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Effects of space-charges on thermally stimulated currents
453—456.
Solid State Communications. Vol.30, pp. Pergamon Press Ltd. 1979. Printed in Great Britain.
EFFECTS OF SPACE—CHARGES ON THERMALLY STIMULATED CURRENTS C.De Blasi, S.Galassini, C.Manfredotti, G.Micocci and A.Tepore Istituto di Fisica, Universitã di Lecce, Lecce (Received 8 August 1978;
(Italy)
in revised form 4 December 1978 by R.Fieschi)
Evidence is presented of space—charge effects in thermally stimulated cur — rents (TSC) measured at relatively high fields in homogeneous samples sandwiched between two electrodes. A new method is proposed for estimating traps depths and trap concentrations from TSC curves and the method is checked with classical SCLC and TSC results obtainded on n—GaSe samples. (I) The classical theories of TSC were developed under various assumptions, one of which is so obvious that it is never written down explicitly i.e. that the elec— tric field in the sample is constant. Now, the electric field can have various influen— ces on TSC curves, particularly for samples that are sandwiched between two electrodes. For example, it can alter the position or the relative height~2~of the peak. Some of these effects are well known, particular— ly for p—n junctions and Schottky barriers, i.e. for non—homogeneous samples. For homo— geneous samples, however, these effects have been much less investigated(s). Space—charge phenomena related to polarization and depola— rization effects which cause ionic thermo— currents in dielectrics have been more ex— tensively studied(~’~~. Recently(6), a theory of TSC for high electrical fields hss been proposed, in which a complete collection of thermally detrapped carriers is assumed, which gives one a possibility for determinin— ing the exact energy distribution of the traps. When using these theories, one must be cautious in assuming ohmic conduction by putting the carrier concentration n den — ved from the theory directly into the relation j=nepE, because E could easily be not constant throughout, the sample. In fact, the thermally detrapped carriers do move in the space—char~e created if
by
all
the applied
the other voltage
is
trapped
carriers
high enough,
and,
soace—
On the other hand, the measurement of TSC under space—charge conditions could be advantageously used as an alternative method of the classical TSC method, particularly when trap densities are relatively lcw.An example of this application will be presented in this paper, together with a very simple model for carrying out the data analysis. The development of a general model for TSC in homogeneous samples in the space—charge regime is in progress. Our simple model can be described as follows. Assume that one illuminates a sample contained between two electrodes, through one electrode, at a low temperature and with the bias voltage applied. Now, if the absorption coefficient is high enough, hole—electron pairs will be created near the illuminated surface. Under the action of the electric field, holes (minority carriers) will migrate toward the illuminated surface, filling the relavant traps or recombining, while electrons will migrate toward the other sur— face. If the electric field is low enough, the space—charge produced by both the trapped and free carriers will be limited to a depth of the order of the trapping length LUT+E (where p is the carrier mobility, ~ is the trapping time and E the electric field) which is much less than the sample its
influence
thickness.
Therefore,
on the behaviour
of
the TSC
charge effects are likely observable. For instance, for a sample of 100pm thick and with a trap concentration of 1012 cm3, applied voltages, of the order of 30 volts
current will be negligible. Vice—versa, if the electric field is high enough, a situa— tion can be reached in which L becomes of the order of the sample thickness. In
would suffice to satisfy the (whpre Q is the total charge
this case if the light intensity is large enough to saturate traps, space—charge
condition Q=CV in the tra9s
and C is the sample capacitance) which repre— sents a rough threshold for space—charge
effects will be important (even for low trap concentrations) with noticeable
effects.
eff~ct~ on 453
the TSC
curves.
As
in SCLC mea—
454
EFFECTS OF SPACE —CHARGES ON THERMALLY STIMULATED CURRENTS
surements, the electric ger be a constant across
field the
will no Ion— sample width
eventually reached. In the following, dence for space—charge
the only case and
yes all
the is
present that now
30, No. 7
from the area under the TSC peak, or the trap—filled limit TFL, when this
and the simple ohmic expression for TSC j=nepE, where n(T) is deduced from theore— tical models, is not valid anymore. Since difference between normal SCLC effects
Vol.
from is
experimental evieffects
in
TSC
cur—
will be presented, and the validity of the assumptions will be checked. More—
injection of carriers is effected by in — creasing the temperature and by emptying the traps, and that injection occurs prac—
over, traps
tically at the
layer), exactly the same behaviour as in SCLC is expected, with the same equations. In a first approximation, since the peak position is related to trap energy, the
stigation were n—type GaSe platelets grown by an iodine assisted chemical transport 7~. Details concerning both sample method( preparation and experimental apparatus are reported in Ref.8. The samples typically had an electrode area of about 7 mm2 and a
current
thickness
as
over the whole sample, instead cathode only ( the accumulation
at
the
the
TSC
square
of
maximum
the
will
voltage
of
increase
V
In
2
j max where
6=n/n
=
3
is
concentration, the dielectric kness. From
e~
~—
d ratio
300 (1)
3 free/trapped
carrier
p the carrier mobility, C constant and d sample thic— general
theory,
one has
n=
where
n
t
N
(2)
=
=
shallow • density
of
density
of deep
of electrons
trapped
shallow
=
c E= =
If
the
are
traps of
probability
from a
filled
trap (see ref.l) effective density of the conduction band shallow trap depth capture probability bination center
conditions
assumed
i.e.
an
for
strong
~‘/3<
and
of
shallow
about
curves
is
shown
130
to
to
1 K/sec
observed
have
at
in Fig.l.
dif—
For
the
clearness, not all the measu— are reported. At about 130 Ks
clearly distinct peak is visible responds to a trap at 0.2 eV, as in Ref.9 (sample F7). Particular taken
pm.
80
apply
bias voltages
When one plots
drift the
in
that con— reported care was the range
mobility
current
(see
intensity
high, only behaviour,
the last one. An example of this for the sample F8, is shown in
Fig.2,
where
only a
quadratic
0.65
eV,
both cases
are presented:
behaviour
for
and an ohmic—quadratic
the
trap at
behaviour
of
a
in
recom—
retrapping
the trap at 0.54 eV(8). The analysis of these curves has carried out according to the previous
been mo—
del, by assuming the mobility data and the same behaviour with temperature as repor— ted in Ref.lO. The trap densities have been
taken from
previous TSC
measurements(8)
6N instead of being sults are listed
again evaluated. The re— in Table I. The agreement
obtains Pn n=
3(N
)
—
~ and,
of
to
from
for states
1/1N~~>l one
scan
at the peak as a function of bias voltage one obtains an “ohmic region followed by a ‘quadratic” one or, if the voltage is
traps
probability
3N c exp(—E t /kT)= detrapping
N
voltages
sake of red curves
in
electron =
rates
used. A Set of TSC
ferent
50 pm
traps
cYv~h capture
P
from
temperature
of constant electron Fig.2, Ref.9).
• density
t Nt=
will be used to estimate concentrations. used in the present inve—
ranging the
K heating
been
(1) the
the method depths and The samples
if
(3)
n~
n<
between the present results and the pre— vious TSC and SCLC measurements is good, which justifies the model introduced in this paper.
N E~ =—~—n t
=
—~-
N
exp(—E
/kT)
(4)
t t
Obviously,
if
TFL would
be reached,
also the trap density could be determined ~ the present method. Another test can be performed as follows: the “knee” between the ohmic and qua—
which is approximately the same expression as for the SCLC case. Therefore, one can obtain E just in the same way as in SCLC,
dratic regions in Fig.2 should correspond roughly to the case where the trapping length L equals the sample thickness, ac—
from thetquadra tic behaviour or j as a max function of V (eq.l). The trap concentra— t tion N can be estimated at low fields
cording to model. In this way, one can • • • + estimate a trapping 9 sec, time compared T for with electrons T~l08 of about 4x10
Vol.
30, No. 7
EFFECTS OF SPACE
—
CHARGES ON ThERMALLY STIMULATED CURRENTS
b
4—
2
Ii
I.
Ii
:~i
—
Ii~I \~\ Ii~:,’ ~
Iii,
•_•.\\\ ...\ •..
Ii~,/ ‘‘ 1. ~
/j
I,~•,i /c/•
0
•~. •~. “•~. ...
_.,
\‘~
-
100 Fig.l
‘.‘
150
T(~K)
A series of TSC curves taken on the sample F7 with applied
—
voltages of 40, 60, 80, 100 and 140 volts.
10~—
A
I Iv
A
i~~n-
10 Fig.2
—
100
v(voIt)
Voltage dependence of the intensity of the two current peaks that correspond to a trap depth of 0.54 eV and 0.65 eV respectively (see Table I, sample F8).
455
456
EFFECTS OF SPACE—CHARGES ON THERMALLY STIMULATED CURRENTS
T A B L E
I
—
Vol. 30, No. 7
Comparison between the values of the trap depth (E) and the trap density (N) obtained in previous works and in the present one.
(8) Sample
E(eV)
F8
F7
sec calculated
TSC
(9) _~
N(cm
)
E(eV)
N(cm
3x10
0.65
3xl0
13
0.63
0.20
4xl015
————
E(eV)
Present work N(cm
0.56
3x10
0.67
3x1013
0.25
4xl015
————
3xl013
TSC data~8~ using
the relation T+=(Ntatvth)~, i~8xlO9 Sec taken directly
)
13
0.54
from old
SCLC
and with from nuclear
measurementsGl).
In conclusion
the method
)
13
seems
can be made more rigorous with a theoretical treatment of TSC Un—
der
conditions.
SCLC
REFERENCE S 1. See for example DUSSEL,G.A. and BUBE,R.A., Phys.Rev.l55, 764 (1967) and referenceS therein. 2. KULSHRESHTHA,A.P. and SAUNlERS,I.J., J.Phys.D: Appl.Phys.8,
1787 (1975)
3. HEIJNE,L., Philips Res.Repts.Suppl.4, (1961) 4. BUCCI,C., FIESCHI,R.
and GUIDI,G., Phys.Rev.148, 816 (1966)
5. LEAL FERREIRA,G.F. and Q~0SS,B., in Electrets,
Charge Storage and Transport
in Dielectrics, ed. by M.M.Perlmann (Proc.Miami Meeting, Electrochem. Soc., Princeton 1973) pp.252—259 Van TURNHOUT,J., ibidem pp.230—251 6. SIMMONS,J.G., TAYLOR,G.W. and TAN,M.C., Phys.Rev.B 7, 374 (1973) 7. CARDETTA,V.L., NANCINI.A.M., MANFREDOTTI,C. and A.RIZZO, J.Cryst.Growth 17, 155
(1972)
8. MANFREDOTTI,C.,MURRI,R.,QUIRINI,A. and VASANELLI L., Phys. (a) 38, 685 (1976)
Status Solidi
9. MANF~lED0TTI,C., QUIRINI,A., RIZZO A. and VASANELLI L., Solid State Consaun. 15, 1347 (1974) 10. OTTAVIANI,G., CANALI,C., NAVA,F., ZSCHOKKE,1.,
Solid
11. MANEIEDOTTI,C.,
State
to
work. It complete
SCHNID,Ph., MOOSER,E., MINDER,R. and
Comnun. 14, 933 (1974)
MURRI,R. and VASANELLI,L., Nucl.Instrun.Methods 115,349(1974)
Solid State Communications. Vol.30, pp. Pergamon Press Ltd. 1979. Printed in Great Britain.
EFFECTS OF SPACE—CHARGES ON THERMALLY STIMULATED CURRENTS C.De Blasi, S.Galassini, C.Manfredotti, G.Micocci and A.Tepore Istituto di Fisica, Universitã di Lecce, Lecce (Received 8 August 1978;
(Italy)
in revised form 4 December 1978 by R.Fieschi)
Evidence is presented of space—charge effects in thermally stimulated cur — rents (TSC) measured at relatively high fields in homogeneous samples sandwiched between two electrodes. A new method is proposed for estimating traps depths and trap concentrations from TSC curves and the method is checked with classical SCLC and TSC results obtainded on n—GaSe samples. (I) The classical theories of TSC were developed under various assumptions, one of which is so obvious that it is never written down explicitly i.e. that the elec— tric field in the sample is constant. Now, the electric field can have various influen— ces on TSC curves, particularly for samples that are sandwiched between two electrodes. For example, it can alter the position or the relative height~2~of the peak. Some of these effects are well known, particular— ly for p—n junctions and Schottky barriers, i.e. for non—homogeneous samples. For homo— geneous samples, however, these effects have been much less investigated(s). Space—charge phenomena related to polarization and depola— rization effects which cause ionic thermo— currents in dielectrics have been more ex— tensively studied(~’~~. Recently(6), a theory of TSC for high electrical fields hss been proposed, in which a complete collection of thermally detrapped carriers is assumed, which gives one a possibility for determinin— ing the exact energy distribution of the traps. When using these theories, one must be cautious in assuming ohmic conduction by putting the carrier concentration n den — ved from the theory directly into the relation j=nepE, because E could easily be not constant throughout, the sample. In fact, the thermally detrapped carriers do move in the space—char~e created if
by
all
the applied
the other voltage
is
trapped
carriers
high enough,
and,
soace—
On the other hand, the measurement of TSC under space—charge conditions could be advantageously used as an alternative method of the classical TSC method, particularly when trap densities are relatively lcw.An example of this application will be presented in this paper, together with a very simple model for carrying out the data analysis. The development of a general model for TSC in homogeneous samples in the space—charge regime is in progress. Our simple model can be described as follows. Assume that one illuminates a sample contained between two electrodes, through one electrode, at a low temperature and with the bias voltage applied. Now, if the absorption coefficient is high enough, hole—electron pairs will be created near the illuminated surface. Under the action of the electric field, holes (minority carriers) will migrate toward the illuminated surface, filling the relavant traps or recombining, while electrons will migrate toward the other sur— face. If the electric field is low enough, the space—charge produced by both the trapped and free carriers will be limited to a depth of the order of the trapping length LUT+E (where p is the carrier mobility, ~ is the trapping time and E the electric field) which is much less than the sample its
influence
thickness.
Therefore,
on the behaviour
of
the TSC
charge effects are likely observable. For instance, for a sample of 100pm thick and with a trap concentration of 1012 cm3, applied voltages, of the order of 30 volts
current will be negligible. Vice—versa, if the electric field is high enough, a situa— tion can be reached in which L becomes of the order of the sample thickness. In
would suffice to satisfy the (whpre Q is the total charge
this case if the light intensity is large enough to saturate traps, space—charge
condition Q=CV in the tra9s
and C is the sample capacitance) which repre— sents a rough threshold for space—charge
effects will be important (even for low trap concentrations) with noticeable
effects.
eff~ct~ on 453
the TSC
curves.
As
in SCLC mea—
454
EFFECTS OF SPACE —CHARGES ON THERMALLY STIMULATED CURRENTS
surements, the electric ger be a constant across
field the
will no Ion— sample width
eventually reached. In the following, dence for space—charge
the only case and
yes all
the is
present that now
30, No. 7
from the area under the TSC peak, or the trap—filled limit TFL, when this
and the simple ohmic expression for TSC j=nepE, where n(T) is deduced from theore— tical models, is not valid anymore. Since difference between normal SCLC effects
Vol.
from is
experimental evieffects
in
TSC
cur—
will be presented, and the validity of the assumptions will be checked. More—
injection of carriers is effected by in — creasing the temperature and by emptying the traps, and that injection occurs prac—
over, traps
tically at the
layer), exactly the same behaviour as in SCLC is expected, with the same equations. In a first approximation, since the peak position is related to trap energy, the
stigation were n—type GaSe platelets grown by an iodine assisted chemical transport 7~. Details concerning both sample method( preparation and experimental apparatus are reported in Ref.8. The samples typically had an electrode area of about 7 mm2 and a
current
thickness
as
over the whole sample, instead cathode only ( the accumulation
at
the
the
TSC
square
of
maximum
the
will
voltage
of
increase
V
In
2
j max where
6=n/n
=
3
is
concentration, the dielectric kness. From
e~
~—
d ratio
300 (1)
3 free/trapped
carrier
p the carrier mobility, C constant and d sample thic— general
theory,
one has
n=
where
n
t
N
(2)
=
=
shallow • density
of
density
of deep
of electrons
trapped
shallow
=
c E= =
If
the
are
traps of
probability
from a
filled
trap (see ref.l) effective density of the conduction band shallow trap depth capture probability bination center
conditions
assumed
i.e.
an
for
strong
~‘/3<
and
of
shallow
about
curves
is
shown
130
to
to
1 K/sec
observed
have
at
in Fig.l.
dif—
For
the
clearness, not all the measu— are reported. At about 130 Ks
clearly distinct peak is visible responds to a trap at 0.2 eV, as in Ref.9 (sample F7). Particular taken
pm.
80
apply
bias voltages
When one plots
drift the
in
that con— reported care was the range
mobility
current
(see
intensity
high, only behaviour,
the last one. An example of this for the sample F8, is shown in
Fig.2,
where
only a
quadratic
0.65
eV,
both cases
are presented:
behaviour
for
and an ohmic—quadratic
the
trap at
behaviour
of
a
in
recom—
retrapping
the trap at 0.54 eV(8). The analysis of these curves has carried out according to the previous
been mo—
del, by assuming the mobility data and the same behaviour with temperature as repor— ted in Ref.lO. The trap densities have been
taken from
previous TSC
measurements(8)
6N instead of being sults are listed
again evaluated. The re— in Table I. The agreement
obtains Pn n=
3(N
)
—
~ and,
of
to
from
for states
1/1N~~>l one
scan
at the peak as a function of bias voltage one obtains an “ohmic region followed by a ‘quadratic” one or, if the voltage is
traps
probability
3N c exp(—E t /kT)= detrapping
N
voltages
sake of red curves
in
electron =
rates
used. A Set of TSC
ferent
50 pm
traps
cYv~h capture
P
from
temperature
of constant electron Fig.2, Ref.9).
• density
t Nt=
will be used to estimate concentrations. used in the present inve—
ranging the
K heating
been
(1) the
the method depths and The samples
if
(3)
n~
n<
between the present results and the pre— vious TSC and SCLC measurements is good, which justifies the model introduced in this paper.
N E~ =—~—n t
=
—~-
N
exp(—E
/kT)
(4)
t t
Obviously,
if
TFL would
be reached,
also the trap density could be determined ~ the present method. Another test can be performed as follows: the “knee” between the ohmic and qua—
which is approximately the same expression as for the SCLC case. Therefore, one can obtain E just in the same way as in SCLC,
dratic regions in Fig.2 should correspond roughly to the case where the trapping length L equals the sample thickness, ac—
from thetquadra tic behaviour or j as a max function of V (eq.l). The trap concentra— t tion N can be estimated at low fields
cording to model. In this way, one can • • • + estimate a trapping 9 sec, time compared T for with electrons T~l08 of about 4x10
Vol.
30, No. 7
EFFECTS OF SPACE
—
CHARGES ON ThERMALLY STIMULATED CURRENTS
b
4—
2
Ii
I.
Ii
:~i
—
Ii~I \~\ Ii~:,’ ~
Iii,
•_•.\\\ ...\ •..
Ii~,/ ‘‘ 1. ~
/j
I,~•,i /c/•
0
•~. •~. “•~. ...
_.,
\‘~
-
100 Fig.l
‘.‘
150
T(~K)
A series of TSC curves taken on the sample F7 with applied
—
voltages of 40, 60, 80, 100 and 140 volts.
10~—
A
I Iv
A
i~~n-
10 Fig.2
—
100
v(voIt)
Voltage dependence of the intensity of the two current peaks that correspond to a trap depth of 0.54 eV and 0.65 eV respectively (see Table I, sample F8).
455
456
EFFECTS OF SPACE—CHARGES ON THERMALLY STIMULATED CURRENTS
T A B L E
I
—
Vol. 30, No. 7
Comparison between the values of the trap depth (E) and the trap density (N) obtained in previous works and in the present one.
(8) Sample
E(eV)
F8
F7
sec calculated
TSC
(9) _~
N(cm
)
E(eV)
N(cm
3x10
0.65
3xl0
13
0.63
0.20
4xl015
————
E(eV)
Present work N(cm
0.56
3x10
0.67
3x1013
0.25
4xl015
————
3xl013
TSC data~8~ using
the relation T+=(Ntatvth)~, i~8xlO9 Sec taken directly
)
13
0.54
from old
SCLC
and with from nuclear
measurementsGl).
In conclusion
the method
)
13
seems
can be made more rigorous with a theoretical treatment of TSC Un—
der
conditions.
SCLC
REFERENCE S 1. See for example DUSSEL,G.A. and BUBE,R.A., Phys.Rev.l55, 764 (1967) and referenceS therein. 2. KULSHRESHTHA,A.P. and SAUNlERS,I.J., J.Phys.D: Appl.Phys.8,
1787 (1975)
3. HEIJNE,L., Philips Res.Repts.Suppl.4, (1961) 4. BUCCI,C., FIESCHI,R.
and GUIDI,G., Phys.Rev.148, 816 (1966)
5. LEAL FERREIRA,G.F. and Q~0SS,B., in Electrets,
Charge Storage and Transport
in Dielectrics, ed. by M.M.Perlmann (Proc.Miami Meeting, Electrochem. Soc., Princeton 1973) pp.252—259 Van TURNHOUT,J., ibidem pp.230—251 6. SIMMONS,J.G., TAYLOR,G.W. and TAN,M.C., Phys.Rev.B 7, 374 (1973) 7. CARDETTA,V.L., NANCINI.A.M., MANFREDOTTI,C. and A.RIZZO, J.Cryst.Growth 17, 155
(1972)
8. MANFREDOTTI,C.,MURRI,R.,QUIRINI,A. and VASANELLI L., Phys. (a) 38, 685 (1976)
Status Solidi
9. MANF~lED0TTI,C., QUIRINI,A., RIZZO A. and VASANELLI L., Solid State Consaun. 15, 1347 (1974) 10. OTTAVIANI,G., CANALI,C., NAVA,F., ZSCHOKKE,1.,
Solid
11. MANEIEDOTTI,C.,
State
to
work. It complete
SCHNID,Ph., MOOSER,E., MINDER,R. and
Comnun. 14, 933 (1974)
MURRI,R. and VASANELLI,L., Nucl.Instrun.Methods 115,349(1974)