasive density, abrasive/mm2; D is wire outer diameter, μm; and l is the cut SiC crystal length whose value is 10 mm in the model. Therefore, the values of the force of FNθ and FTθ applied to the finite element model can be acquired as Eq. 5 [18]:
2sin FN lr FN F sin F T 2 lr T
(5)
where r is the outer radius of the wire, r =D/2.
Fig. 5 Sketch of the force model of wire sawing SiC crystal: section view of the wire Considering the complexity and randomness of the abrasives distribution on the wire surface, the wire is not introduced in simulation model, and the sawing force is applied on the crystal according to Eq. 5. The SiC crystal feed and wire movement is simulated by setting multiple dynamic load steps. In the simulation model, the sawing process parameters were selected as: the wire saw speed is 0.5 m/s, 0.75 m/s, 1.0 m/s, 1.5 m/s, 2.0 m/s and 3 m/s respectively, and the crystal feed rate is 0.05 mm/min, which is the same as the experimental
process parameters, so that the simulation results can be compared with the experimental results. The wire outer diameter is 400 μm, and the size of diamond abrasives on wire surface is 30~40 μm with the abrasive density ρ is 110 /mm2. Removal of material is simulated by using the birth
and death algorithm, which is realized by the element failure and deleted in FEM. The slicing process is divided into several dynamic steps. In each step of simulation, the node force of the elements after cut is set to zero and does not participate in calculation in the subsequent step, and stress is loaded to the newly formed kerf simultaneously, then finally, the simulation of the slicing process is realized. 4.4 Calculation of the Microcrack Damage Depth In the post-processing of ABAQUS, the numerical simulation calculation of the initiation and propagation of the microcrack is realized by defining the output of state quantity STATUS of the brittle cracking model to control the failure and deletion of elements. The maximum distance of the unfailed element in the slice to the [0001] Si plane is considered as the microcrack damage depth.
5 Results and Discussion 5.1 Maximum Principal Stress and Stress Change Rate in the Wire Sawing Process As a typical hard and brittle crystal material, the maximum principal stress is the main factor affecting the initiation and propagation of microcracks in subsurface of the SiC single crystal wafer cut during wire sawing. In order to study the variation and distribution of the maximum principal stress at different positions on the slice, the stress calculation points in the sliced SiC wafer of HIJK-LMUV in Fig.4 in stable sawing stage are selected, and their depths and coordinates are respectively: sawing depth 4 mm, (6.6, 2, 6), (6.6, 5, 6), (6.6, 8, 6); sawing depth 5 mm, (6.6, 2, 5), (6.6, 5, 5), (6.6, 8, 5); and sawing depth 6 mm, (6.6, 2, 4), (6.6, 5, 4), (6.6, 8, 4). The positions of the calculated points are shown in Fig.6.
z
Feed direction
H
I
(6.6,2,6)
(6.6,5,6)
(6.6,8,6)
(6.6,2,4)
(6.6,5,4)
(6.6,8,4)
J
K
y
Fig. 6 Position of stress calculation points in the sliced SiC wafer of HIJK-LMUV
Fig.7 shows cloud pictures of the maximum principal stress distribution when the sawing depth is 4mm and 6mm adopting the wire speed is 3 m/s, and the crystal feed speed is 50 μm/min. The value of maximum principal stress is the largest in the area of wire saw cutting, that is, the largest stress value appears at the saw kerf. The change rules of the maximum principal stress of calculation points in the sliced SiC wafer with the sawing depths for the stable sawing stage (sawing depth 2~8 mm) are shown in Fig. 8.
(a) Sawing depth 4 mm
(b) Sawing depth 6 mm
Fig. 7 Cloud pictures of the maximum principal stress distribution (vc = 3 m/s, vw =0.05 mm/min)
Fig. 8 Changes of the maximum principal stress of each calculation point in the sliced SiC wafer with the sawing depths (vc = 3 m/s, vw =0.05 mm/min)
As seen in Fig.8, as the sawing depth increases, the stress of each calculation point increases, and the peak values of the maximum principal stress which are between 0.6 MPa~0.95 MPa occurs when the wire is sawing to the stress calculation point. As the sawing process continues, when the wire is away from the calculation point, the stress gradually decreases until zero. There are differences in the maximum principal stress values of points on the same sawing depth position along the wire movemen direction, and values of the wire saw cutting out from crystal are slightly greater than that of the wire saw cutting into. This is mainly because the ingot keeps the feed during sawing, so the sawing force of the same sawing depth of the wire cutting out from crystal are slightly greater than that of the wire cutting into crystal, which is also in accordance with the actual machining process. According to the criterion of microcrack initiation by Eqs.3, it is known that the initiation and propagation of microcracks are related to the stress change rate. The stress change rate was used to characterize the magnitude of stress variation at each calculation point.
max 0
(6)
where max is the maximum principal stress of the calculation point during the sawing process， and 0 is the average stress of the calculation point during the sawing process.
Fig. 9 is the variation rule of the principal stress change rate with the sawing depth at each stress calculation point. The peak of stress change rate is between 4~5, and the principal stress change rate begins to increase as the wire saw approaches the calculation point. When the wire saw cuts to the calculation point, the principal stress change rate of the sliced wafer reaches a maximum. And the stress change rate decreases gradually until zero with the wire saw far away from the calculation point. Due to the material brittle fracture removal, the node strain of the sliced wafer mesh unit increases to the maximum value when cutting the calculation points and then decreases to zero during the finite element simulation, and the material is cut off to form a new wafer surface and form the microcrack damage in the subsurface in this process.
Fig. 9 The variation of principal stress change rate at different calculation points with the sawing depth (vc = 3 m/s, vw =0.05 mm/min) 5.2 Subsurface Microcrack Damage Depth of Sliced SiC wafer In the finite element simulation, the removal of sliced wafer units can be obtained through the output of the “STATUS” value in the post-processing of ABAQUS, and the microcrack damage depth of each calculation point can be obtained according to the output results. Fig.10 is the subsurface microcrack damage of sliced SiC wafer and extraction of the damage depth which is
9.46 μm at (6.6, 5, 5) coordinate point when sawing depth is 5 mm in finite element model. Fig.11 shows the surface microtopography of sawn SiC wafer. There exit some brittle fractures and lots of
pits, which reveals that the formation of the sawn surface is the result of the brittle regime
material removal. Fig.12 is experimental measurement of subsurface microcrack damage depth of sliced SiC wafer by using the BIST. Five points with 1mm interval distance for each other in
the middle of a specimen were taken to measure the subsurface microcrack damage depth.
SiC wafer surface
Fig. 10 Extraction of the subsurface microcrack damage depth in FEM
Fig. 11 Surface microtopography of sawn SiC wafer
Microcrack damage depth
Fig. 12 Measurement of Subsurface microcrack damage depth of sliced SiC wafer
The subsurface microcrack damage depths of sliced SiC wafer under different process parameters can be obtained by applying the corresponding loads in the FEM, and Fig.13 shows comparison of simulated microcrack damage depth values with experimental measurements values. The simulation results coincide well with the experimental values with the change of wire sawing speed, and the simulation values are less than the experimental measurements values. The main reason is that the finite element simulation model ignores the influence of the crystal internal defects, the vibration of wire saw and the sawing temperature field on the propagation of microcrack. In addition, the BIST was used in the sawing experiment to analyze the subsurface microcrack damage depth, which means the microcrack propagation depth displayed on the edge of the specimen is generally a little greater than the actual subsurface microcrack damage depth of the sliced wafer. As shown in Fig. 13, when the wire saw speed increases from 0.5 m/s to 3 m/s, the microcrack damage depth of specimen decreases from 42 μm to 10.5 μm. It indicates that the microcrack damage depth reduces when the wire saw speed increases at a certain ingot feed speed that can improve the machined surface quality. The increase of wire saw speed reduces the material removal rate of single abrasive per unit time that can reduce the load of the abrasives applied and the cutting resistance, therefore the microcrack damage depth of sliced wafer decreases.
Fig. 13 Comparison of simulated microcrack damage depth values with experimental measurements
Fig.14 shows the relative error between the simulation and the experimental values of microcrack damage depth. It can be seen from Fig.14 that the relative error is larger when the
wire saw speed is lower at a constant ingot feed speed of 0.05 mm/min. In the actual wire sawing process, if the feed speed of the ingot is constant, the decrease of wire speed will increase the bending deformation of wire saw. However, in the finite element simulation model, the cutting trajectory of the wire saw is assumed to be a straight line. When the difference between the actual processing situation and the simulation model is greater, the relative error becomes greater, which means there is a matching range between ingot feed rate and wire speed in actual machining. In general, the relative error range is between 10%~15.92%. Although some factors in the actual processing will affect the experimental results, and there are some simplifications in the finite element model, however, the finite element simulation model established in this paper can predict the microcrack damage depth of SiC wafer machined by wire saw, which has positive guiding significance for analyzing the relationship between sawing process parameters and microcrack damage depth, and optimizing of the sawing parameters to improve the slicing quality.
Fig. 14 Relative error between simulation and experimental values of microcrack damage depth 5.3 Prediction Microcrack Damage Depth under Different Sawing Parameters The FEM was used to predict microcrack damage depth under different ingot feed speeds and wire speeds and analyze the effect of process parameters on damage depth. Fig.15 and Fig.16 shows the variations of subsurface microcrack damage depth predicted under different process parameters, and also separately shows the influence of ingot feed speed and wire speed on the microcrack damage depth.
The feed speed of SiC single crystal in wire sawing is usually set between 0.04 mm/min and 0.10 mm/min. Slow feed speed can improve the subsurface quality but bring a low processing efficiency, and fast feed speed will cause the wire to bend that will lead to the decrease of sawn subsurface quality and serious wear of wire. Influence of crystal feed speed on microcrack depth of SiC wafer under different wire speeds is shown in Fig.15. It can be seen that when the wire saw speed is constant and the feed speed increases from 0.03 mm/min to 0.09 mm/min, the microcrack damage depth values increase that can reduce the quality of subsurface. For instance, when the wire speed is 3 m/s, the microcrack damage depth increases from 9.57 μm to 12.95 μm when the feed speed increases from 0.03 mm/min to 0.09 mm/min. Thus it can be seen that when the speed of the wire saw is constant, the microcrack damage depth also increases gradually with the increase of feed speed. It is because that as the feed speed increases, the indentation depths of the abrasives into the machined surface increase, the sawing force and the bending deformation of the wire increases, which enhances the friction of abrasives and sliced surfaces, therefore, the damage depth of microcrack increases. It is found in simulation that when the wire speed is 15 m/s and the feed speed is less than 0.005 mm/min, there is almost no microcrack initiation on the sliced wafer subsurface. The possible reason is that there is no grid unit in the area of stress calculation point reaching the fracture energy of the microcrack initiation, so there is no failure and removal of the unit, which is consistent with
the ductile regime removal mechanism of hard and brittle materials.
According to the indentation fracture theory, ductile regime material removal can be achieved when the force applied to the abrasive is less than the critical load to form lateral cracks. It can be seen from Fig.16 that when the ingot feed speed is constant and the wire speed increases from 3 m/s to 15 m/s, the microcrack damage depth values decrease which can improve the quality of subsurface. For instance, when the ingot feed is 0.09 mm/min, the microcrack damage depth can decrease from 12.95 μm to 7.77 μm when the wire speed increases from 3 m/s to 15 m/s. With the increase of wire saw speed, the load applied to a single abrasive decreases because of an increase in the number of abrasives involved in wire sawing in unit time, thus the average material removal rate per unit time of a single abrasive reduces.
Fig. 15 Influence of ingot feed speed on the microcrack damage depth
Fig. 16 Influence of wire speed on the microcrack damage depth According to the indentation fracture mechanics theory, the microcrack propagation in subsurface of brittle material is related to the indentation depth and applied load of abrasives. A thinner subsurface microcrack damage depth can be obtained when setting a smaller abrasive cutting depth or applying a smaller load to the abrasives. Increase of wire speed makes the number of abrasives sawing in unit time rise that reduces the sawing load of a single diamond abrasive. And decrease of feed speed makes the average cut depth of abrasives decrease, therefore, the subsurface microcrack damage depth of sawn wafer decreases. Considering of processing efficiency in the actual processing, the wire saw speed can be increased to reduce the
depth of microcrack damage and improve the quality of sliced wafer.
6. Conclusion In this paper, the finite element simulation model for analysis of the microcrack damage depth in wire sawing SiC single crystal was established by using the software ABAQUS, based on the constitutive model of material brittle fracture. Simulation calculation of subsurface microcrack damage depth was realized by setting failure and deletion of mesh elements, and the validity of the FEM was verified by the sawing experiment. Further, microcrack damage depths in wire sawing under different ingot feed speeds and wire speeds were predicted and the influence of process parameters on microcrack damage depth was discussed. The following conclusions can be drawn from this work:
During the wire sawing process, the maximum principal stress and stress change rate of the crystal and sliced wafer become greater when the wire is close to the sawing area.
The finite element model can be used to calculate and predict the microcrack damage depth of wire sawn SiC wafer. The simulation results are lower than the experimental results, with a consistent change trend and a relative error range of 10%~15.92%.
Increase of wire speed and decrease of feed speed will make the subsurface microcrack damage depth of sawn wafer decrease. Considering of processing efficiency in the actual processing, the wire saw speed can be increased to reduce the depth of microcrack damage and improve the quality of sliced wafer.
Acknowledgment The work is financially supported by the National Natural Science Foundation of China (No. 51875322), the Key Research and Development Program of Shandong Province, China (2016GGX103007,
2017GGX30139),
and
China
Postdoctoral
Science
Foundation
(2017M622190).
References 1. C.W. Hardin, J. Qu, A.J. Shih, Fixed Abrasive Diamond Wire Saw Slicing of Single-Crystal SiC Wafers, Mater. Manuf. Proces. 19 (2004) 355-367. 2. H. Huang, Y. Zhang, X.Xu, Experimental investigation on the machining characteristics of single-crystal SiC sawing with the fixed diamond wire, Int. J. Adv. Manuf. Technol. 81 (2015)
955-965. 3. P. Wang, P. Ge, Y. Gao, W. Bi, Prediction of sawing force for single-crystal silicon carbide with fixed abrasive diamond wire saw, Mat. Sci. Semicon. Proc. 63 (2017) 25-32. 4. P. Wang, P. Ge, Z. Li, M. Ge, Y. Gao, A scratching force model of diamond abrasive particles in wire sawing of single crystal SiC, Mat. Sci. Semicon. Proc. 68(2017) 21-29. 5. S. Li, B. Wan, R. Landers, Surface roughness optimization in processing SiC monocrystal wafers by wire saw machining with ultrasonic vibration, P I Mech Eng B J Eng. 288 (2014) 725-739. 6. K. H. Pang, E. Tymicki, A. Roy, Indentation in single-crystal 6H silicon carbide: Experimental
investigations
and
finite
element
analysis,
Int.
J.
Mech.
Sci.
https://doi.org/10.1016/j.ijmecsci.2017.11.021. 7. G. Xiao, S. To, G. Zhang, The mechanism of ductile deformation in ductile regime machining of 6H SiC, Comp. Mater. Sci. 98 (2015) 178-188. 8. A. Esmaeilzare, A. Rahimi, S.M. Rezaei, Investigation of subsurface damages and surface roughness in grinding process of Zerodur glass–ceramic, Appl. Surf. Sci. 313 (2014) 67–75. 9. J. Chen, Q. Fang, P. Li, Effect of grinding wheel spindle vibration on surface roughness and subsurface damage in brittle material grinding, Int. J. Mach. Tool. Manu. 91 (2015) 12–23. 10. S. Wurzner, A. Falke, R. Buchwald, H.J. Moller, Determination of the impact of the wire velocity on the surface damage of diamond wire sawn silicon wafers, Energy Procedia. 7 (2015) 881–890. 11. P. Wang, P. Ge, Y. Gao, M. Ge, T. Liu, Effect of wire speed on subsurface cracks in wire sawing process of single crystal silicon carbide, Eng. Fract. Mech. 184 (2017)2 73-285. 12. X. Chen, J. Li, D. Ma, X.Hu, X. Xu, J. Wang, M. Jiang, Slicing large-diameter SiC single crystal by using diamond wire saw, J. Funct. Mater. 36 (2005) 1575-1577. 13. Y. Gao, P. Ge, T, Liu, Experiment study on electroplated diamond wire saw slicing single-crystal silicon, Mat. Sci. Semicon. Proc. 56 (2016) 106-114. 14. T. Liu, P. Ge, W. Bi, Y. Gao, Subsurface crack damage in silicon wafers induced by resin bonded diamond wire sawing, Mat. Sci. Semicon. Proc. 57 (2017) 147-156. 15. H. Xu, S. Jahanmir, Simple technique for observing subsurface damage in machining of
ceramics, J. Am. Ceram. Soc. 77 (1994) 1388-1390. 16. S. Agarwal, P. Rao, Experimental Investigation of Surface/Subsurface Damage Formation and Material Removal Mechanisms in SiC Grinding, Int. J. Mach. Tool. Manu.48 (2008) 698-710. 17. M. HAN. Preliminary study on molecular dynamic simulation of radiation damage for 4H-SiC [D]. Master thesis of Harbin Engineering University, 2013:4-5. 18. Z. Li , P.Ge, W. Bi, T. Liu, P.Wang, Y. Gao, Coupling stress caused by thermal and slicing force in KDP crystal slicing with fixed abrasive wire saw, Int. J. Adv. Manuf. Technol. 96 (2018) 4333-4343.
PII: DOI: Reference:
S0272-8842(18)32553-7 https://doi.org/10.1016/j.ceramint.2018.09.088 CERI19487
To appear in: Ceramics International Received date: 23 July 2018 Revised date: 3 September 2018 Accepted date: 10 September 2018 Cite this article as: Yufei Gao, Yang Chen, Peiqi Ge, Lei Zhang and Wenbo Bi, Study on the Subsurface Microcrack Damage Depth in Electroplated Diamond Wire Saw Slicing SiC Crystal, Ceramics International, https://doi.org/10.1016/j.ceramint.2018.09.088 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Study on the Subsurface Microcrack Damage Depth in Electroplated Diamond Wire Saw Slicing SiC Crystal Yufei GAOa,b*, Yang CHENa,b, Peiqi GEa,b, Lei ZHANGa,b, Wenbo BIa,b a
School of Mechanical Engineering, Shandong University, Jinan 250061, China
b
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, China
*
Corresponding author.
Email addresses: [email protected] (Y.F. Gao).
Abstract: At present, the fixed-abrasive wire saw machining technology is widely used in the slicing process of SiC single crystal. And the subsurface microcrack damage depth of wire sawn SiC wafer is an important quality control parameter. In this paper, experimental and numerical analysis of the subsurface microcrack damage depth of single-crystal SiC in wire sawing is presented. A finite element model (FEM) which was used for simulation and calculation of subsurface microcrack damage depth in wire saw slicing SiC crystal wafer was established. The variations of maximum
principal stress and stress change rate of sawn crystal and slice in wire sawing were analyzed, and the validity of the FEM was verified by sawing experiment. Further, microcrack damage depths under different ingot feed speeds and wire speeds were predicted and the influence of process parameters on microcrack damage depth was discussed. Research results show that the microcrack damage depth values of simulation are lower than the experimental measurement, but with a consistent change trend of a relative error is less than 15.92%. The subsurface microcrack damage depths of sawn wafer decrease with the increase of wire speed and decrease of feed speed. The research results can be helpful to develop precision and high quality slicing technology of SiC single crystal. Keywords: SiC crystal; wire saw slicing; microcrack damage depth; finite element simulation
1 Introduction Silicon carbide (SiC) single crystal is an important material for production of high-temperature, high-frequency, anti-radiation, high-power electronic devices, especially in extreme conditions and harsh environments, and the characteristics of SiC devices are far better than the Si devices and GaAs devices[1-3]. In general, the machining process of SiC single crystal mainly includes wire sawing, grinding, lapping, and polishing, and wafer cutting is the
first and a key machining procedure that directly affects on subsequent machining cost, and therefore there are some studies focusing on the wire saw slicing SiC single crystal. Hardin et al. [1] and Huang et al. [2] analyzed the influences of process parameters on SiC wafer surface quality and sawing force using different electroplated diamond wire saw and process parameters respectively. Wang et al. theoretically proposed a force model in diamond wire sawing of SiC crystal [3,4]. Li et al. carried out an experimental study of wire saw machining single crystal SiC with ultrasonic vibration and developed an empirical mode for predicting the sliced surface roughness [5]. In respect to the processing characteristics of material ductile regime removal, Pang et al. presented an experimental investigation and finite element analysis of indentation in single-crystal 6H silicon carbide [6], and Xiao et al. studied the mechanism of ductile deformation in ductile regime machining of 6H SiC by employing MD simulations [7]. In the previous studies, there are few studies on subsurface damage of SiC single crystal in fixed abrasive wire saw slicing. During the wire saw slicing SiC single crystal, the material is mostly removed by the brittle mode that can inevitably produce microcrack damage in the slice subsurface [1]. The subsurface microcrack damage not only reduces the slice mechanical strength, but also affects the subsequent process and production cost, which is an important index to evaluate the quality of processing. And sawing process is the key to control the microcrack damage depth of the slice. Therefore, there is great significance to study the depth of microcrack damage in wire saw machining for optimizing the technological parameters and guiding subsequent process. At present, threre are methods of theoretical and experimental analysis for studying subsurface damage depth of machining brittle materials. The theoretical relationship between the subsurface microcrack damage depth and the surface roughness of the processed material has been researched based on the theory of indentation fracture mechanics [8,9]. Wurzner et al. presented that a faster wire speed would leads to lower crack depth in diamond wire sawing multicrystalline silicon wafers [10]. Wang et al. thought the wire saw process can be regarded as quasi-static when analyzing subsurface cracks, according to his analysis results of the influence of wire speed on subsurface cracks inside single crystal SiC[11]. Many studies have found that the material removal of single-crystal SiC was dominated by brittle fracture in fixed diamond
wire sawing[1,2,12], therefore, the primary subsurface damage form is microcrack damage which can be reflected as chipping damage and observed by using the bonded interface sectioning technique (BIST)[13-16]. And the BIST is a simple method which is usually used for observing subsurface microcrack damage depth of brittle material in grinding or wire sawing [13-16]. Establishing the relationship between the sawing process parameters and microcrack damage depth will be an effective guidance for obtaining high-quality wafer. The finite element analysis method which can quickly and nondestructively calculate and analyze the stress distribution in machining brittle materials, can be applied to the prediction of microcrack damage depth. In this paper, experimental and finite element analysis of the subsurface microcrack damage depth of single-crystal SiC in diamond wire sawing is presented. The slicing experiment was conducted using an electroplated diamond wire saw, and the BIST was used to examine the subsurface microcrack damage depth of sawn SiC crystal specimens. A FEM for analysis of the microcrack damage depth in wire sawing SiC single crystal was established, based on the constitutive model of material brittle fracture. The changes of maximum principal stress and stress change rate related to subsurface microcrack depth have been analyzed. The microcrack damage depth has been simulated and calculated, and compared with the experimental results. Furthermore, the relationship between the sawing process parameters and the microcrack damage depth of SiC wafers has been analyzed. The research results can be helpful to further understand the distribution and change of sawing stress field in the slicing SiC crystal process and predict microcrack damage depth by using the finite element simulation model. which can provide an important theoretical value for developing of precision and high quality slicing technology of SiC single crystal.
2 Experiment on Measuring Microcrack Damage Depth of Wire Sawn SiC Wafer 2.1 Sample Preparation The wire sawing-induced subsurface microcrack damage depth was observed and measured by employing the BIST and scanning electron microscope (SEM). In this measurement, two specimens with same dimension were first prepared, one surface of each specimen was polished with surface roughness is less than 10 nm. Then polished surfaces with same dimensionare
bonded together by using an adhesive and applying pressure subsequently, which makes the two specimens like an ingot. The two specimens used in wire sawing experiment are 4H-SiC single crystal with length×width×height as 20 mm×10 mm×5 mm, and the two planes of 20 mm×10 mm were bonded after polished. The cutting direction of the wire saw along the newly formed surface by splicing two planes of 5 mm×10 mm. The specimens are separated after finishing the slicing experiment, and prepared for SEM examination after cleaned by ultrasonic. The process of sample preparation is shown in Fig.1. Polished Surfaces
Pressure
Sliced Surface Microcrack damage depth
Bonded
Pressure
20mm 5mm 10mm
wire saw
Sliced Surface
Polished Surface
vs vw
Sliced Surfaces
Step 2
Step 1
Step3
Fig. 1 The process of sample preparation: step 1: bonding two specimens, step 2: wire sawing, and step 3: SEM examination the subsurface microcrack damage depth. 2.2 Experimental Apparatus and Processing Parameters The diamond wire saw apparatus used in machining experiments is shown in Fig.2. The diamond wire is wrapped around the wire spool and moves when the wire spool is turning, the ingot feeds perpendicularly to the wire move direction to achieve sawing. The wire speed of this wire saw machine can be adjusted by stepless speed regulation between 0 and 3 m/s, and the minimal feed speed of ingot can be 0.015 mm/min. Diamond Wire
Wire spool
(a)
Diamond wire Wire move direction Tension wheel
Nozzle Feed direction
Work idler wheel
Idler
Ingot
Wire spool
(b) Fig. 2 Wire saw apparatus: (a) appearance, (b) schematic. The electroplated diamond wire saw with outer diameter is 0.4 mm is used in the experiment, and the abrasives size on the wire surface is 30~40 μm. The ingot feed speed is set as 0.05 mm /min, and the wire speed is set as 0.5 m/s, 0.75 m/s, 1.0 m/s, 1.5 m/s, 2.0 m/s and 3 m/s respectively. Tap water is used as a coolant.
3 Brittle Cracking Criterion of SiC Single Crystal in Wire Saw Slicing During the wire saw slicing of SiC single crystal, the microcracks in the cutting layer are constantly initiating and propagating to form the brittle swarf and realize the brittle fracture removal of materials. So the Brittle-Cracking-Model of the finite element analysis software ABAQUS has been selected as the material constitutive model of the SiC single crystal to simulate the discontinuous brittle fracture characteristics of material in wire sawing. Through the failure and removal of the elements in the FEM, the microcrack propagation depth is simulated numerically, so as to achieve the purpose of calculating the microcrack damage depth. The Brittle-Cracking-Model uses the Rankine criterion that means when the maximum principal stress of the material exceeds the damage stress, the microcracks will initiate and extend along the normal direction of the crack surface. Fracture energy (Gf) which refers to the energy consumption required for cracking per unit area is selected as the crack initiation criterion of SiC crystal material. According to the fracture energy cracking criterion and characteristics of brittle mode cutting in wire sawing SiC single crystal process, the fracture energy critical value GIf of I type crack (Opening crack model) has been chosen as the cracking
criterion, which is used to define the relationship between the subsequent cracking stress and strain, as shown in Eqs. 1 to Eqs. 3. Gf
(1)
G If
1 2 G If K IC2 E
(2)
u
G f du
(3)
0
Where, —Poisson ratio; E —Young's modulus (MPa);
K IC —Fracture toughness
( Mpa mm )； —Maximum principal stress (Mpa)； u —Node point strain Value (mm).
4 Finite Element Model of Wire Sawing SiC Single Crystal 4.1 Process of Wire Sawing Simulation Analysis Fig.3 shows the finite element simulation process, and the finite element analysis model of wire sawing SiC crystal was established by using ABAQUS software. 4H-SiC was used as the simulation material and the sawing trajectory is along the (0001) crystal plane of SiC crystal. Creating a 3D wire sawing modle Preprocessing Defining material properties FEM solving Meshing n=n+1 Setting analysis steps Y Setting geometric and load boundary
Setting “brittle cracking model” Constitutive model
The node n of the unit Gf
N STATUS=1
G If
Total failure node number n=N
N
Unit reserved
Y STATUS=0
Unit deleted
Fig. 3 Finite element simulation process of wire sawing SiC crystal
4.2 Finite Element Model Fig.4 shows the schematic and FEM of wire saw cutting SiC single crystal. According to the support and location in the actual sawing process of SiC single crystal, the crystal planes ABCO, DEFG and COGF are applied to the fixed constraint, and the SiC crystal slice is represented as HIJK-LMUV in FEM. The crystal size was set as 10 mm 10 mm 10 mm, and the (0001) crystal plane was chosen as the sawed surface, the sawed slice thickness was 0.4 mm and the two kerfs were set with 0.4 mm width to simulate the process of two wires sawing simultaneously to get one slice. Meshing model used the eight-node linear hexahedral uncoordinate element C3D8I. The finer structured meshing was used on the slice and kerf, and the scanning meshing was used in other parts of the crystal. The mesh independence was also verified by changing the mesh size and numbers on the basis of verification of grid convergence. The mesh numbers of 51243、67658、81204 and 92361 are calculated respectively. The analysis results show the maximum stress values are 2.002 MPa and 2.015 Mpa respectively when adopting mesh numbers of 81204 and 92361, which means the calculation results are very close. The final mesh number of the model is selected as 81204 based
on the comprehensive consideration of computational efficiency and accuracy.
(a)
Kerf Sliced wafer
(b) Fig. 4 The schematic (a) and finite element model (b) of wire sawing SiC crystal wafer
4H-SiC which belongs to hexagonal crystal system was chosen in FEM analyse in this paper, and the material parameters of SiC crystal are shown in table 1[17]. Table 1 Material parameters of the SiC crystal Material parameters
Value
Density /g·cm-3
3.21
Hardness(Knoop)/ GPa
28.8±3.5
volume modulus /Pa
22×1010
Poisson's ratio
0.142
Material parameters Thermal conductivity /W/(cm·K) Fracture toughness /MPa·m1/2 Young modulus / GPa Thermal expansion coefficient /(×10-6·K-1)
Value 3.7 4.6 340～420 4.3
4.3 Sawing Force Analysis and Applied to the Finite Element Model Fig.5 shows the force model of the section view of diamond wire sawing SiC crystal. The wire is tightly pressed on the crystal in the cutting process under the action of the normal sawing force, and the contact area of the wire and the crystal can be considered as a long and narrow circular arc. Where vc and vw represents the wire speed and the crystal feed speed, respectively. FN is defined as the total normal sawing force loading to the crystal whose direction is vertical to the kerf, and FT is the total tangential sawing force whose direction is consistent with the
moving direction of the wire saw；FNθ is the distributed normal force and FTθ is the distributed tangential force at the positions of the θ angles, respectively. Then the total normal sawing force FN and the tangential sawing force FT can be calculated by using Eq. 4 [3].
FN 1.0322 vw 0.9355 vs 0.8785 0.0423 D l 0.9355 0.8785 0.0423 vs D l FT 0.6224 vw
(4)
where ρ is the abrasive density, abrasive/mm2; D is wire outer diameter, μm; and l is the cut SiC crystal length whose value is 10 mm in the model. Therefore, the values of the force of FNθ and FTθ applied to the finite element model can be acquired as Eq. 5 [18]:
2sin FN lr FN F sin F T 2 lr T
(5)
where r is the outer radius of the wire, r =D/2.
Fig. 5 Sketch of the force model of wire sawing SiC crystal: section view of the wire Considering the complexity and randomness of the abrasives distribution on the wire surface, the wire is not introduced in simulation model, and the sawing force is applied on the crystal according to Eq. 5. The SiC crystal feed and wire movement is simulated by setting multiple dynamic load steps. In the simulation model, the sawing process parameters were selected as: the wire saw speed is 0.5 m/s, 0.75 m/s, 1.0 m/s, 1.5 m/s, 2.0 m/s and 3 m/s respectively, and the crystal feed rate is 0.05 mm/min, which is the same as the experimental
process parameters, so that the simulation results can be compared with the experimental results. The wire outer diameter is 400 μm, and the size of diamond abrasives on wire surface is 30~40 μm with the abrasive density ρ is 110 /mm2. Removal of material is simulated by using the birth
and death algorithm, which is realized by the element failure and deleted in FEM. The slicing process is divided into several dynamic steps. In each step of simulation, the node force of the elements after cut is set to zero and does not participate in calculation in the subsequent step, and stress is loaded to the newly formed kerf simultaneously, then finally, the simulation of the slicing process is realized. 4.4 Calculation of the Microcrack Damage Depth In the post-processing of ABAQUS, the numerical simulation calculation of the initiation and propagation of the microcrack is realized by defining the output of state quantity STATUS of the brittle cracking model to control the failure and deletion of elements. The maximum distance of the unfailed element in the slice to the [0001] Si plane is considered as the microcrack damage depth.
5 Results and Discussion 5.1 Maximum Principal Stress and Stress Change Rate in the Wire Sawing Process As a typical hard and brittle crystal material, the maximum principal stress is the main factor affecting the initiation and propagation of microcracks in subsurface of the SiC single crystal wafer cut during wire sawing. In order to study the variation and distribution of the maximum principal stress at different positions on the slice, the stress calculation points in the sliced SiC wafer of HIJK-LMUV in Fig.4 in stable sawing stage are selected, and their depths and coordinates are respectively: sawing depth 4 mm, (6.6, 2, 6), (6.6, 5, 6), (6.6, 8, 6); sawing depth 5 mm, (6.6, 2, 5), (6.6, 5, 5), (6.6, 8, 5); and sawing depth 6 mm, (6.6, 2, 4), (6.6, 5, 4), (6.6, 8, 4). The positions of the calculated points are shown in Fig.6.
z
Feed direction
H
I
(6.6,2,6)
(6.6,5,6)
(6.6,8,6)
(6.6,2,4)
(6.6,5,4)
(6.6,8,4)
J
K
y
Fig. 6 Position of stress calculation points in the sliced SiC wafer of HIJK-LMUV
Fig.7 shows cloud pictures of the maximum principal stress distribution when the sawing depth is 4mm and 6mm adopting the wire speed is 3 m/s, and the crystal feed speed is 50 μm/min. The value of maximum principal stress is the largest in the area of wire saw cutting, that is, the largest stress value appears at the saw kerf. The change rules of the maximum principal stress of calculation points in the sliced SiC wafer with the sawing depths for the stable sawing stage (sawing depth 2~8 mm) are shown in Fig. 8.
(a) Sawing depth 4 mm
(b) Sawing depth 6 mm
Fig. 7 Cloud pictures of the maximum principal stress distribution (vc = 3 m/s, vw =0.05 mm/min)
Fig. 8 Changes of the maximum principal stress of each calculation point in the sliced SiC wafer with the sawing depths (vc = 3 m/s, vw =0.05 mm/min)
As seen in Fig.8, as the sawing depth increases, the stress of each calculation point increases, and the peak values of the maximum principal stress which are between 0.6 MPa~0.95 MPa occurs when the wire is sawing to the stress calculation point. As the sawing process continues, when the wire is away from the calculation point, the stress gradually decreases until zero. There are differences in the maximum principal stress values of points on the same sawing depth position along the wire movemen direction, and values of the wire saw cutting out from crystal are slightly greater than that of the wire saw cutting into. This is mainly because the ingot keeps the feed during sawing, so the sawing force of the same sawing depth of the wire cutting out from crystal are slightly greater than that of the wire cutting into crystal, which is also in accordance with the actual machining process. According to the criterion of microcrack initiation by Eqs.3, it is known that the initiation and propagation of microcracks are related to the stress change rate. The stress change rate was used to characterize the magnitude of stress variation at each calculation point.
max 0
(6)
where max is the maximum principal stress of the calculation point during the sawing process， and 0 is the average stress of the calculation point during the sawing process.
Fig. 9 is the variation rule of the principal stress change rate with the sawing depth at each stress calculation point. The peak of stress change rate is between 4~5, and the principal stress change rate begins to increase as the wire saw approaches the calculation point. When the wire saw cuts to the calculation point, the principal stress change rate of the sliced wafer reaches a maximum. And the stress change rate decreases gradually until zero with the wire saw far away from the calculation point. Due to the material brittle fracture removal, the node strain of the sliced wafer mesh unit increases to the maximum value when cutting the calculation points and then decreases to zero during the finite element simulation, and the material is cut off to form a new wafer surface and form the microcrack damage in the subsurface in this process.
Fig. 9 The variation of principal stress change rate at different calculation points with the sawing depth (vc = 3 m/s, vw =0.05 mm/min) 5.2 Subsurface Microcrack Damage Depth of Sliced SiC wafer In the finite element simulation, the removal of sliced wafer units can be obtained through the output of the “STATUS” value in the post-processing of ABAQUS, and the microcrack damage depth of each calculation point can be obtained according to the output results. Fig.10 is the subsurface microcrack damage of sliced SiC wafer and extraction of the damage depth which is
9.46 μm at (6.6, 5, 5) coordinate point when sawing depth is 5 mm in finite element model. Fig.11 shows the surface microtopography of sawn SiC wafer. There exit some brittle fractures and lots of
pits, which reveals that the formation of the sawn surface is the result of the brittle regime
material removal. Fig.12 is experimental measurement of subsurface microcrack damage depth of sliced SiC wafer by using the BIST. Five points with 1mm interval distance for each other in
the middle of a specimen were taken to measure the subsurface microcrack damage depth.
SiC wafer surface
Fig. 10 Extraction of the subsurface microcrack damage depth in FEM
Fig. 11 Surface microtopography of sawn SiC wafer
Microcrack damage depth
Fig. 12 Measurement of Subsurface microcrack damage depth of sliced SiC wafer
The subsurface microcrack damage depths of sliced SiC wafer under different process parameters can be obtained by applying the corresponding loads in the FEM, and Fig.13 shows comparison of simulated microcrack damage depth values with experimental measurements values. The simulation results coincide well with the experimental values with the change of wire sawing speed, and the simulation values are less than the experimental measurements values. The main reason is that the finite element simulation model ignores the influence of the crystal internal defects, the vibration of wire saw and the sawing temperature field on the propagation of microcrack. In addition, the BIST was used in the sawing experiment to analyze the subsurface microcrack damage depth, which means the microcrack propagation depth displayed on the edge of the specimen is generally a little greater than the actual subsurface microcrack damage depth of the sliced wafer. As shown in Fig. 13, when the wire saw speed increases from 0.5 m/s to 3 m/s, the microcrack damage depth of specimen decreases from 42 μm to 10.5 μm. It indicates that the microcrack damage depth reduces when the wire saw speed increases at a certain ingot feed speed that can improve the machined surface quality. The increase of wire saw speed reduces the material removal rate of single abrasive per unit time that can reduce the load of the abrasives applied and the cutting resistance, therefore the microcrack damage depth of sliced wafer decreases.
Fig. 13 Comparison of simulated microcrack damage depth values with experimental measurements
Fig.14 shows the relative error between the simulation and the experimental values of microcrack damage depth. It can be seen from Fig.14 that the relative error is larger when the
wire saw speed is lower at a constant ingot feed speed of 0.05 mm/min. In the actual wire sawing process, if the feed speed of the ingot is constant, the decrease of wire speed will increase the bending deformation of wire saw. However, in the finite element simulation model, the cutting trajectory of the wire saw is assumed to be a straight line. When the difference between the actual processing situation and the simulation model is greater, the relative error becomes greater, which means there is a matching range between ingot feed rate and wire speed in actual machining. In general, the relative error range is between 10%~15.92%. Although some factors in the actual processing will affect the experimental results, and there are some simplifications in the finite element model, however, the finite element simulation model established in this paper can predict the microcrack damage depth of SiC wafer machined by wire saw, which has positive guiding significance for analyzing the relationship between sawing process parameters and microcrack damage depth, and optimizing of the sawing parameters to improve the slicing quality.
Fig. 14 Relative error between simulation and experimental values of microcrack damage depth 5.3 Prediction Microcrack Damage Depth under Different Sawing Parameters The FEM was used to predict microcrack damage depth under different ingot feed speeds and wire speeds and analyze the effect of process parameters on damage depth. Fig.15 and Fig.16 shows the variations of subsurface microcrack damage depth predicted under different process parameters, and also separately shows the influence of ingot feed speed and wire speed on the microcrack damage depth.
The feed speed of SiC single crystal in wire sawing is usually set between 0.04 mm/min and 0.10 mm/min. Slow feed speed can improve the subsurface quality but bring a low processing efficiency, and fast feed speed will cause the wire to bend that will lead to the decrease of sawn subsurface quality and serious wear of wire. Influence of crystal feed speed on microcrack depth of SiC wafer under different wire speeds is shown in Fig.15. It can be seen that when the wire saw speed is constant and the feed speed increases from 0.03 mm/min to 0.09 mm/min, the microcrack damage depth values increase that can reduce the quality of subsurface. For instance, when the wire speed is 3 m/s, the microcrack damage depth increases from 9.57 μm to 12.95 μm when the feed speed increases from 0.03 mm/min to 0.09 mm/min. Thus it can be seen that when the speed of the wire saw is constant, the microcrack damage depth also increases gradually with the increase of feed speed. It is because that as the feed speed increases, the indentation depths of the abrasives into the machined surface increase, the sawing force and the bending deformation of the wire increases, which enhances the friction of abrasives and sliced surfaces, therefore, the damage depth of microcrack increases. It is found in simulation that when the wire speed is 15 m/s and the feed speed is less than 0.005 mm/min, there is almost no microcrack initiation on the sliced wafer subsurface. The possible reason is that there is no grid unit in the area of stress calculation point reaching the fracture energy of the microcrack initiation, so there is no failure and removal of the unit, which is consistent with
the ductile regime removal mechanism of hard and brittle materials.
According to the indentation fracture theory, ductile regime material removal can be achieved when the force applied to the abrasive is less than the critical load to form lateral cracks. It can be seen from Fig.16 that when the ingot feed speed is constant and the wire speed increases from 3 m/s to 15 m/s, the microcrack damage depth values decrease which can improve the quality of subsurface. For instance, when the ingot feed is 0.09 mm/min, the microcrack damage depth can decrease from 12.95 μm to 7.77 μm when the wire speed increases from 3 m/s to 15 m/s. With the increase of wire saw speed, the load applied to a single abrasive decreases because of an increase in the number of abrasives involved in wire sawing in unit time, thus the average material removal rate per unit time of a single abrasive reduces.
Fig. 15 Influence of ingot feed speed on the microcrack damage depth
Fig. 16 Influence of wire speed on the microcrack damage depth According to the indentation fracture mechanics theory, the microcrack propagation in subsurface of brittle material is related to the indentation depth and applied load of abrasives. A thinner subsurface microcrack damage depth can be obtained when setting a smaller abrasive cutting depth or applying a smaller load to the abrasives. Increase of wire speed makes the number of abrasives sawing in unit time rise that reduces the sawing load of a single diamond abrasive. And decrease of feed speed makes the average cut depth of abrasives decrease, therefore, the subsurface microcrack damage depth of sawn wafer decreases. Considering of processing efficiency in the actual processing, the wire saw speed can be increased to reduce the
depth of microcrack damage and improve the quality of sliced wafer.
6. Conclusion In this paper, the finite element simulation model for analysis of the microcrack damage depth in wire sawing SiC single crystal was established by using the software ABAQUS, based on the constitutive model of material brittle fracture. Simulation calculation of subsurface microcrack damage depth was realized by setting failure and deletion of mesh elements, and the validity of the FEM was verified by the sawing experiment. Further, microcrack damage depths in wire sawing under different ingot feed speeds and wire speeds were predicted and the influence of process parameters on microcrack damage depth was discussed. The following conclusions can be drawn from this work:
During the wire sawing process, the maximum principal stress and stress change rate of the crystal and sliced wafer become greater when the wire is close to the sawing area.
The finite element model can be used to calculate and predict the microcrack damage depth of wire sawn SiC wafer. The simulation results are lower than the experimental results, with a consistent change trend and a relative error range of 10%~15.92%.
Increase of wire speed and decrease of feed speed will make the subsurface microcrack damage depth of sawn wafer decrease. Considering of processing efficiency in the actual processing, the wire saw speed can be increased to reduce the depth of microcrack damage and improve the quality of sliced wafer.
Acknowledgment The work is financially supported by the National Natural Science Foundation of China (No. 51875322), the Key Research and Development Program of Shandong Province, China (2016GGX103007,
2017GGX30139),
and
China
Postdoctoral
Science
Foundation
(2017M622190).
References 1. C.W. Hardin, J. Qu, A.J. Shih, Fixed Abrasive Diamond Wire Saw Slicing of Single-Crystal SiC Wafers, Mater. Manuf. Proces. 19 (2004) 355-367. 2. H. Huang, Y. Zhang, X.Xu, Experimental investigation on the machining characteristics of single-crystal SiC sawing with the fixed diamond wire, Int. J. Adv. Manuf. Technol. 81 (2015)
955-965. 3. P. Wang, P. Ge, Y. Gao, W. Bi, Prediction of sawing force for single-crystal silicon carbide with fixed abrasive diamond wire saw, Mat. Sci. Semicon. Proc. 63 (2017) 25-32. 4. P. Wang, P. Ge, Z. Li, M. Ge, Y. Gao, A scratching force model of diamond abrasive particles in wire sawing of single crystal SiC, Mat. Sci. Semicon. Proc. 68(2017) 21-29. 5. S. Li, B. Wan, R. Landers, Surface roughness optimization in processing SiC monocrystal wafers by wire saw machining with ultrasonic vibration, P I Mech Eng B J Eng. 288 (2014) 725-739. 6. K. H. Pang, E. Tymicki, A. Roy, Indentation in single-crystal 6H silicon carbide: Experimental
investigations
and
finite
element
analysis,
Int.
J.
Mech.
Sci.
https://doi.org/10.1016/j.ijmecsci.2017.11.021. 7. G. Xiao, S. To, G. Zhang, The mechanism of ductile deformation in ductile regime machining of 6H SiC, Comp. Mater. Sci. 98 (2015) 178-188. 8. A. Esmaeilzare, A. Rahimi, S.M. Rezaei, Investigation of subsurface damages and surface roughness in grinding process of Zerodur glass–ceramic, Appl. Surf. Sci. 313 (2014) 67–75. 9. J. Chen, Q. Fang, P. Li, Effect of grinding wheel spindle vibration on surface roughness and subsurface damage in brittle material grinding, Int. J. Mach. Tool. Manu. 91 (2015) 12–23. 10. S. Wurzner, A. Falke, R. Buchwald, H.J. Moller, Determination of the impact of the wire velocity on the surface damage of diamond wire sawn silicon wafers, Energy Procedia. 7 (2015) 881–890. 11. P. Wang, P. Ge, Y. Gao, M. Ge, T. Liu, Effect of wire speed on subsurface cracks in wire sawing process of single crystal silicon carbide, Eng. Fract. Mech. 184 (2017)2 73-285. 12. X. Chen, J. Li, D. Ma, X.Hu, X. Xu, J. Wang, M. Jiang, Slicing large-diameter SiC single crystal by using diamond wire saw, J. Funct. Mater. 36 (2005) 1575-1577. 13. Y. Gao, P. Ge, T, Liu, Experiment study on electroplated diamond wire saw slicing single-crystal silicon, Mat. Sci. Semicon. Proc. 56 (2016) 106-114. 14. T. Liu, P. Ge, W. Bi, Y. Gao, Subsurface crack damage in silicon wafers induced by resin bonded diamond wire sawing, Mat. Sci. Semicon. Proc. 57 (2017) 147-156. 15. H. Xu, S. Jahanmir, Simple technique for observing subsurface damage in machining of
ceramics, J. Am. Ceram. Soc. 77 (1994) 1388-1390. 16. S. Agarwal, P. Rao, Experimental Investigation of Surface/Subsurface Damage Formation and Material Removal Mechanisms in SiC Grinding, Int. J. Mach. Tool. Manu.48 (2008) 698-710. 17. M. HAN. Preliminary study on molecular dynamic simulation of radiation damage for 4H-SiC [D]. Master thesis of Harbin Engineering University, 2013:4-5. 18. Z. Li , P.Ge, W. Bi, T. Liu, P.Wang, Y. Gao, Coupling stress caused by thermal and slicing force in KDP crystal slicing with fixed abrasive wire saw, Int. J. Adv. Manuf. Technol. 96 (2018) 4333-4343.