IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 68, NO. 6, JUNE 2019

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Electron Paramagnetic Resonance Study on 28Si
Single Crystal for the Future Realizationof the Kilogram
Shigeki Mizushima , Naoki Kuramoto , Kenichi Fujii , and Takahide Umeda
Abstract— For the future realization of the kilogram using
the X-ray crystal density (XRCD) method, isotopically enrichedsilicon crystals grown by the floating zone method are employed.
In this paper, we present quantitative electron paramagnetic
resonance (EPR) measurements on 28 Si single crystal AVO28 toincrease the reliability of mass deficit correction in the XRCD
method. We detected phosphorus impurity in the crystal anddetermined its concentration to be 3.2(5) × 1012 cm−3 , which isconsistent with that estimated using Fourier transform infrared
spectroscopy. In addition, the EPR measurements revealed thatthe concentrations of nine types of vacancy defects with unpaired
electrons in the crystal are less than 1 × 1012 cm−3 at 25 K bothin a dark environment and under illumination. As a result, thenecessary mass deficit correction due to these vacancy defects is
estimated to be 0.0(2) µg for 1-kg AVO28 spheres.
Index Terms— Electron paramagnetic resonance (EPR), kilogram, measurement uncertainty, metrology, silicon crystal,vacancy defects.

I. I NTRODUCTION

THE X-ray crystal density (XRCD) method is one of
two independent methods that can realize the future
realization of the kilogram with the highest accuracy [1].
The mass of a 28 Si single-crystal sphere with a diameterof approximately 93.7 mm is determined by counting thenumber of silicon atoms in the sphere along with using several
basic physical constants, including the Planck constant h. If asignificant number of defects exist in the crystal, then themass deficit caused by their presence must be corrected. Here,the mass deficit is defined as the mass difference between two
silicon spheres with a diameter of 93.7 cm, one of which ismade of an ideal crystal, and the other of which is made of areal crystal containing defects. Fig. 1 shows the schematic ofa normal structure, monovacancy defect V , and substitutional
impurity defect in silicon crystals.

Manuscript received June 26, 2018; revised October 16, 2018; accepted
November 8, 2018. Date of publication December 17, 2018; date of current
version May 10, 2019. This work was supported by JSPS KAKENHI underGrant 17K05112. The Associate Editor coordinating the review process was
Dr. Michael Lombardi. (Corresponding author: Shigeki Mizushima.)
S. Mizushima, N. Kuramoto, and K. Fujii are with the National Metrology Institute of Japan, National Institute of Advanced Industrial Scienceand Technology, Tsukuba 305-8563, Japan (e-mail: s.mizushima@aist.go.jp;
n.kuramoto@aist.go.jp; fujii.kenichi@aist.go.jp).
T. Umeda is with Institute of Applied Physics, University of Tsukuba,
Tsukuba 305-8573, Japan (e-mail: umeda@bk.tsukuba.ac.jp).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIM.2018.2884044

Fig. 1. Ball-and-stick models of a normal structure, monovacancy defect V ,and substitutional impurity defect in silicon crystals. Gray lines: chemicalbonds between atoms.

Several studies on defects in silicon crystals have been
conducted to realize the kilogram using silicon crystals.
Deslattes and Kessler [2] reported a qualitative difference
between a silicon crystal with a natural isotope ratio of
National Metrology Institute of Japan (NMIJ), formerly
National Research Laboratory of Metrology, and that ofPhysikalisch-Technische Bundesanstalt by employing electron
paramagnetic resonance (EPR) spectroscopy. They detected
the EPR signals of impurities only from the NMIJ’s crystal.
Gebauer et al. [3] determined that the vacancy concentration
in a silicon crystal grown by the floating zone (FZ) method
ranges from 1 × 1014 cm−3 to 4 × 1014 cm−3 using positronannihilation lifetime spectroscopy (PALS) that detects neutral or negatively charged vacancies. They performed electron
irradiation with low doses to obtain a quantitative calibration
using an estimated introduction rate of 0.1 cm−1 for monovacancies. They did not find any relation between the average
positron lifetime and the position in the radial direction of thecrystal. They concluded that a decomposition of the positron
lifetime spectra does not give reliable results because of the
low intensities of the defect components. They estimated thathexavacancy V6 is a candidate for explaining their PALS
results. D’Agostino et al. [4] developed a method to measure
the void concentration of 1014 cm−3 in a silicon crystal witha few percent uncertainties using Cu decoration and neutron
activation.
At present, the International Avogadro Coordination(IAC) project estimates a vacancy defect concentrationof 3.3(1.1) × 1014 cm−3 in 28 Si crystals grown by the
FZ method, which was determined using PALS [5]. The
IAC considers that this value represents the vacancy content
per unit volume for all vacancy types including
 vacancy
agglomerates and voids, which is expressed asn nc(Vn ),0018-9456 © 2018 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted,
but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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where n is the vacancy size (n = 1 for monovacancy V ,n = 2 for divacancy V2 , n = 3 for trivacancy V3 , etc.),
and c(Vn ) is the concentration of the vacancy Vn . The value
3.3(1.1) × 1014 cm−3 corresponds to a mass deficit correctionof 6.6(2.2) µg for a 1-kg 28 Si sphere. To confirm the reliabilityof this value, it is desirable to perform further measurements
using other independent methods.
To date, a lot of detailed studies on vacancy defects in silicon crystals have been conducted using EPR spectroscopy [6],which is one of the high-sensitivity methods for identifying
and quantifying vacancy defects. This paper reports the quantitative EPR measurement on 28 Si single crystal AVO28 toincrease the reliability of mass deficit correction in the XRCD
method. This paper is the extension of a presentation at the2018 Conference on Precision Electromagnetic Measurements(CPEM 2018) and a two-page summary published in the
CPEM 2018 Digest [7].
This paper proceeds as follows. Section II describes thedefect concentration measurement method using EPR spectroscopy. Section III shows the preparation of a sample cut
out from the AVO28 crystal. Section IV describes the measurement results using EPR spectroscopy. Section V discusses
the measurement results obtained. Finally, Section VI presents
the conclusions of this paper.
II. M EASUREMENT M ETHOD
EPR spectroscopy detects unpaired electrons localized
at defects such as vacancies and impurities in a sample.
EPR spectra are recorded by irradiating the sample placedin a microwave cavity resonator with the microwave(frequency ν) and sweeping an external magnetic field B.
Resonant microwave absorptions (i.e., EPR signals) are
observed under the resonance condition, where the energy ofa microwave photon is equal to the Zeeman splitting of theenergy levels of an unpaired electronhν = gμ B B(1)where h is the Planck constant, g is the gyromagnetic factor(g-factor) of the unpaired electron, and μB is the Bohrmagneton. The g-factor for free electrons has been determined to be 2.002 319 · · · with a relative standard uncertaintyof 2.6 × 10−13 [8]. The g-factor of the electron localized
at a defect has an inherent deviation caused by spin-orbit
coupling. Therefore, measurements of the g-factor are usefulfor classifying defects.
Furthermore, since the wave function of the unpaired electron has a spatial distribution reflecting the arrangement of
atoms around a defect, the angular dependence of the g-factor
provides information on the symmetry of the defect in a crystal
sample. By choosing a particular Cartesian coordinate system,
the effective value of the g-factor for the defect in a certain
direction geff is given by1/2geff = gx2 cos2 θx + g 2y cos2 θ y + gz2 cos2 θz(2)where gx , g y , and gz are the principal values of the g-factor
and cosθx , cosθ y , and cosθz are the direction cosines of themagnetic field in the selected Cartesian coordinate system.

Fig. 2. Simulation results of the anisotropic EPR signal of the positively
charged monovacancy defect V + with the principal values of gx = 2.0087(3),g y = 1.9989(3), and gz = 1.9989(3) [11]. This defect shows axial symmetry
about the <100> direction of the crystal. (a) Angular dependence of EPRline positions. Angle θ : angle between the [100] direction of the silicon single
crystal and the magnetic field rotating in the (01̄1) plane. (b) First-derivative
EPR spectra for θ = 0°, 30°, 60°, and 90°. For this simulation, a microwave
frequency of 9.421 GHz and Lorentzian lineshapes with a half-width at halfmaximum  = 0.1 mT was assumed. In an EPR spectrum, multiple EPR
lines appear depending on the direction of the magnetic field owing to therotational symmetry of the crystal. Taking into account the symmetry of thesilicon crystal, the maximum number of EPR lines observed is 12.

When the arrangement of atoms around the defect has cubic
symmetry such as tetrahedral group Td , all three principal
values of the g-factor are equal and such an EPR signal isexpressed as “isotropic.” Otherwise, the EPR signal is referred
to as “anisotropic.”
Watkins [6] identified anisotropic EPR signals of vacancy
defects in silicon crystals, generated by high-energy electron irradiation. The principal values of the g-factor range
from 1.9989 to 2.0087 for positively charged monovacancy
defect V + and from 2.0028 to 2.0151 for negatively charged
monovacancy defect V − . Such anisotropy of EPR signals is
caused by the geometrical distortion of the four silicon atoms
around a vacancy defect due to the Jahn–Teller effect [9].
In addition, charged divacancy, trivacancy, tetravacancy, andpentavacancy defects V2± , V3− , V4− , and V5− and monovacancy
defects trapped by impurities (V O)− and (V P)0 in silicon crystals have been identified by EPR spectroscopy [6], [10]. Theseanisotropic signals of the vacancy defects should appear in themagnetic field ranging from 334 to 337 mT at the microwave
frequency of 9.421 GHz used in our study. Fig. 2 shows
the simulation results of anisotropic EPR signals of the positively charged monovacancy defect V + in a silicon single
crystal [11] as an example, which is available using the webbased database system [12].

MIZUSHIMA et al.: EPR STUDY ON 28 Si SINGLE CRYSTAL FOR THE FUTURE REALIZATION OF THE KILOGRAM

The angular dependence of the EPR signals observed forirradiation-damaged silicon crystals is explained by the geometrical distortion of atoms around each type of vacancy,
based on the Jahn–Teller effect. Because the atoms around thevacancy in undamaged silicon crystals should have the geometrical distortion similar to that of the irradiation-damaged
silicon crystals, based on the Jahn–Teller effect, we believethat the identification performed on irradiation-damaged samples using EPR is applicable to undamaged samples used inthis paper.
Among the 415 types of defects in silicon identified inprevious EPR studies [13], the largest vacancy agglomerate
is negatively charged pentavacancy defect V5− [14]. On theother hand, to the best of our knowledge, the largest vacancy
agglomerate estimated using PALS is hexavacancy defect V6
in an electron-irradiated FZ silicon doped with phosphorus foran estimated positron lifetime of 400 ps [15].
Furthermore, when the wave function of an unpaired electron spreads to the position of an impurity atom having nuclear
spin I , where I is an integer or half-integer, the EPR signal
splits into (2I + 1) lines owing to the hyperfine interaction.
Since the number of lines and splitting width of the hyperfine
splitting depend on the impurity atom and the wave function of
the unpaired electron, they are useful for identifying impurity
defects.
The 28 Si single crystal used in this paper contains 29 Si
atoms, which have a nuclear spin I = 1/2, with an amount-ofsubstance fraction of only 4 × 10−5 [16]. This brings about
relatively narrow line widths of the EPR signals and makes
it possible to acquire high-resolution EPR spectra. This is agreat advantage in determining a small amount of vacancy
defect concentration compared to the measurement on silicon
crystals with a natural isotope ratio, which contains 29 Si atoms
with an amount-of-substance fraction of approximately 0.047,
causing inhomogeneous broadening in the EPR signals owing
to the hyperfine interaction.
Quantitative determination of the number of EPR-active
defects can be achieved through comparison with a reference
sample with a known number of unpaired electrons. This isbased on the measurement principle that each EPR absorption
intensity is proportional to the number of unpaired electrons ina sample. When we use the reference sample with the numberof unpaired electrons n R , the number of unpaired electrons
localized at a certain type of defect X in the test sample n X ,is given by

nX =

AX
AR



TX
TR


nR

(3)

where (AX /AR ) is the ratio of the EPR absorption intensities
for the test and reference samples and (TX /TR ) is the ratioof the absolute temperatures of the test and reference samples
being measured. Here, we used Curie’s law, which states thatthe magnetization of the paramagnetic material is approximately inversely proportional to the absolute temperature.
The concentration of defect X with an unpaired electronin the test sample cX is obtained by dividing the numberof unpaired electrons localized at the defect n X by a sample

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volume Vs
cX = n X /Vs .

(4)

We used a crystal of copper(II) sulfate pentahydrate
CuSO4 ·5H2 O (molar mass M = 249.69 g mol−1 ) with amass of 12.53 mg as the reference sample, which retains
one unpaired electron per molecule. The number of unpaired
electrons in the reference sample n R was estimated to be
3.02(3) × 1019. The EPR absorption intensity of the reference
sample AR was determined at TR = 298 K before measurements on the test sample using the same instrument.
All EPR measurements were carried out using a Bruker
Bio-Spin E500 X-band spectrometer equipped with a superhigh-Q cavity ER 4122SHQ. The signal-to-noise ratio of
the instrument is 3000 for the paramagnetic radical standard
material, called weak pitch, having a linear density of unpaired
electrons of around 1013 cm−1 . The detectable minimum
number of unpaired electrons in the sample placed in the
microwave cavity resonator was estimated to be around 1010,
which is ultimately limited by the thermal noise of the detector
and amplifiers [17]. The quality factor of the microwave
cavity resonator Q reaches 7500 under the best measurement
conditions. The sample temperature was controlled from 4 K toroom temperature using an Oxford ESR900 He-flow cryostat.
Standard magnetic field modulation technique was employed
at a frequency of 100 kHz with a modulation width of 0.1 mT.
In quantitative EPR measurements, it is necessary to avoid
microwave saturation that causes the underestimation of EPR
signal intensities. Without microwave saturation, the intensityof any EPR signal should be proportional to the square rootof the microwave power. Therefore, the intensity of the EPR
signal was examined beforehand at four microwave powersof 0.002, 0.02, 0.2, and 2 mW.
Furthermore, out-of-phase second-harmonic EPR signals
under rapid-passage conditions [18] were observed to selectively detect defects with long electron spin relaxation times inthe sample. It was found that the concentrations of defects withlong electron spin relaxation times were below the detection
limit of our measurement in the expected magnetic field range
from 334 to 337 mT for the EPR-active vacancy defects.
III. S AMPLE P REPARATIONThe sample for EPR spectroscopy was prepared from semicircular disk-shaped sample 9.R1, cut out from the tail sideof 28 Si single-crystal Si28-10Pr11 (referred to as AVO28) [5].
The sample has a rectangular solid shape with the dimensionsof 1.8 mm × 3.4 mm × 10.4 mm. The axial distance
between the sample and the seed of the AVO28 crystal wasapproximately 420 mm, and the radial distance from the center
was approximately 35 mm. The dimensions of the sample
were designed by taking into account the internal dimensionsof the microwave cavity resonator and the distribution of
the microwave field B1 in the microwave cavity resonator.
The volume of the sample at 20 °C was determined to be
Vs = 0.065 029(5) cm3 from the crystal density [16] andthe mass measured using a vacuum mass comparator [19].
Fig. 3 shows a photograph of the sample and the crystal
orientations.

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Fig. 3. Photograph of the mirror-polished crystal prepared from semicircular
disk-shaped sample 9.R1, cut out from the tail side of the AVO28 crystal.
The indices on the right side indicate the crystal orientations.

To detect a small EPR signal from the bulk crystal, we must
reduce the EPR signals of defects near the sample surfaces,
which were formed during the manufacturing process. For
this purpose, the surface area of 1.09 cm2 , out of the total
surface area of 1.21 cm2 , was mirror polished. Half of theremaining surface is the as-etched surface, and the other halfis the as-cut surface finished using a dicing saw. From ourexperience, the silicon surface, properly cut using a dicing
saw, is almost equivalent to the mirror-polished surface interms of the surface density of dangling bonds. After our
EPR measurement, it became apparent that chemical etchingis necessary to minimize the dangling bond density on thesample surfaces.
The sample surfaces were then precisely cleaned to reduce
the signal of the surface contaminants. The cleaning was
conducted in four cleaning steps by successively using thefollowing solutions: sulfuric acid peroxide mixture, ammonia
peroxide mixture, hydrogen chloride peroxide mixture, anddiluted hydrofluoric acid.
IV. M EASUREMENT R ESULTS
To detect vacancy defects in the sample, EPR measurements
were conducted in the presence of a magnetic field from 332 to
341 mT. EPR spectra were recorded at four different directions
θ = 0°, 30°, 60°, and 90° by rotating the sample about
the [01̄1] direction, where θ represents the angle between
the magnetic field and the [100] direction. Fig. 4 shows
the first-derivative EPR spectra under 100-W halogen lamp
illumination at 25 K. The halogen lamp illumination generates
a large number of electron–hole pairs in the silicon crystal
sample, provides additional unpaired electrons, and reveals
the defects that cannot be observed in a dark environment.
To guide light from the halogen lamp to the sample, a quartz
glass rod, on which the sample was mounted, was employed.
Electron–hole pairs excited near the sample surfaces underillumination spread into all parts of the sample. The reason forthis is that the minority carrier diffusion length L = (τ D)1/2
is estimated to be greater than a silicon sample thickness

Fig. 4. First-derivative EPR spectra of the AVO28 crystal sample underillumination. To investigate angular dependence, the sample was rotated about
the [01̄1] direction. Angle θ : angle between the magnetic field and the [100]direction. Each spectrum is accumulated for 3.7 h to improve the signalto-noise ratio. These spectra were measured without microwave saturation
for phosphorus impurity and defects on mechanically damaged surfaces at a
microwave power of 2 mW.

of 1.8 mm. Here, τ is the minority carrier lifetime in silicon
crystals and D is the diffusion coefficient of carriers in silicon
crystals. If we use a value of the minority carrier lifetimeτ = 21.6 ms [20] and a value of the diffusion coefficientof carriers D = 350 cm2 s−1 for electrons at 25 K [21],the minority carrier diffusion length is estimated at 27 mm.
The observed EPR spectra identified the following three
types of defects.
1) Phosphorus (31 P, Nuclear Spin I = 1/2) Impurity:
The constituent element is represented by Si4 −− P•,
where the lines symbolize chemical bonds and the
dot symbolizes an unpaired electron. Phosphorus is atypical substitutional impurity in the silicon crystal. The
identification is based on the facts that the spectra show
a doublet hyperfine splitting of 4.04 mT owing to a 31 P
hyperfine interaction, and the g-value of the spectral
center is 1.9990(1) and isotropic, which are in good
agreement with the well-established EPR signal of phosphorus donors in silicon crystal [22], [23]. This isotropic
signal results from the tetrahedral symmetric structure,
where four silicon atoms bond to a phosphorus atom
without geometric distortion. The observed linewidth of
the spectra was 2 = 0.24 mT.
The number and concentration of the phosphorus impurity with unpaired electrons under illumination are determined to be 0.21(3) × 1012 and 3.2(5) × 1012 cm−3 ,respectively, based on (3) and (4). Table I shows
the numerical values used for this determination andits uncertainty evaluation. The phosphorus EPR signal
fell below the detection limit in a dark environment.
This indicates that unpaired electrons of the phosphorus donors transferred to other compensating defects
in the sample in a dark environment (Si4 −− P •→Si4 −− P + •). This is known as a “compensation”

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TABLE IU NCERTAINTY E VALUATION OF C ONCENTRATION OF P HOSPHORUS I MPURITY W ITH U NPAIRED E LECTRONS U NDER I LLUMINATION

phenomenon, namely, a decrease in the number ofcharge carriers in a semiconductor material, which contains both donors and acceptors. We suggest that suchcompensating defects originate from boron impurity
with a relatively high concentration at the tail of the
AVO28 crystal and also from the defects on mechanically damaged surfaces described in the following.
2) Defects Formed Near the Mechanically-Damaged
Surfaces of Silicon Single Crystal (Si3 ≡ Si•): The
identification is based on the result that the g-value ofthe observed spectral center is close to 2.0055(2) [24]and isotropic. Most of these defects may be formed at
microcracks near the as-cut surface with a surface areaof 0.06 cm2 , finished using a dicing saw or mirrorpolished surfaces. The linewidth of the spectra on the
28 Si single crystal used in this paper is 2 = 0.41 mT,
which is clearly narrower than that reported for natural
isotope ratio crystals of 0.7–0.8 mT [24].

The number of EPR-active defects on the mechanicallydamaged surfaces was determined to be 1.67(23) × 1012
in a dark environment and 0.68(10) × 1012 underillumination. They are larger than the number of phosphorous impurity defects observed under illumination,
0.21(3) × 1012. We judge that unpaired electrons ofphosphorus impurities acting as donors move to defects
on the mechanically damaged surfaces, hiding the EPR
signals of phosphorus in a dark environment. Under
illumination, some of the unpaired electrons at defects
on the mechanically damaged surfaces transfer to phosphorus impurity defects, thus recovering the EPR-active
state (Si4 ≡__ P + • → Si4 ≡__ P•).
3) E’ centers (O3 ≡ Si•), oxygen-vacancy defects in thequartz glass rod, on which the sample was mounted.
The identification is based on the observation of
isotropic and easily saturable signals with averageg-value close to 2.0008 [25]. The microwave saturation

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TABLE IIC ONCENTRATIONS OF N INE T YPES OF VACANCY D EFECTS W ITH U NPAIRED E LECTRONS AND THE
C ORRESPONDING M ASS D EFICITS FOR A 1-kg 28 S I S INGLE C RYSTAL

occurred even at a microwave power of 0.02 mW.
This signal is detectable without the silicon sample andis irrelevant to the silicon sample.
However, anisotropic EPR signals of the vacancy defects
were not observed in the expected magnetic field rangeof 334 to 337 mT under illumination. This result indicatesthat the concentrations of nine types of vacancy defects with
unpaired electrons V + , V − , V2+ ,V2− ,V3− ,V4− ,V5− , (V O)− , and(V P)0 , which were previously identified by Watkins [6] andLee and Corbett [10] using EPR spectroscopy, are all below
the detection limit of our EPR measurement, estimated asaround 1 × 1012 cm−3 . This value of the detection limit wasestimated from the fact that the signals of the phosphorus
impurity with unpaired electrons having a concentration of
3.2(5) × 1012 cm−3 , which split into two spectra, are clearly
distinguished from background noise, as shown in Fig. 4.
Similar EPR measurement conducted in a dark environment
also revealed that anisotropic EPR signals of the vacancy
defects were below the detection limit of our measurement.
Table II shows the evaluated concentrations of the nine
types of vacancy defects with unpaired electrons and thecorresponding mass deficits for a 1-kg 28 Si single crystal. Each
concentration of vacancy defects with unpaired electrons isestimated to be 0.0 × 1012 cm−3 . The standard uncertainty
is estimated to be 0.6 × 1012 cm−3 , assuming a uniform
distribution with a half-width of 1 × 1012 cm−3 , which is theestimated detection limit of our EPR measurements. The total
mass deficit due to vacancy defects with unpaired electrons δmis estimated to be 0.00(23) µg for a 1-kg 28 Si single crystal
using the following equation:
δm = δm V + + δm V − + δm V + + δm V − + δm V −22

3+ δm V − + δm V − + δm (V O)− + δm (V P)0
4

5

(5)

where δm V + , δm V − , · · · , δm (V P)0 represent a mass deficit due
to each type of vacancy defect.
The vacancy concentrations estimated in this paper are
limited to those for the nine types of vacancy defects in silicon
crystals, as identified in previous EPR studies. Therefore,
it should be noted that the mass deficit estimated in this paper
corresponds only to these nine types of vacancy defects.
The standard uncertainty of the total mass deficit due tovacancy defects with unpaired electrons u(δm) is given byu(δm) = u(δm V + ) + u(δm V − ) + u(δm V + )2+ u(δm V − ) + u(δm V − ) + u(δm V − )234+ u(δm V − ) + u(δm (V O)− ) + u(δm (V P)0 )5(6)

where u(δm V + ), u(δm V − ), · · · , u(δm (V P)0 ) are the standard
uncertainties of mass deficits δm V + , δm V − , · · · , δm (V P)0 .
In this estimation, we assume that correlation coefficients
between the mass deficits are +1.
V. D ISCUSSION
The sample cut out from 28 Si single crystal AVO28 was
measured at 25 K using EPR spectroscopy. Under illumination, the number and concentration of EPR-active phosphorus

MIZUSHIMA et al.: EPR STUDY ON 28 Si SINGLE CRYSTAL FOR THE FUTURE REALIZATION OF THE KILOGRAM

impurity (Si4 ≡__ P•) in the sample were determined to be
0.21(3) × 1012 and 3.2(5) × 1012 cm−3 , respectively. In adark environment, the number of EPR-active defects on themechanically damaged surfaces (Si3 ≡ Si•) was determined
to be 1.67(23) × 1012 . The clear observations of low concentrations of phosphorous impurity and defects on mechanicallydamaged surfaces demonstrate that EPR measurements usedin this paper have adequate sensitivity to vacancy defects at aconcentration of 1 × 1012 cm−3 .
The concentration of phosphorus impurity obtained inthis paper, 3.2(5) × 1012 cm−3 , agrees with that of sample 4.12 of the AVO28 crystal shown in [26, Table 3],10(10) × 1012 cm−3 , which was estimated from measurement
results using Fourier transform infrared (FTIR) spectroscopy
for 28 Si crystal Si28-23Pr11. It is worth noting that thephosphorus impurity in the silicon crystal serves as a common
scale for EPR and FTIR measurements.
The measured surface density of defects on
the mechanically damaged surfaces gives a valueof 1.67(23) × 1012 / 1.21(2) cm2 = 1.4(2) × 1012 cm−2 .
This value is comparable to that of hydrogenated amorphoussilicon (a-Si:H) films, determined using photothermal
deflection spectroscopy, around 1012 cm−2 [27].
On the other hand, anisotropic signals of nine types ofvacancy defects were not observed in the expected magnetic
field ranging from 334 to 337 mT both in a dark environment
and under illumination. The concentrations of the nine typesof vacancy defects were estimated to be 0.0(6) × 1012 cm−2 ,respectively. Consequently, the mass deficit correction forthese vacancy defects is evaluated to be 0.0(2) µg fora 1-kg AVO28 crystal.
There are vacancies without unpaired electrons that cannot
be detected by EPR. At present, it is difficult to estimate theconcentrations of these vacancies. However, we believe thatthe comparison of EPR signals in a dark environment andunder illumination reveals a significant portion of vacancy
defects.
Substitutional nitrogen atoms in a silicon crystal (Si4 −− N•)
were identified using EPR by Murakami et al. [28] andSprenger et al. [29]. However, in our experiment, the EPR signal of nitrogen impurity, which was considered to be containedin the AVO28 crystal with a relatively high concentration,
was not detected. This can be explained by the geometricalstructure of atoms determined by Jones et al. [30], where mostof the nitrogen atoms in silicon crystals exist in the form ofinterstitial atoms without unpaired electrons (Si3 ≡ N:, where
the colon sign symbolizes a lone pair of electrons).
To the best of our knowledge, vacancies captured by nitrogen impurities have not been identified using EPR. They are
not listed in the collected EPR data of the 415 types of defects
in silicon [13].
Abe et al. [31] observed an FZ silicon crystal after copper
decoration using X-ray topography. They reported that thevacancy concentration has a maximum value at the center ofthe radial direction of the crystal. The sample used in our EPR
measurement was located near the rim of the AVO28 crystal.
We need to perform an EPR measurement on the sample near1885

the center of the crystal to obtain additional results in the near
future.
VI. C ONCLUSION
For the future realization of the kilogram using the
XRCD method, it is essential to ensure the reliability ofthe mass deficit correction for vacancy defects. Therefore,
we conducted quantitative EPR measurements on 28 Si single
crystal AVO28 at 25 K both in a dark environment and underillumination. The following conclusions were obtained.
1) Isotropic EPR spectra from phosphorus impurity anddefects near the mechanically damaged surfaces wereobserved. The concentration of phosphorus impurity in the AVO28 crystal was determined to be
3.2(5) × 1012 cm−3 under illumination, which wasconsistent with that estimated using FTIR spectroscopy,
10(10) × 1012 cm−3 .
2) Anisotropic EPR signals of vacancy defects in the
AVO28 crystal were not observed. This demonstrates
that the concentrations of the nine types of vacancy
defects in the silicon crystal with unpaired electrons,
which were identified in previous EPR studies, wereless than the detection limit of our EPR measurement,
around 1 × 1012 cm−3 .
3) As a result, the mass deficit correction due to the nine
types of vacancy defects was estimated to be 0.0(2) µg
for 1-kg AVO28 spheres.
ACKNOWLEDGMENT
Several parts of the sample preparation process were conducted in the clean room for analog–digital superconductivity(CRAVITY) at the National Institute of Advanced Industrial
Science and Technology and MicroNano Open Innovation
Center of Micromachine Center.
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Shigeki Mizushima was born in Toyama, Japan,
in 1972. He received the B.S. and M.S. degrees inphysics from The University of Tokyo, Tokyo, Japan,
in 1995 and 1997, respectively.
He is currently with the National Metrology
Institute of Japan, National Institute of Advanced
Industrial Science and Technology, Tsukuba, Japan.
His current research interests include electron paramagnetic resonance study on silicon crystals, massmeasurement using a mass comparator, and gravity
measurement using an absolute gravimeter.
Naoki Kuramoto was born in Sagamihara, Japan,
in 1971. He received the B.S., M.S., and Ph.D.
degrees in chemistry from Saga University, Saga,Japan, in 1993, 1995, and 1998, respectively.
From 1995 to 1998, he was a Research Fellow with the Japan Society for the Promotion of
Science, Tokyo, Japan, (DC1, for doctoral course
student). From 1998 to 1999, he was with theTokyo University of Agriculture and Technology,
Tokyo, in the field of physical acoustics. In 1999, hejoined the National Metrology Institute of Japan/the
National Institute of Advanced Industrial Science and Technology (formerly,
the National Research Laboratory of Metrology), Tsukuba, Japan, where he iscurrently the Group Leader of the Mass Standards Group. He has developed
an optical interferometer to measure the volume of 28 Si-enriched spheres by
optical frequency tuning to lead the new definition of the kilogram based on
the Planck constant. His current research interests include laser interferometry
and mass standards.
Dr. Kuramoto is a member of the Japan Society of Applied Physics,
the Chemical Society of Japan, and the Society of Instrument and Control
Engineers.
Kenichi Fujii received the B.E., M.E., and Ph.D.
degrees from Keio University, Yokohama, Japan,
in 1982, 1984, and 1997, respectively. His doctoral
dissertation focused on the absolute measurement of
the density of silicon crystals.
In 1984, he joined the National Metrology Instituteof Japan (formerly, the National Research Laboratory of Metrology), Tsukuba, Japan. In 1988, hestarted an absolute measurement of the density of silicon crystals for the determination of the Avogadro
constant. He developed a scanning-type optical interferometer for measuring the diameter of the silicon sphere. From 1994 to 1996,
he was a Guest Researcher with the Electricity Division, National Institute ofStandards and Technology, Gaithersburg, MD, USA, where he was involvedin the watt balance experiment. He is currently the Prime Senior Researcher
with the Research Institute for Engineering Measurement, Tsukuba.
Dr. Fujii is the member of the CODATA Task Group on Fundamental
Constants and the Consultative Committee for Units of the International
Committee on Weights and Measures. He serves as the Coordinator for
the International Avogadro Coordination Project and the Chairperson for theWorking Group on Density and Viscosity of the Consultative Committee for
Mass and Related Quantities.
Takahide Umeda received the B.E., M.E., andPh.D. degrees from the University of Tsukuba,
Tsukuba, Japan, in 1994, 1996, and 1999, respectively. His Ph.D. dissertation focused on localized
electronic states in solar-cell materials studied byelectron spin resonance (ESR) spectroscopy.
From 1998 to 1999, he was a Doctoral and a PostDoctoral Fellow with the Japan Society of Promotionof Science, where he investigated ESR spectroscopy
on crystalline silicon surfaces. From 1999 to 2003,
he was a Researcher with the Fundamental ResearchLaboratory and Silicon Systems Research Laboratory, NEC Corporation,
Tsukuba, Japan. Since 2003, he has been an Associate Professor with the
University of Tsukuba, Tsukuba, Japan, where he has been a Faculty ofPure and Applied Sciences since 2010. His current research interests include
magnetic resonance spectroscopy on defects and impurities in semiconductors
and semiconductor devices, e.g., silicon and its large-scale integrated circuits,
silicon carbide and its power transistors, gallium nitride, and diamond.