PRL 109, 187603 (2012)

week ending
2 NOVEMBER 2012PHYSICAL REVIEW LETTERS

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,5T. Makino,6 T. Ohshima,6 and E. Janzén1
1

Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, 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 (VC ) in 4H-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 Z1=2 lifetime-limiting defect andthe EH7 deep defect—are related to the double acceptor (2j0) and single donor (0jþ) levels of VC ,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 bondsof 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 defectis called a negative-U center. A typical example of anegative-U defect is the monovacancy in Si [2].
In 4H-SiC, calculations without charge correction [3]suggested that VC is a negative-U center for negative andpositive charge states. With including charge correction,
the negative-U behavior is not found in some calculations[4] while it remains in another [5] for VC in the negative
charge state. A recent calculation using hybrid density
functionals [6] found the negative-U behavior of VC at
the quasicubic k site, VC ðkÞ, with the double negative(2j0) charge states lying slightly (< 0:1 eV) lower than
the single negative (j0) charge state. The symmetry
lowering (to C1h ) of VC was confirmed by electron paramagnetic resonance (EPR) in 4H- and 6H-SiC [7–9]. The
EPR signal of the positive vacancy [VCþ ðhÞ and VCþ ðkÞ][7,9] and VC ðhÞ (Ref. [8]) have been observed and no clear
data indicating the negative-U behavior of VC have so far
been reported.
VC is predicted to have low formation energies inboth Si- and C-rich conditions [3,4,6]. VC is frequently
detected by EPR in high-purity semi-insulating substrates
and is believed to play an important role in carrier compensation [10]. It has been shown from deep-level transient
0031-9007=12=109(18)=187603(5)spectroscopy (DLTS) that the two most common and unavoidable defect levels in as-grown 4H-SiC layers grownby chemical vapor deposition (CVD) are the Z1=2 level [11]at 0:56–0:71 eV below the conduction band minimum
EC and the EH6=7 level at EC  ð1:55–1:65Þ eV [12,13].
The Z1=2 level in 4H-SiC is known to be a negative-U
center associated with two higher-lying levels, Z1 at
0:52 eV and Z2 at 0:45 eV below EC [14]. Different
defect models such as the divacancy [15], nitrogen-related
defect [16] or N-dicarbon interstitial complex [17] weresuggested for Z1=2 . The Z1=2 center was found to appear
always together with the EH6=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 irradiationeven with low-energy (116–210 keV) electrons which displace C atoms only, creating defects in the C sublattice[13,19] and (ii) very close to each other in all kind ofsamples regardless of growth, irradiation, or annealing
conditions used [13]. The Z1=2 and EH6=7 levels were,
therefore, suggested to belong to the same defect such as
VC or a VC -related complex [20]. It has been shown that theconcentrations of the Z1=2 and EH6=7 levels can be efficiently reduced by C implantation and annealing [20] or bythermal oxidation [21,22], supporting the VC -related defectmodel. However, due to the lack of experimental evidence
indicating the negative-U behavior of VC , the origin of theZ1=2 defect remains to be identified. Concurrent with the
reduction of the Z1=2 concentration, a significant increaseof the carrier lifetime was observed [21–23], confirmingthat Z1=2 is the dominant lifetime-limiting defect in thematerial and, hence, technologically important for device
applications.

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where the N donors were completely compensated bydeep levels. The thickness of the CR varies with theelectron fluence (from 25 m for sample D to
45 m for sample A). In the CR, the Fermi level islocated at EC  0:53 eV as estimated from the series
resistance of the Schottky barrier diodes. No EPR signalof VC 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 VC 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 inaddition to the VC ðhÞ signal [Fig. 1(b)]. Under illumination, the signals of VC ðhÞ and the new line increase substantially [Fig. 1(c)]. After illumination, the signals are
persistent in darkness. The principal values of theg tensor and the Si hyperfine (hf) A tensor determined at
140 K for VC ðhÞ are gk ¼ 2:0040, g? ¼ 2:0038, and the
A values (in unit of mT) Ak ¼ 9:92, A? ¼ 7:72 (for Si1
atom along the c axis) and Axx ¼ 4:11, Ayy ¼ 4:05, Azz ¼
5:21 (for three Si2–4 atoms in the basal plane). For the newspectrum, the corresponding parameters are gk ¼ 2:0046,
EPR intensity (linear scale)In this Letter, we report the result of our EPR study ofn-type 4H-SiC epitaxial layers irradiated with low-energy
electrons (250 keV) which generate mainly VC , C interstitials and their associated defects. (The Si vacancy can becreated by 250 keV electrons but its concentration is below
the detection limit of EPR.) With the presence of only VC
in absence of other EPR signals, which are dominant insamples irradiated by high-energy electrons, we could
detect both the signals of VC ðhÞ and VC ðkÞ. Using EPR
and photoexitation EPR (photo-EPR) we could determine
the ionization energy of the single and double acceptor
states of VC and to reveal its negative-U properties. Theenergy levels of VC obtained by EPR correlate well withthose determined by DLTS for the negative-U Z1=2 center[14], allowing an unambiguous identification of the Z1=2
center as the doubly negatively charged (2j0) state of VC .
Our study of the depth profile of the carrier concentration
by capacitance-voltage (C-V) measurements and DLTS
also shows that the Z1=2 and EH6=7 centers in implanted
and annealed samples are of double acceptor and single
donor type, respectively, supporting the identification ofthese deep levels to different charge states of VC .
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  1017 cm3 . Two sets of samples,
each consisting of five samples, labeled A–E, were preparedfor 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 1018 cm2 ). EPR measurements were performed on a X-band ( 9:4 GHz) Bruker
E500 spectrometer equipped with a He-flow cryostat allowing 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 wereused as a light source. In photo-EPR experiments, weused the second order of a 600 g=mm grating which gives
a dispersion of 3:2 nm=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 of6 meV in the photon energy, the error in determinationof the energy threshold is expected to be within 10 meV.
For DLTS and C-V measurements, we also used n-typeepitaxial layers ( 10 m thick) with a net doping concentration of 2:5  1015 cm3 and implanted with 4.3 MeV
28 Si ions at room temperature to doses of 1–4  108 cm2
which result in a nonuniform defect distribution with a peakat 1:8 m. The implanted samples were then annealed at1150  C in N2 flow for 3.5 h followed by thermal evaporation 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 compensated region (CR) in highly irradiated samples (A–D)(a) sample E, in dark(b) sample A
in dark

VC(k)

VC(h)

(c) sample Chν=1.46 eV

9.415 GHz
T=100 K

4H-SiC, B||c
334

335
336
Magnetic field (mT)

337

1
0.8

(d)

VC(k)

0.6
EPR intensity (a.u.)

PRL 109, 187603 (2012)

0.4

VC(h)
0.74 eV

0.2

4H-SiC
sample E
T=100 K

0
1
0.8
0.6
0.4

(e)

0.78 eV
0.74 eV

VC(h)

0.2
0
0.6

VC(k)

0.8

4H-SiC
sample C
T=100 K1
1.2
Photon energy (eV)

1.4

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  1018 cm2 , C: 5:7  1018 cm2 andA: 7:5  1018 cm2 ) measured at 100 K (a)–(b) in darkness and(c) under illumination. The dependence of the EPR intensity ofVC ðhÞ and VC ðkÞ on the photon energy in (d) sample E and(e) sample C. The error in determination of the energy thresholdin the spectral region is within 0:01 eV.

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PRL 109, 187603 (2012)PHYSICAL REVIEW LETTERSg? ¼ 2:0035, Ak ¼ 3:69, A? ¼ 2:96 (for Si1 ), and Axx ¼
6:05, Ayy ¼ 5:94, Azz ¼ 7:49 (for Si2–4 ). The angle 
between the principal Azz and the c axis is 75.9 for
VC 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
Si2–4 are larger than that of Si1 . From the obtained g tensor
and the Si hf tensors, this new spectrum is identified to berelated to VC ðkÞ [24].
Photo-EPR experiments were performed on samples E
and C. The dependence of the EPR intensity of VC ðhÞ andVC ðkÞ on the photon energy is shown in Fig. 1(d) for
sample E and in Fig. 1(e) for sample C. The temperaturedependence of the VC signal in darkness and the photoEPR data can be explained by the scheme of energy levelsof a negative-U VC center in Fig. 2 with the (2j0) level
lying lower than the (j0) level. In the single negative
charge state, VC prefers to capture another electron to
become doubly negatively charged and lowers its energy.
Thus, at low temperatures, VC is in the 2 charge state(S ¼ 0) and no EPR signal can be observed. At elevatedtemperatures (> 90 K), the higher-lying (j0) state can be
partly populated due to internal thermal excitation of electrons from the (2j0) level and, hence, a weak signal of
VC could be detected in darkness [Fig. 1(b)]. We assign theenergy threshold of 0:74 eV for observing the VC ðkÞ
signal in sample E [see Fig. 1(d)] to the optical transition
from the (2j0) level to EC . The corresponding transition
for VC ðhÞ is 0:78 eV [Fig. 1(d)]. In sample C, the VC ðhÞ
signal already weakly appears in darkness (at 100 K).
When the photon energy reaches h  0:74 eV, theVC ðkÞ signal appears as expected [Fig. 1(e)]. The VC ðhÞ
signal starts decreasing at h  0:74 eV. We attributed thish-site k-site EH7 Z1(-|0) ~0.74(2-|0) ~0.78~0.74~1.8 eV
(0|+)

Z2
~0.52

EC
~0.45

~0.56-0.67~0.71 Z1/2

~1.55 eV
EH7

VC

Z1/2 & EH7

Photo-EPR

DLTS

EV

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 opticaltransitions 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 thelevels determined by photo-EPR are aligned to the corresponding levels determined by DLTS the optical transitions from the(j0) and (2j0) states to the conduction band involve different
Franck-Condon shifts for VC ðhÞ and VC ðkÞ. The photo-EPR data
for the (0jþ) level are from Ref. [25].

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threshold ( 0:74 eV) to the transition from the (j0)level of VC ðhÞ to EC which reduces the population of the(j0) level and, hence, the VC ðhÞ signal.
In agreement with previous studies [25], we also foundthat in n-type 4H-SiC irradiated with 250 keV electrons VC
is the dominant EPR defect and Z1=2 and EH7 are thedominant DLTS centers. The obtained energy transitions
from the (2j0) level of VC to EC [  0:74 eV for VC ðkÞand 0:78 eV for VC ðhÞ] are very close to the ionizationenergy of the Z1=2 level (EC  0:56–0:71 eV) [14,15].
The transition from the (j0) level of VC ðhÞ to
EC ( 0:74 eV) is also close to the ionization energyof the higher-lying states Z1 ( EC  0:52 eV) andZ2 ( EC  0:45 eV) [14]. (The optical transitions involvea Franck-Condon shift in the range of 0:03–0:3 eV,
which is also in good agreement with the recent calculated
values [5].)Since the VC ðhÞ signal can be detected in darkness insamples A–D at T > 90 K, whereas VC ðkÞ can only be
weakly seen in sample A at T  100–130 K, it is likely thatthe energy separation between the (2j0) and (j0) levels
is smaller for VC ðhÞ and larger for VC ðkÞ. Therefore, weassign VC ðhÞ to Z1 and VC ðkÞ to Z2 . The optical transitions
from the acceptor states of VC to EC are shown in Fig. 2.
For comparison, the ionization energies of Z1=2 center
determined by DLTS [14,15] are also shown in Fig. 2.
The same DLTS defect in 6H-SiC (the E1 and E2 centers)also shows a similar order of the energy levels of E1 (VC at
h site) and E2 (VC at two cubic k1 and k2 sites with double
intensity) [26]. Here we reassign the charge states proposed
in Ref. [14] from (0jþ) to (j0) for Z1 and Z2 and from(j þ) to (2j0) for Z1=2 . The energy transitions observedin our photo-EPR experiments are smaller than those obtained before in Ref. [25]. In those photo-EPR experiments
on low-doped ( 7  1014 cm3 ) samples [25], the concentration of VC is limited by the N concentration (morethan 2 orders of magnitude less compared to the doping
level in our samples A–E) and, therefore, the VC signal wasmuch weaker and could only be detected with excitationenergies above 1:0 eV [25]. The obtained energies of
acceptor levels of VC are rather close to those reported inrecent hybrid functional calculations [6]. However, after
charge correction, the negative-U behavior of VC ðhÞ disappeared [6]. It is clear that the methods used for charge
correction in conventional [4] or hybrid functional calculations [6] result in an overcorrection.
The threshold 1:8–1:9 eV present in previous photoEPR experiments [27,28] has recently been reassigned tothe transition from the valence band EV to the (2þjþ)level of VC [5]. However, the reassignment was made byconsidering 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-typematerial [8,25] with the Fermi level located close to the(2j0) state of VC and neither VC nor VCþ signals could be

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2 NOVEMBER 2012PHYSICAL REVIEW LETTERS

detected in darkness. However, the same threshold of
1:8 eV for activating (or recovering) the VCþ signal occurs also in n-type material [8,25]. This shows that the1:8 eV threshold can only correspond to a transition
which excites electrons from the (0jþ) level to EC as
illustrated in Fig. 2. The threshold correlates well with
the DLTS EH6=7 level, or more precisely, the EH7 levelin material irradiated with low-energy electrons [13,19,25]
where the VC EPR center and the Z1=2 and EH7 DLTS
centers are the clearly dominant defects [25]. The FranckCondon shift involved in the 1:8 eV optical excitation isin the range of 0:25 eV, corroborating the association
with the EH7 level at 1:55 eV below EC .
The double acceptor nature of Z1=2 and donor behavior
of EH6=7 , inferred from the EPR data, are unambiguously
confirmed by C-V measurements performed on Siimplanted and annealed high-purity (epitaxial) n-typesamples where the concentration of other deep-level defects is more than 1 order of magnitude lower than that of
Z1=2 and EH6=7 . At a sample temperature of 190 K, thethermal emission rate of electrons from the Z1=2 level (andthe EH6=7 level) to EC is negligible compared to both theprobe (1 MHz) and sweep (1 Hz) rates used and therecorded 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 Z1=2 , Fig. 3(a). At
300 K, Z1=2 responds to the sweep voltage but not to theprobe one, and an anomalous peak occurs at 2:4 m in
Fig. 3(a). The occurrence of such a peak is a unique featureof a nonuniform distribution of deep acceptorlike traps[29], and no evidence is found for a donorlike behaviorof Z1=2 , arising from the EC  0:5 eV levels. Indeed, thedata measured at 700 K, where Z1=2 responds to both theprobe and sweep voltages, unambiguously rule out any
donor activity of Z1=2 since the electron concentration at
the maximum position of the defect profile ( 1:8 m) is
essentially equal to the shallow nitrogen donor concentration. Moreover, at 700 K an intermediate case occurs for
the EH6=7 center, responding to the sweep voltage but not
the probe one, and as shown in Fig. 3(b), excellent agreement is obtained between the measurements and simulations assuming EH6=7 to be a donor. The simulations are
based on a refined version of the model originally developed by Kimerling [29] and as illustrated in Fig. 3(a),also the data at 190 and 300 K are closely reproducedby the simulations regarding Z1=2 as a double acceptor.
In fact, Z1=2 and EH6=7 are found to exhibit identicalconcentration-versus-depth profiles except for a two-toone ratio between the absolute values, showing the double
acceptor and single donor behavior of Z1=2 and EH6=7,
respectively, and fully supporting the conclusion from the
EPR data that they originate from the same defect, VC .
In summary, using N-doped n-type 4H-SiC epitaxial
layers irradiated with low-energy electrons (250 keV),

2.8

Carrier concentration (1015 cm-3)

PRL 109, 187603 (2012)

2.4

300 K

simulation:
deep acceptor
190 K
300 K

2
190 K

1.6
2.8
2.6
2.4

(a)
700 K

simulation:
shallow donor
deep donor
included

2.2

(b)

2
0.50

1.0

1.5

2.0

2.5

3.0

Depth (µm)

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 thesimulations, Z1=2 and EH6=7 are considered as a double acceptor
and a single donor, respectively. The influence on the carrier
concentration is negligible for EH6=7 at low temperatures and for
Z1=2 at high temperatures.

we were able to detect the VC signal at both the h andk site and to obtain more accurate energies of the single anddouble negative charge states of VC , showing its
negative-U system. The direct correlation between EPR
and DLTS data enables an unambiguous identificationof the DLTS Z1=2 center [ EC  ð0:56–0:71Þ eV] to the(2j0) of VC and its higher-lying Z1 ( EC  0:52 eV)
and Z2 ( EC  0:45 eV) states to the (j0) states of
VC ðhÞ and VC ðkÞ, respectively. The carrier concentrationversus-depth profiles, obtained at different temperatures
and with Z1=2 and EH6=7 as the decisive centers, fully
support the conclusion from EPR that they are related tothe double acceptor (2j0) and single donor (0jþ) statesof VC , respectively.
Support from the Swedish Energy Agency, the Swedish
Research Council VR/Linné Environment LiLI-NFM, theKnut 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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