1. Experimental Evaluations of the Strength of Silicon Die by 3-Point-Bend versus Ball-on-Ring Tests
Jie-Hua Zhao, John Tellkamp, Vikas Gupta and Darvin Edwards
Texas Instruments Incorporated
13536 North Central Expressway, MS940, Dallas, Texas 75243
Phone: , Fax: ,

2. Test Method I: 3-Point BendingL t
Die Backside
Die front side
Stress
location
3-point bend test
Span: about L=6.4mm,
die thickness about t=0.38mm,
die width w=5mm
Stress on back side of die can be calculated by a simple formula
Only geometry and peak load are needed to get the die breaking strength

3. Test Method II: Ball-on-Ring Test
Force P
Die thickness t
Hole diameter 2a
Die width 2R
Contact diameter 2z
Al Support
Die
Steel Push pin with ball head

4. Wafer Dicing for Both BOR and 3PB
10 mm
5 mm
Schematic is not to scale
3-Point-Bend Test
Ball-on-Ring Test
Wafer was diced to 5X10 mm and 10X10 mm dies.
3-point-bend: 5X10 mm BOR: 10X10 mm
Backgrinding scratches have a defined pattern.
3PB is uni-axial loading (stress along x-direction only). When picking the dies, it is important to cover all representative directions. e.g., all dies in ¼ of the wafer

5. Ball-on-Ring Test Theory
P: force load
t: the disk thickness
R: radius of the disk
: Poisson’s ratio of disk
a: radius of the circular support
b: radius of the region of uniform loading at the center (need to be determined)
z: contact radius of the loading ball with the specimen
To determine b, the following formulas are useful:
Reference: G. de With and H. H. M. Wagemans, Ball-on-ring test revisited, Journal of American Ceramic Society, vol 72, no. 8, pp (1989)

6. Simplified Formula of Ball-on-Ring Test (ball radius is much larger than die thickness)
For die thickness of 0.381m (15mil), ball radius=1mm, it is save to assume z>1.724t. Therefore, b=t. The formula in previous slide reduces to this one
P: force load
t: the disk thickness
R: radius of the disk
n: Poisson’s ratio of disk
a: radius of the circular support
Advantage of BOR test:
Bi-axial stress: Simultaneously put stresses in both x-direction and y-direction: Better to mimic the package-induced stress
Better for characterizing backgrinding-induced surface defects: High stress near the die center, almost no stress on die edges. Sawing-induced edge chipping defects do not interfere with surface defects in this test

7. Probabilistic Mechanics of Die Cracking
The die strength (stress value when die cracks) data are expressed in terms of a 3-parameter Weibull distribution:
For low percentage (e.g., 0.1%) die cracking failure, the Weibull distribution can give some extrapolation of failure rate based on die strength test data from a relatively small sample size (e.g., 50).

8. Die Strength vs. Surface Flaw Depth
Die strength (critical stress at breaking point) is related to Si fracture toughness K1c.
The fracture toughness of single crystal Si is a material property. Experimental value of K1c = 0.82 to 0.95 MPa m1/2, depending on the orientation of crystal
Assumption: micro-cracks are very sharp. Blunt crack may be more forgiving.
A good estimate of how much damage the process induces by looking at the measured die strength data.
Examples:
If a die cracks at 300MPa, the deepest crack is about 2.5um.
If the deepest crack is about 10um deep, the die can not sustain about 160MPa tensile stress

9. Die strength test results for Process I (backgrinding only):
3-Point-Bend
Ball-on-Ring

10. 3-Point-Bend Ball-on-Ring
Die strength test results for Process II (backgrinding followed by backside polishing):
3-Point-Bend
Ball-on-Ring

11. 3-Point-Bend Ball-on-Ring
Die strength test results for Process III (backgrinding followed by backside metallization)
3-Point-Bend
Ball-on-Ring

12. Summary of 3PB vs. BOR Tests
Backside polishing and backside metallization processes increase the die strength significantly: Consistent with both Ball-on-Ring and 3-Point-Bend tests (except for the case of 0.1% 3PB extrapolation data)
Die strength values obtained by 3-Point-Bend test are consistently lower than the Ball-on-Ring test. This is due to the edge defects caused by the sawing process
A tail of low strength data points in the 3-Point-Bend tests implies that monitoring and improving the sawing process is also a important factor to ensure zero-ppm of die cracking.
3P Weibull Parameters
Stress Cumulative failure rate
Slope
Scaling (MPa)
Cut-off (MPa)
Correlation
Sample Set
0.10%
1.00%
63.20%  f 0
R2 (%)
Backgrinding only, BOR
205
213
347
1.808
146.0
201.4
99.47
Backgrinding only, 3PB
182
196
338
2.329
164.5
173.3
98.36
Backgrinding followed by Polishing, BOR
325
342
744
1.552
423.5
320.2
99.39
Backgrinding followed by Polishing, 3PB
159
237
558
4.885
527.4
31.0
99.41
Backgrinding, backside Metallization, BOR
378
483
787
9.401
787.2
0.0
98.02
Backgrinding, backside Metallization, 3PB
259
515
4.223
385.7
129.6
99.62

13. BOR Application: Backgrinding Process Optimization
Wafer #101: 320 grit grinding followed by fine grind removal of 100um with 1500 grit finish
Wafer #110: 320 grit grinding followed by fine grind removal of 30um with 1500 grit finish
Wafer #07: 320 grit grinding only
Wafer #104: 320 grit grinding followed by fine grind removal of 100um with 2000 grit finish
Wafer #109: 320 grit grinding to 16mil then followed by chemical spin-etch to 14.6mil

14. BOR Die Strength: Backside Etch vs. No Backside Etch
Backside etch makes significant improvement in terms of die strength compared to backgrinding only process
Backside etch removes some deep scratches produced by the 320 grit grinding
2000 grit or 1500 grit grinding removes deep scratches, at the same time it produces additional slightly shallower scratches

15. Summary of Process Optimization Using BOR
The stress formula of Ball-on-Ring test for thin Si die is reduced to a simple formula, which only needs information of loading force value and geometric parameters of the die and supporting base
Ball-on-Ring test can be used for process optimization of wafer back grinding.
Although the final finishes are the same (1500 grit) for some processes, the die strength can be different. (e.g., The Process with 100um final Si removal with 1500 grit wheel is better than the Process with 30um final Si removal with 1500 grit wheel.)
The grit of the final grinding wheel is also important. The 2000 grit wheel is better than the 1500 grit wheel in the final 100um removal case.
The rough grit grinding in the early stage of process produces deep scratches. Some of the deep scratches produced by the 320 grit wheel are more than 100um deep, which causes a small percentage of weaker die strength.
Backside etch improves the die strength significantly

16. Acknowledgements William Wresh Dr. Roger Stierman Dr. Shih-Fang Chuang
Andy Tran
Lance Wright

17. Backup

18. A Refresher of Weibull Distribution
Waloddi Weibull suggested a distribution function to characterize the strength of brittle materials. The general form of a Weibull distribution (cumulative distribution function or CDF) has the form of
Weibull chose a simple form of (x) , which needs to be a positive, non-decreasing function, and vanishing at value x0, but not necessarily equal to zero, such as:
Then three-parameter Weibull distribution has the following familiar form:
When x0 is zero, the three-parameter Weibull distribution reduces to two-parameter Weibull distribution:
As Weibull pointed out in his hallmark paper that the choosing of function (x) can be fairly arbitrary if one "tests it empirically, and stick to it as long as none better has found".
*** Weibull W. A statistical distribution function of wide applicability. Journal of Applied Mechanics, vol. 18, pp (1951)