Defect Chemistry and Electrical Properties of Titanium Dioxide. 2

602

J. Phys. Chem. C 2008, 112, 602-610

Defect Chemistry and Electrical Properties of Titanium Dioxide. 2. Effect of Aliovalent Ions J. Nowotny,* T. Bak, M. K. Nowotny, and L. R. Sheppard Centre for Materials Research in Energy ConVersion, School of Materials Science and Engineering, The UniVersity of New South Wales, Sydney, NSW 2052, Australia ReceiVed: June 13, 2007; In Final Form: October 2, 2007

The present work considers the effect of aliovalent ions (donors and acceptors) on the concentration of electronic charge carriers (electrons and electron holes) in titanium dioxide at elevated temperatures (873-1373 K) and the related electrical properties. The data are derived in the form of diagrams representing (i) the concentration of electronic charge carriers and (ii) electrical conductivity as a function of the effective concentration of acceptors. These diagrams may be used to predict the effect of acceptors and donors on the electrical conductivity for both n- and p-type TiO2. It is shown that the concentration of aliovalent ions, added intentionally (dopants) or unintentionally (impurities), has a substantial effect on the semiconducting properties already at the level of several parts per million and, therefore, cannot be ignored. This effect increases with the increasing oxygen activity. The determined critical concentrations of acceptors at 1073 K decreases from 10-3 at p(O2) ) 10-10 Pa to 10-6 at p(O2) ) 75 kPa. These data indicate that well-defined TiO2 specimens must include an analysis of impurities showing the concentration of aliovalent ions at the level of several parts per million.

1. Introduction Semiconducting properties of nonstoichiometric oxides are closely related to the extent of nonstoichiometry and the related defect disorder. The related charge transport may be considered in terms of the concentration of the charge carriers, including electrons, electron holes, and ions. At elevated temperatures, the latter term may assume substantial values. Since the nonstoichiometry of metal oxides is closely related to oxygen activity, the concentration of intrinsic defects is frequently related to the oxygen activity at elevated temperatures corresponding to equilibrium.1,2 These relationships, which may be assessed using the measurements of defect-related properties, such as electrical conductivity, thermoelectric power, and weight, are commonly considered solely in terms of the intrinsic ionic defects, while the concentration of impurities is ignored. This is the reason for the observed discrepancy between the reported experimental data, which, consequently, resulted in a great variety of defect disorder models that are proposed to explain these data. Titanium dioxide is not an exception. Figure 1 shows the scatter of the electrical conductivity data reported for undoped (but not necessarily pure) TiO2.3-11 As seen, these data differ in both absolute values and the effect of oxygen activity on the electrical conductivity. The observed differences have been frequently considered in terms of different defect disorder models.12-22 These models, however, commonly ignore the effect of impurities. Part 1 of the present study reported the effect of oxygen activity on the concentration of both ionic and electronic defects for TiO2 involving different concentrations of aliovalent ions.22 The purpose of the present work is to determine the effect of aliovalent ions, within a wide range of concentrations, on the concentration of electronic charge carriers and the related electrical conductivity of TiO2. This will be achieved through the use of defect disorder diagrams derived for undoped TiO2. * To whom correspondence should be addressed. E-mail: J.Nowotny@ unsw.edu.au. Phone: +61 2 9385 6459. Fax: +61 2 9385 6467.

Figure 1. The electrical conductivity data at 1273 K as a function of oxygen activity reported in the literature.3-11

These data will then be used for the assessment of the effect of impurities, usually present at low concentrations, on semiconducting properties of TiO2.22 2. Definition of Terms It has been documented that properties of TiO2 are closely related to its nonstoichiometry and the related defect disorder.1,2

10.1021/jp0745642 CCC: $40.75 © 2008 American Chemical Society Published on Web 12/20/2007

2. Effect of Aliovalent Ions of TiO2

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Since electrical properties are very sensitive to defect disorder, the measurements of these properties, such as electrical conductivity, may be used for assessment of the defect disorder. The latter one may be represented in the form of a diagram showing the concentration of defects, including both ionic and electronic defects, as a function of oxygen activity, p(O2), in equilibrium.1,2 It was shown that TiO2 includes the following defects.1,11,23-25 (1) Oxygen Vacancies. These are the predominant defects within a wide range of p(O2). At elevated temperatures, these defects are doubly ionized and exhibit relatively high mobility. Therefore, changes of p(O2) lead to fast establishment of their concentration on the equilibrium level.24 (2) Titanium Vacancies. The concentration of these defects in oxidizing conditions is comparable to that of oxygen vacancies; however, the mobility of titanium vacancies is substantially lower than that of oxygen vacancies. Therefore, the changes of p(O2) leads to an extremely slow change of their concentration, which may reach the equilibrium level only after prolonged annealing.25 Consequently, at elevated temperatures that are commonly applied in the studies of electrical properties, the concentration of these defects can be considered as quenched and practically independent of p(O2). (3) Titanium Interstitials. These are the minority defects within a wide range of p(O2). At elevated temperatures, these defects are tri- or tetravalent.1 These defects are often ignored in the considerations of electrical properties due to their relatively low concentration. (4) Electronic Defects. The concentration of these defects is determined by defect disorder and the related charge neutrality condition.1 Semiconducting properties of TiO2 are determined by these defects. Further considerations will be based on the following simplifying assumptions: (1) The concentration of all foreign acceptor-type ionic defects may be represented by an effective concentration of singly ionized acceptors, [A′]; and (2) the concentration of all foreign donor-type ionic defects may be represented by an effective concentration of singly ionized donors, [D•]. The basic condition of any defect disorder in thermal equilibrium is the charge neutrality condition, which requires that the lattice is electrically neutral. Therefore •••• • 2[V••O] + 3[Ti••• i ] + 4[Tii ] + [D ] + p ) n + [A′] + 4[V′′′′ Ti] (1)

The condition expressed by eq 1 is valid within a wide range of p(O2). This conditions, however, is awkward for practical applications. Therefore, defect disorder of TiO2 is frequently considered in terms of simplified charge neutrality conditions, which are valid within narrow ranges of p(O2).23 For the purpose of further considerations, the concentration of all kinds of defects, which are independent of p(O2), may be represented by an effective concentration of acceptors, which is defined as follows • A ) 4[V′′′′ Ti ] + [A′] - [D ]

(2)

In the specific case of pure TiO2, which is free of aliovalent foreign ions, it can be simplified as

A ) 4[V′′′′ Ti ] ) Apure

(3)

For an acceptor-doped TiO2, the effective concentration of acceptors is

A ) 4[V′′′′ Ti ] + [A′]

(4)

A > Apure

(5)

Therefore

In analogy, for donor-doped TiO2, we have • A ) 4[V′′′′ Ti ] - [D ]

(6)

A < Apure

(7)

Therefore

The effective concentration of acceptors, A, will later be used in the assessment of the effect of aliovalent ions (donors and acceptors) on electrical properties. The defect disorder diagrams, derived for specific values of A, may then be used for the determination of the concentration of electronic charge carriers. These, consequently, may be used for the determination of the electrical conductivity

σ ) enµn + epµp + z[i]µi

(8)

enµn + epµp . z[i]µi

(9)

σ ) enµn + epµp

(10)

When

we have

The p(O2) exponent of the electrical conductivity in n- and p-type regimes in the vicinity of the n-p transition is -1/4 and 1/4, respectively.23 Therefore

σ ) σ0np(O2)-1/4 + σ0pp(O2)1/4

(11)

where σ0n and σ0p denote the pre-exponential factors. The p(O2) exponents in eq 11 may be considered in terms of the p(O2) dependence of the concentration of electronic charge carriers when electrical conduction is determined by electronic charge carriers and when mobility terms, µn and µp, are independent of p(O2). The quantitative analysis in the present work, outlined below, will be performed at the following simplifying assumptions: (1) The effect of isovalent ions, incorporated substitutively, on defect disorder can be ignored because its incorporation into the TiO2 lattice does not affect the charge neutrality. Although the effect of the isovalent ions, such as carbon, on electronic properties of TiO2 has been observed,24 it seems that this effect is mainly related to the effect of carbon through either its effect on oxygen activity, affecting defect disorder, or the formation of new phases. (2) The effect of the ionic component of the electrical conductivity will be ignored as it is negligibly small compared to the electronic conductivity components. 3. Effect of Aliovalent Ions on Electrical Properties 3.1. Electronic Charge Carriers. The concentration of electronic defects, n and p, data were determined using the diagram reported before.22 Isothermal plots of the logarithm of n and p as a function of log A at p(O2) ) const at 873-1373 K are shown in Figures 2-7. As seen, the effect of A on both n and p may be ignored below a certain critical value, Ac, which depends on p(O2) and temperature. However, the effect of the effective concentration of acceptors on the concentration of

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Figure 2. Effect of the effective concentration of acceptors, A, on the concentration of electronic charge carriers for TiO2 at 873 K.




electronic charge carriers becomes substantial above Ac. This critical value can be determined by intersections of the linear

dependencies of n or p as a function of log A in the following regimes: (1) the regime corresponding to low values of A in



which n and p are independent of A and (2) the regime corresponding to larger values of A, in which the slope log (n, p) versus log A becomes substantial. The procedure of graphical determination of the critical value Ac is shown in Figure 8. The data in Figures 2-7 indicate the following effects: (1) The Ac decreases with oxygen activity. This means that the sensitivity of electrical properties for the presence of impurities increases with p(O2). (2) The Ac increases with temperature. This means that electrical properties are more sensitive for the presence of impurities at lower temperatures. (3) The sensitivity ranges are the same for both n- and p-type TiO2. 4. Electrical Conductivity The concentrations of the electronic charge carriers derived in Figures 2-7 and their mobility terms determined recently by the authors26 were used for the determination of theoretical values of the electrical conductivity for pure TiO2. Isothermal plots of the electronic component of the electrical conductivity, log σ, as a function of log [A′] at p(O2) ) const at elevated temperatures (873-1373 K) are shown in Figures 9-14. The variable A in Figures 2-8 is the effective concentration of acceptors, A, expressed by eq 2, while the variable [A′] in Figures 9-14 is the concentration of singly ionized acceptors introduced intentionally or present as impurities. As seen in Figures 9 and 10, the conductivity at 873 and 973 K remains constant within the [A′] range, of which the maximum value is equivalent to the Ac in Figures 2 and 3. At larger [A′] values, and for p(O2) > 10 Pa, the increase of [A′] leads to an increase of the electrical conductivity; however, for p(O2) ) 10 Pa, the conductivity decreases with [A′]. At 1073 (Figure 11) and 1173 K (Figure 12), the picture is similar to that at 873 and 973 K. A small minimum of σ observed for p(O2) ) 10 Pa



is related to the n-p transition that takes place within 10-4 > [A′] > 10-2 at 1073 K and within 10-3 > [A′] > 10-1 at 1173 K. As seen in Figures 13 and 14, representing the temperatures of 1273 and 1373 K, respectively, the increase of [A′] above a certain critical value leads to an increase and decrease of the conductivity at p(O2) ) 75 kPa and p(O2) ) 10 Pa, respectively. In all cases, the increase of temperature leads to an increase of the critical value of [A′], below which the conductivity is independent of [A′]. Figures 15-20 represent the effect of donors, defined by eq 6, on electrical conductivity. These data indicate the following effects: (1) The increase of [D•] does not have an effect on electrical conductivity within a certain limit, which corresponds to [D•] < 3 × 10-6 at 873 K; [D•] < 3 × 10-5 at 973 K; [D•] < 3 × 10-4 at 1073 K; [D•] < 1 × 10-3 at 1173 K; [D•] < 3 × 10-3 at 1173 K; and [D•] < 1 × 10-2 at 1373 K. (2) The increase of [D•] above the critical values results in a sharp increase of conductivity by several orders of magnitude. (3) The electrical conductivity at p(O2) ) 75 kPa exhibits a sharp minimum at 873 K, which becomes more shallow at increasing temperatures (up to 1273 K). 5. Effect of Impurities The data in Figures 2-20 allow one to assess the effect of aliovalent ions, acceptors and donors, on the concentration of electronic charge carriers and the electrical conductivity. These data indicate the following: (1) The effect of the aliovalent ions on properties may be ignored below certain critical values, which depends on temperature and oxygen activity. The effect of temperature and oxygen activity on the critical value Ac, below which the concentration of electronic charge carriers are independent of A, is shown in Figure 21. (2) The concentration


Figure 8. The plot of electronic charge carriers for TiO2 at 1173 K versus the effective concentration of acceptors, A, showing the procedure for the determination of the critical concentration of Ac.

Nowotny et al.

Figure 10. Effect of the concentration of singly ionized acceptors, [A′], on the electrical conductivity for TiO2 at 973 K.

Figure 11. Effect of the concentration of singly ionized acceptors, [A′], on the electrical conductivity for TiO2 at 1073 K. Figure 9. Effect of the concentration of singly ionized acceptors, [A′], on the electrical conductivity for TiO2 at 873 K.

of aliovalent ions, added intentionally (dopants) or unintentionally (impurities), has a substantial effect on the semiconducting

properties already at the level of several parts per million and, therefore, cannot be ignored. (3) The effect of acceptors increases with increasing oxygen activity. At 1073 K, the critical concentrations of acceptors decreases from 10-3 at






Figure 15. Effect of the concentration of singly ionized donors, [D•], on the electrical conductivity for TiO2 at 873 K.

p(O2) ) 10-10 Pa to 10-6 at p(O2) ) 75 kPa. (4) The effect of acceptors decreases with temperature. The critical concentrations of acceptors increases from 10-6 at 873 K to 10-2 at 1373 K. (5) The effect of donors depends on oxygen activity;

however, the observed tendency is complex. (6) The effect of donors decreases with temperature. The critical concentrations of donors increase from 10-5 at 873 K to 10-1 at 1373 K.


Nowotny et al.





The data obtained in the present work indicate that the TiO2 specimens are sensitive to the presence of impurities, especially aliovalent ions. Therefore, the effect of impurities on properties must not be underestimated. As seen in Figure 21, the changes

in the effective concentration of the acceptor already at the parts per million level lead to substantial changes of the concentration of electronic charge carriers. Consequently, the reports on TiO2 must include an analysis of impurities. This conclusion is valid


J. Phys. Chem. C, Vol. 112, No. 2, 2008 609 TABLE 1: The Comparison of Different Spectroscopic Impurity Analysis Results for Undoped NiO27 concentration [ppm]


Figure 21. Isothermal plots of the critical value of the effective concentration of the acceptors as a function of temperature for TiO2.

for all oxide semiconductors, although the critical levels of impurities, above which the effect on properties is substantial, may vary from oxide to oxide. The information about the results of the impurity analysis is especially important when the defect-related data for different specimens are compared. It seems that the scatter of data observed in Figure 1 is mainly due to the effect of impurities. However, in most cases, such data have not been reported. The effect of aliovalent ions, present as impurities and/or deliberately added, on properties of TiO2 may be assessed using the defect diagrams determined in the present work. Specifically, these defect diagrams allow one to assess the effect of aliovalent ions, involved in the quantity A, on the concentration of electronic charge carriers. These data indicate that the impurity analysis is an essential part of the characterization of oxide semiconductors, such as

element

company 1

Ca Fe Si Ti Cr Cu

50-500 10-100 5-50 5-50 1-10 1-10

company 2 70 300 trace

company 3

company 4

40 50

14 4400 24 13 140

200 10 5

TiO2. The impurities may have a substantial effect on several properties of TiO2-based photoelectrodes and photocatalysts, including the following: (1) Charge-transport kinetics within a TiO2-based photoelectrode. The charge-transport data impact on the charge-transport-related energy losses in photoelectrochemical cells.27 (2) Surface composition. Even traces of impurities at the outermost surface layer may be responsible for either (i) blocking the active surface sites for water splitting or (ii) enhancement of photoreactivity due to imposition of new surface active sites.28 (3) Segregation-induced electric fields in the near-to-surface layer. Even if the content of an impurity in the bulk phase is below the detectibility level and may be ignored, its segregation-induced enrichment of the near-tosurface layer may be substantial. This, in consequence, leads to either the formation of strong electric fields responsible for charge separation or reduction of the existing electric fields.29 The consideration of the effect of impurities in the present work has been limited to aliovalent ions since isovalent ions have no appreciable effect on the concentration of electronic defects and, consequently, on electrical properties.30 There is a great variety of methods for analysis of impurities, including proton-induced X-ray emission (PIXE),31 laserinduced breakdown spectroscopy (LIBS),32 and inductively coupled plasma mass spectrometry (ICPMS).33 Different methods are usually selective to specific elements, and therefore, the results of the impurity analysis performed by different methods may differ substantially. As seen in Table 1, the results of the impurity analyses for the same specimen of NiO provided by different companies differ substantially. The services for the impurity analysis are usually expensive. However, since the knowledge of the impurity content is essential, the impurity-related data should be considered as a part of basic characterization of studied materials. The results obtained in the present work may be used to predict the effect of impurities on electrical properties. 6. Conclusion Defect disorder diagrams have been used to predict the effect of the concentration of aliovalent ions (donors and acceptors) in titanium dioxide on the concentration of electronic charge carriers (electrons and electron holes) and the related electrical properties. The following effects have been established: (1) The effect of aliovalent ions, added intentionally (dopants) or unintentionally (impurities), on the concentration of electronic charge carriers and related electrical properties depends on temperature and oxygen activity. (2) The electrical conductivity is independent of the concentration of aliovalent ions below a certain critical value. The effect of the aliovalent ions on the electrical conductivity above this value becomes substantial and cannot be ignored. (3) The observed effect of aliovalent ions increases with the decrease of temperature. (4) Aliovalent ions, added intentionally (dopants) or unintentionally (impurities), have a substantial effect on the properties already at the level of several parts per million and, therefore, cannot be ignored.

610 J. Phys. Chem. C, Vol. 112, No. 2, 2008 These data, which were determined from defect disorder diagrams, were used to predict the n-p transition point and electrical conductivity for both n-type and p-type TiO2 in the range of 873-1373 K. The obtained data indicate that the conductivity models derived in the present work are comparable with the experimental electrical conductivity data, and a good agreement between the two was revealed. Acknowledgment. The present work was supported by the Australian Research Council, Mailmasters Pty Ltd, Brickworks Pty Ltd, Avtronics (Australia) Pty Ltd, and Rio Tinto Ltd. This project was performed as part of the UNSW R&D program on solar hydrogen. References and Notes (1) Kofstad, P. In Nonstoichiometry, Diffusion and Electrical ConductiVity of Binary Metal Oxides; Wiley, New York 1972 (2) Kroger, F. A. In The Chemistry of Imperfect Crystals; North Holland: Amsterdam, The Netherlands, 1974, p 275. (3) Blumenthal, R. N.; Kirk, J. C.; Hirthe, W. M. J. Phys. Chem. Solids 1967, 28, 1077. (4) Blumenthal, R. N.; Kirk, J. C.; Hirthe, W. M. J. Electrochem. Soc. 1967, 114, 172. (5) Odier, P.; Baumard, J. F.; Panis, D.; Anthony, A. M. J. Phys. Chem. Solids 1975, 12, 324. (6) Singheiser, L.; Auer, W. Ber. Bunsen-Ges. 1977, 81, 1167. (7) Balachandran, U.; Eror, N. G. J. Mater. Sci. 1988, 23, 2676. (8) Carpentier, J. L.; Lebrun, A.; Perdu, F. J. Phys. Chem. Solids 1989, 50, 145. (9) Son, J.; Yu, I. Korean J. Ceram. 1996, 2, 131. (10) Nowotny, J.; Radecka, M.; Rekas, M. J. Phys. Chem. Solids 1997, 58, 927. (11) Nowotny, M. K.; Bak, T.; Nowotny, J. J. Phys. Chem. B 2006, 110, 16270. (12) Yahia, J. Phys. ReV. 1963, 130, 1711. (13) Tannhauser, D. S. Solid State Commun. 1963, 1, 223.

Nowotny et al. (14) Blumenthal, R. N.; Coburn, J.; Baukus, J.; Hirthe, W. M. J. Solid State Chem. 1966, 27, 643. (15) Baumard, J. F.; Panis, D.; Ruffier, D. ReV. Int. Hautes Temp. Refract. 1975, 12, 321. (16) Marucco, J. F.; Gautron, J.; Lemasson, P. J. Phys. Chem. Solids 1981, 42, 363. (17) Kim, K. H.; Oh, E. J.; Choi, J. S. J. Phys. Chem. Solids 1984, 45, 1265. (18) Marucco, J. F.; Poumellec, B.; Gautron, J.; Lemasson, P. J. Phys. Chem. Solids 1985, 46, 709. (19) Millot, E. J. Mater. Sci. Lett. 1985, 4, 902. (20) Lebrun, A.; Carpentier, J. L.; Perdu, F.; Tellier, P. C. R. Acad. Sci. Paris 1987, 304, 629. (21) Fujitsu, S.; Hamada, T. J. Am. Ceram. Soc. 1994, 77, 3281. (22) Nowotny, J.; Bak, T.; Nowotny, M. K.; Sheppard, L. R. Defect Chemistry and Electrical Properties of Titanium Dioxide. 1. Defect Diagrams. J. Phys. Chem. C 2008, 112, 590. (23) Nowotny, M. K.; Bak, T.; Nowotny, J. J. Phys. Chem. B 2006, 110, 16283. (24) Nowotny, M. K.; Bak, T.; Nowotny, J. J. Phys. Chem. B 2006, 110, 16293. (25) Nowotny, M. K.; Bak, T.; Nowotny, J. J. Phys. Chem. B 2006, 110, 16302. (26) Nowotny, J.; Bak, T.; Nowotny M. K.; Sheppard, L. R. In preparation for publication. (27) Nowotny, J.; Bak, T.; Nowotny, M. K.; Sheppard, L. R. Int. J. Hydrogen Energy 2007, 32, 2609. (28) Nowotny, J.; Bak, T.; Nowotny, M. K. J. Phys. Chem. B 2006, 110, 18492. (29) Nakajima, T.; Sheppard, L. R.; Prince, K. E.; Nowotny, J.; Ogawa, T. AdV. Appl. Ceram. 2007, 106, 82. (30) Price, J. B.; Wagner, J. B., Jr. Z. Phys. Chem. (Frankfurt/Main, Ger.) 1966, 49, 258. (31) Denker, A.; Optitz-Couterau, J.; Campbell, J. L.; Maxwell, J. A.; Hopman, T. L. Nucl. Instrum. Methods 2004, B219/220, 130. (32) Rusak, A. A.; Castle, B. C.; Smith, B. W.; Winefordner, J. D. Crit. ReV. Anal. Chem. 1997, 27, 257. (33) Martin-Esteban, A.; Slowikowski, B. Crit. ReV. Anal. Chem. 2003, 33, 43.

Defect Chemistry and Electrical Properties of Titanium Dioxide. 2

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