NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

On the Effect of Ramp Rate in 

Damage Accumulation of the 

CPV Die-Attach

Preprint

Nick S. Bosco, Timothy J. Silverman, 

and Sarah R. Kurtz

Presented at the 2012 IEEE Photovoltaic Specialists Conference

Austin, Texas

June 3–8, 2012

Conference Paper

NREL/CP-5200-54092

June 2012
NOTICE

The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC 

(Alliance), a contractor of the US Government under Contract No. DE-AC36-08GO28308. Accordingly, the US 

Government and Alliance retain a nonexclusive royalty-free license to publish or reproduce the published form of 

this contribution, or allow others to do so, for US Government purposes.

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, process, or service by trade name, 

trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors 

expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.

Available electronically at http://www.osti.gov/bridge

Available for a processing fee to U.S. Department of Energy

and its contractors, in paper, from:

U.S. Department of Energy

Office of Scientific and Technical Information

P.O. Box 62

Oak Ridge, TN 37831-0062

phone: 865.576.8401

fax: 865.576.5728

email: mailto:reports@adonis.osti.gov

Available for sale to the public, in paper, from:

U.S. Department of Commerce

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

phone: 800.553.6847

fax: 703.605.6900

email: orders@ntis.fedworld.gov

online ordering: http://www.ntis.gov/help/ordermethods.aspx

Cover Photos: (left to right) PIX 16416, PIX 17423, PIX 16560, PIX 17613, PIX 17436, PIX 17721

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
1

On The Effect of Ramp Rate in Damage Accumulation of the CPV 

Die-Attach

Nick S. Bosco, Timothy J. Silverman, and Sarah R. Kurtz

National Renewable Energy Laboratory, Golden, Colorado, 80401, USA

Abstract–It is commonly understood that thermal cycling at 

high temperature ramp rates may activate unrepresentative 

failure mechanisms. Increasing the temperature ramp rate 

of thermal cycling, however, could dramatically reduce the 

test time required to achieve an equivalent amount of 

thermal fatigue damage, thereby reducing overall test time. 

Therefore, the effect of temperature ramp rate on physical 

damage in the CPV die-attach is investigated. Finite 

Element Model (FEM) simulations of thermal fatigue and 

thermal cycling experiments are made to determine if the 

amount of damage calculated results in a corresponding 

amount of physical damage measured to the die-attach for a 

variety of fast temperature ramp rates. Preliminary 

experimental results are in good agreement with simulations 

and reinforce the potential of increasing temperature ramp 

rates. Characterization of the microstructure and resulting 

fatigue crack in the die-attach suggest a similar failure 

mechanism across all ramp rates tested.

Index Terms — Photovoltaic Cells, Soldering, Materials 

Reliability, Reliability Theory.

I. INTRODUCTION

Thermal fatigue in the CPV die-attach will result 

in cracking and ultimately lead to thermal runaway and 

cell failure [1]. Simulating the extent of thermal fatigue 

both in an accelerated test environment and in service 

conditions is therefore of primary importance to develop a 

lifetime prediction. Currently, the IEC 62108 

qualification thermal cycling sequence requires at least 28 

days to complete. Considering the efforts of the IEC QA 

Task Force to develop lifetime-related accelerated test 

procedures will likely seek to extend the thermal cycling 

sequence, developing a more damaging yet shorter test is 

of primary interest. Previous work demonstrated that the 

normalized test time (wall clock time required to 

complete a test that induces an equivalent amount of 

thermal fatigue damage) may be significantly reduced by 

increasing the temperature ramp rate of the cycle [2]. 

According to this work, just increasing the temperature 

ramp rate from 3.75 to 7.5 °C/min will halve the 

normalized test time, Fig. 1. This simple adjustment to 

the thermal cycling sequence could, therefore, be 

extremely valuable in moving forward with development 

of an economical lifetime-related thermal cycling 

sequence.

Fig. 1. FEM simulation results: normalized test time vs. cycle 

temperature ramp rate.

In development of such a sequence, its equivalence to 

outdoor exposure is paramount. In an analysis of one 

year of climatic data in Golden, Colorado it is found that 

while CPV cell temperature ramp rates up to 30 °C/min 

are experienced, over 95 % are under 6 °C/min, Figs. 2 

and 3. Since the current approach uses a FEM to 

calculate equivalent damage between the accelerated 

thermal cycle and outdoor exposure, it must be validated 

to work across a large regime of temperature ramp rates in 

order to be confidently applied in developing a highly 

accelerated thermal cycling test sequence.

Fig. 2. Cumulative Density Function of CPV cell temperature 

ramp rates experienced during one year in Golden, Colorado.
2

Fig. 3. Histogram of CPV cell temperature ramp rates 

experienced during one year in Golden, Colorado.

We have previously reported progress on developing a 

thermal fatigue model to simulate both service and 

accelerated testing conditions [3]. The model employed 

was developed to consider both the high- and low-stress 

regimes of creep (inelastic strain) where the physical 

mechanism changes from dislocation climb and glide to 

grain boundary sliding. The crux of the method is to 

calculate the amount of inelastic strain energy (damage) 

accumulated upon failure through accelerated thermal 

cycling and relate this to the amount of on-sun exposure 

that will accumulate a similar amount of damage. A key 

assumption is that the inelastic energy accumulated at the 

temperature ramp rates of accelerated testing results in a 

similar amount of physical damage as when accumulated 

at temperature ramp rates commensurate with service 

conditions.

In the current work, we repeat thermal cycling 

experiments to failure with four temperature ramp rates: 

7.5, 15, 60 and 140 °C/min. Each test is also simulated to 

calculate the amount of damage accumulated. The thermal 

cycling experiments will determine if the amount of 

damage calculated through simulation for the different 

ramp rates result in a corresponding amount of physical 

damage to the die-attach. The result of this work will 

provide confidence for moving forward to develop an 

efficient highly accelerated thermal cycling sequence for 

lifetime-related evaluations.

II. METHODS

A. Experimental

To conduct the thermal cycling tests, either a chamber 

that uses forward bias of the CPV cell for the heat source 

or a traditional oven style chamber is used [4]. The test 

articles are commercial CPV cell assemblies consisting of 

a 1 cm2 III-V multijunction solar cell soldered to a 

substrate with eutectic PbSn solder. For the current study, 

four temperature profiles are explored and are primarily 

distinguished by their unique temperature ramp rates. 

Profiles 1 and 2 are performed with forward bias heating

(blue curves) with temperature ramp rates of 140 and 

60 °C/min, respectively, with a maximum temperature of 

110 °C and minimum temperature of –40 °C and 

symmetric dwell times of 40 seconds, Fig. 4. These test 

are performed with only one sample each. Profile 3 is 

also conducted with forward bias heating for a ramp rate 

of 15 °C/min, a maximum and minimum temperature of 

110 and –40 °C and symmetric dwell times of five 

minutes, Fig. 5. Profile 4 is conducted in an oven style

chamber (red curve) and achieves a temperature ramp rate 

of 7.5 °C/min with a maximum temperature of 110°C and 

minimum temperature of –40 °C, Fig. 5. Profiles 3 and 4 

are conducted with 15 samples each.

Prior to and periodically through cycling, each sample 

is ultrasonically imaged to monitor crack growth in the 

die-attach layer. Cycling on all test articles is conducted 

at least until the defined failure criterion is achieved: a 

3.5 area% crack in the corner of the die-attach. Following 

failure, each sample is cross-sectioned and the limiting 

crack and die-attach microstructure imaged.

Fig. 4. Measured temperature profiles 1–2.

Fig. 5. Measured temperature profiles 3–4. Forward bias 

heating (blue) and conventional temperature chamber (red).

B. Modeling and Simulation

A 3D finite element model (FEM) of the CPV cell 

assembly used in this study was generated using 
3

COMSOL. The rate-dependent creep behavior and the 

time-independent plasticity of the solder is characterized 

by Anand’s model [5]. This constitutive model accounts 

for the two different creep mechanisms of Sn-containing 

solders: grain boundary sliding or dislocation glide (low 

stress and high temperature) and dislocation climb (high 

stress and low temperature).

An accumulated energy approach is taken to evaluate 

the solder’s lifetime. This approach considers the 

inelastic strain energy density as a damage indicator [6]. 

Accordingly, both crack initiation and growth are 

functions of the average inelastic strain energy density 

(plastic work) accumulated per thermal cycle. In the 

current study, the two phases of failure are not 

differentiated, therefore only the total plastic work is 

considered as the metric for damage. It is proposed that a 

typical cell assembly will fail after it has sustained a 

characteristic quantity of damage.

Each thermal cycle was simulated with the FEM model.

Due to the extremely fast temperature ramp rates, exact 

control of the assembly’s temperature is difficult. 

Therefore each assembly’s actual temperature measured 

through cycling serves as the input for each simulation.

III. RESULTS AND ANALYSIS

A. Thermal Cycling

The results of the thermal cycling experiments are 

summarized in Figs. 6 and 7. Crack area percent was 

measured relative to the complete cell area from CSAM 

images. Crack area emanating from multiple corners was 

not differentiated in the measurements and therefore is 

included in the total area calculation. Crack growth with 

number of cycles is presented in Fig. 6. Imposed on this 

plot is the defined failure criterion of a 3.5 area% crack. 

The number of cycles to failure was evaluated with a 

Weibull fit for the 7.5 and 15 °C/min data sets while a 

linear interpolation was employed for the 60 and 

140 °C/min rates since they each only contained a single 

sample. The number of cycles to failure are calculated to 

be 1210 and 690 for the 7.5 and 15 °C/min tests and 710 

and 610 for the 60 and 140 °C/min tests, respectively. 

The measurements are plotted in terms of test time in Fig. 

7. Here the expected trend is observed: the faster ramp 

rate tests reach the failure criteria faster than the slower 

ramp rate tests.

Fig. 6. Crack growth vs. number of cycles

Fig. 7. Crack growth vs. test time

B. Simulation

The results of the FEM simulation are summarized in 

Figs. 8 and 9. Reported first is the amount of inelastic 

strain energy accumulated for each cycle, normalized with 

respect to the most damaging cycle: the 15 °C/min ramp 

rate, Fig 8. The current results are consistent with 

previous simulations when the large difference in cycle 

times between the 7.5 and 15 °C/min, and 60 and 

140 °C/min profiles is considered, i.e. for similar cycle 

times, the faster ramp rate cycle is more damaging [2]. 

Also presented in Fig. 8 is the corresponding 

experimental observation of physical damage per cycle, 

similarly normalized to the 15 °C/min ramp rate cycle. 

This value is obtained by assuming even incremental 

crack growth is occurring every cycle until failure.
4

Fig. 8. Normalized inelastic strain energy (damage) per cycle 

for the four accelerated thermal cycles simulated.

The consequence of increasing the temperature ramp 

rate on overall test time is illustrated in Fig. 9. This plot 

is constructed by considering the amount of time each 

cycle requires achieving a similar amount of accumulated 

damage, and normalized with respect to the cycle that 

accumulates damage slowest. Simulations suggest that 

changing the ramp rate from 7.5 to 15 °C/min reduces test 

time by over 60 % and further reductions may be 

achieved with the very fast temperature ramp rates 

explored in this study: just over 5% of the time is required 

for the 140 °C/min profile to achieve a similar amount of 

thermal fatigue damage. Similarly imposed on the 

simulation results are the experimental observations 

related to crack growth: test time required to produce an 

equal sized crack.

A comparison of the simulated damage rate and the 

experimentally observed crack growth rate is presented in 

Fig. 10. A line of slope one that represents perfect 

agreement between simulation and experiment is also 

included on the plot. Points lying above the line suggest 

that crack growth is occurring faster than the simulation 

suggests, and points lying below suggest slower than 

expected crack growth. Considering the single point 

measurements for the two faster ramp rate cycles, it 

appears the experimental observations are in good

agreement with simulation.

Fig. 9. Resulting accumulated damage from simulated cycles 

presented in Fig. 4.

Fig. 10. Comparison of simulation and experiment.

To illustrate the significance of this work, the test time 

required to complete the current IEC 62108 thermal 

cycling sequence is considered, Table I. The energy 

accumulated during the defined test was first simulated

[7]. Next, the energy per cycle for two alternative tests 

was calculated through similar simulations. Reported are 

both the number of cycles required to achieve a similar 

amount of thermal fatigue damage as the defined test, and 

the actual time required to complete the tests. By 

increasing the temperature ramp rate from the highest IEC 

definition of 5 °C/min to 15 °C/min the time required to 

complete an equivalent test is reduced from 28 to 10 days.

TABLE I

EQUIVALENT TEST TIMES FOR INCREASING TEMPERATURE RAMP 

RATES OF THE IEC 62108 THERMAL CYCLING QUALIFICATION TEST

Option Ramp

(°C/min)

Cycles Time (days)

TCA-2 5 500 28

TCA-2* 7.5 530 22

TCA-2** 15 350 10

*,** cycle profiles adjusted only by changing temperature ramp 

rate.

C. Microscopy

Optical micrographs of the test articles cross sections’ 

are presented in Fig 11-14. Imaged in each micrograph is 

a section of the die-attach crack precipitated through 

thermal fatigue. Also apparent is the character of the 

lead-tin solder microstructure, composed of separate lead 

and tin rich phases. The path of the fatigue crack is 

consistent through all samples: in the solder near the cell 

interface.
5

Fig. 11. Optical micrograph of the 7.5°C/min sample 

illustrating the fatigue crack initiating at the edge of the cell.

Fig. 12. Optical micrograph of the 15°C/min sample 

illustrating the fatigue crack initiating at the edge of the cell.

Fig. 13. Optical micrograph of the 60°C/min sample 

illustrating the fatigue crack initiating at the edge of the cell.

Fig. 14. Optical micrograph of the 60°C/min sample 

illustrating the fatigue crack initiating at the edge of the cell.

IV. CONCLUSIONS

Preliminary simulations indicated that the rate of 

inelastic energy (damage) accumulation dramatically 

increases with increasing temperature ramp rates in 

accelerated thermal cycling. Thermal cycling experiments 

with temperature ramp rates up to 140°C/min were 

explored. The resulting experimentally measured crack 

growth was found to be consistent with FEM simulations. 

This agreement between simulation and experiment 

provides confidence for using this simulated energy 

approach to develop efficient thermal cycling test 

sequences. The prospect of this work is a significant 

decrease in overall accelerated test time to reach an 

equivalent amount of thermal fatigue damage.
6

ACKNOWLEDGEMENT

This work was supported by the U.S. Department of 

Energy under Contract No. DE-AC36-08-GO28308 with 

the National Renewable Energy Laboratory and by 

Amonix, Inc. through funding from the California Public 

Utilities Commission through the California Solar 

Research, Development, Demonstration and Deployment 

(CSI RD&D) Program.

REFERENCES

[1] N. Bosco, C. Sweet, T. Silverman, and S. Kurtz, "CPV 

Cell Infant Mortality Study," Presented at the 7th 

International Conference on Concentrating. 

Photovoltaic Systems (CPV-7), April 2011 2011.

[2] N. Bosco, T. Silverman, and S. Kurtz, 

"SIMULATION AND EXPERIMENT OF 

THERMAL FATIGUE IN THE CPV DIE ATTACH," 

in International Conference on Concentrating 

Photovoltaics (CPV-8), Toledo, SP, 2012.

[3] N. Bosco, T. Silverman, and S. Kurtz, "Modeling 

Thermal Fatigue in CPV Cell Assemblies," 

Photovoltaics, IEEE Journal of, vol. 1, pp. 242-247, 

2011.

[4] N. Bosco, C. Sweet, and S. Kurtz, "Reliability testing 

the die-attach of CPV cell assemblies," in 

Photovoltaic Specialists Conference (PVSC), 2009 

34th IEEE, 2009, pp. 000917-000922.

[5] G. Z. Wang, Z. N. Cheng, K. Beker, and J. Wilde, 

"Applying Anand Model to Represent the Viscoplastic 

Deformation Behavior of Solder Alloys," ASME 

Journal of Electronic Packaging, vol. 123, pp. 247-

253, 2001.

[6] R. Darveaux, "Effect of simulation methodology on 

solder joint crack growth correlation," in Electronic 

Components and Technology Conference, 2000. 2000 

Proceedings. 50th, 2000, pp. 1048-1058.

[7] T. J. Silverman, N. S. Bosco, and S. Kurtz, "Relative 

lifetime prediction for CPV die-attach layers," 

Proceedings of the 2012 IEEE International Reliablity 

Physics Symposium, 2012.