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Abstract
First-principles analyses are performed on the diamond europium vacancy (EuV) color center. Three different models indicate that the structure of the EuV color center contains a stable vacancy around the Eu atom. Energy band calculations show that the stable EuV color center has spin polarization and its spin-up energy level structure is highly suitable as a single-photon source. The zero-point transition energy is 1.989 eV (623 nm). The existence of metastable energy levels in the EuV is also predicted. Nitrogen atoms have a negative impact on the electronic structure of the EuV, in comparison to diamond color centers such as NE8 and TiV-N.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Research on single-photon sources is being conducted rapidly, and the numerous advantages of a diamond color center have aroused great interest among researchers all over the world [1]. Diamond is an insulating material with a wide band gap of 5.4 eV which is greater than the span of visible light energy. The host material has minimal interference with the defect electron energy level introduced in the band gap. Diamond is colorless, non-toxic, and biocompatible, and the generation of single-photons in diamond is stable and controllable at room temperature [2]. Diamond color centers have a wide range of applications in quantum spintronics [3], photonics [4], biomedical markers [5], and magnetic sensors with high sensitivity in various spin information devices [6,7], quantum computing devices [8,9], and many other areas. Since the first report of photodetection magnetic resonance at room temperature of nitrogen-vacancy (NV) color centers in 1997 [10], single-photon sources based on diamond have been developed, and numerous diamond color centers have been reported. One of the most distinct color centers is the negatively charged NV color center (NV−), which has a spin-triplet state [11] and a strong optical transition observed by uniaxial stress measurements. The zero-phonon line (ZPL) of the NV− is 1.945 eV (637 nm) and this color center has an extremely long spin coherence time at room temperature [12]. In 2004, Gaebel [13] discovered a new type of diamond color center consisting of a nickel-nitrogen complex (NE8), in which light-excited undetected defects were found at room temperature. The emission wavelength was 800 nm, and the emission bandwidth was 1.2 nm, indicating that NE8 is a good material for use as a telecommunications fiber. In 2009, Aharonovich [14] used a focused ion beam implantation method to inject Ni and Si atoms into a large diamond crystal prepared by chemical vapor deposition. An unidentified Ni-related diamond composite color center was found. The room temperature photoluminescence spectrum was narrow and in the near-infrared region at 768 nm, and the lifetime was up to 2 ns. These photophysical properties were superior to those of the single-photon emitting nitrogen-vacancy and Ni-N complexes. In 2013, Liu et al. [15] studied the Cr-related color center using first-principles studies. They found that the formation energy of Cr2V-NC is lower than that of Crint-, CrC-, Cr2V-, and Cr2V-OC in a N-rich environment. In addition, the Cr2V-NC structure introduced strong spin polarization in the energy band structure of diamond, which is conducive to the emission of a single-photon source. In 2017, the Cheng research group theoretically predicted a new type of diamond color center with Si atoms (SiV) [16]. The structure of the SiV color center is analogous to that of the NV− color center. Similar to the diamond NV color center structure, the structure consisted of a replacement Si atom and a surrounding C vacancy. The two zero-phonon lines of this color center structure were found to be 1.12 and 1.22 eV, and this color center had more spin manipulation freedom than the NV−. In 2018, Czelej et al. [17] theoretically verified that the experimentally observed N3 (titanium-nitrogen) and OK1 (titanium-vacancy-nitrogen) centers contain neutral Ti-N and TiV-N defects. They also predicted that a low-energy excited state is present in the middle of a few spin channels in TiV-N0, which can be used as a single-photon source near the infrared region.
Although current research on diamond color centers has achieved numerous results and applications, the most commonly studied diamond color centers are the NV color center [18–19], the SiV color center [20], and the NE8 color center [21]. These color centers each have their advantages and disadvantages in practical applications. For instance, the NV color center can exhibit the quantum spin state, but its excited state fluorescence lifetime is long and cannot achieve the highly efficient emission of a single photon source [22]. The SiV color center has high excitation efficiency, but it does not exhibit the quantum spin state [23]. The NE8 color center has the advantages of short fluorescence lifetime and high rate of single-photon generation, as well as stability at room temperature. On the other hand, the controllable preparation of the NE8 color center is still immature, limiting its practical use [24].
Rare earth luminescent materials have strong absorption capacities, high conversion rates, stable physical properties, linear light emission profiles, and high purity luminescent color. In addition, the thermal stability and luminescence output of hybrid matrix materials are improved by the incorporation of rare earth complexes. Hence, rare earth luminescent materials are some of the mainstream materials for applications in lighting, anti-counterfeiting, solar energy conversion, detection, and display.
The photoluminescence properties of rare earth lanthanide compounds have been attracting much attention for decades [25]. Most studies on rare-earth electroluminescent complexes focus on lanthanide compounds because of their unique narrow emission bands in the visible and near-infrared spectral regions [26]. These materials have high application potential as optical amplifiers, optical waveguides, and photoluminescent diodes. Excitation in the lanthanide rare earth elements is due to the internal f-f orbital transitions within the 4f shell. Because the partially filled 4f shell is shielded by the full 5s2 and 5p6 shells, the ligands in the first and second coordination spheres interfere, to a limited extent, with the electronic configuration of the lanthanide ions. As a result, the properties of lanthanide luminescence are affected, particularly the long lifetime of photons with narrow-band emission, and the excited states [27]. Thus, studying these luminescent lanthanide compounds in hybrid materials is of great interest. For the current research, Andrew Magyar et al. [28] prepared Europium defects diamond through experiments. It shows that impurities can be effectively controlled into the diamond by electrostatic assembly and chemical vapor deposition growth, and it also provides a basis for the preparation of the color center of europium related defects in diamond. In the study of Denny E.P. vanpoucke et al. [29], they have calculated the supercell structure of 64 atoms, theoretically studied the stability of the color center of europium related defects in diamond. The results also show that europium has been successfully doped into diamond by their experiments, indicating that europium-containing material can remain after exposure to diamond growth plasma if drop-cast on the surface. However, it can’t be proved by experiments that the color center of europium related defects in diamond is formed. Combined with the results of the above researches, there is not much theoretical research on the color center about the europium related defects in diamond, and there is still a lot of knowledge about it waiting for us to explore. It is need to further improve the structure research, explore its electrical properties and consider the influence of common elements doping into the color center for this research. Different from the phenomenological theory of experiment, we utilize ab initio calculations and simulations to study how a Europium vacancy affects the energy band diagrams and optical properties of diamond. We also incorporated nitrogen defect impurities into the lattice and studied how this alters the energy bands.
2. Calculation method
The electronic structure calculations were carried out using the spin-polarized density functional theory (DFT) and the projector augmented wave method [30,31]. The generalized gradient approximation of (Perdew-Burke-Ernzerhof)PBE formalism for the exchange and correction functional was conducted and implemented in the Vienna ab initio simulation package (VASP) [32,33]. A 128-site supercell was studied, corresponding to a diamond cube of 4×2×2 non-primitive cubic cells. The calculated lattice constant of the diamond supercell is a = b=c=3.568 Å after relaxation; this is in good agreement with the experimental value of 3.567 Å [34]. As rare-earth elements have a unique 4f orbital, the parameter settings U=7.397 and J=1.109 [28] were calculated, and Brillouin zone sampling was carried out by using gamma centered 5×5×5 K-point mesh. The plane wave cut-off energy was 450 eV. The criteria for terminating electronic or ionic iterations was 10−5 eV and the atoms were relaxed until the internal forces were within 0.01 eV/Å. The electronic structures of the C, N, and Eu atoms were 2s22p2, 2s22p3, and 4f76s2, respectively.
The crystal binding energy equation is defined as follows:
To further analyze the formation difficulty of each structure and to reveal the possible valence state, the defect formation energy was calculated using the established model. The defect formation energy is as follows:
3. Results and discussion
Based on a diamond supercell that contains 128-site C atoms, a EuV color center structure with Eu as the main doping element and one to three vacancies around the Eu atom was constructed (i.e., Eu1V, Eu2V, and Eu3V). These structures are shown in Figs. 1(a), 1(b), and 1(c). Since the difference in atomic radii between a Eu atom and a C atom is large, the Eu atom was not considered to be substituted for the C atom. The relaxation calculations were performed on the established supercells. The binding energies of each structure were calculated using Eq. (1). The binding and total energies are shown in Table 1.
Table 1. Total energy, binding energy and defect forming energy of the diamond Eu-related defects
Analytical calculations show that the largest binding energy is for one vacancy near the Eu atom (in comparison to two and three vacancies), which indicates that the Eu1V structure is theoretically highly stable. After relaxation, the Eu atom moves in the direction of the vacancy and forms a double vacancy structure with Eu at the center. The defect formation energies of the different valence states (0, + 2, + 3) were also calculated for the three kinds of vacancy defect structures of diamond with Eu doping, and are shown in Table 1. A lower defect formation energy means it is easier to form the crystal. It can be seen from the calculated results that compared with the two and three vacancy structures, a Eu atom in the center of a double vacancy (Eu1V after relaxation) is readily formed, and the valence state may be zero. From these combined results, it can be concluded that a structure consisting of a Eu atom in the center of a double vacancy is the most stable structure. Therefore, the Eu1V structure will be used in further calculations.
The differential charge density of the EuV (Fig. 2) was calculated to clearly observe the bonding between the Eu atom and the surrounding C atoms. The results show the existence of large differential charge densities between the Eu atom and the surrounding six C atoms. A charge transfer occurs between the Eu atom and the six C atoms and it can be deduced that the Eu atom indeed forms bonds to these neighboring C atoms. This may be due to the presence of vacancies that have excess unpaired electrons. The three C atoms adjacent to the vacancies actively move closer to the Eu atom to form a new stable structure.
Fig. 2. Differential charge density of the diamond EuV. The C atoms around the Eu atom were numbered for convenience.
To quantitatively analyze the electron transfer of the Eu atom and the surrounding C atoms, bader charge analysis was performed and the calculated data is shown in Table 2. When the Eu and C atoms form a bond, the charge of the Eu atom is reduced from 17e to 15.781e, and the charge around the C atoms is increased by 0.177-0.227e. Thus, the Eu atom loses electrons during the bonding process and an ionic bond is formed.
Table 2. Bader charge analysis of the Eu atom and the peripheral C atoms
Figure 3 shows the bonding of the Eu atom to the surrounding C atoms after relaxation. The six C atoms move closer to the Eu atom. This structure is similar to that of the NE8 [35], SiV [36], CrV [15], and PrV [37] color centers. The bond lengths and bond angles in the diamond EuV structure are shown in Table 3.
Table 3. Bond lengths and angles for a Eu atom bonded to the surrounding C atoms in the diamond EuV structure
The change in atomic positions causes a redistribution of the outer charge. Due to the existence of defects, the electronic energy level is re-arranged. To understand the electronic structural properties of the EuV, the calculation of its energy band structure is necessary. Figure 4 shows that the structure demonstrates a spin polarization phenomenon which is favorable for single-photon production. The spin-down energy band is different from the spin-up energy band. The band gap of the spin-up energy band is 0.422 eV, and the degenerate energy levels were all split and moved up, which is beneficial for the excitation of the system's electrons. The spin-down band structure is denser than that of the spin-up; this is less favorable for electron excitation. The zero-point transition energy of the color center is estimated. Theoretically, the electronic transition between the spin-up unoccupied energy level and the occupied energy level corresponds to the experimentally observed zero phonon line (ZPL) energy. The energy difference between the calculated ground state, a1, and the excited state, e, is 1.989 eV (623 nm), see Fig. 5. This agrees with the experimental fluorescence spectrum of the ZPL observed previously [30] (emission at ca. 620 nm). There is also an energy level, a2, present between the excited state (e) and the ground state (a1). Therefore, the microstructure of the Eu-related color center observed in the experiment [30] is equivalent to the EuV structure constructed in the current study. The existence of a metastable energy level structure will reduce the efficiency of photon generation.
Fig. 4. Energy band structures of the diamond EuV; (a) the spin-down band, and (b) the spin-up energy band.
Fig. 5. The electronic transition energies of the EuV color center. The energy of the diamond EuV is is 1.989 eV (623 nm).
To study the contribution of each electron orbital to energy level transitions, the density of states (DOS) of the diamond EuV defects and the projected density of states (PDOS) of the six C atoms that bond with the Eu atom were calculated and are shown in Fig. 6. It can be seen that the a1 energy level mainly originates from the p orbital electrons of the C atoms and the f orbital electrons of the Eu atom. The a2 energy level primarily stems from the p orbitals of the C atoms. The “e” energy level mostly originates from the f orbital contributions of the Eu atom. The f orbitals of the Eu atom near the Fermi level and the p orbitals of the C atoms are hybridized. The calculation results also reveal the unique f-f transition characteristics of rare earth elements.
Fig. 6. The total density of states (T-DOS) of the EuV color center and the projected density of states (PDOS) of the six neighboring C atoms.
In general, N impurities are common in diamonds. Therefore, this work also considers the possible composite defects in a diamond lattice containing a EuV when N impurity atoms are introduced. From the understanding of the previous stable structure (Eu1V), and considering the possibility of a co-doped structure, the surrounding six C atoms were sequentially replaced by N atoms. Models with varying numbers of N atoms surrounding the EuV were constructed, see Fig. 7.
Fig. 7. Schematic of the diamond EuV composite structure, with N impurity atoms. (a) the EuV-N structure, (b) the EuV-2N structure, (c) the EuV-3N structure, (d) the EuV-4N structure, (e) the EuV-5N structure, and (f) the EuV-6N structure.
These six structures were relaxed, and the binding energies were calculated according to Eq. (1). The results are listed in Table 4. The binding energies are all between 7.36 and 7.46 eV; the fluctuation is small. These results indicate that if this type of diamond structure contains N atoms as defects or impurities, all six of the above variations may co-exist at a low energy cost.
Table 4. The total energies and the crystal binding energies of the diamond EuV composite structures with N impurity atoms
The energy band diagrams for each of the six structures were calculated and are shown in Fig. 8 and Fig. 9.
Fig. 8. The energy bands of the diamond EuV composite structures with N atom defects. (a) the spin-up of the EuV-N band structure, (b) the spin-down of the EuV-N bands tructure, (c) the spin-up of the EuV-2N band structure, (d) the spin-down of the EuV-2N bands tructure, (e) the spin-up of the EuV-3N band structure, (f) the spin-down of the EuV-3N bands tructure.
Fig. 9. The energy bands of the diamond EuV composite structures with N atom defects. (g) the spin-up of the EuV-4N band structure, (h) the spin-down of the EuV-4N bands tructure, (i) the spin-up of the EuV-5N band structure, (j) the spin-down of the EuV-5N bands tructure, (k) the spin-up of the EuV-6N band structure, (l) the spin-down of the EuV-6N band structure.
By analyzing the energy bands of each diamond composite defect structure, it is found that EuV-N, EuV-2N, EuV-3N, and EuV-4N retain the properties of a semiconductor, however, the energy levels near the Fermi level are dense when 1∼4 N atoms are doped into the EuV, this will lead to the formation of many intermediate states, meaning these are not conducive to the formation of a single photon source by single electron transition. Furthermore, EuV-5N and EuV-6N no longer display semiconductor properties. As the concentration of the N atoms increases, greater energy differences occur in the band diagrams. Compared with the original EuV band, the band does not contain too many split degenerate states when 5 or 6 N atoms doping, and the impurity band in the diamond band gap almost adheres to the boundary energy band of diamond, showing the band gap narrowing effect. Therefore, the presence of N atoms has a large effect on the electronic properties of the diamond EuV structure.
4. Conclusions
In this study, the structures and optical properties of diamond doped with Eu were revealed using first-principles calculations. The individual EuV structure and the effects of N impurities in diamond were analyzed. The results verified the bonding between the Eu atom and the surrounding six C atoms in the EuV structure. It was confirmed by first-principle calculations, and from the emission spectrum of the EuV observed in previous experimental work, that the Eu atom was in the center of double vacancy. This was found to be a stable arrangement. The energy band diagram indicated that a defect level appeared in the diamond band gap due to the addition of doping atoms, and spin polarization in the system was confirmed. The zero-point transition energy of the EuV structure was estimated to be 1.989 eV, corresponding to a photon wavelength of 623 nm. A metastable energy level was found in the band diagram of the diamond EuV color center. This may be detrimental to the quantum efficiency. It was considered that N atoms in the diamond may form a compound defect structure with the EuV and six possible structural models were constructed. These six structures may co-exist at a low energy cost, however, their energy band structures are dense and therefore not conducive to the formation of diamond color centers. This work provides a new theoretical basis for realizing a diamond color center with an optimal optical performance.
Funding
National Natural Science Foundation of China (61765012); Natural Science Foundation of Inner Mongolia (2019MS05008); National Key Research and Development Program of China (2017YFF0207200, 2017YFF0207203); Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region (2017CXYD-2, KCBJ2018031).
Disclosures
The authors declare no conflicts of interest.
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