Analysis of Wafer Warpage in Diamond Wire Saw Slicing Sapphire Crystal

Abstract

During the diamond wire saw cutting process of sapphire crystals, warpage is one of the key parameters for evaluating wafer quality. Based on the thermoelasticity theory and diamond wire saw cutting theory, a finite element model for thermal analysis of diamond wire saw cutting sapphire crystals was established in this paper. The variation laws and internal connections of the temperature field and thermal deformation displacement field of the wafer during the sawing process were analyzed. A calculation and analysis model for the warpage of sapphire crystal wafer cut by wire saw was established based on the node thermal deformation displacement field of the wafer, and the rationality of the simulation results was verified through sawing experiments. This simulation calculation model constructs the mapping relationship between the process parameters of diamond wire sawing and the sapphire wafer warpage during sawing. The influence of wafer thickness, diamond wire speed, feed rate, diamond wire diameter, and tension on the warpage of the wafer was studied using the simulation model. The results indicate that the highest temperature occurs in the sawing area during cutting. The wafer thickness decreases and the warpage increases. The wafer warpage decreases with the increase of the diamond wire tension and diameter, and increases with the increase of diamond wire speed and feed rate. The research results provide a reference for understanding the variation of wafer warpage during sawing and optimizing sawing process parameters.

1. Introduction

Sapphire crystals are widely used in the optoelectronics and microelectronics industries, such as transparent infrared window materials, micro substrate substrates, laser substrates, optical components, etc. [1,2]. The key process of sapphire crystal in the mechanical processing stage is: slicing → grinding → lapping → polishing. Slicing is the first critical process of transforming sapphire crystals into wafers, and currently diamond wire saw slicing technology is widely used [3,4]. Sawing processing can cause many quality problems with wafers, among which warpage is one of the important issues.

Warpage is a key geometric parameter for evaluating slice quality and belongs to bulk defects. Once it forms, it is difficult to improve in subsequent lapping and polishing processes, directly affecting the final wafer quality. When a warped wafer is ground, the crystal axis will deviate from the wafer axis with the grinding. The warpage of the wafer in the slicing process is a serious problem in the manufacturing of high-precision substrates [5]. Therefore, understanding the effect of process conditions on wafer warpage in diamond wire saw cutting and optimizing slicing process parameters is of positive significance for effectively controlling and improving wafer warpage and ensuring wafer quality.

Existing research suggests that the factors causing wafer warpage during sawing processing are mainly related to the distribution of the sawing temperature field, which is caused by wafer deformation due to sawing heat. However, research in this area is not sufficient. According to the research of Yamada et al. [5] and Gupta et al. [6], the warpage of sliced wafers is predominantly produced by the non-uniform local thermal expansion of the ingot in the vicinity of the location of the cut during the slicing cycle by the heat generated from the cutting action. Bhagavat et al. [7] studied the temperature field variation of single crystal silicon cut by wire saw using the finite element method. The authors suggested a method to obtain a relatively flat profile of temperature in order to reduce slice warpage due to heat generation during slicing by intelligent control of boundary conditions. Huang et al. [8] used the finite element method to study the temperature field distribution on the outer surface of sapphire ingots cut by the diamond wire saw. The research has found that the maximum temperatures increased with the increase of cutting depth, and were always found to be located in the middle of slicing zone. In addition to the thermal deformation of the wafer itself during slicing processing being able to cause wafer warpage, the thermal deformation of wire guide can also cause the position of the diamond wire to shift, resulting in slice warping. However, this problem can be improved by improving the equipment structure [9]. In addition, the warpage of the wafer during processing is related to its own thickness, and the thickness of the wafer affects its ability to resist deformation [10,11]. As the wafers move towards a larger size and ultra-thin thickness, their stiffness decreases and their ability to resist warpage and deformation weakens. Based on the research conclusions of comprehensive scholars, during the diamond wire saw cutting process, the temperature in the cutting area increases and heat is generated, causing thermal deformation of the wafer and resulting in warping deformation. The main reason for the difference in warpage of wafers obtained by different sawing processes is due to the inconsistent degree of thermal expansion deformation at different positions of the wafer. So far, there have been no systematic studies on the influence of diamond sawing process parameters on the warpage of sapphire wafers, and there is a lack of understanding of the influence of process parameters on the warpage of wafers. Although it is possible to carry out sawing experiments to conduct analysis and research by measuring wafer warpage, a large amount of data is required. Adjusting different process parameters for sawing and measurement in the experiments is time-consuming, laborious, and of high economic cost. In contrast, the theoretical simulation calculation model embodies the advantages of fast calculation, is time-saving and labor-saving, and has a low economic cost.

During the diamond wire saw cutting process, almost all the energy consumed by the diamond abrasives on the surface of the saw wire for crystal cutting is converted into cutting heat. Part of the cutting heat is carried away by air and coolant, and about one-third to one-half of the heat is absorbed by the crystal [5]. The time difference between the heated parts of the slice results in uneven temperature distribution, causing the wafer to warp and deform under the action of thermal expansion and contraction. It is difficult to measure the temperature distribution in the cutting area during the diamond wire saw cutting process. Li et al. [12] used experimental methods to measure the temperature in the cutting zone of a free abrasive multi-wire saw, but were unable to determine the temperature field distribution throughout the entire cutting process. Finite element simulation is an effective method for analyzing the temperature field and thermal deformation of sawing [13,14].

Based on the theory of thermoelasticity, a finite element model for thermal analysis of diamond wire saw cutting sapphire crystals was established in this paper, and the relationship between the temperature field and thermal deformation displacement field of the wafer and the process parameters was analyzed. The influence of wafer thickness, saw wire diameter, saw wire speed, and feed rate on wafer warpage was studied using the simulation model based on the node thermal deformation displacement field of the as-sawn sapphire C-plane. The research results provide a reference for understanding the variation of wafer warpage during sawing and optimizing sawing process parameters. By using the simulation calculation model of wafer warpage established in this paper, the influence of various process parameters on the warpage of sapphire wafers can be analyzed, the warpage of sapphire wafers cut by diamond wire saw under different process conditions can be calculated, and rapid prediction of sapphire wafer warpage can be achieved. The use of this simulation calculation model can avoid conducting multiple sawing experiments, saving costs such as time, manpower, and financial resources.

In this paper, the theoretical basis of temperature field analysis for sawing is introduced in Section 2, the details of finite element modeling are introduced in Section 3, and sawing experiments are conducted in Section 4. In Section 5, the simulation results of the temperature field and thermal deformation of the wafers are analyzed in Section 5.1, and the rationality of the simulation calculation model is verified by experimental results in Section 5.2. Then, based on the established simulation calculation model, the wafer warpage under different sawing process conditions is calculated and analyzed in Section 5.3. Finally, the research conclusions are summarized in Section 6.

2. Theoretical Analyses

2.1. Heat Flux

Figure 1 is the schematic diagram of diamond wire saw cutting. The diamond wire is wound around a guide wheel and driven by power to move back and forth. The sapphire crystal is fed in the direction perpendicular to the diamond wire, and the diamond abrasives fixed on the surface of the wire achieve a cutting effect to remove material and form the kerf. As the processing progresses, the wafer is cut to form. The sawing process generates heat in the sawing area, and its heat flux density is the heat passing through the cross-sectional area of the workpiece per unit area per unit time. The heat flux q_v into the workpiece in the sawing process can be described as follows [7]:

$$q_{\mathrm{v}}={\displaystyle \frac{\epsilon P}{A}}$$

(1)

where ε represents the energy partition of the heat transfer into the workpiece in slicing. Yamada et al. [5] suggested that approximately one-third to one-half of the heat during sawing is absorbed by the crystal, and ε was defined as 0.667 by Huang et al. [8]; therefore, the same numerical value is used for ε in the calculation of this paper. P is the consumed power for the wire sawing process, and P can be calculated as the product of tangential sawing force Ft exerted on the workpiece by the diamond wire and the wire speed v_c [7,13], as P = F_t × v_c. And F_t can be calculated by using the formula F_t = 0.6224(v_w)^0.9355(v_c)^−0.8785(η)^0.9355 DL_x [15], where v_w is workpiece feed rate, η is the abrasive density on diamond wire surface, and D is the wire outer diameter. A is the cross-sectional area of the kerf, which can be approximately expressed as A = L_x × d, where L_x is the length of contact between the diamond wire and the workpiece during cutting, d is the kerf width, and the approximate relationship with the wire outer diameter D is: d = D + 20 μm [16]. The length of the diamond wire (indicated by the blue dashed line) cutting into the interior of the crystal shown in Figure 1 is L_x. According to the relationship between L_x and the width L of the cut crystal shown in Figure 1, the approximate relationship is as follows: L_x = L_x × cosα, and α is the wire bow angle, and the value is 1.5° [13]. In the finite element model, when the workpiece feed rate is v_w, the length of material cut along the feed direction in each analysis step t_inc is v_w × t_inc. The heat flux density entering the workpiece during this process is:

$$q_{\mathrm{v}}={\displaystyle \frac{\epsilon P}{A}}{v}_{\mathrm{w}}{t}_{\mathrm{inc}}$$

(2)

Based on the above equation, the heat flux into the workpiece can be described as follows:

$$q_{\mathrm{v}}={\displaystyle \frac{\epsilon F_{\mathrm{t}}{v}_{\mathrm{c}}{v}_{\mathrm{w}}{t}_{\mathrm{inc}}}{L_{\mathrm{x}}d}}$$

(3)

2.2. Mathematical Model of the Temperature Field

The temperature of the wafer during the diamond wire saw cutting process redistributes with the movement of thermal load, and the cutting temperature field is related to the loading time of the thermal load; therefore, it belongs to non-steady state heat transfer.

During the sawing process, the position of the heat source changes. According to Fourier heat transfer law and energy conservation law, the differential equation for the three-dimensional transient temperature field of heat transfer without an internal heat source during the sawing workpiece process is established as:

$${\displaystyle \frac{\partial }{\partial x}}\left(k_x{\displaystyle \frac{\partial T}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(k_y{\displaystyle \frac{\partial T}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(k_z{\displaystyle \frac{\partial T}{\partial z}}\right)=c_T\rho {\displaystyle \frac{\partial T}{\partial t}}$$

(4)

where k_x, k_y, and k_z are the thermal conductivity coefficients of sapphire crystal along the x, y, and z directions, respectively. c_T, ρ, and T are the specific heat capacity, density, and temperature of the crystal, respectively. The left side of Equation (4) represents the heat transferred into the crystal from the x, y, and z directions, while the right side represents the heat required to raise the temperature of the crystal.

In order to solve the equation, the following three kinds of boundary conditions are specified in the computational domain. The boundary conditions during the heat transfer process of wire saw cutting sapphire crystal include ${\Gamma }_1$, ${\Gamma }_2$, and ${\Gamma }_3$.

The prescribed temperature on the boundary of ${\Gamma }_1$

$$T\left(x,y,z,t\right)=\overline{T}\left(t\right)$$

(5)

The heat flux density boundary conditions ${\Gamma }_2$ can be expressed as:

$$k_x{\displaystyle \frac{\partial T}{\partial x}}{n}_x+k_y{\displaystyle \frac{\partial T}{\partial y}}{n}_y+k_z{\displaystyle \frac{\partial T}{\partial z}}{n}_z=q_{\mathrm{v}}$$

(6)

where n_x, n_y, and n_z are the direction cosine of the normal outside the boundary.

The convective heat transfer coefficient boundary conditions for ${\Gamma }_3$ can be expressed as:

$$k_x{\displaystyle \frac{\partial T}{\partial x}}{n}_x+k_y{\displaystyle \frac{\partial T}{\partial y}}{n}_y+k_z{\displaystyle \frac{\partial T}{\partial z}}{n}_z=h\left(T_{\infty }-T\right)$$

(7)

where h is the convective heat transfer coefficient, and $T_{\infty }$ is the ambient temperature.

The boundary conditions should meet the following equation.

$${\Gamma }_1+{\Gamma }_2+{\Gamma }_3=\Gamma$$

(8)

The initial condition for the temperature is set to be at an ambient temperature for the entire workpiece.

3. Finite Element Modeling

3.1. Material

Square sapphire crystal is selected as the material to be processed and analyzed by sawing along the C-plane. The material parameters are shown in

Table 1. Material parameters of the sapphire crystal.

Material Parameters	Value	Material Parameters	Value
Density/g·cm−3	3.95	Thermal conductivity/W/(cm·K)	132.5
Hardness (Moh’s)/GPa	9	Fracture toughness/MPa·m1/2	2.02
Volume modulus/GPa	250	Young modulus/GPa	320~340
Poisson’s ratio	0.28	Thermal expansion coefficient/(×10−6·K−1)	5.8

[17].

3.2. Modeling and Solution

Based on ABAQUS software (v.5.4), a finite element model of diamond multi-wire sawing sapphire crystal is established, as shown in Figure 2. In the finite element model, the dimensions of the workpiece are set to 10 mm × 10 mm × 6.9 mm, and the bottom surface of the workpiece is completely fixed. The diamond wire moves along the x-axis. At the same time, to achieve the feed of the workpiece relative to the diamond wire in the y-direction during the cutting process, the feed of the diamond wire relative to the workpiece in the y-direction should be set in the simulation model. This is achieved by applying cutting heat flux to the kerf in the simulation model instead of the actual diamond wire used in machining. The cutting process of forming five slices from six kerfs was simulated, with a kerf width of 0.3 mm and a slice thickness of 0.5 mm. Using the sequential coupling method for calculation, the temperature field generated during the sawing process was first calculated, and the thermal deformation caused by the temperature field was first calculated. In the finite element model, an eight-node linear heat transfer hexahedral element DC3D8 and an eight-node linear hexahedral element C3D8I are used. The total number of units is 41,280, and grid independence verification has been conducted.

When calculating the temperature field, all surfaces exposed to the air are set as natural convection boundary conditions, with a natural convection heat transfer coefficient of 5 W/m²·°C [7], and the value of the forced convective heat transfer coefficient between the workpiece and the coolant is 3 × 10⁴ W/m²·°C [18]. The ambient temperature is set to 25 °C. The simulation of the sawing process is divided into multiple steps, with each step using the birth and death element method to remove a certain depth of material. The killed element is considered to be cut off, and it is no longer subjected to a sawing action and is deleted in space, allowing the cutting heat flow to act on the new cutting area, thus simulating the entire sawing process. Figure 3 shows the finite element simulation flowchart.

3.3. Calculation of Wafer Warpage Based on Finite Element Method

The warpage of a wafer is defined as the difference between the maximum and minimum distances between the wafer center plane and the reference plane, as shown in Figure 4, i.e., warpage = Smax − Smin. Among them, the reference plane is an imaginary reference plane.

Yamada et al. [5] proposed a method for calculating wafer warpage based on finite element simulation. The total thickness deviation of the wafer is assumed to be zero, i.e., TTV = 0. In finite element analysis, the sapphire wafer before deformation is considered as the reference plane, and the wafer surface after thermal deformation during sawing is considered as the center plane. Therefore, the deformation displacement of the wafer surface nodes during sawing is used to calculate the wafer warpage, as shown in Figure 5. In this paper, 25 nodes are uniformly taken along the direction perpendicular to the wire moving direction along the wafer cut surface. The wafer warpage is calculated by extracting the thermal deformation displacement of the nodes during the cutting process, similar to the point-by-point scanning method in experimental measurements, as shown in Figure 6.

4. Sawing Experiment

The experiment was conducted by employing a diamond multi-wire saw machine. Figure 7 shows the appearance and schematic of the machine sawing unit in the experiments. The diamond wire is wrapped around two wire wheels, and during the sawing process, the two wire wheels respectively complete the tasks of unwinding and rewinding. When the diamond wire finishes running in a certain direction, the control system can change the wire direction, and at the same time, the roles of the two wire wheels can be switched to achieve the reciprocating moving of the diamond wire. In the cutting area, the diamond wire is wound around three wire guides to form a parallel wire web, and is tensioned by tensioning rollers. During the sawing process, the diamond wire runs and the sapphire crystal is fed upwards perpendicular to the diamond wire to achieve cutting. In this experiment, deionized water was used as the coolant. The nozzle sprays coolant to the cutting area to achieve cooling and lubrication of the workpiece, and the coolant flow rate is 17.5 L/min. The sapphire crystal size is 10 mm × 10 mm × 40 mm, cut along the C plane with a slice thickness of 0.5 mm. The electroplated diamond wire with a nominal diameter of 0.28 mm was used, and four sets of cutting experiments were conducted, and the process parameters are shown in

Table 2. Processing parameters for the sawing experiment.

No.	Wire Speed Vs (m/min)	Feed Rate Vw (mm/min)
1	800	0.1
2	800	0.3
3	1200	0.1
4	1200	0.3

.

After the cutting is completed, five wafers are randomly selected from the sawing area middle position of each set, and after ultrasonic cleaning, the wafer warpage is measured using a KEYENCE laser plane measuring instrument (LJ-X8000) (Osaka, Japan). This method scans and the surface accurately measures the shape and height changes of the wafer, and calculates the warpage of the wafer by analyzing the scan data. The experimental measurement principle of wafer warpage is consistent with the method of extracting thermal deformation information point by point in the simulation model to calculate wafer warpage. The average of the measured values is taken. The experimental results are used to validate the results of the simulation calculation model.

5. Results and Discussion

5.1. Analysis of Wafer Temperature Field and Thermal Deformation

Figure 8 shows the temperature field nephogram generated by the cut crystals and wafers at cutting depths of 2 mm and 8 mm. The temperature in the cutting area is the highest, and the temperature in the sawed part is lower than that in the uncut part. This is because the coolant is directly sprayed on the sawing area and then flows down along the newly formed surface, causing the temperature to drop faster. The temperature field at both sawing depths is symmetrically distributed, and the temperature of the wafers is lower than that of the surrounding uncut sapphire material. This is because the wafers absorb relatively less heat and have a large heat dissipation area.

From Figure 8b, it can be seen that there is a relatively larger area of deep red stress distribution zone (high stress value) on the middle slice, and the temperature field of multiple wafers is symmetrically distributed. Therefore, during the sawing process, the temperature of the middle slice may be the highest, which means that the temperature distribution of wafers 1 and 5, as well as wafers 2 and 4, is consistent. Therefore, the variation of maximum temperature of slices 1, 2, and 3 with sawing depth was analyzed, as shown in Figure 9. In addition, it was found that as the sawing depth increases, the temperature of the wafer gradually increases and tends to stabilize, with a stable sawing temperature of about 34.5 °C. The lower temperature at the beginning of the sawing stage is due to the pouring of coolant from top to bottom. At this time, the cutting depth is shallow, and the coolant can directly enter the sawing area. But as the cutting depth increases, the coolant cannot be directly poured into the cutting area and needs to flow into the cutting area along the cut surface. Therefore, the flow rate of coolant entering the cutting area will inevitably decrease, resulting in an increase in temperature.

The deformation nephogram of wafer No. 3 in the z-direction was extracted when the sawing depth was 4 mm, as shown in Figure 10. The deformation at the sawing position is the largest, reaching up to 54.8 μm, which corresponds to the highest temperature in the sawing area. According to the selected test points on the wafer surface shown in Figure 6, to extract the thermal deformation positions at the maximum temperature of each point, the wafer warpage can be calculated by using the method shown in Figure 5.

5.2. Experimental Verification of Simulation Calculation Model for Wafer Warpage

Figure 11 shows the surface node displacement of wafer during the sawing process obtained based on different combinations of process parameters shown in Table 1. It can be seen that in the combination of process parameters, the values of wire speed and workpiece feed rate are large, and the surface node displacement of the sawn wafer is also large. According to the calculation method of wafer warpage shown in Figure 5, the wafer warpage values calculated based on the finite element simulation model are compared with the measured experimental values, as shown in Figure 12. The values of the two are quite consistent, with simulation calculations being smaller than experimental measurements and an error within 12%. The main reason for this situation is that the finite element simulation ignored the influence of factors such as poor kerf lubrication and diamond wire vibration that may occur during the actual sawing process on wafer warpage. Therefore, the actual measured warpage value of the wafer will be greater than the simulation value. Moreover, as shown in Figure 12, when the diamond wire speed and the workpiece feed rate increase, the error between the simulation calculation values and the experimental measurement values also increases. This indicates that in this case, the influence of some actual situations on the finite element simulation model in sawing increases. Overall, the simulation results of the finite element model are reasonable.

5.3. Wafer Warpage under Different Processing Conditions

5.3.1. The Influence of Wafer Thickness on Warpage

With the development of technologies such as micro substrate substrates, laser substrates, and optical components, the thickness of sapphire wafers continues to decrease. Therefore, this section explores the relationship between wafer thickness and warpage. The finite element model performs simulation calculations based on changes in wafer thickness by setting the wafer thickness as 200 μm, 300 μm, 400 μm, 500 μm, and 600 μm, respectively. Figure 13 shows the relationship between different thicknesses of sapphire wafers and warpage, and the wire saw speed is 1200 m/min, the feed rate is 0.1 mm/min, and the diamond wire diameter is 0.28 mm.

It can be seen that as the wafer thickness increases, the wafer warpage decreases, and the decreasing trend of warpage gradually slows down. The reason for this is that, on the one hand, under the same sawing process conditions, different wafer thicknesses have consistent natural convection heat dissipation capabilities, but thicker wafers have weaker thermal conductivity. On the other hand, the thinner the wafer, the lower its stiffness, and the weaker its ability to resist deformation. Temperature changes cause more pronounced warping and deformation of the wafers. Under the trend of continuous thinning of wafers, optimizing the sawing process to improve the warpage problem of thin wafers is a challenge for diamond wire sawing processing.

5.3.2. The Influence of Diamond Wire Diameter on Wafer Warpage

Reducing kerf loss can increase the number of sapphire wafers produced per unit size, and the thinning of diamond wire diameter has become a development trend by setting the diamond wire diameter as 0.2 mm, 0.22 mm, 0.24 mm, 0.26 mm, and 0.28 mm, respectively. Figure 14 shows the relationship between different wire diameters and wafer warpage. The influence of diamond wire diameter on wafer warpage is mainly reflected in the finite element calculation model by changing the kerf width d. In this simulation calculation, the wire saw speed is 1200 m/min, the feed rate is 0.1 mm/min, and the wafer thickness is 500 μm.

It can be seen that as the diameter of the diamond wire decreases, the wafer warpage gradually increases. This is because as the diamond wire diameter decreases, the sawing kerf becomes narrower, the heat dissipation effect deteriorates, and the amount of heat entering the wafer through thermal conduction increases. However, the heat dissipation ability of the wafer weakens, and the temperature in the sawing area increases. Therefore, the warpage of wafers cut by diamond wires of different diameters is not consistent.

5.3.3. The Influence of Sawing Process Parameters on Wafer Warpage

By changing the wire speed vc in Equation (3) to calculate the correspondent heat flux density, the relationship between wire speed and wafer warpage is established based on simulation calculation of the finite element model. Figure 15 shows the effect of wire speed on wafer warpage at different feed rates. In simulation calculations, the wafer thickness is 500 μm and the diamond wire diameter is 0.28 mm. It can be seen that as the wire speed increases, the wafer warpage gradually increases. This is because the higher the wire speed, the greater the cutting power of the wire saw, and the more heat is generated during cutting. However, the cutting heat loss coefficient remains constant during this process, the amount of heat entering the wafer per unit time increases, the heat dissipation capacity of the wafer remains unchanged, and the wafer warpage increases. Previous studies have shown that increasing the wire saw speed can improve the surface quality of slices [2,3], but a higher wire saw speed leads to an increase in wafer warpage, from the perspective of wafer geometry quality.

By changing the wire speed vw in Equation (3) to calculate the correspondent heat flux density, the relationship between feed rate and wafer warpage is established based on simulation calculation of the finite element model. Figure 16 shows the effect of feed rate on wafer warpage at different wire speeds. It can be seen that as the feed rate increases, the wafer warpage gradually increases. This is because as the feed rate increases, the amount of material cut per unit time increases, resulting in an increase in heat generation. At the same time, the amount of heat entering the wafer per unit time increases. However, the heat dissipation capacity of the wafer remains basically unchanged, and the wafer warpage increases.

From the above research results, it can be seen that in the current pursuit of high wire speed and large feed rate sawing processes to achieve efficient cutting, how to achieve effective lubrication and cooling of narrow saw kerf is the key to achieving low wafer warpage sawing processes.

6. Conclusions

This paper establishes a finite element model for thermal analysis of sapphire crystal during diamond wire saw cutting, and analyzes the wafer temperature field distribution and the variation law and internal relationship of node thermal deformation displacement field during the sawing process. Based on the thermal deformation displacement field of wafer surface nodes, a calculation and analysis model for the sapphire wafer warpage in wire sawing was established. After the rationality of the finite element model was verified through sawing experiments, the influence of wafer thickness, diamond wire diameter, and sawing process parameters on the warpage of sapphire wafers was studied based on the finite element simulation model. The following conclusion was drawn:

(1)

The temperature and deformation at the sawing position is the largest. As the cutting depth increases during sawing, the temperature of the wafer gradually increases and tends to stabilize.

(2)

The thickness of sapphire wafers cut by the diamond wire saw decreases, and the smaller the diameter of the diamond wire used, the greater the warpage of the cut wafers.

(3)

The sawing process parameters mainly affect the wafer warpage by influencing the heat density and power during sawing. The warpage of sapphire wafers increases with the increase of the saw wire speed and feed rate. How to achieve effective lubrication and cooling of a narrow kerf in sawing processing is the key to obtaining low warpage wafers.