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[T. Teraji](https://orcid.org/0000-0002-7731-0547), [C. Shinei](https://orcid.org/0000-0003-4926-8641), Y. Masuyama, [M. Miyakawa](https://orcid.org/0000-0002-0838-8156), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105)

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[Nitrogen concentration control during diamond growth for NV            <sup>−</sup>            centre formation](https://mdr.nims.go.jp/datasets/c34f3e0f-95b4-4e1f-9613-fb6d8dd2de86)

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Proc R Soc B template (v. 1.0) Phil. Trans. R. Soc. A. doi:10.1098/not yet assigned     *Author for correspondence (TERAJI.Tokuyuki@nims.go.jp).    Nitrogen Concentration Control during Diamond Growth 1 for NV− Center Formation 2 T. Teraji1,* , C. Shinei1, Y. Masuyama2, M. Miyakawa3, T. Taniguchi3 3 1 Research Center for Electronic and Optical Materials, National Institute for Materials Science,  4 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan 5 2 Quantum Materials and Applications Research Center, National Institutes for Quantum Science and Technology, 6 1233 Watanuki-machi, Takasaki, Gunma, 370 – 1292, Japan 7 3 Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science,  8 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan 9  10 Keywords: diamond, HPHT, CVD, nitrogen, doping, NV center, 11  12 13  14 Abstract 15 Negatively charged nitrogen-vacancy (NV−) centers formed in diamond crystals are point defects that have 16 potential applications in various quantum devices such as highly sensitive magnetic sensors. To improve the 17 sensitivity of magnetic sensors using NV− centers, it is essential to precisely control the nitrogen concentration 18 in the crystals. In this paper, we demonstrated that nitrogen concentration in diamond can be controlled with 19 high precision for the following two representative growth methods. One is the high-pressure high-20 temperature (HPHT) synthesis method and the other is chemical vapor deposition (CVD) method. The 21 nitrogen concentration of HPHT-grown diamond decreased semi-logarithmically with increasing contents of 22 titanium or aluminum as nitrogen getter materials. The nitrogen concentration of CVD-grown diamond 23 increased linearly with increasing the flow rate ratio of nitrogen to carbon. NV− centers were formed by 24 controlling the total fluence of electron beams so that approximately 20% of the nitrogen became NV− centers. 25 The coherence time of electron spin of NV− centers obtained by the Hahn-echo pulse sequence T2 of these 26 diamond crystals was inversely proportional to the nitrogen concentration. A comparison of T2 of the NV− 27 centers for HPHT-synthesized and CVD-grown diamonds showed no significant difference between them.  28  29 1. Introduction  30 Recently, the term "quantum technology" has become increasingly common [1]. The term "quantum 31 technology" includes not only research into understanding quantum mechanical effects such as quantum 32  2    Phil. Trans. R. Soc. A.     entanglement and quantum superposition, but also technologies that make use of these features, such as 1 quantum computers, quantum communications, and quantum sensing. Currently, research and development 2 for the practical application of these technologies is progressing rapidly around the world [2, 3].  3 Quantum sensing is one of the major technical areas of quantum technology, and negatively-charged 4 nitrogen-vacancy centers (NV− centers) formed in diamond crystals have attracted much attention [4, 5]. 5 Quantum sensor based on NV− centers can operate at room temperature. In addition, the NV− center can be 6 expected to have high spatial resolution because the sensor cell (NV− center body) is as small as the atomic 7 scale, and high sensor sensitivity can be expected because the sensor can be placed close to the target [6, 7, 8, 9, 8 10]. Because of these unique features of the NV− center, many universities and research institutes around the 9 world are currently conducting basic and practical research on solid-state quantum sensors with room-10 temperature operation and high spatial resolution using the NV− centers. 11 NV− centers have long been known as one of the typical optical centers (color centers) that form in diamond 12 crystals. And since a German research group reported electron spin resonance (optically detected magnetic 13 resonance: ODMR) of a single NV− center at room temperature in 1997 [11, 12], this point defect has attracted 14 worldwide attention as a new quantum defect. NV− centers are defect complex consisting of one substitutional 15 nitrogen and one atomic vacancy. In order to obtain excellent electron spin properties (e.g., spin coherence 16 time), the mother material, diamond, must have high crystallinity [13]. And since only the negatively charged 17 NV center (NV− center) can control the spin state, a high stability of negative charge state of the NV− center is 18 essential, which requires the removal of acceptor impurities as much as possible. In addition, paramagnetic 19 defects in the diamond crystal must be reduced to have long coherent time of electron spin. Furthermore, 20 since the spin state of the NV− center is read from the fluorescence intensity, background light must be 21 reduced for accurate reading, and luminescent centers other than the NV− center must be removed from 22 diamond crystals as much as possible. There is thus a demand on the material side for the diamond that forms 23 the NV− centers [13]. Therefore, the establishment of diamond crystal growth technology suitable for quantum 24 devices is indispensable for improving device performance. 25 In this paper, we describe a diamond crystal growth technique and the formation method of NV− center in 26 diamond crystals for quantum sensing applications using NV− centers, focusing on research results at the 27 National Institute for Materials Science (NIMS). In particular, we discuss the controllability of nitrogen 28 concentration in diamond by nitrogen doping during diamond growth. 29  30 2. Diamond growth technology 31 There are two methods for growing diamond crystals: high-pressure high-temperature synthesis (HPHT) 32 and chemical vapor deposition (CVD) methods. In this chapter, we briefly review these growth methods and 33 describe the current state of research on nitrogen doping. 34  35 (a) Growth method 1: High-pressure/high-temperature (HPHT) synthetic 36 method 37 3     Phil. Trans. R. Soc. A.     Figure 1. carbon phase diagram  Temperature [K]Pressure[GPa]0 1000 2000 3000012108642GraphiteDiamond CVD growth12C enriched HPHT diamond1mm5.5GPa,1500℃Growth pointThe HPHT method [14] is widely used for bulk 1 crystal growth because diamond is 2 thermodynamically stable under high pressure. 3 More than 90% of lab-grown diamond is produced 4 by the HPHT method [15], but high technology is 5 required to grow high-purity single crystals free of 6 impurities such as nitrogen, boron and solvent 7 components. The HPHT method includes the 8 temperature gradient method using a catalyst, the 9 solubility difference method, the non-catalytic 10 conversion method, and the shock compression 11 method. Among these methods, the temperature 12 gradient method is used to grow large, high-13 quality single-crystal diamonds. The details of this 14 technique are described in the following 15 references [16, 17]. 16 Figure 1 shows a phase diagram of carbon, 17 including the eutectic line of nickel and carbon. In 18 the temperature gradient method, carbon materials are dissolved in a metallic solvent under high temperature 19 and high pressure, and then precipitated as single crystals. During growth, it is necessary to control the 20 growth parameters so that the temperature difference is several tens of degrees of centigrade between the part 21 of the sample chamber where the raw material is dissolved (high temperature part) and the part where 22 diamond is grown on seed crystals (low temperature part). Typical growth parameters are a pressure of 5.5 23 GPa or higher and a growth temperature of 1573 K (1300°C) or higher.  24  25 (b) Growth method 2: Chemical vapor deposition (CVD) method 26 For downsizing and generalization of diamond growth equipment, it is desirable to grow diamond under 27 atmospheric pressure or low pressure. However, as shown in the phase diagram (Figure 1), diamond is a 28 stable phase under high pressure, making it difficult to grow diamond under ambient pressure. In the early 29 1980s, the same institute (former national institute for research in inorganic materials NIRIM) proposed two 30 well-known representative diamond CVD growth methods [18], which are the hot-filament CVD method [19] 31 and the microwave plasma CVD 32 method [20, 21]. Most of the diamond 33 growth systems currently available on 34 the market are based on these 35 configurations. 36 The CVD method is a method for 37 growing a thin film by supplying a 38 source material gas containing 39 constituent elements of the thin film 40 into a reaction chamber. In this method, 41 the source material gas is decomposed 42 and a thin film is grown by chemical 43 reaction on the substrate. When a thin 44   Figure 2. (a) Conceptual diagram of plasma CVD, (b) Appearance during microwave-plasma CVD growth  PlasmaSubstrate（diamond single crystal）(b) PlasmaSubstrateMicrowaveCH3CHSource gasCH4, H2, O2 , N2CVD filmHCH3HHH OH2 NH2H2H(a) 4    Phil. Trans. R. Soc. A.     film is grown using a gas containing carbon as a source material, if the growth temperature is high, the 1 substrate surface will be graphitized, making it impossible to grow diamond [22]. For this reason, the CVD 2 method using non-equilibrium plasma is widely used in diamond thin film growth to reduce the substrate 3 temperature (Figure 2(a), (b)). The details of the diamond crystal growth mechanism by this plasma-assisted 4 CVD method are described in the following papers [23, 24]. Using diamond single-crystals as a substrate, it is 5 possible to obtain functional single-crystal thin films with unique doping and stacking structures. In the past, 6 “diamond single-crystal substrate” meant a single-crystal substrate synthesized by the HPHT method. 7 Recently, improvements in the performance of CVD growth equipment have made it possible to grow 8 diamond growth for long periods of time and free-standing CVD diamond wafers are also becoming available 9 [25].  10  11 (c) Impurity doping of diamond 12 Diamond is a group IV semiconductor material with excellent physical properties. Until now, diamond 13 crystals have been studied to improve their quality and purity, mainly for application in electronic devices 14 such as power devices [25]. Doping with impurities that function as donors and acceptors is essential for the 15 fabrication of semiconductor devices, and research is also being conducted on doping concentration control of 16 these impurities. The small lattice constant of diamond limits impurities entering the diamond lattice [26]. 17 Therefore, the elements that can be incorporated during the diamond growth process are limited. Nitrogen, 18 boron, and phosphorus are typical elements as impurities that affect the Fermi level position of diamond. 19 Regarding boron and phosphorus doping during CVD growth, there have been reports systematically 20 demonstrating the growth parameter dependence of impurity concentrations over several orders of 21 magnitude [25, 27]. On the other hand, there are few studies on such doping controllability for nitrogen. This 22 is probably because, unlike boron and phosphorus, nitrogen forms deep electronic levels within the band gap 23 and does not contribute to electrical conduction. Rather, it often has a detrimental effect on device properties, 24 which is why research has focused on removing as much nitrogen as possible from diamond. 25 In HPHT synthetic diamond, about 50~500 ppm of nitrogen is incorporated spontaneously into the grown 26 diamond. These nitrogen-doped diamonds exhibit a yellow color (type-Ib diamonds) [17]. The nitrogen 27 probably comes from high pressure media surrounding the growth cell [16]. It is reported that metal solvent 28 and temperature affect nitrogen incorporation into diamond, resulting in diamond with nitrogen 29 concentrations below 50ppm [16, 28]. This has been interpreted in terms of the solubility of nitrogen in the 30 metal solvent. A linear increase in nitrogen concentration from 2 ppm to 7 ppm was reported as the 31 temperature increased from 1650 °C to 1850 °C [28]. In addition to the relatively small change in nitrogen 32 concentration when changing synthetic temperature, it is not easy to control the temperature with good 33 reproducibility in the long duration in HPHT diamond synthesis process [29]. Therefore, in this study, for the 34 purpose of controlling the nitrogen concentration in a wide range, we have controlled nitrogen concentration 35 by changing the weight ratio of nitrogen getter material in the metal solvent instead of changing synthetic 36 temperature.  37 To reduce nitrogen concentration, nitride-forming metals such as titanium, aluminum and zirconium are 38 frequently used as nitrogen getter materials [16]. It has been reported that the nitrogen content can be reduced 39 below 0.1 ppm by this method [30]. The reduction of nitrogen content is also effective in reducing lattice 40 distortion inside the crystal which is considered to be caused by inhomogeneous distribution of nitrogen [31]. 41 On the contrary, the addition of NaN3 to the metal solvent reportedly yields diamonds with nitrogen 42 concentrations greater than 1000 ppm [32]. Nitrogen in HPHT diamond crystals has various point defect 43 structures [14, 33]. The structure of nitrogen in diamond is predominantly substitutional nitrogen. Point defect 44 complexes consisting of nitrogen atoms and vacancies are also formed. The emission wavelength from these 45 5     Phil. Trans. R. Soc. A.    point defect complexes depends on the number of both nitrogen atoms and vacancies that make up these 1 point defect complexes. The following point defect complexes are commonly observed from HPHT diamond 2 crystals [16, 53]. The N3 center, composed of three nitrogen atoms and vacancies, has a zero-phonon line peak 3 (ZPL) at 415 nm. The H3 center composed of two nitrogen atoms and a vacancy, and appears its ZPL at 503 4 nm. The NV centers are formed from pairs of nitrogen and vacancies, with ZPL of the NV0 center appearing at 5 637 nm and ZPL of the NV- center appearing at 575 nm. Irradiating the crystal with high-energy 6 particles/electrons and then annealing the crystal enhances the intensity of these emissions [34].  7 In order to improve the crystalline quality of diamond, a method of using a seed crystal with few 8 dislocations has been proposed [31]. By combining various quality improvement techniques, high-purity (type 9 IIa) HPHT diamond with a diameter exceeding 10 mm and almost no dislocation defects in the (001) growth 10 sector has been obtained at the research level [30]. The 13C with nuclear spin (natural abundance ratio 1.1%) 11 can be reduced by using 12C isotope-enriched (13C reduced) starting carbon materials. It has been reported that 12 HPHT diamond single crystals with a 12C isotopic concentration of 99.995% were obtained by using 13 polycrystalline diamond films with a 12C isotopic concentration of 99.998% as starting material [35]. 14 In the CVD method, nitrogen doping increases the growth rate of diamond by about 2 to 10 times [24, 36, 37, 15 38], and diamond growth rate of greater than 100 μm h-1 have been reported [36, 39]. As such, the nitrogen 16 doping techniques have been used to grow thick CVD diamond layers or free-standing CVD diamond plates. 17 Nitrogen incorporation efficiencies during diamond growth reportedly range from 3 × 10–5 to 7 × 10–2, which 18 depend on growth conditions and nitrogen dopant gas. Here, the nitrogen incorporation efficiency is defined 19 as the ratio of incorporated nitrogen in diamond crystal to the gas ratio of the nitrogen gas flow rate to the 20 methane gas flow rate (N/C gas ratio) during CVD growth. Nitrogen molecular gas N2 is often used as a 21 dopant, but Tallaire et al., proposed N2O gas as a nitrogen dopant with high incorporation efficiency [40, 41]. 22 The highest nitrogen concentrations are reportedly 35 ppm for free-standing CVD (001) plate [41] and 80 ppm 23 for homoepitaxial (111) thin film [42]. Nitrogen doping frequently causes step bunching on the diamond (001) 24 surface [36, 37, 43, 44, 45]. Chayahara et al., reported that appearance of nonparaxial crystallites is suppressed 25 by adding N2 gas with few percent to methane [46], while Tallaire et al., mentioned that addition of N2 gas at 26 concentration above a few tens of ppm induces the formation of extended or unepitaxial crystallites [41]. 27 Nitrogen-doped CVD film exhibits brownish to dark coloration [40, 47], which might be attributable to the 28 creation of vacancy clusters [48]. Nitrogen related point defects generated in CVD diamond crystals are 29 mainly substitutional nitrogen in a neutral or positive charged state (Ns0 and Ns+), negatively or neutrally-30 charged NV center (NV0 and NV-) and NV- center with hydrogen (NVH- center) [37, 47, 58]. The concentration 31 ratio of [Ns0] (or [Ns+]+ [Ns0]) : [NVH- center] : [NV- center] is reportedly approximately 100 : 10 : 1 [37] or 300: 32 30: 1 [49]. There are limited reports showing the controllability of the nitrogen concentration in diamond, that 33 is, the relationship between the nitrogen concentration in the diamond crystal and the doping gas 34 concentration during CVD growth, and the control range of the nitrogen concentration is less than two orders 35 of magnitude [37, 38]. 36  37 (d) Preferential formation of NV− centers 38 As mentioned above, quantum manipulation of electron spins at the NV− center involves initializing and 39 reading out the electron spin state by light irradiation and controlling (writing) the electron spin state by 40 microwave irradiation. Required electron spin density (i.e., NV− center density) varies depending on the spin 41 control method [50] and device application [1051].  42 Even if diamond growth is performed with the purpose of forming only NV− centers, defects other than NV− 43 centers will be formed in the actual diamond crystal at the same time (Figure 3(a)). In addition to threading 44 6    Phil. Trans. R. Soc. A.     dislocation, defects such as atomic vacancies, interstitial carbon, hydrogen, and aggregate nitrogen [52, 53] 1 may increase spin noise and reduce the formation rate of NV− center. Therefore, they should be removed as 2 much as possible from the crystal.  3 NV0 centers capture negative charges and become negatively charged states (NV−) with electron spins with 4 spin quantum number S=1. Spin manipulation of NV− centers is possible by applying microwave pulses, and 5 magnetic sensitivity is improved by increasing the concentration of 6 NV- centers [NV-]. On the other hand, the NV0 center (S=1/2) cannot 7 be spin-operated and becomes background light (noise). Therefore, 8 increasing the negative charge stability of the NV− centers is 9 important for improving the magnetic sensitivity. In addition to 10 NV0 center, visible-region luminescent defects such as silicon 11 vacancy (SiV−) centers and H3 centers also act as background light, 12 so it is important to remove them [53]. From the above, it can be 13 understood that diamond crystals suitable for quantum devices 14 must be grown based on high-purity crystal growth techniques. 15 Furthermore, in order to increase the coherence time of the 16 electron spin of the NV− centers, 13C with nuclear spins (I=1/2) 17 should be reduced. [54, 55]. Figure 3(b) shows an example of an 18 ideal NV− center formation state. Nitrogen takes a defect structure 19 of NV− center or isolated nitrogen in the neutral charge state (it is 20 called Ns0 or P1 center). Negative charges of NV− centers are 21 supplied from the Ns0. In this sense, the optimum state is one in 22 which [Ns0] is slightly higher than [NV−].  23  24 3. Nitrogen-doped diamond growth 25 (a) Diamond growth conditions 26 In this study, growth of nitrogen-doped diamond crystals was performed by both HPHT and CVD methods. 27 For the synthesis of diamond single crystals by the HPHT method, the temperature gradient method was used 28 [29]. Diamond single crystal was grown on the (001) surface of the seed crystal, and Co-Ti, Fe-Co-Ti, and Co-29 Al (99.98%-99.999%, RARE METALLIC Co., Ltd.) were used as metal solvents. The HPHT condition is as 30 follows; the growth temperature of 1300° C – 1350° C, the reaction pressure of 5.5 GPa, and the growth time of 31 40 – 80 hours. It has been reported that a Cu additive has the effect of suppressing the formation of TiC [56]. 32 Therefore, in this study, Cu was added to the metal solvent when the Ti additive was used as a nitrogen getter 33 material. We used a modified belt-type high-pressure apparatus [ 57 ]. The cylinder bore diameter is 34 approximately 32 mm for the HPHT apparatus FB30H and is approximately 44 mm for the HPHT apparatus 35 FB40H. Graphite (Tokai Kosho Co., Ltd.) was used as the carbon source in most of the diamond synthetic 36 experiments in this study. On the other hand, for the growth of 12C isotopically enriched HPHT synthetic 37 diamond, 12C-enriched CVD diamond (Tomei Diamond Corp.) was used because 12C isotopically enriched 38 graphite is not commercially available.  39 When the nitrogen concentration in the diamond crystal is less than 1 ppm, the effect of spin relaxation of 40 the electron spin of the NV center by the electron spin of nitrogen is small. As a result, the perturbation from 41 the nuclear spin of 13C, whose natural abundance is 1.1%, to the coherence time T2 of NV− centers becomes 42 non-negligible [13]. Therefore, in order to improve T2 of NV− centers, 12C-enrichment has carried out for the 43   Figure 3. Formation of NV- centers in diamond crystals (a) A realistic form with various impurities mixed in. (b) An ideal form consisting of NV- centers and isolated nitrogen (donors). (a) NNNBSiNNSiV centerVacancy Aggregate nitrogenNitrogenNV centerdislocation13CInterstitial carbonNNNNNNNV center(b) NitrogenBoronHHydrogen7     Phil. Trans. R. Soc. A.    HPHT diamond crystals in the nitrogen doping range below 1ppm in this study. The grown single crystal was 1 cut parallel to the {111} plane with a thickness of about 0.2 mm.  2 In the CVD method, nitrogen-doped homoepitaxial diamond film was grown by a microwave plasma CVD 3 developed at National Institute for Materials Science (NIMS) [58]. Details of the microwave-plasma CVD 4 system are described elsewhere [59, 60]. HPHT-grown type-Ib (100) diamond crystals with a dimension of 3.5 5 × 3.5 mm2 in area and 1mm in thickness were used as substrates. Chemical purity of source gasses are 9N for 6 hydrogen (using a palladium purifier), 8N for methane (using a zirconium purifier) and 6N5 for oxygen.  12C 7 isotopically enriched methane whose enrichment was specified to >99.9% was used as a carbon source gas. 8 15N2 gas (chemical purity >3N) whose enrichment was specified to 98% were used as a nitrogen doping gas for 9 samples 1–3. The CVD condition is as follows; the reaction pressure of 110 Torr, microwave power of 1.4 kW, 10 methane concentration ratio (flow rate ratio of CH4 to the total gas flow) of 10%, oxygen concentration (flow 11 rate ratio of O2 to the total gas flow) of 2% and substrate temperature of 1030–1090°C.  12 Microscope images of HPHT crystals and free-standing CVD diamond plates were obtained by using 13 stereomicroscopes (SZ61; Olympus Co. Ltd.). Impurities in diamond crystals were characterized by 14 secondary ion mass spectrometry (SIMS, IMS-7f; CAMECA, Ametek Inc.), electron paramagnetic resonance 15 (EPR, JES-FA100, JEOL Ltd.), Fourier transform infrared (FTIR, FT/IR-6600, JASCO Co.) spectroscopy, and 16 photoluminescence (PL, Nanofinder FLEX; Tokyo Instruments, Inc.) methods. The 12C isotope enrichment of 17 diamond crystals was evaluated by SIMS measurements. 18  19 (b) Grown crystals 20 Figure 4 shows how diamond {111} plates are prepared 21 from crystals grown by the HPHT method. As-grown 22 diamond crystals consist primarily of {100} and {111} 23 growth sectors, as shown in Fig. 4(a). For the 24 characterization of the quantum properties of NV− centers, 25 it is convenient to use {111} crystals because it is necessary 26 to apply a magnetic field in the [111] direction. The {111} 27 crystals are obtained by cutting an as-grown crystal into a 28 plate shape in the direction shown in Fig. 4 (a). Two 29 symmetrical plates can be cut out from one as-grown 30 crystal. The crystals are generally 2−3 mm in size. The 31 color of the {111} HPHT diamond crystals were almost 32 colorless, as shown in Fig. 4(b). No contrast reflecting 33 crystallographic strain was observed in the birefringent 34 image, indicating that the strain was relatively small. 35 Figure 5 shows a microscope image of the as-grown state of CVD-grown diamond, taken in the brightfield 36 reflection mode. The 15N/C ratio in gas phase applied for the diamond growth of this sample was 20,000 ppm. 37 Thickness of CVD layer was 430 μm. The step bunching described in subsection 2(c) was observed on the 38 surface of the as-grown homoepitaxial film. Since defect formation was suppressed by the addition of oxygen 39 in source gases, non-epitaxial crystallites and growth hillocks did not form on the diamond sample surface 40 even after a prolonged growth. The blue dashed rectangle corresponds to the edge position of the substrate. 41 Polycrystalline diamond was partially grown on the edges of the substrate.  42  Figure 4. Method for preparing diamond {111} plates from crystals grown by the HPHT method SeedLaser cutting{111} pair crystals2mm{100}(a) (b) 8    Phil. Trans. R. Soc. A.     To create freestanding CVD diamond (001) 1 crystals, first, the top surface of the sample was 2 laser-cut into a square shape to cut out the 3 polycrystalline diamond portion, and then the 4 sample was laser-cut from the side to remove the 5 CVD layer from the substrate. Figures 5(b) and (c) 6 show microscope images of the freestanding 7 diamond sample taken in the brightfield reflection 8 mode and birefringence image mode, respectively. 9 The color of the diamond sample after being 10 processed into a freestanding plate was relatively 11 transparent, as shown in Fig. 5(b). Four-hold 12 symmetric pattern was observed in the 13 birefringence image, as shown in Fig. 5(c). This 14 symmetric pattern reflects the {111} growth sector 15 of HPHT crystals and is often observed in 16 birefringence images of commercial HPHT-grown 17 type-Ib (001) substrates. High density dislocations 18 in the center part of sample also reflect the dislocation distribution of the HPHT substrate. It means that the 19 strain of the free-standing plate is induced from the substrate and the crystal strain can be minimized by using 20 a low-strain substrate. The isotopic enrichment of diamond crystals obtained from SIMS analysis was 99.96% 21 for 12C and more than 99.5% for 15N [58]. These values meet the specification of these isotopically enriched 22 gases used for the CVD diamond growth, indicating that the isotopic enrichment in the diamond crystals can 23 be controlled by changing the isotopic enrichment of source gases. 24  25 (c) Nitrogen concentration 26 Figure 6 shows the concentration of substitutional nitrogen in the neutral charge state [P1] as measured by 27 EPR measurements. Semi-logarithmic plot of [P1] for HPHT diamond samples as a function of Ti or Al 28 addition [29]. [P1] was found to decrease exponentially with increasing Ti addition. When grown with Co-Ti 29 solvent, [P1] was 100 ppm without Ti addition and about 1 ppm at Ti additive of 2.0 wt%. The variation of 30 [P1] for the same Ti addition was about 100%. This variation is inferred to mainly come from the fact that 31 different growth sectors have different nitrogen incorporation efficiency as explained below. Nitrogen 32  Figure 6. Nitrogen concertation of diamond crystals. (a) diamond grown by HPHT method (Reprinted from M. Miyakawa et al., Jpn. J. Appl. Phys 61, 045507 (2022)., Copyright 2022 The Japan Society of Applied Physics, (b) diamond grown by CVD method (Reprinted from T. Teraji et al., J. Appl. Phys 133, 165101 (2023)).  0.0 0.5 1.0 1.5 2.0 2.510-410-310-210-1100101102103[P1]  [ppm][Ti or Al]  [wt%] made from graphite diamondFe-Co-Ti system Co-Ti system made from graphite diamondFe-60wt%CoFe-40wt%CoFe-45wt%CoFB40HFB30H Co-Al system (made from graphite)Fe-40wt%Co-TiFe-40wt%Co-Alby Sumiya et al.by Sumiya et al.101 102 103 104 105 10610-310-210-1100101102 [N] measured by SIMS [P1] measured by ESRNitrogen Concentration [ppm]N/C gas ratio [ppm](a) (b)  Figure 5. Optical microscope images of homoepitaxial diamond crystals. Brightfield reflection images of the sample (a) in an as-grown state and (b) after removal from the substrate. (c) Birefringence image of the sample after removal from the substrate (Reprinted from T. Teraji et al., J. Appl. Phys 133, 165101 (2023)). As-grown After cutting/polishing 4×4mm(a) (b) (c) 9     Phil. Trans. R. Soc. A.    concentrations are known to vary by growth sector within the crystal [14, 31]. In standard type-Ib synthetic 1 diamonds, nitrogen concentrations of about 100 ppm in the {111} sector, less than 50 ppm in the {100} sector, 2 less than 10 ppm in the {113} sector, and about 1 ppm in the {110} sector have been reported [61]. As shown in 3 Fig. 4(b), the nitrogen concentration of HPHT crystals was evaluated using samples cut to center the {111} 4 growth sector. The region of the {111} growth sector differs from sample to sample, and the rim of the sample 5 is the growth sector with lower [P1] than that of {111} growth sector. [P1] of each sample is obtained by 6 dividing the total number of electron spin of substitutional nitrogen of a sample by the sample volume. 7 Variation in the proportion of the {111} growth sector in the overall sample is considered to be a cause of the 8 variation in [P1] shown in Fig. 6 (a). When Al was used as a nitrogen getter material instead of Ti, [P1] was 9 approximately 40 ppm at Al additive of 2.0 wt%. It means that Al also has a nitrogen getter effect, but its 10 efficiency is lower than that of Ti. Therefore, more Al addition is necessary to control P1 concentration in the 11 range of 0.1 to about 100 ppm [29]. 12 In the case of CVD diamond, not only [P1] is plotted as blue triangles, but also the nitrogen concentration 13 estimated by SIMS is plotted as red circles, as shown in Figure 6(b). This nitrogen concentration was plot as a 14 function of N/C gas ratio. The nearly identical values of [N] and [P1] indicate that most of the nitrogen is 15 incorporated as Ns0 which is substitutional nitrogen in the neutrally charged state. These data were aligned on 16 a straight line (a straight line with a slope of 45 degrees on a log-log plot) over three orders of magnitude of 17 nitrogen concentration. Finally, nitrogen concentration in diamond crystals was successfully controlled from 18 10 ppb to 10 ppm by changing the N/C gas ratio. A slop of this straight line corresponds to the incorporation 19 efficiency, which is a ratio of [Ns0] to N/C ratio in gas phase. The efficiency was estimated to be (1.9±0.2) ×10-4. 20 This value is two orders of magnitude lower than the incorporation efficiency using N2O as a nitrogen source 21 gas [41]. In this study, nitrogen doping was performed with molecular nitrogen under oxygen adding growth 22 conditions. Constituent elements of the plasma in this study are hydrogen, carbon, oxygen, and nitrogen, 23 which is the same as when N2O is used as the nitrogen source gas. This fact suggests a difference of 24 decomposition efficiency of nitrogen related gas in plasma affects the incorporation efficiency. 25  26 4. Formation of NV- center in diamond 27 (a) Control of NV- center concentration 28 The NV− centers were formed using the following procedure. Electron beam irradiation is frequently used 29 for creating vacancies in diamond [62, 63, 64], and heat treatment diffuses the vacancies [65, 66]. In this study, 30 the grown HPHT and CVD diamonds were irradiated with a 2.0 MeV electron beam at about 300 K with a 31 total fluence range from 1×1017 to 1×1018 electronscm-2, with subsequent annealing at 1,000 °C for 2 h in 32 vacuum [67]. Hereinafter, we designate this post process for NV− center formation as “the e-beam/annealing 33 process”. The [NVT] examined for this study was 0.1–4 ppm. This value was controlled by the total fluence of 34 an electron beam. [Ns0] and [NV-] before and after e-beam/annealing process were estimated by EPR 35 measurements. For [NV0] estimation, we first performed PL measurements to know the ratio [NV0]/[NV-]. 36 Then by multiplying [NV0]/[NV-] in PL by [NV-] in EPR, [NV0] was obtained. Details on quantification can 37 be found in the reference [68].  38 10    Phil. Trans. R. Soc. A.     Figure 7 shows color change of diamond samples 1 through the e-beam/annealing process. The color of as-2 grown HPHT diamond crystal was light yellowish, as 3 shown in Fig. 7(a). The [Ns0] of this HPHT synthetic 4 diamond crystal was 6 ppm. When the crystals were 5 treated by the e-beam/annealing process with a total 6 fluence of 7×1017 electron∙cm-2, the color of the {111} 7 growth sector near the crystal center turned purple, as 8 shown in Fig. 7(b). The color of as-grown CVD diamond 9 crystal was brownish, as shown in Fig. 7(c). The [Ns0] of 10 this CVD-grown diamond crystal was 11 ppm. After the 11 e-beam/annealing process of the CVD diamond crystal 12 with a total fluence of 3×1017 electron∙cm-2, the entire 13 surface turned dark purple, as shown in Figure 7(d). 14 As mentioned above, NV centers have different charge 15 states, and negatively charged NV- centers and neutral 16 NV0 centers are often observed simultaneously. The NV0 17 centers increase significantly when the vacancy 18 concentration in the diamond crystal becomes greater 19 than the nitrogen concentration. This situation occurs 20 when the diamond is overexposed to the electron beam 21 [69, 70]. Therefore, it is necessary to determine the total fluence of electron beam so that the NV- center 22 becomes dominant. We clarified that the condition under which NV− centers are predominantly formed is 23 determined by the concentration ratio [NVT]/[NT] [68]. Here, [NVT] = [NV0] + [NV−] and [NT] is the initial [Ns0] 24 or [P1] before the formation of NV− centers (i.e. before the e-beam/annealing process). We found that [NV−] 25 and the negative charge ratio of the NV centers [NV−]/[NVT] simultaneously become large values by setting 26 [NVT]/[NT] to approximately 20% in our samples [68]. In the following experiments, the NV− centers were 27 formed such that the [NVT]/[NT] ratio was approximately 20%.  28  29 (b) Coherence time of NV− centers 30 The spin-echo coherence time T2 of the NV− center was estimated using the Hahn echo pulse sequence [13, 31 71]. A home-built PL system with a pulsed microwave module was used for measurements [50, 72]. A 532-nm 32 laser (gem 532; Laser Quantum Inc.) was used and the power density of the green laser at the specimen 33 surface was set to 15 mW/μm2. Figure 8(a) shows the T2 of the NV− centers as a function of concentration of 34 nitrogen-related paramagnetic defects [NPM]. Here, [NPM] is the sum of [Ns0] and [NVT]. As described in the 35 subsection 4 (a), [Ns0], [NV-] and [NV0] were estimated by EPR and PL measurements [68]. Regarding 36 concentration of NVH- centers [NVH-], EPR measurements have been performed. Here, 15N enrichment of 37 NVH- centers are crucial for accurate concentration estimation of [NVH-] [58, 72].  38 In Fig. 8, the measurement results for HPHT and CVD diamond crystals obtained in this study are plotted 39 as red squares and red circles, respectively; the data for HPHT and CVD diamond crystals reported from 40 Harvard University are plotted as open squares and open circles, respectively. A blue triangle shows the 41 property for the HPHT diamond crystal with the highest AC magnetic sensitivity of 2.6 pT/√Hz reported from 42 the University of Stuttgart [73]. Since the sensing time Tφ of 50 μs was described instead of T2 in the reference 43 [73], T2 was inferred from an assumption that the magnetic-field sensitivity is maximum at Tφ = T2/2. [NPM] and 44 [NV−] of this sample in the reference [73] was 3 ppm and 0.9 ppm, respectively. The purple hexagon is a 45  Figure 7. Color change of diamond samples through the e-beam/anneal process. HPHT samples (a) before and (b) after the process. CVD sample (c) before and (d) after the process. 1mmHPHTCVD(c) (d) (a) (b) 11     Phil. Trans. R. Soc. A.    measurement result of a commercially available diamond specimen from Element6 under the name DNV-B1. 1 These data are distributed along a straight line, indicating a good inversely proportional relationship between 2 T2 and [NPM]. Although there are multiple data for the same [NPM] in the diamond crystal data grown at NIMS, 3 it can be seen that they are distributed on an inversely proportional straight line with good reproducibility. 4 This means that both the HPHT method and the CVD method can control [NPM] by approximately two orders 5 of magnitude. 6 There was no significant difference between the HPHT and CVD samples in this inversely proportional 7 relationship. Compared to HPHT synthetic diamonds, CVD-grown diamonds generally contain hydrogen. In 8 nitrogen-doped CVD diamond (001) single crystal, the hydrogen concentration is reportedly comparable to 9 the nitrogen concentration in the crystal [58]. NVH- centers are often formed in CVD diamond crystals by the 10 incorporation of hydrogen, whose concentration is approximately 1/10 that of nitrogen [37, 49, 58]. 11 Nevertheless, our results suggest that NVH- centers do not affect T2 of NV− centers. Shinei et al. explain that 12 the spin relaxation time of the NVH− center is much shorter than that of the NV− center and is therefore 13 insufficient to disturb the spin coherence of the NV center- [72]. 14 Figure 8(b) shows the T2 of the ensemble NV− centers as a function of concentration of NV− centers. Similar 15 to the [NPM] dependence, T2 was nearly inversely proportional to NV− concentration [NV−]. A similar tendency 16 was observed because diamond crystals were irradiated with electron beams so that the conversion efficiency 17 Ns0 to NV− was approximately 20%. Shot noise, which corresponds to the minimum detectable magnetic field, 18 is inversely proportional to the square root of the product of the coherence time T2 and concentration [NV−]. 19 The product of T2 and [NV−] of 66 and 75 μs ppm was obtained from two NIMS HPHT diamond. These values 20 are close to the 90 μs ppm (blue triangle) reported by the University of Stuttgart, which represents the highest 21  Figure 8. Coherence time of NV centers as a function of (a) nitrogen concentration [P1] and (b) negatively charged NV center concentration [NV−]. As a references, data from Harvard university (open circles for CVD and open rectangles for HPHT diamond samples), data from university of Stuttgart (blue triangle for HPHT sample, sensing time Tφ of 50 μs was used for this plot assuming T2 = Tφ×2.), sample commercialized from Element six (CVD sample named DNV-B1) were shown in the figures. 0.001 0.01 0.1 1 10 100 10000.1110100100010000T2 [ms][NPM] [ppm]NIMS(HPHT)NIMS(CVD)Harvard(CVD)Harvard(HPHT)Stuttgart (HPHT)Tj is assumed as T2CommerciallizedDNV, E6(CVD)0.001 0.01 0.1 1 10 100 10000.1110100100010000  T2 [ms][NV-]  [ppm]Stuttgart (HPHT)Tj is assumed as T2NIMS(HPHT)NIMS(CVD)CommerciallizedDNV, E6 (CVD)(a) (b) 12    Phil. Trans. R. Soc. A.     AC magnetic sensitivity to date [73]. This means that HPHT diamond crystals grown in NIMS are suitable for 1 sensitive sensors, and we have techniques to prepare these diamond samples with higher reproducibility. 2  3 5. Summary 4 In this paper, we demonstrated high controllability of nitrogen concentration in diamond during crystal 5 growth by HPHT and CVD methods. Chapter 2 described the principle of diamond crystal growth by HPHT 6 and CVD methods, and the current status of nitrogen doping aimed at the preferential formation of NV− 7 centers. In Chapter 3, our research results in diamond crystal growth were described, focusing on the 8 controllability of nitrogen doping concentration during diamond growth. We have succeeded in controlling 9 the nitrogen concentration over two orders of magnitude. We showed that nitrogen concentration changed 10 exponentially with the concentration of the nitrogen getter material in the HPHT method, and linearly with 11 the nitrogen/carbon gas ratio in the CVD method. For HPHT crystals, a pair of {111} crystals were cut out from 12 one grown crystal. In CVD diamond growth, it was demonstrated that isotope enrichment (12C and 15N) can be 13 controlled in addition to nitrogen concentration control. As presented in Chapter 4, coherence time T2 of NV− 14 centers of diamond prepared in this manner was inversely proportional to the concentration of nitrogen acting 15 as a paramagnetic defect [NPM] in the range of 1-50 ppm. A similar inverse relationship was found between T2 16 and NV− center concentration [NV−]. The product of T2 and [NV−] is an indicator of magnetic field sensitivity, 17 and this T2 · [NV−] product obtained from our HPHT diamond crystals was comparable to that of the 18 diamond crystal used for obtaining the highest AC magnetic sensitivities. 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