Design of InGaN-ZnSnN2 quantum wells for high-efficiency amber light emitting diodesMd Rezaul Karim, and Hongping Zhao

Citation: Journal of Applied Physics 124, 034303 (2018); doi: 10.1063/1.5036949View online: https://doi.org/10.1063/1.5036949View Table of Contents: http://aip.scitation.org/toc/jap/124/3Published by the American Institute of Physics

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Design of InGaN-ZnSnN2 quantum wells for high-efficiency amber lightemitting diodes

Md Rezaul Karim1 and Hongping Zhao1,2,a)1Department of Electrical and Computer Engineering, The Ohio State University, Columbus, Ohio 43210, USA2Department of Materials Science and Engineering, The Ohio State University, Columbus, Ohio 43210, USA

(Received 19 April 2018; accepted 4 July 2018; published online 20 July 2018)

InGaN-ZnSnN2 based quantum wells (QWs) structure is proposed and studied as an active region

for high efficiency amber (k� 600 nm) light emitting diodes (LEDs), which remains a greatchallenge in pure InGaN based LEDs. In the proposed InGaN-ZnSnN2 QW heterostructure, the

thin ZnSnN2 layer serves as a confinement layer for the hole wavefunction utilizing the large

band offset at the InGaN-ZnSnN2 interface in the valence band. The barrier layer is composed of

GaN or AlGaN/GaN in which the thin AlGaN layer is used for a better confinement of the

electron wavefunction in the conduction band. Utilizing the properties of band offsets between

ZnSnN2 and InGaN, the design of InGaN-ZnSnN2 QW allows us to use much lower In-content

(�10%) to reach peak emission wavelength at 600 nm, which is unachievable in conventionalInGaN QW LEDs. Furthermore, the electron-hole wavefunction overlap (Ce-h) for the InGaN-ZnSnN2 QW design is significantly increased to 60% vs. 8% from that of the conventional InGaN

QW emitting at the same wavelength. The tremendous enhancement in electron-hole wavefunc-

tion overlap results in �225� increase in the spontaneous emission radiative recombination rateof the proposed QW as compared to that of the conventional one using much higher In-content.

The InGaN-ZnSnN2 QW structure design provides a promising route to achieve high efficiency

amber LEDs. Published by AIP Publishing. https://doi.org/10.1063/1.5036949

I. INTRODUCTION

In the past decades, the performance of InGaN based

blue and green light emitters has been improved tremen-

dously although the efficiency of green light-emitting diodes

(LEDs) is still inferior to that of the blue ones. In general,

the efficiency of InGaN LEDs decreases as the emission

wavelength extends from blue to green, amber, and red. In

particular, the efficiencies of amber LEDs have been the

lowest among the visible LEDs to date.1 One fundamental

challenge in improving the radiative efficiency of InGaN

quantum wells (QWs) based light emitters originates from

the characteristic large polarization induced electric field of

III-nitride semiconductors grown along the preferred c-plane

orientation. This leads to charge separation and resultant

reduction in charge carrier radiative recombination rate.2

The detrimental impact from the internal electrostatic field

becomes more severe for InGaN LEDs emitting in wave-

length beyond blue and green, in which higher-In content

InGaN and relatively thicker QWs are required.3

Approaches have been used to overcome the issue of

polarization-induced charge separation in InGaN light emit-

ter devices by growing the structures along the non-polar

(a- and m- planes) or semi-polar orientations.1,4,5 Separately,

novel QW structures such as staggered InGaN QW,6–10

strain-compensated InGaN-AlGaN QW,11,12 type-II InGaN-

GaAsN QW,13,14 InGaN-delta-InN QW,15 and InGaN QW

with delta-AlGaN layer16,17 have been proposed to address

the charge separation issue in conventional InGaN QW

LEDs. These novel QW designs using nanostructure engi-

neering have shown improvements in radiative efficiency.

However, these QW designs still suffer from low efficiency

when the emission wavelength extends to the longer wave-

length regime, since higher In-content is still required in

these QW designs. In addition, rare-earth doped (Er,18 Eu19)

GaN was studied as an active region for green and red emis-

sion. However, the internal quantum efficiencies of these

emitters have not crossed 1% yet.20

Recently, an InGaN-ZnGeN2 based type-II QW struc-

ture has shown great improvement in the radiative efficiency

in blue and green LEDs.21 GaN and ZnGeN2 have similar

bandgaps with a large band offset (DEV� 1.1 eV), whichresults in a type-II heterointerface between InGaN and

ZnGeN2.22–24 The large band offset in the valence band leads

to a strong confinement of the hole wavefunction in the

ZnGeN2 layer. However, the similar large band offset in the

conduction band pushes the electron wavefunction away

from the ZnGeN2 layer, which limits the radiative recombi-

nation rate between electrons and holes.

On the other hand, ZnSnN2 represents the smallest

bandgap (Eg� 1.8 eV) semiconductor among the Zn-IV-N2.From the recent first principles calculations, ZnSnN2 has a

favorable alignment in both valence band (DEV¼ 1.4 eV)and conduction band (DEC¼�0.3 eV) with GaN.22,23 Thisallows a strong confinement of hole wavefunction in the

valence band, without sacrificing the shift of the electron

wavefunction in the conduction band. Therefore, a large

electron-hole wavefunction overlap for high internal quan-

tum efficiency (IQE) is achievable for LEDs with longer

emission wavelength beyond green.a)Email: zhao.2592@osu.edu

0021-8979/2018/124(3)/034303/5/$30.00 Published by AIP Publishing.124, 034303-1

JOURNAL OF APPLIED PHYSICS 124, 034303 (2018)

https://doi.org/10.1063/1.5036949https://doi.org/10.1063/1.5036949https://doi.org/10.1063/1.5036949https://doi.org/10.1063/1.5036949mailto:zhao.2592@osu.eduhttp://crossmark.crossref.org/dialog/?doi=10.1063/1.5036949&domain=pdf&date_stamp=2018-07-20

In this paper, we investigate the design of an InGaN-

ZnSnN2 based QW structure for high efficiency amber LEDs

using the self-consistent 6-band k�p method.11 The polariza-tion field, strain effect, and carrier screening effect were

taken into consideration in the band structure calculation.

The spontaneous emission radiative recombination rates are

calculated for both the InGaN-ZnSnN2 QW and the conven-

tional InGaN QW emitting at the similar wavelength, which

indicates a 210–235� enhancement at different carrierconcentrations.

II. CONCEPTUAL DESIGN

The absence of inversion symmetry in wurtzite III-

nitride materials causes large spontaneous polarization

whereas the lattice-mismatch induced strain in III-nitride

heterostructures gives rise to piezoelectric polarization.3 In

InGaN based QWs with GaN as barriers, the polarization

induced electric field creates band bending. As a result,

charge carriers of opposite polarity are localized in a sepa-

rate spatial regime in the QW25–29 and thus, decrease the

electron-hole wavefunction overlap Ce-h, as shown in Fig. 1.The detrimental effect becomes more severe when higher In

content InGaN or thicker QWs are used targeting for longer

wavelength emission.

In the proposed design, a thin layer of ZnSnN2 is used

as the hole confinement layer in the active region to address

the charge separation issue. The energy bandgap versus

wurtzite lattice parameter diagram of Zn-IV-N2 and III-N as

plotted in Fig. 2(a) reveals that ZnSnN2 is lattice-matched to

In0.31Ga0.69N.24 Most importantly, the band alignment of

ZnSnN2 with unstrained GaN and InN shown in Fig. 2(b)

reveals that there is a large DEV and a close-to-zero DECbetween ZnSnN2 and InGaN.

22,23 Such a band alignment of

ZnSnN2 with InGaN renders a strong hole confinement in

the ZnSnN2 layer but still maintains the uniform distribution

of electron wavefunction in the conduction band. Note that,

first-principles calculations30 suggest that ZnSnN2 has a

spontaneous polarization (see Table I) that is comparable

to that of GaN, which has been taken into account in this

calculation. This QW design also allows us to extend the

transition wavelength into a longer wavelength regime with-

out using high-In InGaN.

Figure 3 schematizes the conceptual design of an

InGaN-ZnSnN2 based QW structure with GaN and GaN/

AlGaN as barriers. The purpose of the thin AlGaN layer is to

better confine the electron wavefunction in the QW active

region. While the peak emission wavelength kpeak, of a con-ventional InGaN QW depends on the In-content and the

thickness of the QW, the InGaN-ZnSnN2 based QW

FIG. 1. Illustration of charge carrier

separation in conventional InGaN QW

with GaN barriers due to large band-

bending caused by polarization field.

FIG. 2. (a) Energy bandgap versus wurtzite lattice constant of III-N and

Zn-IV-N2 semiconductors. (b) Bandgap alignments of InN, In0.31Ga0.69N,

ZnGeN2, and ZnSnN2 with respect to GaN showing conduction and valence

band offsets. The values for Zn-IV-N2 materials were obtained from Ref. 24.

034303-2 M. R. Karim and H. Zhao J. Appl. Phys. 124, 034303 (2018)

structure allows a greater flexibility and wider range of

tuning for kpeak. Particularly, the thickness and position ofthe ZnSnN2 layer within the InGaN QW affect the confined

hole energy levels and hence the kpeak. Hereafter, the con-ventional GaN/InxGa1-xN/GaN QW as shown in Fig. 1 and

the proposed GaN/InyGa1-yN/ZnSnN2/InzGa1-z/AlwGa1-wN/

GaN QW as shown in Fig. 3 will be referred to as IGN QW

and IGN-ZTN QW, respectively.

The QW thickness and In content of the IGN QW were

designed for peak emission wavelength at amber (600 nm).

The total QW thickness LQW of IGN-ZTN QW was kept the

same as that of the IGN QW and the In content in the two

InGaN sub-layers was kept the same.

III. NUMERICAL FORMULATION

A self-consistent 6-band k.p method was used to obtain

the band structure of the proposed as well as the conven-

tional QW structures. The hole energy bands were calculated

using 6 � 6 diagonalized k.p Hamiltonian, whereas the para-bolic energy bands were assumed for electrons. Effects of

strain, spontaneous as well as piezoelectric polarization, car-

rier screening effect, and valence band mixing were taken

into account. In this study, we mainly focus on QW struc-

tures emitting in the visible wavelength regime. This allows

us to assume that the coupling between the conduction and

valence bands is weak. Therefore, the band structure in the

conduction band is assumed as parabolic in the vicinity of

the conduction band minimal. Many body effects and inho-

mogeneous broadening of In-content in the QW were not

considered. Previous studies have shown that the many body

effects, which include bandgap renormalization and the exci-

tonic or Coulombic enhancement can affect the peak gain

and corresponding wavelength.31 Thus, the many body effect

can affect the absolute value of the calculated spontaneous

emission rate and the emission wavelength. However, this

will not change the trend of the results, neither on the design

protocol of InGaN-ZnSnN2 QWs for high efficiency amber

LEDs. Inhomogeneous broadening of QW thickness or In

composition in InGaN based light emitters has been reported

to result in spectral broadening and shift as well as reduction

in laser gain.32 These effects become more obvious when

high In content is used or higher carrier concentration needs

to be considered in the laser operation. In this work, we have

investigated the recombination properties at the relatively

low carrier densities (1–5 � 1018 cm�3) for LEDs’ applica-tion. In order to take into account these effects accurately,

parameters from experiments are necessary, which is out of

the scope of this study. However, this does not affect the

effectiveness of using the concept of InGaN-ZnSnN2 QWs

for high efficiency amber LEDs.

The energy band alignments in the heterostructures were

calculated by iteratively solving Poisson’s equation until the

convergence was reached. The confined energy levels and

corresponding wavefunctions were calculated by solving the

Schr€odinger equation and the Poisson’s equation self-consistently. Overlap between electron and hole wavefunc-

tions was obtained by calculating the spatial overlap between

the normalized envelop functions. Both TE and TM polariza-

tions were considered in the calculation of spontaneous

emission rate. The detailed numerical formalism can be

found in Ref. 11. The material parameters of the III-nitride

semiconductors were taken from Refs. 33 and 34. The mate-

rial parameters of ZnSnN2 were collected from Refs. 22–24,

30, and 35. The parameter values used in the simulation are

summarized in Table I, using the identical notations as in

Ref. 11.

TABLE I. Material parameters of GaN, InN, and ZnSnN2 used in the simu-

lation. The values were obtained from Refs. 33 and 34 (GaN and InN) and

Refs. 22–24, 27, and 35 (ZnSnN2).

Parameter GaN InN ZnSnN2

Lattice constant (Å)

a 3.189 3.545 3.3

c 5.185 5.703 5.462

Energy Parameters (eV)

Eg at 300 K 3.42 0.6405 1.8

D1 (¼Dcr) 0.01 0.024 0.088D1 ¼ D2 ¼ Dso/3 0.00567 0.00167 0Conduction band offset with GaN (eV) 0.7 DEg �0.3Valence band offset with GaN (eV) 0.3 DEg 1.4Conduction-band effective masse

m�k=m0 at 300 K 0.21 0.07 0.13

m�?=m0 at 300 K 0.2 0.07 0.17

Valence band effective mass parameters

A1 �7.21 �8.21 �8.23A2 �0.44 �0.68 �0.49A3 6.68 7.57 7.77

A4 �3.46 �5.23 �2.8A5 �3.4 �5.11 �2.8A6 �4.9 �5.96 �3.89Elastic stiffness coefficients (GPa)

C11 390 223 272

C12 145 115 128

C13 106 92 100

C33 398 224 306

Spontaneous polarization (C/m2) �0.034 �0.042 �0.029Piezoelectric coefficients (pm V�1)

d13 �1 �3.5 �2.9d33 1.9 7.6 5.4

FIG. 3. Schematic of the GaN/InyGa1-yN/ZnSnN2/InzGa1-zN/AlwGa1-wN/GaN

QW showing the band edge alignment. þ and – signs denote low energyregions for holes and electrons, respectively. Position of the conduction band

edge of ZnSnN2 with respect to that of InGaN depends on the In content.

034303-3 M. R. Karim and H. Zhao J. Appl. Phys. 124, 034303 (2018)

IV. ENERGY BAND ALIGNMENT

The band edge alignment of the conduction and valence

bands for the conventional 3.5 nm In0.29Ga0.71N QW and the

2.1 nm In0.1Ga0.9N-0.6 nm ZnSnN2–0.8 nm In0.1Ga0.9N-

1.5 nm Al0.2Ga0.8N QW is plotted in Figs. 4(a) and 4(b),

respectively. Both structures were designed with peak emis-

sion wavelength of �600 nm. The corresponding electronwavefunction (We1) and hole wavefunction (Whh1) in the firstconfined conduction energy states are also plotted. As shown

in Fig. 4(a), the electron and hole wavefunctions are spatially

separated in the IGN QW due to the severe band bending.

Consequently, the electron-hole wavefunction overlap

Ce1-hh1 is only 8%. On the other hand, the IGN-ZTN QW asshown in Fig. 4(b) shows a strong hole wavefunction con-

finement and a significantly enhanced electron-hole wave-

function overlap of 60%.

It is worth noting that the In-content used in the IGN-

ZTN QW (10%) is significantly lower than that used in the

conventional IGN QW (29%). Experimentally, growth of

higher-In content InGaN is challenging due to the require-

ment of lower growth temperature for incorporation of more

indium, which often leads to reduced material quality associ-

ated with severe nonradiative recombinations in LEDs.36–38

Therefore, one can expect the crystalline quality of the pro-

posed IGN-ZTN QW structure to be superior to the conven-

tional IGN QW, since higher growth temperature can be

implemented for the novel structure.

V. SPONTANEOUS EMISSION PROPERTIES

The spontaneous emission spectra of the IGN-ZTN QW

were calculated for carrier concentrations at 1–5� 1018 cm�3,as compared to that of the conventional IGN QW. As shown

in Fig. 5(a), both QW structures show a peak emission wave-

length of �600 nm at the carrier density of 5 � 1018 cm�3.The peak spontaneous emission intensity Ipeak for the

IGN QW increases from 4.0� 1024 s�1 cm�3 eV�1 to 9.9� 1025 s�1 cm�3 eV�1 with the increase in carrier concentra-tion from 1 � 1018 cm�3 to 5 � 1018 cm�3. The Ipeak of IGN-ZTN QW increases from 1� 1027 s�1 cm�3 eV�1 to 2.1� 1028 s�1 cm�3 eV�1, corresponding to approximately210–250� enhancement. Based on the Fermi’s golden rule,the enhancement in Ipeak is attributed to the significantly

increased electron-hole wavefunction overlap in the IGN-

ZTN QW active region. Furthermore, both spontaneous emis-

sion spectra sets show blue shift as the carrier concentration

increases due to the carrier screening effect. However, the

blue shift of kpeak for the IGN-ZTN QW (�3 nm) is muchsuppressed as compared to that of the IGN QW (�11 nm).This indicates that the effective band bending in the novel

QW design is much reduced as compared to the conventional

IGN QW.

The spontaneous emission radiative recombination rate

per unit volume Rsp is calculated by integrating the spontane-

ous emission spectrum over the entire wavelength range. As

shown in Fig. 5(b), Rsp increases monotonically with the

increase in carrier concentration for both QW structures. The

IGN-ZTN QW provides 210–235 times enhancement of Rspas compared to that of the IGN QW. Specifically, the Rspof the IGN-ZTN QW increases from 5.2 � 1025 s�1 cm�3 to1.3� 1027 s�1 cm�33 for carrier concentration at 1–5� 1018 cm�3, whereas the Rsp of the IGN QW is limited to2.2� 1023 s�1 cm�3–6.2� 1024 s�1 cm�3. Note that theinternal quantum efficiency (IQE) of LEDs is determined

by the ratio of radiative recombination rate and the total

recombination rate which includes both the radiative and

nonradiative components. Here, if we take into account

the expected lower nonradiative recombination in the

IGN-ZTN QW, one can expect even larger enhancement

of the IQE from the novel QW design.

VI. CONCLUSION

In conclusion, a novel QW design for amber LEDs using

InGaN-ZnSnN2 QW active layer was investigated. The

ZnSnN2 layer inserted in InGaN QW serves as a strong con-

finement layer for hole wavefunctions due to the large

valence band offset. The close to zero conduction band offset

between InGaN and ZnSnN2 offers additional advantages for

FIG. 4. Energy-band alignment and electron- and hole-wavefunctions for the

first confined energy states in (a) conventional GaN/3.5 nm In0.29Ga0.71N/

GaN and (b) GaN/2.1 nm In0.1Ga0.9N/0.6 nm ZnSnN2/0.8 nm In0.1Ga0.9N/

1.5 nm Al0.2Ga0.8N/GaN QW. Both QWs were designed with �600 nm peakspontaneous emission wavelength.

034303-4 M. R. Karim and H. Zhao J. Appl. Phys. 124, 034303 (2018)

achieving high electron-hole wavefunction overlap. As a

result, the peak spontaneous emission intensity and the spon-

taneous emission radiative recombination rate of the InGaN-

ZnSnN2 QW have shown 210–250 times and 210–235 times

enhancement as compared to those of the conventional

InGaN QW. In addition, by utilizing the smaller bandgap of

ZnSnN2 and the large valence band offset with InGaN, only

low In-content InGaN is required to achieve amber emission.

The proposed IGN-ZTN QW structure is promising to

address the current challenge of low efficiency in InGaN

QW LEDs emitting beyond blue and green. This work has a

great potential to pave a new way to realize high perfor-

mance monolithic III-nitride LEDs emitting in the entire

visible wavelength regime.

ACKNOWLEDGMENTS

The authors acknowledge the support from the National

Science Foundation (DMREF-1533957).

1Department of Energy Solid State Lightening R&D Plan, June (2016).2V. Fiorentini, F. Bernardini, F. D. Sala, A. D. Carlo, and P. Lugli, Phys.

Rev. B 60, 8849 (1999).3B. Damilano and B. Gil, J. Phys. D: Appl. Phys. 48, 403001 (2015).4M. C. Schmidt, K.-C. Kim, R. M. Farrell, D. F. Feezell, D. A. Cohen, M.

Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, Jpn. J.

Appl. Phys., Part 2 46, L190 (2007).5R. M. Farrell, D. F. Feezell, M. C. Schmidt, D. A. Haeger, K. M.

Kelchner, K. Iso, H. Yamada, M. Saito, K. Fujito, D. A. Cohen, J. S.

Speck, S. P. DenBaars, and S. Nakamura, Jpn. J. Appl. Phys., Part 2 46,L761 (2007).

6H. Zhao, G. Liu, J. Zhang, J. D. Poplawsky, V. Dierolf, and N. Tansu, Opt.

Express 19, A991 (2011).7R. A. Arif, H. Zhao, Y.-K. Ee, and N. Tansu, IEEE J. Quantum Electron.

44, 573 (2008).8R. A. Arif, Y.-K. Ee, and N. Tansu, Appl. Phys. Lett. 91, 091110 (2007).9H. Zhao, R. A. Arif, and N. Tansu, IEEE J. Sel. Top. Quantum Electron.

15, 1104 (2009).10S.-H. Park, D. Ahn, and J.-W. Kim, Appl. Phys. Lett. 94, 041109 (2009).

11H. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, IEEE J. Quantum Electron.

45, 66 (2009).12H. Zhao, R. A. Arif, Y.-K. Ee, and N. Tansu, Opt. Quantum Electron. 40,

301 (2008).13R. A. Arif, H. Zhao, and N. Tansu, Appl. Phys. Lett. 92, 011104 (2008).14S.-H. Park, Y.-T. Lee, and J. Park, Opt. Quantum Electron. 41, 779 (2009).15H. Zhao, G. Liu, and N. Tansu, Appl. Phys. Lett. 97, 131114 (2010).16J. Park and Y. Kawakami, Appl. Phys. Lett. 88, 202107 (2006).17S.-H. Park, J. Park, and E. Yoon, Appl. Phys. Lett. 90, 023508 (2007).18J. Heikenfeld, D. S. Lee, M. Garter, R. Birkhahn, and A. J. Steckl, Appl.

Phys. Lett. 76, 1365 (2000).19S. Morishima, T. Maruyama, M. Tanaka, Y. Masumoto, and K. Akimoto,

Phys. Status Solidi A 176, 113 (1999).20I. E. Fragkos, C.-K. Tan, V. Dierolf, Y. Fujiwara, and N. Tansu, Sci. Rep.

7, 14648 (2017).21L. Han, K. Kash, and H. Zhao, J. Appl. Phys. 120, 103102 (2016).22A. Punya and W. R. L. Lambrecht, Phys. Rev. B 88, 075302 (2013).23A. P. Jaroenjittichai, S. Lyu, and W. R. L. Lambrecht, Phys. Rev. B 96,

079907(E) (2017).24W. R. L. Lambrecht and A. Punya, III-Nitride Semiconductors and Their

Modern Devices (Oxford University Press, Oxford, UK, 2013), Chap. 15.25S.-H. Park and S.-L. Chuang, Appl. Phys. Lett. 76, 1981 (2000).26S.-H. Park and S.-L. Chuang, J. Appl. Phys. 87, 353 (2000).27S.-H. Park and S.-L. Chuang, Phys. Rev. B 59, 4725 (1999).28T. Takeuchi, H. Amano, and I. Akasaki, Jpn. J. Appl. Phys., Part 1 39, 413

(2000).29I. H. Brown, P. Blood, P. M. Smowton, J. D. Thomson, S. M. Olaizola, A.

M. Fox, P. J. Parbrook, and W. W. Chow, IEEE J. Quantum Electron. 42,1202 (2006).

30T. R. Paudel and W. R. L. Lambrecht, Phys. Rev. B 79, 245205 (2009).31W. W. Chow, Opt. Express 22, 1413 (2014).32W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, Appl.

Phys. Lett. 71, 2608 (1997).33I. Vurgaftman and J. R. Meyer, Nitride Semiconductor Devices: Principles

and Simulations (Wiley, New York, 2007), Chap. 2, pp. 13–48.34I. Vurgaftman and J. R. Meyer, J. Appl. Phys. 94, 3675 (2003).35A. Punya, T. R. Paudel, and W. R. L. Lambrecht, Phys. Status Solidi C 8,

2492 (2011).36A. Yamamoto, K.-i. Sugita, and A. Hashimoto, J. Cryst. Growth 311, 4636

(2009).37M. Mesrine, N. Grandjean, and J. Massies, Appl. Phys. Lett. 72, 350

(1998).38T. Langer, H. Jonen, A. Kruse, H. Bremers, U. Rossow, and A. Hangleiter,

Appl. Phys. Lett. 103, 022108 (2013).

FIG. 5. (a) Spontaneous emission spec-

tra and (b) spontaneous emission radia-

tive recombination rates of 3.5 nm In0.29Ga0.71N (dashed-dotted lines denoted

by IGN) and 2.1 nm In0.1Ga0.9N/0.6 nm

ZnSnN2/0.8 nm In0.1Ga0.9N/1.5 nm

Al0.2Ga0.8N (solid lines denoted by

IGN-ZTN) QWs for carrier concentra-

tions 1–5� 1018 cm�3. Both QWswere designed with 600 nm peak emis-

sion wavelength at 5� 1018 cm�3 car-rier concentration.

034303-5 M. R. Karim and H. Zhao J. Appl. Phys. 124, 034303 (2018)

https://doi.org/10.1103/PhysRevB.60.8849https://doi.org/10.1103/PhysRevB.60.8849https://doi.org/10.1088/0022-3727/48/40/403001https://doi.org/10.1143/JJAP.46.L190https://doi.org/10.1143/JJAP.46.L190https://doi.org/10.1143/JJAP.46.L761https://doi.org/10.1364/OE.19.00A991https://doi.org/10.1364/OE.19.00A991https://doi.org/10.1109/JQE.2008.918309https://doi.org/10.1063/1.2775334https://doi.org/10.1109/JSTQE.2009.2016576https://doi.org/10.1063/1.3075853https://doi.org/10.1109/JQE.2008.2004000https://doi.org/10.1007/s11082-007-9177-2https://doi.org/10.1063/1.2829600https://doi.org/10.1007/s11082-010-9391-1https://doi.org/10.1063/1.3493188https://doi.org/10.1063/1.2205731https://doi.org/10.1063/1.2431477https://doi.org/10.1063/1.126033https://doi.org/10.1063/1.126033https://doi.org/10.1002/(SICI)1521-396X(199911)176:13.0.CO;2-Dhttps://doi.org/10.1038/s41598-017-15302-yhttps://doi.org/10.1063/1.4962280https://doi.org/10.1103/PhysRevB.88.075302https://doi.org/10.1103/PhysRevB.96.079907https://doi.org/10.1063/1.126229https://doi.org/10.1063/1.371915https://doi.org/10.1103/PhysRevB.59.4725https://doi.org/10.1143/JJAP.39.413https://doi.org/10.1109/JQE.2006.883472https://doi.org/10.1103/PhysRevB.79.245205https://doi.org/10.1364/OE.22.001413https://doi.org/10.1063/1.120155https://doi.org/10.1063/1.120155https://doi.org/10.1063/1.1600519https://doi.org/10.1002/pssc.201001147https://doi.org/10.1016/j.jcrysgro.2009.08.027https://doi.org/10.1063/1.120733https://doi.org/10.1063/1.4813446

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