Charge Transport in Cr-Doped Titanium Dioxide - The Journal of

Apr 11, 2008 - The present work reports the effect of chromium on the mobility terms for electrons and electron holes for TiO2 at 1273 K. These data w...
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J. Phys. Chem. C 2008, 112, 7255-7262

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Charge Transport in Cr-Doped 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: July 19, 2007; In Final Form: January 10, 2008

The present work reports the effect of chromium on the mobility terms for electrons and electron holes for TiO2 at 1273 K. These data were determined by using the concentration data from the defect disorder diagram derived by the authors and the electrical conductivity data for Cr-doped TiO2 reported by Carpentier et al. [J. Phys. Chem. Solids 1989, 50, 145]. It is shown that chromium incorporates into the TiO2 lattice according to two different mechanism depending on chromium concentration. In the concentration range 1-3 atom %, chromium incorporation leads to the formation of acceptors, which are compensated by tri-valent titanium interstitials. However, in the range 4-5 atom %, the acceptor-type defects formed by chromium incorporated in the titanium sites are compensated by oxygen vacancies. The incorporation of chromium results in a relatively insignificant increase of the mobility of electrons from µn ) 0.5 × 10-5 m2 V-1 s-1 for undoped TiO2 to µn ) 1.3 × 10-5 m2 V-1 s-1. The incorporation of Cr results in a drop of the mobility of electron holes from µp ) 2.95 × 10-5 m2 V-1 s-1 for undoped TiO2 to µp ) 0.6 × 10-5 m2 V-1 s-1 for Cr-doped TiO2. The observed mobility changes are considered in terms of the Cr-induced structural changes of the TiO2 lattice.

1. Introduction A number of studies have been reported on electrical properties of TiO2, which are mainly based on the measurements of electrical conductivity.1-5 These data are then considered in terms of defect disorder models.6 Proper interpretation of the electrical conductivity data requires knowledge of both the concentration and the mobility terms. The concentration terms for TiO2 may be determined using the recently derived defect disorder diagrams.7 These concentration data were then used for the determination of the mobility terms8 from well-defined electrical conductivity data9 for TiO2 single crystal. The obtained mobility data, which will be shown below, indicate that electrons and electron holes are transported according to different mechanisms: Electrons. The mobility of electrons exhibits no temperature dependence. These data are consistent with the band transport mechanism. Electron Holes. The effect of temperature on the mobility of electron holes indicate that their transport occurs according to the hopping model. It is well-known that electrical conductivity is sensitive to the presence of aliovalent ions.6 This effect has been recently studied in details for both donor-type addition (Nb)10 and acceptor-type additions (Cr).11 It has been generally assumed that the effect of aliovalent ions on the electrical conductivity is mainly related to their effect on the concentration of electronic charge carriers, while the effect on the mobility terms is insignificant.6 Evaluation of the effect of composition on electrical properties requires knowledge of the experimental data at different concentrations of a specific aliovalent ion. Such data are † The present work was performed within the research and development program on solar-hydrogen. * Corresponding author. E-mail: [email protected]. Phone: +61 2 9385 6459. Fax: +61 2 9385 6467.

Figure 1. Effect of oxygen activity on the electronic component of electrical conductivity for undoped and Cr-doped TiO2 at 1273 K according to Carpentier et al.11 and for high purity TiO2 according to Nowotny et al.9 (solid line: total electrical conductivity, σtot; dashed line: electronic component of electrical conductivity, σn+p).

available for Cr-doped TiO2, which have been reported by Carpentier et al.11 Specifically, Carpentier et al.11 reported the effect of chromium on the electrical conductivity of TiO2 at 1273 K (Figure 1). These data, which correspond to the gas/ solid equilibrium, are suitable for an analysis in terms of defect chemistry. The purpose of this paper is the determination of the effect of chromium on the mobility of both charge carriers. This will

10.1021/jp075652p CCC: $40.75 © 2008 American Chemical Society Published on Web 04/11/2008

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Figure 2. Schematic representation of the effect of oxygen activity on the concentration of ionic and electronic defects for Cr-doped TiO2 within the p(O2) regimes governed by simplified charge neutrality conditions.9

be achieved by using the concentration of electronic charge carriers derived from defect disorder diagrams at the nominated concentration of acceptor-type ions7 and the electrical conductivity data reported by Carpentier et al.11

The strongly reduced regime corresponds to p(O2) ranging between 10-1 and 10-6 Pa at 1323 K.9 In reduced regime defect disorder is governed by the following ionic charge compensation9

[VO••] ) 2[V′′′′ Ti]

2. Effect of Chromium on Defect Disorder 2.1. Undoped TiO2. In strongly reduced conditions the predominant defects are doubly ionized oxygen vacancies, which are compensated by electrons.6,9 Then simplified charge neutrality is ••

2[VO ] ) n

(1)

In these conditions, the concentration of electrons is the following function of p(O2):9

n ) (2K1) p(O2) 1/3

-1/6

(2)

where K1 is the equilibrium constant of the reaction for the formation of oxygen vacancies

1 OO a VO•• + 2e′ + O2 2

(3)

(4)

Then, the concentration of electrons may be expressed as the following function of p(O2):9

n)

( ) K1Ki4 2K3

1/6

p(O2)-1/4

(5)

where K3 is the equilibrium constant of the reaction of titanium vacancies formation • O2 a 2OO + V′′′′ Ti + 4h

(6)

and Ki is the intrinsic electronic equilibrium constant, which may be represented by the expression

Ki ) np

(7)

At 1323 K this regime corresponds to the vicinity of the n-p transition.

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TABLE 1: Cr-Doped TiO2: the Concentrations of Electronic and Ionic Defects within the Regimes Corresponding to Different Oxygen Activities and Governed by Appropriate Simplified Charge Neutrality Conditions regime

extremely reduced n)3

charge neutrality defects n p [V′′′′ Ti ] [V•• O] [Ti••• i ]

[Ti••• i ]

strongly reduced n)2

1 (3K2)1/4p(O2)-1/4 Ki(3K2)-1/4p(O2)1/4 3K3K2/Ki4 K1(3K2)-1/2 (K2/27)1/4p(O2)-1/4

[V•• O]

reduced [Cr′Ti] ) 2

2 (2K1)1/3p(O2)-1/6 Ki(2K1)-1/3p(O2)1/6 (2K1)4/3K3/Ki4p(O2)1/3 (K1/4)1/3p(O2)-1/6 K2/(2K1)p(O2)-1/2

[V•• O]

3 (2K1/[Cr′Ti])1/2p(O2)-1/4 Ki([Cr′Ti]/2K1)1/2p(O2)1/4 4K12K3/(Ki4[Cr′Ti]2) [Cr′Ti]/2 K2([Cr′Ti]/2K1)3/2p(O2)-1/4

oxidized

strongly oxidized

[Cr′Ti] ) p

p ) 4 [V′′′′ Ti]

4 Ki/[Cr′Ti] [Cr′Ti] (K3/[Cr′Ti]4)p(O2) K1([Cr′Ti]/Ki)2p(O2)-1/2 K2([Cr′Ti]/Ki)3p(O2)-1

5 Ki(4K3)-1/5p(O2)-1/5 (4K3)1/5p(O2)1/5 (K3/256)1/5p(O2)1/5 K1/Ki2(4K3)2/5p(O2)-1/10 K2/Ki3(4K 3)3/5p(O2)-2/5

[Cr′Ti] ) 3 [Ti••• i ]

Charge neutrality n p [V′′′′ Ti ] [V••• O] [Ti••• i ]

(3K1)1/3[Cr′Ti]-1/3p(O2)-1/3 ([Cr′Ti]/3K2)1/3p(O2)1/3 (K3/Ki4)(2K2/[Cr′Ti])4/3p(O2)-1/3 K1([Cr′Ti]/2K2)2/3p(O2)1/6 [Cr′Ti]/3

K1, K2, K3 and Ki are the equilibrium constants of the following reactions, respectively: OO a V•• O + 2e′ + 1/2O2 TiO2 a Ti••• i + 3e′ + O2 • O2 a 2OO + V′′′′ Ti + 4h nil a e′ + h•

Equation 5 applies to the entire n-p transition regime, including the p-type charge transport in the vicinity of the n-p transition. In this case, the predominant electronic defects are electron holes and their concentration is the following function of p(O2):9

( )

ranges. These data may be used for a preliminary verification of defect disorder models. The expression 11 also indicates that the concentration of electrons is the following function of chromium concentration:

n ) const[Cr′Ti]-1/2

2 1/6

2K3Ki p) K1

p(O2)1/4

(8)

That regime may be achieved at the p(O2) values that are substantially larger than 105 Pa, while the experimental limit commonly achievable in laboratory conditions is p(O2) ) 105 Pa. On the other hand, as it will be shown in the present work, the p(O2) corresponding to the n-p transition decreases with the decrease of temperature. Therefore, the experimental data in this regime may be achieved only at relatively low temperature (below 1100 K). The following sections will consider possible mechanisms of chromium incorporation into the TiO2 lattice and the related effects on the concentration of electrons. 2.2. Cr-Doped TiO2. 2.2.1. Oxygen Vacancies Mechanism. Chromium incorporation may lead to the formation of oxygen vacancies according to the following reaction:

Cr2O3 a 2Cr′Ti + 3OO + VO••

(9)

where the charge compensation is expressed by the equation ••

[Cr′Ti] ) 2[VO ] Therefore

n)

( ) 2K1

[Cr′Ti]

1/2

(10)

(12)

where const includes all parameters. Therefore, relation 12 may be used for assessment of the mechanism of chromium incorporation into the TiO2 lattice. 2.2.2. Titanium Interstitials Mechanism. The incorporation of chromium into the TiO2 may also lead to the formation of titanium interstitials according to the following reaction:

1 3Cr2O3 + 2TiO2 a 6Cr′Ti + 2Tii••• + 12OO + O2 2

(13)

where the charge neutrality requires that

[Cr′Ti] ) 3[Tii•••] Therefore

n)

( ) 3K2

[Cr′Ti]

1/3

p(O2)-1/3

(14)

(15)

where K2 is the equilibrium constant for the formation of trivalent titanium interstitials

TiO2 a Tii••• + 3e′ + O2

(16)

According to the eq 15, this mechanism is consistent with the following dependence:

p(O2)-1/4

(11)

where K1 is the equilibrium constant of the reaction expressed by formula 3. The defect disorder regimes for Cr-doped TiO2, showing the effect of p(O2) on concentrations of both electronic and ionic defects, that is governed by simplified charge neutrality conditions, is represented schematically in Figure 2. The related expressions are outlined in Table 1 within the respective p(O2)

n ) const[Cr′Ti]-1/3

(17)

where const includes all parameters from eq 15. Therefore, relations 12 and 17 may be used for assessment of the mechanism of chromium incorporation when the effect of chromium on the electrical conductivity is known. 3. Experimental Section The polycrystalline TiO2 specimens were obtained by Carpentier et al.11 by hydrolysis of titanium chloride in ammoniacal

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σ ) e(nµn + pµp)

(18)

where e is elementary charge, n and p denotes the concentrations of electrons and electron holes, respectively, and µn and µp are the respective mobility terms. The concentrations terms, n and p, for the theoretical model were taken from the defect disorder diagrams, which were derived based on the defect equilibrium constants reported before7 and assumed values of the effective concentration of acceptors, A • A ) 4[V′′′′ Ti] + [A′] - [D ]

(19)

where [A′] and [D•] are the representative concentrations of single valent extrinsic acceptors and donors, respectively. Figures 3 and 4 represent the defect disorder diagrams for undoped and Cr-doped TiO2 (1 atom % Cr), respectively. As seen, the n-p transition points determined by these diagrams are consistent with those obtained experimentally (Figure 5). The mobility terms were determined as parameters of a fitting procedure according to Nedler-Mead simplex algorithm12 by minimizing the following summation:

∑j [(σth,j - σj)wj]2 Figure 3. Defect diagram for undoped TiO2 at 1273 K. The value of A ) 3.2 × 10-3 corresponds to the equilibrium concentration of titanium vacancies at this temperature.7

medium. They claim that their microprobe analysis did not detect any impurities beyond the detection threshold of 50 ppm. However, even this threshold number may be in question because the microprobe is designed for the determination of compositions at larger concentrations. Therefore, the microprobe does not seem to have a sufficient sensitivity for the detection of impurities at the ppm level. Moreover, while the effect of impurities on properties is less important for Cr-doped TiO2, it is essential to know the level of impurities in undoped material, which not necessarily is a pure TiO2. Carpentier et al.11 report that the specimens of Cr-doped TiO2 were prepared from a mixture of pure rutile and chromium nitrate. While they claim that their procedure leads to the formation of solid solutions (in the range of 1-5% of Cr), it is not clear to what extent the formed solid solution is homogeneous. The electronic component of electrical conductivity was measured by impedance spectroscopy method in the frequency range 10-105 Hz at 1273 K as a function of oxygen partial pressure in the range of 10-4-105 Pa.11 As seen in Figure 1, the absolute values of the electrical conductivity data reported by Carpentier et al.11 for their undoped TiO2 differ from those for high purity TiO2 single crystal.9 One may expect that this difference results mainly from the level of impurities in the specimens of undoped TiO2 of Carpentier et al.11 4. Procedure and Results The procedure, which is applied for the determination of the mobility terms of electrons and electron holes is based on a comparative analysis of the experimental data for electrical conductivity on one side and the theoretical model of the electrical conductivity, which is based on the following expression:

(20)

where the theoretical electrical conductivity σth is defined by eq 18, σj are experimental values of electrical conductivity, and w is a standard weighting factor, which was assumed as follows:13

w)

1 σ

(21)

The fitting procedure aimed at reducing the simplex size below a pre-selected value, which in our case was 10-8. The fitting results for undoped TiO2 and for two concentrations of chromium are shown as solid lines in Figure 5. The mobility terms determined from the electrical conductivity data of Carpentier et al.11 for both undoped and Cr-doped TiO2 are shown in Figure 6 as a function of chromium content, along with the data determined from the electrical conductivity data for high purity TiO2 single crystal.8 The electrical conductivity exponent of p(O2) for reduced TiO2, which corresponds to pure n-type regime, may be expressed by the following general form:

σ ) σ0np(O2)1/mσ

(22)

where the 1/mσ is the p(O2) exponent determined from the electrical conductivity, which is sensitive to defect disorder. The procedure of its determination has been reported elsewhere.9 5. Discussion 5.1. Effect of Oxygen Partial Pressure on Electrical Conductivity. The experimental data of Carpentier et al.11 on the effect of oxygen activity on the electrical conductivity for both undoped and Cr-doped TiO2 at 1273 K are shown in Figure 1, along with the electronic component of data reported for high purity TiO2 single crystal.9 These data indicate the following: 1. The slope of the log σ vs log p(O2) dependence for the data of Carpentier et al.11 for undoped TiO2 and Cr-doped TiO2 is -1/6 and -1/4, respectively. 2. The absolute values of the electrical conductivity data reported by Carpentier et al.11 for undoped TiO2 differ from

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Figure 6. Mobility terms for undoped and Cr-doped TiO2.

Figure 4. Defect diagram for chromium doped TiO2 (1 atom %) at 1273 K. The value of A involves the components related to the concentrations of both titanium vacancies and chromium ions located at the titanium sites.

which is unknown, and the content of the impurities in the single crystal (21 ppm of aliovalent cations).9 3. The slope of the log σ vs log p(O2) dependence for undoped TiO2 according to Carpentier et al.11 (1/mσ ) -1/6) is consistent with the slope reported for high purity single crystals in the n-type regime. 4. Addition of chromium results in a shift of the conductivity minimum, that is related to the n-p transition, from ∼105 Pa for undoped TiO2 to ∼103 Pa for Cr-doped TiO2 at 5 atom %. This shift is consistent with the substitutional mechanism of chromium incorporation leading to the formation of acceptortype centers. 5. The effect of p(O2) on the electrical conductivity for Crdoped TiO2 leads to the log σ vs log p(O2) slope (1/mσ ) -1/ 4), which is consistent with the defect disorder model represented by eq 11, indicating that the acceptors-type defects formed by chromium incorporation are compensated by oxygen vacancies. These data suggest that the defect disorder is governed by the charge neutrality condition (10) in the entire range of chromium content. It is important to note that the defect disorder model represented by expression 11 requires knowledge of oxygen activity, rather than oxygen partial pressure reported by Carpentier et al.11 Therefore, this model requires a verification. This is possible by using the defect disorder models based on the dependence of the electrical conductivity data as a function of chromium concentration, which are expressed by relations 12 and 17. In order to verify expressions 12 and 17, the electrical conductivity components related to electrons and electron holes should be determined. According to the general expressions, the electrical conductivity in the n-p transition regime may be expressed as the following function of the conductivity components related to electrons, σn and electron holes σp:

σ ) σn + σ p

Figure 5. Effect of oxygen activity on the electrical conductivity for undoped and Cr-doped TiO2 (1 and 5 atom % Cr) at 1273 K; the data points are according to Carpentier et al.,11 the solid lines represent the theoretical model expressed by eq 18.

those for high purity TiO2 single crystal at the same temperature.9 This discrepancy is most likely related to the content of impurities in the undoped (but not pure) specimen of Carpentier,

(23)

Taking into account the effect of oxygen activity on the concentration of electrons, both for undoped and Cr-doped TiO2, which are expressed by relations 2 and 11, and formula 7, eq 23 may be expressed in the following form:9

σ ) σ0np(O2)-1/4 + σ0pp(O2)1/4

(24)

where σ0n and σ0p are the parameters independent of oxygen activity. The above equation is valid for both undoped and chromium doped TiO2.

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Figure 7. Plot of the electrical conductivity components related to electrons, σn, and electron holes, σp, determined from the data of Carpentier et al.,11 as a function of oxygen activity.

Figure 9. Electrical conductivity component related to electrons, σn, as a function of chromium content at 1273 K and several oxygen activities.

Figure 8. Oxygen activity corresponding to the minimum of electrical conductivity as a function of chromium content, derived from the data of Carpentier et al.11

It should be noted that both electrical conductivity components, which are associated with electrons (σn), and electron holes (σp), affect the curvature of the log σ versus log p(O2) dependencies observed in the high p(O2) regime. Therefore, in order to determine the electrical conductivity components, a nonlinear least-squares analysis aimed at fitting eq 24 to experimental data was used. The fitting consists of adjustment of the components σ0n and σ0p, at which the term k

(σtot,j - σ0np(O2)-1/4 - σ0pp(O2)1/4)2 ∑ j)1

(25)

reaches a minimum. In the above expression, σtot is the electrical conductivity measured experimentally and j is the sequence number for each experimental point determined at a certain oxygen activity p(O2). The determined data at 1273 K are shown in Figure 7. These data isolate the contributions of σn and σp to the conductivity data determined experimentally as a function of p(O2). Thus determined effect of chromium on the n-p transition point is in Figure 8. 5.2. Effect of Chromium Concentration on Electrical Conductivity. The mechanism of chromium incorporation may be verified by plotting the log σn vs log [Cr′Ti] dependence. As seen in Figure 9, the value of the slope of this dependence,

1/mσ, depends on chromium content. Specifically, the slope is -1/3.3 in the range 1-3 atom % of chromium and -1/2 in the range 4-5 atom % of Cr. The slope 1/mσ ) -1/3.3 is consistent with the mechanism of chromium incorporation according to reaction 13, while the slope 1/mσ ) -1/2 is consistent with the oxygen vacancy mechanism represented by formula 9. These data indicate that the mechanism of chromium incorporation into the TiO2 lattice depends on Cr concentration. Below 4 atom %, the incrporation of chromium leads to the formation of titanium interstitials, while above 4 atom %, the negative charge resulting from chromium incorporation is compensated by oxygen vacancies. The change of the mechanism of chromium incorporation, that is related to the change of the slope in Figure 9, may be considered in terms of the effect of chromium concentration on the formation energy of titanium interstitals and oxygen vacancies. Namely, chromium incorporation, leading to the formation of titanium interstitals, results in an increase of the formation energy of these defects due to increased lattice strain related to the increased concentration of titanium interstitials. This is the most probable reason why the formation of oxygen vacancies is more favorable above 4 atom % of chromium. However, the observed change of the slope of log σn vs log [ Cr′Ti] dependence is deduced from one experimental point only, therefore this effect requires verification. As seen there is an apparent conflict between the model based on the p(O2) exponent, suggesting that condition 10 is valid in the entire range of chromium content and p(O2) values, and the model based on exponent related to Cr concentrations, indicating that the data in the range 1 atom % < [Cr′Ti] < 3 atom % are governed by condition 14, and the data at [Cr′Ti] > 3 atom % are consistent with condition 10. In considering the reasons of

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Figure 10. Oxygen activity (determined electrochemically) vs oxygen partial pressure (determined from flow rates) showing the discrepancy between these two quantities in the experimental conditions applied in our previous work.9

this conflict, it is important to note that the model based on chromium concentration, expressed by relations 12 and 17, is more reliable than the model expressed by eq 11. Specifically, the model expressed by eq 11, which is governed by condition 10, requires knowledge of oxygen activities, which are unknown. Another approach to explain the observed change in the mechanism of chromium incorporation could be related to the effect of chromium on the mobility term. This effect, however, should be ruled out because, as seen in Figure 6, chromium content has little effect on the mobility term in the concentration range 3-5 atom %. The data of oxygen partial pressure may differ substantially from those of oxygen activity. The difference between these two terms, in the range corresponding to higher values of oxygen activities, is represented in Figure 10. The oxygen partial pressure data in Figure 10 were determined from the ratios of gas flow rates set by mass flow controllers, and the data of oxygen activity were determined by using a zirconia-based electrochemical sensor.14 As seen, the values of oxygen activity are lower than those of oxygen partial pressure by 20-30%. The difference between oxygen activity and oxygen partial pressure may be considered in terms of the activity coefficient. There have been a number of defect models reported in the literature, which are based on oxygen partial pressure.1-4,6 However, as seen from Figure 10, the values of oxygen partial pressure may differ from oxygen activity. Therefore, the defect disorder models derived from the dependence of electrical properties vs oxygen partial pressure must be considered as tentative models, which require a verification. On the other hand the defect models based on either (i) oxygen activity or (ii) the concentration of dopants, are much more reliable. Consequently, we assume that the mechanism of chromium incorporation determined from the slope log σn vs log [Cr′Ti] is more reliable than that determined from the slope log σ vs log p(O2). In view of the data obtained in the present work, the defect disorder model outlined in Table 1 requires a modification concerning the relationships in the reduced regime (column 3). Specifically, the relationships in top part of Table 1 are valid at [Cr′Ti] > 3 atom %, while the relationships at 1 atom % < [ Cr′Ti] < 3 atom % are outlined in the bottom part of Table 1. 5.3. Effect of Chromium on the Mobility Term. Figure 6 shows the effect of chromium on the mobility term for TiO2. The mobility data for Cr-doped TiO2 in Figure 6 are shown

Figure 11. Arrhenius plots of the mobility terms determined in the present work along the data reported in the literature.1-5

along the mobility data for both (i) the data of undoped TiO2 reported by Carpentier et al.11 and (ii) the data for high purity TiO2.8 As seen, the mobility of both charge carriers exhibits a little dependence on the content of Cr for Cr-doped TiO2. However, the mobility data for undoped TiO2, determined from the electrical conductivity data of Carpentier et al.,11 are different than those for Cr-doped TiO2. The difference is more significant for electron holes. The difference may be considered in terms of the effect of the established effect of doping on the crystalline structure and the related changes of the lattice parameter. Such effect has been reported for both Li-doped NiO15 and Cr-doped CoO.16 The related changes in the crystal field seems to be responsible for the effects established in the present work. An alternative explanation could be considered in terms of the model reported by Martin17 that is based on the assumption of local interactions of the charge carriers with the ions of the dopant. As seen in Figure 6, the mobility term for undoped TiO2 (µn ) 0.5 × 10-5 m2 V-1 s-1) is smaller that that for Cr-doped TiO2 at 1 atom % of Cr (1.1 × 10-5 m2 V-1 s-1) by the factor of about two. However, the difference between the mobility term for high purity TiO2 and that for Cr-doped TiO2 is less significant. The increase of chromium content above 1 atom % also has a little effect on µn. In conclusion, while the effect of chromium on the mobility of electrons is measurable, the related changes are insignificant. The effect of chromium on the mobility of electron holes is much stronger. This term varies between 2.9 × 10-5 m2 V-1 s-1 for undoped TiO2 (according to the data of Carpentier et al.),11 and 0.7 × 10-5 m2 V-1 s-1 for Cr-doped TiO2 at 1 atom %. However, the mobility term for pure TiO2 (according to the data of Nowotny et al.),8 is µp ) 1.5 × 10-5 m2 V-1 s-1. In analogy to electrons, the mobility term for holes is almost independent of chromium content for [Cr′Ti] > 1 atom %.

7262 J. Phys. Chem. C, Vol. 112, No. 18, 2008 The mobility terms determined in the present work for Crdoped TiO2 are shown in Figure 11 along the literature data reported for undoped TiO2.

Nowotny et al. Acknowledgment. This work was supported by Brickworks Ltd, Mailmasters Pty Ltd., and Avtronics (Australia) Pty Ltd. The support of the Australian Research Council is also acknowledged.

6. Conclusions The present work resulted in the following findings: 1. The charge compensation of defects in Cr-doped TiO2 depends on Cr content. Specifically, the negative charge formed by Cr-induced acceptors is compensated by the following defects: (a) Tri-valent titanium interstitials. These ions are the predominant species in the range 1-4 atom % of Cr. (b) Oxygen vacancies. These defects are the predominant defects in the range 4-5 atom % of Cr. 2. The change of composition for Cr-doped TiO2 does not lead to substantial changes in the mobility of electronic charge carriers. The following specific effects are observed: (a) Electrons. The changes in the mobility of electrons vs Cr content are insignificant in the entire range of composition. (b) Electron holes. The mobility of electron holes is practically independent of chromium content for Cr-doped TiO2 in the range 1-5 atom % Cr. The most substantial change of the mobility term is observed between the undoped (pure) TiO2 and the Cr-doped TiO2 of the lowest chromium content (1 atom % of Cr). The difference in the determined mobility terms between the pure TiO2 specimen and the undoped (but not pure) TiO2 seems to be related to the impurity level present in undoped specimen. Effects 1 and 2, which are related to different compositions, should be therefore considered as independent.

References and Notes (1) Blumenthal, R. N.; Kirk, J. C., Jr.; Hirthe, W. M. J. Phys. Chem. Solids 1967, 28, 1077. (2) Bransky, I.; Tannhauser, D. S. Solid State Comm. 1969, 7, 245. (3) Odier, P.; Baumard, J. F.; Panis, D.; Anthony, A. M. J. Solid State Chem. 1975, 12, 324. (4) Marucco, J. F.; Gautron, J.; Lemasson, P. J. Phys. Chem. Solids 1981, 42, 363. (5) Bak, T.; Nowotny, J.; Rekas, M.; Sorrell, C. C. J. Phys. Chem. Solids 2003, 64, 1069. (6) Kofstad, P. Nonstoichiometry, Diffusion and Electrical ConductiVity of Binary Metal Oxides; Wiley: New York, 1972. (7) Bak, T.; Nowotny, J.; Nowotny, M. K. J. Phys. Chem. B 2006, 110, 21560-67. (8) Nowotny, J.; Nowotny, M. K.; Sheppard, L. R. Charge Transport in Titanium Dioxide. J. Phys. Chem. C 2008, in submission. (9) Nowotny, M. K.; Bak, T.; Nowotny, J. J. Phys. Chem. B 2006, 110, 16270-16282. (10) Sheppard, L. R.; Bak, T.; Nowotny, J. J. Phys. Chem. B 2006, 110, 22447. (11) Carpentier, J. L.; Lebrun, A.; Perdu, F. J. Phys. Chem. Solids 1989, 50, 145. (12) GSL-GNU Scientific Library, www.gnu.org/software/gsl. (13) de Levie, R. Crit. ReV. Anal. Chem. 2000, 30, 59-74. (14) Fabry, P.; Siebert, E. In The CRC Handbook of Solid State Electrochemistry; Gellings, P. J., Bouwmeester, H. J. M., Eds).; CRC Press: Boca Raton, FL, 1996; pp 329-369. (15) Bielanski, A.; Deren, J.; Dyrek, K.; Dziembaj, R.; Nowotny, J.; Wenda, J. Bull. Polon. Acad. Sci. Ser. Sci. Chim. 1970, 17, 357. (16) Kluz, Z.; Nowotny. J.; Sikora, I.; Wagner, J. B., Jr. Bull. Polon. Acad. Sci. Ser. Sci. Chim. 1979, 27, 867. (17) Martin, M. Phys. Chem. Chem. Phys. 2004, 6, 3627.