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Influence of defect reduction and strain relaxation on carrier dynamics inInGaN-based light-emitting diodes on cone-shaped patterned sapphiresubstratesKyu-Seung Lee, Isnaeni, Yang-Seok Yoo, Jae-Hoon Lee, Yong-Chun Kim et al. Citation: J. Appl. Phys. 113, 173512 (2013); doi: 10.1063/1.4803515 View online: http://dx.doi.org/10.1063/1.4803515 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v113/i17 Published by the AIP Publishing LLC. Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors
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Influence of defect reduction and strain relaxation on carrier dynamics inInGaN-based light-emitting diodes on cone-shaped patterned sapphiresubstrates
Kyu-Seung Lee,1,a) Isnaeni,1,a) Yang-Seok Yoo,1 Jae-Hoon Lee,2 Yong-Chun Kim,2
and Yong-Hoon Cho1,b)1Department of Physics, Graduate School of Nanoscience and Technology (WCU), and KI for theNanoCentury, KAIST, Daejeon 305-701, South Korea2Samsung LED Co. Ltd., Suwon 443-743, South Korea
(Received 7 January 2013; accepted 15 April 2013; published online 6 May 2013)
This study investigates optical properties and carrier dynamics of InGaN-based light-emitting
diodes grown on cone-shaped patterned sapphire (CSPS) and planar sapphire substrates. Edge-type
threading dislocations were dramatically reduced in InGaN multiple quantum wells (MQWs) on
CSPS substrates compared to the case of planar substrates. We observed a smaller Stokes shift and
enhanced quantum efficiency for CSPS substrates. From time-resolved optical analysis, we found
that the non-radiative (radiative) recombination rate of MQWs on CSPS is lower (higher) than that
of MQWs on planar substrates, which is consistent with improved crystal quality (strain relaxation)
of the MQWs on CSPS. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4803515]
I. INTRODUCTION
InGaN-based light emitting diodes (LEDs) have been
widely utilized in many applications such as automotive
headlights, backlight units in liquid crystal displays, and var-
ious types of bright lighting fixtures. In order to replace
conventional incandescent bulbs and fluorescent lamps,
quantum efficiency of LEDs must be further improved.
Many techniques have been developed for enhancing inter-
nal quantum efficiency (gint) and light extraction efficiencyof the InGaN-based LEDs, such as the epitaxial lateral over-
growth (ELOG),1 the selective wet etching of p-type GaN,2
the mesh electrode structure for p-GaN contact,3 the airprism embedded structures,4 and the nano-imprint lithogra-
phy.5 In particular, it is widely known that the use of pat-
terned sapphire substrate (PSS) can reduce the whole growth
and process time and increase the production yield.
Moreover, the PSS technique has attracted much attention
for enhancing not only light extraction efficiency by increas-
ing optical scattering due to the periodic hemisphere patterns
but also gint of LEDs by improving GaN template qualitydue to the ELOG-like growth mode.6,7 There have been sev-
eral reports on the improvement of electrical and structural
properties of GaN-thin films and LEDs grown on cone-
shaped patterned sapphire (CSPS) substrates, suggesting that
strain relaxation and improvement of crystal quality due to
patterned sapphire substrate.8,9 Although understanding the
emission mechanism and the role of the strain relaxation and
the defect reduction in the emission from LEDs on CSPS are
very important, the detailed optical properties and carrier
dynamics of InGaN/GaN LEDs grown on CSPS substrates
have not been fully clarified.
This study systematically investigates the optical prop-
erties and carrier dynamics of InGaN/GaN multi-quantum
wells (MQWs) grown on CSPS substrates and conventional
planar sapphire substrates by means of photoluminescence
(PL), cathodoluminescence (CL), PL excitation (PLE), time-
resolved PL (TRPL), high-resolution x-ray diffraction
(HRXRD), and transmission electron microscope (TEM)
techniques. We also fabricated InGaN based LED devices on
CSPS and planar sapphire substrates and measured the elec-
troluminescence, light output power, and external quantum
efficiency (EQE).
II. EXPERIMENTS
InGaN/GaN MQWs LED structures were simultane-
ously grown on CSPS substrates and planar sapphire sub-
strates by metal-organic chemical vapor deposition
(MOCVD). To prepare a CSPS substrate, photoresist was
first coated on a conventional planar sapphire substrate and
then the coated substrate was etched by inductively coupled
plasma reactive ion etching system. After that, processed
substrate was cleaned by piranha acid solutions.6 The diame-
ter, height, and interval of the cone-shaped patterns were 3,
1.5, and 1 lm, respectively. The CSPS and planar sapphiresubstrates was cleaned in H2 at 1020
�C, followed by thegrowth of a 25-nm thick low temperature GaN buffer layer
at 550 �C. After high temperature annealing of the bufferlayer, undoped GaN was grown on both substrates under a
V/III ratio of 1453 for 10 min based on the initial growth
step. After lateral overgrown step, the growth pressure was
changed from 100 to 350 Torr. Si doped n-GaN layers andInyGa1�yN current spreading layers were then grown at a
temperature of 1100 and 950 �C, respectively. Then, InGaN/GaN MQWs consisting of five pairs of undoped InxGa1�xN
wells and Si doped GaN barriers were grown on the n-GaNlayer. After that, a Mg doped p-AlGaN electron blockinglayer (EBL) was grown on the MQWs. LEDs with a size of
650� 200 lm2 were fabricated using a conventional mesastructure method. Indium tin oxide was used as a transparent
a)The first two authors contributed equally to this work.b)Electronic mail: [email protected]
0021-8979/2013/113(17)/173512/5/$30.00 VC 2013 AIP Publishing LLC113, 173512-1
JOURNAL OF APPLIED PHYSICS 113, 173512 (2013)
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conducting layer and Cr/Au was deposited as n- and p-typeelectrodes.
PL experiments were carried out using a continuous-
wave (cw) 325 nm He-Cd laser and a cw 405 nm laser diode,
and a photomultiplier tube was used as a detector. We also
performed PLE experiments using lamp excitation to mea-
sure the absorption edge. TRPL measurements were carried
out with a frequency-doubled, mode-locked Ti-sapphire laser
system at a repetition rate of 40 kHz, an excitation wave-
length of 405 nm (3.06 eV), and a power of 4 mW. The PL
decay curves were obtained by a streak camera system, and
the overall time resolution of the system is better than 20 ps.
To separate radiative and non-radiative lifetimes, we con-
ducted temperature-dependent PL and TRPL experiments
using a 405 nm-line excitation wavelength (below the
bandgap of GaN barriers) at an average power of 4 mW. In
addition, a Keithley electrometer was employed to measure
the current-voltage (I–V) performance of InGaN-based LEDson CSPS and planar sapphire substrates.
III. RESULTS AND DISCUSSION
Figures 1(a) and 1(b) shows CL panchromatic image
and optical transmission microscope image, respectively,
taken at the same area of the GaN template grown on CSPS.
Pt markers were deposited by focused ion beam to ensure the
same position of the flat-surface GaN template on CSPS, vis-
ualizing the correlation between the distribution of CL dark
spots and the exact position of cone-shaped patterns beneath
the flat surface. We found that dark spots (i.e., non-radiative
recombination centers) are mostly located in the area
between the cones due to lattice mismatch as well as in the
top of cone area owing to coalescence. The densities of the
dark spots observed in the CL images were found to be
9.3� 107 and 8.0� 108 cm�2 for GaN thin films grown onCSPS and planar sapphire substrates, respectively, as shown
in Figs. 1(a) and 1(c).8 Figs. 1(d) and 1(e) show the asym-
metric (105) reciprocal space mapping (RSM) for MQWs
grown on CSPS and planar substrates, respectively. All the
diffraction patterns in RSM are vertically well aligned,
wherein the strongest peak is due to GaN layer, and lower
(higher) angle shoulder of the GaN peak is due to the 0-th
order diffractions of InGaN MQWs (AlGaN EBL). This indi-
cates that the complete sample structure, which includes
AlGaN GaN EBL and InGaN MQWs, was fully strained
with the bottom GaN template layer for both samples.
Figures 2(a) and 2(b) show schematic of MQW on CSPS
substrate and the cross-sectional TEM image of MQW region
of InGaN MQW on CSPS substrate, respectively. From the
TEM image, we found that the threading dislocations are
mostly located on the flat region of the sapphire between the
cone-shaped patterns. Based on the CL [Fig. 1(a)] and TEM
[Fig. 2(b)] results, the following three regions can be catego-
rized: (i) a region with numerous dark spots, where vertical
dislocations are generated from the flat area between the
cone-shaped patterns, (ii) a region with almost no dark spots
FIG. 1. Panchromatic CL image of (a)
GaN on CSPS and (c) GaN on planar.
(b) Optical transmission microscope
image of GaN on CSPS including Pt
marker at the same position. [(d) and
(e)] asymmetric (105) x-ray RSMs of
InGaN MQWs grown on CSPS and pla-
nar sapphire substrates, respectively.
173512-2 Lee et al. J. Appl. Phys. 113, 173512 (2013)
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over the entire cone area, where dislocations generated near
the cone boundary bend over, and (iii) a region with localized
dark spots on the apex of the cone area, where coalescence
occurs from the cone boundary due to the lateral overgrowth
mode. Therefore, the lateral overgrowth mode induced by the
cone-shaped pattern causes the complicated pattern of dark
spots and the strain relaxation in the MQW on CSPS sub-
strates.6,8 We also measured symmetric (002) and asymmet-
ric (102) reflection XRD x-scan rocking curves for MQW onCSPS and planar substrates. The full width at half maximum
(FWHM) of the symmetry (002) x-scan curves for MQW onCSPS was found to be slightly reduced (244.08 arcsec) com-
pare to that of MQW on planar substrates (267.84 arcsec),
while that of the asymmetry (102) x-scan curves for MQWon CSPS was much smaller (246.96 arcsec) than that of
MQW on planar substrates (333.72 arcsec), respectively, as
shown in Figs. 2(c) and 2(d). It was reported that FWHM of
the x-ray x-scan curves on the symmetric (002) planes areinfluenced by screw- and mixed-type dislocations, whereas
the x-scan curves on the asymmetric (102) planes are sensi-tive to edge-type dislocation.10 From the FWHM of the x-ray
rocking curves, we also found a significant reduction of
edge-type dislocation density and a slight decrease of screw-
type dislocation density for MQWs on CSPS compared to the
case of MQWs on planar substrate.11 The dramatic reduction
of edge-type threading dislocations on CSPS substrate can
explained by lateral growth mode initiated from the reduced
flat c-plane area, since it has been observed that the initialgrowth starts from the flat c-plane sapphire area betweencones and then lateral overgrowth takes place to cover the
cone regions.6 Although a new type of defect may be formed
on the top of cone area due to coalescence, the total number
of defects would be significantly reduced. The reduction of
edge-type threading dislocations can be considered as the
improvement of the structural quality of InGaN MQWs on
CSPS substrates.
Figure 3 shows PL and PLE spectra of MQW on CSPS
and planar substrates measured at 10 K. We found that ener-
gies of the PL peak energy (EPL) of MQW on CSPS and pla-nar substrates are 2.767 and 2.792 eV, respectively. We use
sigmoidal formula of a¼ ao/{1þ exp[Eeff�E]/DE}, whereEeff is the effective bandgap and DE is the broadening pa-rameter to fit PLE spectra.12 Eeff was found to be 2.825 and2.859 eV for MQWs on CSPS and planar substrates, respec-
tively. Thus, we obtained the Stokes-like shifts (¼Eeff�EPL) of 58 and 67 meV for MQWs on CSPS and planarsubstrates, respectively, as shown Fig. 3. We have observed
three peaks (main peak and two phonon replica peaks) of
MQWs on both CSPS and planar samples to clarify Stokes-
like shift. We found that not only on the main peak, but
smaller Stokes-like shifts were also found at 2nd peak of
MQW (157 meV on CSPS and 202 meV on planar) and 3rd
peak of MQW (248 meV on CSPS and 278 meV on planar)
as shown in Figs. 3(a) and 3(b). The smaller Stokes-like shift
of InGaN MQWs grown on CSPS substrates indicates a
decrease in potential fluctuation and/or strain-induced piezo-
electric polarization due to reduction of dislocations and re-
sidual strain in MQWs on CSPS substrates. Despite reduced
residual strain in MQW on CSPS than planar substrates,6 PL
main peak appeared at slightly lower energy due to a little
higher In-content for MQW on CSPS.
We investigated temperature (T) dependence of gint andmeasured lifetime (sPL) to elucidate radiative lifetime (srad,)and non-radiative lifetime (snrad) as a function of T for bothsamples. sPL was determined when the intensity decreasesfrom maximum to 1/e of its value for simplicity due to the
nonexponential decay behavior of time evolution curves. We
can deduce srad(T) and snrad(T) from gint(T) and sPL(T) as afunction of T by using the well-known relationship gint(T)¼ sPL(T)/srad(T)¼ 1/{1þ[srad(T)/snrad(T)]}, where gint(T)with maximum integrated PL intensity at low T was assumedto be 100%. We used an excitation energy (�3.06 eV) below
FIG. 2. (a) Schematic of MQW on CSPS
substrate. (b) Cross-sectional TEM image
and magnified TEM image of MQW
region of InGaN MQW on CSPS sub-
strate. (c) Symmetric (002) and (d) asym-
metric (102) reflection XRD x-scanrocking curves measured both MQW on
CSPS and planar substrates.
173512-3 Lee et al. J. Appl. Phys. 113, 173512 (2013)
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the bandgap of GaN barriers to exclude the carrier diffusion
process from the GaN barriers.
Figure 4 shows the temperature dependence of sPL, srad,and snrad for InGaN MQWs on CSPS and planar sapphiresubstrates. We observed that sPL (gint) of MQW on CSPSsubstrate is smaller (larger) than that of MQW on planar sub-
strate over the temperature range we used. From the afore-
mentioned relationship between sPL and gint, srad and snradwere extracted out, and it was found that srad (snrad) ofMQWs on CSPS is shorter (longer) than that of MQWs on
planar substrates. In addition, we found that srad (snrad)becomes longer (shorter) as temperature increases for both
samples. Longer snrad (and hence a suppression of nonradia-tive recombination rate) can be attributed to the reduction of
dislocation density in MQWs on CSPS, and shorter srad (andhence an enhancement of radiative recombination rate) is
well consistent with the reduction of the strain-induced pie-
zoelectric field effect caused by smaller compressive strain
in InGaN well layers on CSPS. The latter can be supported
by our previous observations that GaN on planar substrates
involves compressive strain, whereas that on CSPS shows
strain relaxation.6,8 It is worth noting that the transition from
radiative to nonradiative recombination process occurs at
�140 and �285 K for MQW on planar and CSPS substrates,respectively, as indicated by circles in Figs. 4(a) and 4(b).
From the results, we conclude that both the reduction of
defects and the strain relaxation play an important role in
enhancing overall optical properties of InGaN well layers on
CSPS substrates.13,14
Figure 5 shows the EQE and output power for the
InGaN based LEDs on CSPS and planar sapphire substrates
as a function of the injection current. The total output power
of LEDs on planar substrates does not increase linearly with
increasing forward current. At forward-bias current of
FIG. 3. PL and PLE spectra obtained at 10 K for InGaN MQWs grown on
planar (a) and CSPS (b) substrates, respectively. The PLE absorption edges
of the InGaN MQWs grown on CSPS and planar substrates were found to be
2.825 and 2.859 eV, respectively.
FIG. 4. PL lifetime sPL, and radiative and nonradiative recombination life-times (srad and snrad) deduced from the temperature-dependent time-resolvedPL data and integrated PL intensity for InGaN MQWs on (a) planar and (b)
CSPS substrates. An excitation wavelength of 405 nm was used for both PL
and TRPL.
FIG. 5. EQE and output power of LEDs formed on CSPS (triangles) and pla-
nar sapphire (circles) substrates as a function of forward current.
173512-4 Lee et al. J. Appl. Phys. 113, 173512 (2013)
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20 mA, the EQE of LED on CSPS and planar substrates were
15.7% and 12.7%, respectively. We also found that the out-
put power of LEDs on CSPS (10.0 mW) is higher than that
of LEDs on planar substrates (8.0 mW) at forward-bias cur-
rent of 20 mA. Better extraction efficiency due to CSPS may
further contribute to the enhanced EQE of LEDs on CSPS.
Finally, we note that although overall optical properties and
EQE values of LEDs on CSPS were distinctly improved by
the use of CSPS, both LED samples encountered efficiency
droop at high current injection and the change in the degree
of efficiency droop was insignificant. Further detailed studies
are needed to clarify the responsible droop mechanisms
occurred in these samples.
IV. CONCLUSION
We have systematically investigated the optical proper-
ties and carrier dynamics of InGaN MQWs on CSPS and pla-
nar sapphire substrates. InGaN MQWs grown on CSPS
substrates showed a reduction of edge-type threading dislo-
cations, leading to improvement of the structural and optical
properties of the MQWs. We found that defect related
MQWs on CSPS substrates have a smaller Stokes-like shift.
From a time-integrated and time-resolved optical analysis
with temperature, we found that nonradiative (radiative) life-
times for MQWs on CSPS are longer (shorter) than those of
MQWs on planar substrates for all measured temperatures.
The LEDs with InGaN MQWs on CSPS showed higher EQE
and light output power compared to those on planar sub-
strates. These properties of InGaN MQW on CSPS substrate
have significantly increased the overall performance of
LEDs.
ACKNOWLEDGMENTS
This work was supported by WCU Program (No. R31-
2008-000-10071-0) of the Ministry of Education, the
Industrial Strategic Technology Development Program
(10041878) of the Ministry of Knowledge Economy (MKE),
KAIST EEWS Initiative, and the GRC project of KAIST
Institute for the NanoCentury.
1A. Sakai, H. Sunakawa, and A. Usui, Appl. Phys. Lett. 71, 2259 (1997).2S. I. Na, G. Y. Ha, D. S. Han, S. S. Kim, J. Y. Kim, J. H. Lim, D. J. Kim,
K. I. Min, and S. J. Park, IEEE Photon. Technol. Lett. 18, 1512 (2006).3M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K.
Deguchi, M. Sano, and T. Mukai, Jpn. J. Appl. Phys. 41, L1431 (2002).4E. H. Park, J. Jang, S. Gupta, I. Ferguson, C. H. Kim, S. K. Jeon, and J. S.
Park, Appl. Phys. Lett. 93, 191103 (2008).5H. W. Huang, C. H. Lin, C. C. Yu, B. D. Lee, C. H. Chiu, C. F. Lai, H. C.
Kuo, K. M. Leung, T. C. Lu, and S. C. Wang, Nanotechnology 19, 185301(2008).
6J. H. Lee, J. T. Oh, Y. C. Kim, and J.-H. Lee, IEEE Photon. Technol. Lett.
20, 1563 (2008).7K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato,
and T. Taguchi, Jpn. J. Appl. Phys. 40, L583 (2001).8K. S. Lee, H. S. Kwack, J. S. Hwang, T. M. Roh, Y. H. Cho, J. H. Lee,
Y. C. Kim, and C. S. Kim, J. Appl. Phys. 107, 103506 (2010).9J. H. Cho, H. S. Kim, J. W. Lee, S. H. Yoon, C. S. Sone, Y. J. Park, and
E. J. Yoon, Phys. Status Solidi C 2, 2874 (2005).10B. Heying, X. H. Wu, S. Keller, Y. Li, D. Kapolnek, B. P. Keller, S. P.
DenBaars, and J. S. Speck, Appl. Phys. Lett. 68, 643 (1996).11J. C. Zhang, D. G. Zhao, J. F. Wang, Y. T. Wang, J. Chen, J. P. Liu, and
H. Yang, J. Cryst. Growth 268, 24 (2004).12K. P. O’Donnell, R. W. Martin, and P. G. Middleton, Phys. Rev. Lett. 82,
237 (1999).13J. S. Hwang, A. Gokarna, J. K. Son, S. N. Lee, T. Sakong, H. S. Paek,
O. H. Nam, Y. Park, S. H. Park, and Y. H. Cho, J. Appl. Phys. 102,013508 (2007).
14A. Kaneta, M. Funato, and Y. Kawakami, Phys. Rev. B. 78, 125317 (2008).
173512-5 Lee et al. J. Appl. Phys. 113, 173512 (2013)
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http://dx.doi.org/10.1063/1.120044http://dx.doi.org/10.1109/LPT.2006.877562http://dx.doi.org/10.1143/JJAP.41.L1431http://dx.doi.org/10.1063/1.2998596http://dx.doi.org/10.1088/0957-4484/19/18/185301http://dx.doi.org/10.1109/LPT.2008.928844http://dx.doi.org/10.1143/JJAP.40.L583http://dx.doi.org/10.1063/1.3388014http://dx.doi.org/10.1002/pssc.200461337http://dx.doi.org/10.1063/1.116495http://dx.doi.org/10.1016/j.jcrysgro.2004.04.102http://dx.doi.org/10.1103/PhysRevLett.82.237http://dx.doi.org/10.1063/1.2749281http://dx.doi.org/10.1103/PhysRevB.78.125317