2003-01 CARTS Ceramic Life Model Sub-2-Micron 01/03 (245.2K PDF)

Lifetime Modeling of Sub 2 Micron Dielectric Thickness BME MLCC
Michael S. Randall, Abhijit S. Gurav, Daniel J. Skamser, James J. Beeson
Fountain Inn, SC 29644. Phone: (864) 409-5700, FAX: (864) 409-5665,
e-mail: [email protected]
Multilayer ceramic capacitor (MLCC) design is
driven toward increased capacitance per unit
volume, achieved via increased active layer count
combined with decreased dielectric thickness.
Current state of the art MLCC technology
combines <2.0 um dielectric thickness with >350
active layers in an 0805X5R106 design, having
>6 cm2 active area. In order to insure adequate
service life at rated temperature and voltage, it is
imperative that the relationship between highly
accelerated life test (HALT) data and life data
under use conditions be understood.
This paper examines accelerated life performance
of 0805X5R106 6.3V base metal electrode (BME)
MLCC and correlates HALT performance with
time-to-failure (TTF) data under life test
conditions using product from four different
manufacturers. The models generated are used to
predict TTFs under use conditions.
While the model activation energies (Ea) do not
vary significantly between manufacturers, the
calculated voltage stress exponents do, indicating
the importance of establishing individual model
parameters for each MLCC system evaluated.
The models also serve as a reminder that the
combination of voltage and temperature model
parameters, as well as the actual HALT TTF data
and distribution thereof, are necessary in
accurately estimating TTFs under use conditions.
The model is extended to devices having different
active areas and an active area correction factor is
introduced.
Introduction
Typically, one of the most important performance
factors in electronic device development is
reliability of in field service. One very important
component of reliability is TTF. With the
introduction of BME MLCC in the early 1990s,
the ability to predict field failure rates due to
dielectric wear out became even more important
and adoption of HALT test variants as a
predictive method of TTF in the field.
In most types of HALT testing, device leakage
current or insulation resistance is observed over
time as the devices are subjected to high
temperatures and high multiples of rated voltage.
Device failures are indicated when insulation
resistance degrades significantly (typically >1
order of magnitude from the leakage current
measured at time zero). The distribution of
device failure times is then plotted as a function
of time and the failure behavior modeled to
predict median time to failure (MTTF). Figures 1
and 2 illustrate a typical insulation resistance vs.
time chart, or monitored IR curve, and a typical
TTF curve respectively. Figure 3 shows a typical
failure rate curve for a HALT test (i.e., the
“bathtub” curve). This is helpful in understanding
the different regimes of failure in a typical
sampling of devices. More information on HALT
testing is available in numerous other
publications.1-6
10
Insulation Resistance (Meg-Ohm)
Abstract
1
0.01
0.1
0.1
T0
1
Time (hours)
10
TF
Figure 1. Typical HALT monitored IR curve
indicating time zero (T0), time to failure (TF).
Once the HALT characteristics for an MLCC
system are characterized, it is important to be able
to use the TTF data as a predictor of time to
failure in the field (i.e., under non-accelerated
conditions). Calculated time-to-failure data at
maximum rated use temperature and voltage can
then be used to predict TTF field performance
under maximum use conditions.
©2003 Components Technology Institute, Inc. – CARTS’2003 Conference
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values of close to 1 to as high as ~9.3,6 Obviously,
since this value is used as the power for voltage
acceleration in the P-V equation to predict TTF,
the variation noted in n can lead to dramatically
different TTF projections. Thus, it is important to
carefully characterize each system in order to
accurately determine n on a case by case basis.
99.99%
Dielectric Wear Out Failures
99.9%
99%
Normal Percentile
95%
90%
80%
70%
50%
30%
20%
10%
5%
Early Failures
1%
Time Zero Fails
0.1%
0.01%
0.01
0.1
1
10
100
1000
Time to Failure (mins)
Failure Rate
Figure 2. Typical HALT TTF curve indicating 3
failure modes (time zero, early time and dielectric
wear out)
Time
TimeZero
Zero
Failures
Failuresor
orInfant
Infant
Mortals
Mortals(Major
(Major
Defects
Defects) )
Early
Earlyor
orFreak
Freak
Failures
Failures(Minor
(Minor
Defects)
Defects)
Dielectric
Dielectric
Wear
WearOut
Out
In earlier studies, it has been hypothesized that the
variation in n observed may be due to varying
dielectric thickness. It has been hypothesized that
n tends to increase as dielectric thickness is
reduced.7
The goal of the present study is to evaluate TTF
characteristics for very high volumetric efficiency
BME MLCC and to determine if Ea and n are
consistent using MLCC produced by different
manufacturers, as well as to determine how well
P-V calculations predict Life Test performance
for high volumetric efficiency BME MLCC. The
part type evaluated was 0805 X5R 10 µF, 6.3 Vrated (Vr) configuration.
MLCC from four
different manufacturers were evaluated.
Time
Figure 3. Illustration of the “bathtub curve”
typically observed in failure rate during HALT
testing.
Perhaps the most widely accepted TTF predictive
model is that proposed long ago by Prokopowicz
and Vaskas.2 The P-V model involves two
acceleration factors as indicated in the equation:
t1
t2
=
V2
V1
n
exp Ea/k
1 1
T1 T2
Where:
ti= time to failure under conditions i
Vi = voltage under condition i
n = the voltage stress exponential
Ea = the activation energy for dielectric wear
out
k = Boltzmann’s constant (8.62E-5 eV/K)
Ti = absolute temperature for condition i
The P-V equation has been used in numerous
studies on MLCC reliability.2-6 In most of the
studies, the activation energy values for barium
titanate based dielectric (BME and PME) agree
and are typically from 0.9 to 1.7 eV.6 However,
in several instances, the value for the voltage
stress exponential (n) has varied widely from
Experimental
Capacitors of the above type, made by four
different manufacturers were obtained.
The
general characteristics of each manufacturer’s
MLCC were determined (see Table I).
Table I. Characteristics of
0805 X5R 106, 6.3V BME MLCC
MFG
A
B
C
Cap. (µF)
Df (%)
Breakdown
Voltage (V)
IR at 25C (MOhm)
IR at 125C (MOhm)
Dielectric
Thickness (µm)
Electrode
Thickness (µm)
Active Layers
Margins (mm)
LxWxT (mm)
D
11.1
7.3
10.8
8.0
9.3
4.6
9.1
4.6
65
96
144
114
148
105
174
216
112
13
46
94
1.38
1.55
1.74
1.78
1.27
1.67
1.57
1.44
395
0.11
323
0.12
371
0.13
333
0.14
2.05x1.30
x1.30
2.13x1.37
x1.37
2.01x1.
37x1.37
2.11x1.35
x1.35
Active Area
6.5
(cm2)
K (calculated)
2690
0.24
Grain Size (µm)
Notes: All values are averages
©2003 Components Technology Institute, Inc. – CARTS’2003 Conference
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5.9
5.0
5.4
3176
0.49
2817
0.35
3434
0.36
Median time to failure values from the TTF
curves were then used to calculate n and Ea using
the P-V relation. These data were used to
estimate MTTF under Life Test conditions (2 x Vr
and 85C). MLCC (100 pc each) from each
manufacturer were evaluated under those
conditions. Life test data were then compared
with the data predicted from the P-V equation.
Results and Discussion
A representative plot of MTTF vs. inverse
temperature is illustrated in Figure 4. Plots of this
type were used to calculate Ea for each set of
MLCC. Figure 5 illustrates a representative plot
used to calculate the voltage exponential of each
set of parts.
1E+7
1E+6
MTTF (min)
1E+5
1E+4
12.6 V
18.9 V
1E+3
1E+2
25.2 V
1E+1
31.5 V
1E+0
2.4
140C
2.5
125C
2.6
Inverse Temperature (1/K)
2.7
2.8
85C
Thousandths
Figure 4. Representative plot of MTTF vs.
inverse absolute temperature used to calculate Ea.
1E+7
1E+5
MTTF (min)
Each set of MLCC was evaluated using a
MicroInstruments model PE 9051 HALT system.
The parts were mounted in mechanical test
fixtures and 20 pieces were evaluated per HALT
test to generate TTF curves. TTF was defined as
the time when insulation resistance (IR) degraded
to a value of 500 K-Ohm (the lower limit of the
test equipment). Parts were tested at temperatures
ranging from 125C to 140C and at voltages from
2 to 8 times Vr (12.6 to 50.4 V). Since only two
temperatures were evaluated in this part of the
study, an average of MTTF vs. inverse
temperature, for at least four different voltages
was used to calculate Ea for each set of MLCC.
1E+3
125C
140C
1E+1
1E-1
1E-3
0
5
10
15
20
25
30
35
40
45
50
Voltage
Figure 5. Representative plot of MTTF vs. HALT
voltage used to calculate n.
Table II depicts a summary of the HALT study
performed. Values of n were calculated for 125C
and 140C. The n values at 125C and 140C agree
to within 15% for each manufacturer’s product.
Table II. Ea and n summary from HALT study
MFG
A
B
C
D
Ea (eV)
1.34
1.38
1.50
1.49
n
(125C)
1.56
6.27
2.70
3.27
n
(140C)
1.81
6.67
3.10
3.10
Table II Ea data indicate relatively similar
activation energies between all sample sets
evaluated. These activation energy data also
agree well with data from previous HALT
studies.5 However, the calculated voltage stress
exponential
data
vary
widely
between
manufacturers, from a maximum in excess of 6 to
a minimum of about 1.5, even though the
dielectric thicknesses are relatively similar for all
products tested (see Table I).
This variation in n values has a tremendous effect
on predictions resulting from the P-V equation
and denotes the importance of calculating the
value of n for each type of MLCC evaluated. For
example, using MFG A’s HALT MTTF data with
MFG B’s n value would result in a difference in
predicted MTTF under Life Test conditions at
85C and 1.5 x Vr of >15,000 hours which is more
than 8 times higher than the correctly calculated
TTF of ~1900 hours.
©2003 Components Technology Institute, Inc. – CARTS’2003 Conference
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Based upon the above analyses, the MTTFs for
each manufacturer’s product under 3 different
Life Test conditions were predicted (see Table
III). These predicted MTTFs were then compared
with actual test data (see Figures 10-12).
MFG C
1E+10
1E+8
MTTF (years)
Predictions of MTTF based upon the P-V model
using estimated values of n and Ea for each
manufacturer are depicted in Figures 6-9. The
effect of large n is apparent upon MFG B’s TTF
performance at or near maximum use conditions
(85C/6.3V). Interestingly this larger n value also
yields the longest predicted MTTF for MFG B’s
product when used at relatively low temperatures
and voltages, while MFG A’s product, which had
the longest MTTFs (predicted and tested) would
be projected to have shorter MTTFs when used at
relatively low temperatures and voltages. This
predicted observation was not verified
experimentally as the TTFs at low temperatures
and voltages would be very long, and the test
duration required would not be practical.
1E+6
1E+4
1E+2
1E+0
2
35
45
55 5
6
75
855
MFG A
1E+10
MTTF (years)
1E+8
6.3 9.45 12.6
1.5 2.5 3.3 5
1
Voltage
Temp (C)
1E+6
1E+4
Figure 8. MTTF predictions for MFG C under
various conditions using the P-V equation.
1E+2
1E+0
1
1.5 2.5 3.3 5
1E+10
6.3 9.45 12.6
1E+8
Voltage
Temp (C)
Figure 6. MTTF predictions for MFG A under
various conditions using the P-V equation.
MTTF (years)
2
35
45
55 5
6
75
855
MFG D
1E+6
1E+4
1E+2
MFG B
1E+0
2
35
45 5
5
65
7 5
855
1E+10
MTTF (years)
1E+8
1E+6
1
6.3 9.45 12.6
1.5 2.5 3.3 5
Voltage
Temp (C)
1E+4
1E+2
Figure 9. MTTF predictions for MFG D under
various conditions using the P-V equation.
2
35
45
55 5
6
75
855
1E+0
Temp (C)
1
1.5 2.5 3.3 5
6.3 9.45 12.6
Voltage
Figure 7. MTTF predictions for MFG B under
various conditions using the P-V equation.
Table III. MTTF Predictions
MFG/
Est. TTF (h)
85 C, 1.5 x Vr
85C, 2 x Vr
125C, 2 x Vr
A
B
C
D
17,939 1,919 26,741 8,307
11,448 316 10,439 3,820
147
4
80
29
©2003 Components Technology Institute, Inc. – CARTS’2003 Conference
Page 4
illustrates the insulation resistance (IR)
distribution for MFG B under these conditions.
The figure indicates that, by 250 h, there is
significant degradation in the IR values for ~1/2
of the MLCC tested, but that the parts had not
degraded to the point of failure. The second
discrepancy is depicted in Figure 12. The relative
rate of failure for MFG C at 250 hours is slightly
lower than it probably should be based upon the
predicted MTTF, and is likely due to the wide
TTF distribution in this situation.
Predicted MTTFs
B
Percent Fail
100
D
A
C
A
B
C
D
80
60
40
20
0
25
0
50
0
10
00
20
00
40
00
80
00
16
00
0
32
00
0
0
Test Duration (h)
99.99%
99.9%
Figure 10. Predicted vs. actual Life data for
[email protected] x Vr Life test.
99%
95%
90%
B
Percent Fail
100
Normal Percentile
80%
Predicted MTTFs
D
C A
70%
50%
30%
20%
A
B
C
D
80
60
40
10%
5%
Initial
250 hr
500 hr
1000 hr
1%
0.1%
0.01%
0.01
20
0.1
1
10
100
1000
10000
100000
IR Megohms
0
16
00
0
0
0
Figure 13. IR distribution for MFG B at Life test
conditions of 85C and 2 x Vr, indicating ~50% of
the parts exhibiting IR degradation by 250h.
80
0
40
0
0
20
0
10
0
50
0
0
25
0
0
Test Duration (h)
While MTTF is an important factor, the TTF
distribution is also important as it gives an
indication of how reliable MTTF predictions will
be for all parts within the population. Figure 14
illustrates that, excluding early failures (“infant
mortality”), the TTF distributions span ~2 orders
of magnitude in time. The verticality of this
distribution should be considered as a figure of
merit, along with MTTF during product
development.
Figure 11. Predicted vs. actual Life data for
[email protected] x Vr Life test.
Predicted MTTFs
BD C A
A
B
C
D
Percent Fail
100
80
60
40
20
99.99%
0
99.9%
0
250
500
1000
MFG D
99%
Test Duration (h)
MFG C
95%
90%
Normal Percentile
80%
Figure 12. Predicted vs. actual Life data for
[email protected] x Vr Life test.
MFG B
70%
50%
30%
MFG A
20%
10%
With the exception of two instances, the predicted
MTTFs agree well with the Life Test data. The
first discrepancy is illustrated in Figure 10. While
the failure rate for MFG B was highest for the
85C, 1.5xVr conditions, the failure rate is lower
than would be predicted unless the distribution of
failures vs. time is relatively narrow. Figure 13
5%
1%
0.1%
0.01%
0.1
1
10
100
1000
10000
Time to Failure/ mins
Figure 14. HALT TTF distributions for MFGs AD, 125C, 6 x Vr.
©2003 Components Technology Institute, Inc. – CARTS’2003 Conference
Page 5
Summary and Conclusion
The predictions from the P-V equation indicate
that it is relatively accurate in projecting Life Test
TTF for very high active layer, X5R thin layer
BME MLCC. As with all models, the projections
appear to be less accurate as conditions are
extrapolated further from the test conditions.
materials set and dielectric thickness, but with
different active areas. The active area in the
1206Y5V475 sample was ~47% that of the
1210Y5V106 design. It is clear that MTTF is
significantly affected by the change in active area.
1.00
0.90
0.80
When predicting TTFs it is important to consider
the variation within the TTF distribution. The
TTF distributions in this study and others5
indicate that TTF range can easily span one or
more order of magnitude in time, excluding
“infant mortality” failures. It is logical that the
width of the TTF distribution should increase as
dielectric thickness is decreased, due to the
greater variation in dielectric thickness, on a
normalized basis, encountered when reducing
dielectric thickness. It is also logical, from a
defect density standpoint that the range of TTF
should increase as active area is increased, similar
to other measures that are effected by specimen
size (such as mechanical properties, etc.).8 This
should be carefully considered during product
development.
With proper use, the P-V equation accommodates
the effect of dielectric thickness in the V terms
(sometimes more accurately called the “E” or
electric field term).4 The P-V equation does not
consider active area, however. This was not an
issue for the current study, as the active areas of
the devices evaluated were relatively similar (see
Table I). However, when developing numerous
capacitance value MLCC with similar dielectric
thickness and chemistry, it would be
advantageous to be able to predict TTF for the
different capacitance values (active areas).
Within a materials system, MTTF typically
decreases as active area is increased (see Figure
16 for a typical example). In this case, two
repetitions each of HALT were performed on two
different MLCC designs made with the same
1206 4.7 uF, 1
1206 4.7 uF, 2
1210 10uF, 1
1210 10 uF, 2
0.70
Portion Fail
This study indicates the importance of defining
individual voltage exponential (n) values for each
different manufacturer or materials set. This is
crucial for accurate TTF modeling, even though
the devices were of similar value (10 µF),
temperature class (X5R) and voltage rating
(6.3V). It appears that there is significantly less
variation in Ea between manufacturers in this
category of MLCC.
0.60
0.50
0.40
0.30
0.20
0.10
0.1
1
10
100
250
1000
3300
10000
Time (minutes)
Figure 16. TTF distributions (2 repetitions of test
for each active area), depicting the change in
MTTF, within an MLCC system, with increasing
active area (from ~3,300 minutes to ~250 minutes
with a 2.12 fold increase in A in this case).
It is proposed that an appropriate modification to
the P-V equation would be to add a term to
compensate for active area. This modification
would be in the form of:
t1
t2
=
A2
A1
r
V2
V1
n
exp Ea/k
1 1
T1 T2
Where:
Ai = the active area of MLCC design i
r = the area exponential
ti= time to failure under conditions i
Vi = voltage under condition i
n = the voltage stress exponential
Ea = the activation energy for dielectric wear
out
k = Boltzmann’s constant (8.62E-5 eV/K)
Ti = absolute temperature for condition i
In the above case (Figure 16), the value for r is
3.4. It is likely that this value would vary
between MLCC platform sets as with n. Thus, it
would be prudent to determine r for each system
as is recommended above for n. Based upon
limited experience to date, r has been found to be
in the range of 1 to 4. More experimentation is
needed to determine refine the understanding of
this proposed addition to the P-V equation.
©2003 Components Technology Institute, Inc. – CARTS’2003 Conference
Page 6
References
(1) W. J., Minford, “Accelerated Life Testing
and Reliability of High K Multilayer Ceramic
Capacitors, IEEE Transactions CHMT-5, p
297, (1982).
(2) T. I. Propokowicz, A. R. Vaskas, “Final
Report, Research and Development Intrinsic
Reliability Subminiature Ceramic Capacitors,
ECOM Report 90705-F, (Oct. 1969).
(3) G. Maher, “Highly Accelerated Life Testing
(HALT) of K-4500 Low Fired X7R
Dielectric,” Proceedings of the Passive
Components
for
Power
Electronics
Workshop. April 26-27, 2000, Penn State
University. Also presented in parts at the
US-Japan Seminar on Dielectric Studies
November, 1999, Okinawa, Japan.
(4) M. J. Cozzolino, B. Wong, L. S. Rosenheck,
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Degradation in BG Dielectric Characteristic,
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254-264.
(5) J. L. Paulsen, E. K. Reed, “Highly
Accelerated life Testing (HALT) of KEMET
Base Metal Electrode (BME) Ceramic Chip
Capacitors,” CARTS 2001, pp. 265-270.
(6) D. McCauley, H. Park, M. Megheri, M. Chu,
E. Davis, “Influence of BaTiO3 Sources and
Dopant Levels on Reliability Behavior of
BME
Formulations,”
ACerS
Annual
Meeting, St. Louis, MO, April 30, 2002.
(7) J. J. Beeson, R. Vaughan, A. S. Gurav, L. A.
Mann, The Anatomy and Performance of
High Capacitance Value Base Metal
Electrode MLCC,” CARTS 2002, pp. 36-42.
(8) W. D. Kingery, H. K. Bowen, D. R.
Uhlmann, Introduction to Ceramics, Second
Edition, pp. 787-788, Wiley Interscience,
New York, 1976.
©2003 Components Technology Institute, Inc. – CARTS’2003 Conference
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