Effect of Prolonged Oxidation on Semiconducting Properties of

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J. Phys. Chem. C 2008, 112, 13248–13257

Effect of Prolonged Oxidation on Semiconducting Properties of Titanium Dioxide T. Bak, M. K. Nowotny, L. R. Sheppard, and J. Nowotny* Centre for Materials Research in Energy ConVersion, School of Materials Science and Engineering, The UniVersity of New South Wales, Sydney, NSW 2052, Australia ReceiVed: April 7, 2008; ReVised Manuscript ReceiVed: June 5, 2008

The present work reports the effects of prolonged oxidation of titanium dioxide on its semiconducting properties at elevated temperatures. The studies were performed by using simultaneous measurements of both electrical conductivity and thermoelectric power during oxidation at 1123 and 1323 K in the gas phase of controlled oxygen activity, p(O2) ) 75 kPa. The effects of oxidation on these electrical properties are considered in terms of a change in the concentration of titanium vacancies, which are formed during oxidation. It is shown that the increase in the concentration of titanium vacancies results in a change of semiconducting properties, including the following: (1) The shift of the n-p transition point toward lower values of oxygen activity. This shift results in an increase of the oxygen activity regime in which TiO2 exhibits p-type properties. (2) Increase of the ionic electrical conductivity component. (3) Increase of the mobility terms for electrons and decrease of the mobility of electron holes. It is shown that the band gap of TiO2 is 3.1 eV and remains independent of the concentration of titanium vacancies. The data reported in this work may be used for processing TiO2 with controlled semiconducting properties. These data also pave the way for the processing of undoped TiO2 that exhibits p-type properties without the need to incorporate acceptor-type foreign ions. 1. Introduction There has been an increasing interest in the studies of titanium dioxide, TiO2. This interest has stemmed from the wide range of TiO2 applications, which are related to its interesting properties as photocatalysts1–6 and photoelectrodes for water splitting.7–10 It has been shown that TiO2 is the most promising candidate for the generation of solar hydrogen. Properties of TiO2 are closely related to its defect disorder,11,12 which may be determined by using the measurements of defect-sensitive properties, such as electrical properties. Recent studies, including the studies by the authors, led to an accumulation of data on defect-related properties, including electrical conductivity,13–16 thermoelectric power,17 and nonstoichiometry.18,19,21–24 These data led to the derivation of a defect disorder diagram, which allows us to assess the effect of oxygen activity on the concentration of both ionic and electronic defects in TiO2.25 Defect disorder of TiO2 has been considered in terms of three kinds of ionic defects, including oxygen vacancies, titanium interstitials, and titanium vacancies.25 Recent studies have shown that the concentration of oxygen vacancies may be changed relatively fast by the imposition of variable oxygen activity at elevated temperatures corresponding to gas/solid equilibrium.26 This equilibrium will be later termed as the operational equilibrium, and the related kinetics, which is determined by the transport of fast defects (oxygen vacancies and titanium interstitials), is termed kinetic regime I.26 It has been shown that titanium interstitials in oxidizing conditions are the minority defects.15 Therefore, these defects may be ignored in considering the electrical properties of TiO2 at high oxygen activity. The term “operational equilibrium” is introduced in order to distinguish between two kinetic regimes, involving the regime related to fast defects (oxygen vacancies and titanium intersti* Corresponding author. E-mail: [email protected]. Phone: +61 2 9385 6459. Fax: +61 2 9385 6467.

tials) and the regime related to all ionic defects, including titanium vacancies. The equilibration in the latter regime, which is controlled by the transport of titanium vacancies that is exceptionally slow, is termed kinetic regime II.27 Recent studies by the authors have shown that in the time range corresponding to the establishment of the operational equilibrium (kinetic regime I), the bulk concentration of titanium vacancies remains practically constant.26,27 Monitoring of the electrical conductivity and thermoelectric power over extensive periods of time has also shown that measurable changes in the concentration of titanium vacancies may be imposed only after prolonged oxidation lasting several thousand hours at elevated temperatures.27 Therefore, prolonged oxidation may be applied for processing of TiO2 with a controlled concentration of titanium vacancies. So far, little is known on the effect of titanium vacancies on properties of TiO2 due to the fact that the TiO2 specimens studied so far have been equilibrated in the operational equilibrium (kinetic regime I) in which the concentration of titanium vacancies is not well-defined. The determination of the chemical diffusion data related to prolonged oxidation allows us to impose well-defined concentration of titanium vacancies. These data, which have been determined by the authors, will be outlined below. The present work reports, for the first time, the effect of titanium vacancies on semiconducting properties of TiO2, including the n-p transition point, the mobility of electronic charge carriers, and the electrical conductivity component related to ionic charge carriers, at elevated temperatures. It will be shown that a simple binary oxide, such as TiO2, may exhibit a wide range of different properties, which may be imposed by a controlled defect disorder. The concentration of titanium vacancies may have a substantial effect on these properties, even including the change of the conductivity type. The considerations of the experimental data will be preceded by a short outline of defect chemistry of TiO2, including the following:

10.1021/jp803020d CCC: $40.75  2008 American Chemical Society Published on Web 08/02/2008

Prolonged Oxidation of Semiconducting TiO2

J. Phys. Chem. C, Vol. 112, No. 34, 2008 13249

(1) Defect disorder: this will be considered in terms of defect equilibria, the related charge neutralities, and the defect disorder diagram. (2) The effect of defect disorder on electrical properties, including electrical conductivity and thermoelectric power. (3) The chemical diffusion data related to the equilibration kinetics controlled by the rapid and slow defects. 2. Defect Disorder and Defect-Related Properties 2.1. Defect Disorder. With the use of the Kro¨ger-Vink notation,28 the formation of the point defects in TiO2 may be described by the following defect equilibria:15

1 OO a VO•• + 2e′ + O2 2 2OO + TiTi a Tii••• + 3e′ + O2 2OO + TiTi a Tii•••• + 4e′ + O2 O2 a 2OO + VTi′′′′ + 4h• ′ • nil a e + h

(1) (2) (3) (4) (5)

The concentrations of all defects, including both electronic and ionic defects, must satisfy the lattice charge neutrality condition, which may be represented in the following form:

2[VO••] + 3[Tii•••] + 4[Tii••••] + [D•] + p ) n + 4[VTi′′′′] + [A′] (6) [D•]

where and [A′] are the concentrations of singly ionized donor- and acceptor-type foreign ions (as examples), respectively, present as introduced dopants or incidental impurities. In certain conditions, when the concentration of some types of defects compared to the predominant defects is very low and may be ignored, condition 6 may be represented in a simplified form. The studies of defect-related properties, including electrical conductivity and thermoelectric power, have led to the determination of equilibrium constants of the reactions 1, 4, and 5,25 which may be used in the derivation of defect diagrams representing the concentrations of defects in TiO2 over a wide range of oxygen activities. A defect diagram at 1123 K is represented in Figure 1 for an effective concentration of acceptors A ) 4.8 × 10-4, which is defined as •

A ) 4[VTi′′′′] + [A′] - [D ]

(7)

Consequently, for high-purity TiO2, when the terms [A′] and [D•] may be ignored, the quantity A is 4 times larger than the concentration of titanium vacancies. 2.2. Electrical Conductivity. The electrical conductivity, σ, of TiO2 in the n-p transition regime, in which both electrons and holes take part in conduction, includes the components associated with both electronic charge carriers:

σ ) enµn + epµp

(8)

where e is the elementary charge, µ is the mobility, n and p are the concentrations of electrons and holes, respectively, and the subscripts correspond to the specific charge carriers. The most feasible defect disorder model of high-purity TiO2 in the vicinity of the n-p transition point is based on the assumption that15 • The predominant defects are oxygen vacancies. • The minority defects are titanium interstitials. • Titanium vacancies may achieve relatively high concentrations.

Figure 1. Defect disorder of TiO2 in terms of defect concentrations as a function of oxygen activity, p(O2), at 1123 K and the effective concentration of acceptors A ) 4.8 × 10-4, corresponding to the equilibrium concentration of titanium vacancies at that temperature (ref 25).

In this case the condition expressed by eq 6 may be reduced to a simple form:

[VO••] ) 2[VTi′′′′]

(9)

The exponent of the oxygen activity, p(O2), in the n- and p-type regimes in the vicinity of the n-p transition is -1/4 and 1/4, respectively.15 Therefore, 1

1

σ ) σ0np(O2)- 4 + σ0pp(O2) 4 σ0n

(10)

σ0p

where and are the parameters, which are independent of p(O2). It was shown that ionic conductivity at elevated temperatures may attain a substantial value and, therefore, cannot be ignored.15 Then eq 10 assumes the following form: 1

1

σ ) σ0np(O2)- 4 + σ0pp(O2) 4 + σi

(11)

where σi is the ionic component of the electrical conductivity, which in the n-p transition regime is practically independent of p(O2). Electrical conductivity is the product of both concentration and mobility terms. Assuming that the mobility terms are independent of p(O2), the expression for electrical conductivity in the n-p transition regime, expressed by eq 11, assumes the following form:15 1

1

σ ) eµncnp(O2)- 4 + eµpcpp(O2) 4 + σi

(12)

where cn and cp are constants and µn and µp denote the mobility terms related to electrons and holes, respectively.

13250 J. Phys. Chem. C, Vol. 112, No. 34, 2008

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The p(O2) dependence of the electrical conductivity, that is expressed by eqs 10–12, may be considered in terms of the p(O2) dependence of the concentrations of electronic charge carriers when the mobility terms, µn and µp, are independent of p(O2). 2.3. Thermoelectric Power. The imposition of a temperature difference, ∆T, across a specimen results in the generation of an electrical potential difference, ∆V. Knowledge of both ∆V and ∆T allows us to determine the thermoelectric power:

S ) lim

∆Tf∞

∆V dV ) ∆T dT

(13)

For n- and p-type regimes, the following equations describe relations between S and the concentrations of electronic charge carriers:12

(

)

Nn k ln + An e n Np k Sp ) ln + Ap e p

Sn ) -

(

)

(14) (15)

where k is the Boltzmann constant, N is the density of states, A is the kinetic constant, and the subscripts n and p are related to electrons and holes, respectively. It can be seen from eqs 14 and 15, that S is independent of the mobility terms (µn or µp) and, therefore, the combination of data for both thermoelectric power and electrical conductivity allows us to assess both the concentration and mobility terms. When the mobilities of both electronic charge carriers are the same, then the p(O2) corresponding to S ) 0 is identical to that corresponding to the minimum of electrical conductivity (σmin):

p(O2)S)0 ) p(O2)σ(min)

when

µn ) µp

(16)

2.4. Equilibration. When TiO2 reacts with oxygen at elevated temperatures then oxidation and reduction results in shifts of defect equilibria, which are represented by expressions 1–5. Defects are formed or removed at the gas/solid interface. The newly imposed defects diffuse into the bulk phase leading to the imposition of a new equilibrium state. The related diffusion rates may be considered in terms of two kinetic regimes:16 1. Kinetic regime I. This regime corresponds to the transport of fast defects (oxygen vacancies and titanium interstitials) that exhibit high diffusion rates. According to the recently determined data of the equilibration kinetics, a new oxygen activity may be imposed within 0.5 and 2 h at 1323 and 1073 K, respectively.15,16 2. Kinetic regime II. The kinetics in this regime is determined by the diffusion rate of titanium vacancies, which is exceptionally slow (it takes 3-4 months at 1323 K to impose an equilibrium concentration of titanium vacancies in a TiO2 disk that is 1 mm thick). The chemical diffusion data for TiO2 single-crystal27 and polycrystalline specimens29 are shown in Figure 2. As seen, the diffusion data are different for TiO2-PC and TiO2-SC, indicating that the effect of grain boundaries on the transport of defects is substantial. As also seen, the diffusion data in kinetic regime I and kinetic regime II differ by 4-5 orders of magnitude. These data are reflective of the difference in the diffusion rate of the fast defects (oxygen vacancies and titanium interstitials) and the slow defects (titanium vacancies). The diffusion data in Figure 2 may be used for the determination of time required for the processing of TiO2 with controlled concentration of titanium vacancies.

Figure 2. Arrhenius plot of the chemical diffusion coefficient for TiO2 single-crystal (ref 27) and polycrystalline TiO2 (ref 29) in kinetic regimes I and II.

3. Experimental Section High-purity single-crystal TiO2 grown by the Verneuil method (Escete GmbH, Enschede, Holland) was used in the present investigation. The total concentration of detected cation impurities was 32 ppm, including the following: Cu 5 ppm, Ni 5 ppm, Fe 2 ppm, Ag 5 ppm, Si 10 ppm, Mg 5 ppm. Since the valency of these ions is lower than that of the host lattice cation (Ti4+), all of them form acceptor-type centers. The photospectrometry analysis of the impurities (performed by the manufacturer) indicates that the level of impurities is extremely low. In order to prevent cross contamination of the specimen during prolonged annealing, the experiment was conducted in a brand new highpurity alumina tube. The partial pressure of both Al2O3 and Al above the alumina surface is extremely low. Consequently, the transport of Al from alumina to the specimen via a gas phase may be ignored. A slab of dimensions 2 mm × 3 mm × 10 mm was cut from the boule with a diamond saw and then polished with 1 µm diamond paste. The surface of the 3 × 10 mm2 area was perpendicular to the c-axis. The crystal was free of macroscopic defects. The structure identified using X-ray diffraction was rutile. The required oxygen activity in the reaction chamber was imposed by an oxygen/argon mixture flowing through the reaction chamber at a constant flow rate of 100 mL/min. The oxygen activity in the mixture was determined using a zirconiabased electrochemical oxygen probe. The effect of oxygen activity on both electrical conductivity and thermoelectric power data was determined simultaneously over an extensive period of time. The procedure included measurement of the following two properties:



Figure 3. Changes of the electrical conductivity for undoped TiO2 single crystal as a function of time during isothermal oxidation (p(O2) ) 75 kPa) at 1123 and 1323 K, showing kinetic regime I (short kinetics) and kinetic regime II (long kinetics) (ref 25).

• Electrical conductivity. The measurements of electrical conductivity were taken at 10-15 different currents (of two polarities) in the range of 10 nA to 1 mA. The electrical conductivity was measured as a function of oxygen activity. Measurements of electrical conductivity as a function of time were used to monitor the rate of gas/solid equilibration. The time intervals between the electrical conductivity measurements were between 30 s and 15 min. The time gap was adjusted according to the rate of the conductivity change. • Thermoelectric power. The thermoelectric voltage was measured along the direction of the temperature gradient of two different polarities, +∆T and -∆T. The thermoelectric power was determined from 50 to 100 different temperature gradients in the range of 0-5 K. Measurements of both electrical conductivity, σ, and thermoelectric power, S, were taken simultaneously using a hightemperature Seebeck probe.15 Prior to electrical conductivity measurement, the specimen was heated (at a rate of 400 K/h) to the temperature of the measurements (1123 and 1323 K) in the Ar/O2 mixture corresponding to the oxygen activity around 30 kPa. The specimen was isothermally equilibrated in kinetic regime I leading to the establishment of electrical conductivity at a constant level. Then oxygen activity was increased to p(O2) ) 75 kPa, and since that moment both electrical conductivity and thermoelectric power were monitored isothermally over an extensive period of time, involving kinetic regimes I and II. The resulting changes of electrical conductivity at 1123 and 1323 K are shown in Figure 3. 3.1. Oxidation at 1123 K. As seen in Figure 3, the increase of p(O2) from 32 to 75 kPa at 1123 K results in an increase of the electrical conductivity, which assumes a stable value within 0.5 h. At the same time, the thermoelectric power has increased from 420 to 450 µV/K.25 These fast changes of the electrical conductivity, shown in Figure 3 by the continuous line (left side), correspond to kinetic regime I. After the operational equilibrium in kinetic regime I was achieved, the specimen was left in oxidizing conditions over a prolonged period of time. As seen in Figure 3, the electrical conductivity (and thermoelectric power25) still exhibit changes, although these changes are extremely slow. Therefore, the

Figure 4. Effect of prolonged oxidation of undoped TiO2 single crystal at 1123 K on the p(O2) related to n-p transition point derived from thermoelectric power data (S ) 0) (ref 25).

changes recorded experimentally have been measured over the time gaps between 10 and 100 h. Because of the different rate of the equilibration process in this regime (kinetic regime II), a different time scale was used for plotting the experimental data on the right side of Figure 3. The continuous lines in Figure 3 indicate the experimental dependence, and the dashed line corresponds to an interpolated dependence over an additional period of 1000 h when the specimen still remained in the reaction chamber in the same conditions of temperature (1123 K) and p(O2) ) 75 kPa.


Figure 5. Effect of oxygen activity on both electrical conductivity (upper part) and thermoelectric power (lower part) determined for undoped TiO2 single crystal at 1323 K in kinetic regime I, before prolonged oxidation (10 h) and after the prolonged oxidation (3450 h); the vertical lines show the p(O2) values related to the n-p transition point according to the minimum of electrical conductivity (σmin, upper part) and thermoelectric power data (S ) 0, lower part) (ref 25).

The effect of p(O2) on electrical conductivity and thermoelectric power at 1123 K in kinetic regime I has been reported before.25 As seen in Figure 4 the prolonged oxidation results in the shift of the n-p transition point, related to p(O2) at which S ) 0, toward lower p(O2) values over 1 order of magnitude. 3.2. Oxidation at 1323 K. The TiO2 specimen was also studied both before and after the prolonged oxidation at 1323 K. The changes of both electrical conductivity and thermoelectric power before and after the prolonged oxidation of TiO2 at 1323 K, including kinetic regimes I and II, are shown, respectively, in the upper and the lower part of Figure 5, where the line nos. 1 and 2 correspond to the measurements at 10 h (before the prolonged oxidation) and at 3450 h (after the prolonged oxidation). As seen, there is no consistency between the p(O2) values corresponding to the minima of the electrical conductivity and those corresponding to S ) 0. The observed discrepancy seems to be due to the low accuracy of the determination of these quantities which, in this case, are situated at the edge of the applied oxygen activities. Therefore, these data require a verification. As seen in Figure 3, the increase of p(O2) from 26 to 75 kPa results in a decrease of the electrical conductivity, which assumes a stable value within 30 min. At the same time, the thermoelectric power increased from -42 to 41 µV/K.25 After the equilibrium in kinetic regime I was reached, the specimen was left at 1323 K during a prolonged period of time. As seen in Figure 3, the electrical conductivity assumes a stable value after ∼3450 h.

Bak et al.

Figure 6. Arrhenius plot of the chemical diffusion coefficient for undoped TiO2 including both single-crystal (TiO2-SC) and polycrystalline (TiO2-PC) specimens in kinetic regime I, in which the transport is rate-controlled by oxygen vacancies, and in kinetic regime II, in which the transport is rate-controlled by titanium vacancies (refs 16, 26, 27, and 29). For comparison, the data for Nb-doped BaTiO3, in which the diffusion is rate-controlled by titanium vacancies (ref 33), is also included.

Figure 7. Schematic representation of the transport mechanisms of oxygen and titanium vacancies in the TiO2 lattice. The VO and VTi denote oxygen and titanium vacancies, respectively, the singly ionized oxygen ion denotes a quasi-free electron hole, and trivalent titanium ion denotes a quasi-free electron.

4. Discussion 4.1. Kinetics. As seen in Figure 3 representing the changes of the electrical conductivity during oxidation at 1123 and 1323 K, the following two kinetic regimes may be distinguished:26,27 Kinetic regime I: As seen, isothermal increase of oxygen activity to p(O2) ) 75 kPa results in a rapid change of the electrical conductivity, which assumes a stable value after about 0.5 h. The literature data reported so far have been determined within this kinetic regime.13,14 It was shown that the electrical conductivity changes in kinetic regime I are determined by the changes of the concentration of oxygen vacancies, while the


Figure 8. Concentration of titanium vacancies as a function of oxygen activity corresponding to the n-p transition point for pure TiO2 (ref 25).

J. Phys. Chem. C, Vol. 112, No. 34, 2008 13253 the chemical diffusion coefficients related to kinetic regimes I and II is shown in Figure 6. As seen, this difference is about 4 orders of magnitude. Such a big difference is intriguing, since the ionic radius of Ti4+ ion is much smaller than the radius of O2- ion. Peterson, Sasaki, and Hoshino studied the diffusion of oxygen30 and cations of different ionic radius31,32 in rutile, TiO2. They observed that the diffusion of larger cations is faster than that of smaller cations. The tri- and tetravalent cations diffuse by an interstitialcy mechanism involving the simultaneous and cooperative motion of titanium and dopant ions. They reported that small trivalent ions avoid the open channels of the crystallographic structure, whereas larger divalent ions diffuse rapidly along these channels. The transport of oxygen vacancies and titanium vacancies is represented in Figure 7. As seen, the jump of a vacancy in one direction is equivalent to the jump of an ion in the opposite direction. A similar effect of the slow transport of titanium vacancies was observed for BaTiO3.33 The diffusion rate of titanium vacancies in the latter case is even slower than that for undoped TiO2. 4.2. Effect of Oxidation on Defect Disorder. In order to estimate the concentration of titanium vacancies in kinetic regime I, the theoretical dependence between the effective concentration of acceptors, A, and the p(O2) was determined using the relationship between the concentration of electrons and oxygen activity:25

n5 + An4 - Kin3 - 2K1p(O2)-1/2n2 - 3K2p(O2)-1n 4K3p(O2)-1 ) 0 (17)

Figure 9. Changes of the concentration of titanium vacancies for undoped TiO2 single crystal during prolonged oxidation at 1123 and 1323 K, including the data determined from the effect of p(O2) on the n-p transition (curves 1) and obtained by fitting of the theoretical dependence (eq 8) to experimental data (curves 2).

concentration of titanium vacancies remains practically constant.17,26,27 Kinetic regime II: When the specimen equilibrated in kinetic regime I is left over an extensive period of time, the electrical conductivity continues to change very slowly indicating that the system undergoes equilibration with a rate which is substantially slower than that in kinetic regime I. As seen in Figure 3, the electrical conductivity exhibits slow changes, which are measurable over several thousand of hours. The changes of the electrical conductivity in this regime are rate-controlled by the transport kinetics of titanium vacancies.27 Taking into account that equilibration in kinetic regime I allows the establishment of the uniform concentration of oxygen vacancies, while the concentration of titanium vacancies remains quenched, the effects in this regime are limited to the changes of the concentration of these defects (oxygen vacancies). However, oxidation in kinetic regime II results in the incorporation of titanium vacancies. Therefore, the studies of TiO2 in this regime allow us to determine the effect of the latter defects on properties of TiO2. So far, little is known about the effect of titanium vacancies on the charge transport in TiO2. As seen in Figure 3, the rate of the equilibration in kinetic regimes I and II, and the related transport of oxygen vacancies and titanium vacancies, are entirely different. The difference in

where K1, K2, K3, and Ki are equilibrium constants of the reactions 1–3 and 5, respectively. At the oxygen activity corresponding to the n-p transition the concentrations of electrons and electron holes are equal; therefore,

n ) Ki1/2

when

p(O2) ) p(O2)n-p

(18)

Consequently, for the n-p transition point eq 17 can be rewritten as

A)

2K1 1/2

Kip(O2)

+

3K2 3/2 Ki p(O2)

+

4K3 2 Ki p(O2)

(19)

For high-purity TiO2 it can be also assumed that

A ) 4[VTi′′′′]

(20)

Figure 8 shows thus obtained calibration curves in terms of log ′′′′ [VTi ] versus log p(O2)n-p. Assuming that the n-p transition occurs at the p(O2) value corresponding to S ) 0, the values of A determined after different time intervals of prolonged oxidation are represented by curves 1 in Figure 9. The second approach to determine A was based on fitting of the theoretical dependence for the electrical conductivity expressed by eq 8 to the experimental data (in kinetic regime I), which were determined at different time intervals during the prolonged oxidation. In this case both the concentrations of electrons and electron holes depend on A. Curves 2 in Figure 9 represent the dependencies obtained using this approach. The observed large discrepancy between the lines 1 and 2 related to 1323 K is due to the fact that the n-p transition at this temperature lies on the extreme part of the experimental range corresponding to high p(O2) values. As also seen, there is a good consistency between the lines related to 1123 K.


Bak et al.

The equilibrium in kinetic regime I corresponds to the annealing within ∼10 h when the fast defects (oxygen vacancies and titanium interstitials) reach equilibrium, while the concentration of titanium vacancies do not correspond to equilibrium due to the kinetic reasons. As seen in Figure 9, the concentration of titanium vacancies increases during the prolonged oxidation at 1123 K from 3 × 10-5 at 10 h to 1.1 × 10-4 after 2500 h. The effect observed during the prolonged oxidation at 1323 K is less substantial. 4.2.1. Oxidation at 1123 K. The effect of prolonged oxidation on the p(O2) corresponding to the n-p transition, denoted as p(O2)S)0, is shown in Figure 4. As seen, the prolonged oxidation results in a shift in the n-p transition point (determined at S ) 0) to lower p(O2), which corresponds to p(O2) ) 8.3 kPa, p(O2) ) 1.2 kPa, and p(O2) ) 0.7 kPa. The observed decrease of the p(O2) related to the n-p transition point is consistent with the increased concentration of titanium vacancies (acceptor-type defects), which are formed during the prolonged oxidation. A similar effect has been observed in polycrystalline TiO2.34 At this stage it is interesting to note that the electrical conductivity data for SC-TiO2 differ from those for PC-TiO2.35 The difference is due to the contribution of local electrical properties of grain boundaries in the polycrystalline specimen, which exhibit different defect disorder. It is clear that these data demonstrate that the incorporation of titanium vacancies makes it possible to process undoped TiO2 that exhibits p-type properties in the absence of foreign acceptortype dopant ions. This phenomenon has not been observed before. 4.2.2. Oxidation at 1323 K. As seen in Figure 5, the n-p transition point before and after prolonged oxidation is p(O2)S)0 ) 38.9 kPa and p(O2)S)0 ) 33.8 kPa, respectively. The related changes of the concentration of titanium vacancies as a function of the oxidation time are shown in Figure 9. As seen, the observed increase of the concentration of titanium vacancies is substantially less significant than that at 1123 K. This indicates that at 1323 K their concentration from the very beginning was closer to the equilibrium value. However, the accuracy of the determination of n-p transition, which in this case corresponds to the p(O2) at the edge of the experimental range, was substantially lower. 4.3. Electrical Conductivity Components. As shown above, the electrical conductivity data should be assessed in terms of all three types of charge carriers, which are associated with electrons (σn), electron holes (σp), and ions (σi). Therefore, the curvature of the log σ versus log p(O2) dependencies (Figure 5) observed in the high p(O2) regime should be associated with the gradual change of the electrical conductivity components related to electrons and electron holes (their concentrations at the n-p transition are practically equal). In order to determine the electrical conductivity components, a nonlinear least-squares analysis aimed at fitting eq 11 to the experimental data was used. The fitting consisted of adjustment of the components σ0n, σ0p, and σi until the term expressed by formula 21 reaches a minimum: k

∑ [σtot,j - σ0npj(O2)- 4 - σ0ppj(O2) 4 - σi] 1

1

2

(21)

j)1

where σtot is the electrical conductivity measured experimentally and j is the sequence number for each experimental point. 4.3.1. Oxidation at 1123 K. The electrical conductivity components at 1123 K, which were determined by the procedure described above, are shown in Figure 10 as a function of log p(O2). These data, which isolate the contributions of σn, σp, and

Figure 10. Effect of oxygen activity on the electrical conductivity components for undoped TiO2 single crystal determined at 1123 K in different stages of prolonged oxidation corresponding to 10 (no. 1), 1050 (no. 2), and 2470 h (no. 3).

Figure 11. Effect of prolonged oxidation at 1123 K on the ionic component of electrical conductivity for undoped TiO2 single crystal.

σi to σtot as a function of p(O2), allow the following conclusions to be made: (1) The n-p transition point, demarcated by the intersection between the log σn versus log p(O2) and log σp versus log p(O2) lines, decreases from p(O2)σ(min) ) 9.5 kPa to p(O2)σ(min) ) 1.2 kPa, where p(O2)σ(min) is the p(O2) corresponding to the minimum of the electrical conductivity. The related p(O2) data determined from thermoelectric power are plotted in Figure 4 as a function of time of prolonged oxidation at 1123 K. These data are reflective of the effect of titanium vacancies on the n-p transition point. As seen, the p(O2) data determined from the electrical conductivity are larger than those determined by the thermoelectric power (S ) 0). Assuming that at S ) 0 the concentrations of electrons and holes are the same, the discrepancy between these two sets of data are related to the difference between the mobility terms. (2) As seen in Figure 10, the prolonged oxidation results in an increase of the ionic conduction component. This effect is shown in Figure 11. This effect is consistent with the charge neutrality expressed by eq 9, which requires that the increased concentration of titanium vacancies during the prolonged oxidation is compensated by increased concentration of oxygen vacancies, which contribute most to the ionic conductivity component. The mobility data in Figure 12 were determined by fitting, to the experimental conductivity data, the theoretical dependence



Figure 12. Effect of prolonged oxidation on the mobility of electrons and electron holes (upper part) and the effective concentration of acceptors (lower part) for undoped TiO2 single crystal at 1123 K.

Figure 14. Effect of prolonged oxidation at 1323 K on the mobility terms for the electronic charge carriers (upper part) and the effective concentration of acceptors, A (lower part).

Figure 13. Effect of oxygen activity on the electrical conductivity components for undoped TiO2 single crystal determined at 1323 K before and after prolonged oxidation.

expressed by eq 8, which ignores the ionic conductivity term (σi ) 0). The fitting parameters, A (which determines n and p), µn, and µp, were found by applying a fitting procedure according to the Nedler-Mead simplex algorithm,36 which minimizes the following summation:

Figure 15. Arrhenius plots of the minimum of total electrical conductivity data for undoped TiO2 single crystal including the experimental data before and after prolonged oxidation.

conductivity, and wj are the standard weighting factors, which are defined as follows:37

k

∑ [(σth,j - σtot,j)wj]2

(22)

j)1

where σth is defined as a theoretical electrical conductivity expressed by eq 8, σtot are the experimental values of electrical

wj )

1 σtot,j

(23)

The concentrations of electrons and electron holes, corresponding to each experimental point σtot, were obtained by solving


Bak et al. the effect of titanium vacancies on the scattering mechanism decreases with temperature. 4.4. Band Gap. According to Becker and Frederikse39,40 the minimum of electrical conductivity, which corresponds to the n-p transition, is the following function of temperature, T: 1

( )

E0g β exp 2k 2kT

( )

σmin ) 2e(µnµpNnNp) 2 exp

(24)

where Nn and Np are the densities of states of electrons and electron holes, respectively, β is the temperature coefficient of the band gap, k is the Boltzmann constant, and E0g is the band gap at absolute zero. The term β is obtained from

Eg ) E0g - βT

Figure 16. Arrhenius plots of the minimum of the electronic component of electrical conductivity data for undoped TiO2 single crystal before and after prolonged oxidation.

eqs 1–7. The fitting procedure aimed at achieving the simplex size below a preselected value, which in our case was 10-8. The observed increase of A with the time of oxidation in Figure 12 is consistent with the increase of the concentration of titanium vacancies. As seen in that figure, the mobility of electrons increases with the time of prolonged oxidation from 0.65 × 10-5 m2 V-1 s-1 at 10 h to 0.8 × 10-5 m2 V-1 s-1 after 2470 h. At the same time the mobility of electron holes decreases with the time of prolonged oxidation from 0.76 × 10-5 to 0.67 × 10-5 m2 V-1 s-1. The observed effect of A on the mobility terms may be considered in terms of the following scenarios: (1) Effect of the crystal field induced by the changes of the lattice parameter. Although the effect of the concentration of cation vacancies on lattice parameter has been reported for other binary oxides, such as NiO,38 the effect for TiO2 requires experimental verification. (2) Effect of titanium vacancies on scattering of electronic charge carriers. The opposite effect for electrons and holes indicates that the nature of these interactions is electrostatic. 4.3.2. Oxidation at 1323 K. The electrical conductivity components as a function of oxygen activity within the n-p transition regime are shown in Figure 13. The n-p transition point, demarcated by the intersection between the log σn versus log p(O2) and log σp versus log p(O2) lines, decreases from p(O2)σ(min) ) 125 to 91 kPa. In analogy to the procedure applied at 1123 K, the values of A, µn, and µp were determined by fitting the theoretical dependence 8 to the experimental data. The determined effect of prolonged oxidation on the mobility terms and the quantity A is shown in Figure 14. The data in this figure indicate the following effects: (1) The prolonged oxidation results in an increase of the quantity A, which is consistent with the theoretical model assuming that oxidation leads to an increase of the concentration of titanium vacancies. (2) The mobility of electrons remains almost constant although, as seen in the enlargement, it slightly increases in analogy to the effect observed at 1123 K. (3) In analogy to the effect observed at 1123 K, the prolonged oxidation results in a decrease of the mobility term of electron holes. Although the observed effect of titanium vacancies on the mobility terms at 1323 K is consistent with that observed at 1123 K, the effects are substantially weaker. This indicates that

(25)

where Eg is the band gap at the test temperature. Figure 15 shows the Arrhenius plot of the minimum of the electrical conductivity, σmin (determined at 1123, 1273, and 1323 K), for the following sets of data: (1) The experimental data of the electrical conductivity before the prolonged oxidation. These data indicate that the band gap is E0g ) 3.2 eV. (2) The experimental data of the electrical conductivity after the prolonged oxidation. These data indicate that the band gap is E0g ) 3.0 eV. The values of Eg determined before and after prolonged oxidation, which are shown in Figure 15, suggest that titanium vacancies lead to reduction of the band gap. However, these data were determined from eq 24 by using the experimental values of the electrical conductivity, which according to Figures 10 and 13 include a substantial contribution of the ionic conductivity component. The data of the band gap determined from the electronic conductivity component alone are shown in Figure 16. As seen, in this case the band gap before and after the prolonged oxidation is 3.1 eV. These data, that are in a good agreement with the band gap data reported in the literature, indicate that the contribution of the ionic conductivity component leads to an apparent Eg value that is elevated compared to the real value. Consequently, prolonged oxidation leading to an increase of the concentration of titanium vacancies does not have an effect on the width of the band gap. 5. Conclusions The present work has assessed the effect of prolonged oxidation on semiconducting properties of undoped TiO2. The observed changes in properties are related to the formation of titanium vacancies. The present work has shown that the increase of the concentration of titanium vacancies leads to the following specific effects: (1) Change of the oxygen activity related to the n-p transition point to lower values. This effect paves the way for processing of undoped TiO2 that exhibits p-type properties without the need to incorporate aliovalent ions. The latter process may lead to undesired effects, such as decrease of the lifetime for the light-induced charge carriers and increased recombination.41 (2) Increase of the ionic component of the electrical conductivity. This effect is the direct consequence of the increased concentration of oxygen vacancies, which are mainly responsible for ionic charge transport. (3) Increase of the mobility of electrons and decrease of the mobility of electron holes. This effect is likely related to the changes of the crystal field induced by the variation of the lattice parameter.

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Effect of Prolonged Oxidation on Semiconducting Properties of

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