NASA Electronic Parts and Packaging (NEPP) Program

Voltage Acceleration Factors for
Infant Mortality Failures and Deratingof Solid Tantalum Capacitors
Alexander Teverovsky
Dell Services Federal Government, Inc.
Work performed for NASA GSFC, Parts, Packaging, andAssembly Technologies Office, Code 562,
Alexander.A.Teverovsky@nasa.gov

To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

1Acronym Table
FR
HALT
IM
LSST
OEM
RT
TCM
TDDB
TTF
WGT

failure rate
highly accelerated life testing
infant mortality
life step stress testingoriginal equipment manufacturer
room temperaturethermo-chemical modeltime dependent dielectric breakdown
time-to-failure
Weibull grading test

To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

2Outline Failures of tantalum capacitors as time dependent
dielectric breakdown (TDDB).
 Justification for Weibull Grading Test (WGT).
 Errors associated with WGT.
 Results of highly accelerated life testing (HALT).
 Results of life step stress testing (LSST).
 Voltage acceleration factors.
 Voltage derating as a means toincrease reliability of tantalum
capacitors.
 Conclusions.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

3

Life Test Failures as TDDBH  Thermo-chemical model (TCM) of TDDB: TTF  to  exp  E  kT H -energy for ions displacement,  - field acceleration parameter, to - time constant.

 Time-to-failure, TTF, can be calculated based on distribution of
breakdown voltages, VBR: H H V 
H
V BR   BR   ln 1  p  
1


V 


  to  exp
 1 TTF  to  exp  exp 
kT
kT
V
kT
V


BR 
BR 



100uF 16V at 125C 24V
100

100uF 16V 144hr at RT 32V
1.E-04
cumulative probability, %current, A

90

1.E-05

1.E-0650

simulation
experiment

10

Simulation at
=40.2V, =5.8
H=1 eV, t0=10-3 hr

5

1.E-07
0.01

0.1

1

10

time, hr

100

1000
1
1.E-2

1.E-1

1

10

100

1000

time, hr Scintillations during life testing should be considered as failures.
 Life test results can be simulated using the TDDB model, but
parameters should be adjusted.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

4Modeling of Infant Mortality Failures
 Experimental distributions of TTF for chip Ta capacitors in most cases
can be described as 2-parameter Weibull function with  < 1
 Majority of test failures can be considered infant mortality (IM) failures.
Monte-Carlo simulation of VBR
distributions at different Times to failure calculated based on
TDDB model

35V capacitors with characteristic VBR=95V

Life Test Simulation 35V capacitors at 85C 52.5V

100

100

90

90

10
5

b=5
1
5.E-1

1.E-1

0.05 (3)50b=3cumulative probability, %cumulative probability, %

50

b=10

b=40

b=20
20

100

breakdown voltage, V

200

0.11 (5)10
51.1 (40)

0.25 (10)

1
5.E-1

1.E-1
1.E-1

0.52 (20)
1

1.E+1

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

1.E+7

1.E+8

1.E+9

time, hr At the range of BR that is typically observed for tantalum capacitors (5 to20), simulations show that all failures, up to the end of life, are defectrelated IM failures (life test <1).
 High quality lots with tight VBR distributions ( BR ~40) fail due to wear-out.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

5Weibull Grading Test
 To reduce the probability of failures under steady-state operating conditions,
all hi-rel capacitors are screened by WGT.
 WGT is a combination of burn-in (screening to remove IM failures) andreliability qualification (testing to assess the failure rate, FR).
 If < 1 and failures are monitored during the testing, then the test can be
stopped when the necessary FR is achieved.
F(t)

WGT
normalcond.

63%

  t  F (t )  1  exp        

 norm  WGT  t  ( t )     

 1

 norm  AF WGT

WGT (tWGT )  AF  norm AF  tWGT 
_WGT_normt

Original notion [Didinger’64]: “to pay for only as muchgrading as needed, without the risk of getting too little oroverpaying for too much reliability”.

 The notion that reliability cannot be screened out, but should be built-in
by design and technology is related to random and wear-out failures.
 If all failures are due to IM, then any lot can be screened out to as highFR level as necessary.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

6

WGT Conditions
 WGT conditions per MIL-PRF-55365:
o 85 oC for 40 hr and voltages from 1.1VR to 1.53VR.
o Failure is defined as a blown 1A or 2A fuse.
o Failures calculated at 2 hr and 40 hr of testing.
o FR is calculated using an empirical equation obtained ~ 40 years ego:V AF  7.03412025  10 9  exp18.77249321 
VR 


V

u
1
 Considering that at V = VR AF= 1: AF  exp( B  u )VR
B is the voltage acceleration constant (B = 18.77249321 ?) Life test at 85 oC can confirm  ~1%/1000hrs which is more than 100
times greater than is required for T-grade capacitors.
MIL-PRF-55355 requires 2000 hrs testing of 102(1) parts 2 ( ,2n  2) 1
105

at V = VR and 85 oC or 24(0) at V = 2/3VR and 125 oC.  
2
AF N  t Existing life test conditions are not sufficient to assure the required
reliability level, so FR is determined by WGT.
 Long-term reliability is determined by a 40-hr accelerated test!
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

7

WGT Problems
F(t) Two groups of problems for FR assessment
63%
using WGT: test conditions and calculations.
 Problems with test conditions:

WGT
normalcond.

  ln1  F (t )  1
o Verification of contacts in fixtures.


t
AF
o Only 300 samples are used for calculations.
_WGT _norm to Test results with different fuses might be different.
o Short current spikes below ~10A (scintillations) will remain unnoticed.
o Only two points to draw the F(t) line and calculate  and .

 Problems with calculations:WGT(VWGT, tWGT)FR  norm VR, AF  tWGT o Early failures (before 15 min) are neglected.
o Calculations do not account for the uncertainty in time-to-failures.
o Only two points are used for calculations.
o If no failures observed, wear-out degradation (e.g. due to field-induced
crystallization or Vo++ migration) can be missed.

AF

 The most significant errors in FR, up to 3 orders of magnitude,
are due to incorrect voltage acceleration factors.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

8

HALT at Different Test Conditions
 HALT for tantalum capacitors is limited compared to ceramic capacitors
by low breakdown voltages (typically from 2.5VR to 3.5VR).
Results of HALT for 22 F, 50 V and 4.7 F, 50 V capacitors at different
voltages and temperatures
22uF 50V capacitors at different BI conditions

4.7uF 50V capacitors at different BI conditions

99

99

125C 80V

90

90

75V 125C

112.5V 22C

87.5V 85C
100V 22C

130C 60V
50

22C 100V10

22C 87.5V

5

1
1.E-3

cumulative probability, %cumulative probability, %

50

1.E-2

1.E-1

1

time, hr

10

100

1000

87.5V 22C

75V 22C
10

5

1
1.E-2

1.E-1

1

10

100

1000

time, hr H 
V  1 Model prediction for characteristic life:    o  exp kT  nVR 
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

9

Statistical Analysis Using ALTA-PRO
The characteristic life can be presented as a general log-linear
relationship:   exp 0  1 X 1   2 X 2 
Based on TDDB model, the following conversion was used:H1
H2  
X1   0  ln  0 
k  n  VR
T
k
1

PART

X2 

Example of HALT results for three part types.
Sus
Fail
H,
pen 
t0, hr
1
2
0
ures
eV
ded

V
T

n

B_85

4.7uF 50V

90

1170.24 -15.06 12761.6-68.61

2.9E-07

1.1

3.7

9.6

22uF 50V

40

41

0.40 -28.13 21026.1-124.49

6.1E-13

1.8

3.4

17.4

22uF 63V

59

43

0.24 -28.45 25072.2-145.03

4.4E-13

2.1

3.5

20.6

 Results for 7 different part types showed that the acceleration
constant B varies from 10 to 20.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

10Life Step Stress Testing (LSST)V  LSST is a fast method to assess AF.
  exp 0  1  VR 
 Weibull-exponential cumulativedamage model was used.
V (V )
 exp1    1  exp(B  u )AFV  Step duration 20 to 40 hrs.
 (VR )
 VR   Testing at 22 oC, 85 oC, and 125 oC
allows for estimation of the voltage acceleration
constant (B) and effective activation energy (Ea).
Example of LSST for 33uF 10V capacitors at 85 oC

Gr.2 Microchip 33uF 10V at 85C

Microchip 33uF 10V at 85C

99.0

2.6

40
failures
V/VR

50.0

2

20

1.8
10
1.6

V/VR

2.2

cumulative probability, %30
f ailures

90.0

2.4

10.0

5.0

1.4

0
0

40

80
time, hr

120

160
1.0
1.E-1

1

1.E+1

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

1.E+7

1.E+8

1.E+9

time, hr

To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

11

Specifics of LSST
 The model parameters, 1, 2, and  were computed using ALTA-PRO
utilizing a maximum likelihood estimation (MLE) method.
 LSST simulation: V/VR varied from 1.75 to 3 at 6 20-hour steps.
Three test results with 18 samples each were generated: 1 - early failures (three failures at
each step after 1, 2, and 3 hr); 2 - failures occurred at the end of steps (after 17, 18, and 19hrs); 3 - failures were distributed evenly through the steps (after 1 hr, 10 hr, and 19 hr).

 Results: 2×103 < < 2×1010 hr, 0.2 <  < 2.8, 0.7 < B < 12.
Effect of TTF distributions on the use-level life calculations
SST simulation

SST simulation

99.0

100

3.5
early F
end F
uniform F
V/VR

end F
b=2.8, B=0.7

uniform F
b=0.8, B=-2.5

3
2.5

40

2

20

1.5

0

cumulative probability, %

50.0

60

stressf ailures, %

80

90.0

early Fb=0.2, B=-12

10.0

5.0

1
0

20

40

60
time, hr

80

100

120
1.0
1.E-1

1.E+1

1.E+3

1.E+5

1.E+7

1.E+9

1.E+11 1.E+12

time, hr

 Inaccuracy in TTF might result in substantial errors of reliability estimation.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

12

Life Step Stress Testing Results
Microchip 10uF 10V Use Level Probability Weibull

 High quality tantalum capacitors
might fail due to wear-out
mechanisms at high voltage stressconditions.

90.0

125C
50.0

Unreliability

85C
22C

10.0

5.0

1.0
1.E+3

1.E+4

1.E+5

1.E+6

1.E+7

1.E+8

1.E+9

1.E+10Time

4.7uF 6.3V Microchip
99.0

90.0

125C
50.0

cumulative probability, % 5 types of tantalum capacitors havebeen tested using LSST.
 One out of 5 groups had  > 1 indicating
wear-out.
 Inception time was ~100 years at 125 oC
and >1010 years at RT.
 This group had high VBR thus indicatinghigh quality dielectric.
 Early failures were likely due to defects
in the oxide.

99.0

85 C

22C

Early
failures

10.0

5.0

1.0
1.E+4

1.E+6

1.E+8

1.E+101.E+12

1.E+14

1.E+16

1.E+18

time, hr

To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

13

Results of LSST at 85 oC
 At 85 oC: 6 < B < 18. Some lots deviate substantially from the accepted
standard voltage acceleration constant (Bs = 18.77).
 FR calculated at conditions simulating Weibull grading test per MILPRF-55365 showed that microchip capacitors can be screened to highFR levels up T-level (0.001%/1000hr).
Part(C, VR)

case

QTY



0

1=-B

(VR),hr

WGT FR,%.1000hr

33uF, 10V

R

40

0.19

26.98

-14.12

3.85E+05

1.6E-02

10uF, 10V

R

43

0.62

35.05

-18.23

2.01E+07

6E-03

47uF, 10V

T

60

0.34

31.87

-9.92

3.39E+09

4.7E-04

4.7uF, 6.3V

M

40

1.4

29.40

-6.02

1.43E+10

1.2E-11

4.7uF, 50V

C

40

0.32

29.7

-14.2

1.2E+08

5E-4

 Acceleration constants determined by LSST are consistent with HALT
results and indicate substantial variations from the standard value.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

14

Voltage Derating Derating is a reduction of operating electrical and temperature stresses
used by original equipment manufacturers (OEM) to increase reliabilityof components compared to the rated conditions.
 For capacitors that passed WGT the probability of failure during a
mission duration (tM) can be determined using Weibull functions, F(t):P (t M ) F (t M  AF  tWGT )  F ( AF  tWGT )1  F ( AF  tWGT ) Suppose tM = 10 years and the required reliability is P(10) < 3×10-5.
At FR = 0.001%/1000 hr (10-8 1/hr) and V = VR, P(10) is ~ 8.8×10-4, which
exceeds the required level.

 At B = 18.772 derating to 0.8VR would reduce P(10) to below 2×10-5,which is in compliance with the requirements.
 If the acceleration constant B is much smaller than it is assumed by
MIL-PRF-55365, then a more severe derating is necessary.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics
Engineers (IEEE) Components, Packaging and Manufacturing Technology Society (CPMT)Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21st15

Effect of Voltage Derating on the
Probability of Mission Failure
F (t M  AF  tWGT )  F ( AF  tWGT )P (t M ) 
1  F ( AF  tWGT )AF  exp( B  u )

V
u
1
VR

  t  F (t )  1  exp            tWGT  AF  (V )  
FR (V )


 1

1

 



 Assuming tWGT = 40 hr and
1.E-04
nominal failure rate calculated at B
1.E-05-8 1/hr, the=18.772FR=
10
1.E-06characteristic life, (V) was
1.E-07
1.E-08calculated at a given 
1.E-090.2
2
20  The probability of failure, P(t ),Mmission duration, years
B=18.8, b=0.5, d=1
B=18.8, b=0.5, d=0.75
during mission time, tM was
B=18.8, b=0.5, d=0.5
B=10, b=0.5, d=1
calculated at different voltage
B=10, b=0.5, d=0.75
B=10, b=0.5, d=0.5
B=10, b=0.5, d=0.25
derating d = V/VR.

probability of failure

1.E-02
1.E-03To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

16

Voltage Derating, Cont.’d Suppose B = 10, then AF would be ~100 times less than at
B=18.77, and the part that have nominal FR =10-8 1/hr would
have FR = 10-6 1/hr and P(10) = 8.4%.
 At this conditions voltage derating to 0.5VR would reduce AF to
0.0067, decrease FR to 6.7×10-9 1/hr and P(10) to 5.6×10-4,
which is still larger than the required level.
 For such a capacitor derating down to 30%VR is necessary.
 Substantial errors of FR estimations refute the notion of WGTand the benefits of this test for the user.
 Excessive derating requires using capacitors with larger size andweight that makes them more susceptible to assembly failures.
 Without the knowledge of acceleration factors OEM cannot make adecision on how significant derating should be.
 The uncertainty in AF is compensated by a severe voltage derating.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

17

Conclusion
 IM failures in tantalum capacitors can be simulated using thethermo-chemical model of TDDB and Weibull distributions ofbreakdown voltages at BR<40.
 Incorrect AFs used for WGT can change FR up to 103 times.
 The values of AF can be obtained using HALT andapproximation of the test results with a general log-linear
relationship.
 Although step stress testing allows for a fast estimation of AF,
errors due to the uncertainty of time-to-failures might besubstantial.
 Voltage acceleration constant B for tantalum capacitors varies
for different part types in the range from 6 to 20.
 Substantial deviations of B from the “standard” value (B=18.77)
requires severe voltage derating.
To be presented by Alexander Teverovsky at the 2013 Institute of Electrical and Electronics Engineers (IEEE) Components, Packagingand Manufacturing Technology Society (CPMT) Workshop on Accelerated Stress Testing & Reliability Accelerating Reliability into the 21stCentury, October 9 - 11, 2013, San Diego, California, and published on nepp.nasa.gov.

18