The author analyzes the luminous efficiency of the phosphorconversion white lightemitting diode (LED) that consists of a blue LED chip and a yellow phosphor. A theoretical model is derived to find the relation between luminous efficiency (LE) of a white LED, wallplug efficiency (WPE) of a blue LED chip, and the phosphor absorption ratio of blue light. The presented model enables to obtain the theoretical limit of LE and the lower bound of WPE. When the efficiency model is applied to the measured results of a phosphorconversion white LED, the limit theoretical value of LE is obtained to be 261 lm/W. In addition, for LE of 88 lm/W at 350 mA, the lower bound of WPE in the blue LED chip is found to be ~34%. The phosphor absorption ratio of blue light was found to have an important role in optimizing the luminous efficiency and colorimetric properties of phosphorconversion white LEDs.
I. INTRODUCTION
Recently, solidstate lighting based on white lightemitting diodes (LEDs) has attracted great interest as a highenergyefficiency and environmentfriendly lighting technology
[1

4]
. Now, the luminous efficiency (LE) of white LEDs far exceeds that of incandescent and fluorescent lamps, which enables the white LEDs to be used in various lighting applications such as back lights in liquidcrystal displays, automobile lamps, and general illumination. By further increasing the luminous efficiency and lowering the production cost, the white LEDs are expected to widely replace current light bulbs in the near future.
Currently, most white LEDs are manufactured as a phosphorconversion type, which consists of a GaN/InGaNbased blue LED and a yellow phosphor excited by the blue LED. In this phosphorconversion white LED, part of blue light emitted from the blue LED chip is absorbed in the phosphor and converted into yellow light from the phosphor. The unabsorbed blue light is transmitted out of the phosphor. By properly mixing the yellow light of the phosphor and the transmitted blue light, white light with moderate chromaticity coordinates and correlated color temperature (CCT) can be produced. During the last several years, there has been rapid progress in the luminous efficiency of the phosphorconversion white LEDs. The luminous efficiency (LE) of commercially available white LEDs can be higher than 120 lm/W, and that of R&D LED samples has been reported to be as high as 180 lm/W
[5]
.
However, there has been lack of study on the theoretical analysis of LE in the phosphorconversion white LEDs. The analysis of LE in the phosphorconversion white LED is not so simple compared with that in the multichipbased white LEDs owing to the conversion processes in phosphors. Although the theoretical limit of LE in phosphorconversion white LEDs has been believed to be 260~300 lm/W
[5]
, theoretical models to obtain the limit theoretical value of LE have not been clearly presented. In this paper, we rigorously analyze LE of phosphorconversion white LEDs based on the photometric study of white light. The analytical model is used to find the theoretical limit of LE using the measured spectrum of the phosphorconversion white LED. It will be shown that the presented model can be used to obtain some information on the efficiency of the measured white LED such as the radiative conversion efficiency of the phosphor and the wallplug efficiency (WPE) of the blue LED chip used in the phosphorconversion white LED.
II. THEORY AND ANALYSIS
LE of an LED,
η_{lm}
is defined as the luminous flux of the LED divided by the electrical input power.
where
I
and
V
are current and voltage applied to the LED, and Φ
_{lm}
is the luminous flux. LE can also be written as below using WPE,
η_{WPE}
and output power of the LED chip,
P_{chip}
.
For phosphorconversion white LEDs, the luminous flux is express as
where
I
is the wavelength light and
V
(
λ
)is the eye sensitivity function.
V
(
λ
) is a dimensionless quantity which is normalized to 1 at 555 nm.
P_{b}
(
λ
)and
P_{y}
(
λ
) are the power spectral density of the blue and the yellow light, respectively, which can be obtained by the spectral measurement of the white LED. Then, output power of the blue light,
P_{b}
and the yellow light,
P_{y}
from the white LED is respectively given by
We denote
α
as the ratio of the absorbed power at the phosphor to the output power from the blue LED chip. Then, the absorbed power of blue light at the phosphor,
P_{abs}
and the transmitted output power of blue light,
P_{b}
are given by
Consequently, LE is written as
Eq. (6) relates LE of the phosphorconversion white LED with WPE of the blue LED chip inside the white LED. Since
η_{lm}
can be experimentally measured,
η_{WPE}
of the LED chip can be determined if
α
is known.
Here, we introduce a quantity,
R
which is defined as the ratio of the yellow light power to the blue light power.
By using Eq. (5),
R
can be expressed as
P_{abs}
can be written as
where
η_{phos}
(
λ
) is the efficiency of the phosphor which includes the conversion efficiency from blue to yellow light (Stokes shift efficiency) and radiative efficiency of the phosphor. Therefore, Eq. (8) is rewritten as
η_{phos}
(
λ
) can be regarded as the product of the radiative efficiency of a phosphor and the Stokes shift efficiency. That is,
where
is the radiative efficiency of a phosphor which is assumed to be independent of emission wavelength and
is the average wavelength of the blue light spectrum. Then,
R
is given by
Eq. (12) implies that
can be determined once
α
is known since
R
,
P_{y}
(
λ
), and
are obtained experimentally. However, in order to obtain
α
from Eq. (6),
η_{lm}
of the white LED and
η_{WPE}
of the blue LED should be determined simultaneously, which is not an easy task. Instead, when
is assumed to be 100%, the lowest limit of
α
can be obtained from Eq. (12). Then, the theoretical limit of
η_{lm}
is determined from Eq. (6) by using the obtained lowest limit value of
α
and
η_{WPE}
value of 100%. In this way, the limit theoretical value of LE can be obtained once the spectrum of a white LED is given. In addition, when
η_{lm}
of the white LED is measured, the lower bound of
η_{WPE}
of the blue LED chip can be obtained from Eq. (6).
The theoretical analysis of the LE in phosphorconversion white LEDs presented in this section will be applied to the experimentally measured results of a specific white LED in the following sections.
III. EXPERIMENT
Characteristics of a commercial phosphorconversion white LED sample were measured by using an LED characterization system with a calibrated integrating sphere. A packaged LED white sample was soldered on a metal printed circuit board (PCB) which was mounted on a heat sink. The temperature of the metal PCB was maintained at 25 ℃ by a temperature control system with a thermoelectric cooler. Then, electrooptical characteristics were measured by applying current and voltage to the LED.
Photometric properties of the white LED were measured under continuouswave operation up to 350 mA.
Fig. 1
shows the measured spectrum of the white LED when injection current is 350 mA. Typical spectral shape of the phosphorconversion
Spectrum of a commercial phosphorconversionwhite LED measured at 25 ℃.
Luminous flux and luminous efficiency of the whiteLED as injection current increases up to 350 mA.
white LED with a blue LED and a yellow phosphor is observed. In this sample, the peak wavelength of blue light from the InGaN LED chip and yellow light from the phosphor exist around 450 and 555 nm, respectively.
Figure 2
shows the luminous flux and LE of the LED as current increases. The luminous flux increases linearly with injection current and it reaches ~100 lm at 350 mA. The peak value of LE is ~122 lm/W at 30 mA. However, LE decreases gradually with increasing current when current is larger than 30 mA, and it is reduced to ~88 lm at 350 mA. This decrease in LE of the white LED results mainly from the “efficiency droop” phenomena of the blue LED chip
[6

8]
.
Colorimetric characteristics of the measured white LED were also evaluated based on the standard by Commission International de I’Eclairage (CIE). The chromaticity coordinates in the CIE
xy
chromaticity diagram were measured to be (0.33, 0.35) at 350 mA. And, the CCT and the general color rendering index of the LED were obtained to be 5400 K and 0.75, respectively.
IV. RESULTS AND DISCUSSION
The theoretical limit of LE of the measured phosphorconversion white LED is calculated from Eqs. (6) and (12) using the spectrum in
Fig. 1
. Assuming that the radiative efficiency of the phosphor,
is 100%, the lowest limit of
α
can be obtained from Eq. (12).
P_{b}
and
P_{y}
in Eq. (4) are calculated by integrating the spectral region of the blue and the yellow light, respectively. Then, the ratio of the yellow light power to the blue light power,
R
is found to be 2.51 from Eq. (7). Using the obtained values of
R
and
the ratio of phosphor absorption,
α
is calculated to be 0.762 from Eq. (12). Consequently, from Eq. (6), LE is obtained as
Therefore, the maximum LE of the measured white LED will be 261 lm/W assuming that both WPE of the blue LED chip and the radiative efficiency of the yellow phosphor are 100%. By using the measured LE of the white LED in
Fig. 2
, the lower limit of WPE of the blue LED chip can be deduced from Eq. (13). The peak value of LE at 30 mA was 122 lm/W, which corresponds to WPE of >46.8%. That is, the maximum WPE of the blue LED chip inside the measured white LED is higher than 46.8%. The LE at 350 mA was measured to be 88 lm/W, which corresponds to WPE of >33.7%. Accurate values of WPE can be obtained when the radiative efficiency of the phosphor,
is known. Conversely, if the WPE of the blue LED chip is known, the radiative efficiency of the phosphor could be determined.
Eq. (13) implies that the theoretical limit of LE in the measured phosphorconversion white LED is 261 lm/W. The theoretical maximum LE can be increased further by optimizing the spectrum of the white LED because LE is strongly influenced by the spectral distribution of emitted light. Eq. (3) implies that good overlap of the yellow light spectrum with the eye sensitivity function is important for increasing LE. In addition, relative output power of the blue and the yellow light also plays an important role in LE. In order to see the effect of the relative ratio of the blue and the yellow light, LE is calculated as a function
Theoretical limit of the luminous efficiency inphosphorconversion white LEDs as a function of the ratio ofphosphor absorption, α
(a) Chromaticity coordinates in the CIE xy diagram and(b) correlated color temperature in phosphorconversion whiteLEDs as a function of the ratio of phosphor absorption, α.
of the ratio of phosphor absorption,
α
. In this modeling, it is assumed that the blue LED chip and the phosphor are the same as those used in the white LED on which we experimented. So, the spectral distribution of the blue and the yellow light are not changed, and only the relative strength of peak intensity in the blue and the yellow light changes as
α
varies.
Figure 3
shows the theoretical limit of LE as a function of
α
. The maximum theoretical LE increases linearly from 214 to 300.4 lm/W as
α
increases from 0.6 to 0.9. Since the yellow light emitted from the phosphor shows much better overlap with the eye sensitivity function than the blue light, increasing the yellow light spectral intensity relative to that of blue light one is advantageous for increasing LE of the white LED. Therefore, higher LE is expected by increasing the phosphor absorption of the blue LED light.
However,
α
also changes the colorimetric properties of the white LED. For given a LED spectra, chromaticity coordinates and CCT are calculated based on the CIE colorimetric standard
[9

12]
.
Fig. 4
shows the chromaticity coordinates and the CCT as a function of
α
. As
α
increases, both
x
and
y
coordinates in the CIE
xy
chromaticity diagram increase and the CCT decreases. This is because the chromaticity coordinates shift toward the yellowish region of the chromaticity diagram as the yellow light spectral intensity increases relative to that of the blue light. As shown in
Fig. 3
, the theoretical limit of LE can be higher than 300 lm/W when
α
is 0.9. In this case, however, the chromaticity coordinates deviate from the Planckian locus too much, which may not be suitable for general lighting applications. Therefore, it is important to carefully optimize
α
considering both LE and color quality of the white light. In addition, by further optimizing the spectral distribution of the blue and the yellow light, even higher LE can be achieved with moderate color properties.
V. SUMMARY
The LE of the phosphorconversion white LED was analyzed based on the photometric study of white light. The investigated white LED consists of a GaNbased blue LED chip and a yellow phosphor. We developed a theoretical model describing the relation between LE of a white LED, WPE of a blue LED chip, and the ratio of phosphor absorption of blue light. When the model was applied to a commercial phosphorconversion white LED, the theoretical limit of LE was obtained to be 261 lm/W and the lower bound of WPE in the blue LED chip was found to be ~34% for LE of 88 lm/W at 350 mA. The theoretical model developed in this work is expected to be used advantageously for optimizing LE and color properties of phosphorconversion white LEDs.
Acknowledgements
This work was supported by the MKE(The Ministry ofKnowledge Economy), Korea, under the ITRC(InformationTechnology Research Center) support program supervisedby the NIPA(National IT Industry Promotion Agency)"(NIPA2012C109012000007) and by National ResearchFoundation of Korea Grant funded by the Korean Government(2012R1A1A2039630).
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