First-principles calculations of electronic and optical properties of aluminum-doped β-Ga2O3 with intrinsic defects

Accepted Manuscript First-principles calculations of electronic and optical properties of aluminumdoped β-Ga2O3 with intrinsic defects Xiaofan Ma, Yuming Zhang, Linpeng Dong, Renxu Jia PII: DOI: Reference:

S2211-3797(17)30286-3 http://dx.doi.org/10.1016/j.rinp.2017.04.023 RINP 669

To appear in:

Results in Physics

Received Date: Revised Date: Accepted Date:

21 February 2017 11 April 2017 17 April 2017

Please cite this article as: Ma, X., Zhang, Y., Dong, L., Jia, R., First-principles calculations of electronic and optical properties of aluminum-doped β-Ga2O3 with intrinsic defects, Results in Physics (2017), doi: http://dx.doi.org/ 10.1016/j.rinp.2017.04.023

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First-principles calculations of electronic and optical properties of aluminum-doped β-Ga2O3 with intrinsic defects Xiaofan Ma, Yuming Zhang, Linpeng Dong, and Renxu Jia* (Wide Bandgap Semiconductor Technology Disciplines State Key Laboratory, Xidian Univ, Xi’an 710071, China;) *

Corresponding author.

Electronic mail: [email protected]

Abstract：In this manuscript, the effects of intrinsic defects on the electronic and optical properties of aluminum-doped β-Ga2O3 are investigated with first-principles calculations. Four types of defect complexes have been considered: AlGa2O3VO (Al-doped β-Ga2O3 with O vacancy), AlGa2O3VGa (Al-doped β-Ga2O3 with Ga vacancy), AlGa2O3Gai (Al-doped β-Ga2O3 with Ga interstitial) and AlGa2O3Oi (Al-doped β-Ga2 O3 with O interstitial). The calculation results show that the incorporation of Al into β-Ga2O3 leads to the tendency of forming O interstitial defects. And the bandgap of AlGa2O3 is 4.975eV, which is a little larger than that of intrinsic β-Ga2O3.When O vacancies exist, a defect energy level is introduced to the forbidden band as a deep donor level, while no defective energy levels occur in the forbidden band with O interstitials. After Al-doped, a slightly blue-shift appears in the intrinsic absorption edge, and an additional absorption peak occurs with O vacancy located in 3.69eV. Key Words: first-principle calculation; intrinsic defects; bandgap; absorption peak.

1

1. Introduction β-Ga2O3 is a wide bandgap semiconductor (~ 4.9 eV) with significant chemical and physical stabilities, which has gained widely interests in recent years [1, 2]. Compared with other wide bandgap semiconductor like SiC and GaN, β-Ga2O3 has higher breakdown voltages and faster electron drift velocity, and they could be manufactured at low cost with high volume [3]. With these advantages, β-Ga2O3 has been successively applied for the power devices, such as MESFET, MOSFET and SBD [4-6]. Besides, it is a promising candidate for use in UV optoelectronic devices [7, 8], resistance random access memory devices [9], high temperature gas sensors [10], semiconducting lasers [11], and solar cells[12, 13]. The bandgap of β-Ga2O3 should be tuned to realize high sensitive wavelength-tunable photodetectors or to introduce shallow impurity levels for good electronic properties [14]. The dopant of indium is a candidate for the bandgap engineering of Ga2O3 but only tunable bandgap from 3.8eV to 5.1 eV can be obtained [15]. In order to exert the advantage of wide bandgap of gallium oxide effectively in deep-UV transparent TCO applications, bandgap tunable films by doping Al were considered. Al is a candidate to enlarge the bandgap of β-Ga2O3 because Al2O3 has a bigger bandgap (8.8 eV for bulk material, 6.4 eV for amorphous Al2O3 films) and the similar electron structures of Al and Ga make the alloy (AlGa)2O3 possible. Until now, many experimental studies have been carried out to explore the electrical and optical properties of Al-doped β-Ga2O3. Kokubun et al [16] prepared β-Ga2O3 thin films grown on (0001) sapphire substrates by the sol-gel method and the X-ray diffraction showed that β-Ga2 O3 polycrystalline films were formed at heat-treatment temperatures above 600°C. While with increasing heat-treatment temperature over 900°C, the lattice constants of the β-Ga2O3 films decreased, yet the bandgap increased. 2

Oriented [401] β-Ga2O3 films were grown on sapphire substrate (0001) by pulsed laser deposition (PLD) technique by Goyal A et al[17], in which the crystalline structure and optical band gap were studied as a function of growth temperature, laser beam energy, annealing temperature and time. Similar results about band gap were also found. Fabi Zhang et al[18] deposited bandgap tunable (AlGa)2O3 films on sapphire substrates used pulsed laser deposition method and measured that the bandgap of (AlGa)2O3 films increased continuously from about 5 to 7 eV with the Al content covering the whole Al content range. However, there are few theoretical research about Al-doped β-Ga2O3 and no further exploration about electronic states consisting of the energy band in Al-doped β-Ga2O3 system. As we all know, intrinsic defects (vacancies and interstitials) play important roles on the properties of the material and even change the optical and electronic properties of the system. Especially the oxygen vacancies defects, they may vary the optical and even nonlinear optical properties of some materials such as LiNbO3 [19-21], ZnO, Al2 O3 and TiO2 [22-24]. For β-Ga2O3, many researchers have reported the impact of oxygen vacancies on the properties of the material and related devices [25, 26]. The intrinsic defects, such as oxygen vacancies and gallium interstitials can change the conduction type of β-Ga2O3. These defects also induce extra emission levels in the photoluminescence spectrum. So it is necessary to take the intrinsic defects into account in the calculations. But the Al-doped β-Ga2O3 with native defects has not been discussed systematically. Based on above-mentioned issues, we have performed systematic studies on the Al-doped β-Ga2O3 with native defects using first-principles calculations based on density functional theory (DFT), which have been used for many studies of the material properties such as optics, 3

magnetism and electronic structures [27-29]. In this paper, the atomic structures, formation energies, electronic properties and optical properties of the Al-doped β-Ga2O3 with native defects are researched. For comparison, corresponding undoped defective Ga2O3 systems have also been considered. Description of the computational method are present in Section 2. Results and discussion are shown in Section 3. Section 4 provides a final brief conclusion.

2. Computational methods According to previous study[30], we considered a 1×2×2 supercell based on monoclinic β-Ga2O3 , including 32 Ga atoms and 48 O atoms as shown in Fig. 1. We constructed an Al-doping model by substituting one Al atom for one Ga atom, which is denoted by AlGa2O3. There are two different locations for gallium atoms and three different sites for oxygen atoms. We confirmed that the Ga in octahedron are the more stable substitution sites than that of tetrahedral for aluminum atom by comparing the formation energies of the two Al-doped structures. Many intrinsic defects have to be considered in the Al Ga2O3 structure, in which O vacancy (Al Ga2O3 VO), Ga vacancy (AlGa2O3VGa), Ga interstitial (AlGa2O3Gai) and O interstitial (AlGa2O3Oi) are represented as 1, 2 and 3, as labeled in Fig.1. In order to confirm the Ga and O vacancies sites, we have compared the formation energies of defective AlGa2O3 structures, which is similar to the determination of Al substitution. For the sites of interstitial Ga and O, we adopted the reference results, in which interstitial Ga and O atoms locate at the same site[31]. All models presented in this study were calculated using Cambridge Serial Total Energy Package (CASTEP) code which is based on the density functional theory (DFT)[32]. Under the Generalized Gradient Approximation (GGA) functional[33], the exchange-correlation energy was described with the Perdew-Burke-Ernzerhof (PBE) scheme. Using the ultrasoft pseudo-potential 4

method,

electron–ion

interactions

have

also

been

modeled.

The

electronic

states

3 4 4 , 2 2 , and 3 3 are considered as the valence states for Ga ,O and Al, respectively. In order to avoid the error caused by the underestimation of the bandgap, the PBE scheme of General Gradient Approximation plus Hubbard U(GGA+U) [34, 35] was used to describe the exchange correlation effect, which can give an accurate description by controlling the Hubbard U parameter[30]. Under this correction, the reasonable results can be obtained. Before the properties calculation, the structural relaxation was employed. The internal coordinates and lattice parameters were relaxed with Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization method[36]. With an energy cutoff of 450 eV, the electron wave functions were expanded in plane wave. The energy tolerance, tolerance of the force, maximum displacement and maximum stress were 1× 10 eV/atom, 0.03 eV/Å, 0.001 Å and 0.05 Gpa, respectively. A 4×8×4 mesh of Monkhorst–Pack k-points was used for integrations of the Reduced Brillouin zone[37].

5

Fig.1. The Al-doped β-Ga2O3 supercell with various intrinsic defects. The Ga, O and Al atoms are demonstrated by grown, red and purple spheres, respectively. Number 1and 2 represent the vacancy sites of O and Ga, respectively. The green sphere labelled with number 3 denotes the interstitial sites for both O and Ga.

3 Results and discussion 3.1 Atomic structure and formation energy The lattice parameters of β-Ga2O3 calculated are a=12.52 Å, b=3.09 Å and c=5.89 Å, β=103.69 º. The lattice parameters from the GGA calculations are in good agreement with the experimental and other theoretical values shown in Table1, which means our calculated results are reliable. Based on the calculated structure, the supercells of Al-doped β-Ga2O3 are optimized. Compared with the intrinsic structure, the volume of Al Ga2O3 decreases by 4.7‰ and the average bond length for Al-O bonds is smaller than that of corresponding Ga-O bonds. These differences come from the smaller Al3+ radius (0.535 Å) than Ga3+ radius (0.62 Å). It is necessary to calculate the formation energy in order to confirm that whether native defects are easy to form in AlGa2O3 systems. The defect formation energy is defined as    6

 −  ＋ ∑ 

,

where  is the total energy of the supercell with defect,

 is the total energy of perfect intrinsic supercell,  denotes the number of atom(i) removed from ( > 0) or added to (  < 0) the perfect supercell, and



represents the chemical

potential of the corresponding atom. The chemical potentials of Al and O satisfy the relation of 3µ$ + 2µ&'  µ&' () , which is strongly related with the atmosphere of the synthesis process. The upper limit of the O chemical potential in O-rich atmosphere is given by the energy of O2, and the lower limit in O-poor atmosphere corresponds to that in bulk Al2O3 . The calculated formation energy of AlGa2O3 is shown in Table 1, and the calculated formation energies for native point defects in Ga2O3 and Al Ga2O3 systems are shown in Table 2. Corresponding undoped defective Ga2O3 systems are represent as Ga2O3 -VO, Ga2O3-VGa, Ga2O3-Gai and Ga2O3-Oi. It is well known that structures with lower formation energy are more easily formed. From Table 2, it is found that in both Ga2O3 and AlGa2O3 systems, the formation energy of O vacancies are the lowest under O-poor atmosphere while it is O interstitial under O-rich atmosphere. Therefore, only these two types of native defects in undoped Ga2O3 and Al Ga2O3 systems are considered in the following calculations and analyses. The formation energy of O vacancy in AlGa2O3 is larger than which in undoped Ga2O3, while the formation energy of O interstitial in AlGa2O3 is lower than which in undoped Ga2O3 . In order to explain the differences of the formation energy, schematic representation of atomic positions for VO and Oi in Ga2O3 and AlGa2O3 are presented in Fig. 2 .The average bond lengths for Ga-O bonds in undoped Ga2O3 and Al-O bonds in AlGa2O3 systems for the same site atoms are shown in Fig.3. The schematic representations in Fig.2(a) indicate the variations of the atoms positions after O vacancy introduced in Ga2O3 and Al Ga2O3 systems, in which the bond length variations in AlGa2O3 7

are more obvious than those in Ga2O3. So there are obvious lattice distortions around Al impurity than Ga atom, which cause the larger formation energy when O vacancy introduced in AlGa2O3 system than undoped Ga2O3. In the meantime, from Fig.3, it is found that after O vacancy introduced, the change of average bond length for Al-O bonds in AlGa2O3 systems is larger than that of Ga-O bonds in Ga2O3 systems for the same site atom, which is consistent with the conclusion above. As shown in Fig.2(b) and Fig,3, the lengths change of four Ga-O bonds in Ga2O3 system are more obvious than Al-O bonds in AlGa2O3 system, meanwhile the change of average bond length for Al-O bonds in AlGa2O3 systems is the same as the Ga-O bonds in Ga2O3 systems , which implies that the more obvious lattice distortion occurs in undoped Ga2O3 system after O interstitial defect introduced comparing with the AlGa2O3 system. So the formation energy of Ga interstitial in undoped Ga2O3 system is larger than that in AlGa2O3 system, and the incorporation of Al in β- Ga2O3 leads to the tendency of forming O interstitial defects.

Table 1 The optimized structures of β-Ga2 O3 compared with theoretical and experimental results Functional

Optimized structure a(Å)

b(Å)

c(Å)

β(°)

Calculated β-Ga2O3

GGA

12.52

3.09

5.89

103.68

Ref[38]

GGA

12.44

3.08

5.88

103.71

Ref[39]

HSE06

12.27

3.05

5.82

103.82

Ref[40]

B3LYP

12.34

3.08

5.87

103.90

Experimental[41]

-

12.23

3.04

5.80

103.70

8

Table 2. Calculated formation energies for native point defects in Ga2O3 and AlGa2O3 systems under O-poor and O-rich condition. Defect

VO

VGa

Gai

Oi

Condition

formation energies (eV) Undoped Ga2O3

AlGa2O3

O-poor

0.867

1.055

O-rich

4.241

4.429

O-poor

8.648

8.381

O-rich

3.617

3.321

O-poor

7.504

4.526

O-rich

12.564

9.586

O-poor

6.827

6.620

O-rich

3.454

3.245

9

Fig.2. Schematic representation of atomic positions for (a) Ga2O3-VO and AlGa2O3VO (b) Ga2O3-Oi  00] directions. and AlGa2O3Oi along [001] and [1

10

Fig.3.The average bond lengths for Ga-O bonds in undoped β-Ga2O3 and Al-O bonds in Al Ga2O3 systems for the same site atom.

11

Fig.4. Band structures of (a) β-Ga2O3, (b) AlGa2O3, (c)Ga2 O3-VO(d) Al Ga2O3 VO, (e) Ga2 O3-Oi, and (f) Al Ga2O3Oi 3.2 Electronic structures In order to further investigate the effects of the intrinsic defects on the electronic structure of Al-doped β-Ga2O3, the band structures and partial density of states (PDOS) are calculated shown in Figs.4 and 5. As shown in Fig.4(a) and 4(b), the bandgap of Al Ga2O3(4.975eV) is a little bigger than the 12

intrinsic β-Ga2O3 (4.933 eV) with a direct band structure, which is consistent with experimental results.[1, 2, 18] The defect energy levels are introduced to the forbidden bands as the deep donor levels shown in Fig.4(c) and 4(d). Due to the presence of oxygen vacancy, three unpaired electrons exist in the unit cell and a deep donor level occurs in band gap. However, no defective energy levels occur in the forbidden bands in the Ga2O3-Oi and AlGa2O3Oi models displayed in Fig.4(e) and (f), which may be since the energy levels introduced from O Interstitial atom come into the conduction band and enhanced state densities in conduction band bottom (CBM). The bandgaps of the defect models are slightly changed, which may be due to the relatively large concentration of intrinsic defects for the size of models. The partial density of states (PDOS) of β-Ga2O3, AlGa2O3, Ga2O3 -VO, Al Ga2O3 VO, Ga2O3-Oi and AlGa2O3Oi systems provide the contributions of various states to the energy bands. As shown in Fig.5, the Ga-4s, Ga-4p and O-2p states all contributed significantly to the valence band maximum(VBM) of all the systems. While for all Al-doped systems, Al-3p state also contributed a little to the VBM. And the CBM is contributed from Ga-4s and Ga-4p states. Meanwhile for Al-doped systems, Al-3p and Al-3s state contribute a little. In the two models with O vacancies presented in Fig.5(c) and (d), Ga-4s, Ga-4p, O-2p contribute to defective level in the forbidden band can be found, while Al-3p states also contribute a little to the Al Ga2O3 VO system. Because of the formation of three unpaired electrons of Ga or Al due to the O vacancy, Ga-4s and Ga-4p states contributed more to defective levels. In Ga2O3-Oi and AlGa2O3Oi models shown in Fig.5(e) and (f), O-2p states contributed more to the CBM than the models without O interstitial defects shown in Fig.5(a) and (b), which is consistent with the 13

analysis about energy bands in Fig.4(e) and (f) above. For the O interstitial atom, the peaks of state density arise at 0eV and 6eV, which means defective levels are introduced into the VBM and CBM.

Fig.5. Density of states of (a) β-Ga2O3, (b) AlGa2O3 , (c)Ga2O3-VO(d) AlGa2O3VO, (e) Ga2O3-Oi, and (f) AlGa2O3Oi

14

Fig.6. Band structures and PDOS of (a) Ga2O3-VO and (b) AlGa2O3 VO 3.3 Optical properties It is well known the matter of optical properties can be described by means of the dielectric function:

ε*ω+  ε *ω+ + ,ε *ω+

(1)

The dielectric function is mainly connected with the electronic response, in which the imaginary part of the dielectric function ε *ω+ is related to the dissipation (or loss) of energy within the medium while the real part ε is related to the stored energy within the medium. The imaginary part of complex dielectric function ε *ω+ is calculated by summing the transitions between occupied and unoccupied electronic states, which is calculated as follows[42]:  π.  .

ε *ω+  - / ω. 0 ∑,8 1〈,|4|5〉 7 *1 − 7 +×δ98,: − ,: − ω; ) <

(2)

Where = is the electron charge, > is the mass of free electrons, ω is the frequency of incident 15

photons., and 5 are the initial and final states, 4 is the dipole matrix, respectively. 7 denotes the Fermi distribution function for ,-th state with wave function vector <. According to the Kramers-Kronig transformation, the real part ε can derived from the imaginary ε , which can be given as follows: @ ω′ ε . 9ω′; ω′



ε *ω+  1 + π ? 1

(3)

*ω′. ω. +

where ? denotes the principal value of the integral. From the dielectric function, absorption coefficient can be derived and defined by: ⁄

A*ω+  √2*ω+CDε *ω+ + ε *ω+ − ε *ω+E

(4)

The Imaginary part of complex dielectric function G *H+ and absorption spectra of the intrinsic and Al-doped β-Ga2O3 with two types of defects are shown in Fig.7 and Fig.8. In general, the absorption spectra has a similar tendency with the previous G *H+ results and to explore the optical properties, we can only analyze absorption spectra. In the Al Ga2O3 model, a slightly blue-shift occurs in the intrinsic absorption edge because of an enlarged optical band gap comparing with Ga2O3. When intrinsic defects introduced, there were red-shifts of the optical absorption edges can be found in AlGa2O3 systems, which are due to the defective levels. The absorption peaks in the defective models are as follows: Ga2O3-VO (~3.69eV) and AlGa2O3VO (~5.32eV), which are resulted separately from transition processesⅠand Ⅱshown in Fig.6. The absorption peak in 3.69eV in Ga2O3-VO system may be introduced by processⅠ: the transition between O-2p state in VBM and Ga-4s state in CBM. The absorption peak in 5.32 eV in AlGa2O3VGa system may be introduced by processⅡ: the transition from O-2p state in defective level to Ga-4s state and Al-3p state in CBM. It is noticed that the peak in 3.69eV is with the higher intensity, which may be due to the parallel band effect. 16

Fig.7. Imaginary part of complex dielectric function of the intrinsic and Al-doped β-Ga2O3 with two types of defects

Fig.8. Absorption spectra of the intrinsic and Al-doped β-Ga2O3 with two types of defects

4 Conclusions In conclusion, we investigated the atomic structure, formation energy, electronic and optical properties of Al-doped β-Ga2O3 with native defects. For comparison, undoped β-Ga2O3 with native defects have also been calculated. After Al-doped, the volume of AlGa2O3 decreased a little because of the smaller radius of Al3+. Taking the intrinsic defects into consideration, the formation energy results indicated that interstitial O is easier to form under O-rich atmosphere condition. Under O-poor atmosphere condition O vacancies are energy favorable. So we only research the 17

systems with O vacancy and O interstitial defects. The formation energy of O interstitial in AlGa2O3 is lower than which in undoped Ga2O3, means that the incorporation of Al into β-Ga2O3 leads to the tendency of forming O interstitial defects. In order to explain the differences of the formation energy, we analyzed the corresponding variation of atomic positions and the average bond lengths. More obvious lattice distortion occurs in undoped Ga2O3 system after O interstitial defect introduced comparing with the AlGa2O3 system. By exploring the band structures and state densities, we found that the bandgap of Al Ga2O3 is 4.975eV, which is a little bigger than intrinsic β-Ga2O3 and consistent with experimental results. The Ga-4s, Ga-4p and O-2p states contribute significantly to the VBMs of all systems. And the CBMs are mainly constituted by Ga-4s and Ga-4p states. For the AlGa2O3VO model, a defect energy level contributed from Ga-4s, Ga-4p, O-2p states is introduced to the forbidden band, as a deep donor level, while Al-3p state also contributes a little. For the Al Ga2O3 Oi model, no defective energy levels occur in the forbidden band, since the energy levels introduced from O Interstitial atom come into the conduction band and enhance state densities in conduction band bottom. From the imaginary part of complex dielectric function and absorption spectra, we found that a slightly blue-shift occurs in the intrinsic absorption edge for the Al Ga2O3 model, because of an enlarged optical band gap comparing with Ga2O3. There are absorption peaks in the defective models: Ga2O3-VO (~3.69eV) and AlGa2O3VO (~5.32eV). Combining with the energy bandgaps and PDOS results, we find the corresponding transition processes.

18

Acknowledgements Authors would like to acknowledge that this work is supported by the National Natural Science Foundation of China (Grant No. 51472196) and Shaanxi New-star Plan of Science and Technology (Grant No. 2016KJXX-63).

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