This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail.
Powered by TCPDF (www.tcpdf.org)
This material is protected by copyright and other intellectual property rights, and duplication or sale of all or
part of any of the repository collections is not permitted, except that material may be duplicated by you for
your research use or educational purposes in electronic or print form. You must obtain permission for any
other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not
an authorised user.
Alatalo, M.; Kauppinen, H.; Saarinen, K.; Puska, M.J.; Mäkinen, J.; Hautojärvi, P.; Nieminen,
R.M.
Identification of vacancy defects in compound semiconductors by core-electron annihilation:
Application to InP
Published in:
Physical Review B
DOI:
10.1103/PhysRevB.51.4176
Published: 15/02/1995
Document Version
Publisher's PDF, also known as Version of record
Please cite the original version:
Alatalo, M., Kauppinen, H., Saarinen, K., Puska, M. J., Mäkinen, J., Hautojärvi, P., & Nieminen, R. M. (1995).
Identification of vacancy defects in compound semiconductors by core-electron annihilation: Application to InP.
Physical Review B, 51(7), 4176-4185. https://doi.org/10.1103/PhysRevB.51.4176
PHYSICAL
REVIEW B
VOLUME
51,
NUMBER
7
15 FEBRUARY
1995-I
Identification of
vacancy
defects in
compound
semiconductors
by
core-electron
annihilation:
Application
to InP
M.
Alatalo,
H.
Kauppinen,
K.
Saarinen,
M. 3.
Puska,
3.
Makinen,
P.
Hautojarvi,
and
R. M. Nieminen
Laboratory
of
Physics,
Helsinki
University
of
Technology,
FIN
021-50
Espoo,
Finland
(Received 21
June
1994)
We
show that the
Doppler
broadening
of
positron
annihilation
radiation
can be
used in
the
iden-
tification of
vacancy
defects in
compound
semiconductors.
Annihilation of
trapped
positrons
with
surrounding
core electrons
reveals chemical
information
that
becomes
visible when
the experimental
background
is
reduced
by
the
coincidence technique.
We also
present
a
simple
calculational
scheme
to predict
the
high-momentum
part
of
the
annihilation
line. The
utility
of the
method is
demon-
strated
by
providing
results
for
vacancies in InP. In
electron
irradiated
InP
the isolated
In and P
vacancies
are distinguished
from
each other
by
the
magnitude
of the
core
electron
annihilation. In
heavily
Zn-doped InP
we detect a
native
vacancy
defect and
identify
it to a
P
vacancy
decorated
by
Zn
atoms.
I. INTRODUCTION
Positron
annihilation
spectroscopy
has turned
out
to
be a
powerful
technique
to
study
vacancy
defects in
semiconductors. A
vacancy
defect acts as a
positron
trap.
The
trapped
positron
lifetime is
proportional
to
the
open
volume of the
defect,
and,
therefore,
single
and
multiple
vacancies can be identified. It
is also
possible
to
distinguish
between
difI'erent
charge
states of vacancies
based on
changes
in
positron
lifetime or
trapping
rate.
'
Comparing
the
observed
changes
in the lifetimes
with
the
results of the
recent first
principles
calculations for
the atomic
relaxations
helps
to understand the
configura-
tions of the
neighboring
atoms
in
difI'erent
charge
states.
The most
recent O,b
initio calculations
are also able to
take into account
the
positron
induced relaxation and
the
ensuing pcsitron
lifetimes are in
fair
agreement
with
experiments.
The
association of
the
positron
lifetime to
the
open
volume of the
defect has thus a solid
theoretical
basis.
However,
the
positron
lifetime measurements
give
no
information on the
chemical
surroundings
of
the
anni-
hilation event and
cannot
identify
the sublattice of
the
vacancy
or whether
the
vacancy
is
isolated or
complexed
with
impurity
atoms. Therefore, combining
the
lifetime
measurements
with
a
method
giving
additional
informa-
tion
on the
nearest-neighbor
atoms
of the
defect would
be
of
great
value in
the
identification
of
point
defects
and defect
complexes,
especially
in
compound
semicon-
ductors.
In
this
paper
we
demonstrate
the
applicability
of the
Doppler
broadening
of the
annihilation
radiation to
the
identification of defects in
semiconductors. The
Doppler
broadening
experiments provide
information on the
mo-
mentum
distribution
of
the annihilating
electrons. One
can
easily
distinguish
between the
low-momentum
part
of the
spectrum,
arising
mainly
from the
annihilation
with the valence
electrons,
and the higher-momentum
parts
coming
from the core
electrons. The
umklapp
an-
nihilations contribute
at high-momentum
regions.
Their
amplitude,
however,
decreases
with
increasing
momen-
tum. The core electrons
are
tightly
bound to the
nu-
clei and thus
the high-momentum
parts
of
the
Doppler
spectrum
carry
information on the
type
of the atoms in
the
region
scanned
by
the
positron.
In
the case of
open
volume
defects the
positron
wave function is localized
and
overlaps
more
strongly
with the core electrons of the
near-neighbor
atoms than with those of the more
distant
atoms. In
compound
semiconductors, therefore,
vacan-
cies in
difI'erent
sublattices should
give
different
signals
to the
Doppler
spectrum. Moreover,
impurity
atoms
as-
sociated to the
vacancy
may
also be
distinguished.
In the
conventional single-detector
Doppler
technique
the
intensity
of the
high-momentum annihilation
quanta
is
comparable
to
the
background,
which makes it
difIicult
to make
any
conclusions on the
shapes
and
magnitudes
of
the
Doppler
curve.
To reduce the
background
we have
used the
coincidence measurement of both
511-keV
p
rays
in the
Doppler
experiment
which allows us to
study
the
spectrum
up
to the
momenta
of
4.
8
a.
u.
,
corresponding
to the
angle
of
35
mrad between the two
annihilation
p
in an
angular
correlation
experiment.
The
rest of the
paper
is
organized
as
follows.
~'.
n Sec.
II
we describe the
experimental
setup
used in
the
coinci-
dence
Doppler
measurements.
In
Sec. III we
present
the
theoretical
background
and describe
a
simple
scheme
to
calculate the
high-momentum
parts
of the
Doppler
spec-
trum. The method is
demonstrated
in
Sec. IV
by
provid-
ing
results for bulk
Si,
GaAs,
and
InP. As
more
specific
examples
of the defect
applications,
we
have identified
vacancies and
vacancy-impurity
complexes
in InP. These
results,
as well
as
some
problems
related
to this
method,
are
discussed in Sec. V.
Finally,
we
present
our
conclu-
sions in Sec. VI.
0163-1829/95/51(7)/4176(10)/$06.
00
51 4176
1995
The American
Physical
Society
51
IDENTIFICATION
OF VACANCY
DEFECTS IN
COMPOUND.
. .
4177
II.
EXPERIMENTAL METHOD
A.
Experimental
techniques
Positrons in a
sample
annihilate with electrons
emit-
ting
two
511-keV
p
rays.
The
511-keV
annihilation
line
is
Doppler
broadened
due to the
longitudinal
momen-
tum
component,
pl.
of
the
annihilating
electron-positron
pair:
E~=(511+RE)
keV.
The
Doppler
shift AE
=
zpL,
c
is
typically
several
keV,
and it
can
thus be
easily
de-
tected
with a
high-purity
(HP)
germanium
p-ray
de-
tector that
has a resolution of 1.
0
—
1.
5
keV
[full
width
at
half
maximum
(FWHM)]
at 511 keV. Because of
the momentum conservation, the
relative direction
be-
tween the
two
emerging
p-rays
deviates from
180'
by
a
small
angle,
0
=
pT
/mpc
due
to
the
transversal
mo-
mentum
component
pT.
Both
the
Doppler
broaden-
ing
and
one-dimensional
angular
correlation
experiments
(1D-ACAR),
measure the
equivalent
momentum compo-
nent
denoted
by
p,
p,
=
2b,
E/c
=
O, mpc,
where
m,
o
is
the electron mass and c
is
the
speed
of
light.
Equation
(1)
implies
that AE
=
1
keV
in
the
Doppler
experiments corresponds
to
p,
=
0.54 a.u. or
0,
=
3.
91
mrad in the
1D-ACAR
experiments,
if we
define that the
longitudinal
momentum
component
is
along
z
axis in
Eq.
(1).
As the
resolution of the Ge
detector is
of
the same order
as the
Doppler
broadening,
the
details
of
the positron-
electron momentum distribution
are smeared out in the
Doppler
data as
compared
to
the results of the ACAR
ex-
periments. Normally
the
Doppler
spectrum
suffers also
from
relatively
high
background
radiation. If a Na
positron
source
is
used,
the
background emerges mostly
from
the
Compton
scattering
of the
1.
28
MeV nuclear
p
rays
emitted
together
with the
positron.
The peak-
to-background ratio
of the
Doppler
spectrum
is
typi-
cally
100
—
200,
which makes
the detection of the high-
momentum annihilation
events difficult.
Due to these
limitations in the
detection
system,
the
Doppler
re-
sults
have
been
conventionally presented
only
in
terms
of integrated
shape
parameters,
which describe
the
rel-
ative amounts
of
valence
(S-parameter)
and core
(W-
parameter)
electron
annihilations.
In
order to
study
the
high-momentum tails of
the
Doppler
spectra,
we have
used a
NaI detector in
a
co-
incidence with
a HP
Ge
detector. A
Na
e+
source
is sandwiched
between two
pieces
of
the semiconductor
sample.
The
Ge
detector is
used to
detect the
annihila-
tion
p
spectrum.
The NaI
scintillation
detector is
placed
in
collinear
geometry
with the Ge
detector in
order to
de-
tect
the two
511-keV
p
rays
from
the
e+-e
annihilation.
When
pulses
from
both
detectors
arrive
in
coincidence,
the
pulse
from the Ge
detector is
recorded in
the
memory
of a multichannel analyzer
(MCA).
In this
experiment
.
the
background
is
removed
from the
high-energy
side of
the
511-keV
peak,
but in
the
low-energy
side the
back-
ground
largely
remains due
to
the
Compton
scattering
of
the
511-keV
p
rays.
Compared
to
conventional
Doppler
spectroscopy,
the
counting
rate
in the
coincidence
system
is
reduced
only
by
the factor
determined
by
the
efficiency
of the NaI detector.
In our
system
the resolution
of
the
Ge detector
at
511-keV
is 1.
2
keV with
6-p s
shaping
time
and
1.6 keV
with
2-ps
shaping
time
in
the
spectroscopy
amplifier.
In
the
experimental
setup
described
above,
the
coinci-
dence rate
n
and the peak-to-background ratio
p/b
are
related.
When
n
decreases,
p/b
increases
as
the
source-
detector
spacing
d
increases.
We have used
a
positron
source
of
17
pCi
and
d=22
cm,
which results to n
=
170
1/s
in the
511-keV
peak
and
p/b
=
2 x
104
on
the
high-energy
side of the
peak.
In
a
typical
experiment
(1—
4)
x10 annihilation
events
were
collected
in
the whole
spectrum.
The
Doppler
spectrum
suffers from
pileup
distortion,
which is
due
to the
piling
up
of the
pulses
especially
in
the
preamplifier
stage
of the circuit. A
pileup
rejection
signal
is used to
gate
the
MCA,
but the
remaining
pileup
effect can
still be seen as a
slowly
decaying
tail above 520
keV. The
pileup
effect is
minimized
by
using
a
2-ps shap-
ing
time in the
spectroscopy
amplifier.
With
this
setup,
the
intensity
of the
pileup
component
is
2.
3%
of the core
annihilation
spectrum
at
DE=2.
6
—
9.
0
keV
(8,
=
10
—
35
mrad),
and
the
energy
resolution of the
system
is
1.6
keV.
In the
final
analysis
the
remaining
pileup
component
is
subtracted
from
the
spectrum.
We have also
subtracted a
constant
background
radiation from all the data.
Figure
1 illustrates the
difference between
coincidence and
con-
ventional
noncoincidence
Doppler
measurements. In
co-
incidence
measurements the
background
level
is reduced
by
two orders
of
magnitude.
The
high-momentum tail
arising
from
annihilations with
core electrons is
clearly
observable
at
the
energies
above
515
keV.
After
pileup
and
background
subtraction the
Doppler
spectrum
above
511-keV
corresponds
to the
convoluted
momentum
distribution
f
(e,
)
=
r(e,
)
G(0,
),
(2)
10'
.
104
.
10
10'
.
10
Core
contributi
above
10'
505
I
510
I
515
I .
~ ~ ~ I
520
525 530
ENERGY(keV)
FIG. 1.
Doppler
broadened
annihilation line
shapes
mea-
sured with
the
Ge detector.
The
figure
shows the data
ob-
tained
with
and
without the
coincidence
technique
using
a
NaI detector in
collision
geometry
with the Ge
detector.
4178
M.
ALATALO et
al.
where
G(0,
)
is
the
Gaussian resolution
function of the
Ge-detector,
with
FWHM=1.
6 keV
(6.
2
mrad),
and
I'(8
)
is the
integrated
electron momentum distribution
dis-
cussed
further in Sec. III. Above
15
mrad the
con-
tribution
from the valence electrons
and the resolution
function
is
negligible
and thus
f
(0,
)
—
I'(0,
).
The
statis-
tics in the
spectra
is sufhcient
up
to
35 mrad.
Therefore,
comparisons
between
the
experimental
and
theoretical
core-electron
momentum distributions
can be done in the
range
of 15
—
35
mrad. In
this
comparison
we
present
all
the
experimental
data as
a function
of
the
angle
0
cal-
culated from
Eq.
(1).
B.
Decomposition
of the
annihilation
line
In
practice the
vacancy
concentration
in semiconduc-
tor
crystals
is
often
not
large
enough
to induce
complete
positron
trapping.
In this
case
the
Doppler
spectrum
has
to
be
decomposed in order
to obtain
the
annihilation
line
of
positrons
trapped
at
the
vacancy defects. To
achieve
this
the
samples
were
studied
with
a conventional
fast-
fast lifetime
spectrometer
with
a time
resolution
of
245
ps.
A
10-
pCi
Na
source
was sandwiched
between
two
pieces
of
the
sample
and
about
3x10
counts
were
col-
lected
in each
spectrum. In the
samples
that
contained
vacancies
a two
component lifetime
spectrum
from
the
shape
of
f„(0,
).
On the
other
hand,
the
magni-
tude of
the core-electron
annihilation
can
be
investigated
using
the TV
parameter
(6)
where
A~
=
f&
'
f
(0,
)
d0,
and
Aq~q
—
—
J'
f
(0,
)
d0,
are
areas
of the
measured
Doppler
curve.
The
boundaries
Oq
and
02
are
chosen
in
such a
way
that
W
reHects
mainly
the
core-electron
annihilations in the
system studied, and
we
have
used
the values
0q
—
—
15
mrad
(AE
=3.
8
keV)
and
02
—
—
20 rnrad
(AE
=
5.
1
keV).
When
differences
in
the
shape
of the
core annihilation
spectrum
f„(0)
are
negligible,
big
changes
may
still
be
observed
in
the
W
parameter.
Notice that
the total area
Aq
q
is calculated
from
one
half of the
peak
starting
from the
centroid.
This
is due to our
experimental
system,
in which
the
back-
ground
is
removed
only
from the
high-energy
side of the
peak.
III. THEORY
The momentum
distribution
of the
annihilating
electron-positron
pair
can be
written as
n(t)
=
n
(I,
e
'~
'
+
I e
'~
')
was
fitted
to
determine
the
vacancy lifetime
component
=
w2
and the
average
lifetime
7,
=
P,
I,7;
.
The
bulk
lifetime
Tb
is
obtained
from
a
sample
in
which
there
is no observed
positron
trapping.
In bulk
samples
the
measured
and
corrected 511-keV
annihilation
line
is
straightforwardly
the
momentum
dis-
tribution
fb(0
)
of the
electrons
in the
homogeneous bulk.
In
samples
where
the
lifetime
analysis
indicates
positron
trapping
at
vacancies, both
the
bulk
and
vacancies
con-
tribute
to the
measured
spectrum. If
we assume
only
one
type
of
defect,
the
measured
distribution
is
a
composition
p(p)
=
vrroc
)
~
dre'~'g, '~(r,
r)
~,
where the summation
is over
all
occupied
electron
states,
p
is the total
momentum of
the
annihilating
pair,
and
@,
'~(r,
r)
is the two-particle
wave
function restricted
to
the case of
the
positron and electron
residing
at
the same
point.
@,
'.
(r, r)
can be
approximated
using
the
single-
particle
wave
functions
g+(r)
and
g
(r)
for
the
positron
and
electron,
respectively,
and
the enhancement
factor
p;(r),
taking
into
account the
short-range
electron
pileup
at the
positron,
where
fb(0,
)
and
f„(0
)
are
annihilation
lines in
the bulk
and at
the
vacancies,
respectively,
and
g„
is the
frac-
tion of
positron
annihilating at
the defect.
Knowledge of
fb(0
)
and
q„allows
us to solve
the
equation for
f„(0,
).
Analogically,
the
average
positron
lifetime
can be
stated
as
=
(1
—
g„)rg+
g„v.
„.
The
positron
lifetime
measurements
yield
w,
wb,
and
7„and the
equation can be
solved
for
g„.
Hence,
the
annihilation
line
for
vacancies
f„(0
)
can
be
extracted
from
Eq.
(4).
The annihilation
line
at vacancies
f„(0,
)
is
especially
interesting
in
the
high-momentum
region
(0
)
10
mrad)
where
the
core-electron
contribution
is
dominant.
At
vacancies
the
high-momentum
distribution
re8ects
the
chemical
environment
of
the
vacancy.
Hence,
the
atoms
surrounding
the
vacancy
defect
could
be
identified
simply
In
what
follows,
we
shall
make a
simple
approximation
for both the
electron
and
positron
wave
functions.
Be-
cause
we are
mainly
interested
in
the
high-momentum
part
of the
Doppler spectra, arising
from the
core
elec-
trons,
we
omit the
contribution
of the
valence
shells,
tak-
ing
the
valence
electrons
into
account
at a later
stage,
through
a
proper
normalization.
This allows
us to
ap-
proximate the
electron-core
wave
functions
vP,
(r)
by
the
ones
obtained for
free
atoms.
We
use a
nonrelativistic
program,
based
on
density
functional
theory
and the
lo-
cal
density
approximation
(LDA),
to
calculate the
wave
functions
for
the core
states.
The
positron
wave
func-
tion is
also
assumed
to
be
spherical around each
nucleus.
In
practice
it is
obtained
by
using
the
linear-muKn-
tin-orbital
(LMTO)
method
within the
atomic-spheres
approximation
(ASA).
The
positron
potential
corre-
sponds
to the self-consistent
bulk
electron structure
and
it is
constructed
(within
the
LDA)
as a sum
of
Coulom-
bic and
correlation
parts.
We use
the
positron
profiles
IDENTIFICATION
OF
VACANCY
DEFECTS IN COMPOUND.
.
.
4179
for
bulk
states
also
for atoms surrounding
the vacancy
defects. According
to
our
LMTO-ASA
—
Green's-function
calculations for
the
vacancy,
the
shape
of the
spherically
averaged
positron
wave function
around a
neighboring
atom
differs
only
slightly
from
that in
the
perfect
bulk.
Therefore,
this
approximation
does not
appreciably
afFect
the momentum
distributions
obtained as
Fourier
trans-
forms. With these
approximations
we
write
the
contribu-
tion of the
n,
I
core state
to the momentum
distribution
as
dr r R
i
(r
)
R
i+o
(r)
j
( (pr
)
x
V'~(n
(r))l
where
R
&(r)
and
Ri+o(r)
are the
radial
parts
of
the
elec-
tron and
positron
wave
functions,
respectively,
and
jr,
(pr)
is
the
lth
spherical
Bessel function.
Moreover,
the
en-
hancement factor
p(n
(r))
is
calculated
from the total
electron
density
n
(r)
using
the
LDAi2'
with
the
in-
terpolation form
suggested
by
Boronski and Nieminen.
The
angular
distribution,
corresponding
to the measured
Doppler
spectrum
is obtained
from
Eq.
(9)
by
integrat-
ing
p(0,
)
=
)
A'p,
(0
),
where
the index i runs over the core states.
Above,
in
Eq.
(13)
the areas below
the
p,
(8,
)
curves
are normalized to
unity.
Then the
integral
of
the
momentum
distribution
over 0
gives
the total core
annihilation
rate.
Finally,
the
theoretical
counterpart
of the
experimental
W
parameter
Eq.
(7)
is calculated as
w=)
A,
1
1/A,
.
„
(14)
where
At
t
is the total area
of
the
angular
distribution
curve for
core state i and
A~
is the
corresponding
area
in
the
TV
window,
Oi
&
0
&
02.
IV.
RESULTS
AND
DISCUSSION
where
the summation
is
over
all different
core
and valence
contributions.
The core
contribution
to the
Doppler
curve
is obtained
as
dppp„i(p),
(10)
where
0,
=
p,
/moc.
The contributions due
to
the different core
states,
cal-
culated with
Eq.
(10)
must be added
together
in
order
to
get
the
total core
part
of the
Doppler
curve.
In
order
to describe the solid in
a
realistic
way,
we have
to find
the
proper
weights
for
the
contribution of
each
nl
shell
of
each different atom
type
in a bulk or in a defected sys-
tem. This
can
be done
by
calculating
the
corresponding
partial
positron
annihilation rates. For this
purpose
we
use the method of
superimposed
atoms where the
elec-
tron
density
and the Coulomb
potential
are obtained
by
superimposing
free-atom
densities and
potentials.
The
total
potential
acting
on the
positron
is the
sum
of the
Coulombic
potential
and
the correlation
potential
cal-
culated
in the LDA as in the case of our
LMTO-ASA
calculations.
In the
superimposed
atom calculations we
use a 64
atom
supercell
(63
in the
case
of
vacancies).
The
electron
density
and the
positron potential
are
calculated
on
a
mesh with 32 x
32
x
32
points forming
a
simple
cubic
lattice.
The
positron
wave function is
obtained
by
a
re-
laxation method.
A
certain valence or core contribution
to the annihilation rate
is
calculated as
n+(r)I'(n
(r))
dr,
n'(r)
n r
where
n
(r)
is
the electron
density
contribution in ques-
tion,
n+
(r)
=
1
g+
(r)1
is
the
positron
density,
and
I'(n
(r))
is the
annihilation
rate in the
LDA,
i4
calcu-
lated
using
a correction
due
to the reduced
screening
in
semiconductors.
Moreover,
the
positron
lifetime w is
obtained as
the inverse of the
total
annihilation rate
At
t
n+
(r)1
(n
(r)
)
dr,
(12)
A.
Core-electron
momentum distribution
in
bulk
semiconductors
To
demonstrate the
physics
behind our
method,
and
also
to
clarify
the interpretation
of the
Doppler
data,
we
first
show results for bulk
Si,
GaAs,
and InP.
Figure
2(a)
presents
the
experimental
and
Fig.
2(b)
the calculated
curves for
these three
semiconductors.
In
this and
all
the
subsequent
Doppler
curves,
the total areas
under the
curves are
scaled to
unity.
In
these
figures,
the effects
of
the dominant
core shells are
clearly
seen.
In
GaAs,
most of
the core
annihilation occurs with
Ga and As 3d
electrons,
which
are
relatively
tightly
bound to the
nuclei
and
quite
localized in r
space.
Therefore,
the
correspond-
ing
momentum
distribution
is
broad and extends
to
large
momentum
values. In
InP,
on
the
other
hand,
the
domi-
nant
contribution to the core annihilation
comes from In
4d
electrons.
They
are
less
tightly
bound,
and
extend
to
a
wider
region
in
r
space
and thus
give
a
narrower
and
more
rapidly
descending
contribution to
the
angular
cor-
relation
curve. Since
there are no
d
electrons in
Si,
and
the
annihilation
is less
likely
to
occur with Si 2s
and
2p
electrons
because of the smaller
screening
of
the
nuclear
Coulomb
repulsion,
the
core
part
of the
momentum
dis-
tribution lies
lower than it does in the
case of
GaAs and
InP.
The
contributions
of
the
difFerent
core shells
are
demonstrated in
Fig.
3,
which
presents
the components
A'p,
(9,
)
[see Eq.
(13)]
and the total
curves
of
Fig.
2. In
the case of InP
[Fig.
3(a)]
the dominant
contribution
up
to
28
mrad
comes from
In 4d. At
very high
momenta,
P
2p
gives
the
largest
contribution. In GaAs
[Fig.
3(b)],
Ga
3d is
seen to
give
more contribution
than As
3d,
but
the
shape given
by
these
dominant shells
is
very
similar.
In
these
figures,
the contributions
from
P
3s
and As
4s
