This document discusses reliability prediction based on multiple accelerated life tests. It provides examples of analyzing field data to determine failure rates and extract acceleration factors for different failure mechanisms. The key points are that traditional reliability models do not properly account for multiple failure mechanisms, and a physics-based approach is needed to separate mechanisms and make accurate reliability predictions over different operating conditions.

1. May 9, 2016
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Reliability Prediction based on
Multiple Accelerated Life Tests
Prof. Joseph B. Bernstein
Faculty of Engineering
Ariel University
Josephbe@ariel.ac.il

2. May 9, 2016
2
Handbooks look to find MTBF
Suppliers need to report FIT; (l)
MTBF = 109/FIT
FIT = 109/MTBF

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3
Constant Rate Model Works !!!
If it ain’t broke, don’t fix it.

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Field Data Results
Example
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
0
2
4
6
8
10
12
14
16
18
20
Feb-03
Dec-03
Oct-04
Aug-05
Jun-06
Apr-07
Feb-08
Dec-08
CumulativeWorkingMonths
MonthlyFailedICs
CumulativeWorkingMonths
MonthlyFailed ICs
0.00%
0.02%
0.04%
0.06%
0.08%
0.10%
0.12%
0.14%
Feb-03
Dec-03
Oct-04
Aug-05
Jun-06
Apr-07
Feb-08
Dec-08
FailureRate[%]
MonthlyFailure Rate CumulativeFailure Rate
LOOK !?! Constant Rate
MTBF model works !
6-Sigma monitored failure
return for electronic system.
This is typical for most
observed electronic devices.

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MILITARY HANDBOOK 217
PREDICTION (part-count)
λp =λb πT πC πV πSR πQ πE
Where;
lp= part failure rate,
lb= base failure rate,
πT= temperature factor,
πC= capacitance factor,
πV= voltage stress factor,
πSR= series resistance factor,
πQ= quality factor,
πE= environment factor.
Values are assigned to the base failure rate and each
stress factor from tables in MIL-HDBK 217
One failure rate per part, but do factors multiply ?

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A B C D
Success =
RT(ABCD)
Success = Probability of Zero Failures
Reliability of each component is modeled as a
constant rate Poisson Process, l:
Ri = e-lit
So each factor adds to lT
RT = e-lA t ·e-lB t ·e-lC t ·e-lD t = e- lT t
Where: lT = lA + lB + lC + lD

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JEDEC Publication JEP 122G Rev. Oct. 2011
I Bet You didn’t know JEDEC says this:
2 Terms and definitions (cont’d)
quoted failure rate: The predicted failure rate for typical
operating conditions. (This is the FIT)
NOTE: The quoted failure rate is calculated from the observed
failure rate under accelerated stress conditions multiplied by an
accelerated factor; e.g…..
“ When multiple failure mechanisms and thus
multiple acceleration factors are involved, then
a proper summation technique, e.g., sum-of-
the-failure rates method, is required.”

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Proper Failure Rate Estimation
Serial System Reliability
Model
FM1 FM2
FM3
Nth Component
Each component is comprised of
several sub-components in
proportion to their function and
relative reliability stress.
lO = lO'·PO =(B1-OlHCI +B2-OlTDDB +B3-OlEM +B4-OlNBTI )·PO
lD = lD'·PD =(B1-DlHCI +B2-DlTDDB +B3-DlEM +B4-DlNBTI )·PD
lS = lS '·PS =(B1-SlHCI +B2-SlTDDB +B3-SlEM +B4-SlNBTI )·PS
lJ = lJ'·PJ =(B1-JlHCI +B2-JlTDDB +B3-JlEM +B4-JlNBTI )·PJ
Base Failure rate can be determined at
various accelerated conditions in order
to normalize the matrix and make
physics based reliability assessment
from test data combined with knowledge
of the application

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3.00E+08
4.00E+08
5.00E+08
6.00E+08
7.00E+08
8.00E+08
9.00E+08
1 1.5 2 2.5 3
Performance vs. Reliability
I could double the speed for free If I KNOW the
reliability, maybe I CAN improve performance !?!?
Why not operate here?
Here is Nominal
Freq.
(Hz)
(45 nm FPGA)

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“In G-d we trust; all others
must bring data.”

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Multiple Mechanisms Don’t Add Up !!!
Single Mechanism Model (traditional thinking):
–AFsystem = AFThermal* AFElectrical
–So, 1/MTTFuse = 1/(MTTFtest *AFMM)
Multiple Mechanism Model:
–1/MTTFuse = P1/(MTTFtest *AFmech1) + P2/(MTTFtest *AFmech2)
–Therefore, the effective AF for multiple mechanisms is:
AFMM =1
P1P2
AFmech1AFmech2
•The True acceleration factor is the SMALLER one, not the one
which exposes a failure at accelerated test.
+

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To Accelerate is
Human,
But, To
extrapolate
DIVINE

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Separation of Mechanisms - MTOL
Failure Mechanisms can be separated by
properly selecting test conditions.
This is in contrast to HTOL at One condition.
Multi-Temperature Overstress Lifetest
•High T, High F and Low Voltage tests EM
•High T, Low F and High Voltage tests NBTI
•Low T, High F and High Voltage tests HCI

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FPGA Ring-Oscillator Verification
•FPGA is built from
the basic CMOS
Cells in the listed
technology node
•Entire device is filled
with oscillators
•Continuous
measurements
eliminates recover !
•45nm and 28nm
2n + 1 stages
•150 oscillators of 3 stages
•50 oscillators of 5 stages
•20 oscillators of 33 stages
•3 oscillators of 333 stages
•1 oscillator of 1001 stages
•Incorporates Averaging
with number of stages

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y = 7.159E+08e-1.173E-03x
706000000
708000000
710000000
712000000
714000000
716000000
718000000
0 2 4 6 8 10 12
Ring Frequency versus square-root of time
Degradation Slope Considering
Physics
Slope(a) = DF/F0/Dsqrt(t)
TTF = 10%/Slope
FIT = 109/TTF
FIT = 109 x (10a)2
Square-root of time (hrs)
Frequency (Hz)
a

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28nm Ring Oscillator Frequency
Distribution
0.00E+00
2.00E-02
4.00E-02
6.00E-02
8.00E-02
1.00E-01
1.20E-01
1.40E-01
1.60E-01
1.80E-01
2.00E-01
5000000 50000000 500000000
Weibull Plot of
High Frequency
rings
b = 7.8
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
8.2 8.4 8.6 8.8
Weibull
Weibull Plot shows
Poisson distribution of
degradation within
the chip after less
than 100 hours of
degradation
Log (Freq)
b=1.4
-6
-5
-4
-3
-2
-1
0
1
2
0.001 0.01 0.1 1
Weibull

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Model Parameter Extraction
0.01
0.1
1
10
100
30 35 40 45 50 55
EA = 0.52 eV
-61
-60
-59
-58
-57
-56
-55
-54
-53
35 40 45 50 55
EA = -0.38 eV
FIT = V 23
0.000001
0.000100
0.010000
1.000000
100.000000
10000.000000
1 1.5 2 2.5 3 3.5
HCI Arrhenius
BTI Arrhenius
HCI Voltage factor
Through separation of
mechanisms, Activation
energies and voltage/current
acceleration factors are
determined at the chip level

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Simple to use Excel File
G(HCI)= 22.7 Ea(HCI)= -0.375
G(BTI)= 3.8 Ea(BTI)= 0.52
G(EM)= 3.8 Ea(EM)= 1.24
V(oper)= 1
T(oper)= 318
Kboltz= 0.00008617
Conditions
KT T°C V F(GHz) HCI BTI EM Measured Ratio Calculated FIT
Experimental
0.01818187 -62 1.2 1 56847640831 3.62741E-11 4.80938E-30 30 95% 2.86E+01
0.03429566 125 1.2 1 3516678.425 2.48596E-05 3.96698E-16 997.4 99% 9.88E+02
0.03670842 153 1.2 1 1713998.047 6.73446E-05 4.27115E-15 3672 100% 3.67E+03
0.02050846 -35 2.5 0.5 4.71349E+16 1.30044E-07 8.96311E-26 23750000 100% 2.38E+07
0.03679459 154 1.2 0 0 6.96163E-05 0 2420 100% 2.42E+03
0.04291266 225 2.8 1 8.82364E+13 0.228176427 1.41211E-11 11535700 107% 1.24E+07
0.03558821 140 2.2 0 0 0.001927405 0 66200 101% 6.70E+04
0.02162867 -22 2.8 1 4.78991E+17 1.51187E-06 6.31726E-24 240000000 101% 2.41E+08
0.02438611 10 3 1 3.22896E+17 4.90037E-05 5.36768E-21 156000000 104% 1.63E+08
INVERSE MATRIX P-values
-4.45217E-28 2.12157E-17 -3.96313E-20 5.03873E-10
0 0 14364.46052 34761994.46
2.34129E+14 -8513.801753 -2.26489E+14 3.11618E+17
Spreadsheet
shows 7-orders
of magnitude
agreement ±
5%
Constants
extrapolated from
experiments

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1
10
100
1000
10000
100000
1000000
10000000
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100110120130140150
FIT
Temp °C
1.4V at 2 GHz
1.2V at 1 GHz
1.2V at 10 MHz
FIT vs. Temperature for 45nm FPGA
Reliability Prediction !!!
3 Dominant Mechanisms throughout the useful range of
operating conditions
HCI
EMBTI

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0.0001
0.001
0.01
0.1
1
10
100
1000
10000
100000
-50 -30 -10 10 30 50 70 90 110 130 150
Prediction for 28nm
BTI
FIT
(1.0 V nominal)
1 V
0.8 V
1.2 V

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Observations
•What reliability prediction tool can
give you these results?
•No handbook can calculate the effects of
multiple mechanisms simultaneously.
•Reliability must fit the engineering goals !
•Physics Based Reliability
Qualification is Required