Native point defects of semiconducting layered Bi2O2Se

Bi2O2Se is an emerging semiconducting, air-stable layered material (Nat. Nanotechnol. 2017, 12, 530; Nano Lett. 2017, 17, 3021), potentially exceeding MoS2 and phosphorene in electron mobility and rivalling typical Van der Waals stacked layered materials in the next-generation high-speed and low-power electronics. Holding the promise of functional versatility, it is arousing rapidly growing interest from various disciplines, including optoelectronics, thermoelectronics and piezoelectronics. In this work, we comprehensively study the electrical properties of the native point defects in Bi2O2Se, as an essential step toward understanding the fundamentals of this material. The defect landscapes dependent on both Fermi energy and the chemical potentials of atomic constituents are investigated. Along with the bulk defect analysis, a complementary inspection of the surface properties, within the simple context of charge neutrality level model, elucidates the observed n-type characteristics of Bi2O2Se based FETs. This work provides important guide to engineer the defects of Bi2O2Se for desired properties, which is key to the successful application of this emerging layered material27.


Results and Discussion
Our calculations are based on density functional theory within the generalized gradient approximation, 20 using the Cambridge Sequential Total Energy Package 21 . 90 atoms' Bi 2 O 2 Se supercell is used as the host of various native point defects, where the lattice constants are fixed to the calculated values. Cutoff energy of the plane wave basis set is 680 eV. All atoms are relaxed in each optimization cycle until atomic forces on each atom are smaller than 0.01 eV Å −1 and the energy variation between subsequent iterations falls below 5 × 10 −6 eV. Total energies are evaluated on 3 × 3 × 3 Monkhorst−Pack k-meshes. Unlike other layered materials which have individual atomic layers stacked by van der Waals interactions, Bi 2 O 2 Se lacks a well-defined van der Waals gap but displays out-of-plane electrostatic interactions between planar covalently bonded oxide layer (Bi 2 O 2 ) and Se square array, as shown in Fig. 1a. The calculated band structure and atomic projected density of states (PDOSs) are shown in Fig. 1b. Indirect band gap of 0.76 eV with conduction band minimum (CBM) near Γ point is in good agreement with the value of 0.80 eV measured by angle-resolved photoemission spectroscopy 15 . The electronic states near the CBM and the valence band maximum (VBM) originate mainly from the Bi and Se/O p-orbital bands, respectively.
Bi 2 O 2 Se is a ternary semiconductor with ample defect configurations. We consider ten of them in this work, including vacancies, interstitials and antisites in the relevant charge states. The formation energy ∆ α H ( , q) f of defect α in charge state q depends on the chemical potentials μ of the atomic constituents as well as the electron chemical potential, namely, Fermi energy ε F . In Bi 2 O 2 Se, where α E( , q) is the total energy of the supercell containing a type α defect and charge q, E(Bi O Se) 2 2 is the total energy of the defect free supercell, n's and q are the numbers of the atoms and electrons, respectively, that transferred from the defect free supercell to the reservoirs in forming the defect cell. C Freysoldt is the charge state and cell size correction to the defect-formation energy 22 . According to Freysoldt et al., the correction consists of three contributions: a lattice term, a self-interaction term and a potential alignment term 22 . The lattice term accounts for the electrostatic interaction of the defect charge in the supercell with its array of periodic images in the remaining crystal. We use Gaussian defect charge distribution. The lattice energy includes the self-interaction term of the defect charge with its own potential, which must be removed from the correction term. The potential alignment term allows for a meaningful comparison of the formation energies of different charged defects as the charged defect in the supercell will introduce a constant shift of the electrostatic potential and the valence band maximum compared to the ideal host system. As the dielectric anisotropy in layered material systems could be strong, we generalize the Freysoldt scheme to account for the anisotropy. This is achieved by using the dielectric tensor for the calculation of Coulomb interaction potential in the reciprocal space. The dielectric tensor is computed from density-functional perturbation theory. A correction for filling the CBM and emptying the VBM has also been considered 23 . Freysoldt correction leads to well-converged defect formation energies (Fig. S1). The chemical potentials are allowed to vary over a restricted range determined by equilibrium thermodynamics 24 : ε F is bound between the VBM and CBM of Bi 2 O 2 Se, and μ's are bound by the values that (i) will cause precipitation of solid elemental Bi in the trigonal phase, molecular O and solid elemental Se in the trigonal phase, i.e.,  (iii) will cause the formation of solid binaries Bi 2 O 3 and Bi 2 Se 3 in the monoclinic and trigonal phases, respectively, i.e., The calculated range of atomic chemical potentials for stable Bi 2 O 2 Se is shown on the two-dimensional "μ O vs μ Se " plane in Fig Se v remains to be the most stable defect throughout the band gap under the (Se-poor, Bi-rich) condition (Fig. 3a). O v has slightly higher formation energy. The unintentional n-type doping of Bi 2 O 2 Se is therefore likely to be due to the existence of Se v and O v . Under the (Se-rich, Bi-poor) condition, their formation energies increase and they dominate only in the p-type Bi 2 O 2 Se, counteracting the p-type conductivity.
We then consider Bi in at the center of the Se square, which is found to be energetically favorable compared with other interstitial sites. Bi in occurs exclusively in the positively charged state (charge states from 3− to 3+ are considered), thus acting as a shallow donor. A ξ(3+/2+) transition level occurs at 0.19 eV above the VBM. However, because Bi in has quite high formation energy in n-type Bi 2 O 2 Se even under the (Se-poor, Bi-rich) condition, it is not likely to be present to drive unintentional conductivity of Bi 2 O 2 Se. The atomic structure of Bi in 2+ is shown in Fig. 5a. It can be seen that the interstitial Bi atom repels the two Bi atoms right below and above in the Bi 2 O 2 layers to the centers of the O squares. Next, we consider two kinds of Bi antisites. For Bi Se , a ξ(1+/0) transition level occurs at 0.30 eV above the VBM (charge states from 1− to 5+ are considered), indicating that it is a deep donor center. It is the third most stable defect next to Se v and O v in p-Bi 2 O 2 Se under the (Se-poor, Bi-rich) condition, compensating the p-type conductivity. The formation energy of Bi Se rapidly increases with anion chemical potentials and Bi Se becomes less likely to exist under the (Se-rich, Bi-poor) condition. The atomic structure of neutral Bi Se is shown in Fig. 5b.
For Bi O , transition levels ξ(4+/2+) and ξ(2+/0) occur at 0.33 eV and 0.50 eV above the VBM, respectively (charge states from 1− to 5+ are considered). Therefore, it is a deep donor center and it compensates the p-type  conductivity of Bi 2 O 2 Se. However, it has quite high formation energy even in the (Se-poor, Bi-rich) condition, so it is not likely to exist. It is obvious that Bi O is a negative-U defect, with transition level ξ(4+/3+) higher than ξ(3+/2+), and ξ(2+/1+) higher than ξ(1+/0). Negative-U behavior has been typically related to unusually large local lattice relaxations that stabilize particular charge states. Here, substitutional Bi in the 4+ charged state undergoes displacement ~1 Å vertical to the Bi 2 O 2 plane (Fig. 6) right above a Se ion, which is found to be energetically favorable, it repels the Se ion out of the Se square plane and forms seleninyl ion SeO −2+q (charge states q from 2− to 2+ are considered). The atomic structure of O in° is shown in Fig. 7a. O in remains neutral throughout the band gap, rendering on average −1 intermediate oxidation state for Se and O atoms in the seleninyl ion. Its formation energy is relatively high under the (Se-poor, Bi-rich) condition compared with O v and Se v , but is reduced under the (Se-rich, Bi-poor) condition, becoming the most favorable defect in the Fermi energy range between 0.13 eV and 0.58 eV above the VBM. For Se in at the edge center of the Se square, which is found to be energetically favorable, it repels the two neighboring Se ions at the vertices, forming triselenide anion Se 3 −4+q (charge states q from 2− to 4+ are considered). The atomic structure of Se in° is shown in Fig. 7b. Se in assumes positively charged state as long as the Fermi level is below the transition level ξ(1+/0) at 0.26 eV above the VBM, acting as an acceptor compensating center in p-type Bi 2 O 2 Se. On average, each Se atom in the triselenide anion acquires intermediate oxidation state between −2 and 0. It has higher formation energy than O in does. PDOSs of O in° (Se in 0 ) (Fig. 7c,d) show that the seleninyl ion SeO −2 (triselenide anion Se 3 −4 ) has filled antibonding frontier orbital states below  Next, we consider Bi v . It is a shallow acceptor which occurs exclusively in the negative charge state, with transition levels ξ(1−/2−) and ξ(2−/3−) occur at 0.28 eV and 0.66 eV above the VBM, respectively (charge states from 3-to 0 are considered). PDOSs (Fig. S3) of Bi v 0 provide alternative way of understanding the shallow acceptor effect of Bi v , where we see that it is ready to accept electrons near the VBM by thermal excitation at steady state, leaving holes in the valence band. The formation energy of Bi v under the (Se-poor, Bi-rich) condition is relatively high compared with those of Se v and O v . Under the (Se-rich, Bi-poor) condition, however, the formation energy of Bi v rapidly decreases and Bi v becomes the dominant defect in n-type Bi 2 O 2 Se, compensating the prevalent conductivity. The atomic structure of Bi v 3− is shown in Fig. 8a. Finally, we consider O Bi and Se Bi . O Bi occurs exclusively in the negative charge state (charge states from 5− to 1+ are considered) and acts as a shallow acceptor. The transition level ξ(1−/2−) occur at 0.28 eV above the VBM. The atomic structure of O Bi 2− is shown in Fig. 8b. The substitutional O atom undergoes large displacement to the Se square layer, locating in the center of two neighboring Se atoms. The formation energy of O Bi is high even under the (Se-rich, Bi-poor) condition. Thus, it is not likely to exist.
For Se Bi , the transition level ξ(0/1−) occurs at 0.31 eV above the VBM. Thus, it compensates donors. The formation energy of Se Bi under the (Se-poor, Bi-rich) condition is quite high but rapidly decreases with increasing anion chemical potentials. Under the (Se-rich, Bi-poor) condition, Se Bi becomes the second most likely compensating center next to Bi v in n-type Bi 2 O 2 Se. The atomic structure of Se Bi 1− in Fig. 8c shows that the substitutional Se atom displaces toward the center of the underlying Se square.
Here to, we have studied the electrical properties of ten types of native point defects. As previously pointed out, the electrical conductivity of material can be significantly affected by its native point defects. In Bi 2 O 2 Se FETs, whose channels remain conducting at V g = 0, the total resistance decreases with increasing gate bias 15 , which is a clear signature of n-type characteristics. Figure 3 implies the possibility of (Se-poor, Bi-rich) fabrication condition for the Bi 2 O 2 Se FETs since Se v and O v , which are shallow donors, are the most likely defects under this condition.
The conductivity of Bi 2 O 2 Se can alternatively be understood within the context of charge neutrality level (CNL) model 25 . The CNL model is useful because it is simple and gives good chemical trends, while requiring no specified details of surface chemical bonding which are outside of the scope of this work. The CNL is the  demarcation between the surface states that are predominantly donor-like (valence band states) and acceptor-like (conduction band states), namely, at CNL they have equal densities. Mathematically, the CNL is the branch point of the imaginary bulk band structure of the semiconductor. It is calculated as the zero of the Greens function of the band structure averaged over the Brillouin zone: where δ is a small number to be used if the CNL lies inside a band. It can also be expressed as a sum over special points of the Brillouin zone (such as the Monkhorst-Pack grid) 26 : The CNL is then a weighted average of the valence and conduction band DOS: In this definition, the CNL is an intrinsic property of the bulk semiconductor; it does not depend on the interface, or interface bonding, or whatever it is attached to. According to equation (7), the CNL of Bi 2 O 2 Se is calculated to be ~0.7 eV above the VBM, very close to the CBM. In the absence of gate bias, the Fermi level at the surface of Bi 2 O 2 Se is aligned with the CNL to ensure charge neutrality, resulting in surface electron accumulation. This explains why Bi 2 O 2 Se based FETs are in the ON state when V g = 0 and show n-type behavior.

Conclusion
In summary, we have systematically studied all anion and cation deficiency related native point defects of Bi 2 O 2 Se in all relevant charge states. The abounding defect behaviors resulting from the ternary elemental compositions and the unique stacking structure are analyzed. Defect landscape is found to vary with Fermi energy and the chemical potentials of the atomic constituents. Our results suggest the possibility of (Se-poor, Bi-rich) fabrication condition of the previously reported Bi 2 O 2 Se FETs 15 . Under this condition, Se v and O v are the dominant defects and they act as shallow donors, accounting for the unintentional n-type conductivity of Bi 2 O 2 Se. Alternatively, the n-type characteristics of Bi 2 O 2 Se FETs can also be understood in the context of the CNL model. The CNL of Bi 2 O 2 Se is computed to be close to the CBM, resulting in surface electron accumulation. This work provides important guide to engineer the defects of Bi 2 O 2 Se for desired properties, which is key to the successful application of this emerging layered material.