Negative-U System of Carbon Vacancy in 4H-SiC
N. T. Son,
1
X. T. Trinh,
1
L. S. Løvlie,
2
B. G. Svensson,
2
K. Kawahara,
3
J. Suda,
3
T. Kimoto,
3
T. Umeda,
4
J. Isoya,
5
T. Makino,
6
T. Ohshima,
6
and E. Janze
´
n
1
1
Department of Physics, Chemistry and Biology, Linko
¨
ping University, SE-581 83 Linko
¨
ping, Sweden
2
Department of Physics, Center for Materials Science and Nanotechnology, University of Oslo,
P.O. Box 1048 Blindern, N-0316 Oslo, Norway
3
Department of Electronic Science Engineering, Kyoto University, Nishikyo, Kyoto 615-8510, Japan
4
Institute of Applied Physics, Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan
5
Graduate School of Library, Information and Media Studies, University of Tsukuba, Tsukuba 305-8550, Japan
6
Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan
(Received 23 August 2012; published 31 October 2012)
Using electron paramagnetic resonance (EPR), energy levels of the carbon vacancy (V
C
)in4H-SiC and
its negative-U properties have been determined. Combining EPR and deep-level transient spectroscopy
we show that the two most common defects in as-grown 4H-SiC—the Z
1=2
lifetime-limiting defect and
the EH
7
deep defect—are related to the double acceptor (2j0) and single donor (0jþ) levels of V
C
,
respectively.
DOI: 10.1103/PhysRevLett.109.187603 PACS numbers: 76.30.Mi, 61.72.jd, 61.82.Fk, 71.55.Ht
It has been suggested by Anderson [1] that the energy
gain associated with electron pairing in the dangling bonds
of a defect and coupled with a large lattice relaxation might
overcome the Coulomb repulsion of the two electrons,
resulting in a net effective attractive interaction between
the electrons at the site (a negative correlation energy U or
negative U). For a vacancy with spread dangling bonds,
reconstructed bonds can be formed leading to symmetry
lowering of the defect. This splits up the degenerate state,
facilitating the electron pairing and the capture of a second
electron may lead to lowering of the energy. Such a defect
is called a negative-U center. A typical example of a
negative-U defect is the monovacancy in Si [2].
In 4H-SiC, calculations without charge correction [3]
suggested that V
C
is a negative-U center for negative and
positive charge states. With including charge correction,
the negative-U behavior is not found in some calculations
[4] while it remains in another [5] for V
C
in the negative
charge state. A recent calculation using hybrid density
functionals [6] found the negative-U behavior of V
C
at
the quasicubic k site, V
C
ðkÞ, with the double negative
(2j0) charge states lying slightly (< 0:1eV) lower than
the single negative (j0) charge state. The symmetry
lowering (to C
1h
)ofV
C
was confirmed by electron para-
magnetic resonance (EPR) in 4H- and 6H-SiC [7–9]. The
EPR signal of the positive vacancy [V
þ
C
ðhÞ and V
þ
C
ðkÞ]
[7,9] and V
C
ðhÞ (Ref. [8]) have been observed and no clear
data indicating the negative-U behavior of V
C
have so far
been reported.
V
C
is predicted to have low formation energies in
both Si- and C-rich conditions [3,4,6]. V
C
is frequently
detected by EPR in high-purity semi-insulating substrates
and is believed to play an important role in carrier com-
pensation [10]. It has been shown from deep-level transient
spectroscopy (DLTS) that the two most common and un-
avoidable defect levels in as-grown 4H-SiC layers grown
by chemical vapor deposition (CVD) are the Z
1=2
level [11]
at 0:56–0:71 eV below the conduction band minimum
E
C
and the EH
6=7
level at E
C
ð1:55–1:65Þ eV [12,13].
The Z
1=2
level in 4H-SiC is known to be a negative-U
center associated with two higher-lying levels, Z
1
at
0:52 eV and Z
2
at 0:45 eV below E
C
[14]. Different
defect models such as the divacancy [15], nitrogen-related
defect [16] or N-dicarbon interstitial complex [17] were
suggested for Z
1=2
. The Z
1=2
center was found to appear
always together with the EH
6=7
defect with the same depth
profile in 4H-SiC CVD layers and to act as dominant
carrier-lifetime-limiting defect in the material [18]. The
concentrations of these two levels in CVD layers were
found to be (i) significantly increased after irradiation
even with low-energy (116–210 keV) electrons which dis-
place C atoms only, creating defects in the C sublattice
[13,19] and (ii) very close to each other in all kind of
samples regardless of growth, irradiation, or annealing
conditions used [13]. The Z
1=2
and EH
6=7
levels were,
therefore, suggested to belong to the same defect such as
V
C
or a V
C
-related complex [20]. It has been shown that the
concentrations of the Z
1=2
and EH
6=7
levels can be effi-
ciently reduced by C implantation and annealing [20]orby
thermal oxidation [21,22], supporting the V
C
-related defect
model. However, due to the lack of experimental evidence
indicating the negative-U behavior of V
C
, the origin of the
Z
1=2
defect remains to be identified. Concurrent with the
reduction of the Z
1=2
concentration, a significant increase
of the carrier lifetime was observed [21–23], confirming
that Z
1=2
is the dominant lifetime-limiting defect in the
material and, hence, technologically important for device
applications.
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0031-9007=12=109(18)=187603(5) 187603-1 Ó 2012 American Physical Society
In this Letter, we report the result of our EPR study of
n-type 4H-SiC epitaxial layers irradiated with low-energy
electrons (250 keV) which generate mainly V
C
, C intersti-
tials and their associated defects. (The Si vacancy can be
created by 250 keV electrons but its concentration is below
the detection limit of EPR.) With the presence of only V
C
in absence of other EPR signals, which are dominant in
samples irradiated by high-energy electrons, we could
detect both the signals of V
C
ðhÞ and V
C
ðkÞ. Using EPR
and photoexitation EPR (photo-EPR) we could determine
the ionization energy of the single and double acceptor
states of V
C
and to reveal its negative-U properties. The
energy levels of V
C
obtained by EPR correlate well with
those determined by DLTS for the negative-UZ
1=2
center
[14], allowing an unambiguous identification of the Z
1=2
center as the doubly negatively charged (2j0) state of V
C
.
Our study of the depth profile of the carrier concentration
by capacitance-voltage (C-V) measurements and DLTS
also shows that the Z
1=2
and EH
6=7
centers in implanted
and annealed samples are of double acceptor and single
donor type, respectively, supporting the identification of
these deep levels to different charge states of V
C
.
The starting material is n-type 4H-SiC layers grown on
4H-SiC substrates. The layers are 100 m thick with the N
concentration of 1:6 10
17
cm
3
. Two sets of samples,
each consisting of five samples, labeled A–E, were prepared
for EPR (with substrate removed) and DLTS measurements.
The layers were irradiated by 250 keV electrons at room
temperature with different fluences (sample A: 7.5, B: 7.2,
C: 5.7, D: 4.3, and E: 3.1, in 10
18
cm
2
). EPR measure-
ments were performed on a X-band ( 9:4 GHz) Bruker
E500 spectrometer equipped with a He-flow cryostat allow-
ing the regulation of the sample temperature in the range
4–295 K. For illumination, a halogen lamp (200 W) and a
0.25 m single grating Jobin-Yvon monochromator were
used as a light source. In photo-EPR experiments, we
used the second order of a 600 g=mm grating which gives
a dispersion of 3:2nm=mm. With a fully open slit (3 mm),
the band width of the excitation is 9.6 nm (or 4–6 meV in
the spectral region 1700–1500 nm). With the error of
6 meV in the photon energy, the error in determination
of the energy threshold is expected to be within 10 meV.
For DLTS and C-V measurements, we also used n-type
epitaxial layers ( 10 m thick) with a net doping concen-
tration of 2:5 10
15
cm
3
and implanted with 4.3 MeV
28
Si ions at room temperature to doses of 1–4 10
8
cm
2
which result in a nonuniform defect distribution with a peak
at 1:8 m. The implanted samples were then annealed at
1150
C in N
2
flow for 3.5 h followed by thermal evapora-
tion of Ni to form Schottky barrier contacts. C-V (using
1 MHz probe and 1 Hz sweep frequency) and DLTS
measurements were performed in the temperature range
150–700 K.
We found from C-V measurements that there is a com-
pensated region (CR) in highly irradiated samples (A–D)
where the N donors were completely compensated by
deep levels. The thickness of the CR varies with the
electron fluence (from 25 m for sample D to
45 m for sample A). In the CR, the Fermi level is
located at E
C
0:53 eV as estimated from the series
resistance of the Schottky barrier diodes. No EPR signal
of V
C
could be detected in darkness at low temperatures
(T<80–85 K for samples A–D and at above 100 K for
sample E) [Fig. 1(a)]. A weak signal of V
C
ðhÞ could be
detected in darkness at T>90 K in the samples A–D.In
the heavily irradiated sample A, a new line was detected in
addition to the V
C
ðhÞ signal [Fig. 1(b)]. Under illumina-
tion, the signals of V
C
ðhÞ and the new line increase sub-
stantially [Fig. 1(c)]. After illumination, the signals are
persistent in darkness. The principal values of the
g tensor and the Si hyperfine (hf) A tensor determined at
140 K for V
C
ðhÞ are g
k
¼ 2:0040, g
?
¼ 2:0038, and the
A values (in unit of mT) A
k
¼ 9:92, A
?
¼ 7:72 (for Si
1
atom along the c axis) and A
xx
¼ 4:11, A
yy
¼ 4:05, A
zz
¼
5:21 (for three Si
2–4
atoms in the basal plane). For the new
spectrum, the corresponding parameters are g
k
¼ 2:0046,
0
0.2
0.4
0.6
0.8
1
0.6 0.8 1 1.2 1.4
0
0.2
0.4
0.6
0.8
1
334 335 336 337
EPR intensity (linear scale)
Magnetic field (mT)
(a) sample E, in dark
(b) sample A
in dark
(c) sample C
h
ν
=1.46 eV
4H-SiC, B||c
9.415 GHz
T=100 K
EPR intensity (a.u.)
4H-SiC
sample C
T=100 K
4H-SiC
sample E
T=100 K
(d)
(e)
Photon energy (eV)
0.74 eV
0.74 eV
V
C
(h)
V
C
(k)
V
C
(h)
V
C
(k)
V
C
(h)
0.78 eV
V
C
(k)
FIG. 1 (color online). EPR spectra in n-type 4H-SiC
CVD layers irradiated by 250 keV electrons with different
fluences (sample E: 3:1 10
18
cm
2
, C: 5:7 10
18
cm
2
and
A: 7:5 10
18
cm
2
) measured at 100 K (a)–(b) in darkness and
(c) under illumination. The dependence of the EPR intensity of
V
C
ðhÞ and V
C
ðkÞ on the photon energy in (d) sample E and
(e) sample C. The error in determination of the energy threshold
in the spectral region is within 0:01 eV.
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g
?
¼ 2:0035, A
k
¼ 3:69, A
?
¼ 2:96 (for Si
1
), and A
xx
¼
6:05, A
yy
¼ 5:94, A
zz
¼ 7:49 (for Si
2–4
). The angle
between the principal A
zz
and the c axis is 75.9
for
V
C
ðhÞ and 69.2
for the new center. The experimental
errors are 0:0001 for the g values and 0:08 mT for
the A values. For the new spectrum, the hf constants of
Si
2–4
are larger than that of Si
1
. From the obtained g tensor
and the Si hf tensors, this new spectrum is identified to be
related to V
C
ðkÞ [24].
Photo-EPR experiments were performed on samples E
and C. The dependence of the EPR intensity of V
C
ðhÞ and
V
C
ðkÞ on the photon energy is shown in Fig. 1(d) for
sample E and in Fig. 1(e) for sample C. The temperature
dependence of the V
C
signal in darkness and the photo-
EPR data can be explained by the scheme of energy levels
of a negative-UV
C
center in Fig. 2 with the (2j0)level
lying lower than the (j0) level. In the single negative
charge state, V
C
prefers to capture another electron to
become doubly negatively charged and lowers its energy.
Thus, at low temperatures, V
C
is in the 2 charge state
(S ¼ 0) and no EPR signal can be observed. At elevated
temperatures (> 90 K), the higher-lying (j0) state can be
partly populated due to internal thermal excitation of elec-
trons from the (2j0) level and, hence, a weak signal of
V
C
could be detected in darkness [Fig. 1(b)]. We assign the
energy threshold of 0:74 eV for observing the V
C
ðkÞ
signal in sample E [see Fig. 1(d)] to the optical transition
from the (2j0) level to E
C
. The corresponding transition
for V
C
ðhÞ is 0:78 eV [Fig. 1(d)]. In sample C, the V
C
ðhÞ
signal already weakly appears in darkness (at 100 K).
When the photon energy reaches h 0:74 eV, the
V
C
ðkÞ signal appears as expected [Fig. 1(e)]. The V
C
ðhÞ
signal starts decreasing at h 0:74 eV. We attributed this
threshold ( 0:74 eV) to the transition from the (j0)
level of V
C
ðhÞ to E
C
which reduces the population of the
(j0) level and, hence, the V
C
ðhÞ signal.
In agreement with previous studies [25], we also found
that in n-type 4H-SiC irradiated with 250 keVelectrons V
C
is the dominant EPR defect and Z
1=2
and EH
7
are the
dominant DLTS centers. The obtained energy transitions
from the (2j0) level of V
C
to E
C
[ 0 :74 eV for V
C
ðkÞ
and 0:78 eV for V
C
ðhÞ] are very close to the ionization
energy of the Z
1=2
level (E
C
0:56–0:71 eV)[14,15].
The transition from the (j0) level of V
C
ðhÞ to
E
C
( 0:74 eV) is also close to the ionization energy
of the higher-lying states Z
1
( E
C
0:52 eV) and
Z
2
( E
C
0:45 eV)[14]. (The optical transitions involve
a Franck-Condon shift in the range of 0:03–0:3eV,
which is also in good agreement with the recent calculated
values [5].)
Since the V
C
ðhÞ signal can be detected in darkness in
samples A–D at T>90 K, whereas V
C
ðkÞ can only be
weakly seen in sample A at T 100–130 K, it is likely that
the energy separation between the (2j0) and (j0) levels
is smaller for V
C
ðhÞ and larger for V
C
ðkÞ. Therefore, we
assign V
C
ðhÞ to Z
1
and V
C
ðkÞ to Z
2
. The optical transitions
from the acceptor states of V
C
to E
C
are shown in Fig. 2.
For comparison, the ionization energies of Z
1=2
center
determined by DLTS [14,15] are also shown in Fig. 2.
The same DLTS defect in 6H-SiC (the E
1
and E
2
centers)
also shows a similar order of the energy levels of E
1
(V
C
at
h site) and E
2
(V
C
at two cubic k
1
and k
2
sites with double
intensity) [26]. Here we reassign the charge states proposed
in Ref. [14] from (0jþ)to(j0) for Z
1
and Z
2
and from
(j þ)to(2j0) for Z
1=2
. The energy transitions observed
in our photo-EPR experiments are smaller than those ob-
tained before in Ref. [25 ]. In those photo-EPR experiments
on low-doped ( 7 10
14
cm
3
) samples [25], the con-
centration of V
C
is limited by the N concentration (more
than 2 orders of magnitude less compared to the doping
level in our samples A–E) and, therefore, the V
C
signal was
much weaker and could only be detected with excitation
energies above 1:0eV [25]. The obtained energies of
acceptor levels of V
C
are rather close to those reported in
recent hybrid functional calculations [6]. However, after
charge correction, the negative-U behavior of V
C
ðhÞ dis-
appeared [6]. It is clear that the methods used for charge
correction in conventional [4] or hybrid functional calcu-
lations [6] result in an overcorrection.
The threshold 1:8–1:9eVpresent in previous photo-
EPR experiments [27,28] has recently been reassigned to
the transition from the valence band E
V
to the (2þjþ)
level of V
C
[5]. However, the reassignment was made by
considering only the photo-EPR data for irradiated p-type
[27] and as-grown semi-insulating [28] materials. Such an
excitation is clearly not possible in irradiated n-type
material [8,25] with the Fermi level located close to the
(2j0) state of V
C
and neither V
C
nor V
þ
C
signals could be
~0.71
~0.52
Z
1
Z
2
EH
7
h-site
k-site
~0.74
(2-|0)
(0|+)
E
C
E
V
~0.45
DLTS
~0.56-0.67
~1.55 eV
Z
1/2
& EH
7
Photo-EPR
~1.8 eV
V
C
Z
1/2
EH
7
~0.74
~0.78
(-|0)
FIG. 2 (color online). Scheme of energy levels of V
C
, deter-
mined by photo-EPR. The Z
1=2
and EH
7
levels determined by
DLTS [11,14,15] are given for comparison. Here the optical
transitions obtained by photo-EPR involve a Franck-Condon
shift in the range 0:03–0:3eV. For clarity, the location of
the states in the scheme does not follow the relative scale and the
levels determined by photo-EPR are aligned to the correspond-
ing levels determined by DLTS the optical transitions from the
(j0) and (2j0) states to the conduction band involve different
Franck-Condon shifts for V
C
ðhÞ and V
C
ðkÞ. The photo-EPR data
for the (0jþ) level are from Ref. [25].
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detected in darkness. However, the same threshold of
1:8eVfor activating (or recovering) the V
þ
C
signal oc-
curs also in n-type material [8,25]. This shows that the
1:8eV threshold can only correspond to a transition
which excites electrons from the (0jþ) level to E
C
as
illustrated in Fig. 2. The threshold correlates well with
the DLTS EH
6=7
level, or more precisely, the EH
7
level
in material irradiated with low-energy electrons [13,19,25]
where the V
C
EPR center and the Z
1=2
and EH
7
DLTS
centers are the clearly dominant defects [25]. The Franck-
Condon shift involved in the 1:8eVoptical excitation is
in the range of 0:25 eV, corroborating the association
with the EH
7
level at 1:55 eV below E
C
.
The double acceptor nature of Z
1=2
and donor behavior
of EH
6=7
, inferred from the EPR data, are unambiguously
confirmed by C-V measurements performed on Si-
implanted and annealed high-purity (epitaxial) n-type
samples where the concentration of other deep-level de-
fects is more than 1 order of magnitude lower than that of
Z
1=2
and EH
6=7
. At a sample temperature of 190 K, the
thermal emission rate of electrons from the Z
1=2
level (and
the EH
6=7
level) to E
C
is negligible compared to both the
probe (1 MHz) and sweep (1 Hz) rates used and the
recorded data yield the true profile of responding electrons,
i.e., the difference between the profile of shallow nitrogen
donors and that of electrons trapped by Z
1=2
, Fig. 3(a).At
300 K, Z
1=2
responds to the sweep voltage but not to the
probe one, and an anomalous peak occurs at 2:4 m in
Fig. 3(a). The occurrence of such a peak is a unique feature
of a nonuniform distribution of deep acceptorlike traps
[29], and no evidence is found for a donorlike behavior
of Z
1=2
, arising from the E
C
0:5eVlevels. Indeed, the
data measured at 700 K, where Z
1=2
responds to both the
probe and sweep voltages, unambiguously rule out any
donor activity of Z
1=2
since the electron concentration at
the maximum position of the defect profile ( 1:8 m)is
essentially equal to the shallow nitrogen donor concentra-
tion. Moreover, at 700 K an intermediate case occurs for
the EH
6=7
center, responding to the sweep voltage but not
the probe one, and as shown in Fig. 3(b), excellent agree-
ment is obtained between the measurements and simula-
tions assuming EH
6=7
to be a donor. The simulations are
based on a refined version of the model originally devel-
oped by Kimerling [29] and as illustrated in Fig. 3(a),
also the data at 190 and 300 K are closely reproduced
by the simulations regarding Z
1=2
as a double acceptor.
In fact, Z
1=2
and EH
6=7
are found to exhibit identical
concentration-versus-depth profiles except for a two-to-
one ratio between the absolute values, showing the double
acceptor and single donor behavior of Z
1=2
and EH6=7,
respectively, and fully supporting the conclusion from the
EPR data that they originate from the same defect, V
C
.
In summary, using N-doped n-type 4 H-SiC epitaxial
layers irradiated with low-energy electrons (250 keV),
we were able to detect the V
C
signal at both the h and
k site and to obtain more accurate energies of the single and
double negative charge states of V
C
, showing its
negative-U system. The direct correlation between EPR
and DLTS data enables an unambiguous identification
of the DLTS Z
1=2
center [ E
C
ð0 :56–0:71Þ eV] to the
(2j0)ofV
C
and its higher-lying Z
1
( E
C
0:52 eV)
and Z
2
( E
C
0:45 eV) states to the (j0) states of
V
C
ðhÞ and V
C
ðkÞ, respectively. The carrier concentration-
versus-depth profiles, obtained at different temperatures
and with Z
1=2
and EH
6=7
as the decisive centers, fully
support the conclusion from EPR that they are related to
the double acceptor (2j0) and single donor (0jþ) states
of V
C
, respectively.
Support from the Swedish Energy Agency, the Swedish
Research Council VR/Linne
´
Environment LiLI-NFM, the
Knut and Alice Wallenberg Foundation, the Norwegian
Research Council (FRINAT program, CAPSiC and
WEDD projects), and the Grant-in-Aid for Scientific
Research (21226008) from JSPS is gratefully
acknowledged.
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1.6
2
2.4
2.8
0.50 1.0 1.5 2.0 2.5 3.0
Carrier concentration (10
15
cm
-3
)
Depth (µm)
2
2.2
2.4
2.6
2.8
simulation:
shallow donor
deep donor
included
700 K
190 K
300 K
simulation:
deep acceptor
190 K
300 K
(a)
(b)
FIG. 3 (color online). Comparison between experimental
(open squares and circles) and simulated carrier concentration
profiles: (a) at 190 and 300 K, and (b) at 700 K. In the
simulations, Z
1=2
and EH
6=7
are considered as a double acceptor
and a single donor, respectively. The influence on the carrier
concentration is negligible for EH
6=7
at low temperatures and for
Z
1=2
at high temperatures.
PRL 109, 187603 (2012)
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187603-4
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PRL 109, 187603 (2012)
PHYSICAL REVIEW LETTERS
week ending
2 NOVEMBER 2012
187603-5
![FIG. 2 (color online). Scheme of energy levels of VC, determined by photo-EPR. The Z1=2 and EH7 levels determined by DLTS [11,14,15] are given for comparison. Here the optical transitions obtained by photo-EPR involve a Franck-Condon shift in the range 0:03–0:3 eV. For clarity, the location of the states in the scheme does not follow the relative scale and the levels determined by photo-EPR are aligned to the corresponding levels determined by DLTS the optical transitions from the ( j0) and (2 j0) states to the conduction band involve different Franck-Condon shifts for V C ðhÞ and V C ðkÞ. The photo-EPR data for the (0jþ) level are from Ref. [25].](/figures/fig-2-color-online-scheme-of-energy-levels-of-vc-determined-lb03v7bx.webp)
