Trivacancy and trivacancy-oxygen complexes in silicon: Experiments and ab initio modeling

Abstract

A center from the family of ``fourfold coordinated (FFC) defects'', previously predicted theoretically, has been experimentally identified in crystalline silicon. It is shown that the trivacancy (V3) in Si is a bistable center in the neutral charge state, with a FFC configuration lower in energy than the (110) planar one. V3 in the planar configuration gives rise to two acceptor levels at 0.36 and 0.46 eV below the conduction band edge (Ec) in the gap, while in the FFC configuration it has trigonal symmetry and an acceptor level at Ec-0.075eV . From annealing experiments in oxygen-rich samples, we also conclude that O atoms are efficient traps for mobile V3 centers. Their interaction results in the formation of V3O complexes with the first and second acceptor levels at Ec-0.46eV and Ec-0.34eV . The overall picture, including structural details, relative stability, and electrical levels, is accompanied and supported by ab initio modeling studies.

Full text

Trivacancy and trivacancy-oxygen complexes in silicon: Experiments and ab initio modeling
V. P. Markevich,
1
A. R. Peaker,
1
S. B. Lastovskii,
2
L. I. Murin,
2
J. Coutinho,
3
V. J. B. Torres,
3
P. R. Briddon,
4
L. Dobaczewski,
5
E. V. Monakhov,
6
and B. G. Svensson
6
1
School of Electrical and Electronic Engineering, University of Manchester, Manchester M60 1QD, United Kingdom
2
Scientific-Practical Materials Research Centre, NAS of Belarus, P. Brovka Str. 19, Minsk 220072, Belarus
3
I3N, University of Aveiro, Campus Santiago, 3810-193 Aveiro, Portugal
4
School of Natural Science, University of Newcastle upon Tyne, Newcastle-upon-Tyne NE1 7RU, United Kingdom
5
Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland
6
Department of Physics, Oslo University, N-0316 Oslo, Norway
共Received 25 September 2009; revised manuscript received 27 November 2009; published 30 December 2009
兲
A center from the family of “fourfold coordinated 共FFC兲 defects”, previously predicted theoretically, has
been experimentally identified in crystalline silicon. It is shown that the trivacancy 共V
3
兲 in Si is a bistable
center in the neutral charge state, with a FFC configuration lower in energy than the 共110兲 planar one. V
3
in the
planar configuration gives rise to two acceptor levels at 0.36 and 0.46 eV below the conduction band edge 共E
c
兲
in the gap, while in the FFC configuration it has trigonal symmetry and an acceptor level at E
c
−0.075 eV.
From annealing experiments in oxygen-rich samples, we also conclude that O atoms are efficient traps for
mobile V
3
centers. Their interaction results in the formation of V
3
O complexes with the first and second
acceptor levels at E
c
−0.46 eV and E
c
−0.34 eV. The overall picture, including structural details, relative
stability, and electrical levels, is accompanied and supported by ab initio modeling studies.
DOI: 10.1103/PhysRevB.80.235207 PACS number共s兲: 61.72.jd, 61.72.Bb, 61.80.Fe, 71.55.Cn
I. INTRODUCTION
A new type of topological defects in semiconductor crys-
tals, the so-called “fourfold coordinated 共FFC兲 defects,” has
been predicted by ab initio modeling studies,
1–3
but so far
there has been no solid experimental evidence for their exis-
tence. We present experimental and ab initio modeling re-
sults, which show that the trivacancy 共V
3
兲 in silicon is a
bistable center in the neutral charge state, where a fourfold
coordinated configuration is the energetically favorable one.
An acceptor level is assigned to the FFC V
3
defect and its
atomic symmetry is determined by means of high-resolution
Laplace deep-level transient spectroscopy 共LDLTS兲 com-
bined with uniaxial stress.
Vacancy-related clusters 共V
n
兲 in silicon are technologi-
cally important defects because of their role in capturing un-
wanted impurities and silicon interstitials so reducing en-
hanced diffusion of dopants in extremely scaled integrated
circuits. Such clusters have attracted a great attention
recently.
3–6
Among the small V
n
共n ⱕ5兲 defects, only the
divacancy 共V
2
兲 has been studied extensively experimentally
and theoretically
4,7–11
and its properties are reasonably well
understood. The available information on the properties of
V
3
, V
4
, and V
5
defects is limited and controversial,
3–5,12
but
in general it is thought that the minimum-energy structures
for the neutral V
n
defects with n from 3 to 5 could have “part
of a hexagonal ring” 共PHR兲 configurations.
4,5
However, from
electron-spin-resonance 共ESR兲 studies of neutron-irradiated
Si, only the V
3
defect structure is consistent with the PHR
configuration 共the Si-A4 ESR signal was assigned to V
3
兲.
12
The A3 and P3 ESR signals were attributed to different con-
figurations of V
4
and P1 ESR signal was assigned to V
5
,
12
but
neither of the suggested defect structures associated with
these signals coincides with the PHR configurations of tetra-
vacancy and pentavacancy.
4,5
Furthermore, it has been ar-
gued recently that the fourfold coordinated configurations are
lower in energy for the V
3
to V
5
defects than the PHR ones.
3
No clear experimental evidence of the existence of V
n
clus-
ters in the fourfold coordinated configurations have been pre-
sented so far and electronic properties of the defects in both
configurations are not well understood.
It is shown in the present work that V
3
is bistable in the
neutral charge state, with the fourfold coordinated configu-
ration being lower in energy than the 共110兲 planar configu-
ration. V
3
in the 共110兲 planar configuration gives rise to two
acceptor levels at 0.36 and 0.46 eV below the conduction
band edge 共E
c
兲, while in the fourfold coordinated configura-
tion, the defect has trigonal symmetry showing an acceptor
level at E
c
−0.075 eV. V
3
is mobile in Si at temperatures
higher than 200 °C and can be trapped by an oxygen atom
so resulting in the appearance of a V
3
O defect. The V
3
O
center is only stable in the 共110兲 planar configuration and
gives rise to two acceptor levels at E
c
−0.34 eV and E
c
−0.455 eV. Some preliminary results on the study of the V
3
center have been published by us in Ref. 13.
II. EXPERIMENTAL AND MODELING DETAILS
Experimental results in the present work were obtained by
means of deep-level transient spectroscopy 共DLTS兲 and high-
resolution Laplace DLTS in combination with uniaxial
stress.
14
Samples for the study were prepared from
phosphorus-doped epi-Si 共
␳
⬇30 ⍀ cm兲, which was grown
on highly Sb-doped 共
␳
⬇0.01 ⍀ cm兲 bulk Czochralski-
grown Si 共Cz-Si兲 wafers. P
+
-n diodes were formed by im-
plantation of boron ions with subsequent annealing at
1200 °C in nitrogen ambient. Oxygen concentration in the
epilayers was determined from the rate of transformation of
the divacancy to the divacancy-oxygen 共V
2
O兲 defect with the
use of data presented in Ref. 9. The oxygen concentration
PHYSICAL REVIEW B 80, 235207 共2009兲
1098-0121/2009/80共23兲/235207共7兲 ©2009 The American Physical Society235207-1

was close to 4⫻10
17
cm
−3
in all the epi-Si samples. Also a
few samples from a phosphorus-doped 共
␳
⬇80 ⍀ cm兲 Si in-
got, which was refined by float-zone 共FZ兲 technique in
vacuum, were studied. According to results of infrared-
absorption measurements, the oxygen concentration in the
FZ-grown samples was lower than 5⫻ 10
15
cm
−3
. For
uniaxial stress measurements, we used three 1⫻ 2⫻7mm
3
bars with each of the long axes oriented in one of the three
main crystallographic directions. The samples for uniaxial
stress measurements were cut from a Czochralski-grown Si
crystal, which was doped with phosphorus to 3
⫻10
14
cm
−3
and had oxygen and carbon concentrations
about 8⫻ 10
17
cm
−3
and 2⫻ 10
16
cm
−3
, respectively.
Schottky barrier diodes were prepared on the FZ-grown
samples and oriented bars by thermal evaporation of Au
through a shadow mask. All the samples were irradiated with
6 MeV electrons using a linear accelerator. The flux of elec-
trons was 1⫻10
12
cm
−2
s
−1
and the temperature of the
samples during irradiation did not exceed 50 °C. Thermal
anneals of the irradiated structures were carried out in a fur-
nace in a dry N
2
ambient.
Ab initio calculations were carried out with a pseudopo-
tential density-functional code, 共
AIMPRO兲,
15
along with the
local-density approximation for the exchange-correlation
potential.
16
Basis sets for valence states are atom-centered s-
and p-like Gaussian functions with four optimized exponents
together with d-polarization functions 共further details and
convergence tests may be found elsewhere
17
兲. In order to
avoid dispersive gap states as well as to account for the con-
siderable strain fields that may occur around vacancy com-
plexes in Si,
18
the crystalline host was modeled as
H-terminated spherical clusters with up to 424 Si atoms. All
atomic sites except the outer Si-H units were allowed to re-
lax with help of a conjugate gradient algorithm. Enthalpies
for electron emission 共acceptor levels兲 are calculated by
comparing the electron affinity of the defect 共A
d
兲 to that of a
marker defect 共A
m
兲 which has well-established level location
in the gap E
c
-E
m,exp
. This procedure has been employed with
success on defects in Si and Ge.
17,19
Accordingly, E
cal
共q
−1/ q兲=E
m,exp
共q −1/ q兲+A
m
共q −1/ q兲−A
d
共q −1/ q兲, with A共q
−1/ q兲=E共q−1兲−E共q兲, where E共q兲 is the total energy of a
defect cluster with net charge q. For the marker, we choose
the V
2
O complex with first and second acceptor levels mea-
sured at E
c
−0.47 eV and E
c
−0.23 eV, respectively.
9,10
III. EXPERIMENTAL RESULTS AND THEIR
DISCUSSION
Figure 1共a兲 shows DLTS spectra for an epi-Si p
+
-n diode
which was irradiated with 6 MeV electrons and then sub-
jected to 30 min heat treatments at 125 °C and 300 °C. All
peaks in the spectra except the one with its maximum at
about 63 K are related to radiation-induced defects. Elec-
tronic signatures 关activation energy for electron emission
共E
n
兲 and pre-exponential factor 共
␣
兲 or apparent capture cross
section 共
␴
na
兲兴 were determined from Arrhenius plots of elec-
tron emission rates for all the traps. A comparison of the
values for traps responsible for the peaks having their
maxima at 63, 91, and 130 K in the spectra 1 and 2 with
those known from the literature allows us to associate these
peaks with electron emissions from the positive charge state
of thermal double donors,
20
the negative charge state of the
vacancy-oxygen 共VO兲 complex,
10,21
and the double negative
charge state of V
2
,
8–10
respectively.
It was found that the capacitance transients measured with
the use of Laplace DLTS 共Fig. 2兲 in the temperature range
210–240 K for the as-irradiated diode 共spectrum 1 in Fig. 1兲
consist of contributions of emissions from two electron traps.
Electronic signatures of the trap responsible for the signal
with the higher magnitude in the spectrum of the as-
irradiated sample in Fig. 2 are consistent with those for elec-
tron emission from the singly negatively charged state of the
divacancy.
8–10
The magnitude of the signal with the lower
magnitude in this spectrum is equal to that of the trap respon-
sible for the peak with its maximum at about 187 K in Fig. 1.
50 100 150 200 250 30
0
E5
E4
(b)
(a)
E
75
1.2
0.8
0.4
-0.2
0
0
3
2
1
V
2
O(-/0)
+E5*
V
2
(-/0 ) + E5
V
2
(-/0)
E4* (L)
E4
E
75
TDD
VO(-/0)
V
2
O(2-/-)
V
2
(2-/-)
∆
C(
pF
)
Temperature (K)
FIG. 1. 共Color online兲共a兲 DLTS spectra for an epi-Si p
+
-n diode
which was subjected to the following subsequent treatments: 共1兲
irradiation with 6 MeV electrons to a dose of 8⫻ 10
13
cm
−2
; 共2兲
and 共3兲 30 min anneals at 125 °C and 300 °C, respectively. Mea-
surement settings were e
n
=80 s
−1
, bias −10 V→ −2 V, and pulse
length 1 ms. The spectra are shifted on the vertical axis for clarity.
共b兲 Difference between the DLTS spectra 2 and 1 in 共a兲.
10 100 100
0
0.00
0.05
0.10
0
.
1
5
E5*
V
2
O(-/0)
E5
V
2
(-/0)
T
meas
=230K
As-Irradiated
30 min @ 300
o
C
LDLT
S
signal (arb. units)
Emission Rate
(
s
-1
)
FIG. 2. 共Color online兲 Laplace DLTS spectra measured at 230 K
for an epi-Si p
+
-n diode, which was irradiated with 6 MeV electrons
to a dose of 8⫻ 10
13
cm
−2
and subsequently annealed at 300 °C for
30 min.
MARKEVICH et al. PHYSICAL REVIEW B 80, 235207 共2009兲
235207-2

It appears that the two later electron emission signals can be
associated with the E4 and E5 共or E4a and E4b兲 traps studied
in irradiated silicon diodes and transistors in recent
papers.
22–26
So, in the following, we will refer to these emis-
sion signals as related to the E4 and E5 traps. Some values of
electronic signatures for the E4 and E5 traps have been
published,
22–26
however, those values were mainly deter-
mined by conventional DLTS and overlapping of the emis-
sion signals caused by the E4 and E5 traps with the much
stronger one due to the V
2
共−/ 0兲 transition limited the accu-
racy of the deduced values. The application of Laplace DLTS
technique allows us to separate readily the electron emission
signals due to the E4 and E5 traps from that due to the
V
2
共−/ 0兲 transition 共Fig. 2兲 and to determine the electronic
signatures of these traps with high accuracy. The values ob-
tained are listed in Table I.
We have also observed the E4 and E5 traps in float-zone-
grown Si samples with low oxygen content after irradiation
with 6 MeV electrons. In the irradiated FZ-Si samples, the
vacancy-phosphorus pair
27
was the dominant vacancy-
related radiation-induced defect. The E4 and E5 traps were
introduced in FZ-Si samples with similar rates as in epi-Si
p
+
-n diodes upon electron irradiation. The two traps annealed
out at the same rates upon isochronal or isothermal anneals
in the temperature range 50–125 °C and in addition they
disappeared at the same rates in both the epi-Si p
+
-n diodes
and FZ-Si samples. Our data on the annealing behavior of
the E4 and E5 traps are consistent with those obtained in
Refs. 22 and 24, where on the basis of an analysis of the
annealing results, a conclusion was drawn that these traps are
related to two different energy levels of the same defect. It is
found in the present work that simultaneously with the dis-
appearance of these traps another defect, which gives rise to
a peak with its maximum at about 44 K, appeared in the
DLTS spectra for both types of samples 关see, e.g., Fig. 1共b兲
and spectrum 2 in Fig. 1共a兲兴. The E
n
value of this trap was
found to be 0.075 eV 共Table I兲 and it will be referred to as
the E
75
trap. Figure 3 shows changes in the normalized con-
centrations of the E4 and E
75
traps in a p
+
-n diode upon
isothermal annealing at 77 °C. An analysis shows that both
the decay of the E4 trap and the growth of the E
75
trap can be
described by monoexponential functions with matching de-
cay and growth rates. In this context, it should be empha-
sized that the maximum absolute concentrations of the traps
are the same and hence, the clear anticorrelation between the
normalized values in Fig. 3 holds also on an absolute scale.
Evidently, the formation of the E
75
trap is directly related to
the disappearance of the E4 and E5 traps.
In agreement with results presented in Ref. 26, we have
found that an application of forward bias injection with a
current density in the range 10–15 A/ cm
2
for 20 min at 300
K to the irradiated p
+
-n diodes, which before biasing were
annealed in the temperature range 50–200 °C, resulted in
the complete regeneration of the E4 and E5 peaks and also in
the disappearance of the E
75
trap. Furthermore, it was found
from many experiments with the sequential annealing and
injection treatments that the E4共E5兲 ↔ E
75
transformations
are fully reversible. It should also be noted that the
E4共E5兲 ↔ E
75
transformations in the electron-irradiated
samples studied did not result in significant changes in con-
centrations of the VO and V
2
centers 关see, e.g., Fig. 1共b兲兴.
The E4 and E5 signals were associated in Refs. 22–26
with two different energy levels of the same intrinsic defect
which appears in Si samples after irradiations with high-
energy particles 共electrons with E ⬎2 MeV, ions, neutrons,
etc.兲. Our results on the introduction rates of the E4 and E5
traps in different samples by electron irradiation, on the an-
nealing behavior of the traps, and on injection-induced trans-
formations are fully consistent with the above suggestions.
Further, it is shown in the present work that the defect can
exist in two configurations with different electronic proper-
ties. We have carried out LDLTS measurements under
uniaxial stress for the E
75
trap in order to obtain more infor-
TABLE I. Electronic parameters of V
3
-related acceptor levels in Si obtained from LDLTS measurements
and positions of the energy levels derived from ab initio calculations. Values of the apparent capture cross
section 共
␴
na
兲 were calculated by dividing the
␣
values by a constant of 6.54⫻ 10
21
s
−1
K
−2
cm
−2
.
Defect label Assignment
E
na
共eV兲
␣
共s
−1
K
−2
兲
␴
na
共cm
2
兲
E
cal
共q −1/ q兲
共eV兲
E4 共E4a兲 V
3
共2−/ −兲 0.359 1.4⫻ 10
7
2.15⫻ 10
−15
0.28
E5 共E4b兲 V
3
共−/ 0兲 0.458 1.6⫻ 10
7
2.4⫻ 10
−15
0.50
E
75
V
3
ⴱ
共−/ 0兲 0.075 2.4⫻ 10
7
3.7⫻ 10
−15
0.12
E4
ⴱ
V
3
O共2−/ −兲 0.337 7.85⫻10
6
1.2⫻ 10
−15
0.28
E5
ⴱ
V
3
O共−/ 0兲 0.455 4.0⫻10
7
6.1⫻ 10
−15
0.42
0 50 100 150 20
0
0.0
0.2
0.4
0.6
0.8
1.0
E4 decay at 77
o
C
E
75
growth at 77
o
C
E
75
decay at 260
o
C
E4
*
growth at 260
o
C
N
orma
li
ze
d
concentrat
i
on
Time
(
min
)
FIG. 3. 共Color online兲 Changes in normalized concentrations
共N / N
max
兲 of E4, E
75
, and E4
ⴱ
traps upon isothermal anneals of an
electron-irradiated epi-Si p
+
-n diode at 77 °C and 260 °C.
TRIVACANCY AND TRIVACANCY-OXYGEN COMPLEXES IN… PHYSICAL REVIEW B 80, 235207 共2009兲
235207-3

mation about the structure of the center in this configuration.
Figure 4 shows the LDLTS splitting pattern for the E
75
trap
under application of uniaxial stress to three samples with the
long axis oriented along each of the three main crystallo-
graphic directions. It was found that the observed splitting
pattern is characteristic for a center with trigonal
symmetry:
28
for the stress orientation along the 具100典 direc-
tion no line splitting is observed, while for stress in the 具110典
and 具111典 directions, the Laplace DLTS peak splits into two
components with the amplitude ratios 1:1 and 3:1, respec-
tively. The magnitudes of the split lines sum to the value for
the unstressed sample. We have tried to study a response of
the E4 trap to uniaxial stress but this experiment has not been
successful because the LDLTS line due to the E4 trap is
rather close to the much stronger line due to electron emis-
sion from the first acceptor level of divacancy and the line
due to the E5 trap. Splitting of all three lines under applica-
tion of stress results in several overlapping emission signals
and, consequently, in an unreliable Laplace DLTS analysis.
There were only negligible changes in the DLTS spectra
upon isochronal annealing of the irradiated p
+
-n diodes in
the temperature range 125–200 °C. Heat treatments in the
temperature range 200–275 °C resulted in the disappearance
of both acceptor states of V
2
and the E
75
trap 共or the E4-E5
pair after injection treatments兲 and the appearance of four
other emission signals 共Figs. 1, 2, and 5兲. Electronic signa-
tures of two of them were identical to those for two acceptor
states of the V
2
O defect.
9,10
An almost one-to-one correlation
was observed between the loss of the E
75
trap and creation of
E4
ⴱ
and E5
ⴱ
, electronic signatures of which were similar to
those of the E4 and E5 traps 共Table I兲. Figure 3 shows the
kinetics of the decay of the E
75
trap and formation of the E4
ⴱ
trap upon isothermal annealing at 260 °C. Both kinetics are
described well by monoexponential functions with the same
rates. These were found to be very close to those of the
decay of V
2
and formation of the V
2
O complexes in p
+
-n
diodes. The transformation of the E
75
trap into the E4
ⴱ
-E5
ⴱ
pair occurred only in p
+
-n diodes made from epitaxial mate-
rial containing oxygen and not in FZ-Si samples. In the irra-
diated FZ-Si samples, the E
75
trap did not disappear even
after anneals at temperatures as high as 400 °C.
In previous studies, the E4 and E5 traps were assigned to
either V
3
or V
4
centers or to the di-interstitial-oxygen 共 I
2
O兲
complex.
22,24,25
It was argued in Ref. 26 that the E4-E5 pair
could be associated with a primary defect located in defect
clusters and closely related to the divacancy. Particularly, the
divacancy perturbed by strain associated with the clusters
was mentioned.
26
Some properties of the defect, which is
responsible for the E4-E5 traps in the electron-irradiated
samples studied, are indeed similar to those of V
2
. Both cen-
ters possess two acceptor levels in the upper part of the band
gap and their elimination rates in oxygen-rich Si samples
upon anneals in the temperature range 200–275 °C are
nearly the same. However, from the LDLTS results, we can
firmly conclude that our irradiation procedure, unlike ion im-
plantation or neutron irradiation, introduces only point de-
fects uniformly distributed in the probed volumes and not
perturbed by any strain. The results obtained in the present
work including the results of uniaxial stress measurements
can only be explained consistently when the E4 and E5 traps
are assigned to V
3
in the 共110兲 planar configuration and the
E
75
trap to V
3
in the “fourfold” configuration. These assign-
ments are consistent with all the results available in the lit-
erature on introduction rates, electronic properties, structure,
and thermal stability of the V
3
defect and explain the contro-
versies mentioned earlier.
3,4,12,22,26,29
There is strong experimental evidence that the elimination
of divacancies in oxygen-rich Si samples is associated with
their interaction with oxygen atoms and results in the forma-
tion of a V
2
O defect. The DLTS signatures of V
2
O are very
similar to those of V
2
.
9,10
The electronic signatures of the E4
ⴱ
and E5
ⴱ
traps are also very similar to those of their E4 and
E5 precursors indicating that the former traps could be re-
lated to a complex of the original center and an oxygen atom.
So, it is reasonable to assign the E4
ⴱ
and E5
ⴱ
traps to accep-
tor states of the V
3
O complex. The electronic signatures and
formation kinetics of the E4
ⴱ
trap resemble those for the L
center, which was observed in Si diodes irradiated with 15
MeV electrons and annealed at 205–285 °C.
30
It was argued
10
2
10
3
10
4
0.00
0.02
0.04
0.06
0
.
08
4
3
2
1
1 - <100>; P = 0 GPa
2 - <100>; P = 0 .5 GPa
3-<110>;P=0.45GPa
4 - <111>; P = 0 .4 GPa
E
75
T
meas
=45K
LDLT
S
signal (arb. units)
Emission Rate
(
s
-1
)
FIG. 4. 共Color online兲 Laplace DLTS spectra of the E
75
trap
taken at 45 K with no stress and the stress applied along three major
crystallographic directions of the Cz-Si samples.
100 200 300 400
2
0
1
[V
2
]
[V
2
O]
[V
2
+V
2
O]
[E
75
(V
3
)]x4
[E4*(V
3
O)]x4
[V
3
+V
3
O]x4
Concentration (10
12
cm
-
3
)
Annealin
g
Temperature (
o
C)
FIG. 5. 共Color online兲 Changes in concentrations of divacancy-
and trivacancy-related defects upon 30 min isochronal annealing of
an electron-irradiated epi-Si p
+
-n diode. Concentrations of the
V
3
-related defects are multiplied by 4.
MARKEVICH et al. PHYSICAL REVIEW B 80, 235207 共2009兲
235207-4

in Ref. 30 that the L center could be related to the V
3
O
defect.
It should be noted that our results on the annealing behav-
ior of the traps assigned by us to the V
3
and V
3
O defects are
fully consistent with the results on the annealing behavior of
V
3
obtained in ESR studies
29
and on the formation of the
V
3
O center obtained in a recent infrared-absorption study.
31
It is also worth mentioning that according to our preliminary
DLTS results on the electron-irradiated n
+
-p diodes and ab
initio modeling, both the V
3
and V
3
O centers also give rise to
two donor levels in the lower part of the gap.
IV. AB INITIO MODELING RESULTS
While multivacancy centers may be regarded as the re-
moval of adjoining Si atoms 关see Fig. 6共a兲兴, a rather different
approach was proposed in the calculations of Makhov and
Lewis
3
who showed that three self-interstitials could deco-
rate all 12 dangling bonds in V
6
resulting in a low-energy
fourfold coordinated V
3
complex 关see Fig. 6共b兲兴. We have
also investigated several structures for V
3
and particular at-
tention was paid to the most stable forms, namely, the PHR
V
3
made up of three neighboring vacant sites with C
2
v
sym-
metry, V
3
共C
2
v
兲 shown in Fig. 6共a兲, and the fourfold coordi-
nated form with D
3
symmetry, V
3
共D
3
兲 shown in Fig. 6共b兲.In
line with Ref. 3, we found that neutral diamagnetic V
3
共D
3
兲 is
0.50 eV more stable than diamagnetic V
3
共C
2
v
兲 and also 0.23
eV more stable than paramagnetic spin-1 V
3
共C
2
v
兲. After add-
ing and removing electrons to the system, V
3
共D
3
兲 turns to be
metastable by 1.19, 0.43, 0.05, and 0.50 eV for double plus,
plus, minus, and double minus charge states, respectively,
where V
3
共C
2
v
兲 stands now as the ground state. We have in-
vestigated the electronic structure of these complexes by in-
spection of the one-electron levels shown in Fig. 6共e兲.Itis
found that the long and twisted bonds in V
3
共D
3
兲 give rise to
states close to the band edges as in amorphous silicon,
whereas silicon radicals in V
3
共C
2
v
兲 lead to much deeper
states around midgap. Let us first look in detail at the latter
and more ordinary form of the defect shown in Fig. 6共a兲.
V
3
共C
2
v
兲 comprises two remote silicon dangling-bond radicals
lying on the 共110兲 symmetry plane of Fig. 6共a兲, plus three
long reconstructed Si-Si bonds perpendicular to the same
plane. While the end radicals give rise to b
1
and a
1
gap states
关Fig. 6共e兲兴, the reconstructions produce three bonding states
below the valence-band top and corresponding antibonding
states 共b
2
, a
2
, and b
2
兲 in the forbidden gap. As we show in
Fig. 6共e兲, the lower b
2
level is responsible for the acceptor
activity of the defect. We note that all three Si-Si reconstruc-
tions are very similar and their proximity leads to a strong
electronic coupling between the isosymmetric b
2
levels. Con-
sequently, these move away from the a
2
state. The electronic
structure of V
3
共D
3
兲 arises from twelve 2.6–2.7 Å long and
twisted Si-Si bonds which hybridize into bonding and anti-
bonding a
1
and e gap levels 关Fig. 6共e兲兴. The upper a
1
state
has essentially an antibonding character between interstitial
silicon atoms 关represented as dark blue balls in Fig. 6共b兲兴 and
their neighbors at the core of the defect. It has therefore the
right attributes to be responsible for a shallow acceptor trap
such as the E
75
.
Adding one electron to V
3
共C
2
v
兲 gives A共−/ 0兲=−3.48 eV
for its first electron affinity. A similar calculation for V
2
O
results in A共−/ 0兲=−3.45 eV, i.e., 0.03 eV above the value of
V
3
. Accordingly, considering that the first acceptor level of
V
2
O lies at E
c
−0.47 eV,
9,10
we place the first acceptor level
of V
3
共C
2
v
兲 at E
c
−0.50 eV. Proceeding to the second electron
affinity, we find that A共=/ −兲 =−2.16 eV for V
3
共C
2
v
兲, which
lies 0.05 eV below the same quantity for V
2
O. This places
the second acceptor level of V
3
共C
2
v
兲 at E
c
−0.28 eV. Similar
calculations for V
3
共D
3
兲 result in first and second emission
enthalpies of 0.23 and −0.10 eV. These results indicate that
while V
3
共C
2
v
兲 possess first and second acceptor levels close
to E5 and E4, respectively, V
3
共D
3
兲 is only able to trap a
single weakly bound electron, i.e., in agreement with the E
75
trap measurements.
It has been previously reported that the marker method
works best when the acceptor 共or donor兲 states from both the
scrutinized defect being studied and the marker have a simi-
lar character, i.e., symmetry and space extent.
19
The acceptor
level of the structure shown in Fig. 6共b兲 arises from an anti-
bonding state on long Si-Si bonds, making the VO complex
with its long Si-Si reconstruction a better marker for this
defect. The Si-Si antibonding state in VO produces an accep-
tor level at E
c
−0.17 eV,
10,21
and comparing electron affini-
FIG. 6. 共Color online兲 Atomic structures of 共a兲 V
3
共C
2
v
兲, 共b兲
V
3
共D
3
兲, 共c兲 V
3
O共C
2
v
兲, and 共d兲 V
3
O共C
1h
兲. V
3
共D
3
兲 is represented
along the 具111典 direction, whereas other structures are viewed ap-
proximately along 具110典. Silicon, oxygen, and vacancy sites are
represented as gray, red 共two-fold coordinated兲, and white balls,
respectively. Three Si interstitial atoms in 共b兲 are represented as
dark blue balls. In 共e兲, we depict the one-electron picture for all four
defects of interest obtained from the Kohn-Sham states within the
valence-band 共VB兲 and conduction-band 共CB兲 edges 共band gap of
the cluster is E
g
=2.4 eV兲. Spin-up and spin-down occupied states
are represented as left- and right-hand circles, respectively.
TRIVACANCY AND TRIVACANCY-OXYGEN COMPLEXES IN… PHYSICAL REVIEW B 80, 235207 共2009兲
235207-5

ties of V
3
共D
3
兲 and VO, we place the acceptor level of V
3
共D
3
兲
at E
c
−0.12 eV. This further supports our assignment of
V
3
共D
3
兲 to the E
75
trap.
The interaction of V
3
with an interstitial oxygen atom was
also investigated by calculations. The effect is that the O
atom stabilizes the planar structure and the V
3
O complex
with C
2
v
symmetry shown in Fig. 6共c兲 is the ground state for
neutral, positively, and negatively charged defects. Here, the
O atom bridges the Si-Si reconstruction at the center of the
defect. Neutral defects were found to be energetically favor-
able in the spin-1 state for both V
3
O共C
2
v
兲 and V
3
O共C
1h
兲. The
latter is metastable by 0.36 eV and it is depicted in Fig. 6共d兲.
A fourfold coordinated V
3
O complex 关after binding an oxy-
gen atom to a V
3
共D
3
兲 structure兴 is metastable by at least 0.2
eV. Using the marker method and comparing electron affini-
ties of V
3
O共C
2
v
兲 to those of V
2
O, we place V
3
O共−/ 0兲 and
V
3
O共=/ −兲 at E
c
−0.42 eV and E
c
−0.28 eV, respectively.
Both levels are less than 0.1 eV away from the analogous
levels calculated for V
3
共C
2
v
兲 and their respective assign-
ments to E5
ⴱ
and E4
ⴱ
are well accounted for. The electrical
activity of V
3
O共C
2
v
兲 arises from a
1
and b
1
deep states 关Fig.
6共e兲兴. These are symmetric and antisymmetric dangling-bond
states localized at the rightmost and leftmost Si radicals
shown in Fig. 6共c兲. The calculated level positions for
V
3
共C
2
v
兲, V
3
共D
3
兲, and V
3
O共C
2
v
兲 are summarized in Table I
together with assignments to the experimental data.
V. CONCLUDING REMARKS
We present an experimental observation of a center from a
family of mysterious “fourfold coordinated defects” in semi-
conductor crystals which was predicted by ab initio
calculations.
1–3
Our results confirm the prediction of Makhov
and Lewis,
3
who showed that the fourfold coordinated con-
figuration could be the lowest-energy state for the neutral V
3
defect in Si. According to the same authors, the small four-
fold vacancy clusters in Si would not have energy levels in
the band gap and, as a result, they would be electrically and
optically inactive, making their direct observation difficult.
However, it is found in the present work that the fourfold
coordinated V
3
in Si has a shallow acceptor level close to the
conduction-band edge. By studying the electron emission
from this level, its exact position and symmetry of the FFC
V
3
defect have been determined. We also demonstrate that V
3
interacts efficiently with oxygen atoms in O-rich silicon
crystals to result in a V
3
O defect. V
3
O is only stable in the
共110兲 planar C
2
v
symmetric configuration. Like the planar V
3
center, the V
3
O complex gives rise to two deep acceptor
levels in the upper half of the gap.
It was also predicted by Makhov and Lewis
3
that the four-
fold coordinated configurations could be the ground states
for the V
4
and V
5
defects. Our preliminary DLTS results on
epi-Si p
+
-n diodes irradiated at room temperature with alpha
particles from a
210
Po source support this prediction. The
DLTS measurements on the diodes irradiated with alpha par-
ticles show that the E4 and E5 signals in these diodes consist
of contributions from other traps in addition to those related
to V
3
共Fig. 7兲. Similar to the V
3
-related E4 and E5, the alpha-
irradiation-induced traps, E4共
␣
兲 and E5共
␣
兲, anneal out in the
temperature range of 50–150 °C and can be restored by for-
ward current injection in the p
+
-n diodes. However, no other
traps apart from E
75
have been detected in the DLTS spectra
after the disappearance of the alpha-irradiation-induced
E4-E5 traps. We suggest that the E4 and E5 DLTS signals in
Si samples irradiated with alpha particles and fast neutrons
26
consist of contributions from the V
4
and V
5
defects in addi-
tion to those due the V
3
center. Similar to V
3
, the V
4
and V
5
clusters are bistable in the neutral charge state with the FFC
configurations being the lowest in energy. The bistabilities of
V
4
and V
5
are the origin of annealing- and injection-induced
phenomena related to the alpha- and neutron-irradiation-
induced E4-E5 traps.
26
It appears that in contrast to V
3
, the
V
4
and V
5
centers do not have energy levels in the fourfold
coordinated configurations.
ACKNOWLEDGMENTS
We would like to thank EPSRC-GB and the Norwegian
Research Council for financial support.
50 100 150 200 250 30
0
E5(α)
E4(
α)
(b)
(a)
E
75
1.2
0.8
0.4
-0.2
0
0
3
2
1
V
2
(-/0 ) + E5(α)
E4(
α)
E
75
TDD
VO(-/0)
V
2
(2-/-)
∆
C(
pF
)
Tem
p
erature
(
K
)
FIG. 7. 共Color online兲共a兲 DLTS spectra for an epi-Si p
+
-n diode
which was subjected to the following subsequent treatments: 共1兲
irradiation with alpha particles from a
210
Po source, 共2兲 annealing at
125 °C for 30 min, and 共3兲 forward bias injection with a current
density 10 A/ cm
2
for 10 min at 300 K. Measurement settings were
e
n
=80 s
−1
, bias −10 V→ −2 V, and pulse length 1 ms. The spec-
tra are shifted on the vertical axis for clarity. 共b兲 Difference between
the DLTS spectra 2 and 3 in 共a兲. For a comparison, the dashed line
presents the difference between the DLTS spectra 2 and 1 shown in
Fig. 1共a兲 for an electron-irradiated p
+
-n diode.
MARKEVICH et al. PHYSICAL REVIEW B 80, 235207 共2009兲
235207-6

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