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On electrical conduction in reduced rutile
Physica 30 1667-1669
Acket, G. A. Volger, J.
1964
LETTER TO THE EDITOR On electrical
conduction
in reduced rutile
A number of studies on electrical conduction in reduced rutile have been made 1) 3) 3) 4) 5) but still uncertainties concerning the interpretation of electron mobility and electron statistics have remained. Frederikse 3) deduced effective masses of 12-30 m, from Seebeck and Hall data on rather strongly reduced material. In a previous paper 3) the present authors reported Hall-measurements on slightly reduced material. The mobility perpendicular to the c-axis was found to be independent of the amount of reduction, but the behaviour of the Hall-coefficient did depend on it. Donor interaction was suggested, but it should be noted that the presence of compensating impurities (Al3+ 6), Fe3+) may not be negligible. In this note we report on the conductivity and Hall-effect ((jK, H//C) of reduced rutile crystals doped with about 100 p.p.m. AleO3. The boules were obtained from
Hall-coefficient of TiO3 samples doped with about 100 p.p.m. Al303 and of various degrees of reduction (j _L C; H // C). the National Lead Company. The mobility was found to equal that of undoped rutile. Hall-data are presented in fig. 1. It is seen that the transition from linear to bended
-
1667 -
G. A. ACKET
1668 curves
in the RH vs l/T plot
undoped
material
ent donor levels. levels
At low reduction
We also performed specimens
is now found
5). These phenomena
are exhausted having
J. VOLGER
at higher
only the deeper
measurements
levels remain
resistivities
between
filled
around
of undoped
300°K
5). In very high resis-
the slope differs from that found at lower resistivity
Compensation
is probably
Such behaviour
the transport
in this region.
Below
on temperature,
by about a factor 3.
250°K
may be found for polar scattering,
contribution
reduced lOssL,cm.
the slopes of the curves
tance material decreases.
as the shallow
10 Sz cm and 2 x
those of the Hall-coefficients
important
than in
impurities.
in fig. 2. In the region with
concentrations
by a model with two differ-
( I c-axis) of the thermopower
room temperature agreement
carrier
can be understood
by the compensating
The results are plotted are in reasonable
AND
the thermopower
due to a dependance
cf. also measurements
of Y ahia
of and
161412. lo-
8642-
%%-’
-
Fig. 2. Thermo-power of reduced temperature resistivities :
pure r-utile; temperature
‘o/ gradient
1 c-axis.
-
13Qcm.
+
1 x
103Qcm.
.c
2 x
105 Dem.
l
28 Qcm. 2 x 102 .Qcm.
0
5 x
10sQcm.
0
1 x
10sQcm.
0 Frederikse
on Tis03
ature transport to a density
7). Neglecting
contribution
the anisotropy
and assuming
to equal .$(/z/e),effective
of states of 1.2- 3 x
Room
the room temper-
masses of 3-5 m, corresponding
1Ozo cm-s were found, except for the 13 .Qcm sample.
These values are much lower than those previously reported 1) 2). We also investigated the dependance of the conductivity on the electric field strength on specimens discharged and voltages
having room temperature
across thin specimens
resistivities
up to 10 kV were used. The current
served by means of an X - Y oscilloscope. cm at room
temperature
of about 1OsQcm. A condenser
by means of a thyratron.
and about
3 x
Maximum 105 V/cm
Capacitances
- voltage
characteristics
were ob-
field strengths
were 3-4 x
at liquid
temperature
parallel and perpendicular to the c-axis. Chemical polishing to be essential in order to avoid alinearities at the contacts.
air
was
of 250 pF 105V/ both
in molten KOH appeared The observed characteris-
tics remained linear even up to the high field strengths mentioned. If indeed masses of about 30 m, would be present the mobility at 90’K would correspond to a relaxation time of about 3 x lo-13 sec. If this relaxation time is not reduced the energy
ON ELECTRICAL
supplied larger
to the electrons than
the band
CONDUCTION
between
width,
two
IN REDUCED
collisions
E, if conservatively
would
RUTILE
be at least
estimated
1669 0.1 eV which
to be 3 x
E G @/ma2 with a = 3 x 10-s cm. We feel that under these circumstances rent-field
characteristics
another
argument
It is doubtful1
would
that the actual whether
should than
Moreover,
be taken
z = O/T;
m g
4m,;
produced
0 = Debye
the angular
variational
parameters
temperature.
The formula 1 the c-axis mechanisms
yields
frequency reasonable
may become
Acknowledgements. assistance and were Zuiver
of the made
“Stichting
Wetenschappelijk
mass value
considered
lattice
in the ionic rather
lattice
as a polaron
for the mobility temperature
based
on a
(670K”)r).
*
es -. E
agreement 100°K
phonon
branch.
4.0 and 2.1 respectively
with the average and 300°K.
Below
For
U. = 5 the
g).
of the mobilities 100°K
other
// and
scattering
important. The
possible
being
a formula
of the longitudinal
between
be
5331014 set-l.
li
authors
are indebted
with the high field experiments.
programme
the electron
CC=&
v and w have the values
in the region
from our effective
much lower than the Debye
0 = w denotes
by
carrier
e.a.9) deduced
for temperatures
the curshould
as they are of the order of the reciprocal
the charge
Feynman
absence
lower and so the band much wider.
times following
meaning
into account,
8) and that their
mass is markedly
the polarization
as an electron.
model by Frijhlich
alinearities
the relaxation
still have their usual physical frequency.
show
is
10-z eV using
voor
to Mr. G. Ruitenberg
These investigations
Fundamenteel
by financial
support
Onderzoek”
(Z.W.O.).
Onderzoek
for his
are part of the research der Materie”
of the “Nederlandse
(F.O.M.)
Organisatie
voor
Received 5-5-64 G. A. ACKET and J. VOLGER Fysisch Laboratorium der Rijks-Universiteit Utrecht, Utrecht, Nederland REFERENCES
1) Breckenridge, R. G. and Hosler, W. R., Phys. Rev. 91 (1953) 793. 2) Frederikse, H. P. R., J. appl. Phys. Suppl. 32 (1961) 2211. 3) Becker, J. H. and Hosler, W. R., J. Phys. Sot. Jap. Suppl. 18 (1963) 152. 4) Bogomolov, 5) Acket, 6) Yahia,
V. N. and Zhuse,
V. P., Fiz. Tverd. Tela 3 (1963) 3285.
G. A. and Volger, J., Phys. Letters 8 (1964) 244. J., Phys. Rev. 130 (1963) 1711.
7) Yahia, J. and Frederikse, H. P. R., Phys. Rev. 123 (1961) 1257. 8) Yakovlev, V. A., Soviet Physics Solid State 3 (1962) 1442. 9) Feynman, R. P., Hellwarth, (1962) 1004.
R. W., Iddings,
C. K. and Platzman,
P. M., Phys. Rev. 127
Acket, G. A. Volger, J.
1964
LETTER TO THE EDITOR On electrical
conduction
in reduced rutile
A number of studies on electrical conduction in reduced rutile have been made 1) 3) 3) 4) 5) but still uncertainties concerning the interpretation of electron mobility and electron statistics have remained. Frederikse 3) deduced effective masses of 12-30 m, from Seebeck and Hall data on rather strongly reduced material. In a previous paper 3) the present authors reported Hall-measurements on slightly reduced material. The mobility perpendicular to the c-axis was found to be independent of the amount of reduction, but the behaviour of the Hall-coefficient did depend on it. Donor interaction was suggested, but it should be noted that the presence of compensating impurities (Al3+ 6), Fe3+) may not be negligible. In this note we report on the conductivity and Hall-effect ((jK, H//C) of reduced rutile crystals doped with about 100 p.p.m. AleO3. The boules were obtained from
Hall-coefficient of TiO3 samples doped with about 100 p.p.m. Al303 and of various degrees of reduction (j _L C; H // C). the National Lead Company. The mobility was found to equal that of undoped rutile. Hall-data are presented in fig. 1. It is seen that the transition from linear to bended
-
1667 -
G. A. ACKET
1668 curves
in the RH vs l/T plot
undoped
material
ent donor levels. levels
At low reduction
We also performed specimens
is now found
5). These phenomena
are exhausted having
J. VOLGER
at higher
only the deeper
measurements
levels remain
resistivities
between
filled
around
of undoped
300°K
5). In very high resis-
the slope differs from that found at lower resistivity
Compensation
is probably
Such behaviour
the transport
in this region.
Below
on temperature,
by about a factor 3.
250°K
may be found for polar scattering,
contribution
reduced lOssL,cm.
the slopes of the curves
tance material decreases.
as the shallow
10 Sz cm and 2 x
those of the Hall-coefficients
important
than in
impurities.
in fig. 2. In the region with
concentrations
by a model with two differ-
( I c-axis) of the thermopower
room temperature agreement
carrier
can be understood
by the compensating
The results are plotted are in reasonable
AND
the thermopower
due to a dependance
cf. also measurements
of Y ahia
of and
161412. lo-
8642-
%%-’
-
Fig. 2. Thermo-power of reduced temperature resistivities :
pure r-utile; temperature
‘o/ gradient
1 c-axis.
-
13Qcm.
+
1 x
103Qcm.
.c
2 x
105 Dem.
l
28 Qcm. 2 x 102 .Qcm.
0
5 x
10sQcm.
0
1 x
10sQcm.
0 Frederikse
on Tis03
ature transport to a density
7). Neglecting
contribution
the anisotropy
and assuming
to equal .$(/z/e),effective
of states of 1.2- 3 x
Room
the room temper-
masses of 3-5 m, corresponding
1Ozo cm-s were found, except for the 13 .Qcm sample.
These values are much lower than those previously reported 1) 2). We also investigated the dependance of the conductivity on the electric field strength on specimens discharged and voltages
having room temperature
across thin specimens
resistivities
up to 10 kV were used. The current
served by means of an X - Y oscilloscope. cm at room
temperature
of about 1OsQcm. A condenser
by means of a thyratron.
and about
3 x
Maximum 105 V/cm
Capacitances
- voltage
characteristics
were ob-
field strengths
were 3-4 x
at liquid
temperature
parallel and perpendicular to the c-axis. Chemical polishing to be essential in order to avoid alinearities at the contacts.
air
was
of 250 pF 105V/ both
in molten KOH appeared The observed characteris-
tics remained linear even up to the high field strengths mentioned. If indeed masses of about 30 m, would be present the mobility at 90’K would correspond to a relaxation time of about 3 x lo-13 sec. If this relaxation time is not reduced the energy
ON ELECTRICAL
supplied larger
to the electrons than
the band
CONDUCTION
between
width,
two
IN REDUCED
collisions
E, if conservatively
would
RUTILE
be at least
estimated
1669 0.1 eV which
to be 3 x
E G @/ma2 with a = 3 x 10-s cm. We feel that under these circumstances rent-field
characteristics
another
argument
It is doubtful1
would
that the actual whether
should than
Moreover,
be taken
z = O/T;
m g
4m,;
produced
0 = Debye
the angular
variational
parameters
temperature.
The formula 1 the c-axis mechanisms
yields
frequency reasonable
may become
Acknowledgements. assistance and were Zuiver
of the made
“Stichting
Wetenschappelijk
mass value
considered
lattice
in the ionic rather
lattice
as a polaron
for the mobility temperature
based
on a
(670K”)r).
*
es -. E
agreement 100°K
phonon
branch.
4.0 and 2.1 respectively
with the average and 300°K.
Below
For
U. = 5 the
g).
of the mobilities 100°K
other
// and
scattering
important. The
possible
being
a formula
of the longitudinal
between
be
5331014 set-l.
li
authors
are indebted
with the high field experiments.
programme
the electron
CC=&
v and w have the values
in the region
from our effective
much lower than the Debye
0 = w denotes
by
carrier
e.a.9) deduced
for temperatures
the curshould
as they are of the order of the reciprocal
the charge
Feynman
absence
lower and so the band much wider.
times following
meaning
into account,
8) and that their
mass is markedly
the polarization
as an electron.
model by Frijhlich
alinearities
the relaxation
still have their usual physical frequency.
show
is
10-z eV using
voor
to Mr. G. Ruitenberg
These investigations
Fundamenteel
by financial
support
Onderzoek”
(Z.W.O.).
Onderzoek
for his
are part of the research der Materie”
of the “Nederlandse
(F.O.M.)
Organisatie
voor
Received 5-5-64 G. A. ACKET and J. VOLGER Fysisch Laboratorium der Rijks-Universiteit Utrecht, Utrecht, Nederland REFERENCES
1) Breckenridge, R. G. and Hosler, W. R., Phys. Rev. 91 (1953) 793. 2) Frederikse, H. P. R., J. appl. Phys. Suppl. 32 (1961) 2211. 3) Becker, J. H. and Hosler, W. R., J. Phys. Sot. Jap. Suppl. 18 (1963) 152. 4) Bogomolov, 5) Acket, 6) Yahia,
V. N. and Zhuse,
V. P., Fiz. Tverd. Tela 3 (1963) 3285.
G. A. and Volger, J., Phys. Letters 8 (1964) 244. J., Phys. Rev. 130 (1963) 1711.
7) Yahia, J. and Frederikse, H. P. R., Phys. Rev. 123 (1961) 1257. 8) Yakovlev, V. A., Soviet Physics Solid State 3 (1962) 1442. 9) Feynman, R. P., Hellwarth, (1962) 1004.
R. W., Iddings,
C. K. and Platzman,
P. M., Phys. Rev. 127