Ab initio study of a cubic perovskite: Structural, electronic, optical and electrical properties of native, lanthanum- and antimony-doped barium tin oxide

Materials Science in Semiconductor Processing 32 (2015) 100–106

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Ab initio study of a cubic perovskite: Structural, electronic, optical and electrical properties of native, lanthanum- and antimony-doped barium tin oxide Amine Slassi LMPHE (URAC 12), Faculté des Sciences, Université Mohammed V-Agdal, Rabat, Morocco

a r t i c l e in f o

Keywords: Density functional theory Boltzmann equations Transparent conducting oxides Cubic perovskite BaSnO3

abstract We use density functional theory and semiclassical Boltzmann equation to investigate the structural, electronic, optical and electrical properties of native, lanthanum- and antimony-doped barium tin oxide. We find that lanthanum dopant introduces shallow donor states close to the bottom of the conduction band, whereas antimony dopant introduces deep states inside the band gap. The transmittance and electrical conductivity for lanthanum-doped barium tin oxide are significantly enhanced offering a good transparent conducting oxide, while are not as desired for antimony-doped barium tin oxide. On the other hand, the antimony-dopant enhances the visible light absorption of barium tin oxide, which might be useful for other applications as photocatalysts. Published by Elsevier Ltd.

1. Introduction The transparent conducting electrode is one of the key in the moderate optoelectronic applications that require a material with good optical transparency and high electrical conductivity such as solar cells, flat panel displays, and smart coatings [1–3] etc. Despite that In2O3, SnO2 and ZnO n-type semiconductors are the most utilized in the optoelectronic field due to their suitable transparent conducting properties [4–6]. There has been a great challenge, in order to expand the application usage, to explore other TCO materials offering better physical properties. Until recently, the BaSnO3 with cubic perovskite-type structure [7] has been extensively investigated as nextgeneration TCO material [8–16]. BaSnO3 has a wide band gap value covering the range 3.2–4 eV and stability at large range of temperature up to 1000 1C. Commonly, the oxide semiconductors that have a wide band gap are electrically insulating materials; however,

E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.mssp.2014.12.031 1369-8001/Published by Elsevier Ltd.

the high electrical conductivity could be obtained by the doping. The degree of ionizations of dopant is crucial for enhancement the free electron concentrations in the conduction band. Therefore, the dopants selected should be useful to explore a good TCO. Some previous experimental works have been shown that the cubic-perovskyte BaSnO3 could be doped by substituting a few of La- on Baatoms [9–14], or Sb- on Sn-atoms [15–18]. The electrical conductivity of La-doped BaSnO3 at room temperature is about of 1690 S cm
1 [12], which is higher than of industry standard TCOs. The carrier mobility reported in the La-doped BaSnO3 system is about of 320 cm2 v
1 s
1 [13], which is the highest value for any TCO. For Sb-doped BaSnO3, the electrical conductivity has only been achieved about of 411.52 S cm
1, whereas the carrier mobility has been about of 1.75 cm2 v
1 s
1 [16]. The reasons for the difference in the experimental values, between La- and Sbdoped systems, have not been well-understood yet. The density functional of state methods is the best powerful tool for well analyzing the different physical properties of materials. In this regard, the cubic perovskyte BaSnO3 theoretical investigations have been extensively

A. Slassi / Materials Science in Semiconductor Processing 32 (2015) 100–106

done by different methods [8,11,12,18–22]. All DFT calculations are agreed that the BaSnO3 has indirect band gap type. However, the main differences are the band gap values when the different exchange–correlation methods have been used. For example, the local density approximation (LDA) [23] and generalized gradient approximation (GGA) [24] fail to describe correctly the band gap by underestimating the band gap value of BaSnO3 up to 1.08 eV and 0.73 eV [22], respectively. A moderate cost method to correct the band gap value such as hybrid functional including the Heyd–Scuseria–Ernzerhof (HSE) [25] and Perdew–Burke–Ernzrhof combined with Hartree– Fock exchange (PBE0) [26]. These open up the band gap to 2.49 eV for HSE [8,20] and 3.21 eV for PBE0 [8]. Additionally, another method cheaper and more sophisticated is Tran–Blaha modified Becke–Johnson (TB-mBJ) [27]; this yield an indirect band gap value up to 2.61 eV for BaSnO3 system [21]. 2. Computational methods The calculations were carried out using WIEN2K package [28,29]. This package is based on the density function theory, which uses the full-potential linearized augmented plane-wave (FP-LAPW) method. The exchange and correlation potential is described by generalized gradient approximation as proposed by Perdew–Burke–Ernzrhof (GGA-PBE) [24] for structural properties calculations, and Tran–Blaha modified Becke–Johnson (TB-mBJ) approximation [27] for electronic, optical and transport properties calculations. The radii of the muffin tin atomic spheres RMT of Ba, Sn, O, La and Sb atoms are 2.5, 2.06, 1.78, 2.5 and 2.06 Bohr, respectively. For wave function in the interstitial region the plane wave cut-off value of KMAX ¼8/RMT is taken. We have used a self-consistent criterion of the total energy with a precision of 0.0001 Ry. The linear response of a medium to an electromagnetic radiation can be described by using the complex dielectric function ε (ω)¼ ε1 (ω)þiε2 (ω). The imaginary part ε2 (ω) of the dielectric function has been obtained from the electronic structure calculations, using the following expression [30]:
2 2 X Z    2 4π e 3 iM j f i ð1
f i ÞδðEf
Ei
ωÞd k ε2 ðωÞ ¼ i;j m2 ω2 ð1Þ where M is the dipole matrix, i and j are the initial and final states, respectively, ƒi is the Fermi distribution as a function of the ith state, and Ei is the energy of electron in the ith state. The real part of function dielectric ε1 (ω) can be extracted using the Kramers–Kronig relation [31]: Z 1 0 2 ω ε2 ðω0 Þdω0 ε1 ðωÞ ¼ 1 þ p ð2Þ π 0 ω02
ω2 with p standing for the principal part of the integral. Indeed, these two parts allow one to determine other optical properties, such as absorption coefficient αðωÞ and the reflectance RðωÞ using the relations as follows [32]: 1=2 pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi αðωÞ ¼ 2ω ε21 ðωÞ þ ε22 ðωÞ
ε1 ðωÞ ð3Þ

101

pffiffiffiffiffiffiffiffiffiffi   εðωÞ
12   RðωÞ ¼  pffiffiffiffiffiffiffiffiffiffi   εðωÞ þ 1 

ð4Þ

The calculated band structure data from DFT is fitted to semi-classic Boltzmann theory via the rigid band approach [33,34], to obtain the electrical conductivity. It follows from these approaches that, the dependence of the conductivity on transport distribution is:

σ αβ ðεÞ ¼

δðε
εi;k Þ 1X σ ði; kÞ i;k αβ N δðεÞ

ð5Þ

In the above relation, denotes the number of k-points that are sampled in the BZ and εi,k is the band structure which is considered as a rigid band. The k-dependent transport tensor is read as:

σ αβ ði; kÞ ¼ e2 τi;k να ði; kÞνβ ði; kÞ

ð6Þ

in this equation, i and k stand for the band index and wave vector, respectively, and τ denotes the relaxation time, να(i,k) is α component of the group velocities, while e is the electron charge. By integrating the transport distribution over energy, the electrical conductivity can be then written as a function of the temperature, T, and the chemical potential, μ, via the following equations:  Z ∂f ðT; εÞ 1 σ αβ ðT; μÞ ¼ σ αβ
μ ð7Þ dε ∂ε Ω

ναβ ðT; μÞ ¼

1 eT Ω

Z



σ αβ ðεÞðε
μÞ


∂f μ ðT; εÞ dε ∂ε

ð8Þ

where α and β stand for the tensor indices, Ω, μ, and ƒ denote the volume of unit cell, Fermi level of carriers, and the carrier Fermi–Dirac distribution function, respectively. The relaxation time is treated as energy-independent constant due to the complexity of carrier scattering mechanisms in the solid. This approach has been already testy on various compounds demonstrating to be a reasonable approximation for evaluating their electrical transport properties [35–37]. 3. Results and discussion 3.1. Lattice constant properties To evaluate the feasibility of doped cubic perovskite BaSnO3 structures; the Lattice constant optimizations have been carried out by minimizing the total energy with respect to the cell parameters. The total energies calculated as a function of cell volume were fitted to Murnaghan's equation of states [38]. The doping modules are sampled by one Ba-atom substituted by La-atom for Ladoped BaSnO3 and one Sn-atom by Sb-atom for Sb-doped BaSnO3 in a periodic 2  2  2 cubic perovskite supercell, as shown in Fig. 1. These lead to a doping concentration of 12.5%. Some experimental works revealed that the Sb- and La-dopants have a large solubility in the BaSnO3 material up to 18% and 10%, respectively. This indicates, to a certain degree, that the concentration selected is viable. The corresponding equilibrium lattice constants are summarized in Table 1. According to the results, the lattice

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A. Slassi / Materials Science in Semiconductor Processing 32 (2015) 100–106

Fig. 1. The 2  2  2 supercell of: (a) pure, (b) La- and (c ) Sb-doped BaSnO3, respectively.

constants increase for both doped BaSnO3 systems, which is in agreement with the experimental conclusions [10,12,15]. For pure BaSnO3 structure, the calculated lattice constant is agreed reasonably well with the experimental measurements [10,12], and other theoretical calculations [8,12,21]. These results imply that our calculation methods are reasonable. The La-doped BaSnO3 shows smaller distortion and doping feasibility, whereas Sb-dopant could somewhat leads to the lattice mismatch. In term of stability, the formation energies of doped systems were calculated according to the following formulas [39]: For La-doped BaSnO3 ¼ EðLa
doped BaSnO3 Þ
EðpureÞ
ELa þ EBa

Lattice constant (A1)

Pure La-doped BaSnO3 Sb-doped BaSnO3

–
0.63 þ 0.46

4.174 4.188 4.19

12 10 8

ð9Þ

6 4

For Sb-doped BaSnO3 Ef

Ef (eV)

ðSb
doped BaSnO3 Þ ¼ EðSb
doped BaSnO3 Þ
E ðpureÞ
E Sb þ ESn

ð10Þ where E(pure) is the total energy of the host BaSnO3 supercell, Ef (La-doped BaSnO3) and Ef (Sb-doped BaSnO3) are the total energies of the supercell containing the impurities; EBa, ESn, ELa and ESb are the total energy per atom of the bulk Ba, Sn, La and Sb unit cell in their reference states, respectively. The calculated formation energies of La- and Sb-doped BaSnO3 are summarized in Table 1. The most stable structure has low formation energy. As shown in Table 1, the La-doped BaSnO3 system has formation energy about of
0.63 eV revealing that this system becomes more stable than pure BaSnO3. It is unusual to find such an improvement in the doped system stability, while La- and Ba-atoms have a significantly difference in the atomic radii, electronicativity and electronic configurations. The formation energy of Sb-doped BaSnO3 is about of þ0.46 eV, which indicates that this system becomes somewhat less stable as compared to pure BaSnO3. However, this low value is still in the acceptable range of the thermodynamic stability. 3.2. Electronic states of pure, La- and Sb-doped BaSnO3 The calculated band structure of pure BaSnO3 using both the GGA-PBE and TB-mBJ functional are illustrated in Fig. 2. The Fermi level is set at 0 eV on the energy axis. For both functional calculations, the valence band maximum (VBM) occurs at M-point, whereas the conduction band minimum occurs at G-point, indicating that BaSnO3

Energy (eV)

ðLa
doped BaSnO3 Þ

Structure model

2 0

Ef

-2 -4 -6 -8 -10 -12 -14 R

Γ

X

M

Γ

12 10 8 6 4 Energy (eV)

Ef

Table 1 Calculated lattice constant, a, and Formation energy, Ef, for pure-, La- and Sb-doped BaSnO3 by using GGA-PBE, respectively.

2 0

Ef

-2 -4 -6 -8 -10 -12 -14 R

Γ

X

M

Γ

Fig. 2. (a) PBE and (b) TB-mBJ calculated band structure for pure BaSnO3.

is an indirect band gap semiconductor. Overall, two approximations give rather the similar distribution of the eigenstates, while the main difference in the band structure between GGA-PBE and TB-mBJ is the improvement in

A. Slassi / Materials Science in Semiconductor Processing 32 (2015) 100–106

103

this is close to our TB-mBJ value. However, the PBE06 gave nearly the exact indirect band gap value to experimental of 3.22 eV [8]. This computational gap value, by using PBE06 functional, has been reported to be better in the previous calculations for cubic perovskite BaSnO3 material. Unfortunately, the computational cost of hybrid functional PBE06 is very high that is unaffordable for a computer screening of large supercell atoms. To further analysis of doping effect on the electronic structure, we calculate the density of states near the Fermi levels of the pure, La- and Sb-doped BaSnO3 in a 2  2  2 supercell within TB-mBJ approach, as illustrated in Fig. 3. For pure BaSnO3, the total and partial density of states are shown in Fig. 3(a), the present results are similar to the previous theoretical investigations [18–21]; showing that the top of the valence band mainly consists of O-2p states hybridized with weak Sn-2p states, indicating that the bonding type in BaSnO3 is covalent. The bottom of the conduction band is mainly dominated by Sn-5s states.

the band gap value when the TB-mBJ is used. GGA-PBE predicted an indirect-band gap value of 0.67 eV, which is in excellent agreement with other standard DFT calculations [19,21]. However, it is still much underestimated from the experimental value ranges [9–18]. In fact, the standard DFT-functional such as GGA and LDA are not able to describe exactly the exchange–correlation energy, due the existence of a derivative discontinuity of this energy with respect the number of electrons [40]. However, TBmBJ yields an indirect band gap value of 2.56 eV, which is in good agreement with other previous calculations using the same methods [21]. Therefore, the calculated band gap value becomes much closer to corresponding experimental value. The basic principle behind success of TB-mBJ is the introduction a parameter to change the relative weight of the two terms in the Becke–Johnson potential (for more details Ref. [27]). By comparing with the calculated hybrid functional values published in the literature [8,20]. The HSE06 revealed an indirect band gap value of 2.48 eV [8],

180 100

TDOS

Density of states (states/eV)

Ba-s Ba-p Ba-d

0.8 0.0 1.6

Sn-s Sn-p Sn-d

0.8

0 7.0

Ba-s Ba-p Ba-d

3.5 0.0 7.0

La-s La-p La-d La-f

3.5 0.0 7.0

Sn-s Sn-p Sn-d

3.5

0.0 1.6

O-s O-p

0.0 7.0

0.8

O-s O-p

3.5

0.0

0.0 -8

-4

0

4

-4

-8

8

0

E-Ef (eV)

4

E-Ef (eV)

TDOS

120 deep states

60 0 0.8 Density of states (states/eV)

Density of states (states/eV)

50 0 1.6

TDOS Shallow states

90

Ba-s Ba-p Ba-d

0.4 0.0 0.8

Sn-s Sn-p Sn-d

0.4 0.0 0.8

Sb-s Sb-p Sb-d

0.4 0.0 0.8

O-s O-p

0.4 0.0 -8

-4

0

4

8

E-Ef (eV) Fig. 3. Total and partial density of states of: (a) pure, (b) La- and (c) Sb-doped BaSnO3 by using TB-mBJ, respectively.

8

A. Slassi / Materials Science in Semiconductor Processing 32 (2015) 100–106

3

BaSnO3 La-doped BaSnO3

E3

Dielectric function (ε2)

Sb-doped BaSnO3

2 E4

1

E0 E2

E1

12 Absorption coeficient (10 4 xcm-1)

104

BaSnO3 La-doped BaSnO3 Sb-doped BaSnO3

10 8

visible light region

6 4 2 0

0 0

1

2

3

4

300

5

400

20

80

60

Reflictivity (%)

BaSnO3 La-doped BaSnO3

Transmittance (%)

500

600

700

800

Wavelength (nm)

Energy [eV]

Sb-doped BaSnO3

40

BaSnO3 La-doped BaSnO3 Sb-doped BaSnO3

15

10 visible light region

visible light region

5

20

0

0 300

400

500

600

700

800

300

400

500

600

700

800

Wavelength (nm)

Wavelenght (nm)

Fig. 4. (a) Imaginary part of dielectric function, (b) transmittance, (c) absorption coefficient and (d) reflectivity of pure-, La- and Sb-doped BaSnO3 by using TB-mBJ, respectively.

These results are in good agreement with the experimental measurements [11]. In the La-doped BaSnO3 case, as shown in Fig. 3(b), the donor-like energy bands derived from La-4f states are induced around the conduction band minimum, consistent with X-ray Photoemission Spectroscopy experiments [11]. Thus, the Fermi level shifts upward to the conduction band giving rise to n-type electrical conducting behavior. Hence, the Burstein–Moss effect [41,42], could be produced as those observed experimentally [12–14], leading to a blueshift in optical transparency of this doped systems. These characteristics are useful for n-type TCO [43]. In contrast, for Sb-doped BaSnO3 case, as shown in Fig. 3(c), deep donor states are appeared within the band gap derived from hybridization between Sb-5s and O-2p states. The experimental photoemission data of Sbdoped BaSnO3 sample also revealed occupied defect states within the band gap and serve as deep donors [18], which is in accordance with our DFT-DOS calculations. The Fermi level is localized below the bottom of the conduction band remains on the semi-conductivity behavior in BaSnO3, suggesting that the electrical conductivity could be not as intended due to large energy requited for injecting the

free electrons from these deep donor states to the conduction band. 3.3. Optical properties The calculated imaginary part of dielectric function,

ε2(ω), of pure, La- and Sb-doped BaSnO3 is shown in Fig. 4

(a). The curve of pure BaSnO3 clearly shows an energy threshold at about 2.65 eV, named E0, mainly comes from intrinsic electron transitions between O-2p states in the top of the valence band and the dominated Sn-5s states in the bottom of the conduction band. Usually, this energy value is referred to as the band gap. After doping, the threshold E0 shifts to higher energy of 3.6 eV for La-doping, named E1, while it shifts slightly to 2.8 eV for Sb-doping case, named E2. These shifts to higher energies correspond to the expansion of band gaps after doping, due to the Burstein–Moss effect [41,42] as often observed in the doped semiconductors. This means that the intrinsic electron transitions from the valence band to the conduction band will require more energy in the La- and Sb-doped BaSnO3 systems, which lead to decreasing in the intrinsic electrical conductivity for doped systems. However, we can see also from the imaginary part of

A. Slassi / Materials Science in Semiconductor Processing 32 (2015) 100–106

dielectric function curves the appearance of new peaks at energies about of 0.17 eV for La-doped BaSnO3, named E3, and 1.6 eV for Sb-doped BaSnO3, named E4. These energy values are in the range of IR- and visible-photons, respectively. The peak E3 at about of 0.17 eV for La-doped BaSnO3, may be due to extrinsic electron transitions between the La4f shallow donor states near the Fermi level and the higher unoccupied states, this suggest that the electron injections into the conduction band are started from low excitation energy. On the other hand, the peak E4 at 1.6 eV is originated from the extrinsic electron transitions between Sn-5s deep impurity states and unoccupied conduction band states, in Sb-doped BaSnO3 system. Meanwhile, the peak E4 energy value explains that the electron injection into the conduction band state requires the visible photon excitations, which could weaken the wavelength transmittance ability in the range necessary for TCO applications. In terms of photocatalytic applications, the wide band gap of BaSnO3, of 3.25 eV, make it unable to utilize the visible part of the solar spectrum. Therefore, the induced localized impurity energy levels in the band gap, as showed in Sb-doped BaSnO3, enhance the visible absorption ability. This improvement in the visible light photoactivity; might be useful for photocatalytic applications [44]. The transmittance is critical parameters for TCOs. So, a good TCO should have a large wavelength transmittance in the visible and UV games. Fig. 4(b) shows the transmittance of pure-, La- and Sb-doped BaSnO3. From this figure, one can clearly see that the pure BaSnO3 has an average transmittance in the visible range around of 80%, which is in accordance with the thin films BaSnO3 experimental measurement [12–14]. The main factor of this large transmittance in the IR and visible ranges is due, in fact, when the photon energy is less than band gap, photons are note absorbed, as shown in (c). So, such energy regions can be considered as transparent. However, the 80% value suggests that all photons that have less band gap energy are not transmittance. These because of some photons in this region are reflected by area of BaSnO3 materials, as shown in (d). After La- or Sb- doping, the transmittance of BaSnO3 is significantly changed. For La-doped BaSnO3, while the transmittance average in the IR- and visible ranges hardly affected by La-dopant, it is significantly increase in the UV range with a blue-shift owing to expansion of the band gap, consistent with the experimental works [14]. This could be considered as suitable for TCO applications. Unfortunately for Sb-doped BaSnO3 the average transmittance is obviously decline in the both IR- and visible ranges due to induced absorption of deep impurity states, as shown in Fig. 4(b), and the reflectivity of area in the Sb-doped BaSnO3, as shown in Fig. 4(d). In point of TCO application, this is not as intended. 3.4. Electrical conductivity The electrical conductivity of pure-, La- and Sb-doped BaSnO3 could be calculated from the band structure data that is fitted to semi-classic Boltzmann theory via the rigid band approach [33,34]. Hence, it is possible to calculate σ/τ as a function of n and T, but it is not possible the calculate σ itself without the knowledge of the scattering rate τ
1. In order to proceed, we used the excremental data from the Ref. [45]. The standard phonon–electron approximation were assumed

105

Table 2 Calculated electrical conductivity values, σ, of pure-, La- and Sb-doped BaSnO3 by using TB-mBJ, respectively. System

σ (Ω
1 cm
1)

Pure La-doped BaSnO3 Sb-doped BaSnO3

6.2  102 4.78  104 1.3  104

as propose by Ong et al. [46], from this purpose the scattering rate is given as τ ¼AT
1n
1/3(τ in s, T in K, n in cm
3), where A is a material constant. The experimental Seebeck coefficient at 1000 K was 170 μK/V, while the electrical conductivity was 1.2  104 Ω
1 m
1 for BaSnO3 ceramic [45]. By combined with our theoretical calculated, we obtained τ ¼1.837  10
5T
1n
1/3. The calculated electrical conductivity for pure-, La-, and Sb-doped BaSnO3, at 300 K that corresponds to the room temperature, is summarized in Table 2. From the values, the electrical conductivity is significantly increased for doped systems as compared to pure system. On the other hand, the Ladopant enhances the electrical conductivity of BaSnO3 more than Sb-dopant. Because this is due in fact that the Ladopand creates shallow donors near the bottom of the conduction band, therefore, the injection free electrons into the conduction band could be carried out from the additional energy levels are not more than 3kbT, while it is larger than 3kbT for deep states that created in the Sb-doped BaSnO3 systems. Therefore, the shallow donors may be ionized at the room temperature increasing the electrical conductivity by contrasting the deep donors require more energy. 4. Conclusion In this paper, we have investigated the structural, electronic, optical and electrical properties of La- and Sb-doped cubic perovskite BaSnO3 through the density functional theory (DFT) and semiclassical Boltzmann equations. The shallow donor states introduced by La-dopant enhance the electrical conductivity leading to blue-shift in the optical transparency, which are ideal for TCO devises. Whereas, the deep donor states created by Sb-dopant enhance the visibleRI absorption, might be of interest for other applications. An experimental point of view, our theoretical results are in good agreement with other previous experimental date. References [1] A. Iwan, I. Tazbir, M. Sibiński, B. Boharewicz, G. Pasciak, E. SchabBalcerzak, Mater. Sci. Semicond. Process. 24 (2014) 110–116. [2] M. Chen, Z.L. Pei, C. Sun, J. Gong, R.F. Huang, L.S. Wen, Mater. Sci. Eng. B 85 (2001) 212. [3] T. Minami, Semicond. Sci. Technol. 20 (2005) S35–S44. [4] K.L. Chopra, P.D. Paulson, V. Dutta, Prog. Photovolt. Res. Appl. 12 (2004) 69–92. [5] N. Romeo, A. Bosio, V. Canevari, M. Terheggen, L. Vaillant Roca, Thin Solid Films 431–432 (2003) 364–368. [6] Claes G. Granqvist, Sol. Energy Mater. Sol. Cells 91 (2007) 1529–1598. [7] Yukio Hinatsu, J. Solid State Chem. 122 (1996) 384. [8] David O. Scanlon, Phys. Rev. B 87 (2013) 161201. [9] B. Hadjarab, A. Bouguelia, M. Trari, J. Phys. D 40 (2007) 5833–5839. [10] N. Ahsan, N. Miyashita, M.M. Islam, K. Man Yu, W. Walukiewicz, Y. Okada, Appl. Phys. Lett. 100 (2012) 172111.

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