Deep-Level Transient-Spectroscopy for. Localized. States at. Extended. Defects in. Semiconductors. H. Hedemann. (*) and W. Schr6ter. Universitit. G6ttingen, IV.
Phys.
J.
IYance
III
(1997)
7
Extended
(*) and W.
Hedemann
G6ttingen,
Universitit
(Receiied
Physikalisches
IV.
Impurity
PACS.71.55.-I 20.Dx
Localized
States
1389
PAGE
at
Schr6ter
accepted
November1996,
12
for
1997,
Semiconductors
in
Defects
PACS.73
JULY
Transient-Spectroscopy
Deep-Level H.
1389-1398
and
Electron
G6ttingen,
Germany
April 1997)
low-dimensional
in
states
22
13, 37073
Bunsenstrafle
levels
defect
(superlattices~
Institut,
well
quantum
structures
structures
multilayers)
and
extended defects the high-temperature sides We prove that for localized states at depending deep-level product of an amplitude function transient spectra can be vrritten as a the pulse length and a shape function depending on By this property localtemperature. on Simulations of deep level ized be distinguished experimentally from bandlike states states. can function and using the same density of states transient spectra for localized and bandhke states analysis in both the differences and show the failures of conventional values illustrate parameter Abstract.
of
Cases.
Introduction
1.
Spatially generally
precipitates are be roughly states, a can which split off classified according to their origin into three groups: (1) bandlike states are from the valence and conduction band by the action of the long-range strain field of the defect, of the defect, originating from the internal and interfacial bond (2) bandlike structure states defects from from of the defect with and (3) localized resulting the point interaction states or local imperfections of its core structure. extended
shallow
While
correlation
at
silicon
in
states
extended
at
interplay
extended
limits
like
Experimentally shallow photoluminescence, optical absorption,
and
electric
bandlike
states.
dipole spin
properties in silicon. Deep electronic states cles to
known
are
create
these could
(*) Author
©
Les
have
detrimental
effects, not
to
be for
#ditions
numerous
analyzed
resonance
extended
at
effects
strong effects
in
be
can
for
a
states
double
have
described bond
and
no
Physique
boundaries,
ND(E),
spin
the
theoretical
effect
on
the
defects, especially at dislocations and like bulk mobility properties on [4] and
microelectronic
and
solar
theoretical
electron-electron-
of their
evaluation
low-temperature effects conductivity, microwave
various
room-temperature metal
silicide
lifetime
parti-
[5,6],
and
technology [7]. To understand but have brought forth data, which appropriate main difficulty is the
cell
(e-mail: hedemann©physik4.gwdg.de)
1997
and
resonance,
significant
or
which
conventional
with
structure
quantitative give rise to
investigations have been performed, interpreted unambigiously. One
and
correspondence
de
[3], but
grain
electronic
atomic
still
are
of
defects
between
defects
dislocations,
like
distribution
with
[1, 2], the
methods
deep
defects
associated
JOURNAL
1390
PHYSIQUE
DE
III
N°7
~
6Ec Ec
~-l
~-l e
c
(( Fig. in
Simplified
1.
band
the
band
equilibration
internal
of
consideration the
time
r,,
origin
of
rates
inverse
effects and
extended
an
edge Ec,
band
electrostatic
determination
of
scheme
conduction
gap;
fi
on
defect
of
emission
and
due
to
the
capture
of
distribution
the
distribution
of
of
constituted
bending
band
of
deep-lying about forty
levels states
an
assembly
common
carriers, R)~, RI
with at
their
extended
single
of
states
&Ec,
barrier
capture ~.
occupation. defects
Thus
reilained
problem of physics for semiconductor open years [8]. Using Deep Level Transient Spectroscopic (DLTS) data of 60°-dislocations and of small NiS12-platelets and simulation of DLTS, it has been shown recently, that deep electronic states defects extended be classified bandlike localized, when electron equilibration at at can as or an
defect
the
taken
is
Furthermore
DLTS,
into
it has
account
been
[9].
using
demonstrated
given
DLTS-data
density
of
NiS12-platelets and
simulation
of
occupation in the neutral a occupation-dependent electrostatic 8tate, the capture barrier, which is built up by long-range fields, -and the capture cross section may be obtained from the fitting of the rate equation for fast internal equilibration to the DLTS-data [10]. To distinguish bandlike and localized defects, the internal extended equilibration at states associated with the defect has to be compared with the inverse time r, extended emission carrier carrier rate, Rp~, and the inverse capture rate, Rp~, of the defect (Fig. 1, [9]). The case, that r, is the smaller time, should hold for bandlike states, which are -extended at the defect, while that r, is the larger time, should the case, of point defect hold for localized clouds. The states that
the
parameters
of
bandlike
of
states,
its
between bandlike and localized features be made from the qualitative states can DLT-spectra. For bandlike states, it has been proven that the high-temperature sides of DLTS-lines mainly independent of the filling pulse length tp [10] cf. Fig. 2a). On the are other hand, simulations performed for localized by dense point defect clouds introduced states in the vicinity of a dislocation suggested, that the high-T-sides of DLTS-lines with different normalization Similar been with results have maxima tp coincide after respect to their [9]. obtained for simulations distributions of energy levels [I Ii. considering other distinction
of the
this
In
paper
wi
describe
in
more
detail
DLTS
on
extended
defects
with
localized
electronic
be high-T-sides of DLTS-lines of localized written states can as a product of an amplitude function depending on the filling pu18e length tp and a 8hape function therefore that depending on As a fingerprint for localized conclude temperature states we the high-T-sides of DLTS-lines in general coincide after normalizing with respect to any point of the highiT-side, e-gthe of the lines (cf. Fig. 2b). A direct comparison of maximum demonstrate for bandlike simulations and localized using the same defect parameters states analysis (Arrhenius-plots) between the models and the failures of conventional the differences states.
of
We
extended
show
defects
that
for
the
both
models.
FOR
DLTS
N°7
LOCALIZED
0.006
STATES
AT
EXTENDED
DEFECTS
1391
o-3
~°~~~
5.1 0-4
0.004
°J
0.003
~ ~
0.002
o.ooi
60
80
200
240
220
260
300
280
TEMPERATURE(K)
~)
o-s 5.1 0-4 ~°°~
l 0-4
0.004
10'5 0.003
~
~ °
0.002
o.ooi
60
80
defect
2.
We for
2
with
Simulated DLT,spectra for bandhke states varying filling pulse length tp from 10~~
High-T-Sides the
summarize
localized
states
probabilities fE
DLTS
of
model
for
for
Localized
localized
represent
of the
a
with
the
density
average
of free
thermal
300
280
defect
of
s
to
and
10~~
for
localized
s; for
(b)
states
further
proposed previously [9]. as differential coupled equations
The
for
at
energy
n,
extended
Table
1.
capture
(vth)
rate
the
equations occupation
E:
Cnne-' =
the
an see
States
of
electrons
at
parameters
states
state
electrons
velocity
(a)
system
~li the
260
TEMPERATURE(K)
~
Fig.
240
220
200
(i
fE)
coefficient and
the
eEfE cn
:=
capture
(1)
(vth) cross
an
given
section
as
an.
the The
product of emission
JOURNAL
1392
rate
of the
eE
system (I) defect
as
level
whole.
a
This
occupation
total
~j
pEfEi
"
E
the
tribution
consider
we
the
with
the
to
defects,
for point
&Ec
defect
the is
with
respect
presented localized
the
to
line
Figure
in
high,T
the
that
[9]
We
maxima.
2b.
to
rates
for
lattice
of
levels.
the
with
activation
Unlike
relaxation.
this
energy activation
eE.
defect
point
will
we
confused
be
not a
obtained
have
follows
what
In
a.
DLT-spectra for
of
sides
to
coupled
distribution
the
to
donor-type and charge exchange be proportional to the total occupation, The barrier representing a concapture of
cloud
should
influence the emission energy~ &Ec does not demonstrated It has been by simulations
locations
(2)
1>
"
according
state
defect
coefficient
occupation
whose
E-th
point
assume
barrier
enthalpy of
total
of the
We
capture
pE
The of the
E
dense
a
band.
conduction
OF,
=
weight
normalized
example,
an
with
&Ec
the
pE is
As
N°7
through the principle of detailed balance. &Ec depending on the occupation F(t) related to the values of fE ma
is
~j
F(~) where
III
determined energy E is if there is a capture barrier
with
coupled
is
PHYSIQUE
DE
the
surrounding
clouds
different
tp
behaviour
same
explain why this
edge-type
after
coincide
dis-
normalization
simulations e.g. in the in general holds for
effect
states.
DLTS-lines of different tp note, that the line maxima, if the signal can be written We
AC
coincide
after
normalization
with
respect
to
e-g-
as
A(tp)S(T),
=
(3)
amplitude function A(tp independent of the temperature T and a shape function S(T) an independent of the pulse length tp. The trivial case of a completely filled defect, where the DLTS-signal does not depend on tp at all, will be excluded in our further considerations. Let us now the kinetics during the phase in more detail. examine ionization Unemission like for a simple point defect the defects for extended non-exponential. While transients are for bandlike of different the emission levels contributing to the defect is never states process independent due to internal charge exchange [10], for localized states, the only coupling of the from the ionization kinetics barrier. Therefore, during the emission stems capture common charge phase and in the space region, where no free carriers are ai>ailable, the emission of the and (neglecting effects of the Debye-tail) the occupation be written states is independent, can with
as
t E
[tp,te]
F(t)
:
~j =
(4)
fE(tp)pEe~~E~~~~Pl,
E
of states. the distribution Based on this expression, the concept of over DLTS-measurements, developed for exponential transients, valid. remains correlation interval of mode define an The experimentally given repetition frequency tj~ and window, such that the DLTS-signal arises only from a subset of levels with rates R, the rate Therefore, we write (4) as window. emission rates falling in this where
the
"rate
windows"
runs
sum
in
t E
[tp,te]
F(t)
~j
fE(tp)pEe~~El~~~Pl
=
+
r(t; tp,T),
(5)
E.eEER
where rates
subset
E
E R
eE
enter
the
of
levels
side of the
the
denotes
rate
window.
entering
DLTS-line
the
summation The
the
rate
subset
function window consists
over
energies
r(t; tp, T)
does
such not
that
strongly depends on deeper part of the
of the
corresponding emission the DLTS-signal. The At the high-T temperature. the
influence
distribution
of
states.
As
a
DLTS
N°7
the
high-T
of the
capture
LOCALIZED
end of the
the
at
consequence, at
FOR
side of the
AT
STATES
phase all states periodic condition8,
emission
lines.
For
phase approach
DEFECTS
EXTENDED
in
the
this
space
charge region
that
means
1393
the
initial
are
values
empty
fE(0)
zero.
kinetics during the capture phase, where capture ionization during the pulse phase plays a role in the capture kinetics. For states falling in the rate window, however, eEte order8 of magnitude I within to two one holds. orders of magnitude lower For a typical DLTS experiment the pulse length tp is some than te, hence we have entp tp /te « I, such that emission of these states during the capture phase is negligible. In other words, the capture kinetics of states in the rate window does not depend on the level anymore: Now
have
we
place.
takes
consider
to
general,
In
the
emission
+w
+w
~
and
fE(tp)
Using
=:
fR(tp)
is
result, (5)
this
~ ~
~~
'
~j)
.
independent of
that
the
~j
F(t)= fR(tp)
[tp,te]
part of the
had
to
transient
fR(tp)) =
~~
f ~),
(6)
r(t; tp,T),
(7)
E [12].
0.
The
and last
influencing a
condition
+
DLTS signal factorizes in a part with only only slight tp-dependence, as long as we have therefore (3) holds for the high-T side, which
the
with
part
pEe~~E(~~~Pl
eEER
E
such
~~
writes
t E
slight T-dependence te » tp and fR(0)
"~~"
Cnne
=
and
shown.
be
of the occupation The proof given here is based on the properties of the spectral distribution probabilities at the end of the filling pulse, fE(tp), and on the rate window concept. Figure 3 function fE(tp) obtained for a point in the middle of the space shows a typical example of the charge region. We derived the factorization (7) using the assumptions te » tp and fE(0) 0, valid for the high-T sides of typical DLTS-lines. Within Figure 3 this corresponds to the idea, that the entering the rate window for higher temperatures middle region states states of the are (II), where fE(tp) does not depend on E. =
3.
DLTS
Simulations
for
experiments,
simple point
Bandlike
and
Localized
Conventional
States:
Analysis
exponential transients. proportional is rate temperature to the pulse (ionization enthalphy AH, capture cross repetition frequency, and the electronic parameters from a linear regression of section a* including the entropy factor) are conventionally obtained Arrhenius-plots of the T~-corrected emission rates en /T~. There have been many attempts in literature conventional analysis also in the case of defects with non-exponential to apply this (e. g. [13-16]). Omling et al. [13] considered an assembly of isolated point defects with transients DLTS Gaussian shapid distribution of levels. They could explain symmetrically broadened a lines and stated that the enthalpy obtained from the conventional analysis of the line ionization for different pulse repetition frequencies refers to the level of the distribution. maxima mean defects, however, a extended barrier For which included is in the capture not common occurs model of Omling. Our proposed model for localized extended defects be states at seen as can of the model of Omling including a capture direct barrier. extension Experimentally, from a defects a broad variety of values for the application of the conventional analysis on extended enthalpy were obtained. An example is the dislocation related the ionization so-called C-line Within
The
DLTS
at the
emission
observed localized
in
plastically
states
[9].
defects
of the
deformed
n-type
line
silicon
are
known
to
[14,16j,
provide
therefore
maximum
which
has
been
analyzed
to be
due to
JOURNAL
1394
PHYSIQUE
DE
N°7
III
0.8
fE(tp) fE(le) 0.6 ~ ~ _
Ill)
$
DA
',
_+
j~
window
rate
',
o,2
(iill
0.0
0°
0~l
03
02
01
05
04
06
eE.te
Fig
Occupation
3. middle
the
probabilities
phase, fE(te), for the
emission
the
at
DLTS,line
of the
end
with
=
~-
the
=
The 0.
=
emission
The
is
strong
enough
to
as
of the
kinetics
capture
the
empty does
states
end
and
of
the
a
during
states
falling
with
E
the
(falling
completely during the emission (III) For E, fE(tp) const. on
states
depend
not
the
at
240 K
=
abscissa log (eEte space charge region. Note, that the -(Ec proportional to energy of the states: log(eEte) sufficient For the deepest states, the emission is not to empty fE(0) and therefore fE(tp) increase phase. The initial values fE(te) of the
eE). (II) fE (0)
and
point in (emission-rate/pulse repetition E)/kT We distinguish three
from
s
frequency) is regions: (I) emission
phase, fE(tp), Figure 2b at T
capture
10~~
tp
phase, shallow
=
fE(tp) decreases with E. The rate window phase takes place (centre indicated with arrow) is generally located in the regions (I) and (II). For higher temperatures, This the deepest emptied during the emission phase, and the region (I) vanishes states even are in the rate window R are independent of E that the initial values fE(tp) := JR (tp) for states means, amplitude function depending on for high factorize in an In this regime, the transients temperatures. function the pulse length ma JR (tp) and a shape depending on the temperature (see text ).
will
We
bandlike
Since and
how
localized
closed
capture
the
demonstrate and
a
be
to
during
emission
states
conventional
a
solution
work
on
extended
defects
equation (I is not at hand, the DLTS-experiment ii ii. The values bandlike and been chosen equal for
differential
for the
numerically to simulate density of state function have
treated
the
analysis would
caused
by
states.
the
rate
equations
of the
have
parameters
localized
(see
states
I).
Tab.
of assumed No » ND (F(tp)( with No, ND being the concentrations we dopant and the deep levels, respectively. This condition has been checked to hold for our simulations. A full integration the space charge regioi1including the Debye-tails over for the has been performed [18], and we solved the rate equations with ieriodic conditions 0) at the begin of tte capture phase have been transients, I.e. the values of the vector fE(t phase, fE(te). chosen to be the values at the end of the emission the
For
the
simulations
shallow
=
bandlike
For
of the
temperatures
properties localized them
for
are
maxima
It
respect
bandlike with
lines
states
turns to
the
out,
spectra that
maxima
(Fig. 2a),
different
tp.
high-T sides of with increasing tp.
the
decrease
typical for DLT
states.
with
(Fig. 2a),
states
These
the
of
bandlike
high-T
the It
states
sides
lines has
clincide,
been
[9,10]. Figure
of the
and
2b
maximum that
the
shows
coincide
spectra
the
already,
stated
after
(see Fig. 2b, insert, and Sect. 2). Compared to the temperatures is only a very slight change in the properties
are
characteristic
for
localized
for
normalizing
there
two
these
results
states.
spectra of the
DLTS
N°7
Table
FOR
Parameter
I.
STATES
LOCALIZED
values
for
used
AT
EXTENDED
DEFECTS
1395
simulations.
material
n-type Si
doping
10~~ cm~~
No
level
capacitance
MHz-bridge
21
meas.
correlation
without
Lock-In
filter,
If-mode
voltage
bias
0.0 V
gate
I
time
pulse
frequency
repetition
of
section
cross
ND F~'/l
of
neutral
occupation
values
eV
0.20
eV
0.50
eV x
10~~~ cm~
0.0
number
states
0.60
5.0
a
entropy
ionization
Apparent
a
enthalpy AHI
level
capture
coefficient
enthalpy AH2
level
upper
II.
s
box-like
states
barrier
capture
the
s
~~
AC/Co
density
lower
10~~
x
17
output
Table
V
-4.0
pulse voltage
10~~ cm~~ 0.0
enthalpies AH and capture cross a* (includ, sections filling pulse length obtained from simulations and tp as on The points do not precisely form a line in an Arrhenius-plot. errors of
emission
entropy factor), dependent
ing conventional
given here
analysis. The effect of this are an
curvature.
bandlike
tp [s] 10~~
AH 0.492
[eV] +
0.003
localized
states
a*[10~~~ cm~]
AH
[eV]
120 + 30
0.475
+
0.003
states
a*[10~~~ cm~] 15 + 2
10~~
0.506
+
0.006
380 + 150
0.473
+
0.003
13 + 2
10~~
0.534
+
0.005
2900 + 1000
0.520
+
0.010
150 + 80
0.465
+
0.010
5
x
10~~
10~~
0.409 + 0.010
+100
0.610 + 0.020
6.7 + 0.4
0.540 + 0.020
120
13000
+10000
500 + 500
analysis of the spectra for bandlike states are given in Figure 4a repetition frequencies is typical for a practical experiment. As be seen, the Arrhenius,plots for different tp differ significantly. While in the region of lower can tp the main effect is a shift of the lines, for higher tp also the slope changes strongly. Similar results have been obtained experimentally by Grillot et al. [19]. The simulated Arrhenius-plots showed slight which have been used to calculate the in Table II. However, curvatures, errors the would hardly be detectable in a real experiment. curvature For localized (Fig. 4b, Tab. II) there is a shift of the lines for small tp in the reverse states direction than for bandlike Both enthalpy and the ionization states. parameters, the apparent The
and
results
Table
II.
of
a
The
conventional
choice of pulse
JOURNAL
1396
,,,
~,,
';,
5
~
.
",, ",
~
~
",(">~, "' ",,
"',
"',
',,
",,
',,,
',,,
2
a
~",~'.,,
~
"'A
~
~
1 Q~
a
'%iq
",,,
'
0-6 0'5 l 0-4 5~i Q-4 l 0~3
.
"Qli~,,
",~
',
~
li
",,
N°7
III
v, [,,
,
,
PHYSIQUE
DE
~~,~, '~,~tq
,,,
~,,,
~,,,
~
,,j~
""~ "v ""~i'y ,,,',,, ',,,~,, ',,
io-s
«
'~,,
5
~,,
'~,_
4
~,,',,,
~,,
',,,, ',,~ ',~',~
s
S-g
4.0
4.1
4~2
4.4
4.3
4.5
a)
4.6
4.8
4.7
4.9
(K-I
000/T
io-2
10'6 io,5 10'4 5*lo'4 lo's
. «
,
.
I
f
D
s
v ~
CV
~ ii
lo's
',,~
"v, ",,
6 5 4
s 2
3.7
3.8
S-g
4.0
4.1
000/T
4.3
4.2
4.4
(K~l
b) Fig.
4.
(b),
vith of
Results
apparent even
Arrhenius,plots of simulated DLT-spectra varying filling pulse length tp from 10~~ s linear regressions given in Table II.
capture
exceed
apparent
the ionization
cross
limits
section, of the
change original
for to
bandhke
10~~
s
states
For
The non-monotonically. distribution. Figure 5
(a)
further
and
apparent summarizes
for
localized
parameters
see
activation the
results
states
Table
I.
energies for
the
enthalpies.
that the use of Arrhenius-plots is only of limited use for extended it can be seen presentation of DLT-spectra for They may be seen as a possibility of a condensed includdifferent pulse repetition frequencies, provided that all parameters of the measurement parameters is far from ing the pulse length are given, but the interpretation of the obtained fitting of experimental bandlike determined clear. For be states, the defect parameters can ma In
general,
defects.
FOR
DLTS
N°7
f
LOCALIZED
STATES
AT
DEFECTS
EXTENDED
1397
o.6
)
lf
o.5
=------
'~,,,
~
E
'~,,, 0.4
o
#
localized bandlike
o.3
.% _q
states states
li ~ ~
il
i~
i#
o-i
o-o
0'6
2
4
s
0'5
5
s
2
0~4
5
4
5
0'3
simulated
DLT
2
3
4
pulse length (s)
Fig.
Apparent
5
bandlike
and
simulations
DLTS-data
[10].
parameter
values
4.
Summary
We
have
pulse length defect
and
have
the
been
of
seen
values
as
a
It
of
has
of
with
respect
distinguish
to
obtained
parameters ascribed to
from
this
at
a
which from
states
DLT
bandlike
analysis
extended of DLTS
not
be
of
the
possible
to
fit
and
depend
for
DLT
on
different
high-T-side,
e.g.
extended
up
an
bandlike
localized on
defects lines
make
spectra for
'average'values for the distribution simply some the presentation of Arrhenius-plots for extended defects should be seen presentation of experimental data, provided that the parameters of the the pulse length, are reported. can
localized
values
also
it is
point of the
of levels
localized
both
that
states
simulated
on
for
demonstrated
to
for
spectra
parameter
states.
high-T-sides
distribution
analysis applied
been
the
the
II.
paper,
localized
model
For
Table
localized
for
model
holds for any
criterion
also
see
forthcoming
a
this
normalization
a
here
case
a
within
result
conventional
shown.
apparent
that
after This
be
can
in
the
in
plots of
Arrhenius
filling pulse length tp.
presented
implications of
shown
lines.
from
the
results
DLTS-spectra
coincide
results
The
of
demonstrate
will
We to
been
of the
maxima
function
a
I, for the
examined It has
spectra.
as
Table
see
enthalpies
ionization
states
the
states.
extended
states,
defects
that
the
pulse length and of levels. Therefore,
the
only
as
a
measurement,
condensed
namely
Acknowledgments The
authors
with
the
would
preparation
like to thank M. Seibt of the manuscript.
Dedicated
to
the
and
memory
L.
Panepinto for
of Prof.
Dr.
Peter
valuable
Haasen.
discussions
and
help
JOURNAL
1398
DE
PHYSIQUE
N°7
III
References
iii
Celli V.,
[2]
Teichler
Gold A. and Thomson R., Phys. Rev. Lett. 8 (1962) 96. Semiconductors 1974, IOP Conf. Proc. No. 23 (Institute of H., Lattice Defects in Physics, London, 1975) p. 374. Science and Technology", W. Schr6ter, Ed., "Materials Teichler H., In Alexander H. and [3] Vol. 4 (VCH Weinheim, 1991) p.249. Nabarro. Ed., Vol. 5 Schr6ter W., In "Dislocations F-R-Nin Solids", Labusch R. and [4] (North Holland, 1980) p. 127. [5] Schroter W., phys. stat. sol. (a) 19 (1973) 159. Schr6ter W., Appl. Phys. Lett. 58 (1991) [6] Kittler M., Mirz J., Seifert W., Seibt M. and 911.
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