The surface residual stress of monocrystalline silicon in ultrasonic vibration–assisted diamond wire sawing

Monocrystalline silicon wafer is the most important raw material in chip manufacturing; wire sawing is the most common processing method of monocrystalline silicon wafer. The residual stress generated by cutting affects the subsequent polishing costs directly, as well as the fracture strength and mechanical integrity of the monocrystalline silicon wafer, thus affecting the service performance. In this paper, the generation mechanism of residual stress was analyzed based on diamond wire sawing technology. Then, based on Drucker-Prager (D-P) plastic constitutive model, the magnitude and distribution of residual stress of monocrystalline silicon chip under different process parameters were simulated by ABAQUS simulation software. Finally, the experiment of ultrasonic vibration–assisted diamond wire saw cutting monocrystalline silicon was conducted, and the residual stress of monocrystalline silicon chips were detected by blind hole method. During the detection, the strain values before and after drilling in three directions of monocrystalline silicon chips were measured by strain gauge rosette, and then the residual stress values were determined according to the strain values and the residual stress calculation theory. The experimental results showed that residual compressive stress remains on the surface of silicon wafer in both conventional wire sawing and ultrasonic vibration–assisted wire sawing. The residual compressive stress increases with the increase of the axial speed of wire saw, decreases with the increase of the wire saw feed speed, and fluctuates with the increase of the workpiece rotation speed. The residual compressive stress on the surface of the silicon wafer by ultrasonic vibration–assisted wire sawing is larger than that by conventional wire sawing. The simulation and experimental results have the same trend, which verifies the validity of the finite element model in this paper and provides theoretical support for the subsequent processing of single crystal silicon.


Introduction
With the development of science and technology, semiconductor materials have attracted wide attention. Monocrystalline silicon is a kind of semiconductor material which is hard and brittle and difficult to process. It is widely used, especially in chip manufacturing. Wire sawing is the main processing method of slicing monocrystalline silicon wafers. It can be divided into free abrasive wire sawing, semi-fixed wire sawing, and fixed abrasive wire sawing according to different types of wire saw. According to whether there is a multi-field auxiliary processing, the processing is divided into conventional wire sawing technology and ultrasonic vibration-assisted wire sawing technology. Ultrasonic assisted machining has high frequency impact vibration and separation characteristics, which can effectively reduce the average cutting force and cutting temperature, thus improving the fatigue resistance, the surface quality, and surface residual stress of the workpiece [1]. The residual stress is mainly caused by the cutting effect of wire saw, the cutting heat effect, and the phase change effect of workpiece; it will affect the fracture strength, mechanical integrity, magnetic properties, and electrical properties of silicon crystal [2,3]. However, a certain amount of residual compressive stress can improve the fatigue resistance of workpiece, so it is of great significance to further study the influence of diamond wire sawing process on the residual stress.
Residual stress measurement technology is the prerequisite for studying residual stress. After decades of theoretical research and engineering application, drilling method has formed a relatively mature technical system, which is the most widely method in residual stress measurement at present [4]. At present, scholars are studying methods for measuring residual stress of monocrystalline silicon wafers. Zheng et al. [5] proposed measuring the residual stress of full-size silicon wafers by near-infrared birefringence polariscopy method. Popovich et al. [6] used micro-Raman spectroscopy to detect residual stress in the damaged layer of MC-Si chip slicing. Babaeeian et al. [7] compared the method of hole drilling by applying the rosette strain gauge with the digital image correlation (DIC) method to detect the residual stress on the composite plate. Mohr's circle method is used in the above comparison. Zhou et al. [8] comprehensively investigated the effects of cutting speed on surface roughness, subsurface damage, residual stress, and grinding force for a constant grain depth-of-cut. The results illustrate that the changes in residual stress relative to the grinding speed are less obvious when the material is removed in ductile mode as opposed to in the brittle-ductile mixed mode. Jiao et al. [9] studied the nanoindentation of monocrystalline silicon at 1 K using molecular dynamics simulation method, and studied the force-displacement curve and corresponding phase transition process in detail. They also found that the phase distribution during the reverse transformation was strongly influenced by the indenter radius and indentation depth due to the different stress fields. Echizenya et al. [10] established a function relationship between stress and etching depth, and the results showed that the residual compressive stress decreased with the increase of wafer depth. Wurzner et al. [11] used one single abrasive to scratch monocrystalline silicon and detected the residual stress through Raman spectroscopy. The results showed that the residual stress generated by scratching was compressive stress; however, the residual stress is not quantified. Dai et al. [12] studied the ultra-precision machining of monocrystalline silicon by using 3d molecular dynamics (MD) simulation method. The advantages and disadvantages of structured and unstructured tools in machining diamond are discussed by comparing with those of unstructured tools. Yang et al. [13] etched the silicon wafer by diamond wire saw slicing with HF/HNO3 solution, and the comparative analysis results of the trend of residual stress before and after etching showed that the maximum residual shear stress and average residual shear stress in the silicon wafer decreased after etching. Kumar et al. [14] studied the maximum residual shear stress of the silicon wafer by diamond wire saw slicing at different growth rates, and detected the distribution of residual stress field inside the wafer through the near-infrared transmission double-emission polarization method. The results showed that fast-growing wafer crystal had a large maximum residual shear stress. Erick et al. [15] studied the influence of different slicing parameters on monocrystalline silicon wafers, and measured the residual stress of the silicon wafers after cutting by Raman spectroscopy. The results showed that the residual stress on the surface of the monocrystalline silicon wafer by wire saw slicing is compressive stress, and the residual compressive stress increases with the increase of the axial speed of the wire saw. The residual stress decreases with the increase of feed speed. Yang et al. [16] investigated machining-induced surface damages such as surface fracture, phase transition, and residual stress, and revealed the surface damage mechanism for micro ball-end milling of mono-crystalline silicon. Pogue et al. [17] studied the influence of free abrasive wire sawing and fixed abrasive wire sawing on the residual stress. The photoelastic method was used to detect the residual stress of the whole layer, and the micro-Raman spectroscopy was used to detect the residual stress on the silicon wafer surface. The results showed that the residual compressive stress on the surface of the silicon wafer is produced by the fixed abrasive wire sawing and the free abrasive wire sawing, and the residual compressive stress produced by the free abrasive wire saw is greater, but there is lower residual tensile stress under the damaged layer of the silicon wafer. Banerjee et al. [18] analyzed the debris generated after cutting silicon ingots with diamond abrasive coated wire saw by Raman spectroscopy. The results showed that one kind of granular chip is crystalline with residual compressive stress, and the other is amorphous with fibrous chip with residual tensile stress.
At present, scholars have also made some progress in the simulation of residual stress. Kiyota et al. [19] proposed a model to compute the mechanical stress and the geometry of the cracks formed by subsurface nanosecond-pulsed laser modification within monocrystalline silicon wafers, and confirmed the residual stress generation due to material transfer caused by volume reduction during melting and resolidification to be the dominant factor in creating subsurface mechanical stress and cracks. Zhang et al. [20] established a thermodynamic coupling cutting simulation model for two-dimensional orthogonal cutting of titanium alloy based on J-C constitutive through ABAQUS, and analyzed the distribution of residual stress under ultrasonic vibration cutting and conventional cutting. Chen et al. [21] studied the phase transformation and distribution of residual stress in ground silicon wafers by step-wire wet etching and confocal laser micro-Raman spectroscopy, and explained the grinding mechanism and the cause of induced residual stress in ground silicon. The results showed that the residual stress of the machined surface is tensile stress, which gradually transitions from tensile stress to compressive stress along the depth direction. With ultrasonic vibration assisted, the residual tensile stress on the workpiece surface is smaller and the maximum residual compressive stress is larger than that in conventional cutting. Liu et al. [22,23] considered the finite element method of silicon anisotropy and used it to analyze the deformation process, then extracted the surface characteristics of the deformed silicon wafer, and finally obtained the residual stress threshold at the bifurcation point by using the linearization technology according to the changing law of deformation characteristics. Xu et al. [24] established a two-dimensional orthogonal thermodynamic coupling model of aluminum alloy by ABAQUS, and compared the residual stress of surface layer in conventional cutting, transverse ultrasonic vibration cutting with longitudinal ultrasonic vibration cutting. The results showed that the surface residual stress in above three different cutting methods are all compressive stress, and the residual tensile stress is transferred along the depth direction, and ultrasonic vibration cutting can significantly increase the surface residual compressive stress. The surface residual compressive stress decreases with both increase of cutting speed and cutting depth, while the residual surface compressive stress also increases with vibration amplitude or frequency. The above literature mainly studied the detection of residual stress on the surface of silicon wafer, but the residual stress of ultrasonic vibration-assisted diamond wire sawing monocrystalline silicon wafer was not discussed and studied. After the ultrasonic vibration assisted is applied, the relative trajectory between the abrasives and the workpiece changes from continuous contact to intermittent contact. With the ultrasonic vibration-assisted wire sawing, abrasives impact the workpiece constantly and the internal stress state of the workpiece changes accordingly.
Firstly, the principle of diamond wire sawing technology was analyzed in this paper, and a simulation model of diamond wire sawing monocrystalline silicon was established by ABAQUS based on D-P constitutive, and the magnitude and distribution of residual stress under different process parameters were simulated. Finally, ultrasonic vibration-assisted diamond wire sawing monocrystalline silicon experiment and blind hole drilling method experiment were carried out to detect the residual stress. Strains in three directions were measured with strain flower, and the variation trend of residual stress was analyzed with the theory of blind hole method measurement.

Principle of ultrasonic vibration-assisted
diamond wire sawing Figure 1 shows the schematic diagram of ultrasonic vibration-assisted diamond wire sawing monocrystalline silicon.
The whole system can be divided into wire saw feed mechanism and workpiece rotation mechanism, which is composed of a wire barrel, two tensioning wheels, two leading wheels, an auxiliary guide wheel, an ultrasonic guide wheel and a loading tray. During cutting process, the wire saw is subjected to constant tensioning force F t from the cylinder. The diamond wire saw wound on the wire barrel is driven by the motor to move around the tensioning wheel, the leading wheel, and the auxiliary wheel at reciprocating speed of v s . At the same time, diamond wire saw moves downward with line speed v w . The monocrystalline silicon workpiece is bonded to the loading tray, and the self-rotating motion with speed n w is realized by a motor drive. The ultrasonic vibration is applied to the ultrasonic regulating wheel, with amplitude A and frequency f respectively. In order to enhance the lubrication effect and reduce sawing heat during wire sawing, a mixture of water and grinding fluid is used as coolant.

Generation mechanism of residual stress
During wire sawing, most of the materials are sawn by fragile removal, and only a small part of the material is sawn by plastic removal (Fig. 2). Fragile removal of materials mainly focuses on the cutting area under wire saw; residual stress gradually disappears on the surface after some part of the materials fracture. However, plastic removal materials are mainly concentrated on both sides of the wire saw. When the materials are scratched by abrasives through plastic removal mode, the residual stress field will be generated under the abrasives and eventually affect the surface of the workpiece. Li et al. [25] proposed that the abrasive pressing depth h at any wire saw cross section position is: where θ is the position angle of abrasives on the section of wire saw; C is the number of abrasive particles unit area; J is the half-cone angle of the abrasive.
Chen et al. [26] obtained the critical pressing depth h c formula of material change from fragile deformation to plastic deformation under single grinding abrasive through both theoretical and experimental research: where K is the correction parameter of external comprehensive influence, K < 1; E is the elastic modulus; H V is Vickers hardness; K IC is static fracture toughness. When the pressing depth of abrasives is greater than the critical pressing depth, h >h c , materials can be removed by brittle fracture, and it will not produce residual stress. When the pressing depth of abrasives is less than the critical pressing depth, h <h c , the material removal method of abrasives is plastic removal, which will produce residual stress and eventually keep on the workpiece surface. When the pressing depth of abrasives is equal to the critical pressing depth, h =h c , at this time, the abrasives are in the critical region, which is a kind of fragile plastic complexed removal method.

Finite element simulation of diamond wire sawing monocrystalline silicon
In the wire sawing process, material is mainly removed by brittleness, and plastic removal is supplemented. When the pressing depth of abrasives is less than the critical cutting depth, the material is removed in a plastic manner, resulting in residual stress, which will finally remain on the surface of the silicon wafer. In this paper, the model of diamond wire sawing monocrystalline silicon was established by ABAQUS, and the magnitude and distribution of residual stress on the silicon wafer surface after cutting were simulated and calculated.

Establish of simulation model
The temperature change is very small during the cutting process; then, the effect of temperature on the residual stress is not considered, and only the effect of the cutting action on the residual stress is considered. Figure 3 shows the simulation model of wire sawing monocrystalline silicon. Since the Mohs hardness value of diamond abrasives is ten and that of monocrystalline silicon is six, the bending condition during wire sawing is ignored, so the diamond wire saw is set as a rigid body without deformation. In order to improve the calculation accuracy and shorten the calculation time, the monocrystalline silicon workpiece was divided into two parts. The wire sawing area grid was refined, while the other area grid was slightly thicker. In order to make the simulation more realistic and convincing, the cutting process adopts the D-P plastic constitutive model proposed by Drucker and Prager for geotechnical materials [27]. In the cutting process, when the shear stress where J 2 is the second invariant of the deviatoric stress tensor S, I 1 is the first invariant of the stress tensor, α is the pressure sensitivity coefficient, and k is the cohesion of the material.
In the cutting process, the separation criterion adopts the shear failure criterion. According to whether the equivalent plastic strain at the element integration point reaches the set value, it is determined whether the element fails.
After constraint is imposed and mesh is divided, process parameters are set in the software. Table 1 shows simulation parameters of diamond wire sawing. Figure 4 shows the simulation process of diamond wire sawing monocrystalline silicon. Figure 4a shows the contact stage between the wire saw and the workpiece. When the abrasive particles on the wire saw contact the workpiece, the stress value in the machining area increases instantly, but does not reach the yield strength of the workpiece. Figure 4b and c show the fracture removal stage of the material. The material in the processing area starts to break after reaching the yield strength so that the material is removed. Figure 4d (   shows the finish stage of machining, in which the cylindrical workpiece is cut into two sections. The machined surface of conventional wire sawing and ultrasonic vibration-assisted wire sawing is shown in Fig. 5. The number of pits on the machined surface of the workpiece after ultrasonic vibration assisted is less and the surface quality is better. The abrasive particles on the side of the wire saw scrape and polish the machined surface, so that the stress keeps on the surface of the silicon wafer.

Analysis of the simulation results about residual stress
The extraction of residual stress requires unloading the workpiece after the wire sawing is completed, removing all the displacement constraints and interactions during machining, and averaging the values of the ten points on the surface.

Effect of axial line speed of wire saw on surface residual stress
It can be seen from Fig. 6, monocrystalline silicon wafer surface keeps compressive stress whether or not ultrasonic vibration assistance. When both the workpiece rotation speed and the wire saw feed speed are constant, the residual compressive stress on the wafer surface increases with the axial speed of the wire saw from 2 m/s to 8 m/s. The residual compressive stress on silicon wafer surface in ultrasonic vibration-assisted wire sawing is larger than that in conventional wire sawing.

Effect of feed speed on surface residual stress
It can be seen from Fig. 7 that the surface of monocrystalline silicon keeps compressive stress regardless of whether or not ultrasonic vibration is applied. When the workpiece rotation speed and the axial speed of the wire saw are constant, the residual compressive stress on the surface of the silicon wafer decreases with feed speed from 1 mm/min to 4 mm/ min, and the residual compressive stress on the surface of the silicon wafer in ultrasonic vibration-assisted wire sawing is larger than that in conventional wire sawing.

Effect of workpiece rotation speed on surface residual stress
It can be seen from Fig. 8 that the surface of monocrystalline silicon is under compressive stress regardless of whether ultrasonic vibration is applied. When the feed speed and axial speed of the wire saw are constant, the residual compressive stress on the surface of the silicon wafer does not change much with the workpiece rotation speed from 10 r/min to 40 r/min. The residual compressive stress on the surface of the silicon wafer in ultrasonic vibration-assisted wire sawing is larger than that in conventional wire sawing.

The experiment of ultrasonic vibrationassisted diamond wire sawing
In order to verify the correctness of the above theoretical model, a reciprocating diamond wire saw slicing machine CHSX5630-XW was used to conduct ultrasonic vibration-assisted diamond wire saw experiment, and the residual stress on the silicon wafer was detected by blind hole method.

Experimental setup
The experimental and detection equipment is shown in Fig. 9. Monocrystalline silicon workpiece is cylindrical body with diameter of 35 mm and length of 50 mm. The saw wire is electroplated with 0.45 mm diameter diamond abrasives. The total length of saw wire is 150 m, and the average diameter of diamond abrasives is 50 μm. During the slicing process, the tensioning force of the diamond wire saw machine is constant. The ultrasonic generator is a self-built test platform. The ultrasonic amplitude of the ultrasonic generator is 10 μm and the frequency is 20 kHz. DWS vibration displacement sensor is used to monitor the vibration of wire saw in real time.
In this experiment, the three factors that have the greatest influence on residual stress were selected to carry out the three-factor and three-level experiment. The factors are as follows: the axial speed of wire saw v s (m/s), wire saw feed speed v w (mm/min), workpiece rotation speed n w (r/min). Three levels were selected for each factor, covering common range of slicing parameters, and the level values were evenly distributed within the selected range. Orthogonal experiment parameters are shown in Table 2. For each group of slicing parameters, conventional wire sawing and ultrasonic vibration-assisted wire sawing were performed.

Principle of measuring residual stress by blind
hole drilling method Figure 10 shows the blind hole drilling method of measuring residual stress diagram. Blind hole method measures residual stress based on the mechanism of stress release. The workpiece surface pasted with certain shape and size of the strain gauges to form three-way strains of flower; then at the geometric center of three-way strain rosette according to certain diameter drilling, breaking the stress balance inside the workpiece, the stress redistribution inside the workpiece reaches the quadratic balance. The strain values 1 , 2 , and 3 before and after drilling were measured by a strain gauge of a certain specification. According to the theory of elasticity, the principal stresses σ 1 and σ 2 and the principal direction angle φ of this point can be calculated by the relationship between stress and strain. Li et al. [28] gave the relationship between principal stress, principal direction angle, and strain in the blind hole drilling method.
where is the included angle between 0° strain gauge and the direction of the first principal stress of residual stress σ 1 ; 1 , 2 , and 3 are the strain in three directions; and σ 1 and σ 2 are the principal stresses in two directions.
In the through-hole state, the theoretical solutions of release coefficients A and B are shown in Eqs. (6) and (7):

Fig. 8 Effect of workpiece rotation speed on residual stress
where μ is the Poisson's ratio; a is the diameter of the hole; r 1 and r 2 are the distances from the center of the hole to the proximal and distal ends of the strain gauge, respectively. In this paper, the blind hole drilling method is used to measure the residual stress, and there is a certain degree of (1 + )a 2 r 2 1 + r 1 r 2 + r 2 2 4r 2 1 r 2 2 − 1 Fig. 9 Ultrasonic vibration-assisted wire sawing monocrystalline silicon experimental and detection equipment Table 2 Orthogonal experiment parameters Group v s (m/s) v w (mm/min) n w (r/min) 1  2  1  10  2  2  2  30  3  2  3  50  4  5  1  30  5  5  2  50  6  5  3  10  7  8  1  50  8  8  2  10  9  8  3  30 difference between the release coefficient and the through hole method. Li [29] gave the relationship between the release coefficient in the blind hole state and the through hole state. The strain release coefficient A when drilling blind holes is not much different from that when drilling through holes, so the above formula can be used to calculate the value when drilling blind holes, but there is a coefficient difference, usually 1.065. The difference between the strain release coefficient B when drilling blind holes is very small compared with that when drilling through holes, so Eq. (7) can be used to directly calculate the value of strain release coefficient B when drilling blind holes. Figure 11 is the experimental platform for measuring residual stress by blind hole drilling method. Although the residual stress measured by blind hole method is a lossy detection, its damage degree to the workpiece is very small.
Because the surface quality of the workpiece after wire sawing is good, there is no need to polish the workpiece surface, and the strain gauge is directly bonded on the surface of the silicon wafer. A BF350-3CA strain gauge (brand name: BF Series High Precision Resistance Strain Gauge) with resistance R = 350 Ω is used in the experiment. After the strain gauge being pasted on the surface of the workpiece, the lead wire and the lead wire are welded together through the internal heat soldering iron. The strain gauge was connected with the strain acquisition instrument by a 1/4 bridge connection, and the drilling instrument was used to drill the blind hole with diameter

Experimental results and analysis
The strain values before and after drilling can be measured by blind hole drilling method under different slicing parameters, and the residual stress of the monocrystalline silicon wafer can be obtained by combining with theoretical calculation. During wire sawing, three pieces of silicon wafers are cut under the same processing parameters, and the strain gauge is used to measure at the same position of each piece of silicon wafer. The residual stress value of each group is calculated by theoretical formula, and the average value is taken as the residual stress on the surface of the silicon wafer. Table 3 shows the residual stress on the surface of the silicon wafer after the conventional wire sawing. Table 4 shows the residual stress on the surface of the silicon wafer after the ultrasonic vibration-assisted wire sawing. It can be obtained that the residual stress on the surface of the silicon wafer after the diamond wire sawing is the compressive stress.

Analysis of residual stress
5.1.1 Effect of the axial speed of wire saw on surface residual stress Figure 12 shows the variation trend of residual stress with the axial speed of wire saw; it can be seen that the residual compressive stress on the surface of the wafer increases with the increase of the axial speed of wire saw v s from 2 m/s to 8 m/s. With the increase of the axial speed of wire saw, the larger contact area between the abrasives on the saw and the workpiece per unit time, thus the average pressing depth of the abrasives decreases, making more abrasives on the side of the saw removed in a plastic mode, resulting in the increase of residual compressive stress on the surface of the silicon wafer. Figure 13 shows the variation trend of residual stress with the wire saw feed speed; it can be seen that the residual compressive stress on the surface of the silicon wafer decreases as the wire saw feed speed increases from 1 mm/ min to 3 mm/min. The reason is that with the continuous increase of feed speed, more materials need to be removed per unit time. The grinding pressing depth on the side of Table 3 The residual stress on the surface of the silicon wafer in conventional wire sawing

Effect of wire saw feed speed on surface residual stress
Group v s (m/s) v w (mm/min) n w (r/min) σ 1 (MPa) σ 2 (MPa)  Table 4 The residual stress on the surface of the silicon wafer in ultrasonic vibration-assisted wire sawing Group v s (m/s) v w (mm/min) n w (r/min) σ 1 (MPa) σ 2 (MPa)  . 12 Effect of the axial speed of wire saw v s on residual stress the wire saw exceeds the critical pressing depth and the workpiece material is removed in a fragile removal mode, resulting in a smaller residual pressure stress on the surface of the silicon wafer. Figure 14 shows the variation trend of residual stress with the workpiece rotation speed; it can be seen that the residual compressive stress on the surface of the silicon wafer fluctuates with the increase of workpiece rotation speed n w from 10 r/min to 50 r/min. On the one hand, the workpiece rotation speed can be equivalent to a part of the axial speed of wire saw, but the speed has little influence on the axial speed of wire saw. On the other hand, the workpiece rotation makes the wire saw better for the secondary processing of the machined surface, but the removal amount is very small, and the influence on the residual compressive stress is also very small.

Effect of ultrasonic vibration on surface residual stress
It can be seen from Figs. 12, 13 and 14, the residual compressive stress under ultrasonic vibration-assisted wire sawing monocrystalline silicon is larger than that of conventional wire sawing while the axial speed of wire saw v s , wire saw feed speed v w , and workpiece rotation speed n w are fixed. The reasons can be analyzed as follows: diamond wire saw cuts monocrystalline mainly in a fragile removal mode, and the flanked areas are removed in a plastic removal mode.
With ultrasonic vibration assisted, the abrasives with high frequency vibration and smash properties can effectively reduce the average sawing force in machining and increase the critical pressing depth [30]. The pressing depth of more abrasives on the side of wire saw is less than the critical pressing depth and removed in a plastic mode, resulting in an increase of residual pressure stress on the surface of the silicon wafer.

Analysis of surface topography
After the wire sawing was completed, the surface of the silicon wafer was detected with the KEYENCE VHX-6000 optical microscope. The surface topography of silicon wafer by conventional wire sawing and ultrasonic vibration-assisted wire sawing is shown in Fig. 15. It can be seen from Fig. 15, under the same process parameters, there are many large pits on the surface of the workpiece by conventional wire sawing. The surface of the workpiece by ultrasonic vibration-assisted wire sawing is relatively smooth, and the reason for the small size of pits is that the abrasive particles impact the workpiece in a short time under ultrasonic vibration excitation. In the ultrasonic vibration cycle, the impact of abrasive particles on the workpiece cutting times are more but the contact time is very short, so the workpiece is easy to be broken into micron and submicron fragments, the size of pits also becomes smaller. Secondly, the ultrasonic vibration changes the trajectory of the abrasive particles, and the abrasive particles rub the workpiece surface repeatedly, which is beneficial to remove the peak of the residual scratches and improve the surface quality of the workpiece.

Conclusion
In this paper, the surface residual stress of ultrasonic vibration-assisted diamond wire sawing monocrystalline silicon wafer was measured based on the blind hole drilling method. The distribution of residual stress under different process parameters was obtained through wire sawing simulation, and the following conclusions were drawn: 1. By measuring the strain value of the silicon wafer before and after drilling with the blind hole drilling method, the principal stresses in two directions are calculated according to the theoretical formula of stress-strain, and it is concluded that the residual stress on the surface of the diamond wire sawing monocrystalline silicon is mainly compressive stress. 2. The simulation model of diamond wire sawing monocrystalline silicon was established by ABAQUS based on D-P constitutive, and the variation trend of residual stress under different process parameters was obtained, which was verified by experiments. The results showed that the residual compressive stress on the wafer surface increases with the increase of the axial speed of wire saw and wire saw feed speed. The residual compressive stress on the wafer surface decreases gradually with the increase of the workpiece rotation speed; the residual compressive stress on the surface of the wafer does not show any significant change. Under the same process parameters, the residual compressive stress on the surface of silicon wafer by ultrasonic vibration-assisted diamond wire sawing is larger than that of conventional wire sawing, and a certain degree of residual compressive stress can improve the anti-fatigue property of silicon wafer. 3. By observing the surface morphology of silicon wafer after sawing, it can be seen that under the same process parameters, the surface morphology of silicon wafer cut by ultrasonic vibration-assisted wire sawing is better than that by conventional wire sawing. The number of pits on silicon wafer cut by ultrasonic vibration-assisted wire sawing is less, the size of pits is smaller, and the surface quality is improved.
Funding This study was supported by the Natural Science Foundation of Shanghai.

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