PHYSICAL REVIEW B 88, 075206 (2013)

Extending spin coherence times of diamond qubits by high-temperature annealing
T. Yamamoto,1,* T. Umeda,2 K. Watanabe,3 S. Onoda,1 M. L. Markham,4 D. J. Twitchen,4 B. Naydenov,5 L. P. McGuinness,5
T. Teraji,3 S. Koizumi,3 F. Dolde,6 H. Fedder,6 J. Honert,6 J. Wrachtrup,6 T. Ohshima,1 F. Jelezko,5 and J. Isoya7
1

Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan
Institute of Applied Physics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
3
National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
4
Element Six Limited, Kings Ride Park, Ascot, Berkshire SL5 8BP, United Kingdom
5Institute for Quantum Optics, University of Ulm, D-89081 Ulm, Germany
6
3rd Physics Institute and Research Center SCoPE, University of Stuttgart, D-70174 Stuttgart, Germany
7
Research Center for Knowledge Communities, University of Tsukuba, 1-2 Kasuga, Tsukuba, Ibaraki 305-8550, Japan(Received 15 October 2012; revised manuscript received 31 July 2013; published 23 August 2013)
2

Spins of negatively charged nitrogen-vacancy (NV− ) defects in diamond are among the most promising
candidates for solid-state qubits. The fabrication of quantum devices containing these spin-carrying defects
requires position-controlled introduction of NV− defects having excellent properties such as spectral stability, along spin coherence time, and a stable negative charge state. Nitrogen ion implantation and annealing enable thepositioning of NV− spin qubits with high precision, but to date, the coherence times of qubits produced this way
are short, presumably because of the presence of residual radiation damage. In the present work, we demonstratethat a high-temperature annealing at 1000 ◦ C allows 2 ms coherence times to be achieved at room temperature.
These results were obtained for implantation-produced NV− defects in a high-purity, 99.99% 12 C-enriched single
crystal chemical vapor deposited diamond. We discuss these long coherence times in the context of the thermal
behavior of residual defect spins.
DOI: 10.1103/PhysRevB.88.075206

PACS number(s): 76.30.Mi, 61.80.Jh, 03.65.Yz

I. INTRODUCTION

Quantum physics offers an enlightening route, capitalizingon the quantum nature of superposition and entanglement, toassist classical components in solving certain computational
problems.1 The physical implementation of a quantum register
is, however, challenging since the quantum regime requires ahigh degree of isolation from the environment: Otherwise,
decoherence leads to loss of quantum information. Solidstate quantum bits (qubits) such as superconducting circuits,2
quantum dots,3 and phosphorus donors in silicon,4 which
are promising for scalability, require low temperatures for
operation. In contrast, electron spins of photoactive defects
in diamond have shown significant potential as solid-state spin
qubits operating under ambient conditions.5 The negatively
charged nitrogen-vacancy (NV− ) defect, comprising a substitutional nitrogen with a vacancy at an adjacent lattice site, is abright fluorescent center with a zero phonon line at 637 nm.6
The |ms = 0 and |ms = ±1 sublevels of the ground-state spin
triplet (S = 1) are separated by ∼2.88 GHz in a zero magnetic
field.7 The individual electron spins can be initialized optically,
manipulated by microwave pulses, and then readout optically,
all under ambient conditions.8,9 In addition to their excellent
properties as solid-state spin qubits, the spin coherence times(T2 ) exceed a millisecond at room temperature (RT).10–12
So far there has been progress for a scalable architecture
comprising two NV− qubits with magnetic coupling13 andentanglement14 demonstrated for NV− centers with nanoscale
separations introduced by nitrogen ion implantation. In thisway, the technical approach of implantation appears promisingfor building a quantum register, but the short T2 of implanted
NV− is a considerable barrier when increasing the number of
qubits. To prolong T2 far beyond the time scale of quantum gate
manipulations remains to be solved before further scalability
can be addressed.
1098-0121/2013/88(7)/075206(8)The coherence time T2 of the NV− spin as measured by a
Hahn echo sequence is determined by several contributions:
 
 
 
1
1
1
1

+
+
13
C
T2
T2
T2 nitrogen
T2 paramag.
+

flip-flop

1
T2

impurity

spin-lattice
relaxation,

defect(1)

where the T2 of NV− is dominated by spectral diffusion due
to the fluctuation of local fields. These may be the result of
nuclear spins (13 C) and/or nitrogen impurity spins (substitutional nitrogen in the neutral charge state, N0S , S = 1/2) known
as the P1 center in electron paramagnetic resonance (EPR)
spectroscopy. The contribution of the last term is small even at
RT since spin-lattice relaxation is inefficient due to the weak
spin-orbit interaction of carbon and the strong bonding (i.e.,high Debye temperature) of diamond. Carbon has two stable
isotopes, 12 C with I = 0 (natural abundance of 98.9%) and13
C with I = 1/2 (1.1%). In a natural abundance sample, T2of NV− at RT is ∼0.65 ms, limited by magnetic noise from the13
C nuclear spin bath.15 By depleting the 13 C content (99.7%
12
C enrichment) and increasing the purity ([N0S ] ∼ 0.05 ppb),
a T2 of 1.8 ms has been attained for a native NV− center (i.e., agrown-in NV− defect formed during crystal growth), in single
crystal (SC) chemical vapor deposition (CVD) diamond.10 It
is thus desirable to use a 12 C-enriched and high-purity (low N
concentration) diamond to achieve a long T2 .
Nitrogen ion implantation into pure diamond is the primary
technique used to fabricate NV− at a desired position.13,14,16–25
Yet the ion implantation process reduces the long coherencetime drastically, presumably due to the presence of unpaired
electrons from residual radiation damage. The T2 of NV−
produced by ion implantation and subsequent annealing is075206-1©2013 American Physical Society

T. YAMAMOTO et al.

PHYSICAL REVIEW B 88, 075206 (2013)

shorter (0.35 ms in Ref. 17) than the limit of natural abundance
diamond (0.65 ms in Ref. 15), being dominated by theparamagnetic defect term in Eq. (1).17,23 Even in 12 C-enrichedsubstrates, the T2 of implanted NV− is at best ∼0.5 ms.14 Thus,
the advantage of 12 C enrichment has, to date, been unattainable
for NV− fabricated by implantation. Importantly, a long T2 of
implanted NV− can be obtained only when the sources of spectral diffusion, deriving from residual defects, are significantly
decreased in a high-purity and 12 C-enriched crystal.
The irradiation of ions or electrons create vacancies andinterstitials at RT. Self-interstitial defects (the EPR R1 andR2 centers) anneal out at 400–450 ◦ C, while most (∼80%)of the created vacancies remain stable.26,27 Vacancies, witha 2.3 eV activation energy of migration, become mobile at∼600 ◦ C.28 Thus, an annealing temperature of ∼800 ◦ C is usually employed for NV− fabrication by implantation. Thermal
annealing has two roles, one to create NV through vacancy
migration towards implanted nitrogen, and the other to remove
unwanted residual defects. The short T2 of implanted NV−
suggests that the annealing at ∼800 ◦ C leaves paramagnetic
residual defects that become the main source of decoherence.
The formation of paramagnetic defects by 17 O ion implantation (100 MeV, 5 × 1014 cm−2 , RT) and subsequentannealing were studied using ensemble EPR measurements
in Ref. 29. Although the defect concentration dependence on
the annealing temperature was not given in detail, various
major paramagnetic defects were identified in the annealing
range of 100–1400 ◦ C. Major paramagnetic defects in theannealing range of 850–1050 ◦ C are 110 vacancy chains
V0n (n  3, neutral charge, C2v symmetry) such as V03 (R5),
V04 (O1), V05 (R6), V06 (R10), V07 (R11), and V08 (KUL11),
where their concentrations decrease with increasing chain
length. Two carbon dangling bonds, one at each end of then-vacancy chains, give a spin S = 1. The vacancy chains(V0n , n  3), with a total concentration of 3.4 × 1017 cm−3
at 900 ◦ C, disappear after annealing at T  1100 ◦ C except
for a small fraction (∼1/10) of R10 (V06 ). At temperatures
greater than 1100 ◦ C, paramagnetic multivacancy clustersof R10 (remaining R10), R8, and R12 dominate, although17
O-related KUL12 (S = 1/2) defects and preexisting KUL1([Si-V]0 , S = 1) defects coexist.
Systematic studies on the temperature dependence of paramagnetic defect concentrations were reported in Refs. 30 and
31. Paramagnetic defects introduced by electron irradiation(2 MeV, 8 × 1019 cm−2 , RT) and subsequent annealing (600–
1400 ◦ C) were measured by ensemble EPR in natural type-IIa
diamond crystals. At ∼600 ◦ C where vacancies are mobile,
divacancy V02 (R4/W6, S = 1, C2h symmetry) anneals in.
While V02 anneals out at ∼850 ◦ C, the formation of a seriesof 110 vacancy chains V0n such as V03 (R5), V04 (O1), V05(R6), V06 (R10), and V07 (R11) starts to develop between∼750 and ∼950 ◦ C. Shorter chains are dominantly formed
among the vacancy chains (V0n , n  3), giving the chain
length of n = 3.8 on average. Each of dominant vacancy
chains, V03 (R5), V04 (O1), and V05 (R6), reach a maximum
concentration (2.3 × 1018 cm−3 in total) at 1000 ◦ C anddecrease with increasing temperature (T > 1000 ◦ C). Instead,multivacancy clusters having a different configuration to thechain type, labeled as R7, R8, and R12,30,32,33 start to appear
at T > 1000 ◦ C. The R12 center (C3v symmetry), being stableeven at ∼1400 ◦ C, is attributed to a multivacancy cluster ofring type.30 It was shown in Ref. 30 that the concentration ofresidual paramagnetic defects is minimized at ∼1250 ◦ C.
Naydenov et al. reported the effect of high-temperatureannealing on T2 of implanted NV− , where single NV− centerswere fabricated by N ion implantation (15 N+ , 150 and 300 keV,
1 × 108 cm−2 ) and annealed at two different temperatures,
800 and 1200 ◦ C.23 The comparison study showed annealing
at 1200 ◦ C has a positive effect, which was observed as anincrease in the proportion of NV centers with a T2  50 μs.
However, the T2 of implanted NV− remained shorter than thebest (0.65 ms) of native NV− in natural abundance.
Here we report a long T2 up to 2 ms of single NV−
centers by implantation after annealing at 1000 ◦ C, using a 12 Cenriched and high-purity diamond. To identify the source of
decoherence, the thermal behaviors of residual defects createdby nitrogen implantation were also studied by ensemble EPR.
We find that a substantial decrease of the concentration ofparamagnetic residual defects occurs at a temperature of∼1100 ◦ C, rather lower than that of ∼1250 ◦ C (Ref. 30 for
electron irradiation). This paper thus consists of two parts: The
first aims at achieving long T2 times of individual implanted
NV− centers and the second is to study the residual defects
by ensemble measurements, where two different fluences ofnitrogen implantation were used according to each purpose.
The samples used for ensemble EPR measurements have been
also characterized by photoluminescence (PL) spectroscopy.
Lastly, the long T2 observed here is discussed on the basis of
the ensemble EPR measurements for residual defects.
II. EXPERIMENTS−

A. Single NV centers fabricated by low fluenceand ex situ annealing

High-purity 99.99% 12 C-enriched SC CVD diamond wasused in order to achieve a long T2 . The sample was implantedwith a 10 MeV 15 N3+ microbeam with a full width at half maximum (FWHM) of 1.5 μm (the microbeam system connectedwith the 3 MV Tandem accelerator at JAEA, Takasaki34,35 ) at
RT in a vacuum of ∼10−6 Torr. The incident beam was scannedwith ∼3 ions per site (2 × 108 ions/cm2 on average) to forma square grid of implantation sites separated by ∼8 μm in thearea of 200 × 200 μm2 (5 × 106 ions/cm2 on average). This
low fluence allows the creation of single NV centers which
can be characterized individually by confocal microscopy.36
To create NV centers, the sample was annealed at 1000 ◦ C for
2 h in a vacuum of 3 × 10−6 Torr. The resultant NV centerswere observed using a home-built confocal microscope with a
532 nm excitation laser. Continuous-wave and pulsed opticallydetected magnetic resonance (ODMR) were measured forsingle NV− centers under a static magnetic field at RT.
B. Ensemble measurements using high fluenceand in situ annealing

For the low fluence (∼1 × 106 /cm2 ) used for the fabricationof single NV− centers, the concentration of paramagnetic
residual defects is far below the detection limit of ensemble
measurements of conventional EPR. Also, individual weakly
luminescent defects such as vacancy clusters are unable to be

075206-2

EXTENDING SPIN COHERENCE TIMES OF DIAMOND . . .

PHYSICAL REVIEW B 88, 075206 (2013)

III. RESULTS
A. Spin coherence times of single NV− centers

Single NV− centers in 99.99% 12 C-enriched SC CVD
diamond by microbeam implantation at RT followed byannealing at 1000 ◦ C were characterized by scanning confocal microscopy and optically detected magnetic resonance(ODMR). Nitrogen has two stable isotopes, 14 N (I = 1,
natural abundance 99.63%) and 15 N (I = 1/2, 0.37%). TheODMR of either the 15 N hyperfine structure or 14 N allowed
determination of whether the observed NV− centers werecreated by implanted (15 N) or preexisting impurities (14 N)
in the substrate.18 The ODMR spectra of single 14 NV−
and 15 NV− centers in the confocal image [Fig. 1(a)] areshown in Fig. 1(b). The triplet and doublet hyperfine

(b)
5 μm

80
60

15 NV

40

-

14 NV -

20

Photons (kcps)

Photons (kcps)(a) 100

22
21

15NV -

20
30

14NV -

29

2.90 2.91 2.92 2.93 2.94
Microwave frequency (GHz)0(c) 1.2

15 NV - center

1.1

Photons (arbitrary units)measured by confocal microscopy. To obtain information forresidual defects, another sample with different implantation
conditions was used for the ensemble EPR measurements:
high-purity natural abundance CVD plates [Element Six Ltd.,
electronic grade, [Ns0 ] ∼ 0.6–0.8 ppb in bulk measured by
EPR, 4.5 × 4.5 × 0.5 mm3 , (100)-oriented single crystal]. The
samples were implanted with N ions at seven different energies
between 4 and 13 MeV in a vacuum of ∼10−7 Torr at elevatedtemperatures from 800 to 1200 ◦ C. The total fluence was
1.4 × 1014 cm−2 since N ions of 1 × 1013 cm−2 for each energy
were implanted at both sides of sample surface. The use of highfluence allows lower sensitivity ensemble EPR measurements
to be performed. In fact, the fluence was chosen to be below∼1 ppm for the average N concentration in the implanted
layer. The number of vacancies created by the implantation
is expected to be ∼1020 vacancies/cm3 by a stopping andrange of ions in matter (SRIM) Monte Carlo simulation,37 far
below the graphitization threshold (∼1022 vacancies/cm3 ).38
In the case of 1.7 MeV N+ implantation (1016 cm−2 ) into
type-IIa diamond crystal, the spin density of the EPR signal
arising from amorphous carbon after in situ annealing at
1000 ◦ C was lower by an order of magnitude than ex situ
annealing.39 In the fluence used in our present work, damage
cascades could overlap [1 × 1013 cm−2 ∼ 1/(3 nm)2 ]. So, we
employed in situ annealing in order to prevent excess vacancies
from accumulating and thus a high degree of crystallinity waspreserved. The samples were first heated to 700 ◦ C over a
few minutes, and then set to the target temperature with aheating rate of ∼10 ◦ C/min. The in situ annealing temperatures
were kept for ∼3 h while changing the beam transport withdifferent energies. Promptly after implantations, samples were
furnace cooled to RT for 1 h. The thermal behaviors of residual
defects were characterized by ensemble measurements of EPR.
Continuous-wave EPR measurements were performed on a
Bruker BioSpin E500 X-band spectrometer. Identification ofparamagnetic defects by ensemble EPR was based on the
angular dependence of the line positions. To align the crystal
orientation with the EPR signals arising from symmetryrelated sites at RT, more than ∼2 × 1012 spins were required
for a typical defect in diamond. The samples have been alsocharacterized by PL (photoluminescence). The PL spectra
were measured at 83 K with an excitation power of a few
tenths of a μW using a home-built spectrometer.

data

1.0

T2 = 2.0±0.2 ms

0.9
1.1
14 NV - center

1.0

data

0.9

T2 = 1.8±0.1 ms

0.8
0.7
0

1

2
3
Time 2τ (ms)45FIG. 1. (Color online) Room temperature characteristics of single
NV− centers fabricated in high-purity, 99.99% enriched SC CVD
diamond by microbeam 15 N3+ (10 MeV) implantation at RT andsubsequent annealing at 1000 ◦ C in vacuum. (a) Confocal microscope
image of NV centers (yellow/red dots) with 532 nm excitation.
(b) ODMR spectra of 15 NV− with the hyperfine splitting
A = 3.1 MHz, and 14 NV− with A = 2.2 MHz. (c) The echo decay
curves of 15 NV− (top) and 14 NV− (bottom) measured by a Hahnecho sequence. The solid lines indicate the fit function E(2τ ) ∝exp[−(2τ/T2 )α ], where the index α = 1.1 for 15 NV− and α = 1.8
for 14 NV− .

structures observed in the ODMR spectra between |ms = 0and |ms = +1 indicate a single 14 NV− with the hyperfine
constant A = 2.2 MHz (bottom) and a single 15 NV− with
A = 3.1 MHz (top), respectively [Fig. 1(b)]. Both 14 NV− and15
NV− centers were located at a depth of ∼3.8 μm, which
agrees well with the projected ion-stopped range of 3.82 μm
by the SRIM Monte Carlo simulation.37 We also found that the14
NV− and 15 NV− centers were observed at the square grid
points with separations of ∼8 μm within an in-plane radius<1.4 μm. Hence, we conclude that the both 14 NV− and 15 NV−
are not native but created by 15 N ion implantation. The 14 NV−
was created through the trapping of a vacancy by a preexisting
14
N atom during annealing, while the 15 NV− was from theimplant. A detailed analysis of the yield of NV− from the twodifferent nitrogen sources will be given elsewhere.40
Figure 1(c) shows the echo decay curves of the single
15
NV− center (top) and 14 NV− center (bottom) taken bypulsed ODMR spectroscopy using a Hahn echo sequence.17
By fitting the data with E(2τ ) ∝ exp[−(2τ/T2 )α ], where α isused as the free parameter, the spin coherence time T2 wasmeasured to be 2.0 ± 0.2 ms for the 15 NV− and 1.8 ± 0.1 ms
for the 14 NV− . Thus, two NV centers consisting of different
nitrogen sources have a similar T2 of ∼2 ms. To confirm the075206-3

T. YAMAMOTO et al.
(a)

PHYSICAL REVIEW B 88, 075206 (2013)

D

microwave
0.2 mW
2 mW
20 mW

o

D
FF

B

A

EPR signal (arbitrary units)

D

C

800 C

A

C

B

C

B

A

C

A

C

B
E

o

FF

C

E

900 C

B. Ensemble measurements of thermal behaviors

D

B

G G
O

FF

E E

B

A

A

E
E

FF

C

C

B

E E

B

A

A

o

1000 Co1100 C

C

C

C
H

o

1200 C

C

H

O+R12
320

325

330
335
340
Magnetic eld (mT)

345

(b)
18

Concentrations (cm-3)

10

350

A (V30, R5)
C (V30)D (V40, O1)
E (V50, R6)
F (V60, R10)

total

17

10

O

sum (A, B, C, D, E, F, G)
16

10

B (V 30)H

15

10

G (V70, R11)
800

R12
900
1000
1100
In-situ anneal temperature (ºC)

1200

FIG. 2. (Color online) (a) Ensemble EPR spectra (B [100], RT,
in dark, 9.428 GHz) of high-purity natural abundance SC CVD
diamond plates implanted with N ions (1 × 1013 cm−2 at each ofseven steps between 4 and 13 MeV) at various in situ annealing
temperatures (800–1200 ◦ C). Multivacancy chain centers (A to G) andother defects (O, H, and R12) were observed. (b) The dependenceof the concentration of paramagnetic centers on in situ annealing
temperature. “Total” was estimated by integrating all EPR spectra,
which includes all signals. The concentrations were calculated byassuming that the defects are formed inside 4.85-μm-thick layers on
both sides of the samples, where 4.85 μm corresponds to the projected
ion stopping range for 13 MeV N ion implantation.

reproducibility of long T2 , we have measured another 99.99%
12
C-enriched crystal with similar implantation and annealing,
and then obtained long T2 of up to 1.6 ms in implanted NV
centers (data not shown).

The long T2 of single NV− as shown above indicatesthat a substantial decrease of paramagnetic residual defects isachieved by employing an annealing temperature of 1000 ◦ C.
We have thus examined the thermal behaviors of residual
defects in the case of N ion implantation in detail. Figure 2(a)shows the EPR spectra (B [100], taken at RT) of N implanted
high-purity SC CVD diamond plates with various in situ
annealing temperatures (800–1200 ◦ C). Ten EPR signals (A toG, O, H, and R12) were distinguished as indicated in Fig. 2(a).
The signals of A to G exhibited a common quartet-line
signature (two distinguishable sites with an intensity ratioof 1:2, each consisting of two fine-structure lines), whichcoincides with the features of the 110 multivacancy chain
with a spin S = 1. We have checked their angular patterns
in magnetic-field rotation experiments from B [100] to
B [011]. By comparing our angular-pattern data with theliterature,29 the defects A, D, E, F, and G were identified as V03(R5), V04 (O1), V05 (R6), V06 (R10), and V07 (R11), respectively.
In addition, the observed fine-structure splitting in V0n withn  4 agreed well with that calculated using the point-dipole
approximation.29,30 We also found that the fine-structure
splitting of the defect B was almost same as the R5 centerat low temperature (77 K).29 Thus, the defect B is probably
a similar defect of R5 (A) where the dynamics causing thetemperature dependence in the R5 (A) might be frozen at RTin the defect B. In Ref. 30, it is reported that a deviation of thefine-structure splitting of V03 (R5) from a theoretical one using
a point-dipole approximation is attributed to a delocalizationof the wave function, which is not negligible for the shortchain length. It is also reported in Ref. 30 that there are a few
different centers ascribed to V03 . Therefore, we speculate thedefects of B and C to be analogs of V03 . All signals assigned
to multivacancy chains (A to G) except for C decreased withincreasing in situ annealing temperature from 800 to 1000 ◦ C,
as can be seen in Fig. 2(a). Note that the EPR spectrum fromV02 (R4/W6) (Ref. 41) was not observed at both RT and 32 K in
this study. At temperatures T  1100 ◦ C, multivacancy chains(A to G) were annealed out and different types of defects wereobserved, as denoted by H and R12 in Fig. 2(a). The R12
center (C3v symmetry, S = 1, overlapping to O) is reported
to be a typical defect appearing in the annealing stages above
1100 ◦ C.29 On the other hand, we tentatively assign that thesignal H is a multivacancy cluster without having the C2v
symmetry of vacancy chain structures. The central broad signal
O is isotropic and may arise from more than two species,
probably including surface damage such as amorphous carbon
as well. At 1200 ◦ C, the signal O turns from decreasing
to increasing, suggesting that the annealing products frommultivacancy chains may contribute to the defect formation. In
fact, the previous work suggested that multivacancy chains areconverted into a ring-type configuration such as the hexagonalvacancy cluster, being stable up to 1400 ◦ C.29,32
The dependence of concentrations of the defects on thein situ annealing temperature is shown in Fig. 2(b). The
most dominant defect was associated with the broad signal
O. This signal was reduced to 5% at 1100 ◦ C as comparedto that at 800 ◦ C. The total concentration of the multivacancy
clusters (A, B, C, D, E, F, G, H, R12) was minimized at

075206-4

EXTENDING SPIN COHERENCE TIMES OF DIAMOND . . .

NV 0excitation
with 404 nm
800oC

1.0
GR1
1000oC
0.5

NVN (H3)

(b)
3

NV 0

800oC
NV
2

900oC
1
1000oC

1200oC
0
500
600
700
Wavelength (nm)(d)(c) 2.3

1.1

800oC
900oC

0.3

2

1000oC

0.3
0.2

excitation
with 532 nm

4

NV +NV 0
NV 0

2

10 8

1200oC

4
2

NV

-

1

640

0.1

6

10
635
Wavelength (nm)

0.2

-

2

-

0.4

0
630

650

3
10 8
6

1.0
0.5

0.1

600
Wavelength (nm)-NV

Integrated intensity (arb. units)

2.1
1.2

IV. DISCUSSION

1200oC

NV /NV 0

PL intensity (arbitray units)

2.2

0
550

800

centers, PL measurements at 83 K using 532 nm excitation
were carried out [Figs. 3(b) and 3(c)]. Both NV0 (ZPL at
575 nm) and NV− (ZPL at 637 nm) peaks were observed inall samples. The integrated intensity of NV0 and NV− lines
as well as their ratios extracted from Fig. 3(b) are plotted inFig. 3(d). We found that while the total intensity of NV− +NV0 decreased with increasing implantation temperature, theNV− /NV0 ratio increased with a rise in temperature.

excitation
with 532 nm

3x10

PL intensity (arbitrary units)

PL intensity (arbitray units)(a)4
1.5x10PHYSICAL REVIEW B 88, 075206 (2013)

NV /NV 00.0
800 900 1000 1100 1200
In-situ anneal temperature (oC)FIG. 3. PL spectra (83 K) of high-purity natural abundance SC
CVD diamond plates implanted with N ions (1 × 1013 cm−2 at eachof seven steps between 4 and 13 MeV) at various in situ annealing
temperatures (800–1200 ◦ C) with (a) 404 nm and (b) 532 nm
excitation laser. (c) The enlarged view of (b) in the range between 630
and 640 nm. (d) The integrated intensity of NV0 (inverted triangles),NV− (squares), NV0 + NV− (triangles), and the NV− /NV0 ratio(circles).

∼1050 ◦ C and at least three orders of magnitude less thanthat at 800 ◦ C. In the case of ion implantation, in both in situ
(present work) and ex situ (Ref. 29) annealing, multivacancy
chains disappear at T ∼ 1050 ◦ C and multivacancy clusters of
ring type appear at ∼1100 ◦ C. Thus, the total concentrationof the paramagnetic residual defects (red line) was minimized
at 1100 ◦ C, rather lower than that of ∼1250 ◦ C for electron
irradiation.30 The number of the paramagnetic defects can be
estimated as 3 spins/ion at 800 ◦ C, 1 spin/ion at 900 ◦ C, andless than 1 spin/ion at T  1000 ◦ C.
The samples used for ensemble EPR measurements havebeen also characterized by photoluminescence (PL) spectroscopy. Figure 3(a) shows 404 nm excited PL spectra
observed at 83 K. The GR1 peak that originates from neutral
vacancy (V0 ) and has a zero phonon line (ZPL) at 741 nm
was observed in the sample implanted at 800 ◦ C. The GR1
peak was not present for implantation temperatures of above
1000 ◦ C, while the H3 peak (ZPL at 503 nm) originatingfrom the (N-V-N)0 center appeared in the sample implanted at
1200 ◦ C. Note that the temperature of 1200 ◦ C is much lower
than that (1700 ◦ C) for the formation of the A center (N-N) by
N diffusion during a high-pressure high-temperature (HPHT)
treatment in type-Ib crystals.42 It is also reported that the A
center may be formed by heating at 1500 ◦ C in vacuo after
electron irradiation.43 In order to obtain information on NV

In our present work, coherence times (T2 ) of single NV−
centers fabricated by 10 MeV 15 N ion microbeam implantation
have been measured. A long T2 of 2 ms was obtained by selecting an ex situ annealing temperature of 1000 ◦ C and the use ofa high-purity, isotopically pure (13 C-0.01%, 12 C-99.99%) substrate. For implanted NV− in 13 C-0.01% SC CVD diamond, T2
times of 0.1 ms (18 MeV N implantation, Ref. 13) and 0.5 ms(1 MeV, Ref. 14) have previously been reported for NV− pairs.
In these studies, the samples were annealed at 800 ◦ C for 2 h
in Ref. 13 and 8 h in Ref. 14, respectively. A comparison withthese T2 times suggests that a modest increase of annealing
temperature from 800 to 1000 ◦ C prolongs T2 significantly. The
T2 time in the present work exceeds the best (0.65 ms) of native
NV in natural abundance (13 C-1.1%) diamond, and reaches
the longest reported so far in 13 C-depleted samples.10–12 The
annealing dependence of residual paramagnetic defects has
been studied by using in situ annealed natural abundance
SC CVD diamonds implanted with N ions of a high fluence(1 × 1013 cm−2 at each of seven steps between 4 and 13 MeV).
These implantation conditions are well suited to ensemble
EPR measurements. The ensemble EPR measurements haveelucidated that residual defects remain at significant concentrations with implantation temperatures up to 800 ◦ C while
they substantially decrease in the 800–1100 ◦ C range. Above
1100 ◦ C, paramagnetic defects having configurations stable athigher temperatures appear. The ensemble EPR measurementssuggest that improvement in T2 of single NV− centers by
employing an ex situ annealing temperature of 1000 ◦ C has
been attained due to a substantial reduction of paramagnetic
defects and therefore the third term in Eq. (1).
Now, we consider the formation of paramagnetic vacancy
clusters in the vicinity of implanted NV− . The statistical depth
distributions of implanted 15 N atoms (black solid line) andvacancies (blue dashed line) as computed by the SRIM code
(stopping and range of ions in matter,37 with a diamond densityof 3.52 g/cm3 , displacement energy of 37.5 eV,44 and a total
number of 8 × 104 incident 10 MeV 15 N ions) are shown in
Fig. 4(a). The average depth of individual 15 N atoms is calculated to be ∼3.82 μm. The vacancy distribution due to 15 N
implantation peaks at ∼3.80 μm, and 43% of vacancies among
the average number of ∼570 vacancies/ion are produced withina depth range of ±100 nm from the center of the peak. On theother hand, the distance of individual vacancies from a 15 N
atom for a typical collision cascade is shown in Fig. 4(b).
Again, 40% of vacancies are created in a small volume, within
a distance of 100 nm from the implanted 15 N atom. For highenergy implantation, such a large number of vacancies near
the implanted N atom contributes to the high NV− formation
yield.16,20 Interactions with the carbon atoms in the target

075206-5

T. YAMAMOTO et al.

PHYSICAL REVIEW B 88, 075206 (2013)(a) 102x103 (b) 250
15 N atoms

1.5

6
1
4
0.5

2
0

200

Number of vacancies

Atoms/µm/ion

vacancies

Vacancies/µm/ion

8

150
100

0

50
0

0
1
2
3
4
Depth from surface (µm)
N atomvacancies

-0.06
3.75

(d)
-0.13

15

N atomvacanciesy (µm)

15x (µm)

(c)
-0.01

0
1
2
3
4
Distance from N atom (µm)

3.80Depth (µm)

3.85

-0.18
3.75

3.80
Depth (µm)

3.85

FIG. 4. (Color online) SRIM Monte Carlo simulation of spatial
distribution for 15 N atoms and vacancies created by 10 MeV 15 N
ion implantation. (a) Statistical depth distribution of implanted 15 N
atoms (black solid line) and vacancies (blue dashed line) obtained as
the average of a total number of 8 × 104 incident ions. (b) Distancefrom individual vacancies to 15 N atom for a typical collision cascade
created by a single 10 MeV 15 N ion. Vacancies (blue circle) near
an implanted 15 N atom (black cross) for a collision cascade areshown in (c) the x-z projection plane and in (d) the y-z plane,
where z implantation direction. Here, 42% of the total number of
559 vacancies are plotted on (c) and (d).

sample cause both carbon displacements from lattice sites andthe trajectory change of the implanted 15 N atom. Secondary
knock-ons can also result in several branches of collisioncascade in the vicinity of the ion track as shown in Fig. 4(c)(x-z projection plane) and Fig. 4(d) (y-z plane) for a single
10 MeV 15 N ion. Thus, vacancies are created along the 15 N
ion track and the branches of recoiling carbon atoms, which isfavorable to the formation of vacancy clusters after annealing.
The resultant vacancy clusters near the NV− are the main
source of decoherence of NV− as observed in Refs. 13 and 14(800 ◦ C anneal). We attribute the long T2 found in the present
work as being essentially due to a reduction of paramagnetic
vacancy clusters near NV− by annealing at 1000 ◦ C.
A number of processes that reduce the concentrationof paramagnetic vacancy clusters take place on annealing.
The divacancy (V02 ) and multivacancy chains (V0n ,n  3) areparamagnetic, whereas the monovacancy of the neutral charge
state (V0 ) is diamagnetic. One possible process to reduce theconcentration of V0n (n  2) is the aggregation of vacancies
by converting smaller clusters into larger ones. In this process,the total concentration of unpaired electron spins decreases
even if the total number of vacancies involved is constant.
In our ensemble EPR studies for samples formed by in situ
annealing during high-fluence implantation, the divacancy was
already annealed out by 800 ◦ C. All of the multivacancy chains(V0n , n = 3–7) decreased with increasing the in situ annealing
temperature from 800 to 1000 ◦ C, except the concentration of C
assigned tentatively to an analog of V03 stayed nearly constant.
Thus, aggregation by increasing the chain length of linear

vacancy chains is not the dominant process in this temperature
range. It was pointed out that the total number of vacancies
involved in the multivacancy chains was ∼1/10 of vacancies
produced initially, which was estimated from GR1 (V0 ) opticalabsorption measurements.29,30 This suggests that while a smallpart of monovacancies contributed to the formation of theparamagnetic multivacancy chains formed by ex situ annealing, a large fraction was annihilated by the recombination ofvacancies with carbon interstitials or forming the diamagnetic
vacancy clusters (see also Ref. 45).29 Similarly, these processes
might cause a substantial reduction of concentrations of themultivacancy chains by in situ annealing (T > 800 ◦ C) in thepresent study. We speculate that such thermal behavior should
also dominate in the case of an ex situ anneal after low-fluenceimplantation, thereby allowing a significant reduction of theparamagnetic defect concentration and a significant increasein T2 , particularly with a 1000 ◦ C anneal.
Next, we consider the difference of the two fluencesused in the present study from the viewpoint of the role ofmobile vacancies in the formation of paramagnetic vacancy
clusters. There is controversy in the vacancy diffusion lengths
determined experimentally.46–48 Here, we use a theoreticalestimation.46 The low fluence was required to fabricate
In this experiment, the vacancy diffusion
single NV− centers.
√
length L = 6Dt is estimated to be 130 nm, where thediffusion coefficient is D = D0 exp[−Ea /(kB T )], with D0 =3.7 × 10−6 cm2 /s (Ref. 49), Ea = 2.3 eV (Ref. 28), and T =1000 ◦ C, and the annealing time is t = 7200 s. L is comparable
to the averaged in-plane straggling length of 10 MeV 15 N
ions (2σ ∼ 180 nm, where σ is the standard deviation of theGaussian fit) and considerably shorter than the spot size of the
microbeam (FWHM of 1.5 μm). When ∼3 ions are implanted
at each implantation site as employed in this study, the distance
between 15 N atoms should be larger than L for most of thecases. Note that the probability of nitrogen atoms locatedwithin ∼300 nm can be estimated to be ∼1%. Thus, it is likelythat NV− and vacancy clusters are formed from vacancies
resulting from the damage cascade caused by the implanted
15
N ion. On the other hand, a high fluence (1 × 1013 cm−2
at each of seven steps of implantation energy) was required
to perform the ensemble measurement of EPR. Since thehigh fluence can cause overlapping of the vacancy profilesof neighboring implants, in situ annealing was employed
to prevent vacancies from accumulating excessively. The
diffusion length L is calculated to be ∼160 nm (T = 1000 ◦ C,
t = 10 800 s), which is longer than the separations of implanted N atoms (10–70 nm). As a result, the vacancies
resulting from individual ion impacts may overlap withneighboring implant spots to form vacancy clusters. In addition to dynamic annealing processes, this may result in adifference in the formation of vacancy clusters between thelow- and high-fluence experiments used in the present study.
As a result, the annealing temperature which minimizes theparamagnetic residual defects might be slightly different for exsitu annealing after low-fluence implantation as used here forsingle NV− center formation, than for in-situ annealing duringhigh-fluence implantation employed to fabricate samples for
ensemble EPR studies. For high fluence, we note that similar
thermal behavior has been observed between in situ (this work)and ex situ (Ref. 29) annealing: Multivacancy chains

075206-6

EXTENDING SPIN COHERENCE TIMES OF DIAMOND . . .

PHYSICAL REVIEW B 88, 075206 (2013)

disappeared at T ∼ 1050 ◦ C and multivacancy clusters of ringtype appeared at T ∼ 1100 ◦ C.
The isotopic purity (13 C-0.01%) of our diamond is expected
to contribute greatly to the long coherence times observed.
However, further improvement may still be possible whencompared to the T2 time of 1.8 ms for a native NV− in 13 C0.3%.10 In Ref. 10, the concentration of isolated substitutional
nitrogen (N0S ) was estimated to be 0.05 ppb (9 × 1012 cm−3 )by extrapolating the correlation of the concentration of N0S
and that of NV− observed in various CVD samples.50 Jahnke
et al. reported that a native NV exhibited a T2 of 2 ms
in 13 C-0.002% polycrystalline CVD diamond.12 This T2 isexpected to be dominated by the paramagnetic nitrogen(S = 1/2) term in Eq. (1), since the N concentration wasdetermined to be [N0S ] ∼ 4 ppb (7 × 1014 cm−3 ) by ensemble
EPR measurements. Given the similar T2 between Ref. 12 andours, the concentration of paramagnetic defects in our sample
is estimated to be a similar value of 4 ppb [1/(110 nm)3 ].
Thus, the 2 ms T2 time of implanted NV− we obtain in 99.99%
12
C-enriched diamond is still determined by the paramagnetic
defect term in Eq. (1). From the ensemble EPR measurements
of in situ annealing of high-fluence implantation, the total
concentration of the paramagnetic residual defects was foundto be minimized at ∼1100 ◦ C. The route explored in thiswork to fabricate qubits with long coherence times may show
some improvement with further optimization with annealing
temperatures between 1000 and 1100 ◦ C.

Although nitrogen ion implantation is a preferable route forfabricating NV− , a sufficient amount of vacancies in thevicinity of an implanted N atom is required to create NV−
centers with high efficiency.19,20,24 However, if vacancies
accumulate excessively, paramagnetic multivacancy defects
remain as residual radiation damage after annealing, andtheir magnetic fluctuations lead to decoherence of NV−
spins. We observed coherence times T2 ∼ 2 ms for NV−
produced by 10 MeV microbeam nitrogen ion implantation
obtained in a 99.99% 12 C-enriched single crystal diamondby annealing at 1000 ◦ C. We also found that paramagnetic
residual defects such as vacancy chains were significantly
reduced by a modest increase of the annealing temperaturefrom ensemble EPR measurements. We thus demonstrate that12
C enrichment, together with a selection of high-temperatureannealing techniques, can extend the T2 of implanted NV− tomuch longer than 0.65 ms that is limited by the nuclear spinbath of natural abundance diamond. Our work opens ways tobuild scalable quantum registers in a nuclear-spin-free latticeby removing the obstacles that shorten T2 in ion implanted
diamond.

ACKNOWLEDGMENTS

The achievement of long T2 coherence times of NV− spinsis a crucial issue for various quantum-device applications.

This study was carried out as the “Strategic JapaneseGerman Joint Research Project” supported by JST and DFG(FOR1482, FOR1493, and SFB716), ERC, DARPA, and
the Alexander von Humboldt Foundation. We thank Brett
C. Johnson for valuable discussions, and Kay D. Jahnke,
Pascal Heller, Alexander Gerstmayr, and Andreas Häußler forassistance with the experiments.

*

11

V. CONCLUSION

Current address: National Institute for Materials Science,
1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan; YAMAMOTO.
Takashi@nims.go.jp
1
M. A. Nielsen and I. L. Chuang, Quantum Computation and
Quantum Information (Cambridge University Press, Cambridge,
UK, 2000).
2
Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, Nature (London) 398,
786 (1999).
3
R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, andL. M. K. Vandersypen, Rev. Mod. Phys. 79, 1217 (2007).
4
B. E. Kane, Nature (London) 393, 133 (1998).
5
F. Jelezko and J. Wrachtrup, Phys. Status Solidi A 203, 3207 (2006).
6
G. Davies and M. F. Hamer, Proc. R. Soc. London, Ser. A 348, 285(1976).
7
N. R. S. Reddy, N. B. Manson, and E. R. Krausz, J. Lumin. 38, 46(1987).
8
F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup,
Phys. Rev. Lett. 92, 076401 (2004).
9
F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, andJ. Wrachtrup, Phys. Rev. Lett. 93, 130501 (2004).
10
G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham,
R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler,
V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, Nat. Mater.
8, 383 (2009).

T. Ishikawa, K. C. Fu, C. Santori, V. M. Acosta, R. G. Beausoleil, H.
Watanabe, S. Shikata, and K. M. Itoh, Nano Lett. 12, 2083 (2012).
12
K. D. Jahnke, B. Naydenov, T. Teraji, S. Koizumi, T. Umeda,
J. Isoya, and F. Jelezko, Appl. Phys. Lett. 101, 012405 (2012).
13
P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp,
M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham,
D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko,
and J. Wrachtrup, Nat. Phys. 6, 249 (2010).
14
F. Dolde, I. Jakobi, B. Naydenov, N. Zhao, S. Pezzagna,
C. Trautmann, J. Meijer, P. Neumann, F. Jelezko, and J. Wrachtrup,Nat. Phys. 9, 139 (2013)
15
M. L. Markham, J. M. Dodson, G. A. Scarsbrook, D. J. Twitchen,
G. Balasubramanian, F. Jelezko, and J. Wrachtrup, Diamond Relat.
Mater. 20, 134 (2011).
16
J. Meijer, B. Burchard, M. Domhan, C. Wittmann, T. Gaebel,
I. Popa, F. Jelezko, and J. Wrachtrup, Appl. Phys. Lett. 87, 261909(2005).
17
T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann,
F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer,
J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, Nat. Phys.
2, 408 (2006).
18
J. R. Rabeau, P. Reichart, G. Tamanyan, D. N. Jamieson, S. Prawer,
F. Jelezko, T. Gaebel, I. Popa, M. Domhan, and J. Wrachtrup,
Appl. Phys. Lett. 88, 023113 (2006).

075206-7

T. YAMAMOTO et al.
19

PHYSICAL REVIEW B 88, 075206 (2013)

B. Naydenov, V. Richter, J. Beck, M. Steiner, P. Neumann,
G. Balasubramanian, J. Achard, F. Jelezko, J. Wrachtrup, and
R. Kalish, Appl. Phys. Lett. 96, 163108 (2010).
20
S. Pezzagna, B. Naydenov, F. Jelezko, J. Wrachtrup, and J. Meijer,
New J. Phys. 12, 065017 (2010).
21
D. M. Toyli, C. D. Weis, G. D. Fuchs, T. Schenkel, and D. D.
Awschalom, Nano Lett. 10, 3168 (2010).
22
S. Pezzagna, D. Wildanger, P. Mazarov, A. D. Wieck, Y. Sarov,
I. Rangelow, B. Naydenov, F. Jelezko, S. W. Hell, and J. Meijer,
Small 6, 2117 (2010).
23
B. Naydenov, F. Reinhard, A. Lämmle, V. Richter, R. Kalish,
U. F. S. D’Haenens-Johansson, M. Newton, F. Jelezko, andJ. Wrachtrup, Appl. Phys. Lett. 97, 242511 (2010).
24
J. Schwartz, P. Michaelides, C. D. Weis, and T. Schenkel, New J.
Phys. 13, 035022 (2011).
25
S. Pezzagna, D. Rogalla, H.-W. Becker, I. Jakobi, F. Dolde,
B. Naydenov, J. Wrachtrup, F. Jelezko, C. Trautmann, and J. Meijer,
Phys. Status Solidi A 208, 2017 (2011).
26
D. J. Twitchen, M. E. Newton, J. M. Baker, T. R. Anthony,and W. F. Banholzer, J. Phys.: Condens. Matter 13, 2045
(2001).
27
K. Iakoubovskii, I. Kiflawi, K. Johnston, A. Collins, G. Davies, and
A. Stesmans, Physica B 340–342, 67 (2003).
28
G. Davies, S. C. Lawson, A. T. Collins, A. Mainwood, and S. J.
Sharp, Phys. Rev. B 46, 13157 (1992).
29
K. Iakoubovskii and A. Stesmans, Phys. Rev. B 66, 045406(2002).
30
J. N. Lomer and A. M. A. Wild, Radiat. Eff. 17, 37(1973).
31
C. A. J. Ammerlaan, in Numerical Data and Functional Relationships in Science and Technology, edited by O. Madelung and
M. Schultz, Landolt-Börnstein, New Series, Group III, Vol. 22,
Pt. B (Springer, Berlin, 1990), pp. 177–206.
32
K. Iakoubovskii and A. Stesmans, Phys. Status Solidi A 201, 2509
(2004).
33
J. M. Baker, Diamond Relat. Mater. 16, 216 (2007).

34

T. Sakai, T. Hamano, T. Suda, T. Hirao, and T. Kamiya,
Nucl. Instrum. Methods Phys. Res. B 130, 498 (1997).
35
T. Kamiya, T. Sakai, Y. Naitoh, T. Hamano, and T. Hirao,
Nucl. Instrum. Methods Phys. Res. B 158, 255 (1999).
36
A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wrachtrup, andC. von Borczyskowski, Science 276, 2012 (1997).
37
J. F. Ziegler, The Stopping and Ranges of Ions in Matter(www.srim.org).
38
C. Uzan-Saguy, C. Cytermann, R. Brener, V. Richter, M. Shaanan,and R. Kalish, Appl. Phys. Lett. 67, 1194 (1995).
39
Y. H. Lee, P. R. Brosious, and J. W. Corbett, Phys. Status Solidi A
50, 237 (1978).
40
T. Yamamoto et al. (unpublished).
41
D. J. Twitchen, M. E. Newton, J. M. Baker, T. R. Anthony, andW. F. Banholzer, Phys. Rev. B 59, 12900 (1999).
42
R. M. Chrenko, R. E. Tuft, and H. M. Strong, Nature (London) 270,
141 (1977).
43
A. T. Collins, H. Kanda, and H. Kitawaki, Diamond Relat. Mater.
9, 113 (2000).
44
J. Koike, D. M. Parkin, and T. E. Mitchell, Appl. Phys. Lett. 60,
1450 (1992).
45
I. Laszlo, M. Kertesz, B. Slepetz, and Y. Gogotsi, Diamond Relat.
Mater. 19, 1153 (2010).
46
J. O. Orwa, K. Ganesan, J. Newnham, C. Santori, P. Barclay,
K. M. C. Fu, R. G. Beausoleil, I. Aharonovich, B. A. Fairchild,
P. Olivero, A. D. Greentree, and S. Prawer, Diamond Relat. Mater.
24, 6 (2012).
47
C. Santori, P. E. Barclay, K.-M. C. Fu, and R. G. Beausoleil,
Phys. Rev. B 79, 125313 (2009).
48
J. W. Steeds, W. Sullivan, A. Wotherspoon, and J. M. Hayes,
J. Phys.: Condens. Matter 21, 364219 (2009).
49
X. J. Hu, Y. B. Dai, R. B. Li, H. S. Shen, and X. C. He, Solid State
Commun. 122, 45 (2002).
50
A. Tallaire, A. T. Collins, D. Charles, J. Achard, R. Sussmann,
A. Gicquel, M. E. Newton, A. M. Edmonds, and R. J. Cruddace,Diamond Relat. Mater. 15, 1700 (2006).

075206-8