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Electrical conductivity and seebeck voltage of Fe2O3, pure and doped, as a function of temperature and oxygen pressure
Solid State Ionics 12 (1984) 271-276 North-Holland, Amsterdam
ELECTRICAL CONDUCTIVITY AND SEEBECK VOLTAGE OF Fe20J, PURE AND DOPED, AS A FUNCTION OF TEMPERATURE AND OXYGEN PRESSURE B.M. WARNES,
F.F. APLAN
and G. SIMKOVICH
The Pennsylvania State University, University Park, PA 16802,
USA
The electrical conductivity and Seebeck voltage were measured on 99.9997% Fe,O, as a function of temperature and oxygen pressure, and on donor- and acceptor-doped samples as a function of temperature. The results indicate Fe,O, is an intrinsic semiconductor above 650” C, where the conductivity is described by u= 9191.2 exp (-1.11 eV/kT)(l/R cm) and it is oxygen-pressure independent. The Seebeck voltage shows Fe,O, is n-type below 800” C and p-type above this temperature. Conductivity measurements on doped samples were used to calculate the carrier mobilities and these are given by the expressions: p (electrons) =(1998/T) exp (-0.17 eV/ kT)(cm*/V s), P (holes) = (9298/T) exp (-0.29 eV/ kT)(cm’/V s). The electrons are the most mobile carrier below =800” C, but the hole is more mobile above 800” C, and this probably explains the conversion from n- to p-type behavior. The concentration of electrons is greater than that of the hole above 6.50” C, and the carrier concentration product is given by (np) = 1.34 x 104* exp (-0.78 eV/ kT). The appropriate defect equation for intrinsic Fe,Os is 0 = n +p and the formation expressions for the minor atomic defects are FezOs+ 2(Fe,tt+ ) + 2Nn + $Oo,, where N = 2 or 3 and Fe,O, + 2Fe;,+3V,+6n+$Oz.
La conductivite tlectrique et I’effet Seebeck ont it6 mesures, d’une part, pour Fe,O, pur (99,9997%) en fonction de la temperature et de la pression d’oxygine et d’autre part, pour Fe,O, dope avec des elements donneurs et accepteurs, en fonction de la temperature. Les resultats montrent que Fe,Os est un semiconducteur intrindque au-dell de 650” C; la conductivite Clectrique s’exprime par la relation (T = 9191,2 exp (-1.11 eV/RT)(l/ff cm) et est independante de la pression d’oxygene. L’effet Seebeck montre que Fe,O, est un semiconducteur de type n aux temperatures inferieures I 800” C et de type p au-d& de cette temperature. Les mesures de conductivitt Clectrique effectutes sur des Cchantillons dopes ont permis de determiner la mobilite des porteurs de charge: w (electrons) = (1998/T) exp (-0,17 eV/kT) (cm’V_’ s-r), CC(trous) = (9298/T) exp (-0,29 eV/kT) (cm’V_’ s-r). Les Electrons sont les porteurs les plus mobiles aux temperatures inferieures a 800” C, mais les trous electroniques sont plus mobiles au-deli de 800” C, ce qui explique probablement le passage d’un comportement de type n a p. La concentration en electrons est plus 6levte que celle des trous au deli de 650” C, et le produit des concentrations en porteurs est don&e par la relation (np) = 1.34X 104* exp (-0,78 eV/kT), avec pour F,O, intrinsbque: 0 = n + p et pour les defauts atomiques minoritaires: Fe,O,-+2Fe~++Nn+~O,, ou N=2 ou 3, et Fe,O,+2Fe;,+3V,+6n+iO,.
1. Introduction During the last fifty years, the defect structure of a-Fe203 has been the subject of numerous studies. In most cases, dc conductivity and Seebeck-voltage measurements were the experimental techniques employed. However, as Gardner et al. [l] have shown, both these measurements are sensitive to trace metal impurities. The Fe203 used by previous investigators was of rather low purity, 98% for Morin [2] to
99.99% for Gardner et al. [3], and consequently, the correspondence between data from different experimenters is poor, as figs. l-4 show. Also, no one group of researchers has performed enough work to determine all the quantities necessary for a complete analysis of the point defects. Hence, in their analysis use of published information of others was necessary in spite of sample differences. This fact probably explains some of the variable results found in the literature. There are however three important qualita-
B. M. Warnes et al. / Electrical conductivity and Seebeck voltage of FezO_?
Mow
Morin
3:
(smlered
In oxygen)
(sincered in 2% oxm)
Gordner,Moss8Tonner
-
Gardner, Moss 8 Tonner
.-*-.
Getger 8 Wagner
--
Fe203
Moth i zuki
2,
Gardner,Swed 8Tonner
1. 0. -I -2. -3. -4,
\
\
-5, 1 -61..--.--0
.......?................ 2
103/T Fig. 1. Published
electrical
3
(I/ K) condnctivity
4
-.-
3
_____Fe203 Geiger 8 Wagner
data of a-FeZ03.
Mom
Fig. 3. Published doped FeZOz.
electrical
conductivity
data of acceptor-
Morin Ehtered
m Oxygen)
2
I
2 ..-> t
0
-I
z 6 0
-2
J
-3
‘\
-4 -6.
-6
103/T Fig. 2. Published Fe,03.
electrical
3
2
I
conductivity
(I/
K)
data of donor-doped
Temperature Fig. 4. Published
Seebeck-voltage
(“Cl data for Fez03.
B.M. Warnes et al. / Electrical conductivity and Seebeck voltage of Fe,O,
tive results from previous studies. First, Tanner et al. [4] have shown that the electrical properties of single and polycrystalline samples correspond well. Hence, grain boundaries have no significant effect on either the activation energy of formation or the mobility of the charge carriers. Also, Chang and Wagner [5] have shown that Fe203 contains iron interstitials, and Gardner et al. [3] have demonstrated the presence of oxygen vacancies as minor defects. Hence, both of these minor atomic defects are present in “pure” Fe203. Finally, Wagner and Koch [6] have shown that the conductivity of Fez03 is independent of oxygen pressure above 1273 K (1000” C); therefore Fe203 is probably an intrinsic semiconductor at high temperature. In this study, the conductivity and Seebeck voltage of 99.9997% Fe203 (metal basis) was measured as a function of temperature and oxygen pressure. Also, the conductivity of five TiOz- and five MgO-doped samples were measured as a function of temperature. Work similar to this study has been done previously, but in this case, higher-purity oxide has been utilized and a sufficient breadth of work has been done to permit quantitative analysis of the majority point defects.
2. Experimental A four-point-probe dc conductivity cell with exchangeable standard resistors in series with the cell was utilized to obtain the electrical conductivity of the samples. Under a constant applied voltage (400 mV), the voltage drop across the inner two leads was measured and then compared to the voltage drop across a standard resistor of similar magnitude. Since the current flow through the unknown and known resistance was equal, the unknown sample resistance could be calculated. With knowledge of the probe separation and the sample cross-sectional area, the conductivity, g, was easily calculated. All electrical contacts on the sample were made of platinum. For Seebeck-voltage measurements, a Pt-Pt + 10% Rh thermocouple was attached to the platinum foil at either end of the sample. Following conductivity measurements, the sample was pushed slightly out of the hot zone of the furnace until a difference in temperature (as measured by the thermocouples at
273
each end of the sample) of between 2 and 10” C was established. The platinum wires of the thermocouples were then used to obtain the potential difference. The sign of the charge of the colder end of the sample was taken as that of the measured potential, and also the sign of the majority conductivity species. The potential was then divided by the temperature difference, and it was designated as the Seebeck voltage, (Y. Most of the experiments were done in air, PO, = 2.13 x lo4 Pa; hence, no gas cleaning and metering equipment was required. At other oxygen pressures around 2.13 x lo4 Pa, oxygen-helium mixtures were used. The oxygen was dried, and the following impurities were removed from the helium: CO, C02, H20, hydrocarbons and oxygen. Experiments at the Fe203-Fe304 equilibrium oxygen pressure involved nitrogen as the carrier gas. Because the atomic weights of nitrogen and oxygen are similar thermal segregation of the gas components was minimized at the low flow rates (~1 cm3/min) used in these experiments. The nitrogen had the same impurities removed as the helium, and, after cleaning, the required oxygen pressure was established by passing it over a mixture of hematite and magnetite maintained at the same temperature as the sample. It is noted that extreme care was taken that sufficient time was given at each temperature for the sample to attain equilibrium with the gas mixture. This involved, at temperatures below 773 K, three to six days until a constant conductivity was obtained. Samples of +Fe203, pure and doped with either TiOz or MgO, were prepared by cold pressing rectangular pellets (0.4 cm X 0.4 cm X 1 cm) and sintering them at 1473 K for two days. The samples were placed on about one half a centimeter of powder material of the same composition as the sample itself during sintering to avoid contamination. The pellets were heated slowly (=60 K/hr) to 1473 K, and also cooled at the same rate. After completion of the experimental work, all the samples were analyzed by emission spectroscopy for the amounts of trace impurities, and by atomic absorption for the dopant concentrations. The analysis indicated that the “pure” oxide contained =3 ppm by weight of uncompensated acceptor impurities, and the measured dopant concentrations are given with the conductivity data.
274
B.M.
0,
conductivity
and Seebeck voltage
of FetO,
-1
\
l
$ -2
Warnes et al. / Electrical
Atm.
h=ID
;aGyBAtm
3
“Q
.
Fe203 - Fe304 Equdibrium &
Q
Po2=Q21 Atm.
Samples 1,283
\\ \
5
IQ’? 8
cj
7
5
? ‘Q
-6
3
oc/loo 0.65
125
ml
103/T Fig. 5. Electrical conductivity function of temperature.
1.45
(I/
-7
1.65 Fe,O,
Fez03*0.043%Ti4\ Fe203+0.07XT102
.
Fe203+0.16%Ti02
x
\ ’ \ \
\
\
o Fe203+0.37XT~02
\
\
\
o Fe203+0.76%Ti02
K)
of high-purity
4
.
-8.. 0.8
as a
1.0
1.2
1.4
103/T Fig. 6. Electrical conductivity function of temperature.
.
1.6
.
1.8
.
.
2.0
(I/ K)
of donor-doped
Fe,O,
as a
3. Results and discussion Fig. 5 depicts the conductivity results obtained on pure a-Fez03 in this study as a function of temperature and oxygen pressure. The oxygen-pressureindependent segment above 923 K indicates intrinsic semiconduction, and a least-squares fit of the data gives ~~=9191.2(Rcm)-’ and Q=l.ll eV in the relation a=u,exp(-Q/kT).
(1)
At temperatures below 923 K, conduction is extrinsic and so it is unimportant in this study of the intrinsic point defects. An attempt to analyze conductivity below 923 K is presently underway. The pressure independence of the conductivity suggests that the transport numbers of the electronic charge carriers is much greater than that of the atomic point defects. In order to obtain the carrier mobilities [p(cm*/V s)] in Fe203 the electrical conductivities of donor- and acceptor-doped samples were measured. Fig. 6 depicts the results for the Ti02-doped samples,
and fig. 7 gives those for the MgO-doped ing the relation a=e(W”+PILp)
ones. Utiliz-
(2)
where e is the electronic charge, n and p are the concentrations of electrons and holes respectively, and p is the mobility, for the conductivity permits calculation of the mobility since, under dopant conditions, the concentration of carriers created by the dopant additions is so large that one may ignore the concentrations of all other carrier species. The electron and hole mobilities were calculated at several temperatures, and the results were fitted to the relation suggested by Jonker and van Houten [7] for the mobility of a hopping polaron ,=(a*ev/kT)exp(-Q/kT), where a is the jump distance, u is the jump frequency, k is Boltzmann’s constant, T is the absolute temperature and Q is the activation energy
(3)
B. M. Warnes et al. / Electrical conductivity 2
109 ....--
8
7
4
6.5..
*I
oc/loo
.
Fa203 + 0.009%
o
Fe203 +0.092#
MgO
MgO
Fig. 8. Electron of temperature.
\ \ \
103/T (I/ K) Fig. 7. Electrical conductivity function of temperature.
275
and Seebeck voltage of Fe203
of acceptor-doped
Fe,O,
as a
of motion. The resulting expressions for the carrier mobilities are (3a)
p,,= (9298/ T) exp (-0.2 eV/kT).
(3b)
Fig. 8 depicts the calculated values. One important result of this study that has not been reported previously is that the electron is the most mobile carrier below -800” C, and the hole is mobile above that temperature. It should be noted, however, that the difference between the two is not large at any temperature above 923 K, so both carriers contribute to intrinsic conduction. If the pre-exponential terms of the theoretical and derived expressions are equated, it is possible to calculate the polaron jump frequencies. Assuming a is the distance between the centers of two octahedral sites, the calculated frequencies are Y, = 3.7 X lO”/s and vP = 1.8 X 1014/s. These values are similar to the frequency of the thermal atomic vibrations above
in Fe,O,
as a function
923 K indicating that these vibrations may assist the hopping of the charge carriers. The Seebeck voltage of pure a-Fe203 was also measured as a function of temperature and oxygen pressure, and the results are shown in fig. 9. The data indicates ferric oxide is an n-type semiconductor
I
-
/1,=(1998/T)exp(-O.l7eV/kT),
and hole mobilities
:: f m
-o. 5
l
Pop= 1.0
0 PO@2 l
otm.
Iotm.
Pop=0.050tm.
Sample 3 Fe20jFe& ’ -1.0
-
400
600
Equlibrum
voltage
of high-purity
1000
800
Temperature Fig. 9. Seebeck temperature.
Pop
Fe,O,
PC) as a function
of
B.M. Warnes et al. / Electrical conductivity
276
below 1073 K, but that it becomes a p-type conductor above that temperature. This transition is probably the result of the hole being the most mobile carrier at high temperatures. The Seebeck voltage is also independent of oxygen pressure above 923 K, and this fact lends support to the contention that a-Fe,O, is an intrinsic semiconductor above 923 K. Kroger [8] has suggested an expression for the Seebeck voltage of a semiconductor with two types of charge carriers. This is given as: a =-(k/e)(l/bn+p) x[2(bn-p)+bnln(A/n)-pln(A/p)],
(4)
where b = n/p, and A equals twice the metal-ion concentration in Fe203, as suggested by Bosman and van Daal [9] for the hopping of small polarons. Solving eqs. (2) and (4) simultaneously, using eqs. (3a) and (3b) and the jacobian matrix gives the intrinsic carrier concentrations shown in fig. 10. The concentration of electrons is greater than that of the holes at all temperatures above 923 K, and this supports Gardner et al. [3] and Chang and Wagner’s [5] conclusions that FefOj contains oxygen vacancies and iron interstitials. However, as the pressure independence of the conductivity indicated, the concentration of these atomic defects is much less than that of either electronic carrier. The intrinsic carrier-concentration product, (np), was calculated at several temperatures, and these
and Seebeck voltage of FezO,
values were fitted to an Arrhenius expression. The resulting equation for the temperature dependence of (np) is (np) = 1.34X 104* exp (-0.78 eV/kT).
(5)
4. Conclusions The measured and calculated quantities indicate there are four important point defects in a-Fe203 above 923 K, the two electronic carriers and the two minor atomic imperfections. So, the appropriate defect equation for intrinsic ferric oxide is O=n+p.
(6)
The formation expressions for the minor defects are: Fe20,+
2(FeET)+2Nn+$O,
(7)
and Fe20,+2Fe,“,+3V,+6n+s0,.
(8)
The conductivity and Seebeck voltage of the pure ferric oxide show that it is an intrinsic semiconductor above 923 K, with both electrons and holes contributing to conduction. Acknowledgement The financial support of the National Science Foundation, Engineering Division, Solid and Particulate Processing Program under Dr T. Mukherjee is gratefully acknowledged.
References [I] R. Gardner, [2] [3] [4] [5] [6]
10’9
[7] L
,
0.8
0.9
1.0 I.1 103/T (I/ K)
Fig. 10. Electron and hole concentrations function of temperature.
in pure Fe,O,
[8] as a
[9]
F. Sweet and D. Tanner, J. Phys. Chem. Solids 24 (1963) 1175. F. Morin, Phys. Rev. 83 (1951) 1005. R. Gardner, F. Sweet and D. Tanner, J. Phys. Chem. Solids 24 (1963) 1183. D. Tanner, F. Sweet and R. Gardner, Brit. J. Appl. Phys. 15 (1964) 1040. R. Chang and J.B. Wagner, J. Am. Chem. Sot. 55 (1972) 211. C. Wagner and E. Koch, Z. Physik. Chem. B32 (1936) 439. G.H. Jonker and S. van Houten, Halbleiter Probleme 6 (1961) 118. F. KrBger, The chemistry of imperfect crystals (Wiley, New York, 1964). A. Bosman and H. van Daal, Advan. Phys. 19 (1970) 1.
ELECTRICAL CONDUCTIVITY AND SEEBECK VOLTAGE OF Fe20J, PURE AND DOPED, AS A FUNCTION OF TEMPERATURE AND OXYGEN PRESSURE B.M. WARNES,
F.F. APLAN
and G. SIMKOVICH
The Pennsylvania State University, University Park, PA 16802,
USA
The electrical conductivity and Seebeck voltage were measured on 99.9997% Fe,O, as a function of temperature and oxygen pressure, and on donor- and acceptor-doped samples as a function of temperature. The results indicate Fe,O, is an intrinsic semiconductor above 650” C, where the conductivity is described by u= 9191.2 exp (-1.11 eV/kT)(l/R cm) and it is oxygen-pressure independent. The Seebeck voltage shows Fe,O, is n-type below 800” C and p-type above this temperature. Conductivity measurements on doped samples were used to calculate the carrier mobilities and these are given by the expressions: p (electrons) =(1998/T) exp (-0.17 eV/ kT)(cm*/V s), P (holes) = (9298/T) exp (-0.29 eV/ kT)(cm’/V s). The electrons are the most mobile carrier below =800” C, but the hole is more mobile above 800” C, and this probably explains the conversion from n- to p-type behavior. The concentration of electrons is greater than that of the hole above 6.50” C, and the carrier concentration product is given by (np) = 1.34 x 104* exp (-0.78 eV/ kT). The appropriate defect equation for intrinsic Fe,Os is 0 = n +p and the formation expressions for the minor atomic defects are FezOs+ 2(Fe,tt+ ) + 2Nn + $Oo,, where N = 2 or 3 and Fe,O, + 2Fe;,+3V,+6n+$Oz.
La conductivite tlectrique et I’effet Seebeck ont it6 mesures, d’une part, pour Fe,O, pur (99,9997%) en fonction de la temperature et de la pression d’oxygine et d’autre part, pour Fe,O, dope avec des elements donneurs et accepteurs, en fonction de la temperature. Les resultats montrent que Fe,Os est un semiconducteur intrindque au-dell de 650” C; la conductivite Clectrique s’exprime par la relation (T = 9191,2 exp (-1.11 eV/RT)(l/ff cm) et est independante de la pression d’oxygene. L’effet Seebeck montre que Fe,O, est un semiconducteur de type n aux temperatures inferieures I 800” C et de type p au-d& de cette temperature. Les mesures de conductivitt Clectrique effectutes sur des Cchantillons dopes ont permis de determiner la mobilite des porteurs de charge: w (electrons) = (1998/T) exp (-0,17 eV/kT) (cm’V_’ s-r), CC(trous) = (9298/T) exp (-0,29 eV/kT) (cm’V_’ s-r). Les Electrons sont les porteurs les plus mobiles aux temperatures inferieures a 800” C, mais les trous electroniques sont plus mobiles au-deli de 800” C, ce qui explique probablement le passage d’un comportement de type n a p. La concentration en electrons est plus 6levte que celle des trous au deli de 650” C, et le produit des concentrations en porteurs est don&e par la relation (np) = 1.34X 104* exp (-0,78 eV/kT), avec pour F,O, intrinsbque: 0 = n + p et pour les defauts atomiques minoritaires: Fe,O,-+2Fe~++Nn+~O,, ou N=2 ou 3, et Fe,O,+2Fe;,+3V,+6n+iO,.
1. Introduction During the last fifty years, the defect structure of a-Fe203 has been the subject of numerous studies. In most cases, dc conductivity and Seebeck-voltage measurements were the experimental techniques employed. However, as Gardner et al. [l] have shown, both these measurements are sensitive to trace metal impurities. The Fe203 used by previous investigators was of rather low purity, 98% for Morin [2] to
99.99% for Gardner et al. [3], and consequently, the correspondence between data from different experimenters is poor, as figs. l-4 show. Also, no one group of researchers has performed enough work to determine all the quantities necessary for a complete analysis of the point defects. Hence, in their analysis use of published information of others was necessary in spite of sample differences. This fact probably explains some of the variable results found in the literature. There are however three important qualita-
B. M. Warnes et al. / Electrical conductivity and Seebeck voltage of FezO_?
Mow
Morin
3:
(smlered
In oxygen)
(sincered in 2% oxm)
Gordner,Moss8Tonner
-
Gardner, Moss 8 Tonner
.-*-.
Getger 8 Wagner
--
Fe203
Moth i zuki
2,
Gardner,Swed 8Tonner
1. 0. -I -2. -3. -4,
\
\
-5, 1 -61..--.--0
.......?................ 2
103/T Fig. 1. Published
electrical
3
(I/ K) condnctivity
4
-.-
3
_____Fe203 Geiger 8 Wagner
data of a-FeZ03.
Mom
Fig. 3. Published doped FeZOz.
electrical
conductivity
data of acceptor-
Morin Ehtered
m Oxygen)
2
I
2 ..-> t
0
-I
z 6 0
-2
J
-3
‘\
-4 -6.
-6
103/T Fig. 2. Published Fe,03.
electrical
3
2
I
conductivity
(I/
K)
data of donor-doped
Temperature Fig. 4. Published
Seebeck-voltage
(“Cl data for Fez03.
B.M. Warnes et al. / Electrical conductivity and Seebeck voltage of Fe,O,
tive results from previous studies. First, Tanner et al. [4] have shown that the electrical properties of single and polycrystalline samples correspond well. Hence, grain boundaries have no significant effect on either the activation energy of formation or the mobility of the charge carriers. Also, Chang and Wagner [5] have shown that Fe203 contains iron interstitials, and Gardner et al. [3] have demonstrated the presence of oxygen vacancies as minor defects. Hence, both of these minor atomic defects are present in “pure” Fe203. Finally, Wagner and Koch [6] have shown that the conductivity of Fez03 is independent of oxygen pressure above 1273 K (1000” C); therefore Fe203 is probably an intrinsic semiconductor at high temperature. In this study, the conductivity and Seebeck voltage of 99.9997% Fe203 (metal basis) was measured as a function of temperature and oxygen pressure. Also, the conductivity of five TiOz- and five MgO-doped samples were measured as a function of temperature. Work similar to this study has been done previously, but in this case, higher-purity oxide has been utilized and a sufficient breadth of work has been done to permit quantitative analysis of the majority point defects.
2. Experimental A four-point-probe dc conductivity cell with exchangeable standard resistors in series with the cell was utilized to obtain the electrical conductivity of the samples. Under a constant applied voltage (400 mV), the voltage drop across the inner two leads was measured and then compared to the voltage drop across a standard resistor of similar magnitude. Since the current flow through the unknown and known resistance was equal, the unknown sample resistance could be calculated. With knowledge of the probe separation and the sample cross-sectional area, the conductivity, g, was easily calculated. All electrical contacts on the sample were made of platinum. For Seebeck-voltage measurements, a Pt-Pt + 10% Rh thermocouple was attached to the platinum foil at either end of the sample. Following conductivity measurements, the sample was pushed slightly out of the hot zone of the furnace until a difference in temperature (as measured by the thermocouples at
273
each end of the sample) of between 2 and 10” C was established. The platinum wires of the thermocouples were then used to obtain the potential difference. The sign of the charge of the colder end of the sample was taken as that of the measured potential, and also the sign of the majority conductivity species. The potential was then divided by the temperature difference, and it was designated as the Seebeck voltage, (Y. Most of the experiments were done in air, PO, = 2.13 x lo4 Pa; hence, no gas cleaning and metering equipment was required. At other oxygen pressures around 2.13 x lo4 Pa, oxygen-helium mixtures were used. The oxygen was dried, and the following impurities were removed from the helium: CO, C02, H20, hydrocarbons and oxygen. Experiments at the Fe203-Fe304 equilibrium oxygen pressure involved nitrogen as the carrier gas. Because the atomic weights of nitrogen and oxygen are similar thermal segregation of the gas components was minimized at the low flow rates (~1 cm3/min) used in these experiments. The nitrogen had the same impurities removed as the helium, and, after cleaning, the required oxygen pressure was established by passing it over a mixture of hematite and magnetite maintained at the same temperature as the sample. It is noted that extreme care was taken that sufficient time was given at each temperature for the sample to attain equilibrium with the gas mixture. This involved, at temperatures below 773 K, three to six days until a constant conductivity was obtained. Samples of +Fe203, pure and doped with either TiOz or MgO, were prepared by cold pressing rectangular pellets (0.4 cm X 0.4 cm X 1 cm) and sintering them at 1473 K for two days. The samples were placed on about one half a centimeter of powder material of the same composition as the sample itself during sintering to avoid contamination. The pellets were heated slowly (=60 K/hr) to 1473 K, and also cooled at the same rate. After completion of the experimental work, all the samples were analyzed by emission spectroscopy for the amounts of trace impurities, and by atomic absorption for the dopant concentrations. The analysis indicated that the “pure” oxide contained =3 ppm by weight of uncompensated acceptor impurities, and the measured dopant concentrations are given with the conductivity data.
274
B.M.
0,
conductivity
and Seebeck voltage
of FetO,
-1
\
l
$ -2
Warnes et al. / Electrical
Atm.
h=ID
;aGyBAtm
3
“Q
.
Fe203 - Fe304 Equdibrium &
Q
Po2=Q21 Atm.
Samples 1,283
\\ \
5
IQ’? 8
cj
7
5
? ‘Q
-6
3
oc/loo 0.65
125
ml
103/T Fig. 5. Electrical conductivity function of temperature.
1.45
(I/
-7
1.65 Fe,O,
Fez03*0.043%Ti4\ Fe203+0.07XT102
.
Fe203+0.16%Ti02
x
\ ’ \ \
\
\
o Fe203+0.37XT~02
\
\
\
o Fe203+0.76%Ti02
K)
of high-purity
4
.
-8.. 0.8
as a
1.0
1.2
1.4
103/T Fig. 6. Electrical conductivity function of temperature.
.
1.6
.
1.8
.
.
2.0
(I/ K)
of donor-doped
Fe,O,
as a
3. Results and discussion Fig. 5 depicts the conductivity results obtained on pure a-Fez03 in this study as a function of temperature and oxygen pressure. The oxygen-pressureindependent segment above 923 K indicates intrinsic semiconduction, and a least-squares fit of the data gives ~~=9191.2(Rcm)-’ and Q=l.ll eV in the relation a=u,exp(-Q/kT).
(1)
At temperatures below 923 K, conduction is extrinsic and so it is unimportant in this study of the intrinsic point defects. An attempt to analyze conductivity below 923 K is presently underway. The pressure independence of the conductivity suggests that the transport numbers of the electronic charge carriers is much greater than that of the atomic point defects. In order to obtain the carrier mobilities [p(cm*/V s)] in Fe203 the electrical conductivities of donor- and acceptor-doped samples were measured. Fig. 6 depicts the results for the Ti02-doped samples,
and fig. 7 gives those for the MgO-doped ing the relation a=e(W”+PILp)
ones. Utiliz-
(2)
where e is the electronic charge, n and p are the concentrations of electrons and holes respectively, and p is the mobility, for the conductivity permits calculation of the mobility since, under dopant conditions, the concentration of carriers created by the dopant additions is so large that one may ignore the concentrations of all other carrier species. The electron and hole mobilities were calculated at several temperatures, and the results were fitted to the relation suggested by Jonker and van Houten [7] for the mobility of a hopping polaron ,=(a*ev/kT)exp(-Q/kT), where a is the jump distance, u is the jump frequency, k is Boltzmann’s constant, T is the absolute temperature and Q is the activation energy
(3)
B. M. Warnes et al. / Electrical conductivity 2
109 ....--
8
7
4
6.5..
*I
oc/loo
.
Fa203 + 0.009%
o
Fe203 +0.092#
MgO
MgO
Fig. 8. Electron of temperature.
\ \ \
103/T (I/ K) Fig. 7. Electrical conductivity function of temperature.
275
and Seebeck voltage of Fe203
of acceptor-doped
Fe,O,
as a
of motion. The resulting expressions for the carrier mobilities are (3a)
p,,= (9298/ T) exp (-0.2 eV/kT).
(3b)
Fig. 8 depicts the calculated values. One important result of this study that has not been reported previously is that the electron is the most mobile carrier below -800” C, and the hole is mobile above that temperature. It should be noted, however, that the difference between the two is not large at any temperature above 923 K, so both carriers contribute to intrinsic conduction. If the pre-exponential terms of the theoretical and derived expressions are equated, it is possible to calculate the polaron jump frequencies. Assuming a is the distance between the centers of two octahedral sites, the calculated frequencies are Y, = 3.7 X lO”/s and vP = 1.8 X 1014/s. These values are similar to the frequency of the thermal atomic vibrations above
in Fe,O,
as a function
923 K indicating that these vibrations may assist the hopping of the charge carriers. The Seebeck voltage of pure a-Fe203 was also measured as a function of temperature and oxygen pressure, and the results are shown in fig. 9. The data indicates ferric oxide is an n-type semiconductor
I
-
/1,=(1998/T)exp(-O.l7eV/kT),
and hole mobilities
:: f m
-o. 5
l
Pop= 1.0
0 PO@2 l
otm.
Iotm.
Pop=0.050tm.
Sample 3 Fe20jFe& ’ -1.0
-
400
600
Equlibrum
voltage
of high-purity
1000
800
Temperature Fig. 9. Seebeck temperature.
Pop
Fe,O,
PC) as a function
of
B.M. Warnes et al. / Electrical conductivity
276
below 1073 K, but that it becomes a p-type conductor above that temperature. This transition is probably the result of the hole being the most mobile carrier at high temperatures. The Seebeck voltage is also independent of oxygen pressure above 923 K, and this fact lends support to the contention that a-Fe,O, is an intrinsic semiconductor above 923 K. Kroger [8] has suggested an expression for the Seebeck voltage of a semiconductor with two types of charge carriers. This is given as: a =-(k/e)(l/bn+p) x[2(bn-p)+bnln(A/n)-pln(A/p)],
(4)
where b = n/p, and A equals twice the metal-ion concentration in Fe203, as suggested by Bosman and van Daal [9] for the hopping of small polarons. Solving eqs. (2) and (4) simultaneously, using eqs. (3a) and (3b) and the jacobian matrix gives the intrinsic carrier concentrations shown in fig. 10. The concentration of electrons is greater than that of the holes at all temperatures above 923 K, and this supports Gardner et al. [3] and Chang and Wagner’s [5] conclusions that FefOj contains oxygen vacancies and iron interstitials. However, as the pressure independence of the conductivity indicated, the concentration of these atomic defects is much less than that of either electronic carrier. The intrinsic carrier-concentration product, (np), was calculated at several temperatures, and these
and Seebeck voltage of FezO,
values were fitted to an Arrhenius expression. The resulting equation for the temperature dependence of (np) is (np) = 1.34X 104* exp (-0.78 eV/kT).
(5)
4. Conclusions The measured and calculated quantities indicate there are four important point defects in a-Fe203 above 923 K, the two electronic carriers and the two minor atomic imperfections. So, the appropriate defect equation for intrinsic ferric oxide is O=n+p.
(6)
The formation expressions for the minor defects are: Fe20,+
2(FeET)+2Nn+$O,
(7)
and Fe20,+2Fe,“,+3V,+6n+s0,.
(8)
The conductivity and Seebeck voltage of the pure ferric oxide show that it is an intrinsic semiconductor above 923 K, with both electrons and holes contributing to conduction. Acknowledgement The financial support of the National Science Foundation, Engineering Division, Solid and Particulate Processing Program under Dr T. Mukherjee is gratefully acknowledged.
References [I] R. Gardner, [2] [3] [4] [5] [6]
10’9
[7] L
,
0.8
0.9
1.0 I.1 103/T (I/ K)
Fig. 10. Electron and hole concentrations function of temperature.
in pure Fe,O,
[8] as a
[9]
F. Sweet and D. Tanner, J. Phys. Chem. Solids 24 (1963) 1175. F. Morin, Phys. Rev. 83 (1951) 1005. R. Gardner, F. Sweet and D. Tanner, J. Phys. Chem. Solids 24 (1963) 1183. D. Tanner, F. Sweet and R. Gardner, Brit. J. Appl. Phys. 15 (1964) 1040. R. Chang and J.B. Wagner, J. Am. Chem. Sot. 55 (1972) 211. C. Wagner and E. Koch, Z. Physik. Chem. B32 (1936) 439. G.H. Jonker and S. van Houten, Halbleiter Probleme 6 (1961) 118. F. KrBger, The chemistry of imperfect crystals (Wiley, New York, 1964). A. Bosman and H. van Daal, Advan. Phys. 19 (1970) 1.