PHYSICAL REVIEW B 73, 075201 共2006兲

Electron paramagnetic resonance and theoretical studies of shallow phosphorous centers in 3C-,
4H-, and 6H-SiC
N. T. Son and A. Henry
Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden

J. Isoya, M. Katagiri, and T. Umeda
Research Center for Knowledge Communities, Graduate School of Library, Information and Media Studies, University of Tsukuba,
Tsukuba 305-8550, Japan

A. Gali
Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111, Budapest, Hungary

E. Janzén
Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden
共Received 22 July 2005; published 1 February 2006兲
Continuous-wave 共cw兲 electron paramagnetic resonance 共EPR兲 at both X-band and W-band frequencies,
pulsed-EPR, and pulsed electron nuclear double resonance 共ENDOR兲 were used to study phosphorus shallow
donors in 3C-, 4H-, and 6H-SiC doped with phosphorus 共P兲 during chemical vapor deposition 共CVD兲 growth.
In 3C-SiC, a spectrum with D2d symmetry and the principal g values, g储 = 2.0051, g⬜ = 2.0046, was detected.
The 31P hyperfine 共hf兲 constants of the center, A储 = 0.53 MHz and A⬜ = −0.13 MHz, were determined frompulsed-ENDOR measurements. A doublet with C3v symmetry 共g储 = 2.0065, g⬜ = 2.0006, and 31P hf constantsA储 = 8.24 MHz, A⬜ = 5.89 MHz兲 was detected in P-doped 4H-SiC. In the 6H polytype, the same P1 and P2
doublets 关Greulich-Weber, Phys. Status Solidi A 162, 95 共1997兲兴 or dPh, dPc1, and dPc2 doublets 关Baranov etal., Phys. Rev. B 66, 165206 共2002兲兴 previously reported in material doped with P by neutron transmutation
were detected. Our cw-EPR, two-dimensional EPR, and electron spin-echo envelope modulation 共ESEEM兲
results confirm that the dPc1 and dPc2 doublets are related to different allowed and forbidden transitions of theP2 center with S = 1 / 2 and I = 1 / 2. Based on the observed 31P hf interaction 共for three polytypes兲 and the 13C
hf interaction with nearest neighbors 共for 4H- and 6H-SiC兲, the P-related spectra are assigned to the groundstates of the isolated shallow P at Si site. The valley-orbit splitting of the shallow P donors was estimated fromthe temperature dependence of the spin-lattice relaxation time and of the cw-EPR signal intensities. Based on
the ab initio supercell calculations of the spin localizations on the P atom and the nearest C neighbors in
4H-SiC and the similarity between the spectra in the 4H and 6H polytypes, we reassign the spectrum in 4H-SiC to the shallow P donor at the quasicubic site 共Pk兲 and the two doublets P1 and P2 in 6H-SiC to the shallow
P donors at two quasicubic sites, Pk1 and Pk2, respectively.
DOI: 10.1103/PhysRevB.73.075201

PACS number共s兲: 76.30.⫺v, 71.55.Ht, 71.15.Mb, 61.72.Bb

I. INTRODUCTION

Controlling the conductivity via doping of shallow donors
or acceptors is essential for the fabrication of semiconductor
devices. In silicon carbide 共SiC兲, nitrogen 共N兲 shallow donors, which substitute for carbon, are easily and unintentionally incorporated during the crystal growth. Phosphorous 共P兲,
which is expected to substitute for silicon, is an alternative
shallow donor to N in SiC. Due to its higher level of electrical activation, P has advantages over N in the high doping
range 共⬎3 ⫻ 1019 cm−3兲, where the electrical conductivity in
N-doped SiC is being saturated.1
SiC has many polytypes differing in the stacking sequences of Si-C bilayers. In the cubic lattice of 3C-SiC, eachsilicon and carbon has one site. However, in the hexagonallattice of 4H-SiC, each silicon and carbon has two inequivalent lattice sites called hexagonal 共h兲 and quasicubic 共k兲sites, which differ from each other by their surrounding arrangement beyond the second neighbors. In the 6H polytype,1098-0121/2006/73共7兲/075201共16兲/$23.00

there are one hexagonal 共h兲 and two quasi-cubic 共k1 , k2兲
sites. A shallow donor occupying different inequivalent lattice sites can have different electronic structure as shown inthe case of the shallow N donors, which can be studied bymagnetic resonance techniques such as electron paramagnetic resonance 共EPR兲 and electron nuclear double resonance
共ENDOR兲 共see Ref. 2 for a review兲.
EPR studies of P in SiC have mainly been performed in
6H-SiC doped with P by neutron transmutation of 30Si in thehost crystal to 31P 共Refs. 2–6兲 or by P ion implantation.7,8These doping techniques and the required high-temperatureannealing are known to introduce also intrinsic defects andtheir associated complexes. The detection of P involving in aparamagnetic center is based on the observation of 31P 共I= 1 / 2, natural abundance 100%兲 hyperfine 共hf兲 interaction.
Unfortunately, in these studies, the identification of the substitutional site of P was severely hampered by the interference of strong EPR signals of N donors in the host crystal
and by the complexity of the presence of additional deep

075201-1©2006 The American Physical Society

PHYSICAL REVIEW B 73, 075201 共2006兲

N. T. SON et al.

defect centers such as residual lattice damages and their associated complexes. Until the recent theoretical study,9which pointed out that a considerable fraction of P might end
up in occupying the carbon site after high-temperature annealing required in these doping methods, P involved in theobserved P-related EPR centers in neutron-transmuted
6H-SiC had always been assumed to substitute for silicon.
The labeling and interpretation of reported EPR spectra arecontroversial. In the first EPR study of neutron-transmuted
6H-SiC,3 the P1 共A储 = 5.63 mT, A⬜ = 5.55 mT兲, and P2 共A储= 5.17 mT, A⬜ = 5.17 mT兲 spectra observed at 77 K weresuggested to be related to the shallow P donors occupying
the k1, k2, and the h sites, respectively, and the P + V spectrum 共A储 = 0.92 mT, A⬜ = 0.72 mT兲 was assigned to a complex involving P and a vacancy. The P1, P2 centers were later
labeled Pa and Pb and were attributed to the excited state of
the shallow P donors, whereas two other spectra 关originallylabeled I1 and I2 共Ref. 4兲 and later changed to P1 and P2
共Refs. 2 and 5兲兴 observed at low temperatures 共T ⬍ 10 K兲
were assigned to the ground state of the shallow P donors
with P1 corresponding to P on the h site and P2 to P on the k1,
k2 sites of the Si sublattice.2,5 In a later EPR study,6 both setsof low- and high-temperature P-related centers were simultaneously observed at 4.2 K, excluding the possibility that
the Pa and Pb are related to the excited states as proposed inRef. 2. The Pa, Pb and P + V centers were instead reassigned
to the ground state of the shallow P donors at the cubic andhexagonal sites of Si sublattice and labeled sPc1, sPc2, andsPh.6 Also in these X-band EPR experiments,6 the P2
doublet2,5 was suggested to be contributed from two overlapping spectra, labeled dPc1 and dPc2. Based on the observationof their satellites, which were attributed to the hf interaction
with one 29Si nucleus, the low-temperature spectra, P1 and P2
共or I1 and I2兲, in Refs. 2 and 5 were assigned to deep levelcomplex defects involving P at the Si site 共PSi兲 and the carbon vacancy 共VC兲, 共PSi-VC兲, at three inequivalent silicon sites
in 6H-SiC with new labels dPh 共A储 = 0.10 mT, A⬜ = 0.05 mT兲,
dPc1 共A储 = 0.62 mT, A⬜ = 0.38 mT兲, and dPc2 共A储 = 0.48 mT,
A⬜ = 0.19 mT兲.6 Recent EPR studies on P-ion implanted
6H-SiC 共Refs. 7 and 8兲 also used the assignment that the Pa
and Pb centers were the ground state of the shallow P donors
at Si site and estimated their valley-orbit splitting. The sumof the concentrations of Pa and Pb corresponded to only
⬃0.08 of the implanted P ions in the samples annealed at
1650 ° C after the implantation at 800 ° C. Optically detected
EPR of 6H-SiC doped with P during sublimation growth10
was reported but the nature of these broad signals is still
unclear. In sublimation-grown samples, the concentration of
the shallow N donors was often rather high 共similar or ordersof magnitude higher than that of the shallow P donors兲, giving rise to the strong EPR signals of the shallow N donors.
The P-related EPR signals were therefore obscured by strong
N spectra and could hardly be studied.11 In recent
calculations,9 the P-related centers with small 共P1 , P2兲 andlarge 共Pa , Pb兲 hf constants were reassigned to the shallow P
donors occupying Si and C lattice sites, respectively. In in
situ P-doped sublimation-grown 6H-SiC, only the strong
EPR signals of the N donors and two weak shoulders, whichwere believed to be the fingerprint of the P + V center, weredetected. Therefore it was suggested that the amount of electrically active isolated P incorporated during growth is insignificant and P may form diamagnetic complexes.9
In our preliminary studies,12 we observed the EPR spectra
P1 and P2 共Refs. 2 and 5兲 or dPh, dPc1, and dPc2 共Ref. 6兲 in
6H-SiC doped with P during chemical vapor deposition
共CVD兲 growth.13 We followed the site assignment of Ref. 2
that the P2 共or dPc1 and dPc2兲 doublet corresponds to the P
substituting for Si at the k1 and k2 sites, and the strong angular dependence of the signal intensity of the dPc1 and dPc2
doublets remains unexplained.
In this paper, we study 3C-, 4H-, and 6H-SiC doped with
P during CVD growth using continuous-wave 共cw兲 EPR,
electron spin-echo 共ESE兲 detected EPR, electron spin-echo
envelope modulation 共ESEEM兲, two-dimensional 共2D兲 EPR,
and pulsed ENDOR. In our pure CVD freestanding layers,
the P spectra can be observed without interference from other
EPR signals such as the shallow N donors in the
sublimation-grown material or N and radiation induced defects in neutron transmuted and P-implanted materials.
Therefore we could detect clear hf structure due to the interaction with nearest-neighbor C atoms in 4H- and 6H-SiC
and unambiguously identify the shallow P donors occupying
the Si sublattice. Section III presents experimental results in
6H-SiC confirming that 共i兲 the P1 and P2 centers2,5 共i.e., I1
and I2 centers4 or dPh, dPc1, and dPc2 centers in Ref. 6兲 arerelated to the ground state of P occupying the Si sublattice,
共ii兲 the P2共Ref. 2兲 共or dPc1 and dPc2 共Ref. 6兲兲 doublet is notarising from two different P centers but correspond to allowed and forbidden transitions of one P center with
S = 1 / 2 and I = 1 / 2. In this section, EPR and ENDOR resultsof P in 3C- and 4H-SiC were presented. We also show that
the P centers in 3C-, 4H-, and 6H-SiC exhibit features characteristic of having a low-lying excited state. The energy
separation between the ground state and the excited state has
been estimated from the temperature dependence of the EPR
signal intensity and of the spin-lattice relaxation time. In Sec.
IV, the theoretical studies of the spin localizations on the Patoms and the nearest-neighbor C atoms of the shallow P
donors in 4H-SiC are presented. The assignment of P centersto the shallow P donors occupying different inequivalent lattice sites and their electronic structure are discussed in Sec.
V.
II. EXPERIMENTIn order to avoid the interference from N and other defects, which can be introduced during neutron transmutation
or P ion implantation and subsequent high-temperature annealing, we used high-purity 3C-, 4H- and 6H-SiC layers
doped with P during CVD growth.13 In 4H- and 6H-SiC
layers, the concentration of shallow P donors was about
1 – 4 ⫻ 1016 cm−3 as determined from secondary ion-mass
spectrometry 共SIMS兲,13 and from capacitance versus voltage
共CV兲 measurements. In 3C-SiC epitaxial layers, the P concentration is estimated to be in the 1017-cm−3 range. The
concentration of the shallow N donors is in the low 1014
-cm−3 range for 4H- and 6H-SiC. The N-doped n-type substrate was removed by polishing in order to eliminate the075201-2

PHYSICAL REVIEW B 73, 075201 共2006兲

ELECTRON PARAMAGNETIC RESONANCE AND…

FIG. 1. 共Color online兲 PL spectrum of P bound excitons in a
6H-SiC CVD layer measured with polarization E ⬜ c at 2 K, showing no-phonon lines 共Pha, Phb, and Phc兲 and their phonon replicas.
The subscript number denotes the phonon energy in meV. Weakno-phonon lines R and S of the N-bound excitons 共NBE兲 areindicated.

interference from the EPR spectra of the N donors. The
thickness of the freestanding layers was about 150 ␮m.
The cw-EPR measurements were performed on a Bruker
ELEXSYS E580 X-band 共⬃9.75 GHz兲 spectrometer and ona home-built W-band 共⬃95 GHz兲 setup. The pulsed experiments such as echo-detected EPR, inversion-recovery, ESEEM, pulsed-ENDOR, and two-dimensional 共2D兲 EPR werealso performed on the ELEXSYS E580 spectrometer. In thepulsed experiments, we used the microwave pulse with themagnetic field B1 ⬃ 0.5 mT. The echo intensity was obtainedby integrating the echo signal within the range of the gate
centered on the top of the echo. By changing the width of thegate, either nonselective detection which collects responses
from all the signals within the excitation bandwidth of the
microwave pulses or a selective detection which virtuallyeliminates the contribution from off-resonance signals is
chosen. In the echo-detected EPR, the intensity of Hahn echo
共90° —␶—180° —␶—echo兲 was measured as a function of
the external magnetic-field strength B. By using a selective
detection, the resolution similar to that of cw EPR is attained. For the pulsed ENDOR measurement, Mims
sequence14 in which radiofrequency pulse 共duration 10 ␮s兲
was inserted between the second and the third pulses ofstimulated echo 共90° —␶—90° —T—180° —␶—echo, ␶= 1.2 ␮s, T = 16 ␮s兲 was used.
III. EXPERIMENTAL RESULTS AND ANALYSISIn all P-doped 3C-, 4H-, and 6H-SiC CVD layers, thephotoluminescence 共PL兲 of the P-bound excitons has been
observed. Figure 1 shows as an example the band-edge PL
spectrum in a 6H-SiC layer with strong no-phonon lines andphonon replicas of the P-bound excitons measured in theconfiguration with the electromagnetic waves of photons polarized perpendicular to the c axis 共E ⬜ c兲. Detailed structures of the spectra were reported elsewhere.13,15 The R and S

FIG. 2. 共Color online兲 High-frequency EPR spectra in P-doped
6H-SiC freestanding layers measured at 6 K for 共a兲 B 储 c and 共b兲
B ⬜ c. The 13C hf line due to one nearest-neighbor C atom of the
Pk1 center can be seen in the ⫻10 scale.

no-phonon lines of the N-bound excitons were also detectedbut very weak. The observation of the strong PL of P-boundexcitons indicates the high purity of our CVD layers. 关In the
sublimation-grown material, the PL of the P-bound excitons
was usually not seen and only the broad PL band from thedonor-acceptor pairs was detected 共Ref. 10兲.兴 In our 3C-,
4H-, and 6H-SiC CVD samples, the EPR signals of the shallow N donors were not observed.
A. EPR spectra and hyperfine interaction
1. 6H-SiC

Figures 2共a兲 and 2共b兲 show the W-band 共⬃95 GHz兲 EPR
spectra in P-doped 6H-SiC measured at 6 K for the magnetic
field B along and perpendicular to the c axis, respectively.
The spectrum consists of two doublets, each due to 31P hyperfine structure. We will show later in Sec. V that these
doublets correspond to the shallow P donors occupying thetwo quasicubic lattice sites of silicon and therefore give theP1 and P2 spectra new labels Pk1 and Pk2, respectively. The
observed 31P hf splitting are Pk1 共0.11 mT兲 and Pk2
共0.615 mT兲 at B 储 c and Pk1 共not resolved兲 and Pk2 共0.22 mT兲
at B ⬜ c. From the symmetry 共C3v兲, the g values and the 31P
hf constants shown in Table I, it is concluded that these doublets are identical to the P1 and P2 spectra in Refs. 2 and 5 or
the I1 and I2 spectra in Ref. 4.
As shown in ⫻10 scale spectrum in Fig. 2共b兲, a weaksatellite line on the low-field side of the Pk1 line could be
detected. The intensity ratio between this satellite line andthe main Pk1 line is about 0.6% which is approximately ahalf of the natural abundance of 13C 共I = 1 / 2, 1.1%兲. Thissatellite is therefore attributed to the low-field component of
the 13C hf structure of the C atom along the c axis in thenearest-neighbor shell. Within the experimental error, the 13C
hf splitting 共⬃0.37 mT⫻ 2 = 0.74 mT兲 was isotropic.
In the X-band EPR spectra of P-doped 6H-SiC at 8 K,
three doublets Pk1, Pk2a, and Pk2b are observed as shown in

075201-3

PHYSICAL REVIEW B 73, 075201 共2006兲

N. T. SON et al.

TABLE I. The principal values of g and hf tensors of the shallow P donors in 3C-, 4H-, and 6H-SiC. The
error in the g values is ±0.0002. The values of the hf splitting are given in mT. The values in parentheses arein MHz. The principal g values were determined from X-band and W-band cw EPR.
Centerg储

g⬜

A储共 31P兲

A⬜共 31P兲

A储共C1兲

A⬜共C1兲

A储共C2-4兲

A⬜共C2−4兲

P 共3C兲
Pk共4H兲

2.00512.00652.00462.0006

Pk1共6H兲

2.00462.0028

Pk2共6H兲

2.00392.0025

共0.53兲a0.294 c,d共8.24兲c,d
0.11d
共3.168兲a0.619d
0.615c
共17.012兲a,b

共−0.13兲a
0.21c,d共5.89兲c,d
0.01d
共0.0654兲a
0.22d
0.22c
共6.155兲a,b0.72e
共20.18兲e0.74c
共20.7兲c
1.09c
共30.6兲c

0.72e
共20.18兲e0.74c
共20.7兲c
1.09c
共30.6兲c

1.09c
共17.1兲c⬃0.61c共17.1兲c⬃0.61caDetermined from pulsed ENDOR with a higher accuracy.
bDetermined from pulsed ESEEM with a higher accuracy.
cDetermined from X-band cw EPR.
dDetermined from W-band cw EPR.
e

Determined from X-band echo-detected EPR.

Fig. 3. At B 储 c 关Fig. 3共a兲兴, two doublets Pk1, Pk2a are observed. With rotating the magnetic field away from the caxis, the intensity of the Pk2a doublet rapidly decreases while
the Pk2b doublet appears and dramatically increases. For theintermediate directions 共between 20° and 70°兲, all the Pk1,
Pk2a, and Pk2b doublets can be seen 关see Fig. 3共b兲兴, whereas
at B ⬜ c, the Pk2b doublet reaches its maximum intensity and
the Pk2a signal is not detectable 关Fig. 3共c兲兴. The 31P hf split-

FIG. 3. 共Color online兲 X-band EPR spectra in P-doped 6H-SiC
freestanding layers measured at 8 K for 共a兲 B 储 c, 共b兲 B is 40° fromthe c axis and 共c兲 B ⬜ c. The scaled-up spectra show the 13C hf linesof nearest-neighbor C atoms.

ting of the Pk1 and Pk2 doublets observed at W band agreewith those of Pk1 共0.11 mT兲 and Pk2a 共0.619 mT兲 at X bandfor B 储 c and with those of Pk1 共not resolved兲 andPk2b 共0.22 mT兲 at X band for B ⬜ c.
As shown in the ⫻10 scale, two pairs of satellite lines
centered at the Pk2a signal were also detected for some angles
close to the c axis 关Fig. 3共a兲兴. The outer pair has a nearly
isotropic splitting of ⬃1.09 mT and the intensity ratio between the sum of the outer pair of the satellite lines and themain line is about 0.9– 1.3 % which corresponds to the natural abundance of 13C. The outer satellites are therefore attributed to the 13C hf lines of one nearest-neighbor C atom along
the c axis 共C1兲. The intensity ratio between the sum of theinner pair of the satellite lines and the main line is about
2.7– 3.4%. The inner satellites with a nearly isotropic splitting of ⬃0.61 mT are therefore assigned to be the 13C hflines of three nearest-neighbor C atoms in the basal plane
共C2−4兲. The anisotropy of these hf splitting is too small to be
detected with the resolution of cw EPR. Two sets 共outer andinner pairs兲 of 13C satellites with both the hf splitting and theintensity relative to the main line similar to those of the Pk2adoublets were also detected for the Pk2b doublets for the directions close to B ⬜ c 关Fig. 3共c兲兴. A better analysis of theintensity ratio was possible, confirming that these hf lines are
due to the interaction with one and three C atoms in thenearest-neighbor shell. The intensity of the inner hf line on
the low-field side in Fig. 3共c兲 is much higher than expected
for the hf interaction with three C nuclei on the Pk2b line.
This is due to the overlapping between the inner hf line of
Pk2b 共with a half hf splitting ⬃0.305 mT兲 and the outer hf
line of the Pk1 line with a half hf splitting of ⬃0.37 mT as
determined from the W-band experiments 关see Fig. 2共b兲兴.
Figures 4共a兲 and 4共b兲 show the pulsed-ENDOR spectra of
the Pk1 center measured for B 储 c and B ⬜ c, respectively. For
B ⬜ c, the Pk1 line overlaps with the low-field component of
the Pk2b doublet in the X-band EPR spectrum and therefore
ENDOR frequencies from both doublets, Pk1 and Pk2b, weredetected 关Fig. 4共b兲兴. The angular dependence of the ENDOR
lines of Pk1 with B rotating in the 共11̄00兲 plane is shown to

075201-4

PHYSICAL REVIEW B 73, 075201 共2006兲

ELECTRON PARAMAGNETIC RESONANCE AND…

FIG. 4. ENDOR spectra in P-doped 6H-SiC measured for 共a兲
B 储 c and 共b兲 B ⬜ c. The magnetic field was set on the Pk1 EPR peak.

FIG. 5. Two-pulse ESEEM time-domain spectrum of the
Pk2a / Pk2b doublets in P-doped 6H-SiC measured at 5 K for B being
40° off the c axis.

have axial symmetry and therefore can be described by thefollowing equation:16

action, which is comparable in magnitude to the nuclear Zeeman interaction, when the direction of the hf field is different
from that of the external magnetic field. In such a case, ESEEM arising from the interference between allowed and forbidden transitions, which are excited simultaneously by microwave pulses, may be observable.17
Figure 5 shows the two-pulse echo decay spectrum measured at 5 K for the magnetic field direction being 40° off
the c axis. In the measurement, the intensity of Hahn echo
共90° —␶—180° —␶—echo兲 was measured as a function of
the interpulse delay ␶ by using the microwave pulses sufficiently strong to excite all four lines of the Pk2a / Pk2b doublets simultaneously and by using nonselective detection. As
can be seen in the figure, a very strong modulation on the
two-pulse echo decay was observed. In the two-pulse ESEEM experiment, the modulation frequencies are the EN␯␣关␯ENDOR共M S = + 1 / 2兲兴
andDOR
frequencies,␯␤关␯ENDOR共M S = −1 / 2兲兴, and the combination frequencies,
␯␣ ± ␯␤ 共Ref. 18兲. After subtracting the slow decay due to thespin-relaxation processes, the time-domain spectrum 共Fig. 5兲
is converted to the frequency-domain spectrum by Fouriertransformation 共FT兲. In the FT-ESEEM spectrum shown in
Fig. 6, the first and the third frequencies 共lines 1 and 3兲
correspond to the ENDOR frequencies whereas lines 2 and 4

␯ENDOR共M S = ± 1/2兲 = 兵关共±1/2兲共A储sin2␪ + A⬜cos2␪兲− ␯共 31P兲兴2 + 关共A储 − A⬜兲sin ␪ cos ␪兴2其1/2 .
共1兲Here M S is the magnetic quantum number of the electron
spin, ␯ 共 31P兲 is the nuclear Zeeman frequency of 31P corresponding to the applied magnetic field, and the angles ␪= 0° and ␪ = 90° correspond to the directions B 储 c and B ⬜ c,respectively. The 31P hf constants obtained from the leastsquares fitting of the observed ENDOR frequencies of Pk1 byusing Eq. 共1兲 are given in Table I and are in good agreementwith the values determined for the P1 center in Refs. 2 and 5.
There is a remarkable difference in the signal intensity
and its angular variation of the Pk2 doublet measured at different frequencies. At 142 GHz, the intensity of the P2 signal
was found to be double as compared to that of P1 and wastherefore attributed to the unresolved spectra originated fromtwo P centers occupying the two quasicubic sites 共k1 , k2兲 of
6H-SiC lattice.2,4,5 In our W-band 共⬃95 GHz兲 experiments,
the intensity of the Pk2 doublet is comparable to or smaller
than that of the Pk1 signal 共see Fig. 2兲. This does not support
the assignment of the P2 doublet in Ref. 2. At high frequencies 共95 and 142 GHz兲, the change of the signal intensitywith the crystal directions is small and completely different
from the strong intensity variation of the Pk2a and Pk2b doublets measured at X-band frequency. At the directions between 40° and 60°, the separation between the Pk2a and Pk2blines in the X-band spectra is about 0.10– 0.11 mT. However,in the Pk2 lines of the W-band spectra 共the line width⬃0.1 mT兲, no indication of an overlapping of two signals
such as splitting or broadening could be detected. We therefore suspect that the Pk2a and Pk2b doublets seen in X-band
experiments are not related to two different P centers as previously suggested2,4–6,12 but may be corresponding to allowed 共⌬M S = ± 1, ⌬mI = 0, here mI is the magnetic quantum
number of the nuclear spin兲 and forbidden transitions
共⌬M S = ± 1, ⌬mI = ± 1兲 of one P center with S = 1 / 2, I = 1 / 2.
This may happen for a system with an anisotropic hf inter-

FIG. 6. Two-pulse ESEEM frequency-domain spectrum of the
Pk2a / Pk2b doublets in P-doped 6H-SiC measured at 5 K for B being
40° off the c axis.

075201-5

PHYSICAL REVIEW B 73, 075201 共2006兲

N. T. SON et al.

FIG. 7. 共Color online兲 A 2D-EPR spectrum showing the contour
plot of the modulation intensities with respect to the modulation
frequency and the magnetic field measured at the same angle as inFig. 6 共B is 40° off the c axis兲.

correspond to the difference and the sum of the frequencies 1
and 3, respectively.
In the ESEEM experiment, only one set of ENDOR frequencies was obtained from the four lines of the Pk2a / Pk2b
doublets. The sorting of the four lines of the two doublets,
Pk2a and Pk2b, to the allowed transitions 共⌬mI = 0兲 and formally forbidden transitions 共⌬mI = ± 1兲 of a center with
S = 1 / 2 and I = 1 / 2 is clearly demonstrated by using the 2DEPR technique.18 In our 2D-EPR experiment, the time-sweep
mode spectra, echo intensity versus ␶, of the Hahn echo were
measured as a function of the external magnetic-fieldstrength B at the same orientation as the above ESEEM experiment, i.e., 40° off the c axis. All four lines of the
Pk2a / Pk2b doublets were excited by strong microwave pulses
and a selective detection was used to extract the modulationfrom the particular EPR transition. For the latter purpose, theecho intensity was obtained by integrating the echo shapesampled in the range of 400 ns with a step of 4 ns. The
FT-ESEEM spectra as a function of B were obtained by converting each time domain spectrum to the frequency domain
spectrum. Figure 7 shows a contour plot of the modulation
intensities with respect to the two axes: the modulation frequency and the magnetic field. The 31P ENDOR frequenciesof 2.7 and 12.6 MHz are observed at the field positions ofboth Pk2a / Pk2b doublets. The difference of the ENDOR frequencies 9.9 MHz occurs only at the field positions of the
Pk2b doublet 共⬃349.95 and ⬃350.3 mT兲, while the sum of
the ENDOR frequencies 15.3 MHz occur only at the fieldpositions of the Pk2a doublet 共349.85 and 350.4 mT兲. Thus
the Pk2a / Pk2b doublets are clearly arising from one P centerwith S = 1 / 2, I = 1 / 2. Although being excited by the microwave pulses, the Pk1 doublet does not give any modulationand therefore gives rise to no peaks in the 2D-EPR spectrum
in Fig. 7.
The angular dependence of the modulation frequencies
with B rotating in the 共11̄00兲 plane is shown in Fig. 8. The
modulation was not observed at 0 ° 共B 储 c兲 and 90° 共B ⬜ c兲
since at these principal directions of the 31P hyperfine tensor
共C3v symmetry兲, the ⌬mI = ± 1 transitions should have zerotransition probability. In Fig. 8, the splitting of the Pk2a andPk2b doublets in the X-band cw-EPR spectra is also plotted.
The splitting of the Pk2a and Pk2b doublets corresponds very
well to the fourth 共line 4兲 and second 共line 2兲 modulation

FIG. 8. 共Color online兲 Angular dependences of ENDOR frequencies 共1 and 3兲, their difference and sum 共2 and 4兲 obtained fromESEEM 共open circles兲 and the hf splitting obtained from cw EPR of
the Pk2a and Pk2b doublets 共filled triangles兲 in 6H-SiC. The solid
curves are calculated from the obtained hf parameters using Eq. 共1兲.

frequencies, respectively. This confirms that the two doublets
Pk2a and Pk2b belong to the same P center with S = 1 / 2 andI = 1 / 2. The angular dependence of the ENDOR frequencies
共lines 1 and 3兲 were fitted using Eq. 共1兲 and the principal
values of the 31P hf tensor, A储 = 17.012 MHz and A⬜
= 6.155 MHz, were obtained. The same values of the hf constants were also obtained from the least-squares fitting of thesecond and fourth modulation frequencies, ␯␣ − ␯␤ and ␯␣+ ␯␤. It should be noted that the 31P hf tensor obtained fromthe angular dependence of the ESEEM frequencies agrees
with that obtained for the Pk2 center from the W-band cwEPR measurements. Thus the four lines of the
Pk2a / Pk2bdoublets are arising from the Pk2 center. The simulation of the angular dependences of the ESEEM frequencies
using the obtained hf coupling constants are plotted as solid
curves in Fig. 8.
The relative intensities between the Pk2a and Pk2b doubletschange with the direction of the magnetic field indicates that
their associated transitions change from allowed to forbidden
transitions and vice versa. This happens in the case when the
hf interaction is anisotropic and comparable in strength with
the nuclear Zeeman interaction. Figure 9 shows the energylevel scheme for S = 1 / 2 and I = 1 / 2 and the allowed and

FIG. 9. Energy-level scheme for a system with S = 1 / 2, I = 1 / 2
for the cases 共a兲 Aeff ⬎ 2gn␤nB ⬎ 0, and 共b兲 2gn␤nB ⬎ Aeff ⬎ 0. HereM S and mI are the magnetic quantum numbers of the electron andnuclear spins, respectively. The equations of the energy for the caseof high magnetic field and isotropic hf interaction is valid only at
the principal directions of the hf tensor 共see text for explanation兲.

075201-6

PHYSICAL REVIEW B 73, 075201 共2006兲

ELECTRON PARAMAGNETIC RESONANCE AND…

FIG. 10. 共Color online兲 The angular dependences of the line
positions of P centers in 6H-SiC measured at X-band frequency
共9.7558 GHz兲 with B rotating in the 共11̄00兲 plane. The curves represent the calculated line positions for all possible EPR transitionsof Pk1 and Pk2 centers using the parameters in Table I and the spin
Hamiltonian Eq. 共2兲. For the Pk2 center, all the EPR transitions
become allowed or partly allowed and can be detected at most of
crystal directions. For the Pk1 center, the transitions 共1 ↔ 4兲 and共2 ↔ 3兲 corresponding to the outside lines 共dashed curves兲 are notdetectable.

forbidden transitions depending on the magnitude of the hf
coupling constant and the nuclear Zeeman interaction. The
levels are split by the electron Zeeman interaction g␤eBM S,
the hf term AeffM SmI and the nuclear Zeeman term −gn␤nBmI
共Aeff ⬎ 0, gn ⬎ 0兲. Here␤e and ␤n are the Bohr magneton andnuclear magneton, respectively. It should be noticed that thesimple equation 共g␤eBM S + AeffM SmI − gn␤nBmI兲 for the caseof high magnetic field and isotropic hf interaction is only
valid at the principal directions of the hf tensor of Pk2 and isused for an easy understanding of the energy-level scheme.
For an arbitrary direction of the magnetic field, the energy
levels are described by more complicated terms.19 Figure
9共a兲 shows the case for Aeff ⬎ 2gn␤nB. The allowed transitions 1 ↔ 4 and 2 ↔ 3 共indicated as thick arrows兲 are determined by the selection rule ⌬M S = ± 1 and ⌬mI = 0. For Aeff
⬍ 2gn␤nB, the transitions 2 ↔ 4 and 1 ↔ 3 become allowed
as shown in Fig. 9共b兲. When the anisotropic hf interaction iscomparable to the nuclear Zeeman interaction, the selection
rules are relaxed and all four transitions may be detectable.
The intensity of the forbidden transitions is determined byboth the relative magnitude between the anisotropic hf coupling constants and gn␤nB and the relative direction between
the anisotropic hf and B.
The angular dependences of the Pk2 doublet 共Pk2a and Pk2b
doublets兲 in 6H-SiC measured with B rotating in the 共11̄00兲
plane are plotted as open circles in Fig. 10. The spin Hamiltonian parameters g and A of 31P, both having C3v symmetry,were determined by fitting the observed line positions ofX-band measurements to the spin HamiltonianH = ␤eB · g · S + S · A · I − gn␤nB · I,
31

共2兲

where S = 1 / 2 and I = 1 / 2, and gn = 2.2632 for P. The leastsquares fitting of the line positions and the calculations of the

FIG. 11. 共Color online兲 Angular dependence of the relative EPR
intensity of all the transitions of the Pk1 and Pk2 centers in 6H-SiC calculated at X-band frequency 共9.7558 GHz兲. At W-band frequencies, the intensity dependence of both the Pk1 and Pk2 centers issimilar to that of the Pk1 center at X-band frequency.

transition probabilities to be described later were carried out
by computer program EPR.FOR using numerical diagonalization of the spin-Hamiltonian matrix. The principal g and A
values of the Pk2 centers obtained are given in Table I. The
analysis of the angular dependence of the line positions measured at W-band frequency gives the same principal g values
and similar 31P hf coupling constants for Pk2. Our g values
are about 0.0003 smaller than that reported in Refs. 2 and 5
and are close to the values given in Ref. 6. In our experiments, the magnetic field was calibrated by measuring simultaneously the signals arising from the substitutional P in Si
共g = 1.9985, isotropic兲 in P-doped Si which was co-mountedwith the P-doped SiC sample. The simulated angular dependences of these doublets using the obtained values and thespin Hamiltonian Eq. 共2兲 are plotted as solid and dashedcurves in Fig. 10. The angular dependences of the relative
intensity of all the four EPR transitions are calculated andshown in Fig. 11. If we assume that the Pk2a and Pk2b doublets were arising from two different centers and obtain the
spin-Hamiltonian parameters from the line positions observed for the limited range of the orientations, the obtained
parameters 共g储 = 2.0039, g⬜ = 2.0025, A储 = 0.615 mT, A⬜
= 0.43 mT for Pk2a and g储 = 2.0038, g⬜ = 2.0025, A储= 0.396 mT, A⬜ = 0.22 mT for Pk2b兲 correspond well to thoseof dPc1 共g储 = 2.0037, g⬜ = 2.0025, A储 = 0.62 mT, A⬜
= 0.38 mT兲 and dPc2 共g储 = 2.0037, g⬜ = 2.0024, A储 = 0.48 mT,
A⬜ = 0.19 mT兲, respectively.6
From Figs. 10 and 11, it is clear that at both X-band andW-band frequencies and for all crystal directions the Pk1 center follows the energy-level scheme in Fig. 9共b兲 and only two
allowed transitions 2 ↔ 4 and 1 ↔ 3 can be detected. The two
forbidden transitions 1 ↔ 4 and 2 ↔ 3 have nearly zero transition probability and cannot be observed 共dashed curves inFig. 10兲. Therefore the hyperfine patterns of the Pk1 spectra
at X band and W band are similar. The situation of the Pk2
center is, however, different. In the case of the Pk2 center at
X-band frequency, the 31P hf interaction is larger than
2gn␤nB for the crystal directions between 0° and⬃50°, andtherefore splitting follows the scheme in Fig. 9共a兲 in which
the 1 ↔ 4 and 2 ↔ 3 transitions are allowed. Between ⬃50°

075201-7

PHYSICAL REVIEW B 73, 075201 共2006兲

N. T. SON et al.

FIG. 13. 共Color online兲 Angular dependence of the line positions of the P center in 3C-SiC measured at 共a兲 9.7592 GHz and 共b兲
94.887 GHz with B rotating in the 共01̄1兲 plane. The curves represent the calculated line positions using the parameters in Table I.
The angles 0° and 90° corresponding to the magnetic-field directions B 储 关100兴 and B 储 关011兴, respectively.

FIG. 12. X-band EPR spectra in P-doped 3C-SiC CVD layers
measured at 8 K for 共a兲 B 储 关100兴 and 共b兲 B 储 关011兴. The inset shows
the spectrum in 共b兲 measured with a four-time-smaller field modulation 共0.005 mT兲. The microwave power is ⬃0.006 mW. 共c兲, and共d兲 The corresponding spectra measured at W-band frequency,
respectively.

and 90°, the 31P hf interaction is smaller than 2gn␤nB and theenergy levels are described by the scheme in Fig. 9共b兲 inwhich the 2 ↔ 4 and 1 ↔ 3 transitions become allowed. At
directions between 20° and 70°, all four EPR transitions canbe detected 共Fig. 11兲. The analysis of the angular dependenceof the Pk2 center at W-band frequency shows that at higher
magnetic fields 共nearly ten times compared to that at X-band
frequency兲, the hf term is much smaller than 2gn␤nB at all
directions. The system therefore follows the energy-level
scheme in Fig.9共b兲 and only the transitions 2 ↔ 4 and 1 ↔ 3
can be detected. The calculations also show that the angularvariation of the intensity of the Pk2 signal at W-band frequency is similar to that of the Pk1 center.
2. 3C-SiC

Figures 12共a兲 and 12共b兲 show the X-band EPR spectra
observed in a P-doped 3C-SiC CVD freestanding film at 8 K
for B 储 关100兴 and B 储 关011兴, respectively. For B 储 关100兴, a spectrum with two lines was detected. These two lines coincide at
B 储 关111兴 and move away from each other when rotating tothe 关011兴 direction. At B 储 关011兴, these lines almost overlap
with each other and can be slightly resolved when using low
microwave power 共0.006 mW兲 and low-field modulation
共0.005 mT兲 关see the inset in Fig. 12共b兲兴. The corresponding
spectra measured at W-band frequency are shown in Figs.
12共c兲 and 12共d兲. From X-band to W-band frequency, thesplitting between the two lines at B 储 关100兴 increases nearly
ten times, indicating that the separation between the twolines is not due to the hf splitting but due to the difference inthe g value. The angular dependence of the line positions
with B rotating in the 共01̄1兲 plane was measured at bothX-band and W-band frequencies and shown in Figs. 13共a兲and 13共b兲, respectively. The center has two magnetically distinguishable sites both at B 储 关100兴 and at B 储 关011兴, and only
one at B 储 关111兴. From the pattern of the rotational plots
shown in Fig. 13, it is determined that the symmetry of thecenter is D2d. Thus the center has three sites which are axially symmetric about 关100兴, 关010兴, and 关001兴, respectively.
The line positions of two sites of which the symmetry axesare 关010兴 and 关001兴, respectively are identical in the rotation
with B ⬜ 关01̄1兴. From the least-squares fitting of the line positions observed, the same principal values, g储 = 2.0051, g⬜
= 2.0046, of the g tensor 共with D2d symmetry兲 were obtained
for both rotations. The simulations of the line positions using
the obtained parameters are plotted as solid curves in Fig. 13.
In order to extract weak 31P hyperfine interaction hidden
underneath the linewidth, we performed pulsed-ENDOR experiments. Figures 14共a兲 and 14共c兲 show the pulsed-ENDOR
spectra for B 储 关100兴 and B 储 关011兴 with the magnetic field
fixed at the EPR line position of the site which is axiallysymmetric about 关100兴. For both directions, two ENDOR
lines centered at ␯共 31P兲 were detected. For B 储 关100兴, theseparation of the two ENDOR lines was the same as Fig.
14共c兲 when the magnetic field was fixed at the high-field
EPR line arising from the two sites which are axially symmetric about 关010兴 and 关001兴, respectively. The angular dependence of the ENDOR lines in the 共01̄1兲 plane shown in
Fig. 14共b兲 indicates that the 31P hf tensor is axially symmetric about the 具100典 direction. From the least-squares fitting of
the angular dependence of the ENDOR frequencies to Eq.
共1兲, we obtain the principal values of the hf tensor A储= 0.53 MHz and A⬜ = −0.13 MHz. The 31P hf tensor has also
D2d symmetry. The principal values are very small and thehyperfine splitting changes the sign when passing the 具111典

075201-8

PHYSICAL REVIEW B 73, 075201 共2006兲

ELECTRON PARAMAGNETIC RESONANCE AND…

FIG. 16. 共Color online兲 X-band echo-detected EPR spectra of Pk
in 4H-SiC measured at 6 K for B along and perpendicular to the caxis showing the hf structure of 31P. The 13C hf lines of one C atom
is also observed and shown in ⫻10 scale parts of the spectra.

FIG. 14. 共Color online兲 ENDOR spectra and the angular dependence of ENDOR frequencies of the P center in 3C-SiC. The angles
␪ = 0° and ␪ = 90° correspond to the directions B 储 关100兴 andB 储 关011兴, respectively. The solid curves in 共b兲 represent the fit using
the hf parameters in Table I.

direction. Since the pulsed-ENDOR measurements confirm
that the center is related to P, the center is labeled the P
center.
3. 4H-SiC

In 4H-SiC layers doped with P during CVD growth, an
EPR doublet was detected. The X-band spectra measured at
8 K for B 储 c and B 储 c are shown in Figs. 15共a兲 and 15共b兲,
respectively. Although there are two inequivalent silicon sites
共h and k兲 in 4H-SiC, only one spectrum was detected in bothX-band and W-band experiments. We label the spectrum as
Pk and the assignment of the center to P at the k site will beshown later. For B ⬜ c or angles between 60° and 90° a sat-

FIG. 15. 共Color online兲 EPR spectra in P-doped 4H-SiC freestanding layers measured at 8 K for 共a兲 B 储 c and 共b兲 B ⬜ c. The
isotropic broad signal at ⬃347.85 mT is not related to the Pk center.
The 13C hf line of one nearest-neighbor C atom could be detected
for the high-field line of the 31P doublet.

ellite line was observed on the high-field side of the Pk line关see the inset in Fig. 15共b兲兴. Its intensity ratio with the mainline is about 0.5–0.6 %, indicating that the structure is due tothe high-field component of the 13C hf structure of the C
atom along the c axis in the nearest-neighbor shell. Similar tothe hf line of P centers in 6H-SiC, this hf splitting is also
isotropic. The low-field component of the hf structure could
not be detected due to overlapping with a broad and isotropic
signal at ⬃347.8 mT 关see Fig. 15共b兲兴. For angles close to thec axis, the Pk signal becomes weaker and the 13C hf structure
could not be observed. In W-band EPR experiments, thebroad signal is well separated from the P signal, but we could
not detect the 13C hf lines as clear as in X-band experiments.
In Fig. 16, echo-detected EPR spectra of Pk in 4H-SiC
measured for B 储 c and B ⬜ c are shown. In the echo-detected
EPR spectra the broad signal was effectively eliminated byutilizing the difference in the phase memory time which is
the time constant of the two-pulse echo decay. As can beseen in the ⫻10 scale spectra in Fig. 16, weak hf lines similar to that in cw-EPR spectra could be detected. Within theexperimental error, the hf splitting is isotropic共⬃0.72 mT兲.
The intensity ratio between the hf line and the main line isalso about 0.5–0.6 %. A part of the simulated spectrum including the hf interaction with one 13C nucleus plotted as asmooth curve at the high-field side of the Pk line at B ⬜ cshows an excellent fit to the experimental data 共the grey
curve underneath兲. This confirms that the satellite lines are
due to the 13C hf interaction with one nearest-neighbor C
atom, which we assign to be the nearest C atom along the caxis. The hf interaction with three nearest-neighbor C atoms
in plane was not resolvable from the main line.
From the angular dependence of the line positions shownin Fig. 17, it is determined that the symmetry of the Pk centeris C3v. In Fig. 17, each open circle represents an EPR line
position measured in the X-band spectra and the solid curves
are the simulated angular dependence using the EPR parameters 共see Table I兲 obtained by fitting of the observed line
positions to the spin Hamiltonian Eq. 共2兲. The analysis showsthat at both X-band and W-band frequencies, the nuclear Zeeman interaction is larger than the hf interaction and the splitting follows the scheme in Fig. 9共b兲. Only the transitions
2 ↔ 4 and 1 ↔ 3 corresponding to the inner doublet can bedetected. The calculations of the relative intensity show that

075201-9

PHYSICAL REVIEW B 73, 075201 共2006兲

N. T. SON et al.

TABLE II. The hf parameters a and b and the corresponding s
and p spin densities of the unpaired electron located on the P atomand their nearest-neighbor C atoms. The anisotropic part of 13C hf
interaction which could not be resolved by cw-EPR measurements
was assumed to be 0. The total spin density for C2-4 is the triplex
value of the sum 共s + p兲.
Center

FIG. 17. 共Color online兲 Angular dependence of the Pk center in
4H-SiC measured at 9.75048 GHz with B rotating in the 共11̄00兲
plane. The curves represent the calculated line positions of all thefour possible EPR transitions of the Pk center 共S = 1 / 2 and I = 1 / 2兲using the parameters in Table I and the spin Hamiltonian of Eq. 共2兲.
The dashed curves represent the transitions with the intensity close
to zero and cannot be detected. The relative intensity of the transitions is similar to that of the Pk1 center in 6H-SiC shown in Fig. 11.

the transitions 1 ↔ 4 and 2 ↔ 3 共dashed curves in Fig. 17兲 areforbidden and could not be detected in our X-band andW-band experiments.
4. LCAO analysis

Since the hf interactions of 31P and 13C have either axial
symmetry or isotropic we can estimate the isotropic and anisotropic parts of the hf tensor and hence the corresponding s
and p spin densities using one-electron linear-combinationof-atomic-orbital 共LCAO兲 approximation. The isotropic partis the trace of tensor A and is related to the spin density inthe s orbital 共␩2␣2兲 by the expressiona = 1/3共A储 + 2A⬜兲 = 共2/3兲␮0g␤egn␤n␩2␣2 .

共3兲

The anisotropic part is the traceless part of an axial tensor
with principal values 共2b , −b , −b兲, where b is expressed via
the spin density in the p orbital 共␩2␤2兲 asb = 共1/3兲共A储 − A⬜兲 = 共2/5兲共␮0/4␲兲g␤egn␤n␩2␤2具r−3典p .
共4兲Here, ␩2 is the spin density on the corresponding atom andthe contribution of the d orbital was not considered 共␣2+ ␤2 = 1兲. The obtained hf values a and b for P centers in 3C-,
4H-, and 6H-SiC are given in Table II. The spin densities on
the s and p orbitals then can be calculated using atomic
constants, 兩␺共0兲兩2 and 具r−3典p, given by Morton and Preston.20
The obtained spin densities at the P atom and the nearestneighboring C atom共s兲 are also shown in Table II.
B. Temperature dependence of signal intensity and spin-lattice
relaxation time

Below we show that the P centers in 3C-SiC, Pk in
4H-SiC, and Pk1 and Pk2 in 6H-SiC exhibit features characteristic of having a low-lying excited state. The energy sepa-

P 共3C兲
31
P
Pk 共4H兲
31
P
C1
Pk1 共6H兲
31
PC1
Pk2 共6H兲
31
P
C1
C2-4

a 共MHz兲b 共MHz兲

s 共%兲

p 共%兲

Total 共%兲

0.09

0.22

0.0007

0.06

0.06

6.67
20.18

0.78
0

0.05
0.53

0.21
0

0.26
0.53

1.492
20.7

0.838
0

0.01
0.55

0.23
0

0.24
0.55

9.774
30.6
17.1

3.169
0
0

0.07
0.81
0.45

0.86
0
0

0.93
0.81
1.35

ration between the ground state and the excited state has
been estimated from the temperature dependence of the cwEPR signal intensity and of the spin-lattice relaxation time.
Later, after assigning the P centers to be the shallow donors,
the splitting is ascribed to valley-orbit splitting.
In our studies of the temperature dependence of the cwEPR signals, the measurements were performed at W-band
frequency using very low microwave powers to achieve thestability in coupling of microwave in the cavity. The temperature dependence of the EPR signal of the P center in
3C-SiC, Pk and Pk1 in 4H-, and 6H-SiC is very similar as
can be seen in Fig. 18. The signal gradually decreases withincreasing temperature and disappears at temperatures above
30– 34 K. The Pk2 doublet in 6H-SiC behaves differently
and can be detected only at temperatures below 12 K 关seeFig. 18共c兲兴.
Here, we consider a simple model consisting of only two
states, the ground state and the excited state with the energy
difference ⌬E, by neglecting higher excited states and the
conduction-band states. The temperature dependence of the
EPR signal intensity of the ground state is given for the caseof ⌬E which is much larger than the Zeeman splitting ␦,
I0共T兲 ⬀ n0共T兲f共T兲.

共5兲

The temperature dependence of the population of the groundstate due to thermal excitation to the excited state isn0共T兲 = N关g0/共g0 + g1兲 exp共− ⌬E/kBT兲兴,

共6兲

where N is the concentration of the EPR center, g0 and g1 are
the degeneracy without including electron spin of the groundstate and excited state, respectively, and kB is the Boltzmann
constant. The fraction excess population of the lower level ofthe electron Zeeman levels is075201-10

PHYSICAL REVIEW B 73, 075201 共2006兲

ELECTRON PARAMAGNETIC RESONANCE AND…

FIG. 18. 共Color online兲 Temperature dependence of the P centers in 共a兲 3C-, 共b兲 4H-, and 共c兲
6H-SiC. EPR measurements were
performed at W-band for 共a兲
B 储 具100典 and 共b兲, 共c兲 B ⬜ c.

f共T兲 = 关1 − exp共− ␦/kBT兲兴/关1 + exp共− ␦/kBT兲兴 = tanh共␦/2kBT兲,
共7兲
where ␦ ⬃ 0.39 meV at the W-band frequency. The calibrated
intensities of the P center in 3C-SiC, Pk in 4H-SiC and Pk1,
Pk2 centers in 6H-SiC are plotted as a function of the reciprocal temperature in Fig. 19. The fits to the EPR intensities
using Eqs. 共5兲–共7兲 are also shown as solid curves in Fig. 19.
The energy separation ⌬E determined for the P centers are
5.4 meV for 3C-SiC, 4.8 meV for Pk in 4H-SiC, 4.2 meV,and 7.0 meV for Pk1 and Pk2 in 6H-SiC, respectively.
The energy separation between the ground state and theexcited state can also be determined from the temperaturedependence of the spin-lattice relaxation time T1 in the temperature range where T1 is governed by the Orbach process
which is the resonant two-phonon process involving an actual excited energy level lying at ⌬E above the studied
level.21 In this process, the temperature dependence of T1 isdescribed by the relation
1/T1 ⬀ exp共− ⌬E/kBT兲.

共8兲

For measuring T1 we performed inversion-recovery experiments in which a pulse sequence 共180° −t − 90° −␶ − 180° −␶

FIG. 19. 共Color online兲 Calibrated EPR intensity of the P signals
in 3C-, 4H-, and 6H-SiC as a function of reciprocal temperature.
The deduced energy separations between the ground and excitedstates of the P-related centers are indicated. The solid curves represent the fits using Eqs. 共5兲–共7兲. The data were obtained from
W-band experiments.

− echo兲 with fixed ␶ and scanned t was used. The first pulse
creates a nonequilibrium population. The Hahn echo generated by the second and third pulses monitors the recovery to
the thermal equilibrium population.
Below 10 K, the inversion-recovery curves of the
P-related centers in 4H- and 6H-SiC could be well fitted bya single exponential function. The temperature dependenceof T1 measured for B ⬜ c is shown in Fig. 20 for Pk in 4H-SiC and for Pk1 and Pk2 in 6H-SiC. As can be seen in the
figure, the logarithm of 1 / T1 in both polytypes is linear to thereciprocal of the temperature with the slope determined byan energy separation ⌬E. The obtained ⌬E values are
4.2 meV for Pk in 4H-SiC, 4.3 meV and 6.0 meV for Pk1 and
Pk2 in 6H-SiC, respectively. These values are in good agreement with those determined from the temperature dependence of the cw-EPR signal intensity.
It should be noted that ⌬E is obtained from the measurement of T1 in the low-temperature region where the decreaseof the signal intensity due to the population onto the excitedstate is not significant. One of the main sources of errors in
the determination of the energy separation via the temperature dependence of T1 comes from the measurement of temperature. In the studied temperature range 5 – 10 K, a small
error in measuring temperature, e.g., 0.5– 1 K, would result

FIG. 20. 共Color online兲 The dependence of the spin-lattice relaxation time T1 on the reciprocal temperature of P centers in 4H-SiC and 6H-SiC. The solid lines represent the fits to experimental
data. The corresponding energy separations between the ground andexcited state of P centers are indicated.

075201-11

PHYSICAL REVIEW B 73, 075201 共2006兲

N. T. SON et al.

in an error of ⬃0.6– 1.0 meV in ⌬E. In cw-EPR experiments, the ⌬E values of the P center in 3C-SiC, Pk in 4H-SiC, and Pk1 in 6H-SiC were determined in a larger temperature range 共6 – 30 K兲 and were therefore less sensitive tothe temperature error. In our W-band experiments, thesample and the cavity are in contact with a thick copper
holder, where the temperature sensor is attached, and thetemperature can be kept stable within 0.05 K during themeasurement. The temperature stability in our X-band spectrometer is also similar. However, the temperature sensor
mounted outside of the resonator for the pulse experiments
and its reading could be slightly different from the real temperature of the sample which is in a small quartz tube inside
the resonator. We expect that the error in measuring temperature can be ⬃0.5 K and less than 1 K in both X-band andW-band experiments.
In the T1 measurements of P in 3C-SiC, the obtained inversion recovery curves at the studied temperatures could not
be fitted to a single exponential function. For successful estimation of ⌬E from measurements of T1, P-doped 3C-SiC
samples with higher quality and lower doping may be required 共our P-doped 3C-SiC CVD layers were grown in theconditions optimized for 4H- and 6H-SiC but not for the 3C
polytype兲.
IV. CALCULATIONS
A. Methodology

Ab initio supercell calculations were carried out to investigate the shallow phosphorus donor at the Si site in
4H-SiC. The donor wave function can spread out large distance from the donor atom in semiconductors. By using theeffective-mass state theory the radii of the donor wave function associated with the ground state can be estimated to be
11 Å.22 We have used a 576-atom supercell 共6 ⫻ 6 ⫻ 2 multiplication of the primitive cell兲 to model the 4H-SiC crystal
where the average diameter of this supercell is somewhat
bigger than 20 Å. 共Here, we note that 6 ⫻ 6 ⫻ 2 multiplication of the 6H-SiC primitive cell would result in a 864-atomsupercell.兲 In a small supercell the donor wave function canstrongly overlap with its periodic images. This is manifestedby the accumulation of the localization of donor wave function at the edge of the supercell. We have inspected the localization of the donor wave function at the edge of the 576atom supercell and we have not found any peaks. Therefore
we believe that the calculated spin distribution in this supercell can be qualitatively compared to the experimental values. 共We note that the donor wave functions of the excitedstates may spread out at larger distances, therefore the inaccuracy of the calculation could be larger for the excitedstates.兲 The effective-mass donor states are split off from theconduction-band states at the edge of the conduction bands.
The minimum of the conduction-band edge 共CBM兲 of
4H-SiC is at the M point.23 In order to study the shallow
donors in 4H-SiC, the donor wave functions should be calculated at the M point. In the above-mentioned 576-atomsupercell calculations the M-point is folded into the ⌫ pointof the reduced Brillouin zone of this large supercell. Sincethe ⌫-point sampling provides convergent charge density inan 576-atom supercell24 we have used this single k point onlyin the calculations.
The calculation on defects in a 576-atom supercell 共evenwith a single k point兲 at ab initio level is computationallyalmost prohibitive but it is possible by using supercomputers.
We have used the parallel version of the code SIESTA25 toaccomplish this task. This program implements density functional theory 共DFT兲 combined with the pseudopotential approximation to eliminate the core electrons, and uses a basis
set consisting of numerical orbitals centered on the atoms. In
the calculations of PSi defects Troullier-Martins pseudopotentials were employed.26 The program requires the use of agrid to compute some of the contributions to the matrix elements and also for performing the Fourier transform toevaluate the Hartree potential and energy by solving the
Poisson’s equation in reciprocal space. We have used a gridfine enough to represent plane waves with kinetic energy
cutoff up to 90 Ry. A high quality basis set was used, consisting of double-␨ plus polarization functions for the valence
electrons. These calculations have been carried out using the
Ceperley-Alder functional27 as parametrized by Perdew and
Zunger.28 We have used spin polarized calculation but it was
beyond of our possibility to take the spin-orbit interaction
into account. We have used the scissor operator to correct the“band-gap” error of this method. In order to optimize thegeometry of the donors the forces acting on the atoms haveto be calculated which is computationally demanding. To accelerate this process we have first optimized the defects in asmaller 96-atom supercell and insert the resulting geometry
into the large 576-atom supercell. Then, those atoms wereagain post-relaxed in the 576-atom supercell until the forceswere below 0.04 eV/ Å. Since we have used pseudopotentials to treat core electrons a direct calculation of hyperfine
constants of the paramagnetic defect is beyond the possibility. However, the spin localization on P and nearestneighboring C atoms can be calculated by this method andcompared to the values derived from experiments.
B. Results

We have investigated P occupying the Si site at both hexagonal 共h兲 and cubic 共k兲 lattice sites in 4H-SiC. We havefound that the relaxation effect is relevant in the first twoneighbor shells around P atom: the distance between the firstneighbor C atoms and P atom is shortened to 1.82– 1.83 Å
while the bond length between the second neighbor Si atoms
and first neighbor C atoms is stretched to 1.91 Å. In the outershells the bond lengths are practically identical to those in
the perfect crystal 共1.88 Å兲. We do not find significant difference in the geometry of PSi共k兲 or PSi共h兲 defects: PSi共k兲 issomewhat more symmetric possessing bond length of 1.82 Å
between P and every neighbor C atom while PSi共h兲 has
0.01 Å longer P-C bond along the c axis. The calculateddonor level at k site 共Pk兲 is at EC-17 meV with A1 symmetry
where EC is the conduction-band edge. 共We note here that we
obtained this symmetry without applying the spin-orbit coupling.兲 The calculated first excited E state is lying 8 meV
higher in energy. The situation is different at the h site 共Ph兲:
the ground state has E symmetry with the level at

075201-12

PHYSICAL REVIEW B 73, 075201 共2006兲

ELECTRON PARAMAGNETIC RESONANCE AND…

EC-19 meV while the first excited A1 state is lying above
only with 4 meV. We have to note here that the LDA KohnSham levels are not the ionization energies. One can have areasonable value for the ionization energies by using the socalled ⌬SCF method, i.e., the energy difference between theneutral state and the ionized 共single positively charged兲 state.
By using this method we have obtained the vertical ionization energies at EC-76 meV/ 56 meV for the k / h sites, respectively. These values are close to the ionization energy of
60.7 meV for P at the k site determined recently from fitting
the donor-acceptor luminescence due to Al-P pairs.29 As acheck, we have calculated the vertical ionization energies of
N donors. The obtained values at EC-142/ 44 meV should becompared to the recently measured ones at ⬃EC-125 meV/ 61 meV 共Refs. 29 and 30兲 at k / h sites, respectively. The N donors have a nondegenerate ground state following by the E state at both sites in agreement with theexperiment. We note that these values are also close to therecently reported thermal ionization energies calculated in asmaller supercell.31
Based on these results we can say that both Pk and Ph areshallower than the NC共k兲 donor in 4H-SiC. For Ph the difference between energies of the E and A1 states are very small.
We could not check whether the order of the levels wouldchange in a bigger supercell. Nevertheless, we could look at
the trend by using a smaller supercell. In a 96-atom supercell
共its average diameter is about 5 Å兲 the A1 state of Ph is
deeper by 101 meV than the E state. 共The level of the A1state is at EC-128 meV in the 96-atom supercell because of
the over localization of the donor state due to the relatively
small size of the supercell.兲 This means that by increasing
the supercell size the E state becomes more stable than the
A1 state for Ph. The difference between the A1 and E states
also slightly decreases for Pk but the former one remains theground state in the large supercell. We incline to claim thatthe ground state of Pk is nondegenerate while the groundstate of Ph has E symmetry. Still, the energy difference issmall for both sites. Therefore we have calculated the localization and the corresponding s , p , d character of the donor
wave function for both the A1 and E states. The results are
summarized in Table III. As can be seen in Table III, the dcomponent is relatively big on the P atom. It is not unexpected because the d orbitals of the silicon atoms contributesignificantly to the lowest conduction-band state.
V. DISCUSSION

In all the studied 3C-, 4H-, and 6H-SiC samples, only the
P-related EPR centers were observed whereas the EPR signalof the N donors was not detectable. In our P-doped 4H- and6H-SiC layers, the concentration of P measured by SIMS
共Ref. 13兲 correlates well with the donor concentration determined by current-versus-voltage 共CV兲 measurements, indicating that P introduced into the layer during CVD growthacts as shallow donors. This is also supported by the observation of strong PL emissions of the P-bound excitons in our
4H- and 6H-SiC CVD layers. The PL lines in 3C-SiC
samples are broad and it is difficult to separate the lines
belonging to N-bound excitons and/or to P-bound excitons.

TABLE III. The localization and s, p, d character of the donor
wave function at different sites in 4H-SiC obtained by the ab initio
supercell calculations. The total spin density for C2-4 is the triplex
value of the sum 共s + p + d兲.
Center/symmetry
Pk / A1
P
C1
C2-4
Pk / EP
C1
C2-4
Ph / EP
C1
C2-4
Ph / A1
P
C1
C2-4

s 共%兲

p 共%兲

d 共%兲

Total 共%兲

0.05
0.88
0.00

0.70
0.01
0.00

0.46
0.00
0.00

1.21
0.89
0.00

0.00
0.00
0.02

0.16
0.00
0.07

0.37
0.00
0.00

0.53
0.00
0.27

0.00
0.00
0.70

0.31
0.00
0.03

0.80
0.02
0.00

1.11
0.02
2.19

0.16
0.07
0.14

0.21
0.16
0.02

0.75
0.00
0.00

1.12
0.23
0.48

The 3C-SiC layers are more conducting compared to the 4Hand 6H-SiC samples. Since the EPR signal of the N donor
was not detected, we believe that P is responsible for the
conductivity of the 3C-SiC layers.
The observation of the 31P hyperfine interaction provided
evidence that P is involved in the centers. The Pk center in
4H-SiC and the Pk1 and Pk2 centers in 6H-SiC exhibit the31
P hyperfine structure in their cw-EPR spectra. The involvement of 31P in the Pk1 and Pk2 centers in 6H-SiC was previously identified by ENDOR,2,5 and also confirmed by ourpulsed-ENDOR and ESEEM experiments. The involvementof 31P in the P center in 3C-SiC is confirmed by pulsedENDOR.
The detection of the 13C satellite lines in the EPR spectrain 4H- and 6H-SiC elucidates that carbon atom共s兲 is/are thenearest neighbor共s兲 and P substitutes for Si. The low concentration of both intrinsic defects and common impurities suchas N in our CVD layers enabled us to observe weak satellite
lines arising from the 13C hf interaction with nearestneighboring C atom共s兲. From the covalent radii 共0.77 Å forC, 1.11 Å for Si, and 1.06 Å for P兲, it is natural to assume
that P resides at the Si site. In previous studies of P in
neutron-transmuted 6H-SiC,1–6 P was assumed to occupy the
Si site since the neutron irradiation transmutes 30Si to 31P onsite. Therefore the P1 / P2 共Pk1 / Pk2 in our notation兲 and the
Pa / Pb centers2,5 were all assigned to the shallow P donors at
the Si site although no hf structure due to the interaction withneighboring C atoms was observed. However, recent theoretical studies9 pointed out that P doped by neutron transmutation is incorporated favorably into the carbon sublatticethrough kinetic effects during the high-temperature annealing
process which is required for the activation of the P donors.

075201-13

PHYSICAL REVIEW B 73, 075201 共2006兲

N. T. SON et al.

The Pa / Pb centers are assigned to P at the C site or a pair of
P at the C site and a carbon antisite 共CSi兲, PCCSi.9 In our
samples of 6H-SiC doped with P during CVD growth, only
the Pk1 / Pk2 spectra were detected and the Pa / Pb centers were
not observed. In 3C-SiC, no direct evidence, such as the hf
structure due to the interaction with the nearest neighbors,
indicating the site occupation of the P center was observed.
However, it is reasonable to expect that the introduction of P
into 3C-SiC lattice during CVD growth is similar to that into
4H- and 6H-SiC and P also substitutes for Si.
The observed EPR centers are not likely to be a pair of P
and a VC, PSi-VC. In our samples, we could not detect any−兲 and the carbon vaEPR signals of the silicon vacancy 共VSi+
cancy 共VC兲, which can be seen sometimes in substrates
grown by high-temperature CVD or by sublimation technique. The near-infrared PL of the silicon vacancy32 was also
not detected. We therefore believe that in our CVD films theconcentration of vacancies must be a few orders of magnitude less than that of P. This is also supported by recent firstprinciples calculations of P doping in 4H-SiC,31 in which theconcentration of complexes between P and vacancies is predicted to be four to five orders of magnitude less than the
total P concentration in equilibrium. The involvement of VC
in the P-related dPh, dPc1, and dPc2 centers 共or Pk1 and Pk2
centers in our notation兲 in 6H-SiC as previously suggested6
is therefore unlikely. The model of PSi-VC pairs was based on
the observation of satellite lines which were attributed to 29Si
hf of two equivalent neighboring Si atoms.6 The splitting ofthese satellite lines corresponds to the 13C hf lines of one
neighboring carbon atom in our spectra. In Ref. 6, the intensity ratio between the satellites and the main line was obtained by fitting the line shape with assuming the overlapping of three spectra of N, dPh, and dPc2 centers. It is likelythat their determination of the intensity of very weak satellite
lines were hampered by the presence of N 共⬃1.2⫻ 1016 cm−3兲 and possibly other intrinsic defects in the
P-doped samples by neutron transmutation using the neutron
dose as high as 1 ⫻ 1020 cm−2. Another argument against themodel of the PSi-VC pairs is that only the centers with C3v
symmetry which matches the vacancy at the nearest carbonsite along the c axis were detected and no C1h-symmetriccenters which should be expected for the configuration withthe vacancy at the nearest carbon site of one of three basal
carbon atoms could be seen.
These EPR centers exhibit the temperature dependence ofthe signal intensities due to the presence of a low-lying excited state which is attributed to the valley-orbit splitting. We
have estimated the valley-orbit splitting also from the temperature dependence of the spin lattice relaxation time.33
There are three equivalent conduction-band minima 共valleys兲
in 3C-SiC in which the conduction-band minimum is at the
X point of the Brillouin zone. In the effective-mass approximation, the hydrogen-atom-like 1s ground state of the shallow donors has threefold degeneracy due to the three
conduction-band minima. Under the Td symmetry of the donor site, the 1s ground state either remains threefold degenerate with a triplet state T2 or splits into a singlet state A1 anda doublet state E. The symmetry of the P center in 3C-SiC islowered to D2d. A T2 state under the Td symmetry gives asinglet state B2 and a doublet E. An E state under theTdsymmetry splits into a singlet state B1 and a singlet state
A1. In 4H-SiC in which the conduction-band minimum islocated at the M point, the threefold degeneracy of the 1s
ground state is split into a singlet state A1 and a doublet state
E under the C3v symmetry of the donor site. In 6H-SiC in
which the conduction-band minimum lies along the M-Lline, the sixfold degeneracy of the 1s ground states splits into
two singlets A1 and two doublets E under the C3v symmetryof the donor site. While the other hydrogenlike excited states
共2p0 , 2s , 2p± , . . . 兲 lie well above these 1s states, the separation between the 1s states 共valley-orbit splitting兲 is rather
small. Thus the intensity of the EPR signal arising from thedonor electrons bound in the ground state of the valley-orbit
splittingdecreases with the increase of the temperature according to the thermally excited population on the low-lying
excited state. In the PL studies of P-doped 6H-SiC,15 a feature associated with the Phc no-phonon line was assigned tobe related to the valley-orbit level lying at 5.2 and 6 meVabove the ground level. In a recent electronic Raman study,
Püsche and co-workers34 determined the valley-orbit splitting for P centers to be 2.2 and 4.3 meV for 4H-SiC, 3.5 and5.3 meV for 6H-SiC. These values are close to ours
共4.2/ 4.3 meV for Pk1 and 7.0/ 6.0 meV for Pk2兲. As temperature increases, not only the relative population of the excitedstate increases but also the jumping rate between the groundand the excited states increases. If the excited state was independently observed, the EPR parameters should be different from those of the donor ground state. Thus the jumping
between the ground and excited states causes line broadening
unless averaging is achieved. The presence of the low-lying
excited state provides an efficient spin-lattice relaxation process known as Orbach process which contributes to line
broadening as the temperature increases. At higher temperatures, a certain fraction of the donor electrons are thermally
excited into the conduction band. The exchange scattering
between the donor electrons and the conduction electrons
might also cause the line broadening.35 With these mechanisms ofthe line broadening, EPR spectra of donors are observable only at relatively low temperatures.
Since the isotropic part of the 31P hf interaction of the P
center in 3C-SiC is very small, it is likely that the donor
electron wave function has a node at the phosphorus nucleus.
Thus the ground state of the P center in 3C-SiC is likely to
be originated from the E state or the T2 state under Td symmetry. As described above, the twofold degeneracy of the E
state is split into A1 and B1 and the threefold degeneracy of
the T2 state is split into a singlet B2 and a doublet E under the
D2d symmetry. Thus the nondegenerate ground state 共B1 or
B2 under the D2d symmetry兲 is achieved by the tetragonal
distortion in the P center in 3C-SiC. Our theoretical studies
for the P occupying the Si site in 4H-SiC has suggested thatthe ground state of the h site should be a doublet E while theground state of the k site should be a singlet A1. The assignment of the Pk spectrum to the k site is also supported by thecalculations of the localization of the donor wave function.
As shown in Table III, the spin densities on the P atom andon the nearest-neighbor carbon atoms are calculated for both
A1 and E states of both k and h sites. The 576-atom supercell
might be not large enough to make a direct comparison be-

075201-14

PHYSICAL REVIEW B 73, 075201 共2006兲

ELECTRON PARAMAGNETIC RESONANCE AND…

tween the theoretical values and the experimental data. Since
the localization of the donor wave function decays at theedge supercell, the results obtained in this supercell may be
used qualitatively. It can be seen that the calculated localization on the P atom is somewhat overestimated compared tothe experiments which could be due to the supercell size.
Nevertheless, only the spin density of the A1 ground state of
the k site fits the experimental data of the Pk center in which
only one set of 13C satellites corresponding to the interaction
with one C atom has been observed. In all the other combinations, the localization on three carbon neighbors 共C2-4兲 ismuch stronger than that on one carbon neighbor 共C1兲, whichis in contradiction with the experimental findings.
The results of calculations in 4H-SiC may be not transferable to the polytype of 6H-SiC because of two reasons: 共i兲the CBM in 6H-SiC is along the M-L line36 and not at the M
point as in the 4H-SiC therefore the character of the donor
wave function can differ, 共ii兲 the radii of the donor wave
function is around 11 Å while the lattice constant of 6H-SiC along the c axis is around 15 Å. This means that thedonor wave function “feels” locally the 6H-SiC environment
differently from that in the 4H polytype.
In previous studies,2,5 the P2 doublet in 6H-SiC was believed to be the coincidence of two different P spectra fromthe 1:2 intensity ratio between the P1 and P2 doublets measured at 142 GHz. It was therefore naturally to assign the P2
doublet 共Pk2 in our notation兲 to be related to P at two quasicubic sites in 6H-SiC and the P1 doublet 共Pk1 in our notation兲 to P at the h site. The assignment was supported byrecent calculations,9 which predicted well the hf coupling
constants for P1 共Ph兲 and P2 共with nearly the same hf splittingfor P at the k1 and k2 site兲. However, as shown in the previous section, the Pk2a / Pk2b doublets indeed belongs to allowed
and forbidden transitions of the Pk2 center, and therefore theP2 doublet is not contributed from two different P centerswith similar g value and hf splitting as previously
suggested.2,5,9,12 It is reasonable to assume that the propertiesof P centers at two quasicubic sites may be similar and canbe quite different from that of the P center at the h site. If P
at one of the two quasicubic sites is detected, one would
expect to observe also the EPR spectrum belonging to P at
the other quasicubic site. In 6H-SiC, only two P-related
spectra were detected. It is therefore likely that these two
spectra belong to P at the two quasicubic sites and the missing spectrum is related to the P donor at the hexagonal site,
Ph. The Pk center in 4H-SiC is indeed similar to the Pk1
center in the 6H polytype in temperature dependence and thespin localization on the P donor and surrounding C atoms. In
the electronic Raman study by Püsche and co-workers,34 theP centers in 4H-SiC have the valley-orbit splitting of 2.2 and5.3 meV. In 6H-SiC, only two Raman lines corresponding to
the valley-orbit splitting of 3.5 and 5.3 meV were observedin the whole energy range between 10 cm−1 共⬃1.24 meV兲and 2000 cm−1 共⬃247.97 meV兲.34 The valley-orbit splitting
corresponding to the third P center in 6H-SiC may be smaller
than 10 cm−1 so that the Raman line is too close to the laserline and is technically not detectable. The missing of the
EPR signal of P at the h site in both 4H- and 6H-SiC is likely
to be related to the E ground state whose degeneracy is not

lifted under the site symmetry of C3v or the energy separation between the A1 and E states is very small 共⬃2.2 meV orless, Ref. 34兲. The degenerate or near-degenerate groundstate is sensitive to local strains and the EPR spectrum might
easily be broadened beyond observation.
In the recent EPR study of in situ P-doped 6H-SiC bysublimation technique,9 besides the strong signal of the N
donors, only the fingerprint of the P + V center was believed
to be detected 共as weak shoulders of the central line of N
spectrum兲. Therefore it was concluded that in the P-doped
samples during sublimation growth the amount of electrically active isolated P is not significant and P may mainly
form complexes, which may be in diamagnetic states andcould not be detected by EPR. However, our studies showthat P incorporated during CVD growth substitutes for Si andacts as shallow donors. The formation of P-related complexes during the growth if occurred should be a minor process and the concentration of P-related complexes is insignificant compared to that of the isolated shallow P donors.
We believe that in the P-doped sublimation samples the signals of the shallow P donors are obscured by the strong signal of the N donors.
VI. SUMARY

In summary, we have observed P-related EPR spectra in
3C- 共P center兲, 4H- 共Pk center兲, and 6H-SiC 共Pk1 and Pk2
centers兲 doped with P during CVD growth. All the centers
are identified to be related to the ground state of the shallow
P donors at the Si site. From the g anisotropy, it is determined that the Pk center in 4H-SiC and the Pk1 and Pk2
centers in 6H-SiC have C3v symmetry and the P center in
3C-SiC has D2d symmetry. The central 31P hf interaction is
resolved in cw EPR for the Pk center in 4H-SiC and the Pk1
and Pk2 centers in 6H-SiC and is extracted by ENDOR for
the P center in 3C-SiC. The 31P hf interaction of the Pk1 andPk2 centers in 6H-SiC is confirmed by ENDOR. The 13C
satellite line共s兲 of the nearest-neighboring C atom共s兲 which
are evidence that the P atom occupies the Si sublattice areobserved for the Pk center in 4H-SiC and the Pk1 and Pk2
centers in 6H-SiC. The valley-orbit splitting of these shallow
P donors were determined from the temperature dependenceof the intensity of cw-EPR signals and of the spin-lattice
relaxation time. In 3C-, 4H-, and 6H-SiC, the obtained
valley-orbit splitting are in the range 4 – 7 meV and close to
the value determined from electronic Raman studies in 4Hand 6H-SiC and from PL spectra of the P bound excitons in
6H-SiC.
The Pk1 and Pk2 centers in 6H-SiC were found to be identical to the EPR doublets P1, P2 共or dPh, dP1, and dP2兲 whichwere previously reported in neutron transmuted material.
Our ESEEM results show that the previously reported dP1
and dP2 doublets observed in X-band EPR or the P2 doublet
measured at high frequencies are not originated from two
different P centers occupying two inequivalent quasicubic
silicon sites of 6H-SiC lattice but belong to allowed andforbidden transitions of one P center, Pk2, with S = 1 / 2 andI = 1 / 2. The analysis of the angular dependence including thenuclear Zeeman interaction provides a satisfactory explana-

075201-15

PHYSICAL REVIEW B 73, 075201 共2006兲

N. T. SON et al.

expected that P introduced into 3C-SiC during CVD growth
also occupies the silicon site.

tion of the angular dependence of the intensity of the Pk2
doublet in6H-SiC. The ESEEM and new ENDOR data provide a more precise determination of the hf coupling constants of the shallow P donors in 6H-SiC.
Comparing spin densities on the P atom and surrounding
C atoms determined by EPR experiments and by ab initio
supercell calculations, we assign the Pk center in 4H-SiC to
the A1 ground state of the shallow P donor occupying thequasicubic site. Expecting that the P centers at the two quasicubic sites have similar properties, which can be quite different from that of the P donor at the hexagonal site, we
attribute the Pk1, Pk2 centers in 6H-SiC to the shallow P
donors at the k1 and k2 quasicubic sites. The missing EPR
spectrum in both 4H- and 6H-SiC is ascribed to the shallow
P donor at the hexagonal site Ph with the degenerate or neardegenerate E ground state. From the identification of P centers at the silicon site in 4H- and 6H-SiC CVD layers, it is

The computer program EPR.FOR was developed by thegroup of Professor J. A. Weil, University of Saskatchewan.
Support for this work by the Swedish Foundation for Strategic Research 共SSF兲 program SiCMAT and by the Grant-inAid for Scientific Research in Priority Areas “Semiconductor
Nanospintronics” 共Grant No. 16031202兲 of the Ministry of
Education, Culture, Sports, Science, and Technology, Japan,
is acknowledged. Support by the Hungarian OTKA
F-038357, and Grant No. 2005008 from the Swedish National Supercomputer Center are appreciated. We are gratefulto Dr. N. Mizouchi for the help in the analysis of 2D-EPR.

1

18

M. Laube, F. Schmid, G. Pensl, G. Wagner, M. Linnarsson, and
M. Maier, J. Appl. Phys. 92, 549 共2002兲.
2
S. Greulich-Weber, Phys. Status Solidi A 162, 95 共1997兲, andreferences therein.
3
A. I. Veinger, A. G. Zabrodskii, G. A. Lomakina, and E. N.
Mokhov, Fiz. Tverd. Tela 28, 1659 共1984兲; 关Sov. Phys. Solid
State 28, 917 共1986兲兴.
4 E. N. Kalabukhova, S. N. Lukin, and E. N. Mokhov, Fiz. Tverd.
Tela 35, 703 共1993兲; 关Phys. Solid State 35, 361 共1993兲兴.
5 E. N. Kalabukhova, S. N. Lukin, E. N. Mokhov, M. Feege, S.
Greulich-Weber, and J -M. Spaeth, Inst. Phys. Conf. Ser. 137,
215 共1994兲.
6
P. G. Baranov, I. V. Ilyin, E. N. Mokhov, H. J. von Bardeleben,
and J. L. Cantin, Phys. Rev. B 66, 165206 共2002兲.
7 J. Isoya, T. Ohshima, A. Ohi, N. Morishita, and H. Itoh, Nucl.
Instrum. Methods Phys. Res. B 206, 965 共2003兲.
8 J. Isoya, T. Ohshima, N. Morishita, T. Kamiya, H. Itoh, and S.
Yamasaki, Physica B 340-342, 903 共2003兲.
9 E. Rauls, M. V. B. Pinheiro, S. Greulich-Weber, and U. Gerstmann, Phys. Rev. B 70, 085202 共2004兲.
10 M. V. B. Pinheiro, S. Greulich-Weber, and J. -M. Spaeth, Physica
B 340-342, 146 共2003兲.
11 K. Semmelroth, F. Schmid, D. Karg, G. Pensl, M. Maier, S.
Greulich-Weber, and J. -M- Spaeth, Mater. Sci. Forum 433-436,
63 共2003兲.
12
N. T. Son, A. Henry, J. Isoya, and E. Janzén, Mater. Sci. Forum483-485, 515 共2005兲.
13 A. Henry and E. Janzén, Mater. Sci. Forum 483-485, 101 共2005兲.
14
W. B. Mims, Proc. R. Soc. London, Ser. A 238, 452 共1965兲.
15 S. G. Sridhara, L. L. Clemen, D. G. Nizhner, R. P. Devaty, W. J.
Choyke, and D. J. Larkin, Mater. Sci. Forum 264-268, 465
共1998兲.
16
A. Schweiger and G. Jeschke, in Principles of Pulse Electron
Paramagnetic Resonance, 共Oxford University Press, New York,
2001兲, p. 58.
17 L. G. Rowan, E. L. Hahn, and W. B. Mims, Phys. Rev. 137, A61
共1965兲.

ACKNOWLEDGMENTS

J. Isoya, M. K. Bowman, J. R. Norris, and J. A. Weil, J. Chem.
Phys. 78, 1735 共1983兲.
19 C. P. Poole, Jr., and H. A. Farach, Theory of Magnetic Resonance
共John Wiley & Sons, New York, 1987兲, p. 57.
20 J. R. Morton and K. F. Preston, J. Magn. Reson. 共1969-1992兲 30,
377 共1978兲.
21 R. Orbach and W. P. Wolf, Proc. R. Soc. London, Ser. A 264, 458
共1961兲.
22 Using average values for the effective mass of the donors and thestatic dielectric constants of 4H-SiC.
23 W. R. L. Lambrecht and B. Segall, Phys. Rev. B 52, R2249
共1995兲.
24 E. Rauls, Th. Frauenheim, A. Gali, and P. Deák, Phys. Rev. B 68,
155208 共2003兲.
25 J. M. Soler, E. Artacho, J. D. Gale, A. Garciá, J. Junquera, P.
Ordejón, and D. Sánchez-Portal, J. Phys.: Condens. Matter 14,2745 共2002兲.
26 N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 共1991兲.
27
D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 共1980兲.
28 J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 共1981兲.
29
I. G. Ivanov, A. Henry, and E. Janzén, Phys. Rev. B 71,
241201共R兲 共2005兲.
30
I. G. Ivanov, B. Magnusson, and E. Janzén, Phys. Rev. B 67,
165211 共2003兲.
31
M. Bockstedte, A. Mattausch, and O. Pankratov, Appl. Phys. Lett.
85, 58 共2004兲.
32 E. Sörman, N. T. Son, W. M. Chen, O. Kordina, C. Hallin, and E.
Janzén, Phys. Rev. B 61, 2613 共2000兲.
33 T. G. Castner Jr., Phys. Rev. Lett. 8, 13 共1962兲.
34
R. Püsche, M. Hundhausen, L. Ley, K. Semmelroth, G. Pensl, P.
Desperrier, P. J. Wellmann, E. E. Haller, J. W. Ager, and U.
Starke, Proceedings of the International Conference on SiC and
Related Materials 2005, Pittsburgh, USA, September 18-23,
2005, Mater. Sci. Forum 共to be published兲.
35 D. J. Lépine, Phys. Rev. B 2, 2429 共1970兲.
36 C. Persson and U. Lindefelt, J. Appl. Phys. 82, 5496 共1997兲.

075201-16