Cation Vacancy in Wide Bandgap III‐Nitrides as Single‐Photon Emitter: A First‐Principles Investigation

Abstract

Single‐photon sources based on solid‐state material are desirable in quantum technologies. However, suitable platforms for single‐photon emission are currently limited. Herein, a theoretical approach to design a single‐photon emitter based on defects in solid‐state material is proposed. Through group theory analysis and hybrid density functional theory calculation, the charge‐neutral cation vacancy in III‐V compounds is found to satisfy a unique 5‐electron‐8‐orbital electronic configuration with T_d symmetry, which is possible for single‐photon emission. Furthermore, it is confirmed that this type of single‐photon emitter only exists in wide bandgap III‐nitrides among all the III‐V compounds. The corresponding photon energy in GaN, AlN, and AlGaN lies within the optimal range for transfer in optical fiber, thereby render the charge‐neutral cation vacancy in wide‐bandgap III‐nitrides as a promising single‐photon emitter for quantum information applications.

Neutral cation vacancy in wide bandgap III‐nitrides including AlN, GaN, and AlGaN is predicted to be suitable for single‐photon emission, it has zero phonon line that lies within the optimal range for transmission in optical fiber and a moderate radiative rate, thereby render it as a promising single‐photon emitter for quantum information applications.

1. Introduction

Single‐photon is suitable to serve as a quantum bit (qubit)^{[ 1 ]} for the encoding, communication, and measurement of quantum information^{[ 2 ]} since it can travel over long distances while interacting weakly with the environment and can be manipulated with linear optics.^{[ 3 ]} Single‐photon emitter (SPE) is hence the central building block for many quantum information technologies. The early‐stage SPE was based on single‐atom,^{[ 4}, ^{5 ]} however, it suffered from drawbacks such as low efficiency and reliability. Solid‐state materials including quantum dots^{[ 6}, ^{7 ]} and color centers^{[ 8}, ^{9 ]} with atom‐like isolated levels are promising types of single‐photon sources due to the convenient combination with advanced technologies of the semiconductor industry. The color center, which is a kind of fluorescent defect in solid‐state material with the wavefunction localized on the atomic scale length,^{[ 10 ]} can potentially realize single‐photon emission at room temperature.^{[ 11 ]} For instance, the diamond's NV (N_CV_C) center,^{[ 12 ]} SiV (Si_CV_C) center;^{[ 13 ]} the silicon carbide's silicon‐vacancy (V_Si) center,^{[ 14 ]} divacancy (V_SiV_C) center,^{[ 15 ]} antisite‐carbon‐vacancy (C_SiV_C) center;^{[ 16 ]} and the zinc oxide's zinc‐vacancy (V_Zn) center^{[ 17 ]} have received a lot of investigations.

In recent years, benefits from the mature technique of material growth and device fabrication, III‐V compounds have become commercial semiconductors,^{[ 18 ]} among them the III‐nitrides that possess wide‐bandgap^{[ 19 ]} meet the criteria of host material for single‐photon emission. In 2017, Berhane et al. had realized the room‐temperature single‐photon emission in GaN.^{[ 20 ]} In 2018, Zhou et al. had reported near‐infrared emitters based on GaN with high photon purity.^{[ 21 ]} In 2020, Xue et al. and Bishop et al. had reported room‐temperature single‐photon emission in AlN,^{[ 22}, ^{23 ]} the antisite‐nitrogen‐vacancy (N_AlV_N) and divacancy (V_AlV_N) were predicted to be possible sources of the single‐photon signal.^{[ 22 ]} As the III‐nitrides belong to ionic semiconductor, the dangling bond energy level lies in the lower part of the bandgap for cation vacancy (V_cation), while it lies in the upper part of the bandgap for anion vacancy (V_anion).^{[ 24 ]} It was found that the defect energy level for nitrogen‐vacancy (V_N) in AlN was close to the conduction band maximum (CBM). Transition metal dopant substitution^{[ 25 ]} and strain‐driven^{[ 26 ]} strategies were proposed theoretically to adjust the defect electronic configuration to make V_N in AlN suitable for single‐photon emission. For V_cation, since its defect energy level was found close to the valence band maximum (VBM), many theoretical investigations were focused on negatively charged V_cation, including its light emission^{[ 27}, ²⁸, ^{29 ]} and carrier doping^{[ 30 ]} property. However, whether V_cation can realize single‐photon emission by tuning its electronic configuration remains unclear.

By reviewing the previous reports, we find most of the successful host materials are in wurtzite and zinc‐blende structures, in which all atoms are tetrahedrally coordinated. The four sp³ dangling bonds (ψ_i, (i = 1, 2, 3, 4)) around a vacancy have the same energy level 〈ψ_i|H|ψ_i〉 = E and inter‐bond interaction 〈ψ_i|H|ψ_j〉 = −Δ/4. Due to the interaction between dangling bonds, the energy level splits into a nondegenerate A ₁ state and a triple degenerate T ₂ state with an energy difference of Δ under the T _d symmetry. The relative position of A ₁ and T ₂ depends on the sign of 〈ψ_i|H|ψ_j〉 as shown in Figure 1, and it determines the relative energy level for different electronic configurations. For the case of 〈ψ_i|H|ψ_j〉 < 0, the many‐electron effect analysis shows that a ‘5‐electron‐8‐orbital’ electronic configuration is suitable for single‐photon emission. Whereas all the defect levels in the spin‐up channel are occupied; in the spin‐down channel, only the low energy A ₁ level is occupied, and all the T ₂ levels are empty, the optical emission corresponds to the transition of A ₁↔T ₂ (details are described in the Supporting Information).

Figure 1.

a) The schematic process of sp³ dangling bond energy level splitting under T _d symmetry. b) The 5‐electron‐8‐orbital electronic configuration when 〈ψ_i|H|ψ_j〉 < 0.

In this work, based on group theory analysis and first‐principles computation, we present a comprehensive study of the single‐photon emission property of V_cation in III‐V compounds. We find that the charge‐neutral V_cation in III‐V compounds can meet the specific 5‐electron‐8‐orbital electronic configuration. Moreover, the charge‐neutral V_cation in wide bandgap III‐nitrides including GaN, AlN, AlGaN, and low In component InGaN are thermodynamically stable and can serve as SPE. The corresponding defect energy level, formation energy, and photon energy of the proposed SPE are presented

2. Experimental Section

It was first characterized whether charge‐neutral V_cation in III–V (III = Al, Ga, In; V = N, P, As) compounds satisfy the 5‐electron‐8‐orbital electronic configuration. The band structures calculated with HSE06 hybrid functional are shown in Figure 2 (the atomic structures are shown in Figure S3, Supporting Information). Taking the Fermi level as a reference, the VBM position of the host material tends to increase as the group III component varies from Al to In when fixing the group V component or as the group V component varies from N to As when fixing the group III component. The orbital contribution of anions around V_cation shows the defect levels of V_cation in the spin‐up channel are fully occupied, while in the spin‐down channel the A ₁ state lies below the T ₂ states and only the A ₁ state is occupied. This indicates a negative inter‐bond interaction (〈ψ_i|H|ψ_j〉) between the anion dangling bonds, the charge‐neutral V_cation in III‐V compounds thus satisfies the 5‐electron‐8‐orbital electronic configuration.

Figure 2.

Band structures for neutral V_cation in III–V compounds calculated with HSE06 functional, here G (0.0, 0.0, 0.0), F (0.0, 0.5, 0.0), Q (0.0, 0.5, 0.5), Z (0.0, 0.0, 0.5), B (0.5, 0.0, 0.0) refer to the high‐symmetry special points in the first Brillouin zone, the Fermi level is set to zero, the orbital contribution of four anions around V_cation is represented by red dots.

To serve as an SPE, the defect energy level of V_cation should lie within the bandgap to make the optical transition do not introduce interference from electronic states of the host material.^{[ 24 ]} The relative position between the defect energy level of V_cation and band edge of host material depends on the energy level of the anion sp³ dangling bond, the corresponding symmetry‐induced splitting, and the bandgap of the host material. For V_cation in III‐phosphide and III‐arsenide, as shown in Figure 2d–i, the T ₂ states in the spin‐down channel are located within the bandgap, while the A ₁ state lies below the VBM, this can be attributed to the low sp³ level of P/As atom. Because the T ₂ states are degenerate and are all unoccupied, the charge‐neutral V_cation in III‐phosphide or III‐arsenide is not suitable for single‐photon emission. Since the sp³ dangling bond energy of the N atom is the highest one among all the group V elements,^{[ 31 ]} the possible case that the A ₁ level lies above VBM should be III‐nitride. As shown in Figure 2a–c, for V_cation in AlN, GaN, and InN, the A ₁ level in the spin‐down channel lies above the VBM. However, the bandgap of InN is too narrow, the defect levels of V_cation are all above the CBM. While V_cation in wide bandgap III‐nitrides of GaN and AlN are suitable for single‐photon emission whereas all the A ₁ and T ₂ levels lie within the bandgap.

Based on our previous analysis, it has been proposed to use charge‐neutral V_cation in wide bandgap III‐nitride as a potential SPE. To numerically assess the single‐photon emission property, the defect level of V_cation in larger supercells of GaN and AlN was calculated, each includes 399 atoms as shown in Figure 3a₁,e₁, with a Γ point only K‐mesh sampling. The defect level diagrams of V_cation in GaN and AlN are shown in Figure 3a₂,e₂ . The energy splitting (Δ) between A ₁ and T ₂ in GaN (1.45 eV) is smaller to that in AlN (1.64 eV). The interatomic distance (see Table S2, Supporting Information) shows that the distance between the N atom around V_cation is smaller in AlN, which results in a larger inter‐bond interaction and thereby larger energy splitting (Δ) in AlN. The energy differences between defect level and VBM/CBM in GaN and AlN are all larger than 0.9 eV, indicating the thermal transition from the host material to the defect state is small.

Figure 3.

a₁–e₁) The atomic supercell structures for V_Ga in GaN, and V_Al in Al_0.25Ga_0.75N, Al_0.5Ga_0.5N, Al_0.8Ga_0.2N, and AlN, the corresponding defect energy levels in the spin‐down channel (the VBM is set to zero) and absorption spectrum for calculated with HSE06 functional are shown in (a₂–e₂) and (a₃–e₃), respectively.

The strain effect on the III‐nitrides epilayer, which can be achieved by mechanical wafer bending experimentally, has been widely investigated. Here the strain effect on the single‐photon emission property of V_cation in GaN and AlN was also studied, biaxial strain vertical to the (0001) direction including a 95% compress strain and a 105% tensile strain was considered. The results (see Figure S9, Supporting Information) indicate that for V_cation in GaN and AlN, both the band edge position of the host material and the defect energy level change under the extrinsic strain, and they are all located within the bandgap in the considered strain range. For specific, the bandgap of the host material and the energy difference between A ₁ and T ₂ increase when applying a compress strain, while they decrease when applying a tensile strain. This offers a way to tune the single‐photon emission property of V_cation experimentally.

To examine whether the proposed SPE is optically active, the absorption spectrum of V_cation was calculated, the results for V_cation in GaN and AlN are shown in Figure 3a₃,e₃ , respectively. Since there are no in‐gap states in the spin‐up channel and the T ₂ states are nearly degenerate in the spin‐down channel, the obvious peak below 2 eV corresponds to the transition from A ₁ to T ₂, this indicates an optical transition can occur between the two states. The small and broad absorption of V_cation in AlN in Figure 3e ₃ includes the transition from VBM to T ₂ and from A ₁ to CBM, the calculated moment matrix |〈ψ_i|p|ψ_j〉|² (see Equation S24, Supporting Information) shows that the corresponding magnitude of A ₁ ↔ T ₂ is about 3 times larger than VBM ↔ T ₂ and A ₁ ↔ CBM, thus the broad absorption has little effect on the single‐photon emission property. The absorption spectrum for V_cation in strained GaN and AlN are shown in Figure S9, Supporting Information, the corresponding absorption peak of V_cation blue (red) shifted under a compress (tensile) strain, consistent with the change of the energy difference between A ₁ and T ₂.

In addition to the binary GaN and AlN, III‐nitride alloy is also widely investigated since it has a tunable bandgap. The single‐photon emission property of V_cation in III‐nitride alloy is now calculated, the wurtzite structure of III‐nitride alloy is built by cluster expansion method,^{[ 32 ]} the corresponding unit cell structures are shown in Figure S1, Supporting Information. The structure of V_cation in III‐nitride alloy is determined by directly remove a cation from the perfect alloy, as indicated later, the formation energy of neutral V_cation is high, such a non‐equilibrium way is practical to generate V_cation in the experimental condition.

For AlGaN alloy as a host material, the atomic structures with low, medium, and high Al composition of 0.25, 0.5, and 0.8 are chosen as representatives. The calculated band structures indicate that the CBM of AlGaN is contributed by the s orbital of the N atom (see Figure S2, Supporting Information). The VBM of AlGaN with low Al composition is contributed by the p _x and p _y orbital of the N atom. For AlGaN with high Al composition, the VBM is mainly contributed by the p _z orbital of the N atom. This results in a different light emission mode in the electrically pumped light emission device,^{[ 33 ]} this property can be used to separate the light signals from host material and V_cation efficiently. The calculated defect energy level and absorption spectrum of V_Al in AlGaN with different Al compositions are shown in Figure 3b–d (the results for V_Ga in AlGaN are shown in Figure S10, Supporting Information), the qualitative property of defect levels of V_cation in AlGaN is the same as that of GaN and AlN. Due to the different interactions between the Al‐N and Ga‐N bond, the N atoms around V_cation move unsymmetrically from their original position. Such a symmetry‐lowing effect caused by the random alloy reduces the coupling between sp³ dangling bonds and splits the degenerated T ₂ states. Also, as shown in Figure 3, the optical transition is allowed between A ₁ and T ₂ for V_cation in AlGaN, the moment matrix (see Equations S19 and S21, Supporting Information) of the broad absorption peak in Figure 3c₃,d₃ is similar to the case of V_cation in AlN, and it does not affect the single‐photon emission property.

For InGaN alloy, previous calculation showed that V_cation was suitable for single‐photon emission in GaN but not InN, which is due to the low CBM position of InN. Since the bandgap of InGaN decreases monotonically with the In component, there should be a maximum In component for V_cation to serve as an SPE in InGaN alloy. Therefore, the effect of different In compositions on the single‐photon emission property of V_cation is calculated, it is found that for V_cation in In_0.25Ga_0.75N, the lowest T ₂ state of V_cation is nearly in resonance with the CBM, in this case, the insulation of the CBM is broken. While for a low In component case of In_0.125Ga_0.875N, all the defect energy levels in the spin‐down channel are located within the bandgap (see Figures S4 and S6, Supporting Information). It was concluded that for V_cation to realize single‐photon emission in InGaN, a maximum component of In should not exceed about 25%. The calculated defect level and absorption spectrum of V_cation in In_0.125Ga_0.875N are qualitatively the same as the case of GaN and AlN, the results are shown in Figure S8, Supporting Information.

To quantitatively characterize the single‐photon emission property of V_cation, the zero‐phonon line (ZPL) was calculated, which is the optical transition energy without the phonon contribution. The excited‐state structure was optimized with a constraint DFT method^{[ 34 ]} by restricting the excited‐state electronic configuration. The results are listed in Table 1, and the corresponding interatomic distances between anions at ground (excited) state are listed in Table S2, Supporting Information. It can be seen that the ZPL of V_cation in pure GaN and AlN shows a monotonic dependence on the strain, it increases (decreases) under the compress (tensile) strain. For AlGaN alloy, though the mixing of Al has a similar monotonic effect on the lattice constant, the local environment for V_cation differs a lot, it affects the geometry of ground and excited states and then affects the ZPL. Even in the same AlGaN alloy, the ZPL of V_Al and V_Ga differs a lot, thus, the ZPL does not show an obvious dependence on the mixing ratio of AlGaN. In recent experimental investigations, the single‐photon emission in GaN with ZPL from 1085 to 1340 nm has been observed,^{[ 21 ]} based on our ZPL results, the V_cation should have contributions to the corresponding single‐photon signal. The ZPL of V_cation in these III‐nitrides has a large overlap with the optimal range of ≈1.2−1.6 μm that can reduce the attenuation^{[ 35 ]} for optical fiber telecommunication. Besides, the calculated radiative lifetime τ_rad of V_cation, as listed in Table 1, are comparable to that of the NV⁻ center in diamond (≈10−30 ns).^{[ 36 ]} These advantages indicate that V_cation is suitable for practical quantum communication application.

Table 1.

Calculated moment matrix |〈ψ_i|p|ψ_j〉|², transition energy ΔE between defect levels, radiative lifetime τ_rad, and ZPL for V_cation in GaN, AlN, AlGaN, and InGaN

	|〈ψi|p|ψj〉|2 [au]	ΔE [eV]	τrad [ns]	ZPL [eV]
VGa in 95% strain‐GaN	1.90 × 10−2	1.97	14.23	1.49
VGa in GaN	1.05 × 10−2	1.45	35.18	0.70
VGa in 105% strain‐GaN	6.06 × 10−3	1.08	81.56	0.57
VAl in Al0.25Ga0.75N	9.22 × 10−3	1.22	48.59	0.68
VGa in Al0.25Ga0.75N	1.31 × 10−2	1.30	32.04	0.92
VAl in Al0.5Ga0.5N	1.61 × 10−2	1.35	25.80	0.76
VGa in Al0.5Ga0.5N	1.31 × 10−2	1.25	34.28	0.70
VAl in Al0.8Ga0.2N	1.60 × 10−2	1.46	24.72	0.84
VGa in Al0.8Ga0.2N	1.71 × 10−2	1.45	23.29	0.96
VAl in 95% strain‐AlN	2.59 × 10−2	2.10	10.83	1.96
VAl in AlN	2.24 × 10−2	1.64	16.03	0.94
VAl in 105% strain‐AlN	8.54 × 10−3	1.36	50.63	0.72
VIn in In0.125Ga0.875N	7.38 × 10−3	1.14	62.78	0.62
VGa in In0.125Ga0.875N	4.48 × 10−3	1.17	100.63	0.56

As one of the key factors for the proposed SPE, the 5‐electron‐8‐orbital electronic configuration should be stable in experimental conditions. Here, the thermodynamic stability of V_cation in GaN, AlN, and AlGaN/InGaN alloy was assessed. The formation energies as a function of the Fermi level are shown in Figure 4. It is seen that different charge states of V_cation defect can be stable in the bandgap, the neutral V_cation is stable in the lower part in the bandgap, indicating the p‐type III‐nitrides is requested to guarantee the 5‐electron‐8‐orbital configuration. Recently, through using superlattice doping,^{[ 37 ]} polarization‐induced doping^{[ 38 ]} techniques, etc., the p‐type doping efficiency in III‐nitrides can be effectively enhanced, it is possible to take advantage of these carrier doping techniques to make charge‐neutral V_cation thermodynamically stable. However, as an impurity, the dopant may affect the property of SPE, the effect of Mg_cation as an example was tested, the results show the major property of SPE will not be affected by the cation dopant as long as the structure and local electronic configuration of V_cation is maintained (see Figures S5 and S7, Supporting Information). For practical application, since the atomic structure of V_cation is simple, there are various techniques to achieve it such as electron irradiation,^{[ 39 ]} and pulse laser irradiation,^{[ 40 ]} the SPE based on V_cation is thus achievable in experimental conditions.

Figure 4.

The formation energy of V_cation in GaN, AlN, AlGaN, and InGaN at N rich condition, the red, blue, and green lines corresponds to V_Ga, V_Al, and V_In, respectively, the corresponding colored area indicates the Fermi level where neutral V_cation is stable.

For the SPE in bulk material, refraction is an issue that strongly influences the signal extracting. In practice, recent structures of III‐nitrides generally have a size of less than a few hundred nanometers, which is far less than the photon wavelength, the refraction issue is thus irrelevant. Since the mono vacancy structure possesses no inversion symmetry, the external field induces charge fluctuation and causes spectral diffusion,^{[ 41 ]} however, its magnitude is not necessarily large for a single vacancy as indicated in a recent theoretical study.^{[ 42 ]} The reported SPE here is only applicable in GaN and AlN among all the III‐V compounds, where the inter‐bond interaction 〈ψ_i|H|ψ_j〉 is negative, and the A ₁ state lies below T ₂. As indicated in Figure 1, when 〈ψ_i|H|ψ_j〉 > 0 the T ₂ states lies below A ₁, which results in a different electronic configuration, further numerical calculations of vacancy with a T_d symmetry in other material is a promising way to searching new SPE.

3. Conclusion

In summary, we have symmetrically investigated the single‐photon emission property of V_cation in the III‐V compound. Based on the group theory analysis and first‐principles calculation with hybrid density functional, we predict that the charge‐neutral V_cation in III‐V compounds has a unique 5‐electron‐8‐orbital electronic configuration, which is suitable for single‐photon emission. Furthermore, we confirm that the charge‐neutral V_cation can only serve as SPE in wide bandgap III‐nitrides among all the III‐V (III = Al, Ga, In; V = N, P, As) compounds. The charge‐neutral V_cation in AlN, GaN, and III‐nitride alloy is thermodynamically stable and the corresponding ZPL lies within the optimal range for low‐loss fiber transmission, which makes this type of SPE particularly useful in practical applications. Our investigation also sheds light on the concept of designing an SPE with a precisely tuned electronic configuration.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Zang H., Sun X., Jiang K., Chen Y., Zhang S., Ben J., Jia Y., Wu T., Shi Z., Li D., Cation Vacancy in Wide Bandgap III‐Nitrides as Single‐Photon Emitter: A First‐Principles Investigation. Adv. Sci. 2021, 8, 2100100. 10.1002/advs.202100100

Data Availability Statement

Research data are not shared.