Breakage Ratio of Silicon Wafer during Fixed Diamond Wire Sawing
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2022-11-02 |
| Journal | Micromachines |
| Authors | Tengyun Liu, Yancai Su, Peiqi Ge |
| Institutions | Qilu University of Technology, Shandong Academy of Sciences |
| Citations | 6 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- A mathematical model was established using elastic thin plate theory and Weibull distribution to systematically study the relationship between stress, fracture strength, and breakage ratio in silicon wafers during fixed diamond wire sawing (FDWS).
- The model confirms that transverse vibration, primarily induced by external machine excitation (50 Hz), is the main cause of wafer breakage, treating the wafer as an elastic cantilever plate.
- The maximum vibration amplitude (up to 160 µm for a 0.2 mm wafer) and maximum stress increase sharply as the cutting depth increases, particularly beyond 0.125 m.
- Wafer thickness is critically linked to yield: the breakage ratio for 156 mm x 156 mm wafers increased from 2% (0.20 mm thickness) to 6% (0.15 mm thickness) upon completion of the sawing stage.
- The theoretical natural frequency (69.32 Hz) showed strong agreement with Finite Element Method (FEM) results (67 Hz), validating the model’s accuracy for predicting mechanical behavior.
- The research provides a necessary framework for optimizing FDWS parameters to reliably achieve ultra-thin silicon wafers, thereby reducing manufacturing costs in the photovoltaic industry.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Wafer Dimensions (L x W) | 156 x 156 | mm | Standard PV ingot section |
| Sawn Wafer Thickness (h) | 0.15, 0.18, 0.20 | mm | Tested thicknesses |
| Silicon Density (ρ) | 2330 | kg/m3 | Material property |
| Modulus of Elasticity (E) | 165 | GPa | Material property |
| Poisson Ratio (µ) | 0.22 | - | Material property |
| Wire Diameter (d) | 100 | µm | Fixed diamond wire |
| Wire Speed (vs) | 2 | m/s | Sawing parameter |
| Feed Rate (vf) | 6 | µm/s | Sawing parameter |
| Excitation Frequency (ωF) | 50 | Hz | External machine vibration source |
| Weibull Scale Parameter (σ0) | 151.3 | MPa | Fracture strength distribution |
| Weibull Shape Parameter (mA) | 3.5 | - | Fracture strength distribution |
| Max Vibration Amplitude | 160 | µm | 0.2 mm wafer at 156 mm cutting depth |
| Max Stress (0.15 mm wafer) | > 80 | MPa | At completion of sawing stage |
| Breakage Ratio (0.15 mm wafer) | 6 | % | At completion of sawing stage |
| Breakage Ratio (0.20 mm wafer) | 2 | % | At completion of sawing stage |
| First Natural Frequency (Theoretical) | 69.32 | Hz | 156 mm cutting depth |
Key Methodologies
Section titled “Key Methodologies”- Wafer Modeling: The silicon wafer is treated as an elastic cantilever plate based on the thin plate theory (Kirchhoff plate theory), fixed at the resin adhesive side (y=0) and free on the cutting edge.
- Free Vibration Analysis: The vibration equation was solved using the method of separation of variables and integral-transform techniques to determine the shape function W(x,y) and natural frequencies (ωmn).
- The first four natural frequencies were calculated and verified against FEM simulations, showing a maximum relative error of 3.43%.
- Forced Vibration and Load Modeling:
- The total cutting force generated by diamond abrasives was simplified as a stationary random fluctuation, modeled as a harmonic force P(t) = F sin ωFt, with an excitation frequency (ωF) of 50 Hz.
- The total transverse load (FZ), which drives lateral vibration, was calculated based on the normal cutting force (FN) and the geometry of the wire contact.
- Dynamic Response Calculation: The forced vibration response w(x,y,t) was obtained by solving the dynamic equation using the vibration theory of a single degree of freedom system, incorporating the Duhamel integral for harmonic excitation.
- Stress Determination: Maximum principal stress (σmax) was calculated for an arbitrary point in the wafer using the stress equations derived from Kirchhoff plate theory, based on the calculated vibration amplitude.
- Breakage Ratio Calculation: The probability of break P(σ) was determined using the two-parameter Weibull distribution model, integrating the maximum applied stress (σmax) over the wafer area (A), utilizing established Weibull parameters (σ0 = 151.3 MPa, mA = 3.5).
Commercial Applications
Section titled “Commercial Applications”- Photovoltaic (PV) Wafer Production: Direct application in optimizing the fixed diamond wire sawing process for monocrystalline silicon, the first key step in PV manufacturing.
- Cost Reduction and Yield Improvement: Providing engineering limits for wafer thinning. By quantifying the yield loss associated with thinner wafers (e.g., 6% breakage at 0.15 mm), manufacturers can balance material savings against yield targets.
- Sawing Machine Design: Informing the design specifications for next-generation diamond wire saws, specifically targeting the reduction of external vibration sources (50 Hz excitation) to minimize transverse wafer vibration.
- Process Control Automation: Establishing critical control points (e.g., cutting depth > 0.125 m) where stress increases sharply, allowing automated systems to dynamically adjust wire speed or feed rate to mitigate fracture risk during the final stages of cutting.
- Adhesive Material Specification: Defining the minimum required adhesive strength for the resin glue used to fix the silicon ingot, ensuring the wafer remains securely attached to the base plate even under maximum stress conditions at the end of the cut.
View Original Abstract
Monocrystalline silicon is an important material for processing electronic and photovoltaic devices. The fixed diamond wire sawing technology is the first key technology for monocrystalline silicon wafer processing. A systematic study of the relationship between the fracture strength, stress and breakage rate is the basis for thinning silicon wafers. The external vibration excitation of sawing machine and diamond wire lead to the transverse vibration and longitudinal vibration for silicon wafers. The transverse vibration is the main reason of wafer breakage. In this paper, a mathematical model for calculating breakage ratio of silicon wafer is established. The maximum stress and breakage ratio for as-sawn silicon wafers are studied. It is found that the maximum amplitude of the silicon wafers with the size of 156 mm × 156 mm × 0.2 mm was 160 μm during the diamond wire sawing process. The amplitude, maximum stress and breakage rate of the wafers increased with the increase of the cutting depth. The smaller the silicon wafer thickness, the larger of silicon wafer breakage ratio. In the sawing stage, the breakage ratio of the 156 mm × 156 mm section with a thickness of 0.15 mm of silicon wafers is 6%.
Tech Support
Section titled “Tech Support”Original Source
Section titled “Original Source”References
Section titled “References”- 2016 - Surface chemical-bonds analysis of silicon particles from diamond-wire cutting of crystalline silicon [Crossref]
- 2016 - Wire sawing technology: A state-of-the-art review [Crossref]
- 2021 - Fabrication of thin resin-bonded diamond wire and its application to ductile mode wire sawing of mono-crystalline silicon [Crossref]
- 2016 - A cost roadmap for silicon heterojunction solar cells [Crossref]
- 2018 - Silicon foil solar cells on low cost supports [Crossref]
- 2018 - Review of status developments of high-efficiency crystalline silicon solar cells [Crossref]
- 2022 - Status and perspectives of crystalline silicon photovoltaics in research and industry [Crossref]