# Recent Advances in Precision Diamond Wire Sawing Monocrystalline Silicon

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## Abstract

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## 1. Introduction

_{3}-HF for isotropic etching [15], employing KOH or NaOH for anisotropic etching [16], and utilizing plasma-etching techniques. However, due to the expensive equipment required and the significant risks posed to operators, chemical methods have not been widely employed in the large-scale production of silicon wafers [17]. The cutting method refers to the cutting of monocrystalline silicon rods into thin slices or wafer shapes [18]. Commonly used cutting methods include wire saw cutting, internal stress cutting, and laser cutting. Wire saw cutting is the most commonly used method in which a monocrystalline silicon rod is placed on a cutting machine and cut into thin slices or wafers via diamond wire sawing (DWS) [19]. The production of silicon wafers typically involves slicing, and the main slicing processes can be categorized into free abrasive wire saw and fixed abrasive DWS techniques. The dominant method of cutting silicon wafers has shifted from free abrasive slurry wire sawing to fixed abrasive DWS [20,21]. The DWS method is effective at cutting monocrystalline silicon material due to the diamond’s high degrees of hardness and sharpness, resulting in high-precision cutting results [22,23]. This method is widely applied in the processes of precision manufacturing semiconductor devices, optical components, and other monocrystalline silicon products [24]. In addition, the thinning process entails the removal of the majority of the monocrystalline silicon wafer’s thickness, leaving only 5% for chip manufacturing [8]. Consequently, reducing the thickness of chip slices becomes a crucial strategy for enhancing the utilization of material and minimizing manufacturing costs [25,26].

_{s}”, while the silicon ingot is fed perpendicular to the diamond wire grid at “v

_{f}”. Xiao et al. [27] modified and simplified the model.

## 2. Models and Simulation for DWS

#### 2.1. Mathematical Model

_{ij}and the critical depth h

_{c}serves as a primary factor in determining the cutting state, as proposed by Nakamura et al. [33]. When 0 < h

_{ij}≤ h

_{c}, the state is in a ductile mode, while when h > h

_{c}, the state is in a brittle mode. Bifano et al. [34] derived an equation for the critical depth h

_{c}, as follows:

_{s}is the hardness, and K

_{c}is the fracture toughness of the specimen. Drawing on micro-indentation mechanics, Lawn and Wilshaw [35] developed a representative crack system for the interaction between an abrasive material and a brittle sample surface. Figure 3b depicts this system. Notably, plastic zones form beneath the surface of the specimen, from which both median and lateral cracks originate. Median cracks typically propagate perpendicular to the sample surface, while lateral cracks generally propagate parallel to it. Marshall et al. [36] derived formulas for determining the depth and width of a lateral crack, which can be expressed as follows:

_{nij}of any given abrasive can be expressed as follows, in which C

_{lhij}represents the depth of a lateral crack, C

_{lwij}denotes the width of the lateral crack, k is a dimensionless constant (k = 0.226) [36], and ν represents the Poisson’s ratio value of the specimen. The equation for the normal load F

_{nij}was derived by Williams as follows [37]:

_{mij}is as follows:

_{e}for the elastic stress field and the plastic stress field X

_{r}beneath the contact impression, which were determined to be 0.032 and 0.026, respectively [38].

_{L}. When material removal takes place in a ductile mode, it occurs through the shearing action of the abrasive. In this case, the average cutting depth of the abrasive corresponds to the undeformed chip thickness, represented as g, as shown in Figure 3d [39] In such cases, the volume of the removed material can be approximated as a triangular prism. To calculate this volume, multiply the height by the area of the triangle. As depicted in Figure 3c, on a cross-section of a processed material, an area A

_{x}removed by abrasive cutting in a brittle fracture mode can be estimated as follows [39]:

_{n}corresponds to the normal force exerted on a single abrasive (in N), while θ signifies the half-angle (in °) of the abrasive edge.

_{L}, can be determined using the following Equation [41]:

_{IC}and measured in MPa·m

^{1/2}, and α, which represents the indentation constant associated with the shape of the abrasive, are important parameters in the equation. For a Vickers indenter with an angle of 140°, the value of α is 0.12.

_{p}during ductile-shear-mode abrasive cutting can be approximately calculated using the following formula [39]:

_{sigd}, can be represented by the following equation [39]:

#### 2.2. Finite Element Methods

#### 2.3. Molecular Dynamics Model

#### 2.4. Summary

## 3. Machining Performance of DWS

#### 3.1. DWS Equipment

_{TP}is applied to tighten the wire saw through the use of cylinders and tensioning wheels. The drum roller is rotated by the motor, causing the wire saw to execute back-and-forth movements with a linear velocity of v

_{s}. Meanwhile, the drum roller, tensioning wheels, guiding wheels, and auxiliary guiding wheels rotate. The same machine frame drives the wheel to feed vertically downward with a feed rate of v

_{w}. At a rotational speed of n

_{w}, the spindle drives the workpiece to execute consistent circular motion along the y-axis.

#### 3.2. Material Removal Rate

^{3}/s, showing a consistent trend with the average normal force. Additionally, the MRR exhibits cyclic variations, including instances in which it reaches a minimum value of zero. These fluctuations can be attributed to wire reversal, which causes the absolute wire speed to drop to zero. Figure 7b illustrates the variations in MRR within the wire reciprocation cycle. The MRR immediately increases or decreases when the wire accelerates or decelerates. Stable fluctuations in the MRR are observed when the wire operates at a consistent speed. These fluctuations are solely attributed to the oscillation of the workpiece. The variation in the MRR within one reciprocating cycle is illustrated in Figure 7c. During the oscillation, the MRR reaches its minimum value when the oscillation angle is close to zero, and it attains its maximum value when the workpiece reaches the extreme position. The maximum value within one reciprocating cycle is nearly twice the minimum value. In summary, the MRR in the wire sawing process is unstable overall, as its fluctuations are strongly influenced by both the wire reciprocation motion and workpiece oscillation. According to Chen and Gupta [114], the MRR per unit contact length is influenced by the cutting depth of each abrasive grain during wire saw cutting, which in turn affects the surface quality. By combining the simulated contact length with the actual contact area, the MRR per unit contact length is mapped onto the surface of the workpiece, as shown in Figure 7d.

#### 3.3. Surface Morphology and Subsurface Damage

#### 3.4. Summary

## 4. Hybrid Machining

#### 4.1. Ultrasonic Vibration-Assisted DWS

_{t}on the wire saw. At the same time, the wire saw is driven by the frame to feed downward at a speed v

_{c}, and the loading tray securely holds the workpiece and enables it to rotate uniformly around its own axis at the specified speed of n

_{w}. Ultrasonic excitation with an amplitude A and as frequency f is applied along the ultrasonic guide wheel feeding direction to make the wire saw perform ultrasonic compound processing [156].

_{w}for both methods. In addition, Wang et al. [161] conducted a comparative study of the surface roughness of workpieces processed via DWS and UV-DWS. The experimental results showed that the surface roughness of the workpiece machined via UV-DWS was 4.3~29.7% lower than the one machined via DWS. Wang et al. [140] investigated the effects of different sawing parameters and ultrasonic vibrations on the sawing temperature when performing DWS on monocrystalline silicon. Under the same sawing parameters, the sawing temperature of UV-DWS is about 1.5 °C higher than that of DWS. The maximum sawing temperature of DWS was 27.9 °C and the maximum sawing temperature of UV-DWS was 29.9 °C, indicating that ultrasonic vibration does not significantly change the sawing temperature. Figure 9e shows the maximum sawing temperatures at different n

_{w}values.

#### 4.2. Electrical Discharge-Assisted DWS

^{2}/min to around 13 mm

^{2}/min. The greatest cutting efficiency was achieved via composite machining. Qiu et al. [171] designed a sawing test for longitudinal and cross-cutting with different feed directions to compare the kerf length of DWS and ED-DWS. The kerf length was used as the machining accuracy index. The results are shown in Figure 10c which shows that the machining accuracy of DWS is 1X+ > 4Y-> 2Y+ > 3X-, and there is no significant difference between longitudinal and crosscutting in ED-DWS. The machining accuracy of ED-DWS is significantly better than that of DWS for both longitudinal and transverse cuts, as shown in Figure 10d. Qiu et al. [172] proposed an environmentally improved method for diamond wire EDM sawing under electroplating liquid cooling conditions. The results showed that the machining accuracy using bath cooling was superior to that of jet cooling for both DWS and ED-DWS. In terms of tension, the stability and envelope values of the tension in ED-DWS with both cooling methods surpass those of DWS, indicating improved machining conditions in ED-DWS [173]. In terms of tension, the stability and envelope values of the tension in ED-DWS with both cooling methods surpass those of DWS, indicating improved machining conditions in ED-DWS.

#### 4.3. Electrochemical -Assisted DWS

#### 4.4. Summary

_{2}, ZrO

_{2}, and TiO

_{2}, metal oxides that were superior to SiO

_{2}in terms of their higher dielectric constants and were attracting attention due to their potential as gate dielectric materials to replace SiO

_{2}and have attracted much attention.

## 5. Outlooks

- (1)
- The development of advanced modeling and simulation techniques can aid in the optimization of the cutting process. By utilizing computational models, the complex interrelationships among the cutting tool, the workpiece, and the process parameters can be analyzed [27,110]. Multiple research methods could be combined, such as mathematical modeling with MD, MD with an FEM simulation, or a combination of these three methods. These models can provide insights into material removal mechanisms, stress distributions, and temperature profiles, enabling the prediction and control of surface quality and subsurface damage.
- (2)
- Optimizing the cutting parameters is crucial for achieving greater precision and surface quality. By systematically studying the effects of these process parameters, it becomes possible to understand their complex interplay and identify the optimal settings. Adjusting the wire tension can influence the stability and vibration characteristics of the diamond wire, which in turn affect the cutting process. By understanding the complex interplay between these parameters, it is possible to identify optimal settings that minimize surface roughness and subsurface damage while maximizing productivity.
- (3)
- Combining UV-DWS, ED-DWS, and EC-DWS methods with DWS can enhance the processing of monocrystalline silicon. By combining these methods, the cutting process can be optimized to achieve greater efficiency, better surface quality, and precise control over the cutting parameters. This combination of techniques holds great potential for advancing the DWS of monocrystalline silicon and similar materials. By combining these methods, the cutting process can be optimized to achieve a higher level of efficiency, better surface quality, and precise control over the cutting parameters. Process methods such as laser ultrasound-assisted DWS or a combination of other auxiliary methods may also be introduced in the future to further improve processing quality [189,190]. Non-silicon-based technologies have gained attention due to their unique properties and potential advantages over traditional silicon-based approaches. These technologies offer different characteristics and performance capabilities that may be advantageous in terms of flexibility, energy efficiency, or higher operating frequencies.
- (4)
- Artificial intelligence (AI) technology is growing in various industries. The integration of internal monitoring and feedback systems can enable real-time process control and quality assurance. Machine learning can enable the real-time monitoring of key process parameters and provide feedback for adaptive control [191,192,193]. By incorporating sensors and measurement techniques [194], it becomes possible to monitor key parameters such as the cutting force, temperature, and surface roughness during the cutting process [195,196]. This information can be used to adjust cutting parameters on the fly and ensure consistent and high-quality results.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Schematic diagram of the material removal pattern: (

**a**) free abrasive cut; (

**b**) fixed abrasive cut; (

**c**) schematic diagram of cutting silicon ingots with fixed abrasive DWS [27].

**Figure 4.**The crack growth angles of {110} monocrystalline silicon plates for a given chiral angle α = 0° and t = 17.28 Å under different loading angles using the FEM method: (

**a**) φ = 0°; (

**b**) φ = 15°; (

**c**) φ = 30°; (

**d**) φ = 45°; (

**e**) φ = 60°; (

**f**) φ = 75°; (

**g**) φ = 90° [52].

**Figure 5.**The probability density of von Mises stress distribution in monocrystalline silicon [74]: (

**a**) under three different applied strains and the same strain rate; (

**b**) under three different strain rates and the same applied strain.

**Figure 6.**DWS processing and manufacturing process: (

**a**) schematic diagram of DWS [1]; (

**b**,

**c**) DWS equipment.

**Figure 7.**The time curve of MRR and the mapping of MRR per unit contact length [110]; (

**a**) variation in MRR throughout the entire sawing process (the red box refers to the effect at 10,000 s in (

**b**)); (

**b**) influence of wire reciprocating motion on MRR (the red box refers to the effect of the workpiece oscillation on MRR in (

**c**)); (

**c**) impact of workpiece oscillation on MRR; (

**d**) distribution of MRR per unit contact length on the workpiece surface.

**Figure 8.**Surface morphology and subsurface damage characteristics in monocrystalline silicon wafer sawing, (

**a,c**) shows the sawn surface in the crystallographic plane {100}, (

**b**,

**d**) location of median microcracks in the subsurface region [113].

**Figure 10.**Electrical discharge-assisted DWS: (

**a**) principle diagram of ED-DWS [125]; (

**b**) surface roughness and cutting efficiency of three machining methods; machining accuracy of DWS (

**c**) and ED-DWS (

**d**).

Types of Models and Simulations | Authors, Year | Purpose | Findings | Remarks |
---|---|---|---|---|

Mathematical model | Li et al., 2019 [42] | Based on indentation fracture mechanics, a mathematical model of the influence of process parameters and wire saw parameters was developed. | The areas of brittle cracks produced by the abrasive can affect the surface morphology of the wafer. | Larger feed rates and line speeds increase the cutting efficiency and make it easier to obtain a surface of brittle excised material. |

Wu et al., 2013 [43] | The effects of crystal defects on the cutting performance of polysilicon were investigated. | At the critical cutting depth of the ductile-brittle transition of the material, there was a significant variation within the particles. | A higher dislocation density is associated with greater fracture toughness and larger critical depth of cut. | |

Yin et al., 2021 [44] | A mathematical model of DWS was established, and the sawing process was numerically calculated. | The critical ratio of the workpiece feed speed to the saw wire motion speed was obtained with a combination of different parameters. | Increasing the speed of the saw wire movement or decreasing the feed speed of the workpiece is more beneficial to achieving material removal. | |

MD model | Liu et al., 2022 [74] | The atomic structures of orthocrystalline silicon crystals and silicon nanowires were compared. | Strain rate sensitivities and critical strain rates were obtained for both structures using a rate reactivity model. | A calculation of both rates revealed that the additional surface of THE SiNW reduced the sensitivity of the strain rate. |

Olufayo et al., 2013 [89] | MD simulation for the atomic visualization of plastic material flow at the tool-workpiece interface during orthogonal cutting. | The simulated MD force and temperature outputs were evaluated to obtain the accuracy of the model. | The MD method can be used to study the atomic reactions on the tool/workpiece surface, revealing the ductile transition response of the nanoprocess. | |

Dai et al., 2017 [90] | MD simulation of the cutting of monocrystalline silicon with laser-fabricated, nanostructured diamond tools. | The effects of different trench orientations, depths, widths, factors, and shapes on the nanoscale cutting process were investigated. | Groove orientation has a significant effect on the nanoscale cutting process, and cutting with V-shaped grooves can improve material removal. | |

FEM | Wei et al., 2018 [52] | The thickness and stress strength factors of monocrystalline silicon, as well as the crack extension angle, were studied via MD simulation and FEM, respectively. | The thickness and stress strength factors, as well as the crack extension angle, were obtained via MD simulation and FEM, respectively. | The critical stress strength factors and crack extension angles are clearly dependent on the chiral angle, thickness, and loading angle of the monocrystalline silicon plate. |

Zhang et al., 2014 [53] | Anisotropic effects in silicon were evaluated using stiffness and flexibility coefficient matrixes. | Proper crystal orientation can improve performance and reduce mechanical bending stress. | For monocrystalline silicon, heat deformation can be approximated by using the isotropic constant Poisson’s ratio. | |

Skalka et al., 2021 [91] | An FE simulation and optimization procedures were used to determine the cohesive energy density of monocrystalline silicon. | The adhesion energy density was evaluated and the material toughness was determined. | The reliability of the model originates from the comparison of the numerical simulation results with the measured data. |

Parameters | Authors, Year | Purpose | Findings | Remarks |
---|---|---|---|---|

Tension | Albrecht and Möhr-ing, 2018 [107] | The effect on the stability of the sawing process was investigated experimentally and by simulation. | At higher tensions (350 MPa and 400 MPa), saw blade displacement remained essentially the same, while higher tensions resulted in reduced displacement. | Adjusting the saw blade parameter tension during the cutting process does not affect the processing time. |

Cutting speed, feed rate, and wire tension | Costa et al., 2020 [108] | To investigate the effect of DWS on the surface integrity of monocrystalline silicon. | For two wire tensions (Twire) = 30 N, the Sa value increased significantly when compared with the specimens sawn using Twire = 20 N. | The most suitable set of cutting parameters is the lowest feed rate and wire tension and the highest wire cutting speed. |

Stiffness of wire web, tension, fluctuation of wire, and reciprocating period | Qiu et al., 2021 [109] | To study the factors affecting the machining accuracy of circular diamond rope saws and their mechanisms. | The roughness value of endless wire sawing was Ra = 1.6 µm and that of reciprocating sawing was Ra = 1.254 µm. | Stable tension corresponds to better machining accuracy. |

Wire speed, feed rate, rocking angle, preload force, and guide roller distance | Lai et al., 2023 [110] | To analyze the effect of machining parameters on sawing force, contact length, and MRR. | Workpiece rocking reduces contact length, with a maximum contact length of about 20% of the workpiece diameter during sawing. | Feed speed, maximum wire feed speed, maximum swing angle and preload force all affect the range of MRR fluctuations. |

Reciprocating period and sawing arc length | Dong et al., 2021 [111] | A reciprocating oscillating motion pattern was introduced in a cutting frame saw to study the cutting performance of sawing. | The depth of the cut and the distribution of the sawing force depend on the position of the saw blade on the saw surface. | The effect of sawing conditions on sawing force is related to the depth of cut of the cutter head. |

Types of Hybrid Machining | Authors, Year | Purpose | Findings | Remarks |
---|---|---|---|---|

UV-DWS | Wang et al., 2022 [156] | Conducting theoretical research on the cutting force of UV-DWS based on abrasive wear. | A theoretical model of UV-DWS force from single to multiple abrasive grains was developed. | Compared with DWS, UV-DWS can reduce the sawing force and improve the flatness of the workpiece. |

Wang et al., 2023 [140] | UV-DWS of monocrystalline silicon SSD. | A mathematical model of UV-DWS damage to silicon wafers was developed, and the law of SSD was analyzed. | The UV-DWS monocrystalline wire silicon model verifies that the SSD varies with different sawing parameters. | |

Wang et al., 2019 [161] | Modeling and validation of UV-DWS cutting force based on impact loading. | The validity of the impact loading was demonstrated using the UV-DWS. | The surface quality of UV-DWS is better than that of DWS. | |

ED-DWS | Wu et al., 2018 [170] | A pilot study of EDM wire cutting and fixed abrasive wire saw compound machining was conducted. | A composite machining method combining EDM wire cutting and fixed abrasive DWS together was studied. | Compared with fixed abrasive DWS, the hybrid processing method reduces silicon surface scratches. |

Qiu et al., 2023 [171] | The machining accuracy of DWS and ED-DWS in longitudinal and transverse sawing was compared. | Better machining accuracy and surface quality are achieved with ED-DWS under bath cooling than under jet cooling. | ED-DWS outperforms DWS in terms of machining accuracy and cutting efficiency. | |

Qiu et al., 2023 [172] | An environmentally improved method of ED-DWS under plating solution cooling conditions was proposed. | Its advantages were compared with those of jet cooling through a series of sawing tests. | The roughness of bath cooling is better than jet cooling, but the fluidity becomes worse and chip removal becomes difficult. | |

EC-DWS | Wang et al., 2017 [179] | Electrochemical discharge-assisted DWS cutting of hard and brittle materials for surface integrity. | Based on the experimental results, each element of the machined surface was analyzed. | The combination of electrochemical discharge and DWS can improve surface roughness. |

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## Share and Cite

**MDPI and ACS Style**

Li, A.; Hu, S.; Zhou, Y.; Wang, H.; Zhang, Z.; Ming, W.
Recent Advances in Precision Diamond Wire Sawing Monocrystalline Silicon. *Micromachines* **2023**, *14*, 1512.
https://doi.org/10.3390/mi14081512

**AMA Style**

Li A, Hu S, Zhou Y, Wang H, Zhang Z, Ming W.
Recent Advances in Precision Diamond Wire Sawing Monocrystalline Silicon. *Micromachines*. 2023; 14(8):1512.
https://doi.org/10.3390/mi14081512

**Chicago/Turabian Style**

Li, Ansheng, Shunchang Hu, Yu Zhou, Hongyan Wang, Zhen Zhang, and Wuyi Ming.
2023. "Recent Advances in Precision Diamond Wire Sawing Monocrystalline Silicon" *Micromachines* 14, no. 8: 1512.
https://doi.org/10.3390/mi14081512