Simulation for light power distribution of 3D InGaN/GaN MQW LED with textured surface

Abstract

In this paper, we introduce a full 3D simulation for light power distribution of an InGaN/GaN MQW LED with a textured surface.
Device simulation was performed with the APSYS software to get power distribution of light sources inside the LED. Based on
this, ray tracing simulation was carried out to get light power distribution outside the LED. During the process of ray tracing,
the textured surface was treated as a special material interface whose reflectivity, transmittance and refraction angle are
obtained with a Finite-Difference Time-Domain (FDTD) method instead of using the usual Fresnel formulas for normal material
interfaces. By comparing the ray tracing results with and without the textured surface, we found that the textured surface
yields a smoother transmitted power distribution and greatly improved power extraction efficiency, which are comparable to
experiment. These effects may be further improved by optimizing the texture geometry.

KeywordsInGaN/GaN–Light-emitting diode (LED)–Light power distribution–Simulation–Textured surface

Full text

Opt Quant Electron (2011) 42:739–745
DOI 10.1007/s11082-011-9470-y
Simulation for light power distribution of 3D InGaN/GaN
MQW LED with textured surface
Li-Wen Cheng ·Yang Sheng ·Chang-Sheng Xia ·
Wei Lu ·Michel Lestrade ·Zhan-Ming Li
Received: 27 September 2010 / Accepted: 3 May 2011 / Published online: 15 May 2011
© Springer Science+Business Media, LLC. 2011
Abstract In this paper, we introduce a full 3D simulation for light power distribution of an
InGaN/GaN MQW LED with a textured surface. Device simulation was performed with the
APSYS software to get power distribution of light sources inside the LED. Based on this, ray
tracing simulation was carried out to get light power distribution outside the LED. During
the process of ray tracing, the textured surface was treated as a special material interface
whose reflectivity, transmittance and refraction angle are obtained with a Finite-Difference
Time-Domain (FDTD) method instead of using the usual Fresnel formulas for normal mate-
rial interfaces. By comparing the ray tracing results with and without the textured surface, we
found that the textured surface yields a smoother transmitted power distribution and greatly
improved power extraction efficiency, which are comparable to experiment. These effects
may be further improved by optimizing the texture geometry.
Keywords InGaN/GaN ·Light-emitting diode (LED) ·Light power distribution ·
Simulation ·Textured surface
1 Introduction
High-brightness light emitting diodes (LED) are an active field or research due to their
applications in many areas (Shur and Zukauskas 2005). Extraction efficiency and the output
L.-W. Cheng (B
)·W. Lu
National Lab for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences,
500 Yu Tian Road, Shanghai 200083, China
e-mail: lwcheng@crosslight.com.cn
Y. Sh e n g ·C.-S. Xia
Crosslight Software China, Suite 906, Building JieDi, 2790 Zhongshan Bei Road, Shanghai 200063,
China
M. Lestrade ·Z.-M. Li
Crosslight Software Inc., 121-3989 Henning Drive, Burnaby, BC V6C 6P7, Canada
123

740 L.-W. Cheng et al.
Fig. 1 3D LED with cross-shaped n contact.The N-type GaN surface is textured.
0.40 0.45 0.50 0.55 0.60
EL Intensity(a.u.)
Wavelength
µ
m
Fig. 2 Normalized electroluminescence (EL) spectrum. Peak is at 480 nm.
distribution of emitted light power are both crucial qualities that LED device developers are
trying to improve (Cheng et al. 2008).
Textured surface technique became popular in order to avoid the problem that external
quantum efficiency is limited by the total internal reflection of emitting light at interface
of semiconductor and air due to large difference of refractive index (Yang et al. 2005). To
form surface texture pattern, several techniques are applied, such as anisotropic photoelect-
rochemical etching process (Fujii et al. 2004), natural lithography (Yang et al. 2005). These
techniques make LED surface roughened in shape of trapezia (Han et al. 2006), pyramid
(Fujii et al. 2004) and V-shaped (Tsai et al. 2006), Surface roughness is critical and must be
controlled by about one-half wavelength according to (Yang et al. 2005). The dimension of
a single texture unit varies near LED peak wavelength (Windisch et al. 1999).
123

Simulation for light power distribution 741
Fig. 3 Schematic diagram of FDTD calculation.
It is important that details of light extraction for these devices be verified and understood
so that further improvement or optimization may be achieved. For computational-aided-
design(CAD) work, additional complications arise when a LED has a textured surface on a
scale similar to the emission wavelength. In that case, the wave nature of the light must be
considered and purely geometric approaches such as ray tracing are no longer sufficient.
In this paper, a full solution is proposed to simulate ray transmitting in LED device with a
textured surface. Firstly, 3D structure of a MQW LED with cross-shaped contact is built up
using CSUPREM. This software is a processing TCAD tool originally intended for silicon
devices (CSUPREM 2010) which has lately been extended to conveniently build and mesh
complicated 3D structures. Then, the APSYS software (APSYS 2010) performs 3D pho-
toelectric simulations on this LED to yield power distribution of the source light emitted
by MQW in this LED. This advanced software simultaneously solves the carrier transport,
Poisson and self-heating equations. Various mechanisms critical for LED analysis, such as
self-consistent quantum wells, spontaneous emission, non radiative recombination and injec-
tion current overflow have been included in the software.
In succession, a 3D ray-tracing (RT) module is applied to simulate how the source rays
escape the LED, and counts spatial power distribution of the escaped light. When rays travel
in a given medium, light power is gradually absorbed and Fresnel equation is calculated to
get power reflectivity and refractivity at material interface. It proves to be especially useful
for tracing ray paths (Sheng et al. 2007).
Due to the wave nature of light, the textured surface is treated as a special material interface
in 3D RT. Its reflectivity and refractivity are calculated not by the Fresnel equation, but by
interpolation from tabulated data extracted from finite-difference time-domain (FDTD) cal-
culation. FDTD is a popular modeling technique to simulate propagation of electromagnetic
wave. In this work, MEEP FDTD software (Meep 2010), (Oskooi et al. 2010) is applied.
To save computational runtime, a 2D cross-section through the textured surface is picked
up and texture unit shape is supposed to be uniform in the FDTD calculation. To get rela-
tionship between light incident angle and optical properties, a point source is put under the
textured surface in order to make different incident angle at different texture unit. By extract-
ing output of FDTD calculation at each texture unit, reflectivity and refractivity at different
incident angle are averaged and normalized for usage of 3D RT simulation.
123

742 L.-W. Cheng et al.
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
incident angle (radian)
incident angle (radian)
λ = 0.4 μm
λ = 0.5 μm
Transmission rate (T) (a. u.)
Reflection rate (R) (a. u.)
(a)
(b)
0.0 0.2 0.4 0.6 0.8 1.0
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
β
(radian)
λ = 0.4 μm
λ = 0.5 μm
Fig. 4 a T, R an d bβdependent on incident angle for the textured GaN surface at different wavelength
2 LED device structure
The structure of the InGaN/GaN MQW LED under study is shown schematically in Fig. 1,
the cross-shaped region shaded in dark blue is the top metal contact. This structure is designed
according to conventional LED structural configuration. The material plane (x-y plane) has a
size of 1000 ×1000 μm. The layer structure consists of 3.0 μm n-doped GaN whose surface
is textured, a five-period InGaN/GaN MQW, topped with a 0.25 μm p-doped GaN epi-layer.
The indium composition in the wells is 20 percent and the thickness is set to 3 nm in order
to produce a peak emission wavelength around 480nm (Fig. 2).
123

Simulation for light power distribution 743
0.0 0.5 1.0 1.5 2.0
Current (A)
simulation result
without textured surface
with textured surface
Power(a.u.)
0102030405060
without textured surface
with textured surface
Power(a.u.)
Current(mA)
experiment measurement
(a)(b)
Fig. 5 Transmitted light power versus current
Fig. 6 Transmitted light power distribution. awithout textured surface; bwith textured surface
123

744 L.-W. Cheng et al.
3 Results and discussions
Firstly, we carry out FDTD calculation for the texture which has a 2D profile and is formed
by a set of equilateral triangles, each of which has height of 0.5 μm and bottom edge length
of 1 μm.
Figure 3shows how the FDTD calculation for the texture is set up. A point source is put
at the corner so that incident angle is different at each textured unit which includes three
triangles. The reflection coefficient is calculated using the power flow through a place at the
bottom of the triangles. The transmission coefficient is defined in the same way using a plane
at the top.
By extracting data after FDTD calculation, reflection (R) and transmission (T) rate at dif-
ferent incident angles (π−α) are obtained. By averaging the transmitted optical energy, the
exit angle βfor each unit is also obtained. Since FDTD is based on time-dependent Maxwell’s
equations and its runtime increases approximately by 4 orders of magnitude when simulation
region size increases, after some tentative simulations, we finally applied 10 textured units
which are suitable for not only gathering enough data but also saving on simulation time.
Each set of FDTD calculation produces T, R and βvalues for the textured n-GaN surface
for a given source wavelength and angle of incidence. Data sets for 10 different wavelengths
ranging from 0.3 to 1.3 μm and for 10 values of αare tabulated and used for the 3D RT.
Runtime of FDTD calculation is less than half hours in Intel I7 920 platform with 8 CPU
threads at 2.66 GHz and 12 GB memory. Figure 4shows two of these data sets.
Finally, a batch of 3D ray-tracing simulation is applied for the 3D LED structure with
textured surface at different current bias(different light source profile). A similar batch sim-
ulation is also run except for that normal Fresnel rules are used at n-GaN surface. Simulation
results in Fig. 5a show that the textured surface increases the transmitted power about 2.35
times, which is accordant with the measurement results (Fujii et al. 2004)inFig.5b.
We also plot the angular dependence of the emitted power as a function of two spherical
coordinate variables phi and theta in Fig. 6. We can see that power is mainly transmitted
through the -z direction (theta =180o)where the n contact is located. Figure 6a indicates
that n contact has strong influence on power distribution if there is no textured surface while
Fig. 6b shows that textured surface strongly smoothes the in-plane angular dispersion of the
transmitted light power.
Through Fig. 4a, we can get that at wavelength of 480nm the LED emitted, peak rate of
power transmission is only about 0.7, which means that if we change geometry of the texture
unit, there is ample opportunity to improve the power transmission rate in the future.
4Conclusion
For the first time we have conducted a 3D simulation for light power distribution of a
InGaN/GaN MQW LED with textured surface. By comparing ray-tracing results with and
without textured surface, we observe notable improvements of the extraction efficiency and
power distribution. Simulation results are comparable to experimental measurements. In
future work, texture geometry may be optimized to get higher LED extraction efficiency.
123

Simulation for light power distribution 745
References
APSYS by Crosslight Software Inc., Crosslight device simulation software—general description. Burnaby,
Canada. (2010) http://www.crosslight.com.
Cheng, P., Li, D., Yuan, Z., Chen, P., Yang, D.R.: Enhancement of ZnO light emission via coupling with
localized surface plasmon of Ag island film. Appl. Phys. Lett. 92, 041119 (2008)
CSUPREM by Crosslight Software Inc., CSUPREM users manual. Burnaby, Canada. (2010) http://www.
crosslight.com.
Fujii, T., Gao, Y., Sharma, R., Hu, E.L., DenBaars, S.P., Nakamura, S.: Increase in the extraction efficiency of
GaN-based light-emitting diodes via surface roughening. Appl. Phys. Lett. 84(6) (2004)
Han, Dae-Seob., Kim, Ja-Yeon., Na, Seok-In., Kim, Sang-Hoon., Lee, Ki-Dong., Kim, Bongjin., Park, Seong-
Ju.: Improvement of light extraction efficiency of flip-chip light-emitting diode by texturing the bottom
side surface of sapphire substrate. IEEE. Photonics. Technol. Lett. 18(13), 1 July, (2006)
Meep software package developed at MIT. (2010) http://ab-initio.mit.edu/wiki/index.php/Meep.
Oskooi, A.F.,Roundy, David., Ibanescu, Mihai., Bermel, Peter., Joannopoulos, J.D., Johnson Steven, G.: Meep:
A flexible free-software package for electromagnetic simulations by the FDTD method. Comput. Phys.
Commun. 181, 687–702 (2010)
Sheng, Yang., Shmatov, Oleksiy., Simon Li, Z.M.: 3D simulation of InGaN/GaN micro-ring light-emitting
diodes. Opt. Quantum Electron. 39(7), 2007
Shur, M.S., Zukauskas, R.: Solid-state lighting: toward superior illumination. Proc. IEEE. 93(10),
1691–1703 (2005)
Tsai, C.M., Sheu J.K., Wang P.T., Lai W.C., Shei S.C., Chang S.J., Kuo C.H., Kuo C.W., Su Y.K.: High
efficiency and improved ESD characteristics of GaN-based LEDs with naturally textured surface grown
by MOCVD. IEEE. Photonics. Technol. Lett. 18(11),1 June, (2006)
Windisch, R., Heremans P., Knobloch A., Kiesel P., Dohler G.H., Dutta B., Borghs G.: Light-emitting diodes
with 31% external quantum efficiency by outcoupling of lateral waveguide modes. Appl. Phys. Lett.
74(16), 19 April (1999)
Windisch, R., Rooman C., Meinlschmidt S., Kiesel P., Zipperer D., Dohler G.H., Dutta B., Kuijk M., Borghs G.,
Heremans P.: Impact of texture-enhanced transmission on high-efficiency surface-textured light-emitting
diodes. Appl. Phys. Let. 79(15), 8 October (2001)
Yang, Chiao-Chih., Horng, Ray-Hua., Lee, Chia-En., Lin, Wen-Yu., Pan, Kuan-Fu., Su, Ying-Yong., Wuu,
Dong-Sing.: Improvement in extraction efficiency of GaN-based light-emitting diodes with textured
surface layer by natural lithography. Jpn. J. Appl. Phys. 44(4B), 2525–2527 (2005)
123