Analysis of Wafer Warpage in Diamond Wire Saw Slicing Sapphire Crystal

At a Glance

Metadata	Details
Publication Date	2024-08-30
Journal	Applied Sciences
Authors	Yihe Liu, Dameng Cheng, Guanzheng Li, Yufei Gao
Institutions	Shandong University
Citations	1
Analysis	Full AI Review Included

Executive Summary

This research establishes a validated Finite Element Analysis (FEA) model to predict and analyze wafer warpage during the diamond wire saw (DWS) slicing of sapphire crystals.

Core Achievement: A simulation calculation model was successfully developed using thermoelasticity theory and sequential coupling FEA (ABAQUS) to map DWS process parameters directly to sapphire wafer warpage.
Validation: The FEA model results showed strong consistency with physical sawing experiments, with an error margin of less than 12%, validating its use for parameter optimization.
Thermal Distribution: The highest temperature and thermal deformation occur directly in the sawing area. As cutting depth increases, the wafer temperature stabilizes around 34.5 °C.
Thickness Dependence: Wafer warpage is inversely related to wafer thickness; thinner wafers (e.g., 200 µm) exhibit significantly higher warpage due to reduced stiffness and deformation resistance.
Process Parameter Influence: Warpage increases with higher wire speed and feed rate, as both parameters increase the heat generation rate and heat density entering the wafer per unit time.
Kerf Management: Decreasing the diamond wire diameter (to reduce kerf loss) increases warpage, primarily because the narrower kerf impairs heat dissipation and increases thermal conduction into the wafer.
Optimization Key: Achieving effective lubrication and cooling within the narrow saw kerf is identified as the critical factor for maintaining low warpage in high-efficiency, high-speed sawing processes.

Technical Specifications

Parameter	Value	Unit	Context
Sapphire Density	3.95	g·cm^-3	Material Property
Thermal Conductivity	132.5	W/(cm·K)	Material Property
Young Modulus	320~340	GPa	Material Property
Thermal Expansion Coeff.	5.8 x 10^-6	K^-1	Material Property
Wafer Thickness (Simulated Range)	200 to 600	µm	Parametric Study
Kerf Width (Simulated)	0.3	mm	FEA Model Setup
Diamond Wire Diameter (Range)	0.20 to 0.28	mm	Parametric Study
Wire Speed (Range)	800 to 1600	m/min	Process Parameter
Feed Rate (Range)	0.1 to 0.5	mm/min	Process Parameter
Ambient Temperature	25	°C	Boundary Condition
Natural Convection Coeff. (Air)	5	W/(m²·°C)	Boundary Condition
Forced Convection Coeff. (Coolant)	3 x 10⁴	W/(m²·°C)	Boundary Condition
Coolant Flow Rate (Experimental)	17.5	L/min	Sawing Experiment
Maximum Stable Sawing Temp.	~34.5	°C	Observed during deep cutting
Maximum Simulated Warpage (High Stress)	11.15	µm	1200 m/min, 0.3 mm/min, 0.28 mm wire
Maximum Experimental Warpage (High Stress)	12.6	µm	1200 m/min, 0.3 mm/min, 0.28 mm wire

Key Methodologies

The study utilized a combined approach of Finite Element Analysis (FEA) and experimental validation to analyze warpage in C-plane sapphire slicing.

FEA Model Setup:
- A 3D geometric model (10 mm x 10 mm x 6.9 mm) of the sapphire crystal was established in ABAQUS (v.5.4).
- The model simulated the formation of five slices (0.5 mm thickness) via six kerfs (0.3 mm width).
- The bottom surface of the workpiece was set as completely fixed.
Thermal and Structural Analysis:
- A sequential coupling method was used: the transient temperature field was calculated first, followed by the resulting thermal deformation displacement field.
- Heat transfer was modeled using eight-node linear hexahedral elements (DC3D8), and thermal stress/deformation used C3D8I elements.
- The birth and death element method simulated the material removal process, allowing the cutting heat flux (q_v) to act on the continuously advancing cutting area.
Boundary Conditions and Heat Flux:
- Heat flux (q_v) into the workpiece was calculated based on consumed power (P = F_t x V_c) and the energy partition coefficient (ε = 0.667).
- Cooling was modeled using forced convection (3 x 10⁴ W/m²·°C) in the cutting zone and natural convection (5 W/m²·°C) on other surfaces.
Warpage Calculation:
- Wafer warpage was defined as the difference between the maximum (S_max) and minimum (S_min) thermal deformation displacements of the cut wafer surface nodes relative to the undeformed reference plane.
- Displacement data was extracted from 25 uniformly selected nodes along the wafer cut surface.
Experimental Validation:
- Sawing experiments were conducted using a diamond multi-wire saw machine on 10 mm x 10 mm x 40 mm sapphire ingots.
- Four sets of parameters were tested, varying wire speed (800 to 1200 m/min) and feed rate (0.1 to 0.3 mm/min).
- Wafer warpage was measured post-slicing using a KEYENCE laser plane measuring instrument (LJ-X8000).

Commercial Applications

The findings and the established simulation model are highly relevant for industries requiring high-quality, geometrically precise sapphire substrates.

Optoelectronics and Microelectronics: Direct application in the manufacturing of sapphire wafers used as substrates for LEDs (Light Emitting Diodes), micro substrates, and laser components.
High-Precision Substrate Manufacturing: Provides a tool for optimizing the slicing process to meet stringent geometric quality requirements for high-end optical and electronic components, where warpage is a critical bulk defect.
Cost Reduction and Yield Improvement: The simulation model allows manufacturers to predict warpage under various conditions, eliminating the need for extensive, time-consuming, and expensive physical trial-and-error experiments.
Ultra-Thin Wafer Production: Essential for controlling warpage in the growing market of ultra-thin (200 µm and below) sapphire wafers, which have inherently low stiffness and high susceptibility to thermal deformation.
Diamond Wire Saw Process Engineering: Provides actionable data for selecting optimal diamond wire diameter, tension, speed, and feed rate to balance high throughput (high speed/feed) with geometric quality (low warpage).

View Original 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.

Tech Support

Original Source

DOI: https://doi.org/10.3390/app14177667

References

2023 - Performance of thermal field-assisted precision lapping for single crystal sapphire wafers
2024 - Atomistic understanding of the variable nano-hardness of C-plane sapphire considering the crystal anisotropy [Crossref]
2024 - Experimental study on normal force of cutting sapphire with multi-wire swing reciprocating wire saw
2023 - Influence of crystal anisotropy and process parameters on surface shape deviation of sapphire slicing
2004 - Warpage analysis of silicon wafer in ingot slicing by wire-saw machine [Crossref]
2006 - Warp of silicon wafers produced from wire saw slicing: Modeling, simulation, and experiments [Crossref]
2008 - A finite element analysis of temperature variation in silicon wafers during wiresaw slicing [Crossref]
2018 - Simulation and experimental research on the slicing temperature of the sapphire with diamond wire [Crossref]
2008 - Effects of thermal deformation of multi-wire saw’s wire guides and ingot on slicing accuracy [Crossref]
2015 - Warping of silicon wafers subjected to back-grinding process [Crossref]