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Accelerated Degradation Data Regarding
SiC MOSFETs for Lifetime and Remaining
Useful Life Assessment Thomas Santini, Airbus Group Innovations - TX4ES
October 22, 2014
Summary
1. Context and Motivation
2. Degradation based reliability assessment
3. Prognostic of Remaining Useful Life
4. Conclusion and Perspectives
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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More Electric Aircraft
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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0
200
400
600
800
A320 A330 A340 A380
Embedded Electrical Power (KW)
1. Reduce Overall Weight
2. Improve Performance & Optimization
3. Improve Reliability & Maintainability
Motivation
1. Improve Power Density
2. Insure High Temperature Capability
3. Meet Reliability Requirements
Technological Challenges
Wide Band Gap Power Electronics
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Wide Band Gap materials are good options for high voltage , high frequency and high
temperature power conversion
SiC MOSFETs are the most mature WGB transistors (available since 2011)
Suffer from Threshold Voltage Instability due to poor SiC/𝑆𝑖𝑂2 interface quality
How can we assess properly the reliability of
those devices ?
Accelerated Degradation Test Methodology
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration factor
models
Lifetime extrapolation
for nominal application
o ALT : The test at an accelerating condition continues until all or a
pre-specified number of units fail.
o ADT : Measurements of critical performance characteristics until a
pre-specified amount of time is reached (right censored data)
Acceleration Lifetime Vs Acceleration Degradation
o Lot of tests to be performed … small amount of time available
o Some Electronic failures could be described as « soft » failures
o Provide opportunities for Prognostic implementation
Why we consider ADT ?
Degradation Tests for VTH Instability Assessment
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
T \ Vgs 20 V 25 V 30 V
50 °C 7 10 10
80 °C 10 10 10
100 °C 10 10 9
High Temperature Gate Bias Test procedure:
Gate biased at a constant voltage
Drain and Source grounded
Regulated temperature (Oven)
Threshold voltage (Vth) measured on
regular basis by constant-current method
HTGB test setup
HTGB tests plan
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
• A non-homogeneous Gamma process could be consider to described
the Threshold Voltage instability
Degradation process
From the data we observe :
1. An increase of the threshold voltage over the course of the ageing test
2. A large variability of the degradation path in the same test conditions
Degradation Tests for VTH Instability Assessment
Stochastic process for Degradation Modelling (1/3)
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application Ageing Time
X
the degradations paths are Gamma distributed
fX t x v t , u =uv(𝑡) xv(t)−1 e−ux
Γ v(t), x ≥ 0
Time-dependent
shape parameter Scale parameter
t1 t2 t3
A Stochastic process (or Random process) is a collection of random
variables representing the evolution of a system over the time
Stochastic process for Degradation Modelling (2/3)
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
Ageing Time
X
How to estimate the degradation path ?
𝐿 = 𝑓 𝑣 𝑡 ,𝑢 (𝑥𝑗)
𝑛
𝑗=1
Maximum Likelihood Method :
Stochastic process for Degradation Modelling (3/3)
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
10
Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application Ageing Time
X
Degradation path estimation :
𝔼(𝑋 𝑡 =𝑣(𝑡)
𝑢
Time-To-Failure First Hitting Point
?
Failure Threshold Due to the gamma distributed deterioration,the lifetime distribution can then be written as:
𝐹 𝑡 = 𝑃𝑟 𝑇 ≤ 𝑡 = 𝑃𝑟 𝑋(𝑡) ≥ 𝐷𝑓 = 𝑓𝑋 𝑡 𝑥 𝑑𝑥∞
𝑥=𝐷𝑓
=Γ(𝛼 𝑡 , 𝐷𝑓𝑢)
Γ(𝛼 𝑡 )
With Γ(𝛼 𝑡 , 𝐷𝑓𝑢) is the incomplete gamma process for 𝛼 𝑡 ≥ 0 and 𝐷𝑓𝑢 > 0
Lifetime Distribution modelling
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
11
Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
How to estimate a Lifetime distribution from our degradation tests?
1. Assume a shape function 𝑣(𝑡) for the gamma process
Shape parameter function
𝑣 𝑡 = 𝑎 ∗ 𝑡𝑏
Degradation Tests for VTH Instability Assessment
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
12
Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
How to estimate a Lifetime distribution from our degradation tests?
2. Extrapolate of the degradation path
• Using the Maximum Likelihood Method we can estimate parameters 𝑎 , 𝑏 and 𝑢
• We can extrapolate the degradation path by : 𝔼 𝑋 𝑡 =𝑎 𝑡𝑏
𝑢
Failure Threshold
Estimated degradation
Confidence Interval
Degradation Tests for VTH Instability Assessment
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
13
Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
How to estimate a Lifetime distribution from our degradation tests?
3. Estimate the pseudo-Lifetime Distribution
T \ Vgs 20 V 25 V 30 V
50 °C 31000
0
7580
0 44000
80 °C 21000 4900 2900
100 °C 2200 1100 260
Use of the distribution Median (𝑡50%) for acceleration factors modeling
Degradation Tests for VTH Instability Assessment
Gate Voltage Acceleration Factor
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
Accelerated Failure Time Model
t50% 𝑧0 = 𝑡50% 𝑧1 ∗ 𝐴𝐹(𝑧0, 𝑧1)
𝑇𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑉𝑚𝑖𝑠𝑠𝑖𝑜𝑛
𝑇𝑠𝑡𝑟𝑒𝑠𝑠𝑉𝑠𝑡𝑟𝑒𝑠𝑠
𝐴𝐹 𝑧0, 𝑧1 = 𝐴𝐹 𝑇𝑚𝑖𝑠𝑠𝑖𝑜𝑛, 𝑇𝑠𝑡𝑟𝑒𝑠𝑠 ∗ 𝐴𝐹(𝑉𝑚𝑖𝑠𝑠𝑖𝑜𝑛, 𝑉𝑠𝑡𝑟𝑒𝑠𝑠)
Gate Voltage Acceleration Factor
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
15
Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
Inverse Power Law :
𝑡50% V =𝐾
𝑉𝛽
Voltage Acceleration Factor
AF V, Vu =𝑡50%(Vu)
𝑡50%(V)=V
Vu
β
With V and Vu respectively the Voltage during test and application
Tj [°c] 𝛽
50 4,8
80 4,9
100 5,2
Exxtracted Activation Energy for various
Gate Stress Conditions
Temperature Acceleration Factor
22 October 2014
Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
Arrhenius Law :
𝑡50% T = γ ∗ expEak ∗ T
Temperature Acceleration Factor
AF T, Tu =𝑡50%(T)
𝑡50%(Tu) = exp Ea
11605
Tu−11605
T
With T and Tu respectively the temperature during test and application
VGS[V] Ea (eV)
20 1,04
25 0,88
30 1,01
Exxtracted Activation Energy for various
Gate Stress Conditions
Mission Lifetime Assessment
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Accelerated
Ageing Test
Parameter shift
measurement
Degradation
modeling
Time-To-Failure
extrapolation
Lifetime distribution
modeling
Acceleration Factor models
Lifetime extrapolation for
nominal application
Median Time-To-failure assessment for continuous constraints Vm = 15V and
Tm = 125°C
𝛾=5 , EA=1 eV-1 and 𝑡50%(25V, 100°C) = 1100h
𝑡50%𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = 𝑡50%𝑠𝑡𝑟𝑒𝑠𝑠 ∗𝑉𝑠
𝑉𝑚
𝛽
∗ exp (𝐸𝐴𝑘∗1
𝑇𝑚−1
𝑇𝑠 )
𝑡50%𝒎𝒊𝒔𝒔𝒊𝒐𝒏 ~ 𝟐𝟕𝟎𝟎𝒉
1st generation of SiC MOSFET does not
match the aeronautic lifetime
requirements
Stochastic process for Reliability and Prognostic
• Degradation phenomenon models by a stochastic process
• Lifetime Distribution Function comes easily from degradation model
• Use of Acceleration Factors model makes it possible to assess reliability in
representative aeronautic application
• Stochastic process- based approach also suitable for Remaining Useful Life
Estimation
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Remaining Useful Life Estimation
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Stochastic approach shows good result in terms of
prognostic horizon and precision
RUL
Conclusion
• Accelerated Degradation test suitable for « soft » failures with irreversible
degradation process
• The use of a non-homogenous Gamma process has been proposed to model the
Threshold Voltage Instability phenomenon
• Accelerated tests valuable for reliability assessment and PHM application
• First step toward PHM implementation…
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Accelerated Degradation data of SiC MOSFETs for Lifetime and Remaining Useful Life Assessment
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Thank You For Your Attention !
Questions ?
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