# Fileset [Kageura_Carbon2024_MDR.pdf](https://mdr.nims.go.jp/filesets/5a4293cd-e69e-4577-99eb-586c5e985e99/download) ## Creator [Taisuke Kageura](https://orcid.org/0000-0002-9792-5223), [Yosuke Sasama](https://orcid.org/0000-0002-8358-6101), Keisuke Yamada, Kosuke Kimura, Shinobu Onoda, [Yamaguchi Takahide](https://orcid.org/0000-0003-0208-7317) ## Rights [Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/) ## Other metadata [Surface transfer doping of hydrogen-terminated diamond probed by shallow nitrogen-vacancy centers](https://mdr.nims.go.jp/datasets/ac0dd490-659b-4e81-9761-a5f1e3c45eb7) ## Fulltext Surface transfer doping of hydrogen-terminated diamond probed by shallownitrogen-vacancy centersTaisuke Kageura,1, 2 Yosuke Sasama,3 Keisuke Yamada,4 Kosuke Kimura,4, 5Shinobu Onoda,4 and Yamaguchi Takahide1, 6, a)1)Research Center for Materials Nanoarchitectonics, NationalInstitute for Materials Science (NIMS), Tsukuba 305-0044,Japan2)National Institute of Advanced Industrial Science and Technology (AIST),Tosu 841-0052, Japan3)International Center for Young Scientists, National Institute for Materials Science(NIMS), Tsukuba 305-0044, Japan4)National Institutes for Quantum Science and Technology (QST),Takasaki 370-1292, Japan5)Graduate School of Science and Technology, Gunma University, Kiryu, 376-8515,Japan6)University of Tsukuba, Tsukuba, 305-8571, Japan1The surface conductivity of hydrogen-terminated diamond is a topic of great interestfrom both scientific and technological perspectives. This is primarily due to the factthat the conductivity is exceptionally high without the need for substitutional dop-ing, thus enabling a wide range of electronic applications. Although the conductivityis commonly explained by surface transfer doping due to air-borne surface acceptors,there remains uncertainty regarding the main determining factors that govern thedegree of band bending and hole density, which are crucial for the design of elec-tronic devices. Here, we elucidate the dominant factor influencing band bending bycreating shallow nitrogen-vacancy (NV) centers beneath the hydrogen-terminated di-amond surface through nitrogen ion implantation at varying fluences. We measuredthe photoluminescence and optically detected magnetic resonance (ODMR) of theNV centers, as well as the surface conductivity, as a function of the nitrogen im-plantation fluence. The disappearance of the conductivity with increasing nitrogenimplantation fluence coincides with the appearance of photoluminescence and ODMRsignals from negatively charged NV centers. This finding indicates that band bendingis not exclusively determined by the work-function difference between diamond andthe surface acceptor material, but by the finite density of surface acceptors. Thiswork emphasizes the importance of distinguishing work-function-difference-limitedband bending and surface-acceptor-density-limited band bending when modeling thesurface transfer doping, and provides useful insights for the development of devicesbased on hydrogen-terminated diamond.Keywords: Diamond, Transfer doping, NV center, Two-dimensional hole gas,Hydrogen-terminated surfacea)Corresponding author. E-mail address: yamaguchi.takahide@nims.go.jp21. INTRODUCTIONDiamond has excellent properties as a wide bandgap semiconductor and quantum ma-terial and has potential applications in power electronics1,2, communication2, computing3,4,and sensing5,6. An unusual property of diamond that could be used for such applications isits surface conductivity when it is terminated with hydrogen1,2,7. P-type surface conductiv-ity appears when hydrogen-terminated diamond is exposed to air even when the diamond isnot intentionally doped, offering a unique solution to the problem of inefficient charge-carriergeneration in diamond through substitutional doping1,7. The surface conductivity can be ba-sically explained by the surface transfer doping concept1,7–9. Here, atmospheric adsorbates,such as water and NO2, on hydrogen-terminated surfaces act as acceptors. Electrons in thevalence band of diamond are transferred to the acceptors, which induces band bending andgenerates holes below the diamond surface. Apart from atmospheric adsorbates, depositedoxides also act as acceptor materials1,2,7.The magnitude of the band bending induced by surface transfer doping and the corre-sponding areal density of holes and ionized acceptors are important information for design-ing devices based on hydrogen-terminated diamond. The hole density directly relates to thesheet resistance and current density. The ionized acceptors behave as scattering sources,and the hole mobility therefore depends on their density. It is generally assumed that theband bending due to electron transfer proceeds until the Fermi level of diamond aligns withthat of the (isolated) surface acceptor material or, equivalently, the surface potential energyof diamond reaches the work-function difference between the diamond and surface accep-tor material7–9. For certain ranges of surface acceptor density and nitrogen concentrationin diamond, however, the band bending due to electron transfer would not be as large asthat10,11. Such a surface transfer doping limited by the surface acceptor density and nitrogenconcentration has not been investigated in detail.In this study, we implanted nitrogen ions with ranging from 1011 to 1013 cm−2 in thesurface of diamond and investigated the implantation-fluence dependence of the surfaceconductivity of air-exposed hydrogen-terminated diamond. Furthermore, we carried outphotoluminescence (PL) and optically detected magnetic resonance (ODMR) measurementson shallow nitrogen-vacancy (NV) centers created from the implanted nitrogen, which pro-vided information on the potential energy and electric field near the diamond surface. The3results of the experiments were compared with simulations based on the Schrödinger-Poissonequations under the assumption that the surface potential is constant or that the surfaceionized acceptor density is constant irrespective of the nitrogen implantation fluence. Theresults suggest that band bending is not exclusively determined by the work-function differ-ence between diamond and the surface acceptor material, but by the finite density of surfaceacceptors, which is approximately 1012 cm−2 under our experimental conditions. This studydemonstrates that shallow NV centers can be used to gain insights into surface transferdoping of hydrogen-terminated diamond.2. METHODS2.1. Experimental methodsTwo samples (Sample A and B) were made from high-purity single-crystal diamond plateswith a nitrogen concentration below 5 ppb and boron concentration below 1 ppb. (SeeAppendix B for details of the sample preparation.) Schematic diagrams of the samples areshown in Fig. 1. Shallow NV centers were created by nitrogen (15N) ion implantation withan implantation energy of 10 keV and subsequent annealing at 1000˚C. The implantednitrogen atoms (and created NV centers) were distributed with a mean depth of ≈15 nmaccording to a SRIM (Stopping and Range of Ions in Matter) simulation12. The surface ofthe samples was divided into four sections that had different nitrogen implantation fluences:1×1011, 2×1011, 5×1011, and 1×1012 cm−2 in Sample A, and 1×1012, 2×1012, 5×1012, and1 × 1013 cm−2 in Sample B. The diamond surface was hydrogen-terminated in a hydrogenplasma in a microwave-plasma-assisted chemical vapor deposition (CVD) chamber.The PL imaging and ODMR measurements were performed using a home-built confocalmicroscope system13. A green laser with a wavelength of 532 nm was used for excitation, andfluorescence from the NV centers was detected with an avalanche photo diode through a 648-nm long-pass filter or guided to a spectrometer through a 561-nm long-pass filter. To obtainthe cw-ODMR spectra, the fluorescence intensity was measured by continuously irradiatingthe sample with the green laser and sweeping the frequency of the applied microwaves. Thesurface conductivity was measured with a two-terminal method using two prober needles incontact with the diamond surface. (See Appendix C for details of the measurement setup.)4The charge state of an NV center can be negative (-1), neutral (0), or positive (+1)depending on the Fermi level EF at its position. These different charge states can be dis-tinguished by making PL and ODMR measurements. (See Appendix A for details.) Thecalculated NV+/NV0 and NV0/NV− transition levels are at E+/0NV = 1.1 eV and E0/−NV = 2.7eV above the valence band maximum14. This means that the NV center is in the NV−state for EF>E0/−NV , NV0 state for E+/0NV E0/−NV , in the NV0 state for E+/0NV 4.7×1011cm−2. As shown in the main text, our experimental results are in better agreement withthe calculation under the constant φ′(0) boundary condition than they are with the calcu-lation under the constant φ(0) boundary condition. However, the constant φ(0) boundarycondition may be appropriate for low implantation fluences ≤2× 1011 cm−2.35S3. NV0 and NV− reference spectraThe reference samples for the NV0 and NV− spectra were prepared by controlling thedensity of donors (nitrogen; P1 center) and acceptors (boron). A NV− reference sample(Sample RNV(−)) was made from a Ib-type HPHT (001) single-crystalline diamond plate(Sumitomo Electric Industries) with a nitrogen concentration of approximately a hundredppm. The diamond plate was irradiated with an electron beam with a fluence of 1018 cm−2and energy of 2 MeV for creating vacancies and annealed in vacuum at 1000˚C for 2 h forforming NV centers. The P1 concentration evaluated by ESR measurements after electronbeam irradiation and before annealing was 134 ppm. The [NV]/[P1] ratio after annealingfor the above condition was estimated to be 1 − 2%. The P1 concentration is sufficientlylarge to make most NV centers be in the negative charge state34. The PL spectrum forthe NV− reference sample was measured with a low excitation power to avoid a photo-induced charge state conversion. NV0 reference samples (Samples RINV(0) and RIINV(0)) wereprepared using two different methods. Sample RINV(0) was made from a IIa-type (001) single-crystalline diamond plate (Element Six) with a relatively low nitrogen concentration of 40ppb (measured by ESR). The isolated nitrogen density was decreased further by convertingnitrogen into a NV center; the diamond plate was irradiated with an electron beam with afluence of 8.5× 1017 cm−2 and energy of 2 MeV and annealed in vacuum at 1000˚C for 2 h.The P1 concentration after the irradiation and annealing was below the detection limit ofthe ESR equipment. The low P1 concentration favors the NV0 state35. Sample RIINV(0) wasmade from a HPHT boron-doped diamond plate with a resistivity of 102 − 103 Ωcm. Thediamond was irradiated with an electron beam with a fluence of 1018 cm−2 and energy of 2MeV and annealed in vacuum at 1000˚C for 2 h.The normalized PL spectra of the NV0 and NV− reference samples are shown in Fig. S5.In a short wavelength range <600 nm, the PL intensity of the NV− reference sample (SampleRNV(−)) is low and indicates that the contribution of NV0 PL is smaller than≈1%. Therefore,we chose the spectrum of Sample RNV(−) as the NV− reference spectrum. The PL spectra ofthe NV0 reference samples prepared with the different methods were in good agreement witheach other. We selected Sample RINV(0), the spectrum of which has a clearer zero phonon line,as the NV0 reference sample. The PL intensities of the NV0 reference sample in a wavelengthrange of 700− 800 nm are nearly the same as 0.4 times the intensities of the NV− reference36spectrum. Therefore, one cannot rule out the possibility that the spectrum of Sample RINV(0)contains PL from NV− centers. We supposed three cases in which 0%, 20% and 40% of thePL of Sample RINV(0) comes from NV− centers. We subtracted the NV− contribution fromthe spectrum of Sample RINV(0) and used it as the NV0 reference spectrum for fitting. (Afterthe subtraction of the NV− contribution, the spectrum is normalized so that the integratedintensity is unchanged.) Figures S6a-c show the fitting results for the three cases. Better fits(for [Nimp] = 1 × 1011 and 5 × 1011 cm−2) are obtained for the ≥20% NV− contribution tothe spectrum of Sample RINV(0). It is also worth noting that the NV0 reference spectrum forthe 20% case is in the best agreement with the spectrum of a single NV0 reported in Ref.36.Figure S6d shows the relative contributions of NV0 and NV− to the PL spectra obtainedby the fitting. Figure S6e shows the NVH/NV+/NV0/NV− relative populations calculatedwith the data shown in Figs. 4b and S6d. (See Section S4 for the calculation.) Figures S6fshows the estimate of NV+/NV0/NV− relative populations. Figures S6d-f show the rangeof uncertainty caused by the uncertainty of the NV− contribution to the PL spectrum ofSample RINV(0). Figures 5a and 5b in the main text shows the results for the case in whichthe NV− contribution to the spectrum of Sample RINV(0) is assumed to be 20%.S4. Analysis of charge states with photoluminescenceWe evaluated the relative population of the charge states (NV+/NV0/NV−) below thehydrogen-terminated surface from the observed PL intensities and spectra by using thefollowing equations. The relative populations of NV+, NV0, and NV− below the oxygen-terminated surface (before hydrogenation), pO+, pO0 , and pO−, followpO+ + pO0 + pO− = 1. (S25)We assume that some of the NV centers are transformed to NVH after hydrogenation. Therelative populations of NVH, NV+, NV0, and NV− below the hydrogen-terminated surface,pHNVH, pH+, pH0 , and pH−, followpHNVH + pH+ + pH0 + pH− = 1. (S26)The ratio of the PL intensity for the hydrogen-terminated surface to that for the oxygen-terminated surface, IHPL/IOPL (Fig. 4b), is given byIHPLIOPL=t0pH0 Γ0 + t−pH−Γ−t0pO0 Γ0 + t−pO−Γ−, (S27)37where Γ0 and Γ− are the photon emission rate of the NV0 and NV− centers, t0 and t− are thetransmittances of the PL signals from NV0 and NV− centers through the 648-nm long-passfilter (used in the PL-intensity measurements). The ratio of the NV0 and NV− contributionsto the PL spectra measured for the hydrogen-terminated surface, cH−/cH0 (Fig. S6d), is givenbycH−cH0=pH−Γ−pH0 Γ0. (S28)From Eqs. S27 and S28, pH0 and pH− can be obtained:pH0 =IHPLIOPL(t0pO0 Γ0 + t−pO−Γ−)1Γ0cH0t0cH0 + t−cH−, (S29)pH− =IHPLIOPL(t0pO0 Γ0 + t−pO−Γ−)1Γ−cH−t0cH0 + t−cH−. (S30)By assuming that pH+ = 0 for a nitrogen implantation fluence of 1013 cm−2 and pHNVH isindependent of nitrogen implantation fluence, one can also obtain pHNVH and pH+ from Eq.S26:pHNVH = 1− pH0 ([Nimp] = 1× 1013cm−2)− pH−([Nimp] = 1× 1013cm−2), (S31)pH+ = 1− pH0 − pH− − pHNVH. (S32)pH0 and pH− were calculated with Eqs. S29 and S30 using the data shown in Figs. 4b andS6d. Here, we assumed that 1/Γ− = 12 ns and 1/Γ0 = 19 ns for high excitation powerconditions37,38. We also assumed that pO+ = 0, pO0 = 0.2, pO− = 0.8 by taking account ofphoto-induced ionization24. The values of pO+, pO0 , and pO− affect the estimate of pHNVH, butdo not affect the final result (Figs. 5b and S6f) on the NV+/NV0/NV− relative populations.The transmittances for the 648-nm long-pass filter were estimated from the NV0 and NV−reference spectra: t− = 0.92 and t0 = 0.55, 0.45, and 0.30 for the 0%, 20%, and 40%cases described in Section S3. pHNVH and pH0 were also obtained with Eqs. S31 and S32.The obtained pHNVH, pH+, pH0 , and pH− are shown in Fig. S6e. Figures 5b and S6f show therelative populations excluding the NVH defects: pH+/(pH+ + pH0 + pH−), pH0 /(pH+ + pH0 + pH−), andpH−/(pH+ + pH0 + pH−).38S5. Calculation of the electric-field-induced shift of the ODMR frequencyWe calculated the electric-field-induced shift of the ODMR frequency by following Ref.39.The spin Hamiltonian of the NV center in the presence of magnetic and electric fields ( ~B,~E) is given byH = (D + kzEz)(Sz2 − 2/3) + γe~S · ~B − kxEx(Sx2 − Sy2) + kyEy(SxSy + SySx), (S33)where ~S are the S = 1 dimensionless electron spin operators, D≈2.87 GHz is the zero-field splitting, γe = geµB/h is the electron gyromagnetic ratio, µB is the Bohr magneton,ge≈2.003 is the electron g-factor, h is the Planck constant, ~B and ~E are magnetic and electricfields, and kz = 3.5 kHz µm V−1 and kx = ky = k⊥ = 170 kHz µm V−1 are the electricsusceptibility parameters. xyz is the coordinate frame defined in Fig. 2 of Ref39, where zis the direction joining nitrogen and vacancy and x is orthogonal to z and contained withinone of the center’s three reflection planes. The ODMR frequencies f± are approximatelyf± = D + kzEz + 3Λ±√R2 − ΛR sinα cos β + Λ2, (S34)where Λ = γe2B⊥2/2D, R =√γe2R2 + k⊥2E⊥2, B⊥ =√Bx2 +By2, E⊥ =√Ex2 + Ey2,tanα = k⊥E⊥/γeBz, β = 2φB+φE, tanφB = By/Bx, tanφE = Ey/Ex. The above expressionfor f± is valid under the conditions, Λ, R << D. We assume that the magnetic and electricfields are parallel to the [001] crystal direction. Therefore, ~B = (√2/3| ~B|, 0, | ~B|/√3) and~E = (√2/3| ~E|, 0, | ~E|/√3). The calculated ODMR frequencies are plotted as a function ofelectric field in Figs. 7g and 7h. Here, D = 2.8705 GHz and | ~B| = 2.29 mT were assumedfor explaining the observed splitting of the ODMR frequencies.39Temperature T 300 KBulk donor (nitrogen) density NN 8.8× 1014 cm−3Bulk acceptor (boron) density NB 1.76× 1014 cm−3Donor (nitrogen) ionization energy ED 1.7 eVAcceptor (boron) ionization energy EA 0.37 eVNV+/NV0 transition level (relative to VBM) E+/0NV 1.1 eVNV0/NV− transition level (relative to VBM) E0/−NV 2.7 eVMean depth of implanted nitrogen zimp 15.1 nmStandard deviation of implanted nitrogen distribution σimp 5.6 nmCreation yield of NV centers from implanted N atoms RNV/N 0.01Bandgap EG 5.47 eVDielectric constant εS/ε0 5.7Spin-orbit splitting energy ∆SO 6 meVEffective mass of heavy hole mHH/m0 0.67Effective mass of light hole mLH/m0 0.26Effective mass of split-off hole mSO/m0 0.375Effective mass of heavy hole along [001] mHHz /m0 0.441Effective mass of light hole along [001] mLHz /m0 0.325Effective mass of split-off hole along [001] mSOz /m0 0.375Effective mass of heavy hole in the (001) plane mHH// /m0 0.288Effective mass of light hole in the (001) plane mLH// /m0 0.536Effective mass of split-off hole in the (001) plane mSO// /m0 0.375Longitudinal effective mass of electron mL/m0 1.56Transverse effective mass of electron mT/m0 0.28Table S1: Parameters used in the calculation. ε0 is the vacuum permittivity. m0 is the rest mass. Theeffective masses are from the experimental results of Ref.40.401086420Energy (eV)2000150010005000Depth (nm)φ(0) = -3.8 V[Nimp] = 1×1011 cm-2EFEVECNV(0/-)NV(+/0)N(+/0)B(0/-)1086420Energy (eV)50403020100Depth (nm)φ(0) = -3.8 V[Nimp] = 1×1011 cm-2EVNV(0/-)EFNV(+/0)ECN(+/0)B(0/-)1013101410151016101710181019Density (cm-3)2000150010005000Depth (nm)N(+)N(0)B(-)B(0)φ(0) = -3.8 V[Nimp] = 1×1011 cm-21013101410151016101710181019Density (cm-3)50403020100Depth (nm)Hole(+)Nimp(+)N(+)B(0)NV(+)φ(0) = -3.8 V[Nimp] = 1×1011 cm-21086420Energy (eV)2000150010005000Depth (nm)φ(0) = -3.8 V[Nimp] = 7×1012 cm-2EFEVECN(+/0)NV(0/-)NV(+/0)B(0/-)1086420Energy (eV)50403020100Depth (nm)φ(0) = -3.8 V[Nimp] = 7×1012 cm-2NV(+/0)EVEFECN(+/0)NV(0/-)B(0/-)1013101410151016101710181019Density (cm-3)2000150010005000Depth (nm)N(0)B(-)N(+)φ(0) = -3.8 V[Nimp] = 7×1012 cm-21013101410151016101710181019Density (cm-3)50403020100Depth (nm)Nimp(+)NV(-)NV(0)NV(+)N(+)B(-)B(0)φ(0) = -3.8 V[Nimp]=7×1012 cm-2abcdefgh41Figure S1: Band diagram, charge transition levels and charge state distribution of nitrogen, boron, andNV centers calculated with the constant φ(0) boundary condition (φ(0) = −3.8 V). a-d Band diagramsand charge transition levels (a,c) and charge state distribution (b,d) for a nitrogen implantation fluence[Nimp] of 1× 1011 cm−2 in a wide depth range (a,b) and in a narrow range near the surface (c,d). e-hBand diagrams and charge transition levels (e,g) and charge state distribution (f,h) for a nitrogenimplantation fluence [Nimp] of 7× 1012 cm−2 in a wide depth range (e,f) and in a narrow range near thesurface (g,h). EC, conduction band minimum; EV, valence band maximum; and EF, Fermi level.abcφ(0) =6543210Density (1010 cm-2)86420Implanted nitrogen density (1012 cm-2) NV(+) NV(0) NV(-)-3.8 V-3.7 V-3.6 Vφ(0) =1.00.80.60.40.20.0Hole density (1012 cm-2)86420Implanted nitrogen density (1012 cm-2)-3.8 V-3.7 V-3.6 Vφ(0) = -1.6 V43210Density (1010 cm-2)43210Implanted nitrogen density (1012 cm-2) NV(+) NV(0) NV(-)Figure S2 Calculated results for the constant φ(0) boundary condition for different values of φ(0). a NV+,NV0, and NV− density as a function of nitrogen implantation fluence for φ(0) = −3.6, −3.7, and −3.8 V.b Hole density as a function of nitrogen implantation fluence for φ(0) = −3.6, −3.7, and −3.8 V. c NV+,NV0, and NV− density as a function of nitrogen implantation fluence for φ(0) = −1.6 V.421086420Energy (eV)2000150010005000Depth (nm)φ'(0) = 0.317 MV/cm[Nimp] = 1×1011 cm-2EFECEVN(+/0)NV(0/-)NV(+/0)B(0/-)1013101410151016101710181019Density (cm-3)2000150010005000Depth (nm)N(+)N(0)B(-)B(0)φ'(0) = 0.317 MV/cm[Nimp] = 1×1011 cm-21086420Energy (eV)50403020100Depth (nm)φ'(0) = 0.317 MV/cm[Nimp] = 1×1011 cm-2EFECEVN(+/0)NV(+/0)NV(0/-)B(0/-)1013101410151016101710181019Density (cm-3)50403020100Depth (nm)Hole(+)Nimp(+)N(+)B(0)NV(+)φ'(0) = 0.317 MV/cm[Nimp] = 1×1011 cm-21086420Energy (eV)2000150010005000Depth (nm)φ'(0) = 0.317 MV/cm[Nimp] = 1.5×1012 cm-2EFECEVN(+/0)NV(0/-)NV(+/0)B(0/-)1013101410151016101710181019Density (cm-3)2000150010005000Depth (nm)N(0)B(-)N(+)φ'(0) = 0.317 MV/cm[Nimp] = 1.5×1012 cm-21086420Energy (eV)50403020100Depth (nm)φ'(0) = 0.317 MV/cm[Nimp] = 1.5×1012 cm-2EFECEVN(+/0)NV(0/-)NV(+/0)B(0/-)1013101410151016101710181019Density (cm-3)50403020100Depth (nm)Nimp(+)N(+)B(-)NV(-)N(0)φ'(0) = 0.317 MV/cm[Nimp] = 1.5×1012 cm-2abcdefgh43Figure S3: Band diagram, charge transition levels and charge state distribution of nitrogen, boron, andNV centers calculated with the constant φ′(0) boundary condition (φ′(0) = 0.317 MV/cm, correspondingto a negative surface charge density of 1× 1012 cm−2). a-d Band diagrams and charge transition levels(a,c) and charge state distribution (b,d) for a nitrogen implantation fluence [Nimp] of 1× 1011 cm−2 in awide depth range (a,b) and in a narrow range near the surface (c,d). e-h Band diagrams and chargetransition levels (e,g) and charge state distribution (f,h) for a nitrogen implantation fluence [Nimp] of1.5× 1012 cm−2 in a wide depth range (e,f) and in a narrow range near the surface (g,h). EC, conductionband minimum; EV, valence band maximum; and EF, Fermi level.103104PL intensity (counts)900800700600500Wavelength (nm) Sample A (background) Sample A Sample B (background) Sample BabcdefghFigure S4 a Raw data of PL spectra measured in regions with nitrogen implantation fluences of 1× 1011(a), 2× 1011 (b), 5× 1011 (c), and 1× 1012 cm−2 (d) in Sample A and 1× 1012 (e), 2× 1012 (f), 5× 1012(g), and 1× 1013 cm−2 (h) in Sample B. Background spectra measured in non-implanted regions are alsoshown.440.0120.0100.0080.0060.0040.0020.000PL intensity (a.u.)900800700600500Wavelength (nm)NV(-)NV(0)Figure S5 PL spectra of NV0 and NV− reference samples. The blue curve is the spectrum of the NV−reference sample (Sample RNV(−)). The green and brown curves are the spectra of the NV0 referencesamples (green: Sample RINV(0), brown: Sample RIINV(0)). The spectra of the NV0 reference samplespossibly contain the PL from NV− centers. (See Section S3.)PL intensity (a.u.)PL intensity (a.u.)PL intensity (a.u.)900800700600500Wavelength (nm)900800700600500Wavelength (nm)900800700600500Wavelength (nm)1×1013 cm-2 (B)5×1012 cm-2 (B)1×1011 cm-2 (A)2×1011 cm-2 (A)5×1011 cm-2 (A)1×1012 cm-2 (A)1×1012 cm-2 (B)2×1012 cm-2 (B)1×1013 cm-2 (B)5×1012 cm-2 (B)1×1011 cm-2 (A)2×1011 cm-2 (A)5×1011 cm-2 (A)1×1012 cm-2 (A)1×1012 cm-2 (B)2×1012 cm-2 (B)1×1013 cm-2 (B)5×1012 cm-2 (B)1×1011 cm-2 (A)2×1011 cm-2 (A)5×1011 cm-2 (A)1×1012 cm-2 (A)1×1012 cm-2 (B)2×1012 cm-2 (B)1.00.80.60.40.20.0Contribution to PL1011 1012 1013Nitrogen implantation fluence (cm-2) NV(-) NV(0)e fcda bNV(-)NV(0)NV(-)NV(0)NV(-)NV(0)0.80.60.40.20.0Ratio1011 1012 1013Nitrogen implantation fluence (cm-2) NV(-) NV(0) NV(+) NVH1.00.80.60.40.20.0Ratio1011 1012 1013Nitrogen implantation fluence (cm-2) NV(-) NV(0) NV(+)45Figure S6 a-c Fitting of the measured spectra (brown curves) with the NV0 and NV− reference spectra forcases in which 0% (a), 20% (b) or 40% (c) of the PL of Sample RINV(0) comes from NV− centers. (SeeSection S3.) The green and blue dashed curves are the contributions from NV0 and NV− centers and theblack dashed curves are the sum of them. The vertical dashed dot (dashed) lines indicate the 575-nm(637-nm) zero phonon line of the NV0 (NV−) centers. The green and blue curves in the bottom panels arethe NV0 and NV− reference spectra. The gray curve is the spectrum of Sample RINV(0). d Relativecontributions of NV0 and NV− to the PL spectra obtained by the fitting. e NVH/NV+/NV0/NV− relativepopulations calculated with the data shown in Figs. 4b and S6d. (See Section S4 for the calculation.) fNV+/NV0/NV− relative populations. In d-f, symbols with crosses, filled symbols, and empty symbolscorrespond to the 0% (a), 20% (b) and 40% cases (c). Circles and squares represent Samples A and B.PL intensity (Mcps)PL intensity (Mcps)a b c de f g h0.100.080.060.040.020.000.300.250.200.150.100.050.001.00.80.60.40.20.03.02.52.01.51.00.50.03.02.52.01.51.00.50.01.00.80.60.40.20.02.01.51.00.50.03.02.52.01.51.00.50.0Figure S7 a-d Photoluminescence images for nitrogen implantation fluences of 1× 1011 (a), 2× 1011 (b),5× 1011 (c), and 1× 1012 cm−2 (d) in Sample A. e-h Photoluminescence images for nitrogen implantationfluences of 1× 1012 (e), 2× 1012 (f), 5× 1012 (g), and 1× 1013 cm−2 (h) in Sample B. The image sizes are20 µm × 20 µm. The excitation laser intensity is 20 µW for an implantation fluence of ≥2× 1012 cm−2and 200 µW for lower implantation fluences.460.100.080.060.040.020.00PL intensity (Mcps)2.952.902.852.80Frequency (GHz)0.100.090.080.070.060.050.04PL intensity (Mcps)2.952.902.852.80Frequency (GHz)0.750.700.650.600.550.50PL intensity (Mcps)2.952.902.852.80Frequency (GHz)2.62.52.42.32.2PL intensity (Mcps)2.952.902.852.80Frequency (GHz)0.800.750.700.650.600.550.500.45PL intensity (Mcps)2.952.902.852.80Frequency (GHz)0.220.200.180.16PL intensity (Mcps)2.952.902.852.80Frequency (GHz)1.51.41.31.21.1PL intensity (Mcps)2.952.902.852.80Frequency (GHz)2.62.42.22.01.81.6PL intensity (Mcps)2.952.902.852.80Frequency (GHz)acegbdfh47Figure S8: a-d Double Lorentzian fits (lines) to ODMR spectra (gray dots) in the regions of nitrogenimplantation fluences of 1× 1011 (a), 2× 1011 (b), 5× 1011 (c), and 1× 1012 cm−2 (d) in Sample A. e-hDouble Lorentzian fits (lines) to ODMR spectra (gray dots) in the regions of nitrogen implantationfluences of 1× 1012 (e), 2× 1012 (f), 5× 1012 (g), and 1× 1013 cm−2 (h) in Sample B. The ODMR spectraare the same as those shown in Fig. 6. The excitation laser intensity is 20 µW for an implantation fluenceof ≥2× 1012 cm−2 and 200 µW for lower implantation fluences. A linear background is assumed for thefitting.ab3.143.123.103.083.06PL intensity (Mcps)3.002.952.902.852.802.75Frequency (GHz)3.153.103.053.002.952.90PL intensity (Mcps)3.002.952.902.852.802.75Frequency (GHz)Figure S9: ODMR spectra observed for different magnetic field orientations. a Two ODMR dips appear,indicating that the magnetic field applied with a permanent magnet is parallel to the [001] direction ofdiamond. b Eight ODMR dips corresponding to the four axes of NV centers appear. The permanentmagnet direction was tilted from that used for a.48a b c de f g h1.051.000.950.90PL intensity (a.u.)3002001000τ (ns)1.051.000.950.903002001000τ (ns)1.051.000.950.903002001000τ (ns)1.051.000.950.903002001000τ (ns)1.051.000.950.90PL intensity (a.u.)3002001000τ (ns)1.051.000.950.903002001000τ (ns)1.051.000.950.903002001000τ (ns)1.051.000.950.903002001000τ (ns)Figure S10 a-d Rabi oscillations measured in regions with nitrogen implantation fluences of 1× 1011 (a),2× 1011 (b), 5× 1011 (c), and 1× 1012 cm−2 (d) in Sample A. e-h Rabi oscillations in regions withnitrogen implantation fluences of 1× 1012 (e), 2× 1012 (f), 5× 1012 (g), and 1× 1013 cm−2 (h) in SampleB. The excitation laser intensity is 20 µW for an implantation fluence of ≥5× 1012 cm−2 and 200 µW forlower implantation fluences.49cdab1.41.21.00.80.60.40.20.0Conductance (10-5 Ω-1)1011 1012 1013Nitrogen implantation fluence (cm-2) Sample A (1st) Sample B (1st) Sample A (2nd) Sample B (2nd)10-910-810-710-610-5Conductance (Ω-1)1011 1012 1013Nitrogen implantation fluence (cm-2) Sample A (1st) Sample B (1st) Sample A (2nd) Sample B (2nd)3.02.52.01.51.00.50.0PL intensity (Mcps) 1011 1012 1013Nitrogen implantation fluence (cm-2) Sample A (1st) Sample B (1st) Sample A (2nd) Sample B (2nd)103104105106107PL intensity (cps) 1011 1012 1013Nitrogen implantation fluence (cm-2) Sample A (1st) Sample B (1st) Sample A (2nd) Sample B (2nd)Figure S11 a,b Nitrogen-implantation-fluence dependence of PL intensity measured on different dates.The first measurements on Sample A (B) were carried out 2-3 (2-4) days after the hydrogenation. Thesecond measurements were carried out 233-234 (232-233) days after the hydrogenation. c,dNitrogen-implantation-fluence dependence of the conductance measured on different dates. The firstmeasurements on Sample A (B) were carried out 6 (7) days after the hydrogenation. The secondmeasurements were carried out 243 (244) days after the hydrogenation.50