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R.D. Hilty and N. Corman, "Tin Whisker Reliability Assessment by Monte Carlo Simulation", Proc. IPO/JEDEC Lead-Free Symposium, 2005.

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R.D. Hilty and N. Corman, "Tin Whisker Reliability Assessment by Monte Carlo Simulation", Proc. IPO/JEDEC Lead-Free Symposium, 2005.
Tin Whisker Reliability Assessment by Monte Carlo Simulation
Robert D. Hilty and Ned Corman
Abstract
Tin whiskers can grow between adjacent terminals of an electronic device causing electrical shorts. Concerns about the impact of this
phenomenon have been widespread, but have not been quantified for reliability risk. We have created a Monte Carlo simulation to
examine the failure rate of tin plated products due to whisker growth. The simulation uses statistical distributions of actual whisker lengths
measured on plated products exposed to the iNEMI and JEDEC tin whisker test methods. These distributions were used to generate
simulations of millions of whiskers, whose likelihood for creating an electrical short is simulated. We have found that the reliability risk is
strongly related to the use of a nickel barrier material, post plating mechanical damage and the plating process used to create the tin
plating. Projected failure rates, in terms of percent defect rates, are provided for various terminal finishes and terminal spacings.
I. INTRODUCTION
n the last few years, researchers have struggled to
identify root causes for tin whisker growth, whisker
mitigation practices and alternatives to tin/lead plating.
It is well understood that tin whiskers pose a reliability
risk for electronic circuits. It is also intuitive that this risk
is greater when the spacing between conductors is
decreased. However, we are not aware of any work in the
literature aimed at quantifying the levels of risk that exist
for failure due to tin whiskering.
I
Whisker growth rates are difficult to predict and measure.
Traditionally reported tin whisker growth rates are in the
range of 0.1 angstroms/S for pure tin systems and Chen et
al recently reported much faster rates, 2-6
angstroms/second on tin-manganese films.1 Predictions
on the maximum whisker length obtained from a tin film
are even more varied. Most reports on whisker length are
empirical evidence of the longest whiskers for a given test
condition.
These data are difficult to use to predict reliability. Tin
whisker growth events seem to be frequent, when we
examine whiskers growing on a finished component.
However, if we examine the likelihood for tin whisker
growth from a metallurgical perspective, it is a much
more rare occurrence. For example, consider a tin plated
sample with a nominal grain size of 2 µm, and a plated
area of 1mm2. This sample contains about 320,000
grains. If we measure a whisker density of 50
whiskers/mm2 then this sample would grow 50 whisker
grains out of 320,000 possible tin grains; this is 156
grains per million grains plated may be susceptible to
whiskering. How many of these whiskers pose a risk of
creating an electrical short with neighboring conductors?
II. TEST METHODS
Our approach to solving this problem is to use a statistical
representation of actual whisker lengths to help predict
the likelihood for failure. The test method has two
independent portions: 1) growing and measuring tin
whiskers and 2) simulating whisker failure rates
numerically.
A. Growing tin whiskers
In order to understand the distribution of tin whisker
lengths that may occur on tin platings, we needed to
create tin plated samples that grew tin whiskers. Two
samples were created. The first was one that was known
to be likely to form tin whiskers, while the second has
some levels of tin whisker mitigation applied to the
plating process.
To make a sample that would have significant tin whisker
growth, a sheet of C26000 (CuZn30) brass was
electroplated with a matte tin that has been proven to
whisker in previous testing.2 The tin plating was
nominally 3 µm thick and was plated directly onto the
brass substrate.
The sample of whisker mitigated tin plating was a low
stress, low carbon content (0.05% C) matte tin deposit
that was plated over 1.27 µm of semi-bright nickel from a
nickel sulphamate plating bath. The nickel was plated
directly onto C51100 (CuSn4) phosphor bronze electrical
contacts. The contacts were cut from the plating carrier
strip then assembled into electrical connectors.
Both of the samples were then exposed to environmental
aging conditions known to promote tin whisker growth.
Three sets of samples were divided then exposed to room
temperature aging, heat/humidity (60 C, 93% relative
humidity) and thermal cycling (-40 to 85 C, air to air, 3
cycles per hour) as per the iNEMI recommended
practices.3 In previous testing, we have found that heat
and humidity conditions grew whiskers the fastest on
copper base metal samples. Inspection of the samples
after 6 months of aging (or 2500 cycles) showed some
whisker growth on all of the samples, but once again, heat
and humidity exposures were the most favorable for
growing tin whiskers.
B. Measurement of tin whiskers
While each of the samples showed some degree of
whisker growth, the lengths for room temperature
exposure and thermal cycling were much smaller than the
lengths for heat and humidity conditioned parts. Thus,
Manuscript received March 29, 2005. Hilty and Ned Corman are with Tyco Electronics, PO Box 3608, Harrisburg, PA 17105. Corresponding author is
Robert D. Hilty at phone: 717-986-3949, fax: 717-986-7070, e-mail: [email protected]
Paper presented at the IPC/JEDEC Lead-Free Symposium, April 2005, San Jose, CA
we focused our measurements on the worst case
conditions, the heat/humidity samples.
Each part was inspected by SEM for whisker length. The
SEM measurement method is reasonably accurate due to
the large depth of field, however there are some
significant limitations. First, the tin platings used for this
study are matte tin deposits. The surface is inherently
rough due to the surface morphology of the growing tin
grains and substrates. This limits the ability to measure
very small tin whiskers (nodules) since they are difficult
to discern from typical surface irregularities. The
smallest tin whiskers measured in this study were 2.5 µm.
Due to the nature of tin whisker growth and incubation of
tin whiskers, the greatest percentage of tin whiskers
measured was expected to be these very short tin
whiskers.
For the highly whiskered part, a representative portion of
the sample was selected for inspection, then every
whisker in that region was measured. In this case, 267
whiskers were measured with a length range of 2 µm to
663 µm. The area over which these whiskers were
observed was measured and the whisker density was
computed to be 2381 whiskers/mm2. An example of the
observed whisker density is provided in Figure 1.
measured every whisker on multiple leads, up to 250 µm
from the end of the terminal. In this case, 103 whiskers
were measured with a length range of 2 µm to 109 µm.
The area over which these whiskers were observed was
measured and the whisker density was computed to be
45.6 whiskers/mm2.
Figure 2. Tin whisker growth that occurs preferentially
on the surface of the matte tin over nickel where the tin
has been damaged during the carrier strip trimming
operation. The left hand portion of the tin plating, which
has not been disturbed, shows no evidence of tin whisker
growth.
C. Simulating Tin Whisker Shorting
The intent of this work is to help predict the likelihood for
electrical shorting between adjacent leads of a typical
component. To form a framework for the analysis, we
used a typical fine pitch component to establish suitable
spacings between contacts and terminal areas that could
potentially lead to shorting.
Figure 1. Tin whisker growth on a known whisker prone
matte tin over brass.
For the whisker mitigated part, dozens of leads were
inspected. Whisker growth was nil in most areas of the
plated terminal. A series of whisker measurements were
made in traditional areas of inspection and the maximum
whisker length was 5 µm. This short length will not
cause an electrical failure in any typical electronic
component. Whisker growth is promoted by stress on tin
deposits and as such, we were able to find longer
whiskers growing at the end of the solder tail, where the
plating carrier strip had been sheared from the terminal
body. Thus, we used only the end of the solder tail as the
area of inspection, which is the worst case scenario. We
The Monte Carlo approach is useful since we can use the
orientation variability to more realistically predict the
likelihood for failure. Generating a 100 µm long whisker
will not necessarily lead to a short in a conductor with
100 µm spacing. Any angle, other than normal to the
terminal surface, will reduce the effective shorting length
of the whisker and reduce the likelihood for shorting.
A few key assumptions were made in this analysis:
Paper presented at the IPC/JEDEC Lead-Free Symposium, April 2005, San Jose, CA
ss
ne
ck
i
Th
A2
φ
cr
SeperationD
1) Whiskers do not grow to short to each other.
Whiskers will only grow to touch another terminal.
Based on our history of observation and presuming a
low whisker density (true for mitigated tin whisker
platings), the likelihood for two tin whiskers touching
each other is very low.
2) For this analysis, the whiskers were presumed to
grow as a filament and in a straight line. While this
does not always happen, it is the worst case scenario
since this produces the longest whiskers.
3) Whisker growth angles and orientations
(described in greater detail below) were assumed to
be random. The rotational angle is truly random.
However, the angle of inclination between the plated
surface and the whisker growth is restricted. In our
analysis we assume 0 to 89 degree freedom in this
angle. SEM observations suggest that this angle is
more commonly between 0 and 80 degrees, but
whiskers have been infrequently observed to grow
nearly parallel to the plated surface.
itl
y1
A1
x2
θ
x1
y2
These three key assumptions are reasonable based on our
history of whisker observation and our desire to examine
those scenarios at greater risk for tin whisker growth.
A Mathcad® program was written to simulate whisker
formation. Referring to Figure 3, an original rectangular
area, A1, and opposing parallel area, A2, are defined
based on the dimensions of a particular connector. The
thickness is the copper strip thickness of the contact
solder tail and the Length is the length of the tail at the
minimum separation distance, Separation D. The areas
A1 and A2 therefore represent the closest spacing
separation areas between two opposing contacts. The
number of whisker locations in A1 is calculated using a
measured whisker density, described above. The location
(x1,y1) of each whisker is randomly generated using
random number functions available in Mathcad®.
Additionally, the random functions were used to identify
a whisker rotation angle θ, from 0 to 360 degrees and an
inclination angle Φ, from 0 to 89 degrees, for each
whisker. A critical whisker length, critl, is defined as the
length necessary for each individual whisker to touch an
infinite parallel plane at the appropriate separation
distance. The distances x2 and y2 are calculated from the
critical length, rotation and elevation angles. These
distances are added to the original location to give the
location for touching the parallel plane in x1,y1
coordinates. These “touching locations” are truncated to
include only those that are located within the thickness of
the original area. Values outside the length of the original
area were not excluded since it was reasoned that the
contact does extend in the length direction but at a greater
separation distance. This assumption was adopted as a
conservative approach.
Figure 3. (Top) Schematic of the spacing between
adjacent conductors and the geometry of tin whisker
growth used for the simulation. (Bottom) Picture of a
SMT component with fine pitch between leads and the
areas used for this study.
D. Statistical Distributions of Whiskers
Actual whisker lengths were simulated by mathematically
generating a distribution based on a best possible fit to
experimentally observed whisker length data. Tin
whisker growth data is not normally distributed. This is
due to the nature of tin whisker growth and the
experimental difficulties involved in measuring very
small whisker lengths (for which there are many). The
two whisker distributions were mathematically fit to a
variety of statistical distributions in an attempt to find a
distribution that generally fits the data but also represents
the extremes of the data well. Fundamentally, we are not
very concerned about modeling whiskers that are very
short, or even medium in length. The longest whiskers
are those that are most likely to cause failures. Further, it
is likely that whiskers longer than those observed in our
experimentation will grow on some samples (on a
statistically large enough sample); thus predicting the
longest whiskers that could grow with this type of
distribution was important. This approach has been used
previously to study etch pit depths in nuclear waste
containers.4
Paper presented at the IPC/JEDEC Lead-Free Symposium, April 2005, San Jose, CA
 X −ε 
S B = γ + η ⋅ ln

λ +ε − X 
 X −ε 
SU = γ + η sinh −1 

 λ 
For the mitigated low density distribution consisting of
103 data points, the SB transformation was applied,
leading to a P-value of 0.656 with γ =4.42865,
η=0.920594, ε=1.08831 and λ=569.8497. For the high
density non whisker mitigated tin distribution consisting
of 267 data points, the SU transformation was a better fit
and produced a P-value of 0.29105 with γ=-3.15904,
η=0.665433, ε=1.79036 and λ=0.199948. A P-value for
an Anderson-Darling test ≥ 0.1 is generally considered a
reasonable fit. This is a 90% Confidence that a Type II
error (incorrectly assuming that the transformed
distribution is Normal) does not occur. Both of these
distributions meet that criteria and can be considered a
good fit to the data.
Figure 4 shows a comparison plot of ordered original
whisker length data (ranked from smallest to largest on
the x-axis and shown as data points) and of simulated
data (shown as a dashed line drawn through the data) for
the mitigated low whisker density plating. The
simulation data is a good fit of the experimental data. In
this image, we have simulated thousands of whiskers, so
we can see that the dashed line extends beyond the
observed whisker distribution.
Whisker Length (mm)
1
0.1
0.01
3
.001
0
0
0.2
0.4
0.6
0.8
1
Ordered whisker number
Figure 4 Comparison plot of ordered original whisker
length data (circles) and SB simulated data (dashed line)
for the whisker mitigated, low whisker density plating.
Figure 5 shows a similar whisker distribution for the
unmitigated tin whisker distribution. Again the
correlation between the simulation and the experimental
data is good.
10
1
Whisker Length (mm)
The statistical package MINITAB© was applied to the
sample populations of whisker lengths to test for
normality and to fit the distributions. While a log normal
distribution was originally considered, it had poor fit,
especially at the extremes. For these experiments, both
the low density and high density whisker distributions
best fit Johnson Transforms.5 That is the transformed
whisker length data was assumed to be normally
distributed and as such the random normal probability
function within MathCad® could be used to produce a
simulated population of whisker lengths after applying an
inverse Johnson Transform. 6
The formulas we used for the Johnson Transformation
were SB and SU and are as follows.
0.1
0.01
3
0.001
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ordered whisker number
Figure 5 Comparison plot of ordered original whisker
length data (squares) and SU simulated data (dashed line)
for the non-whisker mitigated, high whisker density
plating.
E. Predicting Electrical Shorts
Mathcad® was used to simulate tens of millions of tin
whiskers growing at random locations on terminals of
varying spacing and with the two whisker distributions.
The simulated actual whisker lengths were compared to
the lengths required to “touch” the adjacent terminal. A
whisker length equal to or larger than the corresponding
touching length was identified as a failure (a potential
electrical short). One whisker failure defines failure for
the entire area and also for the entire component.
Paper presented at the IPC/JEDEC Lead-Free Symposium, April 2005, San Jose, CA
Finally, this process is repeated many times to simulate
the statistics for possible component failure. Appendix 1
shows a flow chart describing the logic of the Mathcad®
simulation program.
III.
RESULTS
The whisker mitigated tin plating, used for part of this
study, did not form any whiskers in unstressed areas of
the terminal finish. As a result, modeling the failure rate
for this case is a trivial solution and was not pursued.
Terminal spacings would need to be in the range of 10
µm in order to create any significant failure rates. As
such, we focused on the failure rates for non-tin whisker
mitigated tin and whisker mitigated tin, which had been
stressed by post plating trimming of the base metal.
Figure 6 shows the simulated failure rate in percent of a
232 area component using non-tin whisker mitigated tin
plating over brass. From this chart, it is clear that this is
not a recommended practice for fine pitch products. In
order to achieve failure rates of less than 1%, the spacing
between conductors needs to be greater than 6mm. As
can be seen from this chart, the distribution has the
expected ‘S’ shape where the slop increases dramatically
as you approach 0 percent failure rates.
Seperation Distance (mm)
Non-Whisker Mitigated Tin - Failure Rates
higher (i.e., they are presented in terms of percents in
stead of ppm). This chart simply quantifies the
phenomena with which many researchers are already
familiar: tin whiskers can lead to electrical shorts in fine
spaced electrical components.
By comparison, we can chart the failure rate of whisker
mitigated tin plating, as shown in Figure 7. Using the
same axes, we have added the whisker mitigated rates as
a pink line. For equivalent spacing between conductors,
the failure rates are much lower for the whisker mitigated
tin. This work was completed by simulating 500
components with 232 areas per component. While this
simulation produced millions of whiskers, and hence
opportunities for shorting, most of the whiskers were very
short and thus the simulation did not have sufficient
resolution to demonstrate ppm level failure rates. Figure
8 shows the simulated failure rates for whisker mitigated
tin plating with greater resolution of the y-axis
(separation distance between conductors), but the rates
are still provided in terms of percents.
Failure Rates for Mitigated & Non-Mitigated Tin Plating
7
6
Seperation Distance (mm)
This process was repeated to match the number of areas
with the corresponding available areas (terminals) in a
component. One area failure defines a component failure.
Conversely, a passed component has no failures for any
of the areas of the terminals in the device. Components
with various numbers of terminals were tested to
understand the impact of I/O count to failure risk.
5
4
3
2
7
1
6
0
0%
5
20%
40%
60%
80%
100%
% Component Failures
Figure 7. Simulated component failure rate as a function
of terminal separation distance for a non-whisker
mitigated tin plated component (blue line) versus whisker
mitigated tin (pink line).
4
3
2
1
0
0%
20%
40%
60%
80%
100%
% Component Failures
Figure 6. Simulated component failure rate as a function
of terminal separation distance for a non-whisker
mitigated tin plated component.
Normal electronic components are targeting ppm defect
levels. However, these simulated failure rates are much
Paper presented at the IPC/JEDEC Lead-Free Symposium, April 2005, San Jose, CA
Whisker Mitigated Tin
PPM
0
0.35
0.4
0.3
0.35
Separation Distance ( mm )
Separation Distance (mm)
0.4
0.25
0.2
0.15
0.1
0.05
0
0%
20%
40%
60%
80%
Figure 9 shows the higher resolution simulated failure
rates for whisker mitigated tin. The line depicting the
failure rate is somewhat jagged, which demonstrates the
low number of failures used to create these results.
100ppm failure rate is equivalent to one component
failure in the 10,000 components simulated at that lead
spacing. This chart shows that for regions where the tin
is whisker mitigated but has been stressed, a spacing of
about 380 µm is required to get to 0ppm failure rates in
this particular component.
1500
2000
2500
0.3
0.2
0.15
0.1
0.05
0
0.00%
% Failures
In order to improve the resolution of curve at low and
desirable ppm levels of failure rates, the simulation was
expanded. In order to get to 100ppm levels of failure
rates, we needed to simulate 10,000 components per lead
spacing with 232 areas per component. Due to the large
number of whiskers that would have to be simulated for
the non-whisker mitigated tin, this portion of the
simulation could not be accomplished using the available
simulation tools. Thus, we only simulated the whisker
mitigated tin.
1000
0.25
100%
Figure 8. Simulated failure rate chart of whisker
mitigated tin plating with greater resolution in Y-axis.
Chart was created simulating 500 connectors with 232
areas per connector.
500
0.05%
0.10%
0.15%
% Failures
Figure 9. Simulated failure rate chart for whisker
mitigated tin showing greater resolution at low defect
levels. A separation distance of about 380 µm is required
to get to 0ppm failure rates.
The component of interest in this study had 232 areas that
were susceptible to tin whisker shorting. To get a
rudimentary understand of the impact of I/O count, the
simulation was also performed as if the component had
just 2 areas of I/O. Figure 10 shows the failure rates for
the previously described 232 area component as well as a
2 area component (in pink). For equivalent terminal
spacings, the likelihood for failure is much lower in the
low I/O component that for the high I/O component.
There have been reports that some 2 position devices,
such as capacitors, are less likely to whisker and many of
these devices converted to pure tin plating a decade ago.
The results from this work might suggest that the whisker
growth may be equivalent, but the likelihood for failure
(based on the number of I/Os and the relative spacing of
the conductors) is relatively small.
Whisker Failure Rate as a Function of I/O Count
0.4
232 I/O
2 I/O
Separation Distance (mm)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
% Connector Failure
Figure 10. Simulated whisker failures rates for whisker
mitigated tin for two different I/O count components.
Failure rate is non-linearly related to I/O count.
Paper presented at the IPC/JEDEC Lead-Free Symposium, April 2005, San Jose, CA
IV.
CONCLUSIONS
APPENDIX 1
Monte Carlo simulation techniques have been used to
predict failure rates for electrical components due to tin
whisker growth in tin platings. The following
conclusions can be drawn from this work:
1. Tin whiskers are a reliability risk for many
electronic devices.
2. Tin platings that do not incorporate whisker
mitigation strategies are particularly prone to
grow long whiskers that can lead to electrical
shorts.
3. Tin whisker mitigation techniques, such as those
used here, reduce the likelihood for failure,
especially in fine spaced electronic components.
4. Simulated failure rates were lower for
components with smaller I/O counts and the
relationship between I/O count and failure rate is
non-linear.
5. Simulated failure rates in the ppm range are
achievable in tin plated electronic components of
typical fine pitch spacing.
6. Using measured tin whisker distributions helps
to statistically describe the propensity of a tin
finish to grow tin whiskers.
Input:
Whisker Density (Sites/mm^2)
Length(mm), Width(mm)
Separation Distance (mm
)
Calculate: # Whisker Sites for a Single Contact Area
Define Functions to Generate Random:
(x1,y1) Positions, (θ,Φ) Rotation&Inclination Angles
Define Functions to Calculate:
Critical Lengths for each Whisker Site,
(x2,y2) Offset Distances,
Inverse Johnson Transform
Calculate (x1,y1) Whisker Sites, θ rotation and Φ inclination
For Total # of Areas in one Connector.
Calculate Critical Lengths for each Site in one Connector
Calculate corresponding (x2,y2) offsets for each Site
Identify Critical
Lengths touching
Repeat for Each Contact
The authors wish to thank Karen Benjamin of Tyco
Electronics for her assistance with statistical
interpretation and Rick Perko for his continuing support
of tin whisker research at Tyco Electronics.
Repeat for Each Connector
ACKNOWLEDGMENT
Within the Width
Identify
Whisker Lengths
≥
Critical Lengths
Generate Failure Matrix
1 or 0 for a Connector
Output
Σ Connector Failures
REFERENCES
1
Chen, K., et al, “Observations of the Spontaneous Growth of Tin Whiskers on Tin-Manganese Alloy Electrodeposits”,
Phys. Rev. Letters. 94, 066104 (2005)
2
Hilty, R. D., Corman, N, Herrmann, H., “Electrostatic Fields and Current Flow Impact on Whisker Growth”, Submitted
and accepted for publication by CMPT of IEEE, 18AUG04; also presented at ECTC 2004 in Las Vegas.
3
NEMI Tin Whisker Acceptance Test Requirements, NEMI Tin Whisker Users Group, July 28, 2004, available at
www.nemi.org
4
Henshall, G., “Modeling Pitting Degradation of Corrosion Resistant Alloys”, Lawrence Livermore National Laboratory,
UCRL-ID-125300, November 1996.
5
This is not that surprising since the Johnson Transformation is one of the methodologies employed in extreme value
statistics. For additional information, see for example, Wadsworth, H. M., “Handbook of Statistical Methods for Engineers
and Scientists”, McGraw Hill, 1990, pg, 6.29
Paper presented at the IPC/JEDEC Lead-Free Symposium, April 2005, San Jose, CA
6 Y. Chou, A.M. Polansky, and R.L. Manson, "Transforming Non-normal Data to Normality in Statistical Process Control,"
Journal of Quality Technology, 30 April 1998, pp 133-141.
Paper presented at the IPC/JEDEC Lead-Free Symposium, April 2005, San Jose, CA
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