J. Phys. Chem. C 2008, 112, 611-617
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Electrical Properties of Niobium-Doped Titanium Dioxide. 3. Thermoelectric Power L. R. Sheppard, T. Bak, and J. Nowotny* Centre for Materials Research in Energy ConVersion, School of Materials Science and Engineering, UniVersity of New South Wales, Sydney, NSW 2052, Australia ReceiVed: April 19, 2007; In Final Form: October 4, 2007
The present work studied semiconducting properties for polycrystalline specimens of Nb-doped TiO2 (0.65 atom % Nb) by the measurements of thermoelectric power in the temperature range of 1073-1298 K and in the oxygen activity range of 10-13 Pa < p(O2) < 75 kPa. The determined thermoelectric power data allow one to make the following points: (1) The charge transport in Nb-doped TiO2 is closely related to oxygen activity; (2) in reduced conditions, Nb-doped TiO2 exhibits metallic-type properties, which are related to electronic charge compensation; (3) in oxidized conditions, Nb-doped TiO2 exhibits semiconducting properties, which are related to ionic charge compensation; and (4) the thermoelectric power data are consistent with the proposed effect of niobium on the defect disorder model of TiO2.
1. Introduction Properties of TiO2 may be modified by changes of its nonstoichiometry, through the imposition of variable oxygen activity, p(O2), or by the incorporation of aliovalent ions. Both procedures have been used in the processing of TiO2 with the enhanced photosensitivity that is required for photoelectrochemical water splitting and alternative applications.1,2 Extensive studies have been recently reported on the effect of oxygen activity on electrical properties of undoped TiO2,3-28 including electrical conductivity and thermoelectric power. These studies have shown that the thermoelectric power data are very consistent with the electrical conductivity data determined simultaneously at elevated temperatures. The consistency concerns the defect disorder of reduced TiO2. The studies of the effect of Nb incorporation into the TiO2 lattice on electrical conductivity29 and chemical diffusion30 have shown that Nb doping not only results in qualitative changes of these properties but also allows one to obtain quantitative data. The determined electrical conductivity data have led to the discovery of metallictype charge transport for reduced Nb-doped TiO2.29 It was shown that the chemical diffusion coefficient in the metallictype regime exhibits a negative temperature coefficient.30 These data were considered in terms of the effect of niobium on the defect disorder of TiO2.29,30 Measurements of the electrical properties, such as electrical conductivity, are used most commonly to verify the defect disorder of nonstoichiometric compounds, such as TiO2.31-33 However, interpretation of the electrical conductivity data is problematic because this property, which includes both concentration and mobility terms, has a complex physical meaning. Therefore, in order to establish the relationship between the defect concentrations and the electrical conductivity, it must be assumed that the mobilities are independent of the oxygen activity, p(O2). It is important to note that another electrical property, which may be correlated directly with the concentration of charge carriers, is the thermoelectric power. Therefore, simultaneous * To whom correspondence should be addressed. E-mail: J.Nowotny@ unsw.edu.au. Tel: 612-9385.6465. Fax: 612-9385.6467.
measurements of both thermoelectric power and electrical conductivity are especially useful in assessing the defect disorder and the associated properties.33 When these are measured simultaneously in equilibrium, the relationship between them may be determined quantitatively even if the p(O2) is not well defined or unknown.34 The objectives of the present work is the determination of thermoelectric power for the same Nb-doped TiO2 specimen that was studied before29,30 and assessment of the electrical properties, including electrical conductivity and thermoelectric power, in terms of the effect of niobium on the defect disorder and the associated electrical properties. 2. Definition of Terms 2.1. Thermoelectric Power. The thermoelectric power, also termed the Seebeck coefficient or thermopower, is an electrical property that may be used to characterize semiconducting properties of materials. The thermoelectric power may be used to assess the concentrations of electronic charge carriers, which are important quantities for semiconductors. Since the electrical conductivity is the product of the concentration and mobility terms, combination of the electrical conductivity and thermoelectric power data can be used to determine the mobility terms.33 These data may be used to derive defect chemistry models and to evaluate the transport of charge and matter at elevated temperatures. The principles of the determination of thermoelectric power are given elsewhere.33,35 The imposition of a temperature gradient (∆T) across a specimen results in the generation of a potential difference (∆Ψ), which is termed the Seebeck voltage or thermovoltage. Knowledge of both ∆Ψ and ∆T are required to determine the thermoelectric power (S)33
S ) lim
∆Tf0
∆Ψ dΨ ) ∆T dT
(1)
Thermoelectric power can be related to the concentration of electronic charge carriers according to the following expressions for n- and p-type regimes, respectively33
10.1021/jp0730491 CCC: $40.75 © 2008 American Chemical Society Published on Web 12/13/2007
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( (
) )
k Nn Sn ) - ln + An e n Sp )
k Np ln + Ap e p
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(2) (3)
where e is elemenary charge, k is Boltzmann constant, Nn and Np denote the density of states for electrons and electron holes, respectively, n and p denote their respective concentrations, and An and Ap are the kinetic constants associated with scattering of electrons and electron holes, respectively. The most common way to verify the defect disorder models of metal oxides is based on the dependence of S on p(O2)
∂S 1 k ) mS e ∂ log p(O2)
(4)
where mS is a parameter related to the specific defect disorder and the subscript S refers to the case when the parameter is obtained using thermoelectric power data. The equivalent equation using electrical conductivity data to derive 1/mσ allows the assessment of the effect of oxygen activity on the electrical conductivity27
∂ log σ 1 ) mσ ∂ log p(O2)
(5)
Both sets of data may be used for confirmation of the effect of oxygen activity on the concentration of electronic charge carriers (when the mobility term remains independent of oxygen nonstoichiometry). It is well-known that the thermoelectric power achieves a critical value at the n-p transition, namely, S ) 0. Figure 1 shows a schematic representation of the effect of the p(O2) on both the electrical conductivity (σ) and the thermoelectric power (S) for an amphoteric oxide semiconductor, which exhibits both n- and p-type regimes. It can be seen that the slope of the logarithm of electrical conductivity versus the log p(O2) dependence in the n- and p-type regimes adopts negative and positive values, respectively, and that the electrical conductivity at the n-p transition point reaches a minimum. Therefore
σn ) σp
(6)
It also can be seen in Figure 1 that the thermoelectric power versus the log p(O2) dependencies in the n- and p-type regimes are linear. In these two regimes, the formalism is to present the slopes 1/mS as positive values. The parameter 1/mS is well defined when thermoelectric power corresponds to pure the n- or p-type regime. Then, the thermoelectric power data reflect the effects of the majority charge carriers, and the effects of the minority charge carriers are negligible. However, in the n-p transition regime, where two charge carriers are present, the meaning of 1/mS is more complex. When the mobility terms for both electrons and electron holes are the same, then the condition described by eq 6 corresponds to a thermoelectric power of zero. This effect has been examined extensively for undoped BaTiO3.36,37 2.2. Defect Disorder. The present work determines the effect of the p(O2) on the thermoelectric power for Nb-doped TiO2, and this relationship is assessed in terms of the defect disorder models and the related semiconducting properties. These data will then be compared to the data of the electrical conductivity determined for the same specimen.29
Figure 1. Schematic representation of the effect of oxygen activity, p(O2), on both electrical conductivity (σ) and thermoelectric power (S) for an amphoteric oxide semiconductor, showing the slopes of the p(O2) exponent obtained from electrical conductivity (1/mσ) and thermoelectric power (1/mS); the vertical dashed lines demarcate the width of the n-p transition regime in which electrical properties are determined by both charge carriers.
It was shown that the effect of oxygen activity on the electrical conductivity of undoped TiO2 may be considered with the following regimes.27 Strongly Reduced Regime: slope ) -1/6; charge neutrality, 2[V•• O] ) n Reduced Regime: slope ) -1/4; charge neutrality, [V•• O] ) 2[V′′′′ Ti] Oxidized Regime: slope ) 1/4; charge neutrality, [V•• O] ) 2[ V′′′′ Ti] The effect of p(O2) on electrical conductivity of undoped TiO2 at elevated temperatures is shown schematically in Figure 2. The dashed lines in Figure 2 show a schematic representation of these three regimes in terms of slopes of the log σ versus log p(O2) dependences. The electrical conductivity studies of Nb-doped TiO2 reported before29 have shown that incorporation of Nb into the lattice of TiO2 results in a different character of the log σ versus log p(O2) dependences. The defect disorder in this case may be considered within the following three regimes. Strongly Reduced Regime: slope ) -1/6; charge neutrality, 2[V•• O] ) n Reduced Regime I: slope ) 0; charge neutrality, [Nb•Ti] ) n Reduced Regime II: slope ) -1/4; charge neutrality, [Nb•Ti] ) 4[V′′′′ Ti] In consequence, the Reduced Regime observed for undoped TiO2 is split into two regimes for Nb-doped TiO2, including Reduced Regime I (1/mσ ) 0) and Reduced Regime II (1/mσ ) -1/4). The Oxidized Regime observed for undoped TiO2, of
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Figure 3. Effect of oxygen activity, p(O2) on thermoelectric power (S) for undoped and Nb-doped TiO2 according to Baumard and Tani.38
Figure 2. Schematic representation of the effect of oxygen activity, p(O2), on electrical conductivity (σ) for both undoped TiO2 and Nbdoped TiO2, showing the defect disorder regimes and the related p(O2) exponents.
which the slope is positive, is expected to be reached at p(O2), which is substantially larger than the atmospheric pressure. As seen in Figure 2, the presence of Nb practically does not have any effect on electrical conductivity of Nb-doped TiO2 in strongly reduced conditions. Then, the slope of the log σ versus log p(O2) dependence is identical for both undoped and Nbdoped TiO2. Increasing the content of Nb in TiO2 results in a decrease of the p(O2) corresponding to the borderline between the Strongly Reduced Regime and the Reduced Regime I. Therefore, while the effect of p(O2) on the electrical conductivity in the Strongly Reduced Regime is the same, the p(O2) corresponding to the boundary between limits is dependent on the Nb content. 3. Literature Reports Prior data reporting the thermoelectric power of Nb-doped TiO2, under high-temperature conditions capable of achieving gas/solid equilibrium, were reported by Baumard and Tani,38 Poumellec and Marucco,39 and Poumellec et al.40 The most extensive studies on the effect of p(O2) on S for both undoped and Nb-doped TiO2 were reported by Baumard and Tani.38 Their data, which are shown in Figure 3, indicate the following. (1) The character of the thermoelectric power versus p(O2) dependence depends essentially on the Nb content. The slope of their S versus log p(O2) dependence for undoped TiO2 at 1473 K is 1/4.5 in a wide range of p(O2) [10-9 Pa < p(O2) < ∼ 10-2 Pa]. This slope was considered by Baumard and Tani38 in terms of tetravalent Ti interstitials (the related theoretical model leads to 1/mS ) 1/5). (2) Addition of Nb results in a substantial decrease of the slope in the medium p(O2). At 1 atom % of Nb, S exhibits a very weak dependence on p(O2). The slope in the range of 10-6 Pa < p(O2) < ∼ 102 Pa is 1/45. The slope below and above
Figure 4. Effect of temperature (T) on thermoelectric power (S) for Nb-doped TiO2 according to Poumellec and Marucco.39
this p(O2) range is 1/4.5 and 1/5.5, respectively. The earlier value is consistent with the model proposed by Baumard and Tani,38 according to which the predominant defects are tetravalent Ti interstitials. The latter slope is consistent with the strongly reduced regime (the related theoretical model leads to 1/mS ) 1/6). The data of Baumard and Tani38 have shown that the mechanism of Nb incorporation into TiO2 and the resulting effect on the electrical properties depend on oxygen activity. These mechanisms were considered elsewhere.29 The report of Baumard and Tani38 is, so far, the most comprehensive study on the effect of Nb on TiO2. The effect of temperature on S for Nb-doped TiO2, reported by Poumellec and Marucco,39 is shown in Figure 4. These data indicate only a slight temperature dependence of S. However, these data were determined in gas phases of unknown CO/CO2 ratio; therefore, the p(O2) is unknown. Consequently, these data are not well defined and require verification in well-defined conditions. In summary, well-defined data of the effect of p(O2) on thermoelectric power for Nb-doped TiO2 are mainly limited to the work of Baumard and Tani.38 The aim of the present study is to verify these data by simultaneous measurements of both electrical conductivity, reported before,29 and thermoelectric power, reported in this work.
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Figure 5. Example of experimental data showing the determination of thermoelectric power (S) for Nb-doped TiO2 from a plot of thermoelectric voltage (∆V) versus the temperature gradient (∆T) at 1273 K.
Figure 7. Effect of oxygen activity, p(O2), on thermoelectric power (S) for Nb-doped TiO2, showing data reproducibility during oxidation and reduction experiments at 1073, 1198, and 1298 K.
Figure 6. Standard monitoring sheet showing the changes in time (t) of (a) electrical conductivity (σ), (b) thermoelectric power (S), and (c) oxygen activity, p(O2), for Nb-doped TiO2.
4. Experimental Procedures The properties of the polycrystalline specimen of Nb-doped TiO2, including the processing procedures, structure, and microstructure, are described elsewhere.29 The total concentrations of acceptor-type cation and anion (Cl) impurities were 33.9 and 20 ppm, respectively. The size of the rectangular specimen was 1.7 mm × 3.8 mm × 14.9 mm. The thermoelectric power was measured along the temperature difference in two opposite directions, +∆T and -∆T. These data were determined from the slope of 40-50 independent pairs of measurements of the thermoelectric voltages (∆V) plotted against the temperature gradients within the range of -2.5 < ∆T < 2.5 K. The example data for Nb-doped TiO2 at 1273 K are shown in Figure 5. It can be seen that the uncertainties associated with the determination of ∆V and ∆T are 0.1 mV and 0.1 K, respectively, with correlation coefficients for these data sets consistently exceeding 0.99. Figure 6 presents a typical experimental monitoring sheet showing the raw data for changes in (a) electrical conductivity (σ), (b) thermoelectric power (S), and (c) oxygen activity (p(O2)) as a function of time during progressive reduction experiments within a wide range of oxygen activities.
Figure 6 shows that the imposition of a new gas phase (each downward step) results in a very rapid decrease in the p(O2) to a level of 95% of the final value within a few seconds, then assuming the nominal final value within ∼30 min. Oxygen activities in the high and the low p(O2) regimes were imposed by argon/oxygen mixtures at higher p(O2) and hydrogen/water vapor at lower p(O2), respectively. The oxygen activities were monitored during the entire experiment and were determined using a zirconia electrochemical oxygen probe. Experimental temperature fluctuations of the reaction chamber (0.5 K) had a negligible effect on the measured electrical conductivity and thermoelectric power data. The thermoelectric power data were recorded after the electrical conductivity had attained a constant value, which typically occurred within 5-10 h. These data are considered to correspond to conditions of operational equilibrium.29,30 The data in Figure 6 were used to plot S as a function of p(O2). The reproducibility of the experimental data during successive oxidation and reduction runs is shown in Figure 7 for selected temperatures, 1073, 1198, and 1298 K. As seen, the reproducibility of the data within successive runs remains very good. 5. Results and Discussion Figure 8 shows the effects of p(O2) on S in the range of 1073-1298 K during both oxidation and reduction experiments over the entire p(O2) range investigated. As seen, over the entire range of temperatures and p(O2) for Nb-doped TiO2, the S is negative, indicating that the system exhibits n-type properties. This is consistent with the expected effect of donor-type niobium
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Figure 9. Arrhenius plot of electrical conductivity (σ) determined at constant thermoelectric power (S ) -450 and -500 µV/K) for Nbdoped TiO2.
Figure 8. Effect of oxygen activity, p(O2), on thermoelectric power (S) for Nb-doped TiO2 at 1073-1298 K and for undoped TiO2,28 showing experimental results (solid lines) and interpolated data (dashed lines).
on the semiconducting properties of TiO2. The S data are entirely consistent with those for the electrical conductivity,29 thereby confirming the following behavior: (1) The slope of 1/4 in the high p(O2) regime suggests that the system exhibits the Reduced Regime II properties, in which the predominant defects are Ti vacancies that are compensated by donors formed of Nb in the Ti sites. The agreement between the p(O2) exponent determined using electrical conductivity29 and thermoelectric power data indicates that the mobility term is independent of the p(O2) in the Reduced Regime II. (2) At lower p(O2) levels of 10-7 Pa < p(O2) < 102 Pa, S becomes essentially independent of or has only a slight dependence on the p(O2), indicating that the behavior is consistent with Reduced Regime I. These data are consistent with electronic charge compensation of Nb ions. (3) At the lowest p(O2) levels of p(O2) < 10-7 Pa, the data tend toward increasing slopes. The p(O2) slope in this regime has the tendency to reach 1/6, which is consistent with the Strongly Reduced Regime. (4) The thermoelectric power data determined during oxidation and reduction experiments are identical, indicating that the properties of the system are determined under temperature and p(O2) conditions of the equilibrium. For better clarity, the inset in Figure 8 shows S in the lower p(O2) regime. These data indicate the following: (1) The data for 1073 K exhibit behavior that is different from that at higher temperatures. That is, at 1073 K, greater reduction of TiO2 results in an increase in the absolute value of S, while, at higher temperatures, lower p(O2) increases S. (2) In the range of 11981298 K, the slopes tend toward a value of 1/6 at the lowest p(O2) levels, which is consistent with the Strongly Reduced Regime. (3) At the higher p(O2) levels of 10-9 Pa < p(O2)
