PHYSICAL REVIEW MATERIALS 4, 024603 (2020)

Nearly degenerate ground state of phosphorus donor in diamond
C. Shinei ,1 H. Kato,2 H. Watanabe,2 T. Makino,2 S. Yamasaki,2 S. Koizumi,3 and T. Umeda

1,*

1

2

Institute of Applied Physics, University of Tsukuba, Tsukuba, 305-0006, Japan
National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, 305–8568, Japan
3
National Institute for Materials Science (NIMS), Tsukuba, 305-0044, Japan(Received 18 November 2019; revised manuscript received 27 January 2020; accepted 11 February 2020;
published 27 February 2020)

We investigate phosphorus (P) donors in P-doped diamond epitaxial films by means of electron paramagnetic
resonance spectroscopy (EPR). In a diamond thin film on IIa diamond substrate, we could observe an EPR signalof the NIMS1 center, which has been assigned to a neutral P donor with a D2d symmetry. In contrast, we could notobserve this center in another free-standing diamond film with the same P concentration ([P] ∼ 1 × 1017 cm−3 ).
This striking contrast can be reasonably accounted for in a model where the P donor in diamond has a nearly
degenerate ground state due to t2 and e, in contrast to P donors in group-IV semiconductors like Si and Ge,
where a1 singlet ground state is present. We observed a strong uniaxial strain only in the former diamond thinfilm, which was confirmed by Raman microscopy and preferential orientations of NIMS1 EPR centers. This
strain splits the nearly degenerate ground state of the P donor, resulting in the observation of the NIMS1 center.
We point out that the electronic system of the substitutional P donor in diamond is similar to that of interstitial
Li donor in Si.
DOI: 10.1103/PhysRevMaterials.4.024603

I. INTRODUCTION

Diamond is a promising material for electronic devices ofhigh frequency, high power, and high temperature applications[1], and is a host material for quantum technologies using anitrogen-vacancy (NV) center with a long coherence time [2].
From the viewpoints of both power electronics and quantum
applications, a critical issue is how to control the Fermi
levels of this material by n- and p-type doping diamondwith phosphorus (P) and boron (B) impurities, respectively.
The P doping of diamond is much more difficult than the
B doping [3]. Therefore, there is less understanding of then-type diamond and its doping mechanism [4]. In addition,
an unexpected phenomenon was recently reported that the P
doping can enhance the coherence time of the NV centers [5].
Generally, their coherence time is significantly reduced by
the surrounding electron and nuclear spins of the impurities
in diamond. However, practical behavior of the P donors is
opposite to that of other impurities and still unclear. Therefore,
it is important to understand the nature of the electron spinsof P donors as well as the electronic structures of P donors
in diamond.
The P donors in group-IV semiconductors such as Si[6], Ge [7], and SiC [8] can be easily observed by electron
paramagnetic resonance (EPR). In n-type diamond films, EPR
signals of P-related centers were reported by Samsonenko
et al., Zvanut et al., Isoya et al., Casanova et al., Grafet al. [9–13], and Katagiri et al. [14]. Among these P-related
centers, a spin-1/2 EPR center, called the National Institutefor Material Science (NIMS)1 center [14], was assigned to*Corresponding author: umeda@bk.tsukuba.ac.jp

2475-9953/2020/4(2)/024603(7)a neutral P donor, similar to the P donor signals in Si, Ge,
and SiC (3C-, 4H-, and 6H-SiC). The NIMS1 center showeda D2d symmetry, which originates from the t2z ground stateof the substitutional P donor with a D2d -symmetric distortion[14]. Some theoretical calculations [15–17] supported these
EPR observations, while others, including the effective-mass
theory [18–23], predicted that the P donor in diamond shouldhave a singlet a1 ground state that is commonly found in
P donors in other group-IV semiconductors. Therefore, theunderstanding of P donors in diamond is still controversial.
In this study, we propose a solution to this controversy
by comparing two different types of P-doped diamond films.
The two diamond films involved different lattice strains; only
one P-doped film exhibited a strong uniaxial strain due to an
undoped substrate. As a result, a strain-induced appearanceof the P donor signal (the NIMS1 center) was observed. Thisphenomenon was quite similar to the case of Li donors in
Si under uniaxial strain that have a nearly degenerate groundstate of t2 + e. We propose that P donors in diamond shouldhave a similar nearly degenerate ground state of t2 + e.
II. EXPERIMENTAL

As shown in Table I, two P-doped diamond films were
epitaxially grown on a (111) surface of either a type-Ib
HPHT substrate (2 × 2 mm2 ) or type-IIa HPHT substrate(2 × 2 mm2 ) by plasma-enhanced chemical vapor deposition.
We call these two films “sample A” and “sample B”, respectively. The P doping of the two diamond films was carriedout by mixing PH3 (6N) with CH4 (6N) and H2 (9N) withthe gas ratios shown in Table I. The two P-doped films withthe same P concentration ([P] ∼ 1 × 1017 cm−3 ) were finallyobtained with thicknesses of 45 and 10 μm for samples

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PHYSICAL REVIEW MATERIALS 4, 024603 (2020)

TABLE I. Epitaxial growth conditions of two P-doped diamondfilms.

Microwave powerPressure
Temperature
CH4 /H2PH3 /CH4
P doping

Sample A

Sample B

3600 W
150 Torr
900 °C
0.4%
500 ppm∼ 1 × 1017 cm−3

450 W
100 Torr
900 °C
0.05%
200 ppm∼ 1 × 1017 cm−3

A and sample B, respectively. Their P concentrations wereconfirmed by secondary ion mass spectrometry (SIMS). To
prepare a free-standing film, the base substrate of sample A
was removed by laser cutting. The cut surface was polished,
and the damaged layer was completely removed. Before the
EPR measurements, the two P-doped films were chemicallycleaned. To prepare a free-standing film, the base substrate ofsample A was removed by laser cutting. The cut surface waspolished, and the damaged layer was completely removed.
Before the EPR measurements, the two P-doped films werechemically cleaned to remove surface contaminations using
an acid mixture (H2 SO4 : HNO3 = 3 : 1) at 230 °C for 30 min
for sample A or a solution of NaClO3 in HNO3 at 200 °C
for 3 h for sample B. Both the acid treatments cause Otermination of the sample surfaces. This termination simultaneously leads to removing hydrogen, graphite, amorphous
carbon, and other contaminants on the surface. Thus, the twocleaning procedures gave the same effect to the two samples.
The EPR measurements were performed by a Bruker E500
continuous-wave X-band EPR spectrometer with a superhigh-Q cavity and an Oxford ESR-900 continuous-flow He
cryostat. The EPR spectra were measured at temperaturesfrom 4 to 80 K. We used microwave excitation at 9.428 GHz
and magnetic-field modulation at 100 kHz. The modulation
amplitude was set to 0.02 mT. The magnetic field (B) was
rotated in the (1̄10) plane. A magnetic-field angle of 0°
corresponds to B//[111].
To confirm the P doping and the activation of the P donors,
SIMS was carried out on the two P-doped films. Cathodeluminescence (CL) of excitons bound on the P donors was observed at 80 K using a scanning electron microscope equippedwith a liquid nitrogen cooling stage, an ellipsoidal mirror,
and a monochromator fitted with a 300 grooves/mm grating.
The CL signal was focused by the ellipsoidal mirror onto
the entrance slit of the monochromator and detected with acharge-coupled device (CCD) camera. In the CL measurements, the accelerating voltage and the probe current were
13 kV and 100 nA, respectively.
To characterize the lattice strain in P-doped films, Raman
microscopy was performed by a confocal microscope with adouble-grating monochromator (Jobin-Yvon/Horiba U-1000)
and a liquid-nitrogen-cooled CCD detector. The confocal spot
was about 1 μm. The light source was a 532-nm green laser
diode. The grating was 1800 grooves/mm. Three emission
lines from a Ne lamp were used for the wavelength calibration. A diamond -phonon Raman peak (∼ 1330 cm−1 ) was
measured with a resolution of < 0.02 cm−1 . We measured line

FIG. 1. (a) EPR spectra of P-doped diamond(111) epitaxial
films. Only in sample B, was the NIMS1 center of shallow P
donor observed, in addition to H1 center (a typical carbon defect inepitaxially grown diamond). (b) Angular dependence of EPR signals
in sample B measured at 20 K. Open squares and solid squares
correspond to NIMS1 center and H1 center, respectively. Dottedcurves are simulated by EPR parameters of NIMS1 shown in Table II.

profiles on each edge face of the two P-doped samples by astep of 1 μm over a 150-μm length.
III. RESULTS
A. EPR observation of the NIMS1 center (neutral P donor)

In Fig. 1(a), the EPR spectra of the two P-doped films
measured at 20 K are shown for B//[111]. In both sample
A and sample B, a common single peak is observed at thecenter of each spectrum. This EPR signal originates fromthe H1 center, which is a typical carbon defect in epitaxiallygrown diamonds [24]. Only in sample B, is a 3.4-mT doublet
structure observed. This structure is identical to a 31 P hyperfine (HF) structure of the NIMS1 center [14]. In Fig. 1(b),angular dependences of the observed EPR lines in sample B
are shown, in addition to the known angular dependences of
the NIMS1 center simulated by the EPR parameters shown in
Table II. The simulated curves are in excellent agreement withTABLE II. EPR parameters of NIMS1 center. Aiso = (A +2A⊥ )/3 and b = (A − A⊥ )/3 [37]. In this work, we experimentallyobtained A = 5.77 mT and A⊥ = 1.21 mT for a [001]-axially symmetric 31 P HF interaction.
Symmetry
Ref. [14]Present: sample B

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D2d
D2d

g

g⊥

1.9983 2.0072
1.9983 2.0072

Aiso (mT) b (mT)
2.73
2.73

1.52
1.52

NEARLY DEGENERATE GROUND STATE OF PHOSPHORUS …

FIG. 2. Spin densities of NIMS1 center and P concentrations
measured by SIMS. Open circle is refereed from Ref. [14]. A solidline expresses one-to-one correlation between NIMS center andP doping.

the experimental data. These curves were calculated using the
EPR parameters (g// , g⊥ , A// , and A⊥ ) shown in Table II and
the following spin Hamiltonian:H = μB S · g · B + S · A · I,
where μB is the Bohr magneton, S is an electron spin operator(S = 1/2), g is an axially symmetric gyromagnetic-factor (gfactor) tensor with principal values of g// and g⊥ , A is anaxially symmetric HF tensor with principal values of A// andA⊥ , and I is a nuclear spin operator for a 31 P nucleus (I =1/2). Figure 2 shows an approximate one-to-one correlation
between the spin densities of the NIMS1 center and the
P concentrations measured by SIMS. We conclude that theincorporated P atoms in sample B are activated as P donors indiamond. This result is consistent with a previous electricalcharacterization that the carrier concentration derived fromPHYSICAL REVIEW MATERIALS 4, 024603 (2020)

the Hall measurements is consistent with the P concentration
measured by SIMS [25].
On the other hand, sample A only exhibits the H1 centeras is shown in Fig. 3(a). Even at 4.2 K, we cannot observe theNIMS1 center with the donor concentration of 1 × 1017 cm−3
[dotted lines in Fig. 3(b)]. To confirm the activation of the
P donor in sample A, we carried out the CL measurements(Fig. 4). The “FETO ” and “BETO ” CL signals, which originate from the free-exciton and bound-exciton luminescence,
respectively, are detectable in sample A as well as in sample
B. Thus, it is confirmed that the magnitude of the donor
activation in sample A is as high as that in sample B.
The disappearing EPR signal of the NIMS1 center insample A is attributed to a lifetime broadening phenomenon.
In general, when an unpaired electron occupies a degenerateor nearly degenerate energy level, its EPR signal should
disappear due to the lifetime broadening. However, the hidden
EPR signal appears when a strong strain is applied and cancels
the degeneracy. For instance, Watkins et al. [26] reported that
the EPR signal of the Li donor in Si, which has a nearly
degenerate ground state of t2 + e, appeared when a uniaxial
strain was applied to Li-doped Si crystals. Another example
is seen in B-doped Si crystals: Feher et al. [27] revealed thatthe B accepter has a degenerate ground state; hence, its EPR
signal appeared only under a strong uniaxial strain. Therefore,
it is reasonable to consider that the P donor in diamond
has a (nearly) degenerate ground state similar to the above
examples, and that a strong strain is present only in sample B,
resulting in the appearance of the donor EPR signal (NIMS1
center). In the following two sections, we experimentally
evaluate lattice strains in P-doped diamond films.
B. Lattice strain in P-doped diamondfilms studied by Raman shifts

A lattice strain is often evaluated by Raman shifts.
Figure 5(a) shows cross-sectional line profiles of diamond

FIG. 3. EPR spectra of sample A measured at 20 and 4.2 K. (a) Only H1 center can be observed at both temperatures, where a 1.4-mT
doublet structure indicates characteristic 1 H hyperfine interaction of H1 center. (b) Simulation of the NIMS1 EPR signal with spin densityof 1 × 1017 cm−3 (dotted lines). The NIMS1 center was not detectable at either temperature. Vertical scale is common to both the 20 and
4.2 K signals.
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PHYSICAL REVIEW MATERIALS 4, 024603 (2020)

FIG. 4. CL spectra of sample A and sample B. “FET O ” and“BETO ” peaks originate from free excitons of diamond and binding
excitons of neutral P donors, respectively. Vertical scale is common
both to sample A and sample B.

-phonon Raman peak on each edge face of samples A and B.
To determine peak positions of the diamond Raman peak accurately at each focused point, we performed a fitting analysis

using a single Lorentzian peak. In Fig. 5(b), we plot the determined Raman shifts as a function of cross-sectional positions
in samples A and B. In sample B only, a stepwise increase in
the Raman shift was observed just at the boundary (40 μm)
between the substrate and the P-doped film, suggesting thepresence of a strong compressive strain in the P-doped film ofsample B. The stepwise increase is about +0.1 cm−1 , whichapproximately corresponds to a compressive strain of 40 or
150 MPa, supposing that either a hydrostatic strain [28] or abiaxial strain in the (111) plane [29] is applied to a diamond
crystal. The above compressive strains are comparable to theuniaxial strains (6–90 MPa) applied to Li-doped and B-doped
Si that could induce visible EPR signals of Li donors and B
acceptors, respectively [26,27]. Therefore, we can reasonably
expect that in sample B, the P donor shows a strain-induced
EPR signal (the NIMS1 center).
The observed compressive strain is most probably due tothe P doping of diamond. Since the atomic radius of P is 1.4
times larger than that of C, a P-doped diamond must expand
compared to an undoped diamond. Therefore, in sample B,
the P-doped epitaxial layer on the base substrate suffers froma strong compressive strain. In the next section, we further
determine the direction of the compressive strain in sample Bby examining the directions of the D2d -symmetric distortionsof the NIMS1 centers.

C. Lattice strain in P-doped diamond films studied by
preferential orientations of NIMS1 EPR centers

FIG. 5. (a) Cross-sectional Raman mapping of diamond phonon Raman peak on each edge face of sample A and sample
B. In sample A, a free-standing P-doped epitaxial film is shown in
the range between 2 and 50 μm. In sample B, regions over 50 μm
indicate the air region. Raman spectra were measured at every 1-μm
step on each edge face of samples. (b) Raman shifts as a function ofcross-sectional positions. Only in sample B, was an irregular Raman
shift of +0.1 cm−1 detected in the P-doped region, which is due tothe presence of a strong compressive strain in this region (see details
in text). In addition to the stepwise change, a gradual change in the
Raman shift was also observed in sample B. Its magnitude depended
on measured positions in sample B. Furthermore, base levels for
the Raman shift varied from 1330.35 to 1331.25 cm−1 in sample B.
Such behaviors may relate to an inhomogeneity of the IIa substrateof sample B. Regardless of the variations, the stepwise change of+0.1 cm−1 was always observed in every line profile of sample
B. In sample A, a relatively weak gradual change was observed.
Fluctuated Raman intensities in sample A may originates from asurface roughness of its edge face.

Figure 6(a) shows a D2d -symmetric distortion of theNIMS1 center or a substitutional P atom. A tetragonal D2dsymmetry generates three equivalent distorted orientations
along the [100], [010], and [001] axes. In Fig. 6(b), an EPR
spectrum of sample B for B // [110] is shown, where twoorientations of the NIMS1 centers ([001] and [100] + [010])
are distinguishable. We performed a spectrum simulation of
the NIMS1 EPR signal for an ideal case (the NIMS1 centers
uniformly exhibit the three equivalent orientations) and fora preferentially orientated case (the NIMS1 centers exhibit
preferential orientations due to a uniaxial strain). As shownin Fig. 6(b), the preferential orientations are more probable.
Figure 6(c) summarizes each population of the three orientations for the NIMS1 center. The preferential orientation
along the [001] axis was confirmed in sample B. In principle,
a NIMS1 center with a [001] orientation (shrinking along
the [001] axis) is energetically favorable. This suggests thepresence of a strong uniaxial strain along the [001] axis in
the P-doped layer of sample B. This strong uniaxial straincauses the splitting of the nearly degenerate ground stateof the NIMS1 center, as discussed in the next section. We
confirmed using an x-ray diffraction measurement that the
IIa substrate of sample B has an off-angle direction towards
the [1̄1̄2̄] axis, as shown in Fig. 6(d). This direction includes
a more [001] component than [100] and [010] components.
This may be related to the preferential orientation of the [001]distorted NIMS1 center. We roughly speculate that P-induced
strain may correlate with the off-angle direction, which may
strengthen the strain along this direction.

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NEARLY DEGENERATE GROUND STATE OF PHOSPHORUS …

FIG. 6. Presence of a strong strain in sample B revealed by
NIMS1 EPR center. (a) D2d -symmetric distorted structure of NIMS1
center (substitutional P donor). A tetragonal D2d symmetry generates
three equivalent orientations along the [100], [010], and [001] axes.
The epitaxial growth direction along [111] is also indicated. (b) EPR
spectrum of NIMS1 in sample B, when B // [110]. In this B direction,[001] orientation is distinguishable from other two orientations.
In addition to EPR spectrum, the fitting peaks for experimental
signals of NIMS1 center and the simulated peaks of NIMS1 centerfor the ideal population are shown. (c) Population ratios of NIMS
centers with three orientations in an ideal uniform population andin sample B. The nonuniform population in sample B indicatesthe presence of a strong uniaxial strain in P-doped epitaxial layer
on IIa-diamond substrate. (d) Schematic view of sample B and its
off direction.

PHYSICAL REVIEW MATERIALS 4, 024603 (2020)

FIG. 7. Schematic illustration of 1s ground states and excitedstates of substitutional P donors in Si and diamond, in addition to
those of interstitial Li donors in Si. Electronic states (a1 , e, and t2 ,etc.) shown in (a), (b), and (c) are taken from Refs. [34]. Excitedenergy levels (2p0 , 2p±, 3p0 ) in (d) and (e) are taken from Ref. [35].
Valley-orbit splitting in 1s ground state of P donor are schematicallydrawn, because they have not yet been determined. Solid arrows
represent unpaired electrons occupying each 1s ground state. The
electronic system of the substitutional P donor in diamond is similar
to that of interstitial Li donor in Si.
IV. DISCUSSIONS
A. Why P donor in diamond has no singlet a1 ground state?

In this section, we explain why the P donor in diamond
has a nearly degenerate ground state. Nara et al. [30] reported
that the Li donor at a tetrahedral-interstitial site surrounded byeight Si atoms [see Fig. 7(b)] has a degenerate ground state of

D. Strain-induced splitting of nearly degenerate ground statesof the P donor in diamond and Li donor in Si

In contrast with the P donor in diamond, the P donor in Si
can be easily observed by EPR [6], because the P donor in Si
has a singlet (i.e., nondegenerate) a1 ground state as shown in
Fig. 7(a). On the contrary, the interstitial Li donor in Si has
a nearly degenerate ground state originating from t2 + e electronic state [Fig. 7(b)] [26]. These nearly degenerate levels
because fast transitions of the electron spins among the energy
levels, resulting in strong lifetime broadening. Therefore, theEPR signal of the Li donor is only observable under a strong
uniaxial strain that splits the energy levels [Fig. 7(c)]. In thepresent study, we observed the P donor (the NIMS1 center)
only in sample B, which clearly exhibited a strong uniaxial
strain. Therefore, by analogy, we assume that the P donor
in diamond should have a nearly degenerate ground state[Fig. 7(d)].
Furthermore, the above model is also supported by temperature dependence of the NIMS1 center. As shown in Fig. 8,
there is a clear difference in temperature dependence between
the experimental data and the case of paramagnetic spinsaccording to Curie’s law. The difference is accounted for by
the presence of excited states very close to the ground state.
It also suggests the presence of the nearly degenerate groundstate of the P donor in diamond.

FIG. 8. Temperature dependence of normalized EPR intensity
of NIMS1 center. Solid triangles and open squares correspond to
EPR measurements on IIa-diamond substrate/P-doped epitaxial filmwith P doping of 1 × 1017 cm−3 (sample B) and of 1 × 1019 cm−3
(Ref. [36]), respectively. The solid curve indicates normal temperature dependence of EPR intensity according to Curie’s law,which was largely separated from experimental results (expressed
approximately by a dashed smooth curve). This unusual dependenceof the NIMS1 center suggests a close distribution of ground andexcited states of substitutional P donor in diamond.

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TABLE III. P donor levels, dielectric constants, and wave function parameters of P donor centers in group-IV semiconductors.
Fractions of P3s and P3p orbitals, η2 α 2 and η2 β 2 (α 2 + β 2 = 1), arecalculated from isotropic and anisotropic HF constants Aiso and b,
via η2 α 2 = |Aiso /A0 | and η2 β 2 = |b/b0 |, respectively [38]. We used
known isotropic and anisotropic HF constants of A0 = 474.79 mT
and b0 = 13.088 mT for 31 P [38].

Host element

Donor level(meV)

Dielectric
constant

η2 α 2(%)η2 β 2
(%)

η2
(%)

45a
12a
590b

11.7a
15.8a
5.8a

0.88c
0.45d
0.57 e,f0c
0d
11.6e,f

0.88c
0.45d
12.2e,fSiGe
diamonda

Reference [38].
Reference [39].
cReference [6].
dReference [7].
eReference [14].
fThis Work.
bt2 + e because of “the orthogonalization effect” of a 1s corestate of the Li donor to a singlet a1 state. In detail, the interstitial Li donor has a larger amplitude of the wave function
at the Li site than that of the Li donor at the substitutionalsite. In general, the larger amplitude of the wave function on
the donor atom causes the stronger orthogonalization effect,
which is seen in the following two equations.
(φλ , ψki )φλ (r) −(φν , ψki )φν (r),ψki (r) = ψki (r) +
ν

λ





ψki (r) = ψki (r) −(φν , ψki )φν (r),

(1)
(2)

ν

where ψki (r) is a Bloch function for a crystal momentum
vector k and a position r at the ith of the sixfold valley orbitsof a donor in a Td -symmetric crystal field, and the roundbrackets indicate the overlap integral of two wave functions.
ψki (r) is obtained by orthogonalizing ψki with respect to theλth core state of the host element, φλ (r), and the ν th corestate of the donor atom, φν (r) [30]. Equations (1) and (2)correspond to the cases of the substitutional donor atom andthe tetrahedral-interstitial donor atom, respectively. Note that
the Li donor has only the 1s state. Therefore, for Eq. (2) (theinterstitial Li donor), only ψki of the singlet a1 state has anonzero positive coefficient, i.e., the orthogonalization effect:ψki (r) = ψki (r) − (φLi, 1s , ψk, a1 )φLi, 1s (r).


(3)Therefore, the amplitude of ψki (r) is reduced at the interstitial
Li site. This effect lifts up the singlet a1 electronic level ofthe a1 state, resulting in the degenerate t2 + e ground state[26]. This situation is generally called “inverted group-V-likeground state” [30].
From the 31 P HF tensor, we experimentally determine thewave function parameters (3s and 3p orbitals on a P atom)of the NIMS1 center, in addition to those of the P donor
centers in Si and Ge, which are summarized in Table III. In
the NIMS1 center (P donor in diamond), the spin localization(η2 ) on the P donor site is 12.2%, which mostly consistsof 3p orbitals. These features are strikingly in contrast withthe cases of Si and Ge. Assuming the same magnitude of
the spin localization (12.2%) for the singlet a1 ground state,
we estimate the isotropic HF interaction to be 58 mT. On
the contrary, the P donors in Si and Ge show smaller spin
localizations due to higher dielectric constants and shallower
donor levels than those in diamond (Table III). Due to thelarger wave function amplitude of the P donor in diamond,the orthogonalization effect with the respect to the a1 groundstate is stronger in diamond than in Si and Ge. Therefore, it isexpected that the P donor in diamond has the a1 as an excitedstate [Figs. 7(d) and (e)], while those in Si and Ge have a1 as aground state [Fig. 7(a)]. The strong p character of the P donor
in diamond is consistent with the t2 or t2 + e ground states[Fig. 7(d)] [6].
We also discuss the P1 EPR center [31] that arises fromanother substitutional group-V impurity in diamond. For theP1 center, first-principles calculations [19,32] predicted that asubstitutional nitrogen (N) impurity has a singlet a1 groundstate with a C3v symmetry. Therefore, an electron spin of
the P1 center occupies the singlet a1 state and can be easily
observed even at room temperature in various diamond samples [31], which is quite different from the substitutional P
donor center (NIMS1 center). This difference between N and
P mainly originates from the magnitude of their distortion.
The distortion for N is induced by the splitting of bonding andantibonding orbitals between a N lone pair and a C dangling
bond along [111] axis [19,32]. It was theoretically predictedthat such a distortion results in a 25% elongation of the N-Cbond, while six nearest-neighbor C atoms move within only
a 3% variation of their three C-C bonds or N-C bonds. As aresult, the substitutional N atom has a large energy gain due tothe elongation of the N-C bond. For the P1 center, a theoretical
calculation estimated the energy gain of the distortion to be
0.63 eV [19], which is much larger than the theoretical energy
gain of the Jahn-Teller distortion for the substitutional P atom
(4–35 meV) [33].
B. A suggested experimental resolution of previous
theoretical discrepancies

In principle, diamond has the same type of conduction
band edge (consists of sixfold valleys) as Si and Ge, andtheir P donors should generate a singlet a1 state, a doublet
e state, and a triplet t2 state, which are split due to a Td crystal
field of the diamond structure. However, previous theoretical
calculations for the ground state of the P donor in diamond arecontroversial. Jackson et al., Kajihara et al., Sadda et al., Wanget al., Seggev et al., and Lombardi et al. [18–23] predicted thesinglet a1 ground state, while Orita et al., Butorac et al., andAlferi et al. [15–17] predicted the degenerate t2 ground state.
On the basis of our experimental results and the above discussions, we speculate that this controversy may come fromthe degree of accuracy when calculating the orthogonalization
effect with respect to every a1 , e, and t2 state of the P atom.
V. SUMMARY

We investigated phosphorus donors in P-doped diamondepitaxial films by means of EPR spectroscopy. In a diamond

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PHYSICAL REVIEW MATERIALS 4, 024603 (2020)

thin film on a IIa diamond substrate, we could observe an EPR
signal of “NIMS1 center”, which has been assigned to a neutral P donor with a D2d symmetry. On the contrary, we could
not observe this center in another free-standing diamond filmwith the same P concentration ([P] ∼ 1 × 1017 cm−3 ). This
striking contrast can be reasonably explained by proposingthat the P donor in diamond has a nearly degenerate groundstate of t2 or t2 + e, in contrast to P donors in group-IV semiconductors like Si and Ge where the a1 singlet ground state ispresent. We also observed a strong uniaxial strain only in theformer diamond thin film, which was confirmed by Raman
microscopy and preferential orientations of the NIMS1 EPR

centers. This strain splits the nearly degenerate ground stateof the P donor, resulting in the observation of the NIMS1
centers. Finally, we pointed out that the electronic system of
the substitutional P donor in diamond is analogous to that ofan interstitial Li donor in Si, where the a1 singlet ground stateis shifted up in energy by the orthogonalization effect.

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ACKNOWLEDGMENTS

This work was partially supported by MEXT Q-LEAP (JPMXS0118067395), JST CREST (JPMJCR1773), and JAEA
Project on wisdom integration (30I123).

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