Download Optical simulation of phosphor layer of white LEDs

Vol. 34, No. 5
Journal of Semiconductors
May 2013
Optical simulation of phosphor layer of white LEDs
Liao Junyuan(廖骏源)Ž , Rao Haibo(饶海波), Wang Wei(王玮), Wan Xianlong(万贤龙),
Zhou Linsong(周琳淞), Zhou Da(周炟), Wang Xuemei(王雪梅), and Lei Qiaolin(雷巧林)
University of Electronic Science and Technology of China, Chengdu 610051, China
Abstract: A Matlab (2009a) program was developed to simulate the photons emitted by the LED chips. The
photons’ transmission, reflection, and refraction in phosphor layers with different shapes were calculated in this
program. The CCT was calculated at different emergent angles with different layer profiles, such as planar layer,
hemispherical layer (with different diameters), half ellipsoid layer and other irregular shapes. As a consequence
of optimization of angular color uniformity, the trend of configuration of the phosphor layer was discussed and
analyzed.
Key words: Monte Carlo method; white LED; CCT; YAG:Ce3C phosphor coating
DOI: 10.1088/1674-4926/34/5/053008
EEACC: 2520
1. Introduction
This paper mainly focuses on the correlative color temperature (CCT) distribution in different space areas while the
surface of the phosphor layer of a white LED was prepared in
different profiles.
As mentioned in literature before, when an LED is manufactured with the traditional dispensing technology, the CCT
at the center of the light spot is much higher than that at the
edgeŒ1 9 .
In the past 10 years, some methods were developed to
solve this problem, such as conformal coating and remote coating technologyŒ1 . These technologies have greatly decreased
the disparity of CCT over different parts of the light spot. However, those improvements were still not enough to raise the
white LED illumination industry to a higher level, which requires better color uniformity.
In this paper a Matlab program was developed to discuss
the influence of the phosphor coating profile on the color uniformity over the illuminated area.
Fig. 1. Emission spectrum of GaN chips.
2. Model
The model was simplified by using a photon-package to
simulate massive photonsŒ6 . The photon-package has got a
weight, which is the equivalent of light intensity. The weight
decreases while the package transmits, scatters, gets absorbed
or refract-reflects. The original weight satisfies the following
equation:
I D I0 cos ;
(1)
where is the angle between the direction vector of the original
photon-package and the normal vector of the surface of the chip
(0, 0, 1). I0 is the maximum relative light intensity. In most
situations I0 is set to 1Œ7 .
The emission spectrum of an LED chip (Fig. 1) was measured and was fitted by fixed Gauss equation. The wavelength
of the original photon package is randomly evaluated with the
rejection techniqueŒ8 , as shown in Fig. 2.
Fig. 2. Emission spectrum simulated.
The transmission of the photon-package is determined by
the scattering coefficient s and the absorption coefficient a .
The chance that the photon-package gets scattered or absorbed
while it travels the unit length equals to 1/(a C s /. So, by
calculating the inverse function, a random step length equation
† Corresponding author. Email: [email protected]
Received 27 November 2012
© 2013 Chinese Institute of Electronics
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Liao Junyuan et al.
Œ9
was developed :
lD
I n
;
a C s
(2)
where is a randomly-selected real number in [0, 1]. After the
photon has moved a step length, scattering and absorption occurs.
While the photon-package scattered, the direction vector
of the package changed. It is subjected to the Mie scattering
theory. The Mie theory was simplified by Henyey and Greenstein in the 1930s with H–G theory, the azimuth angle of the
direction vector change satisfies the following equationsŒ7 .
p.cos / D
1
2.1 C
g2
' D 2;
g2
;
2g cos /2=3
(3)
Fig. 3. The emission spectrum emitted by sample 1.
(4)
where g is anisotropy coefficient, g is a real number in [–1, 1],
and is a real number selected randomly in [0, 1].
8
(
2 )
ˆ
1 g2
1
ˆ
2
ˆ
1Cg
; g ¤ 0;
<
1 g C 2g
cos D 2g
ˆ
ˆ
:̂2 1; g D 0;
(5)
and ' can be derived from Eq. (5). The direction vector [ux ,
uy , uz ] satisfies the following equationsŒ7 :
8
sin ˆ
ˆ
.ux uz cos ' uy sin '/ C ux cos ;
u0x D p
ˆ
ˆ
ˆ
1 u2z
ˆ
ˆ
ˆ
<
sin uy0 D p
.uy uz cos ' C ux sin '/ C uy cos ;
ˆ
ˆ
ˆ
1 u2z
ˆ
ˆ
ˆ
ˆ
p
:̂ 0
uz D sin cos ' 1 u2z C uz cos :
(6)
When uz D 1Œ7 , then
8
ˆ
u0x D sin cos ';
ˆ
ˆ
<
(7)
uy0 D sin sin ';
ˆ
ˆ
:̂u0 D ˙ cos :
z
While the photon-package arrives at the border of the phosphor layer, the Fresnel theory is used to calculate the parameter
of the reflected and refracted photon package.
The photon reflected will be calculated as above, until the
weight of the photon package gets less than 0.01, and a Russian
Roulette would be applied. An integer X in [1, 100] would
be randomly defined and if it equals to an integer Y , which is
defined in advance (it can be 1, 2, 3, 4 or any integer between
1 and 100), the weight of this photon will multiply by 100,
and it will be calculated further. If X ¤ Y, the photon-package
dies. Then, a new photon-package will be randomly selected
and calculatedŒ8 .
3. Simulated results
The LED chip’s peak emission wave length is set to
465 nm, half wave width 30 nm. For YAG:Ce3C phosphor, the
Fig. 4. The CCT received by the screen.
Fig. 5. CCT in different emergent angles.
peak absorption wave length is set to 465 nm, peak emission
wavelength 565 nm, half emission width 75 nm.
Sample 1: Planar phosphor layer of thickness 1.5 mm, the
scattering coefficient is set to 10 cm 1 and the absorption coefficient 10 cm 1 . 5 105 packages were calculated.
The calculated emission spectrum of sample 1 is shown in
Fig. 3, and the CCT over a half global receiver screen with 20
cm radius is shown in Fig. 4. The CCT at different emergent
angles is shown in Fig. 5. Figures 6 and 7 show the emission
spectrum at specific emergent angles.
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Liao Junyuan et al.
Fig. 6. Emission spectra in different emergent angles.
Fig. 9. The CCT received by the screen.
Fig. 7. Emission spectra in different emergent angles.
Fig. 10. CCT in different emergent angles.
Fig. 8. The emission spectrum by sample 2.
Fig. 11. Emission spectra in different emergent angles.
It can be seen that while the phosphor layer is planar the
CCT at the center is much higher than that at the edge of the
layer.
Sample 2: Spherical phosphor layer, the position of the
center of the sphere is (0, 0, –18.45) mm, the radius of the
sphere is 20.05 mm; the scattering coefficient is set to 10 cm 1
and the absorption coefficient 10 cm 1 . 5 105 packages were
calculated.
The emission spectrum is shown in Fig. 8, and the CCT
over a half global receiver screen with 20 cm radius, is shown
in Fig. 9. The CCT at specified emergent angles is shown in
Fig. 10. Figures 11 and 12 show the light spectrum over different emergent angles.
It can be observed that as the thickness of the center layer
increases, the CCT of all the emergent angles decreases. The
CCT at the center of the chips decreases more rapidly than that
at the edge.
Sample 3: Spherical phosphor layer, center of the sphere
is (0, 0, –8.4) mm, the radius of the sphere is 10.1 mm, the
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Fig. 15. CCT in different emergent angles.
Fig. 12. Emission spectra in different emergent angles.
Fig. 13. The emission spectrum by sample 3.
Fig. 16. Emission spectra in different emergent angles.
Fig. 17. CCT in different emergent angles.
Fig. 14. The CCT received by the screen.
scattering coefficient: 10 cm 1 and the absorption coefficient:
10 cm 1 .
The emission spectrum is shown in Fig.13, and the CCT
shown by a half global receiver screen with 20 cm radius is
shown in Fig. 14. The CCT over different emergent angles is
shown in Fig. 15. Figure 16 shows the emission spectra in different emergent angles.
It can be observed that while the center layer keeps on getting thicker, the number of yellow light packages, which have a
wave length around 565 nm, increases smoothly. The average
CCT emitted keeps on decreasing. The CCT difference at the
center of the light slope decreases to around 5500 ıC. The decreasing amplitude of the CCT at the edge is obviously smaller.
Calculation with different scattering and absorption coefficients were performed.
Sample 4: Planar phosphor layer, with 1.5 mm thickness,
the scattering coefficient is set to 30 cm 1 and the absorption
coefficient 10 cm 1 . 5 104 packages were calculated. The
result is shown in Figs. 17 and 18.
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Liao Junyuan et al.
1
4
coefficient 30 cm . 5 10 packages were calculated. The
result is shown in Figs. 19 and 20.
It is obvious that, compared to sample 1, it can be concluded that while the absorption coefficient rises from 10 to
30 cm 1 almost all the blue photon packages are converted
into yellow ones and the number of yellow photon packages
increases rapidly. However with a drop to 3500 ıC the CCT in
different emergent angles gets better distributed.
4. Conclusions
(1) To get a well-distributed CCT between 4500–5500 ıC，
the phosphor layer with 10 to 20 cm 1 scattering and absorption coefficient should be prepared as thick as 1500 m, and
the thickness of the layer should get thicker smoothly from the
edge (1500 m) to the center of the layer (1700 m).
(2) The increase of thickness at the center of the phosphor
layer leads to a decrease of CCT at all emergent angles. The
decrease at the center is more obvious than that at the edge.
This makes the CCT more uniform.
(3) The deviations of scattering coefficient have little influence on the emission spectrum. However it affects the CCT’s
uniformity a lot. When its value increases the CCT distribution
becomes more uniform, but the light efficiency reduces.
(4) The change of absorption coefficient of phosphor coating can also affect the CCT in all emergent angles. When its
value increases all the CCT over the whole illuminated area
goes down, thus the CCT gets better distributed. However, this
results in a decrease of the illumination efficiency.
Fig. 18. The emission spectrum of sample 4.
Fig. 19. CCT in different emergent angles.
References
Fig. 20. The emission spectrum of sample 5.
It reveals that, compared to sample 1, the light spectrum
does not change much. The CCT in different emergent angles
gets better distributed. However as a result of the experiment,
when the scattering coefficient increases, the light efficiency
gets lower.
Sample 5: Planar phosphor layer, with 1.5 mm thickness,
the scattering coefficient is set to 10 cm 1 and the absorption
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