NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

STEP-STRESS ACCELERATED DEGRADATION TESTING 

(SSADT)

FOR PHOTOVOLTAIC (PV) DEVICES AND CELLS

2010 Workshop on Accelerated Stress Testing & Reliability (ASTR)

October 6-8, 2010

Denver, CO

Jinsuk Lee, Ryan Elmore, Changwon Suh and Wesley Jones

Computational Science Center

National Renewable Energy Laboratory

NREL/PR-2C00-49487

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308 

with the National Renewable Energy Laboratory.
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

 Introduction of SSADT

 What is SSADT?

 Why do we need SSADT?

 What can be estimated from SSADT?

 Reliability testing for PV

 Current reliability testing

 How to apply SSADT to PV area (e.g,. CIGS)

 Statistical process for SSADT

 Inference using the lifetime prediction model

 Discussion

Outline
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

 Develop a step-stress degradation testing (SSADT) for PV reliability 

tests

 Stage 1: construct a statistical model for SSADT - current

 Stage 2: apply to reliability testing for thin film PV

 Develop a lifetime prediction model for PV products (cell level, but 

expandable to module level) 

 estimate lifetime characteristics (mean time, warranty time, failure rate) and activation 

energies

 Explore the current performance tests for Cu(In,Ga)Se2, CIGS, device 

and cells; and provide physical and statistical models for their 

degradation

Objective
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

What is SSADT ? stress

time

SSALT

SSADT

stress

time

ALT

ADT

 Stress vs. Time plot

 3 chambers

 30 testing units

 1 chamber

 10 testing units
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

What is SSADT ?

 Degradation vs. Time plot degradation

time

.7

.5

.3

τ1 τ2 τ3

w1 w1 + (τ2 - τ1)

w2 w2 + (τ3 – τ2)

L(t | s0 =45 ̊C)

L(t | s0 =65 ̊C)

τ L(t | s0 =85 ̊C) 2 – τ1

Cumulative Exposure Model
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

 ALT may offer little help for highly reliable products which are not likely 

to fail during a rather short period of time

 ADT collects the degradation data at higher levels of stress and then 

uses these data to predict the product’s lifetime at a use-condition

Why do we need SSADT?

ALT ADT SSADT

ALT ADT SSADT

 SSADT is an economical and flexible test plan

- In particular, it is not easy to determine suitable test stress levels in ALT/ADT 

for new developing products where we don’t have knowledge of appropriate 

stress levels.
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

 Product lifetime parameters at various use-conditions

- Mean time to failure

- Reliability (Warranty) time

- Failure rate

 Degradation rate at various use-conditions

 Activation Energy (Ea)

 Upper limit level of stress (tolerable stress level)

What can be estimated from SSADT ?

Prediction of 

Mean time to failure 

& Failure rate

Prediction of 

Warranty time

22.31 yrs

5.12E-6
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

 Performance Testing for CIGS (CIGS, NREL, leaded by John Pern)

1. Damp Heat Test: 85°C/85%RH

2. Dry Heat Test: 85°C/4-10%RH

3. Pressure Cooker: 110°C/100%RH/~6psi

4. SSADT

 Measurement for Degradation (J-V measurement System)

 Open-circuit voltage (Voc)

 Short-circuit current (Isc)

 Fill factor (FF)

 Conversion efficiency of the device (η)

 Series resistance (Rs)

 Shunt resistance (Rsh)

Reliability Testing for Cu(In,Ga)Se2, 

CIGS-based Thin film PV
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Statistical Models

 Expected degradation for SSADT (by using CEM)



L(t) =

L(t | s1 ) if 0 ≤ t < τ 1

L(t + w1 −τ 1 | s2) if τ 1 ≤ t < τ 2

 M

L(t + wm−1 −τ m−1 | sm ) if τ m−1 ≤ t < τ m

 

 

  

 

 

 

 Degradation model over time

L(t | si) = L(0) ⋅ exp[−β i

t

α ], i = 1,2,L ,m

 Physical model for temperature and humidity (Generalized Eyring Model)

β i = a ⋅ exp − b

RHi

 

  

 

  ⋅ exp

Ea

k ⋅(273+Ti)

 

  

 

  * Arrhenius Model for Temperature

β i = exp a − Ea

k ⋅(273+Ti)

 

  

 

  

degradation

time

1

0

τ1 τ2 τ3

w1 w1 + (τ2 - τ1)

L(t | s1 )

L(t | s2)

L(t | s3 )
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Degradation of CIGS

1Dry heat: low-pressure air at 85°C

(encapsulated CIGS Modules)

2Damp heat: 85°C/85%RH

(CIGS Modules)

Normalized Efficiency (%)

Time (hr)

Increase 

Humidity

Decrease 

Temp.

1Data source: J. Wennerberg, “Design and Stability of Cu(In,Ga)Se2-Based Solar Cell Modules,” Dissertation, ACTA Universitatis Upsaliensis, 2002. 2 Data source: J. Wennerberg et al., “Cu(In,Ga)Se2-Based thin-film photovoltaic modules optimized for long-term performance,” Solar Energy Materials & Solar Cells, 75, 2003, pp47-55.

65°C/85%RH

65°C/50%RH

85°C/50%RH
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Example of SSADT Data

(LED lamps of fax machine (Tseng & Wen 2000))

Source: S.-T. Tseng and Z.-C. Wen, “Step-Stress Accelerated Degradation Analysis For Highly Reliable 

Products, Journal of Quality Technology, 32, 2000, pp209-216.

s1 s2 s3 s4 s5

Degradation

Time
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Overall Process of Statistical Analysis

Statistical Model

Estimate 

α ; βi (a, b, Ea)

Estimate 

Product’s lifetime; Ea;

degradation rate

Detect 

Upper limit condition

Least square estimation by minimizing

SSE(α,a,b) = ln(−lnL0 (t)) − ln(−lnH0 { (t))}

2

t

∑

Observed data

Given D= criteria for failure,

ˆ t f = − ln D / ˆ β ( 0 )

1/α ˆ 

Least square estimation by minimizing

 Estimate at each stress level

SSE(β 0 ,α(j),ω1 ,L ,ω j−1 ) = ln(− ln H0 (t)) − Α j −α(j) ln(ω j−1 + t −τ j−1 { [ )]}

2

t=tj−1

tj

∑

Detect the violation for the constant assumption 

with

α ˆ (i) −α ˆ ( j) < δ
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Example for detecting a upper limit of stress

ln(wj−1 + t −τ j−1)

ln(− ln H0 (t))

85°C/85%RH

110°C/85%RH

65°C/65%RH

55°C/65%RH

45°C/40%RH

α5=0.931*

α4=0.817+

α3=0.794*

α2=0.781*

α1=0.788*

 “α is independent of stress” is only valid for temperature less than or equal 85°C 

- The issue of “over-stress” can lead to misleading results



SSE(β 0,α(j),ω1 ,L ,ω j−1 ) = ln(− ln H0 (t)) − Α j −α(j) ln(ω j−1 + t −τ j−1 { [ )]}

2

t=tj−1

tj

∑

Note, + : estimated value from Wennerberg et al. (2003) 

* : assumed value
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

 Develop statistical models for a cutting-edge life-testing technique, SSADT, with 

temperature-humidity condition for PV reliability testing

- applicable to all PV reliability testing (including module levels and all PV technologies)

 Discuss the benefits of SSADT

 Consider other applicable degradation models (discussed by Nelson (1990)): 

e.g., some temperature-humidity models

 Study two main areas for SSADT: Statistical inference and Optimal planning

 Discuss about other statistical methods to build a SSADT model and analyze its 

data – e.g., LSE vs. MLE, Bayesian inference, generalized linear models, etc.

Discussion
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

 S.-T. Tseng and Z.-C. Wen, “Step-Stress Accelerated Degradation Analysis For Highly Reliable 

Products, Journal of Quality Technology, 32, 2000, pp209-216.

 J. Wennerberg et al, “Cu(In,Ga)Se2-Based thin-film photovoltaic modules optimized for long-term 

performance,” Solar Energy Materials & Solar Cells, 75, 2003, pp47-55.

 W. Nelson, Accelerated Testing – Statistical Models, Test Plans, and Data Analysis, Wiley & Sons, New 

York, 1990.

 J. Lee and R. Pan, “Bayesian inference model for step-stress accelerated life testing with type-II 

censoring, in Proc. The Annual Reliability and Maintainability Symposium, Las Vegas, NV, 2008.

 J. Lee and R. Pan, “Analyzing Step-Stress accelerated Life Testing Data Using Generalized Linear 

Models,” IIE Transactions, 42, 2010, pp589-598.

Key Reference