This work investigates the influence of residual stress on the performance of InGaN-based red light-emitting diodes (LEDs) by changing the thickness of the underlying n-GaN layers. The residual in-plane stress in the LED structure depends on the thickness of the underlying layer. Decreased residual in-plane stress resulting from the increased thickness of the underlying n-GaN layers improves the crystalline quality of the InGaN active region by allowing for a higher growth temperature. The electroluminescence intensity of the InGaN-based red LEDs is increased by a factor of 1.3 when the thickness of the underlying n-GaN layer is increased from 2 to 8 μm. Using 8-μm-thick underlying n-GaN layers, 633-nm-wavelength red LEDs are realized with a light-output power of 0.64 mW and an external quantum efficiency of 1.6% at 20 mA. The improved external quantum efficiency of the LEDs can be attributed to the lower residual in-plane stress in the underlying GaN layers.

Indium gallium nitride (InGaN) has been used to develop various optical devices with responses over the entire visible spectral range by adjusting the In content. The III-nitride material system can be used to fabricate red, green, and blue (RGB) light-emitting diodes (LEDs). Generating these three primary light colors using the same material system helps realize monolithic integration of micro-LED displays. III-nitride materials are also excellent candidates for phosphor-free white LED lighting with high efficiency and a high color rendering index. InGaN-based blue LEDs can achieve external quantum efficiencies (EQEs) above 80%.1 However, InGaN layers with a high In content suffer from some critical issues related to their low-temperature growth,2–4 a significant lattice mismatch,5,6 and the quantum-confined Stark effect (QCSE),7,8 and these issues must be overcome if high-performance InGaN-based LEDs are to be realized.

Several reports have demonstrated III-nitride-based LEDs in the yellow, orange, and red spectral range.9–19 Previously, we reported the development of InGaN-based deep-red (740 nm) LEDs grown on a c-plane sapphire substrate using a high-temperature InGaN growth technique.11,20 The high-temperature growth significantly improved the crystalline quality of the InGaN layers, demonstrating that the growth temperature is a critical factor affecting the quality of the grown InGaN layers. Rapid growth facilitates the use of higher growth temperatures.21 The use of strain-compensating structures in the quantum wells (QWs) is an important technique for developing high-In-content InGaN-based LEDs with high efficiency.13,21–23 For example, AlN and AlGaN barrier materials can provide tensile strain that compensates for the compressive strain in InGaN QWs. In addition, V-pits generated in the InGaN/GaN superlattice (SL) structure play a crucial role in releasing strain in the InGaN active region;18,24 such V-pits originate from threading dislocations. According to previous reports on InGaN growth on GaN layers, misfit dislocations are easily induced when an InGaN layer is grown on high-quality GaN layers with low dislocation densities.25,26 Therefore, the threading dislocation density is also an important factor for developing high-efficiency LEDs.

The in-plane lattice constant of the underlying layer is a critical factor that influences In incorporation into InGaN.16,19,27 Tuning the lattice constant is a good way to improve the quality of InGaN QWs by increasing the InGaN growth temperature. For instance, the substrate material partially determines the residual stress and lattice constants in the GaN layer; this is due to lattice mismatch between GaN and the substrate. It is well known that GaN layers grown on sapphire substrates are subject to compressive strain.28,29 By contrast, tensile stress is present in GaN layers grown on SiC and Si substrates.30,31 Tensile stress enhances the incorporation of In into InGaN via the pulling effect. Despite the aforementioned attributes, there have been no reports demonstrating high-efficiency red LEDs on Si. Given that sapphire substrates are typically used for producing blue and green LEDs, highly efficient red LEDs on sapphire substrates would enable the development of monolithic InGaN-based RGB LEDs.

In this study, we investigated the improvement of InGaN-based red LEDs by changing the in-plane residual stress of the underlying GaN layers on conventional c-plane patterned sapphire substrates. Introducing thick underlying GaN layers reduces the in-plane residual compressive stress,27–29 which in turn improved the InGaN QW quality. Our aim was to enhance the light-output power of the red LEDs on underlying GaN layers with lower in-plane stress.

The LED structures were grown via metalorganic vapor-phase epitaxy (MOVPE) in a single-wafer horizontal reactor.11,20 The precursors for Ga, Al, In, and N were trimethylgallium (TMGa), trimethylaluminum (TMAl), trimethylindium (TMIn), and ammonia (NH3), respectively. The precursors for n- and p-type doping were silane and bis-cyclopentadienyl magnesium, respectively. We used c-plane sapphire substrates with cone-shaped patterns that were 1.6 μm in height and 2.6 μm in diameter and had a spacing of 0.4 μm.

Figure 1 shows a cross-sectional schematic of the structure of the red LED examined in this work. The LED had a hybrid multiple-QW (MQW) structure that consisted of high-In-content InGaN double QWs (DQWs), a low-In-content single QW (SQW), and a strain-compensating barrier structure to enhance the light-output power.15,23 First, a 2-μm-thick unintentionally doped GaN layer was grown on a c-plane patterned sapphire substrate covered with a low-temperature GaN buffer layer.32 The n-side and active regions consisted of an n-GaN:Si (2–8 μm) layer, an n-Al0.03Ga0.97N:Si (1 μm) layer, 15 SLs of GaN (6 nm)/In0.08Ga0.92N (2 nm), an n-GaN:Si (15 nm), an In0.2Ga0.8N (2 nm) SQW with GaN (2 nm)/Al0.13Ga0.87N (18 nm)/GaN (3 nm) barrier layers, and InGaN (2.5 nm) DQWs as an active region with AlN interlayer (1.2 nm)/GaN (2 nm)/Al0.13Ga0.87N (18 nm)/GaN (3 nm) barrier layers. GaN was used to replace the Al0.13Ga0.87N part in the upper barrier of the second red QW. An additional GaN layer (15 nm) was grown in the active region. Finally, a p-GaN:Mg layer (100 nm) and a p+-GaN:Mg contact layer (10 nm) were grown. The threading dislocation density of all the underlying GaN layers was evaluated as ∼1.5 × 108 cm−2 via atomic force microscopy (AFM). The n-GaN layer growth rate was ∼2.4 μm/h. The n-Al0.03Ga0.97N layer was fabricated with a lower series resistance by high Si doping.33 The V/III and In/(In+Ga) vapor ratios were 18 800 and 0.67, respectively, during the InGaN red DQW growth. The red DQWs and AlN interlayers were grown at the same temperature. The GaN/Al0.13Ga0.87N/GaN barrier layers were grown at a temperature that was 125 °C higher than that used to grow the red DQWs. The AlN interlayers suppressed the decomposition of the high-In-content InGaN QWs during barrier layer growth at higher temperatures. These barrier layers also provide strain compensation to maintain the crystalline quality of the InGaN QWs.15,23 The LEDs were fabricated in a standard face-up configuration. The p-contact electrode consisted of a 90-nm-thick indium tin oxide (ITO) layer that was deposited via e-beam deposition. Mesa etching was carried out via inductively coupled plasma etching to expose the n-Al0.03Ga0.97N layer. Both the n-contact and p-pad electrodes consisted of Cr (50 nm)/Ni (20 nm)/Au (200 nm), which were deposited via e-beam deposition. The device area of each LED was 400 μm × 400 μm. The LED chips were bare without resin molding, and thus, there was no light-extraction enhancement because of molding.

FIG. 1.

Cross-sectional schematic of the structure of InGaN-based red LEDs.

FIG. 1.

Cross-sectional schematic of the structure of InGaN-based red LEDs.

Close modal

Before growing the LED structures, the in-plane residual stress in the as-grown underlying GaN layers was investigated via x-ray diffraction (XRD). The cross section and surface were observed by scanning transmission electron microscopy (STEM) and AFM, respectively. Then, we characterized the electroluminescence (EL) of the LED chips at their peak wavelength, the full width at half maximum (FWHM), and the output–current–voltage (LIV) characteristics at room temperature (RT).

XRD measurements were used to evaluate the in-plane residual compressive stresses in the underlying GaN layers. In general, the GaN lattice spacings along the a and c axes are altered by elastic strain. The in-plane biaxial stress can be calculated using

(1)
(2)

where εxx is the in-plane biaxial strain, each Cij is an elastic constant of GaN, σxx is the in-plane biaxial stress, and ce and cs are the strained and unstrained lattice constants of the c-parameter, respectively.34,35 The unstrained lattice constant cs was 0.51850 nm, and the elastic constants were C11 = 367 GPa, C12 = 135 GPa, C13 = 103 GPa, and C33 = 405 GPa.28,34 The in-plane biaxial stress is defined as positive for tensile stress and negative for compressive stress. The in-plane stresses of the n-GaN layers with thicknesses of 2, 4, 6, and 8 μm were −0.58, −0.54, −0.44, and −0.38 GPa, respectively. The in-plane residual compressive stress decreased with GaN thickness because the lattice constant of the thicker GaN should be closer to that of the freestanding crystal, which indicates relaxation.28 Therefore, the incorporation rate of In into InGaN can be enhanced by a lower in-plane residual compressive stress.27 

Figure 2(a) shows a cross-sectional STEM image of the area around the InGaN active region of an LED structure with an 8-μm-thick underlying n-GaN layer. Figure 2(b) shows a trench defect generated in the red DQWs, which was triggered by In segregation.36,37 These trench defects led to decreased internal quantum efficiency of the active region.23,36,37 Degradation of the InGaN active region severely affects the LED performance. The red InGaN QWs still required optimal growth conditions to suppress the generation of In-rich clusters. V-pits were also formed in the InGaN/GaN SLs in the LED structures, as shown in Fig. 2(c). The V-pits are helpful for carrier injection, screening dislocations, and enhancing radiative recombination.18,24,38 The InGaN/GaN SLs are effective for reducing the forward voltage by enhancing hole injection via the V-pits.18,24

FIG. 2.

Cross-sectional STEM images of (a) the InGaN active region above InGaN/GaN SLs, (b) a trench defect, and (c) a V-pit structure.

FIG. 2.

Cross-sectional STEM images of (a) the InGaN active region above InGaN/GaN SLs, (b) a trench defect, and (c) a V-pit structure.

Close modal

The surface defects were observed by AFM, and Fig. 3(a) shows a typical AFM image of the red LEDs with an 8-μm-thick n-GaN layer. The surface exhibited numerous defects, which comprised mainly trench defects on the red QWs as determined via the STEM results. We prepared red LEDs (λ = 635 ± 2 nm) with underlying n-GaN layer thicknesses in the range of 2–8 μm by adjusting the growth temperature of the red InGaN QWs. Because of enhanced In incorporation into InGaN with the increasing lattice constant of the underlying layer, we were able to increase the growth temperature of the red QWs by ∼5 °C upon increasing the underlying n-GaN layer thickness from 2 to 8 μm. The method is discussed in further detail below. Figure 3(b) shows that increasing the underlying GaN layer thickness reduced the defect density on the LED surfaces, which can be attributed to the increased InGaN growth temperature; this confirmed that the trench defects depended on the InGaN growth temperature. Therefore, we can conclude that a thick underlying n-GaN layer improves the crystalline quality of the LEDs; this is because of the higher possible InGaN growth temperature that is enabled by the reduced in-plane stress.

FIG. 3.

(a) AFM image of red LEDs on 8-μm-thick underlying n-GaN layers. (b) Dependence of surface defect densities on InGaN-based red LEDs as a function of underlying n-GaN layer thickness.

FIG. 3.

(a) AFM image of red LEDs on 8-μm-thick underlying n-GaN layers. (b) Dependence of surface defect densities on InGaN-based red LEDs as a function of underlying n-GaN layer thickness.

Close modal

We then characterized the EL of the red LEDs with different n-GaN layer thicknesses. Figure 4(a) shows that the EL peak emission wavelength red shifted as the residual in-plane stress in the underlying layers decreased, despite having the same MOVPE growth conditions. We reason that this phenomenon can be attributed to enhanced In incorporation in the InGaN QWs, which is based on the dependence of the in-plane lattice constant.16,27 We found that a thicker underlying GaN layer facilitated the growth of high-In-content InGaN-based LEDs. The emission peak wavelength shift corresponded to an increase of ∼5 °C in the growth temperature as the underlying n-GaN layer thickness was increased from 2 to 8 μm. Therefore, the use of a higher growth temperature for the InGaN QWs grown on thicker GaN layers is beneficial. Figure 4(b) shows the in-plane stress dependence of the EL intensity of the red LEDs. In these experiments, the EL peak wavelength of the LEDs was fixed at 635 ± 2 nm by adjusting the growth temperature. The InGaN-based red LEDs exhibited a 1.3-fold EL intensity enhancement because of a decrease in the in-plane stress of the underlying GaN layer. As a result, we found a relationship between the in-plane stress in the GaN layer and the EL intensity. We also reason that the lower in-plane compressive stress of the thick underlying GaN layer suppressed defect formation in the active region, which could be because of strain reduction in the red DQW region and the underlying layer.

FIG. 4.

(a) EL peak emission wavelength and (b) EL intensity as functions of in-plane stress in underlying n-GaN layers at 20-mA injection. There were four samples from each wafer. The dashed lines are visual guides for the average values.

FIG. 4.

(a) EL peak emission wavelength and (b) EL intensity as functions of in-plane stress in underlying n-GaN layers at 20-mA injection. There were four samples from each wafer. The dashed lines are visual guides for the average values.

Close modal

Figure 5(a) shows the EL spectrum of the red LEDs on the 8-μm-thick n-GaN layers. The peak emission wavelength and FWHM were 633 nm and 59 nm, respectively, with a direct current (DC) injection of 20 mA. The red emission spectra exhibited a narrow FWHM, which indicated high-purity illumination in the spectrum. However, we observed an additional emission peak at 475 nm. This could be attributed to the phase-separated component of the red InGaN QWs.9,13,23 Optimization of the growth conditions is needed for further improvement of the compositional fluctuation of In in the InGaN QWs. Figure 5(b) shows the current dependence of the EL peak wavelength and the FWHM. The emission peak wavelength indicated a large blueshift from 654 to 614 nm as the current injection varied from 5 to 100 mA. The large blueshift behavior is typical for InGaN-based LEDs grown along the polar axis and is caused by the QCSE.7,39 The FWHMs started to increase as the injection current exceeded 20 mA, which can be attributed to the heat generated in the QWs via nonradiative recombination.10 

FIG. 5.

(a) EL spectrum of InGaN-based red LEDs at 20 mA. (b) EL peak wavelength and FWHMs as functions of current injection. The inset shows the red LED at a 20-mA driving current.

FIG. 5.

(a) EL spectrum of InGaN-based red LEDs at 20 mA. (b) EL peak wavelength and FWHMs as functions of current injection. The inset shows the red LED at a 20-mA driving current.

Close modal

The light output and forward voltage properties are shown in Fig. 6. An integrating sphere was used to evaluate the L–I characteristics of the red LEDs under DC injection at RT. At 20 mA, the light-output power and forward voltage of the 633-nm red LED were 0.64 mW and 3.3 V, respectively. The EQE and wall-plug efficiency (WPE) were as high as 1.6% and 1.0% at 20 mA, respectively. Notably, the WPE was comparable with that of state-of-the-art red InGaN LEDs.13 

FIG. 6.

Light-output power and forward voltage as functions of injected current for InGaN-based red LEDs.

FIG. 6.

Light-output power and forward voltage as functions of injected current for InGaN-based red LEDs.

Close modal

In summary, we investigated InGaN-based red LEDs and observed enhanced EL efficiency on varying the thicknesses of the underlying n-GaN layers. A thick underlying GaN layer with lower in-plane stress resulted in reduced surface defects on the red LEDs; this could be attributed to the increased growth temperature of the InGaN red DQWs. The light-output power of the red LEDs was enhanced by using a thicker underlying layer. We obtained a light-output power, a forward voltage, and an EQE of 0.64 mW, 3.3 V, and 1.6% at 20 mA, respectively. The reduction of the in-plane compressive stress in the underlying GaN layers was shown to be crucial for enhancing the light-output power of InGaN-based red LEDs on conventional sapphire substrates.

This work was supported financially by the King Abdullah University of Science and Technology (KAUST) (No. BAS/1/1676-01-01).

1.
Y.
Narukawa
,
M.
Ichikawa
,
D.
Sanga
,
M.
Sano
, and
T.
Mukai
,
J. Phys. D
43
,
354002
(
2010
).
2.
N.
Yoshimoto
,
T.
Matsuoka
,
T.
Sasaki
, and
A.
Katsui
,
Appl. Phys. Lett.
59
,
2251
(
1991
).
3.
A.
Koukitu
,
N.
Takahashi
,
T.
Taki
, and
H.
Seki
,
J. Cryst. Growth
170
,
306
(
1997
).
4.
Y.
Yamashita
,
H.
Tamura
,
N.
Horio
,
H.
Sato
,
K.
Taniguchi
,
T.
Chinone
,
S.
Omori
, and
C.
Funaoka
,
Jpn. J. Appl. Phys., Part 1
42
,
4197
(
2003
).
5.
M.
Shimizu
,
Y.
Kawaguchi
,
K.
Hiramatsu
, and
N.
Sawaki
,
Jpn. J. Appl. Phys., Part 1
36
,
3381
(
1997
).
6.
D.
Holec
,
P. M. F. J.
Costa
,
M. J.
Kappers
, and
C. J.
Humphreys
,
J. Cryst. Growth
303
,
314
(
2007
).
7.
T.
Takeuchi
,
S.
Sota
,
M.
Katsuragawa
,
M.
Komori
,
H.
Takeuchi
,
H.
Amano
, and
I.
Akasaki
,
Jpn. J. Appl. Phys., Part 2
36
,
L382
(
1997
).
8.
T.
Takeuchi
,
C.
Wetzel
,
S.
Yamaguchi
,
H.
Sakai
,
H.
Amano
,
I.
Akasaki
,
Y.
Kaneko
,
S.
Nakagawa
,
Y.
Yamaoka
, and
N.
Yamada
,
Appl. Phys. Lett.
73
,
1691
(
1998
).
9.
S.
Nakamura
,
M.
Senoh
,
N.
Iwasa
, and
S.
Nagahama
,
Jpn. J. Appl. Phys., Part 2
34
,
L797
(
1995
).
10.
M.
Funato
,
M.
Ueda
,
Y.
Kawakami
,
Y.
Narukawa
,
T.
Kosugi
,
M.
Takahashi
, and
T.
Mukai
,
Jpn. J. Appl. Phys., Part 2
45
,
L659
(
2006
).
11.
K.
Ohkawa
,
T.
Watanabe
,
M.
Sakamoto
,
A.
Hirako
, and
M.
Deura
,
J. Cryst. Growth
343
,
13
(
2012
).
12.
Y.
Kawaguchi
,
C.-Y.
Huang
,
Y.-R.
Wu
,
Y.
Zhao
,
S. P.
DenBaars
, and
S.
Nakamura
,
Jpn. J. Appl. Phys., Part 1
52
,
08JC08
(
2013
).
13.
J. I.
Hwang
,
R.
Hashimoto
,
S.
Saito
, and
S.
Nunoue
,
Appl. Phys. Express
7
,
071003
(
2014
).
14.
K.
Kishino
,
A.
Yanagihara
,
K.
Ikeda
, and
K.
Yamano
,
Electron. Lett.
51
,
852
(
2015
).
15.
D.
Iida
,
K.
Niwa
,
S.
Kamiyama
, and
K.
Ohkawa
,
Appl. Phys. Express
9
,
111003
(
2016
).
16.
A.
Even
,
G.
Laval
,
O.
Ledoux
,
P.
Ferret
,
D.
Sotta
,
E.
Guiot
,
F.
Levy
,
I. C.
Robin
, and
A.
Dussaigne
,
Appl. Phys. Lett.
110
,
262103
(
2017
).
17.
B.
Mitchell
,
V.
Dierolf
,
T.
Gregorkiewicz
, and
Y.
Fujiwara
,
J. Appl. Phys.
123
,
160901
(
2018
).
18.
F.
Jiang
,
J.
Zhang
,
L.
Xu
,
J.
Ding
,
G.
Wang
,
X.
Wu
,
X.
Wang
,
C.
Mo
,
Z.
Quan
,
X.
Guo
,
C.
Zheng
,
S.
Pan
, and
J.
Liu
,
Photonics Res.
7
,
144
(
2019
).
19.
T.
Ozaki
,
M.
Funato
, and
Y.
Kawakami
,
Appl. Phys. Express
12
,
011007
(
2019
).
20.
K.
Ohkawa
,
F.
Ichinohe
,
T.
Watanabe
,
K.
Nakamura
, and
D.
Iida
,
J. Cryst. Growth
512
,
69
(
2019
).
21.
R.
Hashimoto
,
J. I.
Hwang
,
S.
Saito
, and
S.
Nunoue
,
Phys. Status Solidi C
10
,
1529
(
2013
).
22.
K.
Lekhal
,
B.
Damilano
,
H. T.
Ngo
,
D.
Rosales
,
P.
De Mierry
,
S.
Hussain
,
P.
Vennéguès
, and
B.
Gil
,
Appl. Phys. Lett.
106
,
142101
(
2015
).
23.
D.
Iida
,
S.
Lu
,
S.
Hirahara
,
K.
Niwa
,
S.
Kamiyama
, and
K.
Ohkawa
,
J. Cryst. Growth
448
,
105
(
2016
).
24.
Q.
Lv
,
J.
Liu
,
C.
Mo
,
J.
Zhang
,
X.
Wu
,
Q.
Wu
, and
F.
Jiang
,
ACS Photonics
6
,
130
(
2019
).
25.
S.
Srinivasan
,
L.
Geng
,
R.
Liu
,
F. A.
Ponce
,
Y.
Narukawa
, and
S.
Tanaka
,
Appl. Phys. Lett.
83
,
5187
(
2003
).
26.
M.
Iwaya
,
T.
Yamamoto
,
D.
Iida
,
Y.
Kondo
,
M.
Sowa
,
H.
Matsubara
,
K.
Ishihara
,
T.
Takeuchi
,
S.
Kamiyama
, and
I.
Akasaki
,
Jpn. J. Appl. Phys., Part 1
54
,
115501
(
2015
).
27.
M. C.
Johnson
,
E. D.
Bourret-Courchesne
,
J.
Wu
,
Z.
Liliental-Weber
,
D. N.
Zakharov
,
R. J.
Jorgenson
,
T. B.
Ng
,
D. E.
McCready
, and
J. R.
Williams
,
J. Appl. Phys.
96
,
1381
(
2004
).
28.
K.
Hiramatsu
,
T.
Detchprohm
, and
I.
Akasaki
,
Jpn. J. Appl. Phys., Part 1
32
,
1528
(
1993
).
29.
C.
Röder
,
F.
Lipski
,
F.
Habel
,
G.
Leibiger
,
M.
Abendroth
,
C.
Himcinschi
, and
J.
Kortus
,
J. Phys. D: Appl. Phys.
46
,
285302
(
2013
).
30.
S.
Choi
,
E.
Heller
,
D.
Dorsey
,
R.
Vetury
, and
S.
Graham
,
J. Appl. Phys.
113
,
093510
(
2013
).
31.
W. Z.
Tawfik
,
G. Y.
Hyun
,
S.-W.
Ryu
,
J. S.
Ha
, and
J. K.
Lee
,
Opt. Mater.
55
,
17
(
2016
).
32.
S.
Nakamura
,
Jpn. J. Appl. Phys., Part 2
30
,
L1705
(
1991
).
33.
T.
Sugiyama
,
D.
Iida
,
T.
Yasuda
,
M.
Iwaya
,
T.
Takeuchi
,
S.
Kamiyama
, and
I.
Akasaki
,
Appl. Phys. Express
6
,
121002
(
2013
).
34.
A. F.
Wright
,
J. Appl. Phys.
82
,
2833
(
1997
).
35.
V. S.
Harutyunyan
,
A. P.
Aivazyan
,
E. R.
Weber
,
Y.
Kim
,
Y.
Park
, and
S. G.
Subramanya
,
J. Phys. D: Appl. Phys.
34
,
A35
(
2001
).
36.
J.
Smalc-Koziorowska
,
E.
Grzanka
,
R.
Czernecki
,
D.
Schiavon
, and
M.
Leszczyński
,
Appl. Phys. Lett.
106
,
101905
(
2015
).
37.
H.
Wang
,
Z.
Lv
,
C.
Chen
,
S.
Zhang
,
Y.
Guo
,
B.
Li
,
Z.
Wu
, and
H.
Jiang
,
Appl. Surf. Sci.
494
,
285
(
2019
).
38.
A.
Hangleiter
,
F.
Hitzel
,
C.
Netzel
,
D.
Fuhrmann
,
U.
Rossow
,
G.
Ade
, and
P.
Hinze
,
Phys. Rev. Lett.
95
,
127402
(
2005
).
39.
C.
Li
,
Z.
Ji
,
J.
Li
,
M.
Xu
,
H.
Xiao
, and
X.
Xu
,
Sci. Rep.
7
,
15301
(
2017
).