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7/23/2019 Effect of Thermal Stress and Short-wavelength Visible Radiation_2015
1/6
Effect of thermal stress and short-wavelength visible radiation
on phosphor-embedded LED encapsulant degradation
Prathika Appaiah, Nadarajah Narendran , Indika U. Perera, Yiting Zhu, Yi-wei Liu
Lighting Research Center, Rensselaer Polytechnic Institute, Troy, NY, USA
a r t i c l e i n f o
Article history:
Received 25 November 2014
Received in revised form 9 March 2015
Accepted 10 March 2015
Available online 11 April 2015
Keywords:
Thermal degradation
Encapsulant
Short-wavelength radiation
White LED
Degradation
Reliability
a b s t r a c t
This study evaluated the effects of short-wavelength radiation and thermal stress leading to thermal
degradation of an LED encapsulant, which contributes to reduced light output. The effect of light trans-
mission was measured in encapsulant samples with different YAG:Ce phosphor concentrations mixed in
epoxy, which were subjected to short-wavelength optical radiation and thermal stress. Encapsulant sam-
ples with increasing phosphor concentrations showed lower degradation rates of the encapsulant under
thermal stress, while under short-wavelength optical radiation the samples with phosphor showed
higher degradation rates.
2015 Elsevier B.V. All rights reserved.
1. Introduction
Light-emitting diodes (LEDs) are finding success in numerous
applications including displays, signage, communication, and gen-
eral lighting. LEDs have equaled or surpassed traditional lighting
technologies such as incandescent, halogen, and fluorescent with
respect to efficacy, lifetime, and color rendering. Other value pro-
positions of LEDs are form factor, energy efficiency, and ease of
maintenance, which make them suitable for a variety of applica-
tions at the fixture or luminaire level. Even though LED general
lighting products are expected to be reliable based on reported life-
time, many factors affect their lifetime and therefore their reliabil-
ity, one being the encapsulant of the LED.
White phosphor-converted (pc) LEDs are commonly produced
with the combination of emitted optical radiation from a gallium
nitride (GaN) semiconductor LED and a yttrium garnet (YAG:Ce)phosphor. The phosphor is embedded in an encapsulant and pro-
duces a broad spectrum light by down-converting a portion of
the LEDs emitted optical radiation. The LED encapsulant, typically
made of epoxy or silicone, serves as an optical medium surround-
ing the LED die and helps to increase the extraction of generated
photons. The encapsulant also isolates the LED die from structural,
mechanical, and chemical stresses from the outside environment.
The degradation of the encapsulant plays a vital role in determin-
ing the useful life and reliability of the LED. The phosphor-embed-ded encapsulant is subjected to short-wavelength radiation and
thermal energy from the LED chip and the phosphor, due to the
losses in the down-conversion process, which cause degradation
of the encapsulant material. This degradation results in a reduction
in light output from the LED.
The degradation of encapsulants used in blue LEDs under the
effects of increasing drive current and increasing temperature
has been studied extensively [1]. In past studies, low-power LED
packages with epoxy encapsulant failed based on light output
degradation due to thermal stress[1,2]. This reduction in light out-
put was due to the yellowing of the encapsulant of the LED package
[2,3]. Similarly, in 5 mm pc-LEDs studies showed a reduction in
light output with time due to a change in transmittance of the
epoxy when operated at manufacturer-rated drive currents[3].In blue LEDs, the degradation at lower temperatures was due to
short-wavelength optical radiation but at higher temperatures, the
degradation due to heat was more pronounced[1]. In comparison,
pc-LEDs were found to degrade faster than blue LEDs [5]. This
increased rate in degradation was concluded to be caused by the
presence of phosphors in the epoxy [4,5]. Degradation due to
thermal stress and short-wavelength optical radiation leads to a
discoloration of the encapsulant, leading to a reduction in the relia-
bility of the encapsulant of the LED.
YAG:Ce is the commonly used phosphor for pc-LEDs. Studies
have shown YAG:Ce phosphors are stable at temperatures greater
http://dx.doi.org/10.1016/j.optmat.2015.03.030
0925-3467/ 2015 Elsevier B.V. All rights reserved.
Corresponding author at: Lighting Research Center, 21 Union St., Troy, NY
12180, USA. Tel.: +1 518 687 7100.
E-mail address:[email protected](N. Narendran).
Optical Materials 46 (2015) 611
Contents lists available at ScienceDirect
Optical Materials
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / o p t m a t
http://dx.doi.org/10.1016/j.optmat.2015.03.030mailto:[email protected]://dx.doi.org/10.1016/j.optmat.2015.03.030http://www.sciencedirect.com/science/journal/09253467http://www.elsevier.com/locate/optmathttp://www.elsevier.com/locate/optmathttp://www.sciencedirect.com/science/journal/09253467http://dx.doi.org/10.1016/j.optmat.2015.03.030mailto:[email protected]://dx.doi.org/10.1016/j.optmat.2015.03.030http://crossmark.crossref.org/dialog/?doi=10.1016/j.optmat.2015.03.030&domain=pdf7/23/2019 Effect of Thermal Stress and Short-wavelength Visible Radiation_2015
2/6
than 100 C [6]. Therefore, the main cause of degradation in the
encapsulant is most likely due to the epoxy degradation. In 2013,
Meneghini et al. showed an increase in the temperature of remote
phosphor samples when the irradiance level on the encapsulant
was increased [7]. This degradation of the encapsulant worsens
with an increase in duration and amount of exposure to short-
wavelength radiation and thermal stress.
From previous studies, it is clear that externally applied thermalstress and short-wavelength optical radiation are key factors that
degrade the encapsulant of the LED, but there is no clear under-
standing of the mechanism of degradation. This present study
evaluated the degradation of the LED encapsulant medium under
thermal stress and short-wavelength optical radiation with and
without phosphor in the medium.
2. Experiment
An experiment was designed to understand the effect of short-
wavelength optical radiation and externally applied thermal stress
on LED encapsulant degradation. The study utilized two experi-
mental setups, one to subject the encapsulant sample to applied
thermal stress at a specific temperature by heating the ambientaround the sample, and another to irradiate the samples with
short-wavelength optical radiation from blue LEDs. A separate
measurement setup was used to test the effect of the experimental
conditions by measuring the light transmission. Each encapsulant
sample was made on a glass substrate with a small depression that
contained the encapsulant material. The epoxy encapsulant mate-
rial was mixed with and without commercially available YAG:Ce
phosphor used in general illumination applications and cured in
an oven as per the curing profiles specified by the epoxy manufac-
turer. The epoxy encapsulant used in the study was a commercially
available, optically clear, two-part epoxy. The phosphor concentra-
tions chosen for the experiment were 10 mg/cm2 and 20 mg/cm2.
The weight of the phosphor added to each sample was consistent
with the values given inTable 1.The experimental setup was designed such that the encapsulant
samples were subjected to short-wavelength optical radiation and
external thermal stress separately. The short-wavelength optical
radiation was produced by 4 4 chip on board blue LED arrays
under a single primary lens with a peak wavelength of450 nm.
Each blue LED array was characterized in an integrating sphere
to determine the radiant power and peak wavelength. The LEDs
were placed on a thermoelectric cooler to ensure the operating
temperature was maintained. Temperature measurements were
recorded with thermocouples, which were attached to the refer-
ence temperature measurement locations of the LED array mod-
ules as per the LED manufacturers specifications, and were
maintained at 40 C.
The irradiance on the encapsulant samples was varied bychanging the distance from the LED array module and by changing
the drive currents to the LED array module. The external thermal
stress on the encapsulant samples was created using a heating ele-
ment controlled by a thermal controller. The experimental setup is
shown inFig. 1.
The measurement setup consisted of two integrating spheres
[8] to measure the light transmitted and reflected when the
phosphor samples were irradiated with the test LEDs (peak wave-
length 450 nm). Measurements were taken after the encapsulant
samples were subjected to either externally applied thermal stress
or short-wavelength optical radiation in the experimental setup.
The transmission level of each sample was normalized to that of
a clear epoxy sample that was not treated under either experimen-
tal condition. The normalized light transmission data collected
over time were again normalized to the data of each respectivesample at the initial stage before being subjected to either experi-
mental condition.
3. Results
The measurements from the two integrating sphere system
were normalized to epoxy sample data obtained at the time before
the samples were subjected to experimental conditions. The curve-
fit of the total light, which is the summation of both transmitted
and reflected light, was used for analysis while paired t-tests were
used to determine statistical significance at the 95% confidence
level.
3.1. Effect of external thermal stress as a function of phosphorconcentration
Epoxy with no phosphor and epoxy mixed with phosphor sam-
ples were subjected to a fixed, externally applied thermal stress
inside the experimental setup (Fig. 1), which maintained an ambi-
ent temperature around the encapsulant samples at 90 2 C. The
temperatures of the encapsulant samples and the ambient air were
measured using thermocouples.
The measured light transmission values of the encapsulant
samples are illustrated inFig. 2. The light transmission data were
curve-fit using an exponential function with the form:
y a expbx
where y is the normalized light transmission and x is the time inhours, whilea and b are the curve-fit parameters. The exponential
coefficient b is identified as the degradation rate of the material.
Evaluation of the exponential coefficients indicates that reac-
tion rates were similar for the three encapsulant samples under
the applied thermal stress condition. One-tailed paired t-tests
revealed there was statistical significance at 95% confidence inter-
val between the light transmission degradation of the encapsulant
samples.
To understand encapsulant degradation and the transmission of
the pump (blue) and the converted (yellow) light, the spectral
power distribution (SPD) of each sample was separated into two
parts at the local minima of the SPD between the pump and the
converted. The portion of the SPD with the wavelength segment
Table 1
Phosphor and epoxy weight added in creating encapsulant samples.
Epoxy
(no phosphor)
10 mg/cm2
of phosphor
20 mg/cm2
of phosphor
Epoxy weight (mg) 25.0 25.0 25.0
Phosphor weight (mg) NA 15.6 31.1
Phosphor weight (%) 0 38.4 55.4 Fig. 1. Experimental setup showing samples subjected to heat and short-wave-length radiation.
P. Appaiah et al./ Optical Materials 46 (2015) 611 7
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below the local minima was used to calculate the blue transmis-
sion component while the longer wavelength segment was used
to calculate the yellow transmission component.The normalized blue light transmission degradation rate
reduced as the phosphor concentration increased, as illustrated
in Fig. 3. The normalized blue light transmission for phosphor
mixed in epoxy samples showed an increase in the initial measure-
ments. This observation was more profound in the 20 mg/cm2
phosphor encapsulant sample, as evident from the initial data
points in Fig. 3. The degradation rate was highest for the epoxy
(no phosphor) encapsulant sample followed by the epoxy mixed
with phosphor at 10 mg/cm2 encapsulant sample, while the high-
est phosphor concentration encapsulant sample (20 mg/cm2) had
the lowest degradation rate. In addition, one-tailed paired t-tests
revealed that the degradation rates were distinct at 95% confidence
level when the three samples were compared with one another in a
paired comparison.The normalized yellow light transmission is illustrated in Fig. 4
based on the total transmitted yellow light for the phosphor mixed
in epoxy encapsulant samples. The degradation rate for the higher
phosphor concentration encapsulant sample was lower compared
with the lower phosphor concentration encapsulant sample. A
one-tailed paired t-test revealed that the yellow light total
transmission degradation rates were statistically significant at
95% confidence level between the two encapsulant samples.
Figs. 3 and 4 indicate that the light transmission degradation
decreased as the phosphor concentration in the epoxy increased.
3.2. Effect of short-wavelength optical radiation as a function of
phosphor concentration
To understand the effect of optical irradiation on LED encapsu-
lant material, encapsulant samples having phosphor mixed with
epoxy at 10 mg/cm2 and 20 mg/cm2 concentrations were subjected
to a constant level of short-wavelength optical radiation at 0.28 W/
cm2.Fig. 5shows the light transmission degradation as the phos-
phor concentration was increased. An epoxy encapsulant sample
without phosphor was irradiated at the same optical radiation
level and is also illustrated in Fig. 5. The equation of the trend
for the phosphor sample is given by:
y a1 expb1x a2 expb2x
The degradation rate of the epoxy (no phosphor) encapsulant
sample was lower than that of the phosphor mixed in epoxy
encapsulant samples.
The results showed that an increase in phosphor concentration
led to increased encapsulant degradation under short-wavelength
optical radiation.
Fig. 2. Normalized total light transmission with time for encapsulant samples
subjected to externally applied thermal stress. The parameters (a,b) specify fitted
curves of the formy a expbx.
Fig. 3. Normalized total blue light transmission with time for encapsulant samples
subjected to externally applied thermal stress. The parameters (a,b) specify fittedcurves of the formy a expbx.
Fig. 4. Normalized total yellow light transmission with time for encapsulant
samples subjected to externally applied thermal stress. The parameters (a, b)
specify fitted curves of the form y a expbx.
Fig. 5. Normalized total light transmission with time for encapsulant samples
subjected to short-wavelength optical radiation. The parameters (a1; b1 ,) and (a2; b2)specify fitted curves of the form y a1 expb1x a2 expb2x.
8 P. Appaiah et al./ Optical Materials 46 (2015) 611
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3.3. Effect of varying externally applied thermal stress on a fixed
concentration of phosphor mixed in epoxy encapsulant
To investigate the effect of varying levels of externally applied
thermal stress on light transmission degradation, three encapsu-
lant samples were subjected to temperatures maintained at
73C, 76C and 89 C. The two encapsulant samples had phosphor
mixed in epoxy to a concentration of 20 mg/cm
2
. The normalizedlight transmission over time is illustrated inFig. 6.
The light transmission degradation of the encapsulant samples
increased as the externally applied thermal stress was increased.
3.4. Effect of varying short-wavelength optical radiation on a fixed
concentration of phosphor mixed in epoxy encapsulant
In order to understand the effect of short-wavelength optical
irradiance on encapsulant samples, two sets of samples with a
fixed concentration of phosphor mixed in epoxy at 10 mg/cm2
and 20 mg/cm2, respectively, were subjected to different short-
wavelength optical radiation levels. The irradiance values on the
encapsulant samples were 0.28, 0.50, and 0.57 W/cm2. The results
from the experiment are illustrated in Figs. 7 and 8.
The light transmission degradation increased as the short-
wavelength optical irradiance was increased. The 20 mg/cm2 phos-
phor concentration reiterated the light transmission degradation
trend that was observed with the 10 mg/cm2 phosphor concentra-
tion encapsulant samples.
4. Discussion
4.1. Effect of external thermal stress on phosphor embedded
encapsulant
The results for varying the phosphor concentration under exter-
nally applied thermal stress showed that the encapsulant samples
with phosphor had lower light transmission degradation compared
with the epoxy (no phosphor) encapsulant sample (Fig. 2). Since
YAG:Ce phosphor is thermally stable around 100 C, the cause of
degradation cannot be attributed to the quenching of the phosphor
[7]. Therefore, light transmission degradation is caused by epoxy
degradation under externally applied thermal stress. Past studies
have successfully shown that the addition of inorganic compounds
can reduce the degradation rate of epoxy [9,10]. These studies
found that the organic/inorganic hybrids were found to act as a
thermal insulator and a barrier to oxygen diffusion, therebymaking the composite more thermally stable.
An analysis of the blue and yellow portions of the total trans-
mitted light showed reduced light transmission degradation as
the phosphor concentration in the epoxy encapsulant was
increased (Figs. 3 and 4). The effect of encapsulant light transmis-
sion degradation due to short-wavelength optical radiation experi-
ments showed an increase in the rate of degradation as the
phosphor concentration was increased (Fig. 5). Past studies show
that pc-white LEDs (5 mm type) degrade faster than their blue
LED counterparts due to the presence of phosphor. One plausible
explanation is the increase in localized temperature of the epoxy
due to the heat generated in the phosphor particles during the
conversion of short-wavelength blue light into broadband white
light. This increase in heat is expected to increase with higherphosphor concentration in the epoxy encapsulant medium.
Fig. 6. Normalized total light transmission with time for encapsulant samples with
constant phosphor mixed with epoxy, subjected to varying levels of externally
applied thermal stress. The parameters (a, b) specify fitted curves of the formy a expbx.
Fig. 7. Normalized total light transmission with time for encapsulant samples with
phosphor mixed in epoxy at 10 mg/cm2, subjected to varying levels of short-
wavelength optical radiation. The parameters (a1; b1,) and (a2; b2) specify fitted
curves of the form y a1 expb1x a2 expb2x.
Fig. 8. Normalized total light transmission with time for encapsulant samples with
phosphor mixed in epoxy at 20 mg/cm2, subjected to varying levels of short-
wavelength optical radiation. The parameters (a1; b1,) and (a2; b2) specify fitted
curves of the form y a1 expb1x a2 expb2x.
P. Appaiah et al./ Optical Materials 46 (2015) 611 9
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Encapsulant samples with higher phosphor concentrations will
result in a higher phosphor operating temperature compared with
encapsulant samples with a lower phosphor concentration,
increasing the degradation and reducing lifetime.
The effect of increased thermal stress on phosphor samples
(20 mg/cm2 of phosphor mixed in epoxy) revealed an increase in
encapsulant degradation (Fig. 6). Thermal stressing of the encapsu-
lant material leads to an alteration in the molecules of the polymer.The increase in temperature of a reaction increases the rate of the
reaction and deteriorates the polymer. The minimum energy
required for the initiation of a reaction is known as activation
energy. The sensitivity of a reaction rate to temperature can be
determined using the Arrhenius equation. The rate of a first-order
chemical reaction is given by:
kpd A exp EakT
where kpd; is the rate constant, A is the constant related to the
probability of the reaction occurring at any given temperature, Eais the activation energy measured in eV, k is the Boltzmann con-
stant, and T is the absolute temperature. The activation energy of
the encapsulant samples with phosphor mixed in epoxy subjectedto externally applied thermal stress was evaluated using their total
light transmission results. The calculation of activation energy was
carried out by manipulating the reaction rate equation stated above
to read:
lnkpd Ea1
kT
lnA
Fig. 9shows the variation of lnkpd versus 1=kT while the gra-
dient of this linear relation gives the activation energy of the
degradation.
Calculated activation energy for phosphor mixed in epoxy
encapsulant samples from the present study and epoxy resin
activation energy from past research [11,12] are reported in
Table 2.The activation energy of the encapsulant material increased as
the phosphor concentration increased (Fig. 9 and Table 2). This
suggests that the addition of phosphor reduces the thermal degra-
dation of the epoxy encapsulant. Therefore, presuming that the
reduction of light transmission is caused by epoxy degradation,
since the amount of epoxy in each encapsulant sample was the
same and the thickness of all encapsulant samples was within
0.180.26 mm, the activation energy of the encapsulant samples
should have been the same. The increase in normalized light
transmission and activation energy as the phosphor concentration
was increased therefore can be attributed to the degrading epoxy
(i.e., yellowing of the encapsulant) preferentially transmitting
phosphor-converted yellow light rather than absorbing more of
the blue light emitting from the LEDs.
Under thermal stress, higher activation energy is required for
samples with greater phosphor concentration than for clear epoxy
samples. This shows that the addition of phosphor in the samples
improves the thermal stability of the epoxy/phosphor composite.
4.2. Effect of short wavelength radiation on phosphor embedded
encapsulant
The light transmission in encapsulant samples with phosphor
mixed in epoxy reduced faster as the irradiance levels were
increased. In addition, the increase in the phosphor concentration
in the encapsulant further decreased the light transmission. Past
studies have also observed an increase in temperature of the
encapsulant samples with mixed in phosphor when irradiated with
short-wavelength optical radiation[7]. To assess the temperature
of encapsulant samples when subjected to short-wavelength opti-
cal radiation, two identical encapsulant samples were prepared
with 10 mg/cm2 phosphor mixed in epoxy. These samples were
subjected to the same 0.57 W/cm2 irradiance with one sample
being used for light transmission measurements while the other
encapsulant sample was attached with a thermocouple to measure
the in-situ operating temperature of the encapsulant. The
thermocouple was shielded from optical radiation in a similar
manner to the thermocouple shielding method proposed in past
research[13]. Fig. 10 illustrates the normalized total light trans-
mission and the encapsulant temperature as a function of time.
During the first 100 h of the experiment, a slight reduction in
light transmission from unity at the start of the test to 0.88 at
100 h was observed. This corresponded with a slight increase in
encapsulant temperature from 93C at initiation to 100 C at
100 h. This increase in temperature was caused by the initial epoxy
Fig. 9. Reaction rate variation with temperature of encapsulant samples. Here, mrepresents the slope of the line.
Table 2
Activation energy comparison of encapsulant samples with phosphor mixed in epoxy
and reported data for epoxy resin.
Epoxy
(no phosphor)
10 mg/cm2
phosphor
in epoxy
20 mg/cm2
phosphor
in epoxy
Activation energy,
Ea (eV)
0.180.50
[11,12]
0.53 0.75
Fig. 10. Total light transmission and temperature with time for an encapsulant
sample with 10 mg/cm2 phosphor mixed in epoxy. Inset images show the yellowingof the encapsulant sample at 0, 150, and 200 h.
10 P. Appaiah et al./ Optical Materials 46 (2015) 611
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degradation resulting from the heat generated by the phosphor
during down-conversion of the short-wavelength radiation emit-
ted by the LED. The inset images inFig. 10show the yellowing of
the encapsulant sample. The initial reduction in light transmission
can be correlated to the slight yellowing of the encapsulant.
Approximately 150 h into the test, the temperature increased
rapidly along with a rapid reduction in light transmission. This
was caused by the epoxy absorbing nearly all the short-wavelengthoptical radiation emitted by the LED, contributing toward the heat
generation, which in turn increased the epoxy temperature. This
high temperature in epoxy caused further degradation, which
increased the absorption of optical radiation. The increase in
phosphor operating temperature reduced the phosphor down-
conversion efficiency, generating more heat and in turn degrading
the epoxy. These effects of heat generated in the down-conversion
process and yellowing epoxy led to rapid epoxy degradation, as the
inset images illustrate inFig. 10.
5. Conclusion
The present study was conducted to understand the LED encap-
sulant degradation caused by externally applied thermal stress and
short-wavelength optical radiation.
The thermal stress caused the encapsulant material to degrade
and at increased levels caused degradation rates to increase
further. The addition of phosphor as a whole did not change the
degradation rate of the encapsulant, as the main cause of degrada-
tion was due to epoxy yellowing and not due to phosphor degrada-
tion. The analysis conducted on the blue light emitted by the LEDs
and the phosphor-converted yellow light indicated that the
degraded epoxy acted as a blue light filter, which reduced the blue
light transmission compared with the yellow light. The activation
energy based on the degradation rates for the phosphor mixed in
epoxy samples revealed an increase in activation energy as the
phosphor concentration was increased in the encapsulant sample.
The reduction in degradation can be attributed to the blue light fil-
tering of the yellowing epoxy, as discussed.
The short-wavelength optical radiation degraded the encapsu-
lant samples and as the phosphor concentration was increased,
the degradation increased. Increases in the level of optical radia-
tion on the encapsulant samples further increased the degradation.
The degradation of encapsulant is related to the operating tem-
perature of the phosphor and as the phosphor temperature
increases, the conversion efficiency of the phosphor deteriorates
further, increasing the heat generated in the conversion process
leading to a temperature increase of the encapsulant, as discussed
earlier.
Curve-fitting seems to indicate there are at least two rate
reactions that govern the degradation of the encapsulant when
exposed to short-wavelength radiation, which is different from
the degradation rate when subjected to externally applied thermalstress at a similar encapsulant temperature. Further investigation
is necessary to obtain encapsulant temperature profiles/variations
as the encapsulant samples are exposed to short-wavelength radia-
tion to verify these observations.
Analysis of the data and the results revealed that the main cause
of the degradation is due to the degradation of the epoxy. The tem-
perature of the sample determines the degradation rate, indepen-
dent of how the temperature was increased, the ambient heat, or
short-wavelength radiation.
This experiment does have some limitations. The results from
this experiment are specific to the epoxy used in the study and
may not be generalized for all epoxies. The results might vary if
the epoxies have stabilizers that reduce the sensitivity of epoxy
to thermal stress or short-wavelength radiation. The epoxy
samples used for this study were bought from one manufacturer.
The results also are specific to the YAG:Ce phosphor used in this
study and might vary with different phosphors from differentmanufacturers. The results might vary when using phosphors that
are sensitive to heat. Additionally, it is common to mix a red phos-
phor into YAG:Ce to improve the color-rendering properties of the
white light [14]. In such cases, the encapsulant degradation rate
will be influenced more by the less efficient phosphor.
Role of the funding source
This research received no specific grant from any funding
agency in the public, commercial, or not-for-profit sectors.
Acknowledgments
We would like to thank Bridgelux and Cree for providing the
components for the experiments. We also thank the Lighting
Research Center staff, especially Martin Overington, Jean Paul
Freyssinier, Dr. John Bullough, and Andrew Bierman for their
valuable input. Jennifer Taylor is thanked for her invaluable
contribution towards preparing this manuscript.
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