Density Functional Theory Study on Defect Feature of As Ga Ga As in Gallium Arsenide

We investigate the defect feature of AsGaGaAs defect in gallium arsenide clusters in detail by using first-principles calculations based on the density functional theory (DFT). Our calculations reveal that the lowest donor level of AsGaGaAs defect on the gallium arsenide crystal surface is 0.85 eV below the conduction band minimum, while the lowest donor level of the AsGaGaAs defect inside the gallium arsenide bulk is 0.83 eV below the bottom of the conduction band, consistent with gallium arsenide EL2 defect level of experimental value (Ec-0.82 eV). This suggests that AsGaGaAs defect is one of the possible gallium arsenide EL2 deep-level defects. Moreover, our results also indicate that the formation energies of internal AsGaGaAs and surface AsGaGaAs defects are predicted to be around 2.36 eV and 5.54 eV, respectively. This implies that formation of AsGaGaAs defect within the crystal is easier than that of surface. Our results offer assistance in discussing the structure of gallium arsenide deep-level defect and its effect on the material.


Introduction
As a kind of excellent semiconductor material, gallium arsenide is widely used in fast photoelectric devices and integrated circuit substrate [1] and so forth.As a compound semiconductor material, the defect problems of the undoped semi-insulating GaAs (SI-GaAs), in particular, the unique deep-level defects in the SI-GaAs single crystal material, such as EL2 (Ec-0.82eV) and EL6 (Ec-0.38 eV), which have an important influence on the photoelectric characteristics and the application of materials [2][3][4][5][6][7], are more complex than those of silicon and germanium.By various theoretical and experimental means, many researchers have studied the microstructures of gallium arsenide EL2 deep-levels.For example, Lagowski et al. put forward isolated As Ga antisite defect structure type [8], Wager and van Vechten put forward V Ga As Ga V Ga ternary complex defect structure type [9], Zou et al. put forward As Ga V As V Ga ternary complex defect structure type [10,11], and Morrow proposes the possible As Ga V Ga defect structures [12].Wosinski et al. pointed out that EL2 is not isolated defects [13].The steady and metastable energy levels of EL2 in semi-insulating GaAs were studied by Kabiraj and Ghosh [14].Ternary complex defect model of EL2 defect has been studied by using first-principles by Li et al. [7], and EL2 and EL6 defects and correlations of clusters have been preliminarily discussed by Zhao and Wu [15].These results have a certain role in promoting of the features and applications of gallium arsenide materials.On the basis of the above study on gallium arsenide clusters and defects preliminary [16][17][18][19], in this paper, the As Ga Ga As defect and its features have been studied by first-principles based on density functional theory (DFT), which gives out another kind of microstructure of gallium arsenide EL2 deep-level defects and offers assistance in the discussion of defect features of gallium arsenide deep-level and application of materials.

Computational Methods
Our total energy and electronic structure calculations were carried out within a revised Heyd-Scuseria-Ernzerhof (HSE06) range-separated hybrid functional as implemented in VASP code [20,21].In the HSE06 approach, the screening parameter  = 0.2 Å−1 and the Hartree-Fock (HF) mixing parameter  = 25% which meant 25% HF exchange with 75% GGA of Perdew, Burke, and Ernzerhof (PBE) [22]  exchange were chosen to well reproduce the experimental band gap (∼1.43 eV) of GaAs.The core-valence interaction was described by the frozen-core projector augmented wave (PAW) method [23,24].The electronic wave functions were expanded in a plane wave basis with a cut-off of 300 eV.A 3 × 3 × 3 k-point mesh within Monkhorst-Pack scheme [25] was applied to the Brillouin-zone integrations in total energy calculations.The internal coordinates in the defective supercells were relaxed to reduce the residual force on each atom to less than 0.02 eV⋅ Å−1 .All defect calculations were spin-polarized.In the calculation, firstly, defect structure models in various conditions were optimized and then static self-consistent calculation to the ground state structure was conducted and, finally, the corresponding band structure and density of states (DOS) were obtained.

Results and Discussions
3.1.The Properties of Perfect GaAs. Figure 1(a) shows the perfect GaAs supercell structure model.Figure 1(b) shows the calculated band structure and total density of states (DOS) of the perfect GaAs supercell structure model.
As can be seen from Figure 1(b), the perfect GaAs has a direct band gap structure, and its band gap is 1.5 eV at the Γ point, which is very close to the experimental value (1.43 eV), implying that the selected parameters are reasonable.

Surface Doping As
Ga Ga As Defect.Figure 2(a) shows the supercell structure model of GaAs (001) surface doping As Ga Ga As complex defect.The crystal thickness and vacuum thickness are 8.24 Å and 20.00 Å, respectively.The length of the base vectors A and B is for both 15.99 Å, whereas the length of the base vector C is 28.24 Å.Furthermore, vector angles , , and  are all 90 ∘ .Figure 2(b) shows the band structure and the total DOS of the GaAs (001) surface As Ga Ga As complex defect model.
As can be seen from Figure 2(b), the lowest donor defect level of the As Ga Ga As defect on the gallium arsenide crystal surface is 0.85 eV below the bottom of the conduction band, being consistent with gallium arsenide EL2 defect level of experimental value (Ec-0.82eV), which suggests that As Ga Ga As defect is one of the possible microstructures of gallium arsenide EL2 deep-level defects, and the formation energy of As Ga Ga As defect is 5.54 eV.
One can note that the existence of As Ga Ga As defect changes the band structure and the total DOS of GaAs.This leads to the formation of dangling bond between the neighbors of defects.As a result, the matching surface states can exchange their positions with holes and electrons of the gallium arsenide materials, which affected the photoelectric properties of GaAs materials directly.

Internal Doping As
Ga Ga As Defect.The supercell structure model of the internal deep layer doping As Ga Ga As defect is displayed in Figure 3(a).The distance between the As Ga Ga As defect and the upper interface is 5.65 Å. Figure 3(b) shows the supercell structure model of the internal shallow layer doping As Ga Ga As defect, and the distance between the As Ga Ga As defect and the upper interface is 2.83 Å. Figures 4(a As can be seen from Figure 4, the band structure and DOS of internal As Ga Ga As defect are insensitive to its position.The lowest donor defect level is below the bottom of the conduction band 0.83 eV, being consistent with gallium arsenide EL2 defect level of experimental value (Ec-0.82eV).This suggests that internal As Ga Ga As defect is one of possible gallium arsenide EL2 deep-level defects.Meanwhile, it increases donor level and acceptor level of defects, changes the total DOS of materials, and affects the photoelectric properties of GaAs materials directly, when comparing with the band structure of perfect GaAs as shown in Figure 1(b).The results indicate that the formation energy of internal As Ga Ga As defect is 2.36 eV, showing an independent-position character.Note that the internal As Ga Ga As defect is more stable than the surface As Ga Ga As one, suggesting that formation of As Ga Ga As deep-level defects in the crystal is easier than that on surface.

Conclusions
In this paper, we have carried out the As Ga Ga As deeplevel defect in gallium arsenide by using first-principles calculations based on hybrid density functional theory.Our results show that the lowest donor defect level on the gallium arsenide surface is 0.85 eV below the bottom of the conduction band, while the lowest donor defect level of the As Ga Ga As defect inside the gallium arsenide crystal is 0.83 eV below the bottom of the conduction band, consistent with gallium arsenide EL2 defect level of experimental value (Ec-0.82eV).The As Ga Ga As defect is one of the microstructures of the EL2 deep-level defects in gallium arsenide.We also found that the band structure and density of states of internal As Ga Ga As defect have no relationship with its position and the formation energy of internal As Ga Ga As defect is 3.16 eV, smaller than that of the defect on surface, suggesting that the formation of As Ga Ga As deep-level defects within the crystal is easier than that of surface relatively.The existence of As Ga Ga As defect increases donor level and acceptor level of defects and changes the total DOS of materials and atoms around the defect form the dangling bond.Consequently, the resulting surface states can exchange their positions with holes and electrons of the gallium arsenide materials, which affects the photoelectric properties of GaAs materials directly.

Figure 1 :
Figure 1: (a) Supercell structure model of perfect GaAs.(b) Band structure and the total DOS of perfect GaAs.The Fermi energy is set to zero.
) and 4(b) show the corresponding band structure and total DOS, respectively.

Figure 2 :
Figure 2: (a) Supercell structure model of the surface double antisite As Ga Ga As defect.(b) The band structure and the total DOS of GaAs (001) surface with double antisite As Ga Ga As defect.

Figure 3 :
Figure 3: Supercell structure model of internal double antisite As Ga Ga As defects.(a) Between the As Ga Ga As defects and the upper interface the distance is 5.653 Å.(b) The distance between the As Ga Ga As defects and the upper interface is 2.827 Å.

Figure 4 :
Figure 4: The band structure and the total DOS of GaAs with internal double antisite As Ga Ga As defects.(a) The distance is 5.653 Å between the deep As Ga Ga As defects and the upper boundary.(b) The distance is 2.827 Å between the shallow As Ga Ga As defects and the upper boundary.