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. 2023 Jun 2;8(23):21162–21171. doi: 10.1021/acsomega.3c02161

Temperature, Doping, and Chemical Potential Tuning Intrinsic Defects Concentration in Bi2MoO6: GGA + U Method

Rui Wang †, Liming Zhou †,*, Wentao Wang ‡,*
PMCID: PMC10268639  PMID: 37332826

Abstract

graphic file with name ao3c02161_0007.jpg

Using the GGA + U method, the formation energy and concentration of intrinsic defects in Bi2MoO6 are explored under different chemical conditions, with/without doping, from 120 to 900 K. We find that the intrinsic defect and carrier concentration can be deduced from the small range of calculated Fermi levels in the diagram of formation energy vs Fermi level under different conditions. Once the doping conditions or/and temperature are determined, the corresponding EF is only limited to a special region in the diagram of formation energy vs Fermi level, from which the magnitude relationship of defects concentration can be directly derived from their formation energy. The lower the defect formation energy is, the higher the defect concentration is. With EF moving under different doping conditions, the intrinsic defect concentration changes accordingly. At the same time, the highest electron concentration at the relative O-poor (point HU) with only intrinsic defects confirms its intrinsic n-type behavior. Moreover, upon A–/D+ doping, EF moves closer to VBM/CBM for the increasing concentration of holes/electrons. The electron concentration can also be further improved after D+ doping, indicating that D+ doping under O-poor chemical growth conditions is positive to improve its photogenerated carriers. This provides us with a method to adjust the intrinsic defect concentration and deepens our knowledge about comprehension and application of the diagram of formation energy vs Fermi level.

1. Introduction

Bi3+-based oxides such as Bi2MoO6, Bi2WO6, BiVO4, and BiOCl are promising candidates for various applications, including solar cells, electrode materials, and photo-degradation of organic pollutants.1−3 Bi2MoO6 is the most studied material in the photocatalytic field.4 This is because Bi2MoO6 has good electron conductivity and visible-light response. The effective absorption of solar light is derived from the excellent electronic properties of Bi2MoO6 and the narrow band gap of 2.5–2.8 eV.4 The density functional theory (DFT) calculations results show that the 2p electrons of O dominate its valance band; its conduction band consists predominantly of the 4d orbitals of Mo.5 Nevertheless, pristine Bi2MoO6 has a poor production quantity of superoxide radicals under irradiation. Its little quadratic curvature of the conductive band bottom limits its practical application.6−8 To improve the photocatalytic performance of pristine Bi2MoO6, considerable efforts have been conducted. For example, the morphology control of different dimensions, metal deposition, heterojunction fabrication, surface modification, and metal or nonmetal ion doping.8,9

Introducing intrinsic defects (such as O vacancy; Bi vacancy; Mo vacancy; Bi, Mo, O interstitial; Bi at Mo site and Mo at Bi site, and so on) into Bi2MoO6 is an efficient research method adopted to modify its photocatalytic efficiency.10−16 Therefore, the intrinsic defects of Bi2MoO6 have been widely explored. For example, Ding et al.17 demonstrated that the self-doping of Bi in Bi2MoO6 can form Bi-substituted Mo (BiMo) antisite and induce Mo vacancy. Using the Perdew–Burke–Ernzerhof (PBE) exchange-correction function calculations, they found that the electric charge around the substituted Bi atom for the Mo atom was redistributed. These defects cause a new band consisting of the O 2p orbital to appear in the unchanged band gap to favor its electron excitation. Di et al.18 synthesized the Bi and O–Bi vacancy pairs in Bi2MoO6, displaying improved light absorption. Their DFT calculations observed that the increased density of states (DOS) at the valence band edge and new DOS appearing in the forbidden band improved the carrier concentration and made the excitation of electrons into the conduction band easier. Bi vacancy and Bi interstitial contained in Bi2MoO6 were synthesized by Zhang et al.19 exhibiting higher photoexcitation. Significantly, the single VO defect in Bi2MoO6 is more importantly studied due to its relatively lower formational energy.8,20 Huang et al.21 synthesized different amounts of VO in Bi2MoO6 with the higher tetracycline degradation rate of Bi2MoO6. Bai et al.22 calcined Bi2MoO6 at 450 °C and found that it exhibited much higher photocatalytic performance owing to the existence of VO. Yang et al.23 experimentally achieved effective CO2 photoconversion to CH4 with high selectivity of up to 96.7% from well-designed VO on Bi2MoO6. However, there is still a lack of quantitative description of native defects and carrier concentrations and their possible compensation relationship, which significantly impact the semiconductor catalytic properties in Bi2MoO6.

At the same time, theoretically, no research has been reported on the physics of all the intrinsic defects in Bi2MoO6, except a recent work by Jing et al.24 They calculate the electronic structure and related properties of Bi2MoO6 with the native defects in a neutral state using standard DFT. However, the charged states are neglected. Honestly, the formation energy of a neutral impurity is independent of the Fermi level.25,26 The Fermi level and, thus, the equilibrium concentration of the defects and carriers depend on chemical conditions such as temperature and the growth environment, which are not considered in previous research. Moreover, how intrinsic defects respond and compensate for the existence of extrinsically ionized impurities, such as donors and acceptors in Bi2MoO6, and how this relationship changes with temperature and chemical potentials has seldom been investigated. On the other hand, standard DFT calculation yield significantly underestimated band gaps, i.e., 1.76 eV,24 compared to the experimental value of 2.46 eV.27 Hence, more quantitatively, reliable calculations are required. The generalized gradient approximation (GGA) with on-site Coulomb interactions (GGA + U) within Dudarev’s approach28 is a reliable method for calculating defects’ transition levels and formation energies,29,30 which is implemented in this study.

In this work, we first investigated the formation energy of intrinsic defects and found the lowest energy of donors and acceptor forming Fermi pinning under different chemical potential conditions. Based on this, we then calculated the native defects and carrier concentration from 120 to 900 K and stated the relationship between defect concentration and their formation energies in the small zone of the calculated Fermi level. The highest electron concentration under relative O-poor conditions was found. Lastly, at the presence of A– and D+ doping under different chemical potential from 120 to 900 K, the concentrations of intrinsic defects and carriers were studied again, showing that D+ doping under relative O-poor conditions can be further enhanced. We provide the first study of intrinsic concentration vs their formation energies within the special calculated Fermi level and promote the knowledge of comprehension and application of the diagram of formation energy vs Fermi level.

2. Computational Details

More details about DFT and formation energy calculation methods are shown in Note S1 (Supporting Information).

The lowest Ef(Xq) part in the intersected plots of formation energy of different charged states of a certain defect can naturally form the trace of its formation energy. In this way, a defect constitutes a corresponding formation energy trace consisting of a series of polyline segments. When the traces of acceptors and donors with the lowest Ef(Xq) intersect inside the band gap, the Fermi level is pinned close to the intersection point. If the pinned EF lies below the mid-gap, the system exhibits p-type behavior; otherwise, it is n-type.31

The defect formation energy is indeed a simple linear relationship between chemical potentials and the Fermi level as independent variables, at least if free carriers are ignored, a reasonable approximation if the Fermi level is far enough away from the valence-band edge.32 The defect formation energy becomes a function of the Fermi energy solely, especially when the chemical potentials are fixed.32 Actually, this formula (eq S1) and associated defect formation energy vs Fermi energy plot (Figure 2) are indeed commonly used to analyze, understand, and design the relevant properties of semiconductors without solving the detailed heat equations at a certain temperature. The Fermi-level pinning at the lowest crossing point of acceptor and donor formation energy vs Fermi energy lines at given atomic chemical potentials is often used as theoretical guidance for experiments to tune material performances by controlling growth conditions.33

Figure 2.

Figure 2

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Formation energies (derived from PBE + U calculation) of intrinsic defects VBi, VMo, VO, IBi, IMo, IO, MoBi, and BiMo in Bi2MoO6 under different chemical potential conditions of (a) AU, (b) EU, (c) HU, (d) GU, and (e) NU as shown, plotted as a function of the Fermi level with respect to the valence band maximum (VBM). Red dashed lines indicate each Fermi-level pinning. The Fermi level (EF) at the VBM and CBM is set to 0.00 and 2.635 eV, respectively. The numbers in the polygonal lines denote the favorably charged states of each defect, in which different parallel line segments imply the same charge state, and so as in all the different chemical conditions. The orange, green, and blue areas represent the ranges of later calculated self-consistent Fermi levels with intrinsic defects, A– doping, and D doping as a function of temperature T from 20 to 900 K under charge neutrality conditions, respectively, which can be seen in Table 1 for details.

Nevertheless, free carriers from thermal impurity levels and band-edge activations will always be present under certain doping concentrations at finite temperatures. Impurity excitation and intrinsic excitation will be further enhanced with the increasing temperature. This will affect the Fermi level position, especially when carrier concentrations are large compared to defect densities, which is usually crucial in semiconductors. In fact, the Fermi energy level is ultimately a function of chemical potentials and temperature when the doping concentration is determined. The following calculations of the self-consistent Fermi energy and the equilibrium defect and charge carrier concentrations took the influence of carriers into account.

In the synthesis process, the chemical potentials of Bi, Mo, and O in Bi2MoO6 are not arbitrary but subject to thermodynamic constraints, which can be used to represent actual experimental conditions. More details about the chemical potential calculation are shown in Note S2 (Supporting Information).

The phase diagram can be made when Bi2MoO6 exists stably. Equations S4–S7 defines the chemical potential in the tetrahedron with three vertices determined by ΔμMo, ΔμBi, and ΔμO, and the origin indicates that Mo, Bi, and O are all rich. For the sake of intuition, the tetrahedron is projected on the ΔμMo, ΔμBi two-dimensional plane, and the projection is a triangle referring to Figure 1 for PBE + U calculations. For the triangle’s apex, the origin (0, 0) means that both Bi and Mo are rich, ΔμO = ΔHf(Bi2MoO6)/6 = −2.49 eV; that is, O is poor. Point X (−7.465 eV, 0, 0) means Bi is poor and Mo/O is rich. Point Y (0, −14.93 eV, 0) means Mo is poor, and O/Bi is rich. The point on the hypotenuse XY means ΔμO = 0; that is, O is rich. Each line segment parallel to the hypotenuse represents that ΔμO is equal to a constant, which keeps decreasing from the hypotenuse to the origin. Equations S1,S6–S8 limit the chemical potential stable region to be a trapezoid for GGA + U in the ΔμBi and ΔμMo plane,34 as shown in Figure 1. We consider some representative points with coordinates (ΔμBi, Δ μMo, ΔμO) in units of eV, AU (−3.52, −7.89, 0), GU (−2.53, −5.94, −0.655), HU (−0.86, −4.265, −1.49), EU (−3.10, −8.73, 0), and NU (−2.75, −7.03, −0.40) by PBE + U, respectively, also marked in the figure.

Figure 1.

Figure 1

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PBE + U calculates the accessible range of chemical potentials (orange region) for equilibrium growth conditions of orthorhombic Bi2MoO6. Specific points AU, GU, HU, EU, and NU are chosen as the representative chemical potentials for the following defect formation energy calculation.

Comparing Figure 1 with the previous investigation,24 we find that the PBE + U calculated stable region shaded for Bi2MoO6 is a smaller trapezoid than the irregular pentagon by PBE. Specifically, ΔμO and ΔμMo shrink greatly from [0, −2.28] eV and [−2.28, −8.84] eV to [0, −1.49] eV and [−4.625, −8.73] eV, respectively; however, ΔμBi shrinks slightly from [0, −3.6] eV to [−0.86, −3.52] eV, which mainly caused by the larger translational amount of the formation region of MoO2 from Bi-poor and Mo-rich to Bi-rich and Mo-poor. It is shown that the influence on formation energy after adding U in transition metal in MoO2 (heavier stoichiometric ratio of Mo) is much larger than that in MoO3 (lighter stoichiometric ratio of Mo), so can it be seen in VO2 and V2O5 between PBE and PBE + U.35 The calculated defect formation energies of charged states depend on the selected values for μBi(ΔμBi + EBi), μMo(ΔμMo + EMo), μO(ΔμO + EO), and the Fermi-level positions related to the corresponding chemical conditions, which need to meet the constraints to avoid the formation of the impurity-related competing phases.

3. Results and Discussion

3.1. Formation Energy and Fermi-Level Pinning under Different Chemical Potentials

We have systematically studied the following eight intrinsic defects in the Bi2MoO6 lattice: VBi (Bi vacancy), VMo (Mo vacancy), VO (O vacancy), IBi (interstitial Bi), IMo (interstitial Mo), IO (interstitial O), BiMo (Bi replacing Mo), and MoBi (Mo replacing Bi). The calculated lowest formation energies as a function of the Fermi level for each defect are shown under the different conditions of chemical potentials in Figure 2, in which all possible charge states of higher formation energy of the same defects are not shown for simplification. The formation energy of each charged defect state is lower than that of any other corresponding states shown in Figure 2 for the certain extension of the band gap from CBM to VBM. We note that by fixing the chemical potentials from eq S1, the defect formation energy solely becomes a function of the Fermi energy without considering thermal activation, which acts as a reservoir for electrons.32 The charged defects such as MoBi, IMo, IBi, and VO with positive and zero scopes are donors, while defects such as VMo, VBi, BiMo, and IO with negative and zero scopes are acceptors.

As shown in Figures 1 and 2, the chemical condition is represented by points AU, EU (Bi-poor, Mo-poor, and O-rich), NU, GU (moderate), and HU (the maximum of μO to synthesize Bi2MoO6). At the chemical condition of AU, NU, GU, and HU, the Fermi level is pinned within the n-type conductive region. At point HU, the Fermi level pinned the closest to CBM indicates the narrowest donor energy level and the highest concentration of its charge carriers because of the most easily thermal activation into the conduction bands.31 However, at point EU, the Fermi level is pinned to be at around 0.3 eV below the mid-gap showing p-type conductive behavior especially.

At O-rich AU, the lowest-energy defect is VMo6– for EF > 1.9 eV. When thermal excitation is not considered, the Fermi energy level is pinned by the dominant native donors Mo+1 Bi and acceptors VMoto be at ∼1.3 eV below CBM. One would expect EF to remain trapped roughly mid-gap, resulting in an intrinsically insulating material for intrinsic compensation.36 From AU to EU shown in Figure 2a,b, with the chemical potential of Bi increasing and that of Mo decreasing, the formation energies of MoBi and VBi are increased and the formation energy of the antisite defects BiMo is decreased. In contrast, the formation energy of VO is almost unchanged. Thus, the Fermi level is pinned most nearly at ∼0.9 eV above VBM by Bi1– Mo and VO2+ with the lowest formation energies, indicating n-type conductivity for the occurrence of the most typical self-compensation, which the present articles have never reported. Hence, under O-rich conditions (AU and EU), the Fermi pinning near mid-gap and self-compensation between donors and acceptors would limit its conductive behavior. This means that such extreme O-rich growth conditions should be avoided.

At moderate points NU and GU, the Fermi energy level is also pinned by Mo1+Bi and VMo3– with Fermi-level pinning at the range of n-type conductivity. From NU to GU shown in Figure 2c,d, the chemical potentials of both Bi and Mo increased, and that of O decreased, so the formation energy of MoBi gradually decreased and that of VBi slightly increased from eq S1. As a result, the position of Fermi pinning moved to CBM. From GU to HU (relative O-poor conditions) shown in Figure 2d,e, the chemical potentials of both Bi and Mo still increase and that of O greatly decrease. The formation energy of BiMo decreased and that of VBi unceasingly increased; the Fermi energy level is pinned by Mo1+Bi and Bi3–Mo with the Fermi level pinning closer to CBM, indicating the best n-type conductive properties. Nevertheless, around Fermi pinning at points NU, GU, and HU, the formation energy of the neutral state of BiMo is even lower than the lowest formation energy donors and acceptors of Fermi pinning, suggesting that Bi0Mo is much easier to form.

3.2. Self-Consistent Fermi Energy, Equilibrium Carrier, and Defect Concentrations

The Fermi energy is fixed by the charge-neutral condition rather than a free parameter.32,33 From the computed defect formation energies and total density of states (TDOS) of Bi2MoO6, the computed self-consistent Fermi energy EF and carrier concentrations (n0 for electrons and p0 for holes) and defect concentrations (denoted as[Xq defect]) as a function of temperature T from 20 to 900 K under different chemical potential conditions of AU, HU, NU, GU, and EU are shown in Figure 3. We calculate them using the code SC-FERMI with the dilute defect approximation. The defect formation energies, unit cell parameters, calculated total density of states in pristine crystal, and band gaps are assumed not to change with T for simplicity.36,37

Figure 3.

Figure 3

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Self-consistent Fermi energy (EF, black dashed line, right axis) and carrier and defect total concentrations even with mainly charged states (color solid line, left axis) as a function of temperature from 120 to 900 K for intrinsic defects VBi, VMo, VO, IBi, IMo, IO, MoBi, and BiMo in Bi2MoO6 under different chemical potential conditions of (a) AU, (b) HU, (c) NU, (d) GU, and (e) EU which derived from PBE + U calculations. The Fermi levels in thermodynamic equilibrium are listed in Table 1.

At infinite temperature, the electrons (n0) from CBM and holes (p0) from VBM thermal excitations will always be present to affect the Fermi-level position, the concentrations of which are given by the following:37

3.2. 1
3.2. 2

where Eg is the band gap, fe(E) = [exp((EF – E)/kT) + 1]−1 is the Fermi–Dirac distribution function, and fh(E) is defined as 1 – fe(E) (k is the Boltzmann constant), ρ(E) is the total density of states (TDOSs) of the host cell without defects, and T is the temperature.

If the band gap (Eg) is taken into account with zero energy set at VBM, eq 1 can be written as follows:33

3.2. 3
3.2. 4

The concentration of the defect X with charged state q refers to

3.2. 5

where NX is the density of sites of the host cell where defects can form, gXq is the degeneracy of the defect state q, (Ef(Xq)) is the formation energy of charged defect [eq S1], k is the Boltzmann constant, and T is the temperature. Only defects with adequately low formation energy will be present in large concentrations if the conditions are close to equilibrium, usually in high-temperature growth or annealing.38 Finally, the condition of charge neutrality in a semiconductor system can be expressed as follows:

3.2. 6

where the sum over all of the acceptor and donors is implicitly included. Since the term of [Cq X] in eq 5 depends on a set of defect formation energies {Ef (Xq)} varying with T, which come along with the other terms in the equation depending on EF too. A search algorithm may be used to self-consistently calculate the equilibrium Fermi level positions (EF), carriers, and defect concentrations satisfying eqs S1 and 1–5 in principle, when given a finite T and certain atomic chemical potentials.

3.3. Temperature Effect

Within the temperature range from 20 to 900 K, the shift of computed self-consistent EF has been added to the drawing in Figure 2 and listed in Table 1. The same research method also appears in a previous study.36 The differences between Fermi-level pinning and the computed self-consistent EF mainly come from whether the carrier effect is considered. When variously charged point defects are formed under the constraint of charge neutrality, the self-consistent Fermi levels are further calculated at finite temperatures. They are only tightened in a small area in the band gap, which is marked by an orange-shaded columnar area in Figure 2. It was necessary to note that the concentrations of both defects and their charged states discussed below are all within the strictly constrained and narrow range of the Fermi level. This means the formation energy relationship of defects in the region outside the Fermi level determined by the electric neutral condition will no longer affect the carrier concentration. This provides us with more rigorous and detailed information for the study of defect physics.

Table 1. Detailed Range of Calculated Fermi Energy Level (eV) in Bi2MoO6 Without/With Doping under Different Chemical Conditions from 120 to 900 K.

without/with doping AU EU NU GU HU
A doping 0.842∼1.449 0.658∼0.984 0.932∼1.580 1.802∼1.954 1.807∼2.181
only intrinsic defects 1.487∼1.466 0.928∼0.991 1.702∼1.677 1.975∼1.954 2.187∼2.181
D+ doping 1.699∼1.478 1.490∼0.998 1.933∼1.715 2.029∼1.954 2.316∼2.182
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At the same time, we found that the lower the formation energy the defects have, the higher the concentration within the range of the calculated Fermi energy level (EF), and the defect with the lowest formation energy has the highest concentration. However, EF and all of the defect concentration increases with temperature increase for thermal excitation.39 At O-rich AU shown in Figure 3a, the dominant defects are MoBi1+ and VBi with the typical intrinsic compensation between each other for T < 420 K, and 3[MoBi1+] = [VBi] holds. When T increases, the concentration of MoBi0 increases without affecting the compensation relationship for its neutral state. Therefore, the calculated Fermi level is near the mid-gap, and n0 is less than 1014 cm–3 even at T = 900 K. At the same O-rich EU shown in Figure 3e, BiMo and VO2+ are the important acceptor and donor defects compensating for each other, and 2[BiMo] is equal to [VO2+]. Moreover, the calculated Fermi level is below the mid-gap, and p0 is much lower (less than 1016 cm–3 at 900 K). Therefore, under O-rich conditions (AU and EU), the calculated Fermi energy near mid-gap and self-compensation between donors and acceptors would limit its conductivity.40 The carrier concentration is too low to be used for successful photocatalytic materials.41 This implied that such extreme O-rich growth conditions should be avoided.

At the moderate points NU, GU, and HU shown in Figure 3b–d, with the lowest formation energy within the range of the calculated Fermi level, the concentration of Bi0Mo is higher than that of any other defects. At points NU and GU, n0 are lower than 1016 cm–3. MoBi1+ and VBi are the dominant donors and acceptors with the occurrence of compensation between each other and 3[MoBi1+] = [VBi] holds, consisting of the situation of O-rich point AU. At points HU, the main intrinsic compensation derived from Mo1+Bi and Bi3–Mo with 3[MoBi1+] = [BiMo]. n0 is more than 1017 cm–3 for T > 700 K. With ΔμO decreasing from NU to GU to HU, n0 increases, suggesting that the growth conditions of nearly O-poor are profitable for its conductivity. This is well agreeable with the universal knowledge.42,43

3.4. Doping Effect

In order to further reveal detailed changes in intrinsic defects concentration and the compensation relationship between intrinsic and extrinsic defects, different chemical growth conditions from 200 to 900 K, EF, and carrier and defect concentration as a function of temperature are carried out. The results are shown in Figures 4 and 5. They are following the procedure FROZEN-SC-FERMI,37 in which other charged defects (A– refers to acceptors with +1 charge state, D+ refers to donors with −1 charge state) of fixed concentration ([A–] = [D+] = 1018 cm–3) are introduced, as reported in previous studies.36,37,44 Remarkably, the calculated Fermi level after doping has also been added in Figure 2 to facilitate comparison with only native defects. It is clear that EF moves to VBM when the hole concentration increases during acceptor doping and EF moves toward CBM when the electron concentration increases during donor doping,39 as shown by the cyan and blue zones in Figure 2, respectively.

Figure 4.

Figure 4

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Self-consistent Fermi energy (EF, black dashed line, right axis) and carrier and defect total concentrations even with mainly charged states (color solid line, left axis) as a function of temperature from 120 to 900 K for intrinsic defect VBi, VMo, VO, IBi, IMo, IO, MoBi, and BiMo in Bi2MoO6 in the presence of a fixed concentration of donors [A–] = 1018 cm–3 under different chemical potential conditions of (a) AU, (b) HU, (c) NU, (d) GU, and (e) EU derived from PBE + U calculations are shown. Fermi levels in thermodynamic equilibrium are listed in Table 1.

Figure 5.

Figure 5

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Self-consistent Fermi energy (EF, black dashed line, right axis) and carrier and defect total concentrations even with mainly charged states (color solid line, left axis) as a function of temperature from 120 to 900 K for intrinsic defects VBi, VMo, VO, IBi, IMo, IO, MoBi. and BiMo in Bi2MoO6 in the presence of a fixed concentration of donors [D+] = 1018 cm–3 under different chemical potential conditions of (a) AU, (b) HU, (c) NU, (d) GU, and (e) EU derived from PBE + U calculations are shown. The Fermi levels in thermodynamic equilibrium are listed in Table 1.

Upon A– doping from 20 to 900 K, the intrinsic defect concentration is determined by their formation energy relationship in the cyan zone of Figure 2 once more, which is the range of the newly calculated Fermi energy level increasing with T. At O-rich AU shown in Figure 4a, compensating A– from 20 to 800 K, MoBi2+ is the highest concentration defect with the lowest formation energy in the cyan zone shown in Figure 2a, so [MoBi] is equal to [A–]/2 for the secondary ionization of MoBi. Although the concentration of MoBi0 increases with T increasing, the compensation between MoBi and A– is unchanged for the neutral state of MoBi0. Then, as the temperature further increases to above 800 K, [MoBi] increases above the value necessary to compensate for [A–] owing to the significant thermal activation of [VBi3–].36 At O-rich EU below 800 K shown in Figure 4e, VO is the highest concentration defect for its lowest formation energy in the cyan zone shown in Figure 2b and compensates A–, so [VO2+] = [A–]/2 holds. With T increasing above 800 K, [VO] increases above the value required for compensation [A–] due to the obvious enhancement of thermal excitation of BiMo1–. From the above analysis of intrinsic compensation for A–, the carrier concentration of the system is less than 1016 cm–3. The low efficiency of the A– doping effect under O-rich conditions is displayed.

At the moderate point, NU, as shown in Figure 4c, the lowest formation energy is within the cyan zone of the calculated Fermi level, as shown in Figure 2c; MoBi1+ has the highest concentration, always compensating A–, so [MoBi] = [A–] still holds. At points GU and HU shown in Figure 4d,e, MoBi0 with the lowest formation energy within the cyan zone has the highest concentration from 20 to 900 K but has nothing to do with the intrinsic compensation because of its neutral state. At low temperatures, MoBi compensates A–, so [MoBi1+] is equal to [A–]. At high temperatures, with the thermal excitation of VBi for GU and BiMo3– for HU increasing, [MoBi] increases above the value necessary to compensate for [A–], then [MoBi1+] = ([A–] + 3[VBi]) for GU and [MoBi1+] = ([A–] + 3[BiMo]) for HU holds. n0 is more than 1016 cm–3 for GU and 1017 cm–3 for HU. As ΔμO decreases from NU to GU to HU, n0 is slightly lower than that with only intrinsic defects, suggesting that A– doping is negatively efficient for its conductivity.

After D+ doping from 20 to 900 K, the EF zone moves to CBM due to the increase in electron concentration. The intrinsic defect concentration is newly determined by their formation energy relationship in the blue zone, as shown in Figure 2. However, EF decreases with T increasing because of the increased hole concentration from thermal excitation.39 At O-rich AU in Figure5a, VBi3– with the lowest formation energy in the blue zone compensates D+, and [VBi] = [D+]/3 holds. With T increasing, the thermal excitation of BiMo1– increases, so [VBi] improves above the value necessary to compensate [D+] and also compensates [BiMo1–] simultaneously to satisfy the charge-neutral condition.

At O-rich EU in Figure 5b, BiMo1– has the lowest formation energy in the blue zone and compensates D+ for T < 700 K with [BiMo] = [D+] holding. After that, [BiMo1–] increases above the value necessary to compensate [D+] due to the increase of VO thermal activation. p0 is more than 1016 cm–3, only near 900 K, showing lower conductivity. At the moderate point, NU is shown in Figure 5c, VMo6– with the lowest formation energy that compensates D+ and [VMo] = [D+]/6 holds below 280 K. Then, above 280 K, VBi3– becomes to compensate D+ and [VBi] = [D+]/3 holds. The appearance of high compensation of MoBi0 at high temperatures does not affect the compensation relationship and carrier concentration for its neutral charge state. n0 is less than 1016 cm–3, even near 900 K. At the moderate points, HU and GU are shown in Figure 5b,d, MoBi with the lowest energy in the blue zones in Figure 2d,e has the highest concentration. BiMo3– for HU and VBi for GU compensate for D+ at low temperature and increases above the necessary value of compensation for [D+] due to the increasing thermal activation of with T. With ΔμO decreasing from NU to GU to HU, n0 increases and reaches the highest concentration of more than 1017 cm–3 near 900 K. As ΔμO decreases from NU to GU to HU, n0 is slightly higher than that with only intrinsic defects, suggesting that D+ doping is positively efficient for its conductivity. The O-poor chemical growth conditions are conducive to the conduction of photogenerated carriers.

4. Conclusions

The formation energy and concentration of intrinsic defects in Bi2MoO6 with/without A– and D+ doping are explored under different chemical conditions from 120 to 900 K by the GGA + U method. The highest electron concentration is revealed at the relative O-poor point HU with only intrinsic defects. Moreover, the electron concentration can be further improved after D+ doping, indicating that the O-poor chemical growth conditions are conducive to photogenerated carriers’ conduction. At the same time, we found that the diagram of formation energy vs Fermi level determines the intrinsic defect and carrier concentration under different conditions. During A–/D+ doping, EF moves closer to VBM/CBM for the increasing concentration of holes/electrons. Once the doping conditions are determined, the corresponding EF is only limited to a small region in the diagram of formation energy vs Fermi level, from which the magnitude relationship of defect concentration can be directly derived from their formation energy. The lower the defect formation energy is, the higher the defect concentration is. The defect with the lowest formation energy has the highest concentration. With EF moving under different doping conditions, the intrinsic defect concentration changes accordingly. This provides us with a method to adjust the intrinsic defect concentration and deepens our knowledge about comprehension and application of the diagram of formation energy vs Fermi level.

Acknowledgments

The work is carried out at the Shanxi Supercomputing Center of China, and the calculations are performed on TianHe-2. The authors also thank the Supercomputing Center of USTC for providing the computational time.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c02161.

  • DFT and formation energy calculation method; details about the chemical potential calculation (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao3c02161_si_001.pdf (229.7KB, pdf)

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