Carbon dangling-bond center (carbon Pb
center) at 4H-SiC(0001)/SiO2 interface
Cite as: Appl. Phys. Lett. 116, 071604 (2020); https://doi.org/10.1063/1.5143555
Submitted: 25 December 2019 . Accepted: 07 February 2020 . Published Online: 20 February 2020
T. Umeda, T. Kobayashi, M. Sometani, H. Yano, Y. Matsushita, and S. Harada

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Carbon dangling-bond center (carbon Pb center)at 4H-SiC(0001)/SiO2 interface
Cite as: Appl. Phys. Lett. 116, 071604 (2020); doi: 10.1063/1.5143555
Submitted: 25 December 2019 . Accepted: 7 February 2020 .
Published Online: 20 February 2020
T. Umeda,1,a)T. Kobayashi,2

M. Sometani,3

H. Yano,1

Y. Matsushita,2and S. Harada3

AFFILIATIONS
1Institute of Applied Physics, University of Tsukuba, Tsukuba 305-8573, Japan

2
3

Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan
National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8569, Japana)

Author to whom correspondence should be addressed: umeda@bk.tsukuba.ac.jp

ABSTRACT
We identify a carbon dangling-bond center intrinsically formed at thermally oxidized 4H-SiC(0001)/SiO2 interfaces. Our electricallydetected-magnetic-resonance spectroscopy and ﬁrst-principles calculations demonstrate that this center, which we name “the PbC center,” isformed at a carbon adatom on the 4H-SiC(0001) honeycomb-like structure. The PbC center (Si3C-, where “-” represents an unpaired electron) is determined to be a just carbon version of the famous Pb center (Si dangling-bond center, Si3Si-) at Si(111)/SiO2 interfaces because
we found close similarities between their wave functions. The PbC center acts as one of the major interfacial traps in 4H-SiC(0001) metaloxide-semiconductor ﬁeld-effect transistors (MOSFETs), which decreases the free-carrier density and the ﬁeld-effect mobility of
4H-SiC(0001) MOSFETs. The formation of the PbC centers has the role of reducing the oxidation-induced strain, similar to the case of theformation of the Pb centers.
Published under license by AIP Publishing. https://doi.org/10.1063/1.5143555

Metal-oxide-semiconductor (MOS) interfaces are crucial for various modern electronic devices.1 They are the heart of Si MOS ﬁeld-effecttransistors (Si MOSFETs) in state-of-the-art complementary-MOS integrated circuits.1 The MOS structures are also indispensable to various
power devices such as power MOSFETs for power electronics.2–6 The
development of power MOSFETs is expanding over widebandgap
semiconductors such as 4H-SiC (bandgap, Eg ¼ 3.26 eV),2,3 GaN (Eg¼ 3.4 eV),4 Ga2O3 (Eg ¼ 4.8 eV),5 and even diamond (Eg ¼5.4 eV)6 tomeet the demand of continuously growing electric-power consumption.
However, the performance of their MOSFETs is generally limited due tothe poorer quality of their MOS interfaces, which suffer from many
more MOS interface defects than Si-MOS systems.2–6 In Si, major interface defects are identiﬁed as so-called “Pb centers,”7,8 which are found at
every Si(111),9–11 Si(100),12,13 and Si(110) surface.14 Essentially, Pb centers are a family of Si dangling bonds (DBs) intrinsically formed at Si/
SiO2 interfaces.7,8 Similar to Si-MOS systems, Ge-MOS interfaces also
generate the same type of interface defect, i.e., “Ge Pb centers.”15,16 In
contrast, wideband-gap semiconductors seem to have no such benchmark model for their MOS interface defects. For instance, 4H-SiC/SiO2
interfaces have been widely studied over two decades; however,the search for benchmark models of their interface defects is stillongoing.17–24

Appl. Phys. Lett. 116, 071604 (2020); doi: 10.1063/1.5143555
Published under license by AIP Publishing

In this Letter, we present a spectroscopic and theoretical identiﬁcation of a Pb-like interface defect in 4H-SiC MOS systems, which wecall the “PbC center.” The PbC center is intrinsically formed after thermal oxidation of the 4H-SiC(0001) surface (the Si-face), which is thestandard surface of 4H-SiC wafers. This center is just a carbon versionof the famous Pb center, i.e., an ideal carbon DB at the interface. We
believe that the PbC center is identical to a previous “interface carbon
defect” with a typical density of 3–4  1012 cm2 observed by electron-spin-resonance (ESR) spectroscopy on thermally oxidized 4HSiC(0001)/SiO2 substrates.17,18 Instead of ESR, we here used electrically detected-magnetic-resonance (EDMR) spectroscopy,19–23 whichenabled us to complete a full analysis of 13C and 29Si hyperﬁne (HF)
interactions of this center. Like the Pb center in Si/SiO2 systems, theformation of the PbC center is closely correlated with relaxation of
the oxidation-induced strain at 4H-SiC/SiO2 interfaces, which wasquantitatively conﬁrmed from ﬁrst-principles calculations. The calculations also demonstrated that the PbC center is formed at a carbon
adatom (C adatom) on the 4H-SiC(0001) surface. We also discuss signiﬁcant inﬂuences of the PbC center on the performance of 4H-SiC
MOSFETs.
For highly sensitive EDMR measurements, we prepared n-channel
lateral 4H-SiC MOSFETs with a special dimension (gate length/

116, 071604-1

Applied Physics Letterswidth ¼ 5/2000 lm) on a 4 -off p-type 4H-SiC(0001) epitaxial layer(Al doping of 5  1015 cm3). The 30-nm thick gate oxide wasformed by a standard thermal oxidation at 1200  C using dry O2.
Further details of the fabrication processes are published in previous
papers.25 The MOSFETs exhibited a maximum ﬁeld-effect mobility(lFE) of 7 cm2 V1 s1, which is slightly higher than conventional
values of Si-face 4H-SiC MOSFETs,2,3,25 because of optimal dry oxidation and epitaxial layer. However, this value is still far from an
ideal electron mobility of 4H-SiC (1000 cm2 V1 s12,3), indicating agreat inﬂuence of interface defects. We then conducted bipolarampliﬁcation-effect (BAE) EDMR measurements19 to amplify
EDMR signals of the interface defects. We used a standard lock-in
ampliﬁcation technique synchronized to a magnetic-ﬁeld modulation at 1.56 kHz.18,23 ESR transitions were excited by a microwave at
9.45 GHz and 200 mW at room temperature.
Figure 1(a) shows room-temperature EDMR spectra of the Siface 4H-SiC MOSFET as a function of magnetic-ﬁeld angles. Only onestrong EDMR signal was observed, which is the PbC-center signal (anelectron spin ¼ 1/2), showing slightly c-axial gyromagnetic factors (g)of g// ¼ 2.0029 and g? ¼ 2.0032. We believe that this EDMR signal is

FIG. 1. (a) EDMR spectroscopy on the PbC center at the 4H-SiC(0001)/SiO2 interface as a function of magnetic-ﬁeld angles. For 0 and 90 , the magnetic ﬁeld wasparallel and perpendicular to the [0001] axis, respectively. Solid blue lines in the
angular map (upper plane of this graph) were simulated using the g and HF tensors
shown in the text. EDMR spectra were measured using a source current of 180 nA
with a negative gate bias of 7.5 V and a constant drain current of 10 lA in BAE
EDMR mode. (b) Spectral simulation of 13C and 29Si HF doublet signals (solid bluelines). The 29Si HF structure was ﬁtted to the experimental spectrum by adding
smooth tail curves (dashed blue lines in the upper spectrum). Each HF signal
consists of replica made from the experimental spectrum with relative intensities
shown in ﬁgure. (c) Atomic structures of the PbC center at the 4H-SiC(0001) surfaceand (d) Pb center at the Si(111) surface. In top views, solid circles on Si atoms indicate surface-normal Si bonds. These structures were unrelaxed, and their optimized structures are seen in Fig. 2.

Appl. Phys. Lett. 116, 071604 (2020); doi: 10.1063/1.5143555
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identical to an ESR signal with a spin density of 3–4  1012 cm2
observed in the as-oxidized 4H-SiC(0001) epitaxial layers.17,18 An
extremely higher signal-to-noise ratio of EDMR spectra can reveal afull angular dependence of HF interactions of this center.
As shown in Fig. 1(a), this center clearly exhibits two sets of HF
doublet structures (splitting widths of 16.1–23.7 mT and 6.6 mT),which we assign to HF satellite signals due to a 13C nuclear spin
(nuclear spin I ¼ 1/2, natural abundance p ¼ 1.1%) and 29Si nuclear
spins (I ¼ 1/2, p ¼ 4.7%), respectively. These HF signals can be excellently ﬁtted by HF interactions due to one C site and three equivalent
Si sites, as demonstrated in Fig. 1(b). The former C site generates HF
doublet signals with a relative intensity of 1.1% as shown in the ﬁgure.
The latter Si sites cause a doublet splitting with a relative intensity of
6[(p/2)3 þ (p/2)(1  p)2] ¼ 12.7%, supposing one to three 29Si nuclear
spins at three equivalent Si sites. The 13C HF splitting reveals a c-axial(C3v) symmetry, as seen in the angular map of Fig. 1(a), indicating that
the C site has a c-axial 2p-orbital. The c-axial 13C HF tensor was determined to have A// ¼ 23.70 mT and A? ¼ 16.09 mT.
The above 13C and 29Si HF interactions are in good agreementwith a carbon-DB model such as a Si3C- structure (“-” means a DB)
at the 4H-SiC(0001)/SiO2 interface, which is just analogous to the Pb
center (a Si3Si- structure) at the Si(111)/SiO2 interface.7,10,11 Thelargest HF splitting of 13C with a c-axial symmetry is generated from asurface-normal (c-axial) carbon DB. The second largest HF interaction
due to 29Si is caused by three equivalent Si atoms adjacent to the C DB
site. In Fig. 1(c), we draw the atomic structure of the PbC center at the
4H-SiC(0001) surface, in addition to that of the Pb center at theSi(111) surface [Fig. 1(d)]. Obviously, both surfaces have similar
honeycomb-like structures, except their lattice constants. They commonly have surface-normal Si bonds, as indicated by “•” in the ﬁgure.
The Pb center is formed by breaking one of such Si bonds, as denotedwith “” in Fig. 1(d). In contrast, at the 4H-SiC(0001) surface, there
are no surface-normal C bonds. Thus, we must consider an additional
atomic conﬁguration where a carbon DB stands up. Our conclusion isshown in Fig. 1(c) on the basis of the ﬁrst-principles calculations. A
carbon DB can be formed at a C adatom bonded to three Si atoms on
the 4H-SiC(0001) surface. The advantages of such a conﬁguration are
obvious, though quantitative arguments will be given later. When connecting to a top SiO2 layer, the Si(111) surface shown in Fig. 1(d) must
be affected by a tensile strain due to a larger unit cell of SiO2.7,8,11,26
Eventually, some Si bonds must be disconnected, resulting in the formation of the Pb center.7,8,11 On the other hand, since a unit cell of
4H-SiC(0001) is smaller than that of Si(111), we must disconnect
more Si bonds at the 4H-SiC(0001)/SiO2 interface. A C-adatom structure consumes three Si bonds at the interface, reducing the above constraint. Simultaneously, it can also ﬁx residual C atoms that are
unavoidably emitted during the thermal oxidation of 4H-SiC. Further
discussions are shown in Ref. 27.
From the obtained 13C HF tensor, we can experimentally determine the wave function7,10,13,28,29 of the PbC center, as summarized inTable I. One of the notable features is a very strong spin localization
on a DB site for the PbC center. g2 reaches 80%, which is the largest
value obtained in SiC.29 Such strongest spin localization is also characteristic of the original Pb center in Si.7,10 Table I also shows the s/p
hybridization ratio (a2/b2), which is signiﬁcantly higher for PbC (21%)
than for Pb (13%). This indicates a more sp3-like tetrahedral structure
for PbC, which is naturally understandable by the C-adatom structure.

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TABLE I. Wave-function parameters of PbC and Pb centers. Fractions of s- and p-orbitals, g2a2 and g2b2 (a2 þ b2 ¼ 1), are directly calculated from isotropic and anisotropic
HF constants Aiso and Aaniso, via g2a2 ¼ jAiso/A0j and g2b2 ¼ jb/b0j, respectively.7,10,11,24,28,29 Note that Aiso ¼ (A//þ 2 A?)/3 and Aaniso ¼ (A//  A?)/3.28,29 We used
known HF constants of A0 ¼ 134.77 mT and b0 ¼ 3.83 mT for 13C and A0 ¼ 163.93 mT and b0 ¼ 4.075 mT for 29Si.28 The calculated 13C HF constants of a C adatom
were A//¼ 10.9 mT and A? ¼ 4.0 mT. In lower part, we estimated g2a2 and g2b2 in the same manner from the calculated 13C and 29Si HF tensors for PbC and Pb, respectively.

Centers-orbital(g2a2)

p-orbital(g2b2)

Spin localization(g2)

s/p ratio(a2/b2)

References

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Experiment
PbC at 4H-SiC(0001)/SiO2
Pb at Si(111)/SiO2
porous-PbC at porous-SiC/SiO2
TheoryC adatom (PbC) at 4H-SiC(0001)
Si DB (Pb) at Si(111)

In contrast, the original Pb center bound on the Si(111) surface is stabilized into an sp2-like planar structure.7,8
As tabulated in Table I, in porous-SiC/SiO2 structures, different
PbC centers (we here call “porous-PbC”) were observed,24 showing aquite different nature, e.g., their g2 is only 39% and their a2/b2 (11%)
is close to that of Pb. Since such g2 is widely seen for bulk defects in
SiC,29 the porous-PbC centers may be formed in the bulk side of theinterfaces. Note that for other previous interface defects such as the“Si-vacancy center”20,21 and “dual-PbC centers,”22 complete analyses
on their HF interactions and their wave functions have not yet beenreported.
To examine the PbC center more quantitatively, we carried out
ﬁrst-principles calculations on both the PbC and Pb centers. All calculations were carried out on the basis of density functional theory byusing the Vienna ab initio simulation package (VASP). The projector
augmented-wave method, as implemented in the VASP code,
was applied in the calculations. Figures 2(a) and 2(b) show our
H-terminated 4H-SiC(0001) and Si(111) slab units for optimizing the
calculations on semiconductor surfaces. They include either a PbC center (a DB on a C adatom) or a Pb center (a Si DB formed at the surface).
The lattice parameters of SiC were ﬁxed to the values obtained in ourprevious calculations,30,31 and the defect structures were relaxed using
the Perdew–Burke–Ernzerhof functional32 until the remaining forceswere less than 40 meV/Å. Note that, by calculating the formation energies of 114 types of mono- and di-carbon defects in 4H-SiC(0001)/SiO2
systems, we found that the C adatom shown in Fig. 2(a) appears as oneof the metastable forms of carbon-related defects.30,31
Next, we check the HF constants of the PbC center, which
was performed using the Heyd–Scuseria–Ernzerhof (HSE06) hybrid
functional.34–36 The contribution of core states (A1c)36 is included in
the calculation of HF constants. A single k-point (the C point) was
sampled during the calculations, and spin-polarization was taken into
account. As summarized in Table I, the experimental and theoreticalvalues are basically in good agreement with each other for both the
PbC and Pb centers, ensuring the validity of the C-adatom model aswell as the validity of our calculation strategy. Only an exception was asmaller calculated value for the 2s-orbital (g2a2) of the PbC center. Thislarger deviation may be related to the fact that the isotropic 13C HF
constant is extremely sensitive to the amplitude of the 2s-orbital, which
is more difﬁcult to be calculated accurately compared to other orbitals.

Appl. Phys. Lett. 116, 071604 (2020); doi: 10.1063/1.5143555
Published under license by AIP Publishing

FIG. 2. (a) 488-atom H-terminated 4H-SiC(0001) unit cell including a single PbC
center used for ﬁrst-principles calculations. (b) 503-atom H-terminated Si(111) unit
cell for calculating the Pb center. In (a) and (b), blue, brown, and small whiteballs depict the Si, C, and H atoms, respectively. The vacuum thickness is about
18 Å for each structure. The Si(111) cell was constructed on the algorithm proposed
in Ref. 33. The calculated three-dimensional wave functions related to DB states of
the C adatom and surface Si atom are also drawn with the isosurface of about
30-% of maximum amplitude. The visualization of crystal structures and wave functions was performed using VESTA. (c) Total-energy calculations on 4H-SiC(0001)
unit cells with/without a PbC center under either lateral lattice expansion or compression. The vertical axis indicates relative changes in the calculated total energy,
and the horizontal axis denotes relative changes in the lateral lattice constantof unit cells. Zero of lattice constant was set at the optimized lattice constant of the
H-terminated 4H-SiC slab.

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In Fig. 2(c), we examine the effect of a top SiO2 layer on the 4HSiC(0001) surface through the intentional introduction of an in-planestrain into the 4H-SiC unit cell. Here, we optimized the internal
atomic positions by the HSE06 functional with the varying in-planelattice constants. The horizontal axis indicates the introduction ofeither a tensile strain or compressive strain along two lateral directions.
In the C-adatom structure shown in Fig. 2(a), the bond length between
the C adatom and three Si atoms is expanded by 6% (1.99 Å) compared to the normal C–Si length (1.88 Å). Therefore, the C-adatom
structure should become more stable when it is compressed along thelateral directions. In fact, the energy gain of creating a C-adatom
increases under compressive strain, as shown in Figure 2(c). Namely,
the C-adatom structure has a tendency to shrink; in other words, it
intrinsically involves a local compressive strain. Accordingly, the formation of the C adatoms (the PbC centers) can locally cancel out theoxidation-induced tensile strain.26 We emphasize that such a straininduced formation mechanism is just similar to that proposed for the
Pb center at the Si(111)/SiO2 interface.7,11
The spin density of the Pb center at the Si(111)/SiO2 interface wasfound to be typically 2–3  1012 cm2,7,9–11 which is approximately
50% smaller than that of the PbC center (3–4  1012 cm217,18) at the
4H-SiC(0001)/SiO2 interface. This ratio is similar to that of the atomic
densities between the Si(111) and 4H-SiC(0001) surfaces: 7.8  1014
and 1.2  1015 cm2 for their top Si atoms, respectively,. In Ref. 18, wedemonstrated hydrogen passivation of the PbC center, providing withanother similarity to the Pb center.
Since the above spin density is just comparable to the free-carrier
density in the inversion layer of 4H-SiC MOSFETs (< 9  1012 cm2),25
the PbC center has non-negligible impacts on the performance of the
MOSFETs. Actually, we observed that the PbC center was diminished by 1/10 or less after post oxidation anneal (POA) with NO,
which simultaneously increased lFE over 30 cm2 V1 s1.18 The
physical reasons why the PbC center affects lFE are because (1) thiscenter reduces the amount of mobile electrons via electron captureand (2) charged PbC centers (charged DBs) increase Coulombic
scattering. In fact, an increase of 2  1012 cm2 was observed in
the free-carrier density after NO POA,25 which is comparable to thedensity of PbC. However, the PbC center cannot account for the total
amount of electron traps ( 8  1012 cm225) and other traps
should also be present. The electronic level of PbC will also be important for p-channel 4H-SiC MOSFETs, because of its amphotericnature likewise the Pb center. Its exact location is being examined
experimentally and theoretically. At least, we estimate that its neutral DB level (spin-1/2 state) is located in the midgap region
because the PbC center became EDMR-active under a negative gatebias [c.f., Fig. 1(a)].
In summary, we established a benchmark model of a typicalinterface defect in 4H-SiC(0001)/SiO2 systems. In this most studied
wideband-gap-semiconductor MOS interface, the PbC center (carbon
DB) is intrinsically formed in association with the oxidation-induced
strain. We unambiguously identiﬁed that this center is just a carbon
version of the famous Pb center in Si-MOS systems, based on the ﬁrst
full-analysis on 13C HF interaction of an interfacial C atom.
This work was supported by the Council for Science,
Technology and Innovation (CSTI), Cross-ministerial Strategic
Innovation Promotion Program (SIP), “Next-generation power

Appl. Phys. Lett. 116, 071604 (2020); doi: 10.1063/1.5143555
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electronics” (funding agency: NEDO). This work was also, partly,
supported by Grant-in-Aids (Grant Nos. 18H03770, 18H03873, and
17H02781) from the Ministry of Education, Culture, Sports, Scienceand Technology of Japan. Computations were performed, mainly,
at the Center for Computational Science, University of Tsukuba,
and the Supercomputer Center at the Institute for Solid State
Physics, The University of Tokyo.
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