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

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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

• 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)

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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 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)

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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

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

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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

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

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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

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

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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

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

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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

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

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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

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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