Prediction of Subsurface Microcrack Damage Depth Based on Surface Roughness in Diamond Wire Sawing of Monocrystalline Silicon

At a Glance

Metadata	Details
Publication Date	2024-01-24
Journal	Materials
Authors	Keying Wang, Yufei Gao, Chunfeng Yang
Institutions	Shandong University
Citations	9
Analysis	Full AI Review Included

Executive Summary

This research establishes a fast, non-destructive method for predicting the Subsurface Microcrack Damage Depth (SSD) in monocrystalline silicon (mono-Si) wafers produced by diamond wire sawing, crucial for optimizing subsequent processing steps.

Core Achievement: Developed and validated an improved theoretical model linking the easily measurable surface roughness (SR, R_a) to the critical SSD.
Key Relationship: The relationship is non-linear and increasing, defined by the refined equation: SSD = 21.179 R_a^4/3.
Model Accuracy: The improved model achieved high predictive accuracy, reducing the relative error between predicted and experimentally measured SSD values to less than 5%.
Mechanism Basis: The model is rooted in indentation fracture mechanics, comprehensively considering the effects of tangential force, elastic stress fields, and residual stress fields on median crack propagation.
Refinement Factor: A coefficient (eta = 1.1) was introduced to account for the influence of material ductile regime removal on the measured R_a values, enhancing prediction accuracy for industrial sawing conditions.
Process Effects: Experimental results confirmed that decreasing wire speed (V_s) or increasing feed speed (V_w) leads directly to increased surface roughness and deeper subsurface damage.

Technical Specifications

Parameter	Value	Unit	Context
Improved SSD Prediction Model	21.179 R_a^4/3	µm	Relationship between SSD and Surface Roughness (R_a)
Maximum Relative Error (Improved Model)	< 5	%	Accuracy of SSD prediction vs. experimental measurement
Monocrystalline Silicon Plane	(111)	Crystal Plane	Sawing orientation
Elastic Modulus (E)	187	GPa	Material characteristic (mono-Si)
Hardness (H)	9	GPa	Material characteristic (Mohs hardness)
Static Fracture Toughness (K_IC)	0.82	MPa·m^1/2	Material characteristic
Diamond Wire Diameter	120	µm	Tool specification
Abrasive Particle Size	15-20	µm	Tool specification
Abrasive Tip Half Angle (phi)	65	°	Assumed value for calculation
Median Crack Deflection Angle (beta)	24.785	°	Calculated deflection angle
Tangential/Normal Load Ratio Correction (epsilon)	1.072	Dimensionless	Calculated correction factor

Key Methodologies

The study combined theoretical modeling based on fracture mechanics with controlled sawing experiments and detailed metrology.

Theoretical Model Development:
- The model utilized indentation fracture mechanics to describe crack systems (median and lateral cracks) beneath the abrasive particle.
- The median crack length (SSD) expression was derived, incorporating contributions from both the elastic stress field and the residual stress field (Equation 2).
- The model was revised to account for the combined effects of normal (F_n) and tangential (F_t) loads, including the median crack deflection angle (beta) and dynamic fracture toughness (0.3 K_IC).
- The final theoretical relationship between SSD and SR (R_z) was established by eliminating the normal load (F_n) variable.
Sawing Experiment Setup:
- Equipment: Reciprocating single-wire diamond wire saw.
- Workpiece: Mono-Si ingot cut along the (111) crystal plane (10 mm x 10 mm x 40 mm).
- Six experimental sets were run by varying two key parameters:
  - Wire Speed (V_s): 78 m/min and 48 m/min.
  - Feed Speed (V_w): 0.18, 0.36, and 0.54 mm/min.
Surface Roughness (SR) Measurement:
- Instrument: Contact surface roughness measuring instrument.
- Procedure: R_a values were measured at five points perpendicular to the wire mark and averaged.
- Conversion: Measured R_a was used to approximate the theoretical R_z (peak-to-valley roughness) using the relationship R_z ≈ 5 R_a (for R_a < 2.5 µm).
Subsurface Damage Depth (SSD) Measurement:
- Preparation: Wafer cross-sections were embedded, ground, and polished.
- Etching: Specimens were corroded in hydrofluoric acid solution for 15 s to reveal the microcracks.
- Observation: SSD (longest median crack depth) was measured using an OLYMPUS optical microscope, with five locations observed and averaged per specimen.
Model Refinement:
- Comparison of initial theoretical predictions (SSD = 19.254 R_a^4/3) with experimental data showed predictions were consistently lower.
- A coefficient (eta = 1.1) was introduced to account for the influence of ductile regime material removal on the measured R_a, resulting in the improved, validated model: SSD = 21.179 R_a^4/3.

Commercial Applications

This predictive model provides a critical tool for quality control and process optimization in industries relying on precision slicing of hard, brittle materials.

Photovoltaic (Solar Cell) Manufacturing:
- Enables rapid, non-destructive assessment of wafer quality immediately after slicing.
- Allows for real-time adjustment of wire speed and feed speed to maintain target SSD, minimizing subsequent breakage risk and maximizing yield.
Semiconductor Wafer Production:
- Crucial for manufacturing high-quality mono-Si chip substrates where deep SSD severely compromises mechanical strength and device integrity.
- Provides the necessary data to accurately calculate the required material removal depth (lapping/polishing) to eliminate damage, reducing processing time and cost.
Advanced Materials Processing:
- The underlying fracture mechanics framework is transferable to the wire sawing of other hard, brittle materials (e.g., Silicon Carbide, Sapphire, and certain ceramics).
- Supports the development of automated quality control systems that use surface metrology (R_a) as a proxy for subsurface structural integrity.

View Original Abstract

In diamond wire saw cutting monocrystalline silicon (mono-Si), the material brittleness removal can cause microcrack damage in the subsurface of the as-sawn silicon wafer, which has a significant impact on the mechanical properties and subsequent processing steps of the wafers. In order to quickly and non-destructively obtain the subsurface microcrack damage depth (SSD) of as-sawn silicon wafers, this paper conducted research on the SSD prediction model for diamond wire saw cutting of mono-Si, and established the relationship between the SSD and the as-sawn surface roughness value (SR) by comprehensively considering the effect of tangential force and the influence of the elastic stress field and residual stress field below the abrasive on the propagation of median cracks. Furthermore, the theoretical relationship model between SR and SSD has been improved by adding a coefficient considering the influence of material ductile regime removal on SR values based on experiments sawing mono-Si along the (111) crystal plane, making the theoretical prediction value of SSD more accurate. The research results indicate that a decrease in wire speed and an increase in feed speed result in an increase in SR and SSD in silicon wafers. There is a non-linear increasing relationship between silicon wafer SSD and SR, with SSD = 21.179 Ra4/3. The larger the SR, the deeper the SSD, and the smaller the relative error of SSD between the theoretical predicted and experimental measurements. The research results provide a theoretical and experimental basis for predicting silicon wafer SSD in diamond wire sawing and optimizing the process.

Tech Support

Original Source

DOI: https://doi.org/10.3390/ma17030553

References

2023 - Multi-Objective Optimization of Energy Consumption, Surface Roughness, and Material Removal Rate in Diamond Wire Sawing for Monocrystalline Silicon Wafer [Crossref]
2018 - The impact of subsurface damage on the fracture strength of diamond-wire-sawn monocrystalline silicon wafers [Crossref]
2018 - Study on the Subsurface Microcrack Damage Depth in Electroplated Diamond Wire Saw Slicing Sic Crystal [Crossref]
2023 - Study on Subsurface Microcrack Damage Depth of Diamond Wire As-Sawn Sapphire Crystal Wafers [Crossref]
2015 - Effect of Initial Deflection of Diamond Wire on Thickness Variation of Sapphire Wafer in Multi-Wire Saw [Crossref]
2023 - Investigation of Cutting Rate of Diamond Wire Saw Machine Using Numerical Modeling [Crossref]
2014 - Distribution of Diamond Grains in Fixed Abrasive Wire Sawing Process [Crossref]
2022 - Image-processing-based Model for the Characterization of Surface Roughness and Subsurface Damage of Silicon Wafer in Diamond Wire Sawing [Crossref]
2022 - Experiment and Theoretical Prediction for Subsurface Microcracks and Damage Depth of Multi-Crystalline Silicon Wafer in Diamond Wire Sawing [Crossref]
2017 - Experimentally Validated Finite Element Analysis for Evaluating Subsurface Damage Depth in Glass Grinding Using Johnson-Holmquist Model [Crossref]