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Abstract
This paper determines the stable configuration and electronic structure of Ce-related defects (CeV) in diamonds doped with N, B, and Si impurities using the first-principle method based on density functional theory (DFT) and the Vienna ab-initio simulation package VASP software package. To this end, the zero-phonon line size of the color center of the doped diamond CeV is calculated and the corresponding fluorescence wavelength is measured. The results provide a theoretical explanation of the influence of various impurities on the fluorescence of the CeV color center in diamonds and provides a reference for their fabrication and application.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The field of quantum communication has experienced rapid development over the recent years. Although quantum key distribution (QKD) provides theoretically unconditional security, it requires the emission of single photons at a time from single-photon sources. Therefore, the fabrication of a reliable single-photon source is critical to the implementation of QKD [1]. Owing to their unique characteristics, diamonds have been widely utilized in quantum information processing [2] and other fields. Among other favorable properties, the photoluminescence of the rare earth element exhibits high stability, long lifetime, and narrow bandwidth. Further, they facilitate the production of up-conversion or down-conversion fluorescence [3]. For these reasons, rare earth ions in optical crystals exhibit good benchmark performance in tasks such as storing quantum information over periods exceeding 1 second [4], storing and restoring the quantum state of a single photon [5], and storing the quantum entangled state [6].
A. Yelisseyev, H. Kanda et al. (2007) proposed the optical impurity defect model for substitution sites, interstitial sites, and double half-vacancy transition metals, and identified the primary trend of impurity transformation after annealing. The optics-to-electron paramagnetic resonance correlations have been established reliably only for very few transition metal centers. An investigation of defect structures in transition metals in diamonds and their spectral data revealed that color centers of transition metals have the potential to be used as single-photon sources [7]. K. Xia and R. Kolesov et al. (2015) observed that the trivalent Ce ion in Y3Al5O12 (YAG) replaced the trivalent Y ion to form the color center. [8–10]. By studying the low-temperature infrared absorption spectra of Yttrium Gallium Garnet (YGG), A. Wittlin et al. (2015) proved the existence of at least two Ce3+-related centers in YGG in addition to the primary Ce3+ sites located at the Y-ion substitution sites. The 5d-to-4f fluorescence of Ce3+ has also been observed under high pressure [11–12]. We calculated the structure of the diamond CeV2 color center and its electronic structure using the first-principles method, and theoretically determined that the structure is most stable when the Ce atom is located at the substitution site and there are two vacancies around it (the diamond CeV color center), and Ce atoms form bonds with six carbon atoms, C36, C39, C40, C81, C85, and C123. The energy band and density of states of the diamond CeV2 color center are calculated, and it is proved that the impurity states in the energy band are mainly composed of the 5d and 4f orbitals of Ce atoms. At the same time, the ground state of the diamond CeV2 color center is located in the 4f orbit, and the excited state is located in the 5d orbit. The zero-phonon line (ZPL) of the diamond CeV2 color center has been reported to be 2.528 eV, with a corresponding emission wavelength of 490.82 nm. The potential of nano-diamond CeV2 cores as excellent single-photon sources has also been established [13]. However, impurities are inevitably introduced during fabrication and testing, which interfere with the generation and detection of the color center fluorescence. Therefore, it is necessary to estimate the influence of common impurities on the electronic structure of the diamond CeV2 color center.
Introduction of impurity defects within diamond color centers during their fabrication via chemical vapor deposition (CVD) is inevitable [14]. The most common impurities are N, Si, and B. N impurities result from the exposure of the deposition chamber to the atmosphere or low purity of the starting gas. Since the covalent radius of N is similar to that of carbon, especially at low concentrations, it occupies the center of the diamond lattice, resulting in a substituted N-doped semiconductor diamond film. However, when the concentration is high, several N clusters are combined, altering the bonding in the film and its morphological structure [15]. During the preparation of diamonds via CVD using Si as the substrate, Si atoms enter the sample cavity due to the etching of the Si substrate by the hydrogen plasma, and Si-impurities are introduced during the growth process [16]. The covalent radius of Si is larger than that of carbon. Therefore, the size of crystal grains in Si-doped diamond film is reduced, inhibiting the growth of the (1,1,1) diamond surface and promoting the growth of the (1,1,0) diamond surface [17–19]. Excessive silicon content usually induces a high degree of secondary nucleation in the diamond film, which promotes the formation of graphite phases and increases the number of defects. In turn, the increase in the number of graphite phases quenches the fluorescence of the color center and the increase in the number of defects introduces unknown interference into it. In addition, studies have demonstrated that besides improving the conductivity of diamond films, an appropriate concentration of B-doping also improves the quality and morphology of the crystals [20]. However, excessive B-doping increases the stress and crystal defects in the film, resulting in poor electrical performance. In the in-situ doping of diamond lattices, B and N are the preferred elements [21]. Theoretical studies have revealed that simultaneous introduction of both B and N into the diamond structure enables the B-N composite structure to adjust the energy band of the diamond effectively, thereby improving its N-type semiconductor characteristics.
The aim of this study is to assess the influence of doping using varying concentrations of N, Si, B impurities on the fluorescence of diamond CeV2. To this end, we attempt to detect the existence of these impurities in diamond CeV2-related defects and their influence on their electronic structure. We expect our results to contribute to theoretical guidance for subsequent laboratory preparation and testing of diamond CeV2 color centers.
2. Materials and methods
The first-principle method based on DFT is used in this study to optimize the calculation parameters based on the Vienna Ab-initio Simulation Package (VASP) software [22–23]. Following optimization, the cutoff energy is set to 450 eV, the k-point sampling is taken to be 5 × 5 × 5, and pseudopotential PAW-PBE is selected. PAW-PBE is capable of accurately reproducing the diamond lattice constant as well as the phonon spectrum and its dependence on pressure and temperature. It can also be used to calculate the Raman spectrum of diamond, producing a result that is close to the experimentally measured value [24]. During calculation, the diamond CeV2 color center structure is assumed to be a 128-carbon diamond supercell and it is co-doped with N, Si, and B atoms. The atoms are relaxed until the internal forces are within 0.01 eV/Å and the total energy variation is smaller than 10−5 eV. The optimized diamond lattice constant is calculated to be a = b = c = 3.568 Å, which is consistent with the experimental value, 3.567 Å [25]. The Ce atom has a unique f orbital electron. Thus, during the calculation of the model containing Ce atoms, the calculation parameters of LDAUU = 7 and LDAUJ = 0.7 are set in Calculation file to predict the electron density of states for strongly localized Ce4f electrons more accurately [26].
The crystal cohesive energy is defined as follows:
3. Results and discussion
First, a calculation model for co-doping using N, Si, and B is established based on the stable structure of the diamond CeV2 color center. The bonding positions of C atoms close to the Ce atom are termed adjacent positions. The configurations of the adjacent positions when doped with 1–4 N atoms (CeV2-N, CeV2-2N, CeV2-3N, and CeV2-4N) are depicted in Fig. 1(a–d). The structure of the adjacent positions of the Ce atom when doped with a B atom (CeV2-B) is depicted in Fig. 1(e); that when doped with one B atom and one N atom simultaneously (CeV2-B-N), in Fig. 1(f); that when doped with one Si atom (CeV2-Si), in Fig. 1(g); and that when doped with one N atom and one Si atom simultaneously (CeV2-N-Si), in Fig. 1(h). Subsequently, in each of the eight aforementioned structures, impurity atoms were introduced in the position of the carbon atom (bonding position) leading to bonding with the Ce atom in the stable structure of CeV2. The nearest non-bonding position is closer to the position of the carbon atom. In the figures, the yellow spheres represent Ce atoms, the brown spheres represent C atoms, and the carbon atoms marked with respective atomic numbers represent those that bond with Ce atoms in the stable structure of the diamond CeV2 color center. Finally, the gray spheres represent N atoms, the green ones represent B atoms, and the blue ones represent Si atoms.
Find the total energy in the result of the relaxation calculation, and calculate the cohesive energy. It is evident from Table 1 that in all the co-doped structures, the total energy at the nearest position is smaller than that at the bonding position, while the cohesive energy at the nearest position is larger than that at bonding position. As the stability of the structure is directly proportional to the cohesive energy and inversely proportional to the total energy, the doped CeV2 color center is most stable when the impurity atoms occupy the nearest position.
Table 1. Total energy and Cohesive energy of Ce, B, N, and Si co-doped diamond structures
Now, the electronic structure is assessed based on the stable iterations of each of the eight aforementioned structures, i.e., in the cases when the impurity atoms occupy the nearest positions. Fig. 2 depicts the energy bands of the 8 stable co-doped structures, CeV2-N, CeV2-2N, CeV2-3N, CeV2-4N, CeV2-B, CeV2-B-N, CeV2-Si, and CeV2-N-Si. In the figure, the blue dashed lines represent the energy band with spin-down, and the solid red lines represent the energy band with spin-up.
Fig. 2. Band structures of different types of defects in co-doped diamond. (a) CeV2-N structure, (b) CeV2-2N structure, (c) CeV2-3N structure, (d) CeV2-4N structure, (e) CeV2-B structure, (f) CeV2-B-N structure, (g) CeV2-Si structure, (h) CeV2-N-Si structure.
Based on a comparison of the eight aforementioned energy band structures with the energy band structure of the diamond CeV2 color center [14], the following conclusions can be drawn. With respect to the CeV2-N structure depicted in Fig. 2(a), when doping is performed using a single N atom, no N impurity is observed. A new impurity energy level is generated, and the system continues to exhibit semiconductor properties and obvious spin polarization. In this case, the defects produce spin-polarized impurity states in the diamond band, which is conducive to the formation of single-photon source devices. Compared to the fluorescence transition energies of diamond CeV2 color centers, the energy required for the fluorescence transition following nitrogen doping is 2.58417 eV, with a corresponding fluorescence wavelength of 480.15 nm. Blue shift of the fluorescence spectrum is also observed. With respect to the CeV2-2N structure depicted in Fig. 2(b), When doping is performed using 2 N atoms, a new impurity level is not formed and the system continues to exhibit semiconductor properties. Compared to the CeV2 fluorescence transition energy, following doping with 2 N atoms, the transition energy is observed to be 2.65329 eV, with a fluorescence wavelength of 467.65 nm. Blue shift phenomenon is observed to increase. Similarly, in the case of the CeV2-3N structure depicted in Fig. 2(c), when doping is performed with 3 N atoms, new impurity levels are not produced. The system continues to exhibit semiconductor properties and obvious spin polarization. Compared to the fluorescence transition energy of the CeV2 color center, the transition energy changes to 2.31884eV, with a corresponding fluorescence wavelength of 535.10 nm. In this case, red shift of the fluorescence spectrum is observed. IN the case of the CeV2-4N structure depicted in Fig. 2(d), when doping is performed using 4 N atoms, the energy band of the CeV2 color center is greatly impacted. The 4f energy level produces a new degenerate state and a part of it of it enters the valence band. Further, within the band, the original fluorescence transition energy level is altered. In the case of the CeV2-B structure depicted in Fig. 2(e), the broadening of each energy level is observed to decrease after doping is performed with the B atom. However, no new impurity states are generated and the system exhibits semiconductor properties and obvious spin polarization similar to the CeV2 color center. Its transition energy is 2.71 eV, with a fluorescence wavelength of 457.27 nm. The fluorescence spectrum is observed to undergo blue shift. With respect to the CeV2-B-N structure depicted in Fig. 2(f), when doping is performed using B and N atoms, the energy band is broadened, leading to some dense bands in the diamond band gap. Impurity belt. A new impurity state is produced, which interferes with the generation of color center fluorescence. In the case of the CeV2-Si structure depicted in Fig. 2(g), when doping is performed using Si atoms, an obvious impurity state is generated, which is located within a range of 0.5 eV around the Fermi level. The presence of Si impurities disperses the generation of fluorescence. But the system still exhibits semiconductor properties and obvious spin polarization. Finally, in the CeV2-N-Si structure depicted in Fig. 2(h), doping using N and Si atoms does not produce new impurity states, but it changes the original impurity energy level transition conditions.
The densities of states corresponding to the eight aforementioned stable structures are calculated and compared with the density of states of the diamond CeV2 color center [13]. The following conclusions can be drawn. In the CeV2-N structure, CeV2-2N structure, and CeV2-3N structure, depicted in Figs. 3(a), (b), and (c), respectively, the impurity state in the diamond band gap originates from the strong neighboring C atom, the 2p orbital of the N atom, and the 4f orbital of the Ce atom. The introduction of N atoms does not produce new impurity states due to orbital hybridization. In the CeV2-4N structure depicted in Fig. 3(d), the impurity state in the diamond band gap has identical origins compared to the previous case. However, despite orbital hybridization, doping with 4 N atoms induces a new degenerate state in the 4f energy level and pushes a part of it into the valence band.
Fig. 3. Density of states diagrams of different types of co-doped diamond defects and partial-wave state density diagrams of Ce atoms. (a) CeV2-N structure (b) CeV2-2N structure (c) CeV2-3N structure (d) CeV2-4N structure (e) CeV2-B structure (f) CeV2-B-N structure (g) CeV2-Si structure (h) CeV2-N-Si structure
In the CeV2-B structures depicted in Fig. 3(d) and (e), that the impurity state in the diamond band gap originates from the strong neighboring C atom, the 2p orbital of the B atom, and the 4f orbital of the Ce atom. Due to orbital hybridization, the broadening of each energy level is decreased after the B atom is incorporated, and no new impurity states are generated. In the CeV2-BN structure depicted in Fig. 3(f), a new impurity state energy level is generated because the N atom is not hybridized with Ce, C, and B. In the CeV2-Si structure depicted in Fig. 3(g), the doped Si atoms do not hybridize with Ce and C, resulting in a new impurity state energy level. Further, the original fluorescence transition levels, i.e., the 4f and 5d energy levels, no longer exist. Finally, in the case of the CeV2-N-Si structure depicted in Fig. 3(h), although N and Si atoms intermix with Ce and C atoms to a certain extent, the original fluorescence transitions, i.e., the 4f and 5d energy levels, are destroyed.
The analyses of the energy band diagrams and the density of states diagrams are combined in Table 2. In summary, when N atoms are incorporated, the fluorescence transition energy level increases and the fluorescence wavelength decreases, which induces a blue shift of the fluorescence spectrum. After N-doping is increased to 3 atoms, the fluorescence transition energy level becomes smaller, and the corresponding fluorescence wavelength increases, which induces a red shift of the fluorescence spectrum. When 4 dopant atoms are used, the original fluorescence transition energy level changes and the fluorescence generation of the diamond CeV2 color center is affected. The incorporation of B atoms and the consequent increase of the fluorescence transition energy level reduces the fluorescence wavelength correspondingly, resulting in a blue shift of the fluorescence spectrum. When both B and N exist in the diamond CeV2 color center at the same time, new impurity state energy levels are generated and the fluorescence of the diamond CeV2 color center is disturbed. Doping with Si atoms changes the energy level of the color center fluorescence, which is not conducive to the generation of fluorescence. The two atoms of N and Si are mixed together, the original fluorescence transition levels, 4f and 5d energy levels, do not exist. The diamond CeV2 color center interferes with the excitation of the color center fluorescence.
Table 2. Fluorescence and hybridized orbits of Ce, B, N, Si co-doped diamond CeV2 structure
4. Conclusions
This paper uses the first-principle method to study the CeV2 color center of diamond doped with B, N, and Si atoms. It is found that when the number of N-atoms used in doping is gradually increased, the effect on the spectrum changes from blue shift to red shift. When a certain number of atoms a used, the color center luminescence is affected. The incorporation of B atoms induces a blue shift in the fluorescence spectrum. However, the co-incorporation of B and N atoms affects the generation of fluorescence. The incorporation of Si atoms changes the fluorescence energy level, weakening the fluorescence signal of the detection color center to the extent that fluorescence of the color center may escape detection. Although N impurity cannot be avoided during the preparation of diamond CeV2 color centers in future experiments, our conclusions indicate that its content should be controlled as far as possible. Further, the existence of B and Si impurities, especially Si, should be avoided as they seriously affect the diamond CeV2 color center. The luminescence performance of the diamond center may be undetectable in the presence of these impurities.
Funding
Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region (2017CXYD-2, KCBJ2018031); National Key Research and Development Program of China (2017YFF0207200, 2017YFF0207203); Natural Science Foundation of Inner Mongolia (2019MS05008); National Natural Science Foundation of China (51965053, 61765012).
Disclosures
No conflict of interest exists in the submission of this manuscript. The manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described is original research that has not been published previously and is not under consideration for publication elsewhere, in whole or in part.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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