Abstract
Advanced semiconductor superlattices play important roles in critical future hightech applications such as aerospace, highenergy physics, gravitational wave detection, astronomy, and nuclear related areas. Under such extreme conditions like high irradiative environments, these semiconductor superlattices tend to generate various defects that ultimately may result in the failure of the devices. However, in the superlattice like GaAs/AlAs, the phase stability and impact on the device performance of point defects are still not clear up to date. The present calculations show that in GaAs/AlAs superlattice, the antisite defects are energetically more favorable than vacancy and interstitial defects. The As_{X} (X = Al or Ga) and X_{As} defects always induce metallicity of GaAs/AlAs superlattice, and Ga_{Al} and Al_{Ga} antisite defects have slight effects on the electronic structure. For GaAs/AlAs superlattice with the interstitial or vacancy defects, significant reduction of band gap or induced metallicity is found. Further calculations show that the interstitial and vacancy defects reduce the electron mobility significantly, while the antisite defects have relatively smaller influences. The results advance the understanding of the radiation damage effects of the GaAs/AlAs superlattice, which thus provide guidance for designing highly stable and durable semiconductor superlattice based electronic and optoelectronics for extreme environment applications.
Background
The superlattice (SL) is an artificial material consisting of alternating thin layers of two or more different components. The (GaAs)_{n}/(AlAs)_{m} is one of the most important SL since the development of high electron mobility transistors (HEMT) and quantum cascade lasers (QCLs) a few decades ago [1,2,3,4,5,6]. Recently with the advances of film epitaxy and nanofabrication techniques, the (GaAs)_{n}/(AlAs)_{m} based SLs and nanodevices with (n + m) ranging from 2 to 10 have demonstrated exciting physical properties related to luminescence and optical absorption, twophonon absorption, and Raman as well as infrared spectra, which thus found promising applications in optoelectronics, sensing, LED, energy and laser related civilian and industrial areas [7,8,9,10,11,12]. Meanwhile, toward other critical hightech applications such as aerospace, highenergy physics, gravitational wave detection, astronomy, space travel, nuclear and national security related areas, the semiconductor SLs and devices are exposed to different radiation environments, i.e., Xray, neutrons, electrons, ions, etc., which may result in the generation of defects containing impurities, vacancies, interstitials, antisites, and complex of these. Since the semiconductor materials and related physical properties play an important role in operating and functioning these electronic devices and integrated circuits, small amounts of defects may drastically change their optical and transport properties, especially in multilayer systems [13].
The effects of foreign impurities or intrinsic defects on the semiconductor SLs and their component materials have been extensively investigated in the past decades. Zollo et al. have employed density functional theory (DFT) method to investigate the stability of point defects in GaAs, and found that the antisite defects were more favorable [14]. Kahaly et al. have studied GaAs/AlAs SL structure by DFT method and found the arsenic vacancy (V_{As}) defect at and near the interface led to a conducting quasi 2DEG between insulating dielectric arsenide [7]. Spasov et al. have studied the effects of nitrogen impurities on carrier transport and electronhole recombination in GaAs/AlAs SL diodes [9]. They reported that the N impurities modified the energy of the electronic miniband and impeded electron diffusion through the SL miniband, which may lead to a strong radiative recombination of electronhole pairs [9]. Wang et al. studied the interdiffusion induced by the Zn impurity in GaAs/AlAs SL structures employing an ab initio molecular dynamics (AIMD) method [15]. Their results suggested that the Zn diffusion was assisted by the groupIII elements, which were ejected into the interstitial channel and diffused rapidly, thereby disordering the superlattice [15]. Mitra and Stark found that the presence of vacancies enhanced the Ga/Al intermixing in GaAs/AlAs SL, resulting from the proposed twoatom ring mechanism of diffusion [16]. Recently, an AIMD simulation of radiation response of GaAs/AlAs SL has been carried out [17], in which the minimum energies for each atom to be permanently displaced from its lattice site have been determined, the pathways for defect generation have been provided, and the types of created defects have been identified. It revealed that the created Ga (or Al or As) Frenkel pair and As_{Ga}Ga_{As} antisite pair have profound effects on the density of state distribution and band structure of GaAs/AlAs SL [17].
So far, the stability of point defects in SL structure and the transport properties like carrier mobility still remain unknown. It is thus of vital importance to investigate how the presence of vacancy, interstitial and antisite defects influences the structural stability and electrical properties of GaAs/AlAs SL. In this study, the phase stability of single Ga (or Al or As) vacancy, single Ga (or Al or As) interstitial and single Ga_{As} (or Al_{As} or As_{Ga} or As_{Al}) antisite defects have been studied. It is shown that the antisite defects are energetically more favorable than vacancy and interstitial defects. The band structures of these defective states have been investigated by the hybrid DFT method, which incorporates a portion of exact exchange from Hartree–Fock theory with the rest of the exchangecorrelation energy from other sources (ab initio or empirical) [18], and is expected to offer a more accurate description of electronic structure of semiconductor materials than the standard DFT. In particular, the electron mobility has been predicted. It turns out the interstitial and vacancy defects reduce the electron mobility significantly, while the antisite defects have relatively smaller influences. This work will advance the understanding of the radiation damage effects of the semiconductor superlattice and provide guidance for designing highly stable and durable semiconductor superlatticesbased electronic and optoelectronics for extreme environment applications.
Methods
In this study, the structural relaxations are carried out within the standard DFT framework and the band structures are calculated by the hybrid DFT in the framework of HeydScuseriaEmzefhof (HSE) [19] based on the relaxed structures. All calculations are carried out employing Vienna Ab Initio Simulation Package (VASP) [20]. Projector augmentedwave pseudopotentials are used to describe the interaction between ions and electrons, and the exchangecorrelation effects are treated using the local density approximation in the CeperleyAlder parameterization [21]. The convergence criteria for total energies and forces are 10^{−4} eV and 10^{−3} eV/Å, respectively. The origin point group of AlAs and GaAs crystal is the T_{d} group of zinc blende, as shown in Fig. 1a. The illustration of considered point defects is provided in Fig. 1b. The GaAs/AlAs SL containing two monolayers of GaAs alternating with two monolayers of AlAs is considered in this study and the geometrical configuration is illustrated in Fig. 2, together with the considered point defects.
Results and Discussion
Ground State Properties of GaAs and AlAs
As shown in Table 1, the lattice constants of bulk GaAs and AlAs are determined to be 5.61 and 5.63 Å, respectively, which agree well with the experimental and other theoretical values [22,23,24]. It seems that the lattice mismatch between GaAs and AlAs is small, and the lattice constant of GaAs/AlAs SL is set to be the intermediate value of 5.62 Å. The bulk modulus is calculated by \( B=\frac{1}{3}\left({C}_{11}+2{C}_{12}\right) \) [25], where the C_{11} and C_{12} represent the elastic constants. The bulk modulus of GaAs is calculated to be 76.3 GPa, which is close to the result of 76.5 GPa for AlAs. These results are in reasonable agreement with the theoretical and experimental data [22, 26, 27].
The Defect Formation Energy in GaAs/AlAs Superlattice
For GaAs/AlAs SL and bulk states, the defect formation energy is calculated by \( {E}_f={E}_{def}{E}_{undef}+\sum \limits_i\Delta {n}_i{\mu}_i \) [28]. Here, E_{def} is the total energy of the defective simulation cell after relaxation, E_{undef } is the total energy of the relaxed ideal supercell, Δn_{i} is the change in the number of species i (i = Ga, Al, or As), and μ_{i} is the chemical potential of species i [28].
For bulk XAs (X = Al or Ga), the chemical potentials of As and X obey the following constrains: \( {\mu}_X\le {\mu}_X^{bulk} \), \( {\mu}_{As}\le {\mu}_{As}^{bulk} \), and \( {\mu}_{As}+{\mu}_X={\mu}_{XAs}^{bulk} \), where \( {\mu}_X^{bulk} \), \( {\mu}_{As}^{bulk} \), and \( {\mu}_{XAs}^{bulk} \) correspond to the total energy of bulk X, bulk As and bulk XAs, respectively. The defect formation energies under Xrich condition, i.e., \( {\mu}_X={\mu}_X^{bulk} \) and \( {\mu}_{As}={\mu}_{XAs}^{bulk}{\mu}_X^{bulk} \), and Asrich condition, i.e., \( {\mu}_{As}={\mu}_{As}^{bulk} \) and \( {\mu}_X={\mu}_{XAs}^{bulk}{\mu}_{As}^{bulk} \), are summarized in Table 2. For GaAs, under Asrich conditions the As_{Ga} (As occupying the Ga lattice site) antisite defect is found to be the most energetically favorable, as indicated by the smallest formation energy of 1.57 eV. The next favorable defect is the Ga_{As} (Ga occupying the As lattice site) antisite defect, with the formation energy of 2.31 eV. The As interstitial (As_{int}) has the largest formation energy of 5.20 eV, suggesting that it is more difficult to form than other considered point defects. Under Garich conditions, the V_{Ga}, As_{int} and As_{Ga} defects have larger formation energies, and the V_{As}, Ga_{int} and Ga_{As} defects have smaller formation energies, as compared with the Asrich condition. Obviously, the defect stability depends on the chemical environment. As compared with GaAs, the defect formation energies in AlAs are generally larger, except the cases of As_{int} and As_{X} (X = Al or Ga) under Asrich conditions. The As_{Al} and Al_{As} antisite defects are determined to be the most favorable defect under Asrich and Alrich conditions, respectively. Similar to the case of GaAs, the As_{int} is also unfavorable in AlAs. The defect formation energies under Asrich and Xrich (X = Ga or Al) conditions in bulk XAs are plotted in Fig. 3. Figure 3a shows that the As_{Ga} and Ga_{As} antisite defects are more favorable under Asrich and Garich conditions, respectively. It is noted that the As_{Al} antisite defect is preferable in most cases (see Fig. 3b). Under Alrich condition, the phase stability of Al_{As}, V_{As} and As_{Al} defects are close to each other, as indicated by the formation energies of 3.0, 3.16 and 3.24 eV, respectively. Also, we find that in both GaAs and AlAs, the nonfavorability of As_{int} is independent of the chemical environment. Zollo et al. carried out firstprinciples calculations on GaAs and their DFT results showed that the formation energies of As_{Ga} and Ga_{As} were smaller than those for vacancy and interstitial defects [14], which are consistent with our results.
The E_{f} in GaAs/AlAs SL structure are also calculated under Asrich condition, i.e., \( {\mu}_{As}={\mu}_{As}^{bulk} \), \( {\mu}_{Al}={\mu}_{Al As}^{bulk}{\mu}_{As}^{bulk} \), and \( {\mu}_{Ga}={\mu}_{Ga As}^{bulk}{\mu}_{As}^{bulk} \), and cationrich condition, i.e., \( {\mu}_{Al}={\mu}_{Al}^{bulk} \),\( {\mu}_{Ga}={\mu}_{Ga}^{bulk} \) and \( {\mu}_{As}=\left({\mu}_{SL}^{bulk}{n}_{Al}\times {\mu}_{Al}^{bulk}{n}_{Ga}\times {\mu}_{Ga}^{bulk}\right)/{n}_{As} \), where n_{Al}, n_{Ga}, and n_{As} represent the number of Al, Ga and As atoms in the simulation cell, respectively. As shown in Table 3, the Al_{Ga} defect has negative formation energies, i.e., − 0.62 and − 0.27 eV under Asrich and cationrich conditions, respectively, indicating that the formation of Al_{Ga} antisite defect is an exothermic process. As for Ga_{Al} defect, the formation energies are as small as − 0.01 eV under Asrich condition and 0.29 eV under cationrich condition. Obviously, the formation of Al_{Ga} and Ga_{Al} antisite defects in the GaAs/AlAs SL structure are much easier than other point defects. Under Asrich condition, the formation energies of the second favorable defects of As_{Ga} and As_{Al} are determined to be 1.67 and 1.74 eV, respectively. For the interstitials, the phase stability both follows the trend of Ga_{int} > Al_{int} > As_{int} under Asrich and cationrich conditions. The defect formation energies in GaAs/AlAs SL structure are also plotted in Fig. 3c. As compared with the bulk GaAs, the point defects in GaAs/AlAs SL are generally more difficult to form, except the case of As_{int} (see Fig. 3a, c). The formation energies of As_{int} in bulk GaAs are 5.20 and 5.81 eV under Asrich and Garich conditions, which are slightly larger than the corresponding values of 5.01 and 5.76 eV in GaAs/AlAs SL. As shown in Fig. 3b and c, the stability of point defects in bulk AlAs and SL structure shows different character. The Al_{As} and As_{int} defects are more energetically favorable in GaAs/AlAs SL than bulk AlAs, whereas V_{As} defect is more preferable in bulk AlAs than SL structure. It is noticeable that under Asrich and Alrich conditions, the formation energies of Al_{int} in bulk AlAs are comparable to that in GaAs/AlAs SL. Similar to the case of Al_{int}, the V_{Al} defect in bulk AlAs and SL structure show similar favorability, as indicated by the comparable formation energies. In the case of As_{Al} defect, the formation energy under Asrich condition is smaller (1.46 eV) in SL structure, whereas under cationrich condition, the value is smaller (3.10 eV) in bulk AlAs, suggesting that the stability of As_{Al} depends on the chemical environment.
Comparing the defect stability in bulk AlAs, GaAs and GaAs/AlAs SL, we find that the antisite defects are always more preferable than vacancies and interstitials, especially for the cases of Ga_{Al} and Al_{Ga} in GaAs/AlAs SL. It is also noted that under Asrich and cationrich conditions, the As_{int} defect is the most difficult to form in both bulk states and GaAs/AlAs SL structure.
The Effects of Point Defects on the Band Structures of GaAs/AlAs Superlattice
The Pristine State of GaAs/AlAs Superlattice
The band gaps for bulk GaAs, AlAs and GaAs/AlAs SL are summarized in Table 4, and their band structures are presented in Fig. 4. The hybrid DFT calculations determine the direct band gap of GaAs to be 1.44 eV (see Fig. 4a), which agrees well with the experimental value of 1.52 eV [29] and other calculations [24]. By contrast, the standard DFT predicts a band gap value of 0.5 eV, which largely underestimates the band gap of GaAs. For AlAs, the band structure is of indirect character and the hybrid DFT band gap is 2.16 eV (see Fig. 4b), which is 0.85 eV larger than the DFT result and in good agreement with the experimental value of 2.22 eV [23]. As shown in Fig. 4c, the band gap of GaAs/AlAs SL is determined to be direct and it is consistent with the study of Botti et al., who found the band gap of (GaAs)_{m}/(AlAs)_{m} SL (m ≥ 2) to be direct at the Γ point [3]. In our calculations, the direct band gap for GaAs/AlAs SL is determined to be 2.06 eV by hybrid DFT method, which is in agreement with the experimental value of 2.10 eV [30].
The Effects of Antisite Defects on the Band Structure of GaAs/AlAs Superlattice
In GaAs/AlAs SL structure, the Ga_{Al} and Al_{Ga} antisite defects are more energetically favorable than other point defects. As shown in Fig. 5a and b, the band structures of Ga_{Al} and Al_{Ga} defective states are very similar to that of the pristine state and the band gaps are determined to be 1.98 and 2.01 eV, respectively. This should be due to the fact that the Al and Ga chemical elements have similar valence electron configuration, i.e.,3s^{2}3p^{1} for Al and 4s^{2}4p^{1} for Ga, and no extra electrons or holes are introduced upon the formation of Ga_{Al} and Al_{Ga} antisite defects. The band structures for As_{Ga} and As_{Al} defective states are depicted in the Fig. 5c and d. It turns out that these two defects modify the band structure of GaAs/AlAs SL considerably. Both the As_{Ga} and As_{Al} antisite defects introduce extra electrons and act as ntype dopants. The impurity levels are found to be far from the valence bands and cross the fermi level, as shown in Fig. 5c and d. These deep defect levels may act as the recombination center for carriers.
Figure 6 presents the band structures and partial density of state (PDOS) of defective SL with Ga_{As} and Al_{As} defects. As shown in Fig. 6a, the band structure for Ga_{As} defective SL is of spin splitting character. In the spindown subbands, the fermi level passes through the defect levels introduced by the Ga_{As} defect, indicative of halfmetallic character of the defective SL. According to the definition of halfmetallic gap [31], the band gap of Ga_{As} defective state is about 0.10 eV. As shown in the PDOS of the defective SL with Ga_{As}, the spindown subbands near the fermi level are mainly contributed by p partial waves. Due to the similar valence electron configurations between Ga and Al atoms, the calculated spinup and spindown band structures of Al_{As} defective state are determined (see Fig. 6b), and the band gap is calculated to be 0.15 eV. Overall, the Al_{Ga} and Ga_{Al} antisite defects have negligible effects on the electronic structure of GaAs/AlAs SL. It is also noted that the defective SL with As_{Al} and As_{Ga} defects show metallicity, while the defective SLs with Ga_{As} and Al_{As} are halfmetallic.
The Effects of Vacancy Defects on the Band Structure of GaAs/AlAs Superlattice
The band structures of SL structure with different vacancies are plotted in the Fig. 7, and their corresponding PDOS are depicted in Fig. 8. The spin splitting character of band structure is also found in the case of defective SL with V_{Ga} and V_{Al} defects, as shown in Fig. 7a and b. Indeed, removal of atoms from their original positions leaves four dangling bonds related to the sp^{3} orbitals. During the structural relaxation, the nearest atoms around the vacancy are equally displaced toward the empty lattice site, which results in sitesymmetry defined by the tetragonal D_{2d} point group. The induced defect levels appear near the valence band and locate in the forbidden region of the GaAs/AlAs SL. The band gap is determined to be 0.47 and 0.44 eV for the SL with V_{Ga} and V_{Al} defects, respectively. As shown in the PDOS of defective SL with V_{Ga} and V_{Al} (see Fig. 8a and b), the main influence of the groupIII vacancies is on the p states. As shown in Fig. 7c, the band structure of the defective SL with V_{As} defect splits into spinup and spindown parts, and the defect levels appear near the conduction band. Since the V_{As} defect acts as an ntype dopant, the fermi level shifts to higher energy and crosses the defect level edge. Kahaly et al. have investigated the electrical properties of the GaAsAlAs heterointerfaces and found that V_{As} defect at the interface lead to quasi 2DEG [7], which is consistent with our results. Our calculations show that the vacancies have different effects on the band structure of GaAs/AlAs SL, i.e., the V_{As} defect induces metallicity of GaAs/AlAs SL, and the V_{Ga} and V_{Al} defects reduce the band gap of SL structure significantly.
The Effects of Interstitial Defects on the Band Structure of GaAs/AlAs Superlattice
Figure 9 presents the band structures of SL structure with interstitial defects. It is noted that the fermi level shifts to high energy and crosses the conduction band edge (see Fig. 9a and b), due to the fact that the groupIII interstitials are donorlike defects. Consequently, the defective SLs with Ga_{int} and Al_{int} show metallic character. As shown in Fig. 9c, in the spinup and spindown parts of band structure, the impurity levels appear near the conduction band and the fermi level crosses the impurity level edge, indicating the induced metallicity of defective GaAs/AlAs SL with As_{int}. Obviously, the interstitial defects significantly change the electronic structures of GaAs/AlAs SL and generally induce metallicity of defective SL structure.
Comparing the band structures and representative PDOS of the GaAs/AlAs SL with antisites, vacancies, and interstitials, we find that the defects modify the electronic structures considerably, except the cases of Ga_{Al} and Al_{Ga} antisite defects. Besides, the band gap narrowing and even metallicity are induced, which will influence the performance of GaAs/AlAs SL drastically.
The Effects of Point Defects on the Electron Mobility of GaAs/AlAs Superlattice
The electron mobility at 0 K can be calculated from the equation μ = eτ/m^{∗}, where e is the electron charge, τ is the relaxation time, and m^{∗} is the effective mass of carrier [32]. The electron effective masses can be evaluated from the curvature of the band structures via the relation \( {m}^{\ast }={\mathrm{\hslash}}^2{\left(\frac{d^2\varepsilon }{dk^2}\right)}^{1} \) [32], where ℏ is the reduced Planck constant, k is the wave vector, and ε is the energy of conduction band minimum. As shown in Fig. 4a and b, we obtain m^{*} = 0.057 m_{e} for GaAs and m^{*} = 0.19 m_{e} for AlAs, agreeing well with the experimental values of 0.057 m_{e} for GaAs [33] and 0.124 m_{e} for AlAs [34], where m_{e} is the static electron mass. The relaxation time for AlAs and GaAs is assumed to be 0.17 and 0.48 ps, respectively [35]. The electron mobility of GaAs and AlAs at 0 K are calculated to be 1.48 × 10^{4}cm^{2}/Vs and 1.57 × 10^{3} cm^{2}/Vs, respectively, which is comparable to the experimental values of 0.94 × 10^{4} cm^{2}/Vs for GaAs [36] and 0.28 × 10^{3} cm^{2}/Vs for AlAs [37].
As shown in Table 5, the electron effective mass at the Г point (\( {m}_{\Gamma}^{\ast } \)) is determined to be 0.113 m_{e} for the pristine GaAs/AlAs SL and the relaxation time τ is assumed to be 0.4 ps [38]. The electron mobility along the z direction, i.e., ΓX direction in the Brillouin zone (μ_{Γ − X}) is calculated to be 0.623 × 10^{4} cm^{2}/Vs for ideal GaAs/AlAs SL, which is comparable to the experimental value of 1.0 × 10^{4} cm^{2}/Vs [38]. As for the defective SL with antisite defects, the value of μ_{Γ − X} is comparable with that for the ideal SL, except for the cases of Ga_{As} and Al_{As} defects. The electron mobility along the ΓX direction is determined to be 0.263 × 10^{4} cm^{2}/Vs and 0.311 × 10^{4} cm^{2}/Vs for Ga_{As} and Al_{As} defective states, respectively, which are much smaller than that for the ideal state. It is noted that the Ga_{int}, Al_{int} and As_{int} defects also reduce the electron mobility significantly, as indicated by the values of 0.225 × 10^{4} cm^{2}/Vs for Ga_{int}, 0.243 × 10^{4} cm^{2}/Vs for Al_{int} and 0.315 × 10^{4} cm^{2}/Vs for As_{int}. As compared with antisite and interstitial defect, the vacancies have the most profound effects. For V_{Ga} and V_{Al} defects, the values of μ_{Γ − X} are about six times smaller than that of pristine state. The V_{As} defect also significantly decreases the electron mobility, as indicated by 0.127 × 10^{4} cm^{2}/Vs. Tanaka et al. have investigated the effects of electron irradiation on the electrical properties of GaAs/AlGaAs heterostructures and they found that the electron mobility was reduced at doses greater than 5 × 10^{20} cm^{−2} [10]. Especially, the defect creation in GaAs channel region, rather than nAlGaAs layer, is thought to be the main cause of the mobility degradation [10]. Recently, it has been suggested that the electrons are possibly trapped by defects or impurity and produce metastable states accompanied by lattice relaxation [39]. Consequently, the electronic structure and carrier mobility of GaAs/AlAs SL are influenced significantly by the point defects. Therefore, it is necessary to enhance the radiation tolerance of GaAs/AlAs SL to improve its electronic performance under radiation environment.
Conclusions
In this work, a hybrid density functional theory study is performed to investigate the effects of point defect on the electrical properties of GaAs/AlAs superlattice (SL). The calculated defect formation energies show that the antisite defects are the most favorable in bulk GaAs and AlAs. In GaAs/AlAs SL structure, the antisite defects are always dominant under cationrich and Asrich conditions and the interstitial defects are very difficult to form during the whole range of chemical potentials. It is shown that the different point defects have various effects on the electronic structures of GaAs/AlAs SL. The As_{X} (X = Al or Ga) and X_{As} antisite defects always induce metallicity, although the defective SLs with X_{As} antisites show spin splitting. As for vacancies, the defective SL with V_{As} shows metallicity character, and the group III vacancy defects reduce the band gap of the superlattice significantly. The metallicity is also found in the defective GaAs/AlAs SL with the interstitial defects. The further carrier mobility calculations show that the interstitial and vacancy defects reduce the electron mobility significantly, while the antisite defects have relatively smaller influence.
Abbreviations
 2DEG:

Twodimensional electron gas
 AIMD:

Ab initio molecular dynamics
 Al:

Aluminum
 AlAs:

Aluminum arsenide
 As:

Arsenic
 As_{X} :

As occupying the X lattice site
 DFT:

Density functional theory
 Ga:

Gallium
 GaAs:

Gallium arsenide
 HEMT:

High electron mobility transistors
 HSE:

HeydScuseriaEmzefhof
 LED:

Lightemitting diode
 N:

Nitrogen
 PDOS:

Partial density of state
 QCLs:

Quantum cascade lasers
 SL:

Superlattice
 VASP:

Vienna Ab Initio Simulation Package
 V_{X} (X = Ga, Al or As):

X vacancy
 X_{As} :

X occupying the As lattice site
 X_{int} :

X interstitial
 Zn:

Zinc
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Acknowledgements
The theoretical calculations were performed using the supercomputer resources at TianHe1 located at National Supercomputer Center in Tianjin.
Funding
Haiyan Xiao was supported by the NSAF Joint Foundation of China (Grant No.U1530129). Zijiang Liu was supported by National Natural Science Foundation of China (Grant No. 11464025) and the New Century Excellent Talents in University under Grant No. NECT110906 and the Key Talent Foundation of Gansu Province.
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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
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HX and XZ designed the calculations. MJ conducted the calculations and wrote the manuscript. SP, GY, ZL and LQ contributed the discussion and interpretation of the results. All authors read and approved the final manuscript.
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Jiang, M., Xiao, H., Peng, S. et al. FirstPrinciples Study of Point Defects in GaAs/AlAs Superlattice: the Phase Stability and the Effects on the Band Structure and Carrier Mobility. Nanoscale Res Lett 13, 301 (2018). https://doi.org/10.1186/s1167101827197
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DOI: https://doi.org/10.1186/s1167101827197
Keywords
 Hybrid density functional theory
 Point defect
 GaAs/AlAs superlattice
 Electrical properties