Michael BenedekRF Components Reliability Lead
3-10-2009
Microwave DeviceReliability Characterization-The Mechanics of Life Test
Execution and Analysis
Copyright © 2009 Raytheon Company. All rights reserved.Customer Success Is Our Mission is a registered trademark of Raytheon Company.
Microwave Device Reliability Characterization-The Mechanics of Life Test Execution and AnalysisCo-Authors: Nicholas Brunelle*, Anna Hooven, Bradley Mikesell and Philip Phalon* Jr, Kurt Smith**
* Raytheon RF Components Reliability Team** Raytheon RF Components IR&D Team
Copyright © 2009 Raytheon Company. All rights reserved.Customer Success Is Our Mission is a registered trademark of Raytheon Company.
03/10/2009 Page 3
Perform All Due Diligence Testing to Establish and Maintain the MMIC Fab Process Reliability to ensure ‘NoDoubt’ Mission Assurance
Provide Reliability Expertise Within RFC, IDS and Company Wide
Anticipate Test Capability and Capacity Needs to Enable Nimble Response to Programs’ Needs
Search for New Paradigms in Testing and Reliability Benchmarks Industry Wide
Implement Lean Methods and Automation to Optimize Quantity and Enhance the Quality of Test Execution and Data Analysis
Reliability Lab Charter
03/10/2009 Page 4
Reliability Lab Test Capabilities
Life Testing: Process Reliability Monitoring DC Biased Temperature Accelerated Life Test RF Operational Life Test (S & X-Band) RF Temperature Accelerated Life Test (X-Band) Pulsed DC Electromigration (DC TALT) Current Density Testing (DC TALT)
Characterization: Capacitor Time Dependent Dielectric
Breakdown Testing LabVIEW Based Parametric Characterization Resistor TCR Characterization Light Emission Microscopy Liquid Crystal Failure Analysis
03/10/2009 Page 5
What Affects Reliability? Technical or lay, we all know that the reliability or
longevity of “things” is driven by stress
The list of life reducing stresses include: temperature, temperature cycling, humidity, voltage/electric field, current density, mechanical stress, thermo-mechanical stress cycling, radiation etc
The dominating stresses depend on the application environment.
Most of us would instinctively recognize Temperature as a common stress for many “things”.
Temperature is a common stress driver of reliability
03/10/2009 Page 6
The Focus of Today’s Presentation
Our “things” of interest are microwave devices made of compound semiconductor materials (GaAs, GaN etc)
Temperature and voltage/electric field are the important stresses in the application of microwave devices
In the space/defense environment many of the others are mitigated by the application environment.
This presentation will focus on temperature activated degradation. The reliability metrics from the statistical formalism will be introduced and the procedures to obtain them will be detailed
Main Theme: Thermally activated reliability metrics
03/10/2009 Page 7
Elements of the Statistical Formalism
The Lognormal Lifetime Distribution– Failures are distributed ‘normally’ when plotted on log time scale
The Cumulative Failure Fraction Plot– A linear plot can be taken as evidence for lognormal lifetime distribution
The Arrhenius Reaction Rate Model - t=to*eEa/kT
– The Arrhenius acceleration relationship is then
– ML1/ML2 = eEa/kT1/eEa/kT2
The Reliability Metrics from above are:– Median Life (ML) or MMTF– Sigma (σ) the dispersion – standard deviation of the log of lifetimes– Activation Energy
The Metrics: Median Life, Sigma and Activation Energy
03/10/2009 Page 8
The Lognormal Failures Distribution
Distribution is ‘normal’ when plotted on log time scale
Lognormal Failure Distribution
0.0
0.1
0.2
0.3
0.4
0.5
0.6
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]
Failu
re D
istri
butio
n [a
rbitr
ary]
0
20
40
60
80
100
120
Cum
ulat
ive
Failu
res
[%]
MedianLife
σ=1
15 yrMission
03/10/2009 Page 9
Trade Off Between ML and σ
To maintain ‘Same’ Reliability at lower ML, σ has to be smaller
Lognormal Failure Distribution
0.0
0.1
0.2
0.3
0.4
0.5
0.6
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]
Failu
re D
istr
ibut
ion
[arb
itrar
y]
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
Failu
re R
ate
[FIT
]
σ=0.5σ=1
Failure Rate in FITs through mission time is negligible
FIT is a failure unitAnd it is equivalent with 1 failure/109 hr
03/10/2009 Page 10
The Lognormal Failures Distribution
Note Margin Between Distribution Tail and Mission Time
Lognormal Failure Distribution
0.0
0.1
0.2
0.3
0.4
0.5
0.6
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]
Failu
re D
istri
butio
n [a
rbitr
ary]
0
20
40
60
80
100
120
Cum
ulat
ive
Failu
res
[%]
15 yrMission
MedianLife
.
03/10/2009 Page 11
The Cumulative Failure Fraction Plot
A linear plot is taken as evidence for lognormal lifetime distribution
Cumulative Failure Plot
TTF = 1031e0.516z
10
100
1000
10000
100000
-3 -2 -1 0 1 2 3Z Score
Tim
e-to
-Fai
lure
[hr]
991 20 305 10 50 70 80 90 95Q(z)
Note on the X scale both the Probability and Score scales are shown
The Plot is linearLn(TTF) = σ*z + Ln(ML)
The exponential curve fit in Excel returns the formTTF = ML* eσ*z
The extraction of ML and σ is direct
03/10/2009 Page 12
The Arrhenius Reaction Rate Model
The Ability to Thermally Accelerate Aging is Key to the Process
ML=C * eEa/kT
Or1000/T= A*ln(ML)+C
The Plot is a straight line using these scales
The logarithmic curve fit in Excel returns this form and from the slope A the Activation Energy
Ea=1000k/A=0.0862/A
k is Boltzman’s constant in eV*K-1
Arrhenius Plot
y = -0.0429Ln(x) - 1.3647
1.E+
0
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]
Tch
[°C
] (10
00/T
sca
le)
450400350
300
250
200
150
100
Ea [eV]
1.5
1.0
2.0
Missionconditions
Acceleratedconditions
03/10/2009 Page 13
Life Test Scope
FET Test Vehicles and -20% ΔId Failure Criterion
Life Tests at minimum 3 temperatures are required to establish a credible trend
Tch for the Life Tests is determined from self heating due to DC operating power dissipation and base plate temperature setting
Test Vehicles are 12 Schottky Gate Field Effect Transistors per temperature group
20% Decrease in Drain Current is the Failure Criterion
Drain Current is a key performance parameter and it is correlated with RF Power output capability
03/10/2009 Page 14
Life Test Data Analysis
Times to Failure are indicated by arrows on the Time Scale
Drain Current aging at Tch=329°C - Linear trend plot
Drain Current Aging Trend
-50-40-30-20-10
01020304050
0 500 1000 1500 2000Time [hr]
Del
ta Id
[%
]
1
2
3
4
5
6
7
8
9
10
11
12
Linear Plot
03/10/2009 Page 15
Life Test Data Analysis
Logarithmic trend plot is a better visual indicator of ML
Drain Current aging at Tch=329°C - Logarithmic trend plot
Drain Current Aging Trend
-50-40-30-20-10
01020304050
0.1 1 10 100 1000 10000Time [hr]
Del
ta Id
[%
]1
2
3
4
5
6
7
8
9
10
11
12
Logarithmic Plot
The Times-to-Failare tabulated andranked and usedin the next step
03/10/2009 Page 16
Life Test Data Analysis
The Id trend plot is reduced to the TTF and Z-score data array
The Time-to-Fail values are tabulated and ranked
For each failure the cumulative failed fraction, Q, is calculated using the median ranking formula: Q=(F-0.3)/(N+0.4) F is the number of failed parts; N is the number of parts in the test
Q is converted to the z score using NORMSINV function in ExcelF
cum # failuresQ [fraction]
(F-0.3)/(N+0.4)Z score TTF [hr]
sorted
1 0.05645 -1.58528 450
2 0.13710 -1.09346 570
3 0.21774 -0.77984 670
4 0.29839 -0.52904 700
5 0.37903 -0.30802 950
6 0.45968 -0.10125 1100
7 0.54032 0.101246 1174
8 0.62097 0.308024 1200
9 0.70161 0.529045 1200
10 0.78226 0.779842 1700
11 0.86290 1.093456 1900
12 0.94355 1.585278 2100
The resulting z-score and TTF data is plotted using the Cumulative Failure Fraction Plot
03/10/2009 Page 17
The Cumulative Failure Plot Provides ML and σ Directly
The exponential curve fit in Excel returns the formTTF = ML* eσ*z
The extraction of ML and σ is direct
ML=1031hrσ=0.52
The Cumulative Failure Plot: Tch=329°C
Cumulative Failure Plot
y = 1030.9e0.5156x
10
100
1000
10000
100000
-3 -2 -1 0 1 2 3Z Score
Tim
e-to
-Fai
lure
[hr]
991 20 305 10 50 70 80 90 95Q(z)
03/10/2009 Page 18
The Cumulative Failure Plot Provides ML and σ Directly
The extraction of ML and σ is direct for all 3 temperature groups
Cumulative Failure Plot
y = 364.7202e0.5676x
y = 1030.9456e0.5156xy = 4053.4e0.3487x
y = 0.1000e-0.0000x
10
100
1000
10000
100000
Q(z) [%]
Tim
e-to
-Fai
lure
[hr]
0.01 0.1 99 99.9 99.991 20 305 10 50 70 80 90 95
Failure Criterion = -20% Id
All 3 Cumulative Failure Plots
Tch[°C] ML[hr] σ345 365 0.57329 1031 0.52308 4053 0.35
Tch and ML are ready to be plotted on the Arrhenius coordinates
03/10/2009 Page 19
The Arrhenius Plot for the 3 Life Tests
The Arrhenius Plot Provides Ea Directly
Tch ML 1000/Tch[°C] [hr] [°K-1]
345 365 -1.618329 1031 -1.661308 4053 -1.721
Tch is converted to 1000/Tch in [°K-1] Note negative sign forces Temperature increase bottom to top
ML and 1000/Tch are plotted on the Arrhenius Coordinates Ea=0.0862/A Ea=2.01eV
Arrhenius Plot
y = -0.0429Ln(x) - 1.36471.
E+0
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]
Tch
[°C
] (10
00/T
sca
le)
450400350
300
250
200
150
100
Ea [eV]
1.5
1.0
2.0
Y = -A*Ln(x) - C
03/10/2009 Page 20
Reliability Metrics SummaryThe Reliability Metrics based on all 3 temperature groups used in this example are
Tch[°C] ML[hr] σ Ea[eV]
345 365 0.57329 1031 0.52 2.01308 4053 0.35
The 2.01eV Arrhenius Line Projects ML= 1.3E10 at a Mission Tch=150°CThe Conservative 1.5eV Arrhenius Line Projects ML= 2.1E8 at Tch=150°C
Extrapolate Time Unknown
Ea (eV) t1 [hr] T1 [°C] t2=?? [hr] T2 [°C]
2.01 4.05E+03 308 1.313E+10 150
1.50 1.03E+03 329 2.116E+08 150
Projections are based on the Arrhenius relationshipML1/ML2 = eEa/kT1/eEa/kT2
03/10/2009 Page 21
Reliability Metrics Summary
Normalized Failure Rate Plot is Used to Validate Our Extraction and Calculation Protocols
Normalized Failure Rate Plotsafter Goldthwaite (ref. 5)
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+09
1.E+10
1.E+11
1.E-
7
1.E-
6
1.E-
5
1.E-
4
1.E-
3
1.E-
2
1.E-
1
1.E+
0
1.E+
1
Time/MedianLife
Med
ianL
ife[h
r]*Fa
ilure
Rat
e [F
IT]
σ=3
σ=2
σ=1
03/10/2009 Page 22
The Equipment/Set Up
The Equipment Uses a Servo Feedback Loop Which Adjusts the Gate Voltage to Keep Constant Drain Current
03/10/2009 Page 23
The 2nd Key Stress in the application of microwave devices - Voltage/Electric field
RF Operational Life Tests Are Used to Mitigate High Field Effects Also Known as Hot Electron Effect
Stable Po during RF Life TestStable Po during RF Life Test
04R050, Pout and IddFirst 2 of the 8 devices are DSR
20
22
24
26
28
30
32
34
36
38
40
0 200 400 600 800 1000 1200
Hours
Pout
(dB
m)
Pout 1Pout 2Pout 3Pout 4Pout 5Pout 6Pout 7Pout 8Idd 1Idd 2Idd 3Idd 4Idd 5Idd 6Idd 7Idd 8
Blue Lines are Vd=5VRed Lines are Vd=6V
EquipmentFault
RF Life Test– Output Power Trend04R050, Pout and Idd
First 2 of the 8 devices are DSR
20
22
24
26
28
30
32
34
36
38
40
0 200 400 600 800 1000 1200
Hours
Pout
(dB
m)
Pout 1Pout 2Pout 3Pout 4Pout 5Pout 6Pout 7Pout 8Idd 1Idd 2Idd 3Idd 4Idd 5Idd 6Idd 7Idd 8
Blue Lines are Vd=5VRed Lines are Vd=6V
EquipmentFault
RF Life Test– Output Power TrendRF Life Test Equipment
03/10/2009 Page 24
References
1. F.H. Reynolds, “Thermally Accelerated Aging Of Semiconductor Components”, Proceedings of the IEEE, Volume 62, No2, Feb., 1974
2. D.S. Peck and C.H. Zierdt, Jr, “The Reliability of Semiconductor Devices in the Bell System”, Proceedings of the IEEE, Volume 62, No2, Feb., 1974
3. P.A. Tobias and D.C. Trindade, “Applied Reliability”, Van Nostrand Reinhold Company, Copyright 1986
4. W. B. Nelson, Accelerated Testing Statistical Models, Test Plans, and Data Analysis”, John Wiley & Sons, Inc, Copyright 1990, 2004
5. L. R. Goldthwaite, “Failure Rate Study for the Lognormal Lifetime Model”, Proceedings of the 7th Symposium on Reliability and Quality Control, 1961 p. 208-213
6. B.S. Hewitt and M. Benedek, “Decipher The Mystery of Reliability Statistics, MicroWaves, October, 1978