ARTICLE IN PRESS

Physica B 376–377 (2006) 358–361
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Pulsed EPR studies of Phosphorus shallow donors in diamond and SiC
J. Isoyaa,, M. Katagiria,b, T. Umedaa, S. Koizumib, H. Kandab, N.T. Sonc,A. Henryc, A. Galid, E. JanzéncaGraduate School of Library, Information and Media Studies, University of Tsukuba, 1-2 Kasuga, Tsukuba, Japanb
National Institute for Materials Science, Tsukuba, Japanc
Department of Physics, Chemistry and Biology, Linköping University, Linköping, SwedendDepartment of Atomic Physics, Budapest University of Technology and Economics, Budapest, Hungary

Abstract
Phosphorus shallow donors having the symmetry lower than T d are studied by pulsed EPR. In diamond:P and 3C–SiC:P, thesymmetry is lowered to D2d and the density of the donor wave function on the phosphorus atom exhibits a predominant p-character. In
4H–SiC:P with the site symmetry of C 3v , the A1 ground state of the phosphorus donors substituting at the quasi-cubic site of siliconshows an axial character of the distribution of the donor wave function in the vicinity of the phosphorus atom.
r 2005 Elsevier B.V. All rights reserved.
PACS: 76.30.v; 71.55.i; 81.05.Uw
Keywords: Pulsed EPR; Donors; Diamond; SiC

1. Introduction
Controlling the conductivity by doping shallow donor oracceptor impurities is essential in fabrication of semiconductor electronic devices. In the effective mass theory(EMT), the dopant atoms binding one electron or hole aredescribed as solid state analogues of hydrogen atom with
the Coulomb potential reduced by 1=s (s , the static
dielectric constant) and the effective mass of the relevant
conduction band of the host crystal [1]. The bound electron
has a 1s like ground state and 2s; 2p; 3s; 3p; . . . like excitedstates. Among the differences of shallow impurity statesfrom the hydrogen atom is 1s ground state degeneracy
originating from the presence of the equivalent minima inthe conduction band which occurs in semiconductor
crystals with the conduction band minima located not at
the center of the Brillouin zone ðk ¼ 0Þ.
The degeneracy of the 1s ground state is partly lifted by
the site symmetry of the impurity atom (valley–orbitCorresponding author. Tel.: +81 298 59 1000; fax: +81 298 59 1458.

E-mail address: isoya@slis.tsukuba.ac.jp (J. Isoya).
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2005.12.092

splitting). In the case of group-V impurity in silicon, thesixfold degeneracy due to six conduction band minima is
split by T d symmetry to a singlet 1sðA1 Þ, a doublet 1sðEÞ
and a triplet 1sðT 2 Þ with the ground state 1sðA1 Þ. The
singlet state which is a symmetric superposition of all sixvalleys has a non-vanishing value for jcð0Þj2 and gives riseto an isotropic hyperﬁne splitting. For the doublet andtriplet states which have a node at the donor nucleus
ðjcð0Þj2 ¼ 0Þ, no isotropic hyperﬁne interaction is expected.
The phosphorus donor in silicon exhibits the T d symmetry
with the isotropic 31 P hyperﬁne splitting of 4:2 mT and theisotropic g-value of 1.99850 [2]. In the case of group-V
impurity in germanium, the fourfold degeneracy is split byT d symmetry to a singlet 1sðA1 Þ and a triplet 1sðT 2 Þ withthe ground state 1sðA1 Þ. The phosphorus donor in
germanium exhibits the T d symmetry with the isotropic
31
P hyperﬁne splitting of 2:1 mT and the isotropic g-valueof 1.5631 [3].
The valley-orbit splitting is due to the interaction of thelocalized donor electron and the donor core (called thecentral cell correction) and is dependent on the donor
species (chemical effect). While the other hydrogen-likeARTICLE IN PRESS
J. Isoya et al. / Physica B 376–377 (2006) 358–361

Electron paramagnetic resonance (EPR) has been
proved powerful in providing detailed information about
the structure of the shallow donor impurities in silicon andgermanium. Here, we have applied pulsed EPR techniques.
Echo-detected EPR, in which the intensity of Hahn echo
(901- - -t- - -1801- - -t- - -echo) is measured as a function of
the external magnetic ﬁeld, has been utilized to eliminate
unwanted, disturbing signals by choosing the value of t andthe repetition rate of the pulse sequence in accumulationand to obtain spectra free from distortion due to passage
effects encountered in continuous wave EPR for a systemwith a relatively long relaxation time. Pulsed electron
nuclear double resonance (ENDOR) was used to extract
weak hyperﬁne interaction hidden underneath the line
broadening (3C–SiC:P) or to identify the origin of thedoublet (diamond:P). The valley-orbit splitting is estimatedfrom the temperature dependence of the spin-lattice
relaxation time when the spin-lattice relaxation is dominated by the Orbach process which is resonant two-phonon
process with the phonons of energy comparable to thetransition between the ground state and the excited state[4]. The three-pulse inversion recovery (1801- - -t- - -901- - t- - -1801- - -t- - -echo) was used to measure the spin-lattice
relaxation time. Pulsed experiments were carried out usinga Bruker Elexys E580 spectrometer, and samples were kept
in an Oxford ER4118CF cryostat. Temperature wascontrolled with an Oxford ITC503 temperature controller.
3. Results and discussion
In Fig. 1, echo-detected EPR spectra of diamond:P,3C–SiC:P, and 4H–SiC:P are shown. In diamond:P and4H–SiC:P, the 31 P ðI ¼ 1=2; 100%Þ hyperﬁne splitting wasresolved. From the number of distinguishable sites whenthe magnetic ﬁeld ðBÞ is along a high symmetry direction (2sites in both B==½1 0 0 and in B==½0 1 1 and one site in
B==½1 1 1 for both diamond:P and 3C–SiC:P, one site bothin B==c and in B ? c for 4H–SiC:P) and from the patternof the rotational plots, it is determined that the symmetryof the phosphorus donors is D2d for diamond:P and3C–SiC:P and C 3v for 4H–SiC:P. By using pulsed
ENDOR, it is conﬁrmed that the doublet structure indiamond:P (Fig. 1(a)) is arising from the 31 P hyperﬁneinteraction. The two-line structure at B==½1 0 0 ofEcho intensity [arb. units]342(a)

344

346
348
Magnetic field [mT]

350352

Echo intensity [arb. units]

2. Experiment

349.5

350.0
Magnetic field [mT](b)

Echo intensity [arb. units]

excited states ð2p0 ; 2s; 2p ; . . .Þ lie well above these 1s states,
the separation between/among the 1s states (valley-orbitsplitting) is rather small.
We have studied the phosphorus shallow donors indiamond, 3C–SiC, and 4H–SiC in which phosphorus
impurities are introduced during the CVD growth. The
present work concerns with the effect of a lower symmetry
brought either by the hexagonal symmetry of the hostcrystal (4H–SiC:P) or by local distortion in the case of
cubic symmetry of host crystal (diamond:P, 3C–SiC:P).

359

X 50

349.0
(c)

349.5
350.0
Magnetic field [mT]350.5

Fig. 1. Echo-detected EPR spectra of phosphorus donors: (a) diamond:P(10 K, B==½1 1 1; 9:7246 GHzÞ, (b) 3C–SiC:P ð5 K; B==½0 0 1; 9:8181 GHzÞ,(c) 4H–SiC:P ð6 K; B==½0 0 0 1; 9:8177 GHzÞ.

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360
Table 1EPR parameters

Diamond:P(10 K)
3C–SiC:P (5 K)
4H–SiC:P (6 K)
Si:P (Ref. [2])Symmetry

gjjg?

Ajj ðmTÞA? ðmTÞ

D2d
D2d
C 3v
Td

1.99051
2.00512.0065
1.99850(isotropic)

2.00573
2.00462.0006

5.68
1:9  1020.2944.2 (isotropic)

1.14
4:6  1030.21Table 231
P hyperﬁne and orbital parameters

Diamond:P(10 K)
3C–SiC:P (5 K)
4H–SiC:P (6 K)
Si:P (Ref. [2])Aiso ðmTÞb ðmTÞZ2b2 =a22.66
3:2  103
2:38  101
4.2

1.51
7:9  102
2:8  10200.121
6:1  104
2:6  103
8:8  103

1989
4.3
0

3C–SiC:P (Fig. 1(b)) is arising from the difference in the gvalue (site splitting). And the weak 31 P hyperﬁne interaction hidden underneath the line broadening was extracted
by pulsed ENDOR technique. The spin-Hamiltonianparameters were determined by ﬁtting the line positions
ðg; A of diamond:P, 4H–SiC:P, g of 3C–SiC:P) and theENDOR frequencies (A of 3C–SiC:P) to the spinHamiltonian:
H ¼ be B  g  S þ S  A  I  gn bn B  I.

(1)

Here S ¼ 1=2 and I ¼ 1=2, and gn ¼ 2:2632 for 31 P. The
principal values of g; A and the hyperﬁne and orbitalparameters are listed in Tables 1 and 2. The 31 P hyperﬁneinteraction is divided into the isotropic part Aiso and theanisotropic part ðAjj ¼ Aiso þ 2b; A? ¼ Aiso  bÞ. To discuss the distribution of the donor wave function, we use thefractional unpaired population ðZ2 Þ on the phosphorus
atom and the sp hybrid ratio ðb2 =a2 , where a2 þ b2 ¼ 1Þobtained by assuming that the one-electron linear combination of atomic orbital (LCAO) approximation should beapplicable for interpreting the hyperﬁne parameters. In theestimation ðZ2 a2 a0 ¼ Aiso ; Z2 b2 b0 ¼ bÞ, we used a0 ¼
474:79 mT and b0 ¼ 13:088 mT.
In both, diamond:P and 3C–SiC:P, we note that thewave function of the donor electron on the phosphorus
atom is almost purely p-like. Thus, the ground state is not
likely to be A1 . Diamond has Si-like conduction band
structure with the minimum located at k0 ð0:74Þ along theD-axis, near the X point [5]. Under the T d symmetry of an
unrelaxed substitutional site, the sixfold degeneracy of the1s ground state due to six minima of the conduction bandis split into a singlet 1sðA1 Þ, a doublet 1sðEÞ, and a triplet
1sðT 2 Þ. In 3C–SiC:P, the threefold degeneracy of the 1sground state due to three minima of the conduction bandwith the conduction band minimum at the X point [6] iseither remains threefold degenerate with a triplet state T 2or splits into a singlet A1 and a doublet E under the T dsymmetry. With lowering symmetry from T d to D2d , thedoublet E is split into A1 and B1 and the triplet T 2 is split
into a singlet B2 and a doublet E. For both diamond:P and3C–SiC:P, since the wave function on the phosphorus has
predominant p-character, the ground state is likely to be B2(T 2z in T d ) which has a node at the donor nucleus.
In 4H–SiC:P, the p-character of the wave function of thedonor electron on the phosphorus atom is large (the spratio 4Þ. In 4H–SiC:P, the threefold degeneracy of the 1s
ground state arising from the three equivalent conduction
band minima with the conduction band minimum locatedat M point is split into a singlet A1 and a doublet E under
the C 3v symmetry of the donor site [7]. While each silicon
and carbon has two inequivalent lattice sites called
hexagonal ðhÞ and quasi-cubic ðkÞ sites, only one kind of
EPR spectrum was observed, which we assign to be arisingfrom phosphorus shallow donors at SiðkÞ site. An ab initio
calculation using a 576-atom supercell has predicted that
A1 is lower than E for phosphorus at the SiðkÞ site, while E
is lower than A1 for phosphorus at the SiðhÞ site. The
calculation has predicted that the spin density on the axial
carbon is much larger than that of the three basal carbon
atoms for the ground state A1 of the phosphorus at SiðkÞ,while the spin density on the three basal carbon atoms ismuch larger than that on the axial carbon atom for theground E state of the phosphorus at SiðhÞ. The observationof one set of 13 C hyperﬁne satellite arising from one
nearest-neighbor carbon atom (Fig. 1(c), isotropic within
the resolution of echo-detected EPR with the fractional
spin density Z2 5  103 Þ supports the assignment that theobserved EPR spectrum is arising from the phosphorus
donor at SiðkÞ. The absence of the EPR spectrum from thephosphorus at the SiðhÞ site is ascribed to the degenerate
ground state E which is likely to be broadened by local
strains. From the temperature dependence of the spinlattice relaxation time, the valley-orbit splitting, i.e., theenergy separation between the ground and excited states
within the 1s manifold has been estimated to be 4.2 meV for
4H–SiC:P. This rather small valley-orbit splitting suggeststhat the relative energy positions of A1 and E might be wellaffected by the difference in the arrangement of nextnearest neighbors between SiðkÞ and SiðhÞ sites. Thus, theexperimental observation agreesqualitatively with theresults of the ab initio calculation that the ordering of A1and E could be different between the two inequivalent
silicon sites.

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4. Summary

References

As a summary, phosphorus donors, diamond:P,3C–SiC:P, and 4H–SiC:P are studied by pulsed EPR. In
the cubic lattices of diamond and 3C–SiC, the predominantp-character of the wave function density on the phosphorus
atom is ascribed to the B2 ground state (which corresponds
to T 2z of the T d symmetry) under the symmetry of D2d . In
the hexagonal lattice of 4H–SiC, the observation of one setof 13 C satellites and the sp hybrid orbital of phosphorus
pointing toward the carbon atom suggests that the extent
of the donor wave function is quite non-spherical at least in
the vicinity of the phosphorus atom for the A1 ground state
under the C 3v symmetry.

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