The objective of the present study is the estimation of the depth to which the wire sawing process causes damage to the wafer surfaces. Previous analyses were carried out by means of the four line bending test. The characteristic of this test implied that the failure could be due to surface cracks located in the central zone of the wafer or near the edges. In order to evaluate the influence of the edge or surface cracks a new study has been carried out using the ball/ring on ring test. Description and results of the tests are presented. The preliminary analysis of the failure stress using analytical methods confirms the expected results. A Finite Element model developed to get more information of the test results is also presented

Alarcón Álvarez, Enrique

Barredo Egusquiza, Josu

Fraile de Lerma, Alberto

Hermanns, Lutz Karl Heinz

Jimeno, Juan Carlos

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Study of the Edge and Surface Cracks Influence in the Mechanical Strength of Silicon Wafers

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

STUDY OF THE EDGE AND SURFACE CRACKS INFLUENCE 
IN THE MECHANICAL STRENGTH OF SILICON WAFERS 
 
 
J. Barredo1, L. Hermanns1, A. Fraile1, J. C. Jimeno2 and E. Alarcón1 
Author for correspondence: Josu Barredo 
1Department of Structural Mechanics and Industrial Constructions, Polytechnical University of Madrid, c/ José Gutiérrez 
Abascal 2, 28006 Madrid, Spain. Tel: +34-91-336-53-46, email: jbarredo@etsii.upm.es 
2Microelectronic Technology Institute, Basque Country University-Engineering School, Alameda de Urquijo s/n, 48013 
Bilbao, Spain, email: jc.jimeno@ehu.es 
 
 
ABSTRACT: The objective of the present study is the estimation of the depth to which the wire sawing process 
causes damage to the wafer surfaces. Previous analyses were carried out by means of the four line bending test. The 
characteristic of this test implied that the failure could be due to surface cracks located in the central zone of the 
wafer or near the edges. In order to evaluate the influence of the edge or surface cracks a new study has been carried 
out using the ball/ring on ring test. Description and results of the tests are presented. The preliminary analysis of the 
failure stress using analytical methods confirms the expected results. A Finite Element model developed to get more 
information of the test results is also presented.  
Keywords: Cost reduction, Defects, Characterization 
 
 
1 INTRODUCTION 
 
The use of thinner wafers is commonly accepted as a 
clear way to reduce the cost of solar panels. However, 
thinner wafers present different mechanical properties 
and PV industry needs a thorough knowledge of them. 
Many studies concerning the mechanical properties of 
silicon wafers have been carried out last years [1], [2], 
[3], [5] and [7]. 
Many cracks are produced in the cutting process of 
the ingot,. A clear way to reduce the breakage rate in the 
production process is to remove the most damaged 
superficial layers. Therefore, the estimation of the 
damaged depth becomes a very useful information [1].  
The ball/ring on ring test has been employed and the 
results obtained have been compared with those obtained 
in previous studies when the four line bending test was 
used. The characteristic of the ball/ring on ring test 
implies that the failure is due to cracks located in the 
central zone of the wafer. It’s expected a smaller depth 
results than for the four line bending test since in the 
previous case both edge and surface cracks may have 
caused failure [2], [3].  
 
2 OBJECTIVE 
 
As already mentioned, previous studies by the 
authors [1] concerning the thickness of the damaged 
layer due to the wire sawing process were carried out by 
means of the four line bending test. For comparison, the 
mechanical strength has been represented versus the 
decreased thickness per face (figure 1).  
According to figure 1, it seems that from 30 μm per 
face of decreasing thickness, the strength keeps a 
constant value. Therefore, it could be concluded that 
cracks produced in the wire sawing process reside in the 
most superficial layer and it has a thickness of 
approximately 30 μm.  
Some authors suggest that the depth of the damage is 
up to 15 μm [4] and [5]. The damaged depth by the wire 
sawing process depends on many parameters like the 
number of uses of the wire or the velocity of the cutting 
process.  
Anyway, it’s suspected that the damage caused by 
the wire sawing process is higher near the edges than in 
the central zone of the wafer. In order to assess this 
hypothesis, the influence of surface and edge cracks in 
the mechanical strength has been studied. 
 
Mean values of maximum bending strength
0
50
100
150
200
250
300
350
0 10 20 30 40 50 60 70 80
Decreased thickness per face (microns)
B
en
di
ng
 s
tr
en
gt
h 
(M
Pa
)
 
Figure 1: Strength versus decreased thickness  
 
3 THE BALL/RING ON RING TEST 
 
3.1 Comparison with the four line bending test 
It’s known that the failure in wafers is due to the 
combination between the stress state in the wafer and the 
cracks existing inside them [1], [2]. In the four line 
bending test (figure 2) the stressed zone between the 
supports extends over the whole wafer. 
 
 
Figure 2: The four line bending test 
 
Cracks located in the central zone and near the edges 
are able to cause the wafer failure. So, the results of the 
tests include both failure mechanisms. 
In the ball/ring on ring test, stresses near the central 
zone are much higher than borders stresses, so the failure 
24th European Photovoltaic Solar Energy Conference, 21-25 September 2009, Hamburg, Germany
2116
is due to surface cracks in the central zone [2] [3].  
 
 
Figure 3: Ring-on-ring and ball-on-ring test 
 
The direct comparison of stress results between the 
two tests is not possible without considering the size 
effect. As already has been mentioned, the wafer strength 
depends on the stress level and the corresponding critical 
crack size. So the bigger the stressed zone the higher is 
the probability to find a critical crack in it. For this 
reason, the results must be referred to a reference area 
before comparison.  
In spite of this, there are other types of results that 
can be extracted from the tests without taking into 
account the size effect. A similar curve as the one 
presented in figure 1 should be obtained when employing 
the ball/ring on ring tests. Although the values in 
mechanical strength may be different, the thickness of 
damaged surface could be obtained. This result may 
explain the different values observed in the literature 
about the depth of the damage caused by the wire sawing 
process.  
 
3.2 The ball/ring on ring test machine 
In order to get a wide applicability for different 
samples dimensions, the testing machine has several 
rings of different diameters. The force transducer has a 
capability up to 200 N. The displacement of the ball or 
the top ring is imposed and both the force and the 
displacement are recorded. In order to get a quasi-static 
test, the velocity is very low. In this case, the imposed 
displacement had a velocity of 5 μm/s. The results of the 
tests are shown ahead. 
 
3.3 Sets of wafers 
Unfortunately only three different set of wafers were 
available to prepare. All of them have an original 
thickness of approximately 250 μm. Each group was 
subjected to caustic soda baths of different duration. 
Finally, they were cut in four pieces by means of a laser 
giving four samples for each wafer of 62.5mm x 62.5mm 
dimensions. The characteristics of each group are shown 
in table I 
 
Table I: Samples tested 
 
  Number Bath Mean value Mean value 
Group of duration of thickness of decreased 
  samples (min) (μm) thickness  
 A 20 3 229.9 10.9 (μm/face) 
 B 20 6 209.9 20.2 (μm/face) 
 C 24 9 194.6 28.6 (μm/face) 
 
3.4 Testing wafers and results 
Samples of group A were tested with the ring on ring 
device. The support ring employed had a diameter of  
20 mm and the diameter of the top ring was 10 mm. All 
samples broke correctly and they showed a non-linear 
behavior due to large displacement and contact between 
sample and rings. The results are shown in figure 4. 
 
3 minutes of caustica soda bath
0
20
40
60
80
100
120
140
160
0 0.1 0.2 0.3 0.4 0.5 0.6
Displacement (mm)
Fo
rc
e 
(N
)
 
Figure 4: Results of group A 
 
The first attempts to test samples of group B in the 
ring on ring device reveals that buckling occurs. The 
buckling (irregular bending of the outer part of the 
sample [7]) can be observed in figure 5. 
 
 
Figure 5: Buckling in one test 
 
For this reason, samples of groups B and C were 
tested in the ball on ring device. The support ring had a 
diameter of 10 mm and the ball one of 2 mm. Therefore, 
results of tests of group B and C cannot be compared 
directly with results of group A due to the size effect. 
However, results of groups B and C can be compared 
between them.  
 
Results of ball-on-ring tests
0
10
20
30
40
50
60
70
80
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Displacement (mm)
Fo
rc
e 
(N
)
6 minutes bath
9 minutes bath
 
Figure 6: Results of groups B and C 
 
As can be seen in figure 6, the different thicknesses 
result in different stiffness values of the tested wafers. As 
in the case of ring on ring test, the samples tested in the 
ball on ring device showed also a non-linear behavior.  
 
24th European Photovoltaic Solar Energy Conference, 21-25 September 2009, Hamburg, Germany
2117
4 ANALYSIS OF THE TEST RESULTS 
 
4.1 Preliminary analysis 
In a first step, an analytical method has been 
employed. The maximum stress at failure moment has 
been taken from the literature [6]: 
For the ring on ring test: 
 
( ) ( )2 22 1 1r 2 2
2eq
r -r3F rσ = 1-ν -2 1+ν Ln r4πh r
⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦
 (1) 
 
Where F is the fracture load; h is the thickness; ν is 
the Poisson coefficient; r1 is the radius of the inner ring 
and r2 of the outer ring; req is the equivalent sample 
radius. For square samples the equivalent radius is: 
 ( )
eq
L 1+ 22 Lr = =1.207 22
  (2) 
 
Where L is the side length of the sample. 
For the ball on ring test: 
 
( ) ( )
( )
2 2
1 22
r 2 2 2
1 2 eq
3F 1+ν 1-ν r rrσ = 1+2Ln 1r4πh 1+ν 2r r
⎡ ⎤⎛ ⎞⎛ ⎞ + −⎢ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠⎢ ⎥⎝ ⎠⎣ ⎦
 
   (3) 
 
The terms are the same as those defined in equation 
(1). 
Using these expressions, the fracture stress has been 
calculated for each test. For brittle materials the Weibull 
distribution is commonly used to evaluate statistically the 
results [2], [3]. The probability of failure is defined as: 
 
( )mθ- σ σ
fP =1-e  
 
The parameter σθ represents the characteristic 
fracture stress at which 63.2% of all samples fail. The 
Weibull module m informs about how scattered the 
results are. The Weibull fitting of the fracture stresses of 
the tests is represented in figure 7: 
 
 
Figure 7: Adjustment to Weibull distribution 
 
It can be seen that for wafers bathed more than 6 
minutes, the results are very close. The strength is much 
higher than for ones which are bathed only 3 minutes. 
This can be visualized easily in figure 8. 
 
0
500
1000
1500
2000
2500
3000
3500
0 5 10 15 20 25 30
Mean decreased thickness (microns/face)
C
ha
ra
ct
er
is
tic
 fr
ac
tu
re
 s
tr
es
s 
(M
Pa
)
 
Figure 8: Characteristic fracture stress (σθ) versus 
decreased thickness 
 
This result agrees with the assumption that in center 
zone of the wafers the cutting damage is lower than near 
the edges. It can be seen that decreasing more than 20 
μm per face doesn’t improve the strength of wafers. So, 
these results obtained in the preliminary analysis may 
explain the different values of the damaged depth in the 
literature.  
There’re some false assumptions in this preliminary 
study. The most important is that these expressions are 
valid for linear behavior of samples during the test and 
this is not the case. Moreover, the size effect hasn’t taken 
into account. However, a first quick analysis may give an 
idea of the results that we’d expect in a more detailed 
study. 
 
4.2 FE model 
To get a correct interpretation of the test results 
implies to develop a reliable numerical model. As it’s 
clear in figures 4 and 6, samples showed a non-linear 
behavior during the test. Therefore, analytical methods 
may be used to get an idea of the goodness of the results 
but it can’t be considered as the final result of the study.  
The Finite Element Method has been employed in 
this case to analyze the results using the commercial 
software ANSYS. Wafer and supports have been 
modeled with shell elements. The anisotropy of the 
silicon is considered using the following constants: 
 
 c11=165.6 GPa 
 c12=63.9 GPa 
 c44=79.5 GPa 
 
 
Figure 9: Displacements in the FE model 
24th European Photovoltaic Solar Energy Conference, 21-25 September 2009, Hamburg, Germany
2118
 
Nonlinearities due to large deflection and contact 
between the sample and the ring and ball were taken into 
account. The coefficient of friction used has a value of 
0.35. In figure 9 the displacement in the model can be 
seen and in figure 10 a zoom of the contact zone is 
shown. 
 
 
Figure 10: Zoom of the contact zone 
 
However, the adjustment of the model to the test 
result hasn’t been achieved correctly. As can be seen in 
figure 11, the model behaves more rigid than the test.  
 
0
20
40
60
80
100
120
140
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Displacement (mm)
Lo
ad
 (N
)
Test
FE model
 
Figure 11: Fitting of the FE model to the test 
 
In the first steps the fitting is quite good. This implies 
that the linear elastic behavior is achieved correctly. Over 
0.1 mm the FE model curve separates of the test one 
becoming more rigid. Further investigations are being 
carried out in order to solve this handicap. 
 
5 SUMMARY AND CONCLUSIONS 
 
The damage in wafers caused by the wire sawing 
process has been evaluated. Previous studies carried out 
with the four line bending tests showed that removing 
30μm per face, the damaged layers of the wafers has 
been eliminated. It’s suspected that the depth of the 
damage is different in the central zone of the wafer than 
near the edges. Then, the ball/ring on ring test has been 
employed to study this hypothesis since the failure is due 
to cracks far away of the edges.  
The tests are described in detail and the results are 
shown. There were three different groups of samples and 
one of them was tested with the ring on ring and the other 
two with the ball on ring test. Then, the correction by 
size effect is necessary to compare the results.  
As a first step analytical methods have been 
employed in the test results analysis. The failure stress 
has been obtained for each test using expressions from 
the literature. Then, they have been fitted to a Weibull 
distribution and the characteristic fracture stresses of 
each group have been compared. Results show that 
decreasing 20 μm per face, the failure stress becomes 
approximately constant. Expressions employed are valid 
for linear behavior and, moreover, the size effect has 
been neglected. But this first analysis may be useful to 
verify the goodness of the results.  
Finally, a Finite Element model is currently 
developed including nonlinearities. The details of the 
model are shown and also the first fitting to the test. At 
this moment, the adjustment is not quite good but further 
investigations are being carried out to solve it.  
The way to study the difference between the damage 
depth in the central zone or near the edges is explained. 
Tests are described in detail and the numerical model is 
presented. A previous analysis with analytical methods 
gives good results.  
 
6 ACKNOWLEDGEMENTS 
 
This work has been carried out under the sponsorship 
of the University State Secretary, belonging to Spanish 
Ministry of Science and Innovation, in its contract 
TEC2008-06798-C03-03. The presented results have 
been obtained in cooperation with Institute of Solar 
Energy (IES) and Microelectronic Technology Institute 
(TIM).  
 
7 REFERENCES 
 
[1] Barredo et al. “The influence of different surface 
treatments on the mechanical strength of silicon 
wafers”. 22nd European Photovoltaic Solar Energy 
Conference, Milan, Italy, 2007  
[2] Schoenfelder et al. “Comparison of test methods for 
strength characterization of thin solar wafer”. 22nd 
European Photovoltaic Solar Energy Conference, 
Milan, Italy, 2007  
[3] Cotterell et al. “The Strength of the Silicon Die in 
Flip-Chip Assemblies”. Journal of electronic 
packaging, ASME, USA, 2003. 
[4] Kao et al. “Wafer Slicing and Wire Saw 
Manufacturing Technology”. Proceedings of the 
1997 NSF Design & Manufacturing Grantees 
Conference, pp. 239-240, 1997 
[5] Park et al. “Correlation between wafer fracture and 
saw damage introduced during cast silicon cutting”. 
15th Workshop on Crystalline Silicon Solar Cells and 
Modules: Materials and Processes, Colorado, USA, 
2005 
[6] Choi et al. “Slow Crack Growth Behavior and Life/ 
Reliability Analysis of 96 wt % Alumina at Ambient 
Temperature with Various Specimen/Loading 
Configurations”. NASA/TM, 2000   
[7] Coletti et al. “Mechanical Strength of Silicon Wafers 
Depending on Wafer Thickness and Surface 
Treatment”. 21st European Photovoltaic Solar Energy 
Conference, Dresden, Germany, 2006 
24th European Photovoltaic Solar Energy Conference, 21-25 September 2009, Hamburg, Germany
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Study of the Edge and Surface Cracks Influence in the Mechanical Strength of Silicon Wafers

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