Nitrogen-Terminated Diamond (111) Surface for Room-Temperature

Letter pubs.acs.org/NanoLett

Nitrogen-Terminated Diamond (111) Surface for Room-Temperature Quantum Sensing and Simulation Jyh-Pin Chou,† Alex Retzker,‡ and Adam Gali*,†,¶ †

Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, POB 49, Budapest H-1525, Hungary ‡ Racah Institute of Physics, The Hebrew University of Jerusalem, Givat Ram Jerusalem 91904, Israel ¶ Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111, Budapest, Hungary S Supporting Information *

ABSTRACT: The nitrogen-vacancy (NV) center in diamond has shown great promise of nanoscale sensing applications, however, nearsurface NV suffer from relatively short spin coherence time that limits its sensitivity. This is presumably caused by improper surface termination. Using first-principles calculations, we propose that nitrogen-terminated (111) diamond provides electrical inactivity and surface spin noise free properties. We anticipate that the nitrogenterminated (111) surface can be fabricated by nitrogen plasma treatment. Our findings pave the way toward an improved NV-based quantum sensing and quantum simulation operating at room temperature. KEYWORDS: N-terminated surface, (111) diamond surface, nitrogen vacancy, quantum sensing, quantum simulator he negatively charged nitrogen-vacancy (NV−) center in diamond has attracted significant interests because of its remarkable spin and optical characteristics for quantum information processing1,2 (QIP) and sensing applications3,4 operating even at room temperature. Surface functionalization of diamond has become an important topic when these optical defect centers are engineered within a few nanometers from the diamond surface.5 NV centers near the most common (100) diamond surface suffer from short spin coherence times due to surface spin noise,6,7 permanent bleaching caused by surface states in the bandgap,8,9 and low photon collection efficiency due to nonoptimal crystal orientation.10,11 NV centers preferentially align along the [111] axis in (111) as-growth diamonds, thus (111)-oriented diamond greatly improve the collection efficiency.11 However, the lack of optimal (111) diamond surface termination inhibits one to employ these wellaligned near-surface NV centers in QIP and related applications. Here we show by means of combination of experimental data12 and ab initio simulations that nitrogenterminated (111) diamond surface is an ideal choice as it has high electron affinity, is optically and electrically inactive, and can be formed by nitrogen plasma treatment. This surface can realize the quantum simulation of quantum spin liquids. The NV center consists of a substitutional nitrogen and an adjacent carbon vacancy, exhibiting C3V symmetry and can be aligned along one out of the four ⟨111⟩ crystallographic axes of diamond. The alignment homogeneity of the NV centers is a critical issue because the spin sublevels vary depending on the angle between the symmetry axis of NV and the external field.13 The orientation of NV centers perpendicular to the surface

T

© 2017 American Chemical Society

would be optimal to achieve enhanced photon collection efficiency because of the perpendicular polarization of the emitted photons from NV−.14,15 This type of selective alignment can be realized by chemical vapor deposition (CVD) growth of (111) diamond, where the alignment selective approaches 99%. However, the conventional (111) diamond surface has a high density of twins, stacking faults, defects, and impurities,16 thus growing high-quality crystalline (111)-oriented surface is a technical challenge. With an appropriate choice of plasma conditions, the atomically stepfree diamond (111) surfaces can be successfully synthesized by homoepitaxial lateral growth in microwave plasma CVD (MPCVD).17 This implies that well-aligned shallow NV centers can be engineered into high quality (111) diamond with atomically smooth surface by CVD technique. Thus, we consider the (111) diamond for NV− sensor application. The MPCVD growth of diamond results in hydrogenterminated surface,17 however, this diamond surface has a high electric dipole moment that easily attracts negatively polar ions (e.g., water), leading to the creation of a hole accumulation layer at the surface and then inducing strong upward surface band bending. As a consequence, hydrogen termination of diamond leads to a negative electron affinity (NEA).18 This will convert NV− to neutral NV, so the spin sensor will permanently disappear.19−22 The most often applied technique to move Received: December 2, 2016 Revised: March 24, 2017 Published: March 24, 2017 2294

DOI: 10.1021/acs.nanolett.6b05023 Nano Lett. 2017, 17, 2294−2298

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Nano Letters

Figure 1. Band structures of H- and N-terminated diamond (111)-1 × 1 surface. (a) Schematic illustration of H- and N-terminated diamond (111) surface structures and the corresponding band structures. The radii of the colored circles are proportional to the total contribution of corresponding surface atoms. VBM and CBM of bulk diamond are plotted by the two dashed lines at 0 and 5.3 eV, respectively. (b) Schematic energy diagram of H- and N-terminated (111) surfaces; the dashed lines depict the corresponding vacuum level. The shadow regions are the surface-related states. Gray region depicts the hydrogen-related empty image bands whereas the green regions show the corresponding nitrogen-related surface bands. The calculated spin-polarized defect levels of the NV− center are also represented. The empty e defect level lies in the surface band in hydrogenterminated diamond.

Figure 2. (a) Electron affinities of mixed C−H/N terminated diamond (111) surface as a function of N coverage. The coverage equal to zero and one represents the full H- and N-terminated surface, respectively. (b) Formation enthalpies of diamond (111) and (100) surface with different nitrogen coverage by assuming nitrogen plasma treatment where the realistic parameters are temperature T = 700 K, and partial pressure of H and N are 0.05 and 16 Torr, respectively. (c) The resulting (111) nitrogen-terminated surface after nitrogen plasma treatment is illustrated with nearsurface nitrogen-vacancy centers.

morphology that can distort the diamond lattice. On an atomically smooth diamond (111) surface, each carbon atom on the top layer bonds to a single hydrogen atom. This C−H unit at the surface can be substituted by an isovalent N atom that we label by N/C(111). The naive expectation from this picture is that the resultant surface is completely passivated but this should be explored in detail. To this end, we performed density functional theory calculations of H- and N-terminated diamond surfaces. Figure 1a presents the geometric and electronic structures of full coverage H- and N-terminated diamond (111) surface. The H/C(111) surface introduces deep empty states into bandgap in the region of 2.21 eV below conduction band minimum (CBM). These states are delocalized surface-related image states that are also observed in (100) surface.9 These surface-related states are responsible for the photophysical instability of shallow NV centers. In contrast, N-terminated diamond is basically optically inactive; only a few occupied surface bands appear near the valence band maximum (VBM) that do not interfere with the level of NV (see Figure 1b). The NEA value of H/C(111) is −1.63 eV, which is in good agreement with an experimental value of −1.27 eV.33 In contrast, nitrogen termination pushes the electron affinity toward positive values. As shown in Figure 2a,

from NEA to positive electron affinity (PEA) diamond surface is oxygenation.23,24 Theoretical studies25,26 predicted that oxygenated diamond (111) surface is quite reactive and optically active. Ultraviolet photoelectron spectroscopy and temperature-programmed desorption experiments24 indicate that oxygenated (111) diamond surface indeed exhibits PEA, however, oxygen chemisorption will create a lot of defects and facets resulting in amorphization of the diamond surface. Alternatively, fluorination can also form the PEA diamond surface.27 Surface fluorination can be realized by exposing the surface to CF4 or SF6 plasma treatment,28−30 which will etch diamond surface and form a fluorocarbon layer 2−5 nm on the top layer increasing the surface roughness. A mild benchtop approach to nanodiamond fluorination has been developed recently,31 which can avoid fluorine etching and stabilize NV− centers in a mixed CF and COH terminated nanodiamond. However, the surface roughness, either from oxygenation or fluorination, may stabilize defects with unsaturated bonds near the surface that might be responsible for surface-induced spin noise,7,32 which is detrimental for sensor applications. Oxygen and fluorine atoms are often provided by aggressive acids that makes it very difficult to control the surface 2295

DOI: 10.1021/acs.nanolett.6b05023 Nano Lett. 2017, 17, 2294−2298

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Nano Letters

Our findings have important implications both for roomtemperature quantum sensors and for quantum simulation. The (111) nitrogen-terminated diamond can host aligned NV− centers with the largest photon collection efficiency and provides well-defined morphology, stable charge state of NV, and virtually no electron spin noise. Thus, the slow surface noise originates from surface spin−spin interactions5,7,38 which will be completely eliminated in our setup. The origin of the fast noise is still unclear; the leading assumption, however, is that the surface charge thermal fluctuations induce it.6 In that case, the fast noise as well will be reduced substantially due to nitrogen termination. This leads to ultrashallow NV− centers with electron spin coherence times similar to those in bulk diamond that is essential in many sensing protocols.39 In the case that only the slow noise is reduced, the achieved coherence time will still allow sensing single protons.8 In addition, nitrogen have 14N and 15N isotopes with I = 1 and I = 1/2 spins, respectively, that can be freely controlled by choosing the appropriate N precursor. The N-terminated surface provides an array of nuclear spins that can be probed by the NV− electron spins. Recently, Cai et al.2 proposed that this type of surface with ultrashallow NV centers can be used as a quantum simulator. The realization of our proposal to use 14N will enable the investigation of a spin-1 quantum simulator of a quantum spin liquid (QSL), which have attracted a lot of attention in recent years.40 QSLs in most cases are composed out of spin half systems.41−43 It was rather surprising when it was recently discovered experimentally that spin-1 systems on a triangular lattice behave as a spin liquid.44 This unexpected discovery has stimulated theoretical efforts.45 By realizing this proposal it will be possible to probe a triangular spin-1 lattice with controllable Heisenberg interaction and to verify the QSL characteristics as well as dynamics in a highly controlled way with a bottom up approach. This ability could shed new light on the theory of spin-1 QSL and Ba3NiSb2O9 experiments.44 The main experimental challenge in observing the coherent dynamics of the quantum simulator is set by the remaining surface states that will fluctuate and decohere the simulator nuclei. Assuming 5% hydrogen coverage in which surface states will occur with 5% probability, a total of 0.25% of the sites will result in electron spins. This means that a single electron spin appears for a surface size of the order of 45 nm × 45 nm, containing around 400 nuclei. In order to observe global quantum behavior a minimal requirement is that the coherence time of the nuclei will be at least an order of magnitude longer than the interaction time of two nearby nuclei multiplied by the maximal distance of a probing region. If we target a region of 400 sites, which is inaccessible classically, and as the coupling strength of two nearest neighbor nuclei is of the order of 80 Hz, coherence times of the order of a few seconds will be required. In order to reduce this dephasing, a strong microwave drive on the NV could be induced, with the aim to average the NV nucleus interaction to a tiny value (see Methods). In the following estimation, we use a realistic Rabi frequency of 50 MHz. In order to estimate the coherence time of the nuclei, we will concentrate on the nuclei that are in the vicinity of the NV with a coupling strength of the order of half a megahertz. The T1 due to surface electron interaction at these distances is around 550 Hz, that is, 2 ms. Thus, by driving with 100 MHz the interaction will be averaged to zero up to the last rotation and thus a phase of 0.01 (0.5 MHz/50 MHz) will be acquired

we calculate the electron affinity of mixed CH/N terminated diamond surface (N atom replaces CH radical). NEA surface is converted to PEA surface if the N coverage is larger than 0.5 monolayer (ML). Full coverage N/C(111) yield PEA as 3.23 eV that is comparable to that of fluorine-terminated surface.34 We conclude that even mixed CH/N terminated (111) diamond surface with at least 0.5 ML nitrogen termination is a perfect host for NV− quantum sensor. It has been recently demonstrated that high-quality Nterminated diamond (100) surface can be realized by using an indirect radio frequency N2 plasma process that keeps the surface damages minimal caused by the plasma treatment.12,35−37 Those samples were grown at temperature of ∼700 K with a pressure of nitrogen source at 170 Torr. The predominant component is substitutional nitrogen or mixed N/ CH species at the surface, depending on the type of diamond substrate12 where the fraction of nitrogen termination reaches at least 0.5 ML. It has been shown that nitrogen substitutes carbon atom on the top layer of 2 × 1 reconstructed (100) surface, so the resultant nitrogen-terminated surface is stable at room temperature. The resultant 2 × 1 reconstruction pattern12 clearly implies that the original morphology and atomically flat surface could be maintained after nitridation. We computed the formation enthalpy of N- and mixed N/ CH terminated (100) and (111) diamond surface in which we simulate the conditions of a nitrogen plasma by an appropriate choice of chemical potentials. A detailed description of the formation enthalpy can be found in the Methods. The main results are shown in Figure 2b. We found that the formation enthalpy favors the full N-terminated diamond surfaces. Most importantly, N/CH(111) surface exhibits 0.3 eV/atom (at least) lower formation enthalpy than N/CH(100) surface, and this occurs at any mixed terminations. Because N/CH(100) surface was already demonstrated to form in experiments,12 and similar reaction kinetics takes place on (100) and (111) diamond surfaces, the formation of N/C−H(111) diamond surface is even more likely than that of N/C(100) by applying the same conditions in the CVD nitridation process. The microscopic origin of this effect is the favorable bonding configuration of substitutional nitrogen atom on the top carbon layer of (111) diamond, as it can form a perfect pyramid with its three immediate neighbor C atoms situated in the second layer of (111) diamond without any measurable distortion of the diamond lattice. In the case of 2 × 1 reconstructed (100) diamond surface, the substitutional nitrogen in the top carbon layer also forms three nitrogen− carbon bonds but the surface reconstruction stiffens somewhat these bonds compared to those of (111) diamond. According to our calculations, even 0.5 ML N/CH mixed surface yields favorable properties to host NV spin sensor in (111) diamond. At the typical nitridation temperature (T ≈ 700 K), the calculated formation enthalpies indicate that ∼95% of the (111) diamond surface will be terminated by nitrogen and the rest with hydrogen as calculated by the Boltzmann 1 dist ribut ion ρθ /ρ = exp( −Eθ /kBT )/∑θ = 0 exp( −Eθ /kBT ), where ρθ is the distribution of different N coverage (θ) and ρ is the summation of ρθ. Eθ is the formation enthalpy (unit in eV) of the considered N and mixed N/CH termination, kB is the Boltzmann constant (8.617 × 10−5 eV/K), and T is temperature (units in K). We conclude that high quality, atomically smooth N-terminated surface can be formed by nitrogen plasma treatment of (111) hydrogenated diamond. 2296

DOI: 10.1021/acs.nanolett.6b05023 Nano Lett. 2017, 17, 2294−2298

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Nano Letters in 2 ms. As the random phase is accumulated via a random walk process, the coherence time will be 20 s, which brings us to the regime where interesting quantum dynamics could be probed. In summary, we show that atomically smooth N-terminated diamond (111) surface is electrically inactive with positive electron affinity and represents surface spin noise free properties. This provides an ideal host for shallow NV centers for quantum sensing that can be engineered with a single orientation optimal to maximize the photon collection efficiency. We show that such surface termination can open up a new route for NV-based quantum simulations operating at room temperature. Methods. Computational Details. We used the Vienna Ab Initio Simulation Package (VASP46) with the projector augmented wave (PAW)47 method with plane wave basis set for the electrons. Parameters for the surface calculations were established first by using the generalized gradient approximation (GGA) to the exchange correlation functional proposed by Perdew, Burke, and Ernzerhof (PBE)48 in bulk calculations on the primitive cell with a 8 × 8 × 8 k-points for Brillouin-zone sampling. Constant volume relaxations using a cutoff of 370(740) eV in the plane-wave expansion for the wave function (charge density) resulted in an equilibrium lattice parameter of aPBE = 3.57 Å. Increasing the cutoff to 420(840) eV has changed the lattice constant by only 0.003 Å. Therefore, considering the demands of the surface calculations, the lower cutoff energy was selected. To simulate (111)-1 × 1 diamond surface we use a slab consisting of 20 bilayers with 12 Å vacuum layers in a hexagonal cell. The terminators connect with carbon surface atoms on both top and bottom sides. For slab structure optimization, we used 10 × 10 × 1 k-points. The six bilayers in the middle of the slab were fixed and the rest were fully relaxed in this procedure. The atoms were allowed to relax until the forces were below 0.01 eV/Å. The band structures and electron affinity were calculated with a screened hybrid functional HSE06 of Heyd, Ernzerhof, and Scuseria, which is nearly free of the electron self-interaction error and is capable of providing accurate electronic energy levels. We used a 3 × 3 supercell of C(111) and a 4 × 2 supercell for C(100) surfaces to calculate the surface formation enthalpies of different surface terminations. Formation Enthalpy. To obtain the pressure and temperature-dependent surface formation enthalpies of H-, N-, and H/ N-terminated diamond surface, we used the following equation49 H(p , T ) =

kB is Boltzmann constant and EH2 is the energy of a H2 molecule in vacuum. The chemical potential of H and N are expressed as the follows49 μH (p , T ) =

⎛ p⎞ μ N (p , T ) = μ N (p0 , 0 K) + ΔG N(p0 , T ) + kBT ln⎜ 0 ⎟ ⎝p ⎠

noise sources will result in an effective coupling of in a T1 time a random phase of

will be accumulated. As this

completely dephase the system is N =

Ω2 (gδ)2

and thus the

Ω2

coherence time is (gδ)2 T1. This term could further be reduced by an extra drive as shown in ref 52. Thus, in total a good approximation to the coherence time of the nuclei is T1 T2n ≈ . (g / Ω)2 The estimation of the various parameters could be done in the following way. T1 is set by the flip−flop interaction of two nearby electrons, which is half of a kilohertz for 45 nm. g could be estimated by the nearest neighbor nuclei to the electron which is of the order of half a megahertz and a continuous drive of 50 MHz is set for of Ω. Thus, we get a rough estimation of the coherence time of 20 s.

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Etotal is the total energy, FS(T) is the free energy of the H atoms, T is temperature in unit of K. nC, nH, nN, and nS are the numbers of C, H, N, and surface atoms, respectively. pH and pN are partial pressure of H and N. The factor 2 is due to the twosided surface modeling. μC, μH, and μN are the chemical potential of C, H, and N atoms. We used diamond bulk energy as μC. To determine FS(T),50 we calculate the local vibrational modes of CH on the surface

i

and thus gδ

(2nS)

⎡ ⎛ − E H 2 ⎞⎤ 1 E H2 + kBT ln⎢1 − exp⎜ ⎟⎥ ⎢⎣ 2 ⎝ kBT ⎠⎥⎦

gδ T Ω 1

gδ Ω

phase will grow in a random walk process, that is, Ω T1 N , where N is the number of steps, the number of steps to

[Etotal + FS(T ) − nCμC − nHμH (pH , T ) − nNμ N (pN , T )]

∑

(4)

μH2(p0, 0 K) and μN(p0, 0 K) are the energy of H2 and N at temperature of 0 K, respectively. p0 is standard-state pressure, ΔG(p0, T) is the difference of Gibbs free energy, which can be obtained from the thermodynamic tables.51 In order to simulate the nitrogen plasma conditions,12 we used a pressure of 16 Torr for atomic nitrogen, 0.05 Torr for H, and temperature of 700 K. The obtained results are robust, and the calculated trend does not change by varying the temperature and pressure (see Supporting Information). Estimation of Coherence Time. Even in the low concentration of surface charge states that would be achieved by nitrogen-termination coherent control would be needed to increase the coherence time of the nuclei. In order to do so, the techniques presented in ref 52 could be used. In an ideal scenario assuming a coupling of g, electron decay time, T1, and drive of Ω the nuclei will have an effective coherence time of T1 T2n ≈ . Random detuning which will be induced by other (g / Ω)2

(1)

FS(T ) =

⎛ p⎞ 1 1 1 μ (p0 , 0 K) + ΔG H2(p0 , T ) + kBT ln⎜ 0 ⎟ 2 H2 2 2 ⎝p ⎠ (3)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b05023. Details of layer thickness convergence testing and the stability of N-terminated (100) and (111) diamond surface (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

(2) 2297

DOI: 10.1021/acs.nanolett.6b05023 Nano Lett. 2017, 17, 2294−2298

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Jyh-Pin Chou: 0000-0001-8336-6793 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the funding support from the EU FP7 611143 (DIADEMS). J-P.C. and A.G. acknowledge the funding support from the MTA Lendület programme from the Hungarian Academy of Sciences. A.R. acknowledges the support from the EU FP7 323714 (EQUAM) and the Israeli Science Foundation Grant No. 1500/13.

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DOI: 10.1021/acs.nanolett.6b05023 Nano Lett. 2017, 17, 2294−2298