Effect of Hydrogen on Semiconducting Properties of TiO2 Single

ARTICLE pubs.acs.org/JPCC

Effect of Hydrogen on Semiconducting Properties of TiO2 Single Crystal. Jonker Analysis Janusz Nowotny* Solar Energy Technologies, University of Western Sydney, Locked Bag 1797, Penrith, NSW 2751, Australia ABSTRACT: The present work considers the semiconducting properties of TiO2 single crystal in terms of the Jonker formalism (Philips Res. Rep. 1968, 23, 131), which is based on both electrical conductivity and thermoelectric power data. The Jonker analysis is applied for high-purity TiO2 single crystal at elevated temperatures (10731323 K), in reducing and oxidizing conditions imposed by the hydrogenargon mixture (1013 Pa < p(O2) < 105 Pa) and oxygenargon mixture (10 Pa < p(O2) < 105 Pa), respectively. It is shown that the semiconducting properties of TiO2 equilibrated in oxidizing and reducing conditions are distinctively different in terms of the band gap and charge transport. The experimental data obtained in oxidizing conditions at 1223 K are used for the determination of the band gap according to the hopping and band model, respectively: Eg = 3.38 1.1 103T (eV) and Eg = 3.46 1.4 103T (eV). The semiconducting properties of TiO2 in reducing conditions are considered in terms of the effect of hydrogen on the formation of 0 00 0 defect complexes {VTi 3 4OH•} in the bulk phase, which are responsible for reduction of the band gap by approximately 0.1 eV. The discrepancy between the data observed for the TiO2 single crystal (this work) and the data observed for polycrystalline TiO2 (reported before) is considered in terms of the effect of the local defect disorder, and the related semiconducting properties, of grain boundaries. The data obtained in the present work may be used for engineering of TiO2 with enhanced performance in solar energy conversion.

1. INTRODUCTION Titanium dioxide, TiO2, is the promising candidate for photocatalytic water purification and photoelectrochemical water splitting.13 Its performance in both applications is closely related to semiconducting properties, which, on the other hand, are associated with defect disorder.4 Therefore, its enhanced performance may be achieved by the modification of semiconducting properties using defect engineering.4 The studies on semiconducting properties of oxide semiconductors, including TiO2, frequently aim to establish the dependence between oxygen activity and defect-related properties, such as electrical conductivity and thermoelectric power on one hand and oxygen activity on the other hand59 These may be represented by the expressions 1 ∂ log σ ¼ mσ ∂ log pðO2 Þ

ð1Þ

1 k ∂S ¼ mS e ∂ log pðO2 Þ

ð2Þ

where σ is electrical conductivity, S is thermoelectric power, mσ and mS denote the parameters related to electrical conductivity and thermoelectric power, respectively, p(O2) is oxygen activity, e denotes elementary charge, and k is Boltzmann constant. The parameters mσ and mS can be considered in terms of defect disorder.10 According to the theory of defect chemistry, the predominant defects in TiO2 in reducing conditions are oxygen vacancies, r 2011 American Chemical Society

which are compensated by electrons.4 Then the log σ vs log p(O2) slope is 1/mσ = 1/6 and the S vs log p(O2) slope is 1/mS = 1/6 for the electrical conductivity and thermoelectric power, respectively. The efforts to verify the defect disorder models resulted in a collection of conflicting experimental data showing that the slope log σ vs log p(O2) scatters between 1/6 and 1/4.58 This scatter is related to the following effects: different content of impurities; error in the determination of oxygen activity; error in the determination of electrical properties; departure from equilibrium. While the effect related to impurities may be reduced by using high-purity specimens, the effect associated with oxygen activity may be minimized when using so-called Jonker analysis.11 Such analysis requires, however, that both electrical conductivity and thermoelectric power be determined simultaneously in equilibrium. The concept of the Jonker analysis for oxide semiconductors is based on the assumption that the semiconducting quantities, which are the parameters in the Jonker formalism, such as mobility terms, kinetic constants, and density of states, are independent of oxygen activity.11 In this case the application of the Jonker analysis does not require knowledge of oxygen activity data, if both electrical properties are determined simultaneously in equilibrium. Recent studies of polycrystalline TiO2 using the Jonker analysis indicate that the experimental data for reduced TiO2 Received: May 3, 2011 Revised: July 25, 2011 Published: August 06, 2011 18316

dx.doi.org/10.1021/jp204072z | J. Phys. Chem. C 2011, 115, 18316–18326

The Journal of Physical Chemistry C

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Table 1. Equilibrium Constants of Defect Reactions for TiO24 (square brackets denote concentrations, n and p denote concentration of electrons and electron holes, respectively) reaction 1 2 3 4 5

1 0 OO h V•• O + 2e + /2O2 ••• 2OO + TiTi h Tii + 3e0 + O2 + 4e0 + O2 2OO + TiTi h Ti•••• i 0000 O2 h 2OO + VTi + 4h• • 0

nil h e + h

ΔH° (kJ/mol)

constant K1 = K2 = K3 = K4 =

2 1/2 [V•• O]n p(O2) ••• 3 [Tii ]n p(O2) 4 [Ti••• i ]n p(O2) 0000 4 [VTi ]p p(O2)1

Ki = np

ΔS° (J/(mol 3 K))

493.1

106.5

879.2 1025.8

190.8 238.3

354.5

202.1

222.1

44.6

ln K = (ΔS°/R) (ΔH°/RT)

have the tendency to depart from the typical Jonker’s pear-type dependence derived for oxidized TiO2.12 The departure was considered in terms of the effect of hydrogen on semiconducting properties of reduced TiO2. While the departure is not substantial, the observed effect requires a verification. The aim of the present work is to verify the effect observed for polycrystalline TiO2. Assuming that this effect may be related to grain boundaries, the present work is performed using the TiO2 single crystal, which is free of grain boundaries. We anticipate that the studied semiconducting properties can be considered in terms of one of the following scenarios: • If the effect observed for the polycrystalline TiO2 is determined by grain boundaries, then semiconducting properties of TiO2 single crystal are expected to be free of the observed discrepancy in the character of the thermopower versus electrical conductivity dependence for oxidation and reduction. • If the effect observed for the polycrystalline TiO2 is related to the bulk phase, then the observed discrepancy in semiconducting properties for oxidized and reduced TiO2 single crystal is expected to be more substantial. The specific aim of the present work is to consider the effect of hydrogen (protons) on properties of reduced TiO2 single crystal. This effect is important for the following reasons: • The environment of TiO2 as photocatalyst and photoelectrode is water. Consequently, TiO2 remains in equilibrium with the protons, which are present in the aqueous environment. • The hydrogen/water vapor mixture has been frequently used for the imposition of very low oxygen activity. It is important to know if the effect of hydrogen is limited to the imposition of reduced oxygen activity in the gas phase or hydrogen also affects the chemical composition of TiO2 and the related semiconducting properties.

2. DEFINITION OF TERMS 2.1. Nonstoichiometry. Titanium dioxide, TiO2, is a nonstoichiometric compound, which is commonly considered as oxygen deficient (TiO2x).10 Recent studies show that strongly oxidized TiO2 may exhibit a p-type charge transport that is associated with the presence of titanium vacancies.4,13 The chemical formula of titanium dioxide reflecting the nonstoichiometry in both oxygen and titanium sublattices is better represented as Ti1(yO2x.4 Therefore, the formula TiO2 should be considered as a symbolic representation of a wide range of compositions related to the wide range of the parameters of y and x. The semiconducting properties of TiO2 are closely related to oxygen activity and the titanium-to-oxygen ratio.4,10 The associated defect disorder may be considered as the materials-related property. The related parameters y and x can be imposed at elevated temperatures in specific conditions of temperature and oxygen activity.

The defect disorder model may be derived from isothermal changes of electrical properties, such as electrical conductivity8 and thermoelectric power,9 as a function of oxygen activity. It has been shown that these two properties for TiO2 single crystal and polycrystalline specimen are different, even if the specimens are equilibrated in identical conditions. The difference is reflective of the effect of grain boundaries.14 The studies of both electrical conductivity and thermoelectric power at elevated temperatures indicate that defect disorder of TiO2 involves the following defects:4,13 electronic defects (electrons, e0 , and electron holes, h•); doubly ionized oxygen the predominant defects; tetravalent vacancies, V•• O, these0 00are 0 titanium vacancies, VTi , their concentration is comparable to that of oxygen vacancies; tetra- and trivalent titanium interstitials and Ti••• (Ti•••• i i , respectively). These defects are formed as a result of the reaction between the TiO2 lattice and oxygen in the gas phase. The defect equilibria, represented according to the Kr€ogerVink notation,15 and the related equilibrium constants are shown in Table 1. The lattice charge neutrality condition of TiO2 may be expressed as 0000

••• •••• 2½V •• O þ 3½Tii þ 4½Tii þ p ¼ n þ 4½V Ti

ð3Þ

In oxidizing and reducing conditions the condition expressed by eq 3 may be reduced to the following simplied forms, respectively 0000

½V •• O ¼ 2½V Ti

ð4Þ

and n ¼ 2½V •• O

ð5Þ

In contact with water, the properties of TiO2 must be considered in terms of the effect of protons on defect disorder and the related semiconducting properties. Then the charge neutrality assumes the form ••• •••• • 2½V •• O þ 3½Tii þ 4½Tii þ ½H þ p 0000

¼ n þ 4½V Ti

ð6Þ

The defect diagrams for TiO2 in presence of water were reported by Norby.16 It appears that the concentration of defects, including protons, is a complex function of both oxygen and water vapor activities. It has been shown that the propagation of protons in the rutile structure is very fast.17,18 2.2. Electrical Conductivity. The common way of the verification of defect disorder models of metal oxides is based on the determination of the dependence of electrical conductivity, σ, versus oxygen activity, p(O2) (see eq 1). The log σ vs log p(O2) dependence for an amphoteric oxide semiconductor (that 18317

dx.doi.org/10.1021/jp204072z |J. Phys. Chem. C 2011, 115, 18316–18326


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2.4. Electrical Conductivity vs Thermopower. As seen in the upper part of Figure 1, the nonlinear dependence of log σ vs log p(O2) within the minimum of the electrical conductivity is a result of the competitive effect related to both electronic charge carriers (electrons and electron holes) on conduction. The character of the changes of electrical conductivity and thermoelectric power as a function of p(O2), which is shown in Figure 1, represents the symmetrical semiconductor; when the p(O2) values corresponding to σmin and S = 0 are identical. A typical Jonker plot of the thermoelectric power, S, as a function of log σ (where σ is electrical conductivity), which exhibits a pearlike shape is described by the equation11 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! σ 2min k σ σ2 S ¼ ( B 1 2 ln 1 ( 1 min þ D e σ min σ σ2

ð7Þ where B¼

k Eg þ An þ Ap 2e kT

ð8Þ

and D¼ Figure 1. Schematic representation of the effect of oxygen activity on electrical conductivity and thermoelectric power of oxide semiconductors within np transition.

exhibits np transition) is represented schematically in the upper part of Figure 1. When the mobility terms for both electronic charge carriers are equal, the characteristic point of the log σ vs log p(O2) dependence corresponds to the np transition when σ = σmin (where σmin is the minimum of electrical conductivity). The slopes on log σ vs log p(O2) dependences in both n- and p-type regimes are described by eq 1. As seen in Figure 1, only the linear part of the dependence is determined by one type of charge carriers (the nonlinear part is related to both electrons and holes). 2.3. Thermoelectric Power. Thermoelectric power (termed also Seebeck coefficient or thermopower), is a basic quantity in the characterization of electronic structure of materials as well as their thermoelectric properties. This quantity may be related to the concentration of electronic charge carriers.9 On the other hand the electrical conductivity data are determined by the concentration and the mobility terms. Therefore, combined thermoelectric power and electrical conductivity data can be used for the determination of the mobility ratio. In analogy to the relation 1, defect disorder models of metal oxides may also be verified using the dependence of thermoelectric power vs oxygen activity, p(O2) (see eq 2).9 Schematic representation of the plot of S vs log p(O2), in both n- and p-type regimes, is shown in the lower part of Figure 1. The characteristic point of the S vs p(O2) dependence is when S = 0. When the charge transport mechanism in both regimes is the same (symmetrical semiconductor), the point at S = 0 corresponds to the np transition. As seen in Figure 1, the linear dependence of S vs log p(O2), that is related to one type of charge carriers, is observed only in extremely reducing and extremely oxidizing conditions.

A k μp Np e p ln 2e μn Nn eAn

ð9Þ

where Eg is the band gap energy, An and Ap are the kinetic terms, Nn and Np are densities of states, μn and μp are the mobility terms of charge carriers and the subscripts n and p correspond to electrons and electron holes, respectively, k is the Boltzmann constant, and e is elementary charge. The Jonker equation (7) may be transformed into a linear system19 Y ¼ BX þ D

ð10Þ

where

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σmin 2 X ¼ ( 1 σ Y ¼S þ

k 1 þ X ln pffiffiffiffiffiffiffiffiffiffiffiffiffi e 1 X2

ð11Þ

ð12Þ

Graphical determination of the parameters, σmin, B, and D requires knowledge of the experimental data within a wide range of oxygen activities. On the other hand, the linear equation (10) can be fitted to the experimental data only when the data around the np transition allow the determination of σmin. It is essential to note that the transformation of the basic Jonker equation (7) into the linear system (10) requires knowledge of the minimum value of the electrical conductivity, σmin (related to the np transition point).

3. SHORT LITERATURE OVERVIEW The Jonker analysis can be applied for amphoteric oxides that exhibit both n- and p-type properties, such as CoO,19 BaTiO3,20 oxide superconductors,21 CaTiO3,22 as well as TiO2.23 Su et al.21 reported the electrical properties, including both electrical conductivity and thermoelectric power, for several oxide superconductors, including YBa2Cu3O6+y and EuBa2Cu3O6+y, as well as nonsuperconducting system La3Ba3Cu3O6+y. They observed that these combined data determined in the range 9231123 K exhibit 18318



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Figure 2. Isothermal plots of thermoelectric power as a function of log σ for undoped BaTiO3 in the range 10901310 K20.

Figure 3. Linearized Jonker plot for undoped BaTiO3 in the range 10901310 K.20

the Jonker-type behavior confirming their semiconducting properties (band gaps are of the order of 0.5 eV). The studies of electrical properties of CaTiO3, involving both electrical conductivity and thermoelectric power (9731323 K), have shown that this compound exhibits both n- and p-type regimes.24,25 These data indicate that there is a considerable discrepancy between the np transition point determined using the electrical conductivity and thermoelectric power data. The Jonker analysis of these data shows that the mobility of electrons is substantially larger than that of electron holes.22 The observed discrepancy is beyond the range that can be explained by different charge transport mechanisms. The electrical properties of BaTiO3 may serve as an example of the application of the Jonker analysis in the determination of semiconducting properties, which are uniform within the entire range of oxygen activities.20 The Jonker plot, represented by the thermoelectric power vs electrical conductivity dependence in the range 10901310 K, is shown in Figure 2. As seen, the data exhibit an outstanding fit to the Jonker equation, represented by the expression (7) within both n- and p-type regimes. The experimental data also fit very well to the linear system, expressed by eq 10, which is represented in Figure 3. As seen, the electrical conductivity and thermopower data for undoped BaTiO3 cover both n- and p-type regimes symmetrically. The effect of temperature on the band gap results in the linear relationships

critical points of the Jonker pearlike dependence for oxidized TiO2 are different than that for reduced TiO2.12 In order to clarify the difference, studies are needed for the specimen that is free of the effects resulting from impurities and grain boundaries. Therefore, the aim of the present work is to verify the semiconducting properties for high-purity TiO2 single crystal. For the sake of comparison with the data reported for polycrystalline TiO2, the present work is performed in identical conditions, including both oxidized and reduced TiO2.

Eg ðTÞ ¼ 2:9 3:2 105 T ðeVÞ

ð13Þ

4. EXPERIMENTAL High-purity single-crystal TiO2 was grown by the Verneuil method. The concentration of cation impurities was limited to 32 ppm. The rutile structure was identified using X-ray diffraction. Measurements of both electrical conductivity, σ, and thermoelectric power, S, were taken simultaneously on the 2 mm 3 mm 10 mm single crystal slab. The details of the measurements of the electrical conductivity and thermoelectric power are reported in refs 8 and 9, respectively. The oxygen activity in the reaction chamber was imposed using the flow of the following gases (flow rate 100 mL/min): oxidation regime, argon/oxygen mixture; reduction regime, H2/ H2O mixture, diluted with argon. The temperature, which was monitored during the entire experiments, remained constant within (0.5 K. Details are reported elsewhere.8,9

Eg ðTÞ ¼ 2:9 2:47 104 T ðeVÞ

ð14Þ

5. RESULTS

for the hopping and the band models, respectively.20 The former study of semiconducting properties for undoped TiO2 single crystal,23 determined in the range 9851166 K, has shown that the experimental data are not well described by the Jonker formalism due to the following reasons: • The experimental data exhibit a substantial scatter in their absolute values as well as the oxygen activity dependence. • The parameter mS in eq 2 varies between 8.5 and 11.4. These data are inconsistent with the defect disorder model reported for TiO2. The recent study on the determination of semiconducting properties of high-purity polycrystalline TiO2 shows that the

5.1. Electrical Conductivity. The isothermal plots of the electrical conductivity versus log p(O2), in the temperature range 10731323 K, are shown in Figure 4. The solid lines represent the best approximation of the experimental data. The dashed lines represent the extrapolated dependencies. These data allow the following points to be made: • The log σ versus log p(O2) dependencies exhibit minima, which in the first approximation can be related to the np transition points (indicated by the dash-dotted line). • In strongly reducing conditions (p(O2) < 105 Pa) the slope of the log σ vs log p(O2) dependencies is 1/6, which is consistent with electronic charge compensation. 18319



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Figure 4. Effect of oxygen activity on electrical conductivity for highpurity TiO2 single crystal8.

Figure 6. Linearized Jonker plot for high-purity TiO2 single crystal at 1073 K.

Figure 5. Effect of oxygen activity on thermoelectric power for highpurity TiO2 single crystal.9


• In reducing conditions (105 Pa < p(O2) < 1 Pa) the slope of the log σ vs log p(O2) dependencies is 1/4, which is consistent with ionic charge compensation in the n-type regime. • The number of the experimental data points in oxidizing conditions (p(O2) > 1 kPa) is not sufficient to determine the slope of log σ vs log p(O2) dependencies experimentally. However, the derived theoretical models indicate that this slope is 1/4, which is consistent with ionic charge compensation (oxygen vacancies compensated by titanium vacancies). 5.2. Thermoelectric Power. The thermoelectric power data vs log p(O2) are shown in Figure 5. As seen, the slope in strongly reducing conditions (1/6) is consistent with the slope of log σ vs log p(O2). The consistency indicates that thermoelectric power data obtained in strongly reduced conditions, which are related to the argonhydrogen mixture are determined by one type of charge carriers: electrons (the related oxygen activity is determined by the H2/H2O ratio). As seen in Figure 5, at higher p(O2) the dependencies exhibit a substantial deviation from 1/6 linearity. This deviation increases with the increase of oxygen activity due to increasing contribution of minority charge carriers (electron holes). The increasing contribution of holes results in

the np transition corresponding to S = 0. In the first approximation the np transition point determined by thermoelectric power is consistent with the minimum of the electrical conductivity shown in Figure 4. These data are discussed in more details elsewhere.4 5.3. Jonker Analysis. 5.3.1. Linear Plots. The linearized Jonker plots described by eq 10 are shown in Figures 611. Derivation of these plots required knowledge of the minimum of the electrical conductivity, which was determined from Figure 4. Equation 8 may then be used for the determination of band gap using the expression Eg ¼ 2eTB kTðAn þ Ap Þ

ð15Þ

where the parameter B is determined from the slope of the linear eq 10. These plots indicate the following: • The experimental data related to TiO2 in oxidizing conditions can be well described by the straight lines (regime I). This dependence may be used for the determination of the parameters B and D as well as the band gap. • As seen, the data for reduced TiO2 exhibit a clear deviation from the linear dependence. The increasing degree of reduction leads to an increased departure from the linear dependence when X decreases from approximately X = 0.75 to lower values (the transition regime). The departure has the 18320




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Table 2. Effect of Temperature on the Band Gap for TiO2 Single Crystal According to the Results of Jonker Analysis band gap, Eg (eV)


temperature,

model 1

model 2

T (K)

(An = 0, Ap = 0)

(An = 2.5, Ap = 0)

1073

1.80

1.57

1198

2.11

1.85

1223

2.05

1.79

1248 1273

2.06 1.95

1.79 1.68

1323

1.91

1.62

tendency to achieve a maximum value at approximately X = 1 (regime II). The linear dependence in regime I may be used for the determination of the band gap. The determinations were performed assuming the charge transport according to the hopping mechanism (An = 0 and Ap = 0) and the band transport mechanism (An = 2.5 and Ap = 0). The band gaps for oxidized TiO2 are shown in Table 2. The comparison between the band gap determined in this work for TiO2 single crystal (filled circles) and that for polycrystalline TiO212 (hollow circles) is shown in Figures 12 and 13 for the hopping and the band model, respectively. These data allow the following points to be made: • Hopping model. The data for TiO2 single crystal exhibit a linear dependence in the range 11981323 K, with notable departure of the data at the lowest temperature, 1073 K (the latter seems to be related the departure of the system from equilibrium). As seen, the band gap values for single crystal TiO2 at these temperatures are smaller by approximately 0.3 eV. The temperature coefficient of the band gap was determined from its value at 1223 K (2.4 and 2.05 eV for polycrystalline TiO2 and TiO2 single crystal) and assuming that for both specimens Eg = 3.05 eV at room temperature (300 K). The related coefficients are β = 0.9 meV/K and β = 1.1 meV/K, respectively. Then we have

Figure 10. Linearized Jonker plot for high-purity TiO2 single crystal at 1273 K. 18321

EgðPCÞ ¼ 3:48 9 104 T ðeVÞ

ð16Þ

EgðSCÞ ¼ 3:38 1:1 103 T ðeVÞ

ð17Þ



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Figure 12. Effect of temperature on the band gap of both TiO2 single crystal and polycrystalline TiO2 according to the hopping model in the range 10731323 K.

Figure 13. Effect of temperature on the band gap of both TiO2 single crystal and polycrystalline TiO2 according to the band model in the range 10731323 K.

• Band model. The band gap values for both polycrystalline TiO2 and TiO2 single crystals are lower by approximately 0.2 eV. Taking into account the same assumptions as above, the temperature coefficients of the band gap for polycrystalline TiO2 and TiO2 single crystal are β = 1.0 meV/K and β = 1.4 meV/K, respectively. Then we have EgðPCÞ ¼ 3:35 1:0 103 T ðeVÞ

ð18Þ

EgðSCÞ ¼ 3:46 1:4 103 T ðeVÞ

ð19Þ

5.3.2. Pearlike Plots. Efforts to find a single pear-type Jonker plot for the experimental data within both oxidized and reduced regimes were unsuccessful. Therefore, the Jonker plots were derived using the parameters B and D determined from the linear dependencies and σmin determined from the log σ vs log p(O2) dependence in oxidizing conditions. These plots are shown by thick solid lines in Figures 1419.

Figure 14. Isothermal plot of thermoelectric power as a function of log σ for high-purity TiO2 single crystal at 1073 K. Thick- and thin-line “pears” are related to oxidized and reduced TiO2, respectively.


The characters of these plots are schematically represented in Figure 20 in the form of a double pear-type dependence where the solid line and the dashed line correspond to oxidizing and reducing conditions, respectively. While the pear-type plot for oxidized TiO2 is relatively well defined by the parameter σmin determined experimentally and the parameters B and D determined from the linear analysis, the pear-type dependence for reduced TiO2 has been considered in terms of the following scenarios: • In the first approach the parameter B was determined from the band gap of reduced TiO2, which was estimated from the data reported by Dhumal et al.26 and the kinetic parameters related to the hopping and band models. The data of Dhumal et al.26 show that reduction of TiO2 may lead to reduction of band gap by approximately 0.1 eV (in the first approach the parameters σmin and D remained unchanged). The pear-type dependence based on this approach did not describe the experimental data obtained for reduced TiO2. • In the second approach, the pear-type dependence derived above was shifted in order to obtain the best fitting with the 18322



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Figure 20. Schematic representation of the double pear-like model of TiO2 (Dox and Dred denote the estimated parameter D for oxidized and reduced TiO2, respectively).

experimental data for reduced TiO2. The shifted dependence is represented by the thin line. The shifting procedure resulted in a change of both σmin and D as represented in Figure 20.


6. DISCUSSION As seen in Figures 611 and 1419 the semiconducting properties of oxidized and reduced TiO2, which are related to regime I and regime II, respectively, are distinctively different. The difference, which is related to the effect of reduction on the semiconducting properties, can be considered in terms of a quantitative approach but can also be considered in a qualitative sense. The latter suggests that reduction of TiO2 results in a change of semiconducting properties in terms of its electronic structure and the mobility terms. The lattice of oxidized TiO2 (the regime I) consists of both titanium and oxygen ions. The related properties are relatively well defined in terms of its defect disorder that is related to the oxygen activity imposed by the argonoxygen mixture. Then the 18323



Figure 21. Band gaps of different titanium oxides at 300 K. Solid lines represent experimental data13,2628 and the dashed line illustrate the expected dependence. The TiO2O2 system at 1000 K was derived by Geraghty and Donahey29.

only gas phase component, which has an effect on lattice properties, is oxygen. The recent studies show, however, that the parameter σmin must be considered in terms of the associated content of titanium vacancies. However, the content of titanium vacancies does not have a substantial effect on the band gap, that is, Eg = 3.05 eV. As seen in Figures 1419, the picture in reducing conditions (regime II) is more complex. Then the low oxygen activity is imposed by the hydrogenwater vapor mixture. In this case the gas phase components, which have an effect on the properties of the TiO2 lattice, include both oxygen and hydrogen. As seen in Figures 1419, the solid line is relatively welldefined by the best fitting of the parameters σmin, determined experimentally in oxidizing conditions (regime I), and B and D determined from the linear system. This system may be considered in terms of the TiO2 reported before.4 The associated changes in thermoelectric power, which change between positive to negative values, are reflective of the changes of Fermi level. The thin lines are representative of the semiconducting properties of TiO2 involving protons, in addition to titanium and oxygen. It appears that the presence of hydrogen has a substantial effect on the semiconducting properties, which are distinctively different from that of oxidized TiO2. It is interesting to note that the experimental data in regime II exhibit a weak but visible trend to decrease the slope from k ln 10/e to slightly lower values. This change of slope may be considered in terms of increasing interactions between charge carriers, which no longer can be described by the MaxwellBoltzmann statistics. This effect can also be considered in terms of increasing interactions between protons and titanium vacancies resulting in 0000 the formation of {VTi 3 4OH•} defect complexes in the bulk phase of TiO2 reduced in the gas phase including hydrogen. However, the picture at interfaces, such as grain boundaries, in reduced conductions is entirely different due to the following reasons: • The concentration of titanium vacancies in the grain boundary region is substantially reduced as required by equilibrium (4) in Table 2. As seen, reduction of oxygen activity results in shifting this equilibrium to the left. However, the concentration

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Figure 22. The effect of temperature on the electrical conductivity of TiO2 single crystal and polycrystalline TiO2.

of titanium vacancies in the bulk is not affected due to the kinetic reason.0 0 0In consequence, the concentration of defect 0 complexes {VTi 3 4OH•} in the bulk remain practically unchanged. Therefore, their concentration in single crystals is practically not affected. • As required by equilibria (1) (3) in Table 2, reduction of TiO2 results in increased concentrations of donor-type defects (oxygen vacancies and titanium interstitials) at grain boundaries. These defects have the tendency to remove protons from the grain boundary areas. The parameter D for Jonker “pears” corresponding to regime II (marked by thin lines on Figures 1419) is decreased by 200300 μV/K, compared to regime I. This corresponds to the change of the μp/μn ratio by 2050, assuming that the parameters Nn, Np, An, and Ap are constant. However, most likely the observed shift in parameter D is associated with the changes of all these quantites. The band gap of oxidized TiO2 at room temperature is Eg = 3.05 eV. Collection of experimental data for reduced TiO2 as well as for lower oxide phases, such as Ti2O327 and extremely reduced TiO2,26 indicate that the band gap has the tendency to decrease as oxygen activity is reduced (Figure 21). As seen in Figure 21, reduction of TiO2 from p(O2) = 105 Pa to p(O2) = 1010 Pa is associated with the reduction of band gap by 0.1 eV. It is interesting to note that while reduction results in a substantial increase in electrical conductivity, the conductivity for polycrystalline TiO2 is only slightly larger that that for TiO2 single crystal (Figure 22). The observed difference indicates that grain boundaries are enriched with donor-type defects, such as oxygen vacancies and titanium interstitials. Due to the charge neutrality requirements, these defects are responsible for removal of hydrogen from the grain boundary regions. This is the reason why the effect of hydrogen on the semiconducting properties of polycrystalline TiO2 is minimal. On the other hand, the effect observed for TiO2 single crystal is related to higher concentration of titanium vacancies, which are forming the complexes with protons. In summary, the comparison of the pear-type dependences for polycrystalline TiO2 and TiO2 single crystal allows the following points: 18324


The Journal of Physical Chemistry C • The band gap for TiO2 single crystal in reducing conditions at elevated temperatures is lower than that for polycrystalline specimen by 0.20.3 eV. The difference between the two is likely related to the local semiconducting properties of grain boundaries. • The effect of reduction on semiconducting properties for the TiO2 single crystal is substantial. A similar effect for polycrystalline TiO2, determined in the same range of temperatures and oxygen activities, is either neglegibly low or is absent. The reactivity between the TiO2 lattice and hydrogen results in fast incorporation of protons.17,18 The related defect disorder may be considered in terms of the interactions of these protons with titanium vacancies leading 0000 to the formation of {VTi 3 4OH•}-type defect complexes. The data obtained in this work indicate that the effect of hydrogen is predominantly related to00 0bulk properties and is 0 associated with the formation of {VTi 3 4OH•} type defect complexes. One may, therefore, expect that these defects are not present at, and in the vicinity of, grain boundaries. • The semiconducting properties of TiO2 in the argon hydrogen mixture are distinctively different from those of oxidized TiO2. The dual semiconducting properties observed within a single crystalline structure is an unprecedented phenomenon. These properties may be represented by the double pear-type Jonker dependence (see Figure 20). The difference in semiconducting properties is related to the effect of protons on bulk properties, such as electronic structure and charge transport. The effect of protons on the properties of grain boundaries is either negligibly low or absent.

7. CONCLUSIONS The following have been documented: • The band gap of rutile, for TiO2 single crystal at elevated temperatures is smaller than that for polycrystalline TiO2 by approximately 0.3 eV (see Figures 12 and 13). • Equilibration of TiO2 in the gas phase containing hydrogen results in a double effect: reduction of oxygen activity; changes of semiconducting properties, which include the following two components: the component related to reduced oxygen activity and the component associated with proton-related defects. In summary, the present work shows that the effect of hydrogen on semiconducting properties of TiO2 is closely related to bulk defect disorder and, specifically, to the bulk concentration of titanium 0000 vacancies which have the tendency to form {VTi 3 4OH•}-type defect complexes. It seems that these complexes are responsible for the departure of the thermopower vs electrical conductivity dependence from that observed for oxidized TiO2. The discussion of the experimental data indicates that hydrogen results in reduction of the band gap and a substantial increase of the μn/μp ratio that is reflective of the decrease in thermoelectric power. The impact of hydrogen on semiconducting properties observed in the present work indicates that protons must be taken into account in defect engineering of oxide semiconductors with enhanced performance in solar energy conversion. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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’ ACKNOWLEDGMENT The help of Tadeusz Bak in derivation of the diagrams is sincerely appreciated. ’ REFERENCES (1) Carp, O.; Huisman, C. L.; Reller, A. Photoinduced reactivity of titanium dioxide. Prog. Solid State Chem. 2004, 32, 33–177. (2) Fujishima, A.; Hashimoto, K.; Watanabe, T. TiO2 Photocatalysis. Fundamentals and Applications; BKC Inc.: Tokyo, 1999. (3) Linsebigler, A. L.; Lu, G.; Yates, J. T. Photocatalysis on TiO2 Surfaces: Principles, Mechanisms, and Selected Results. Chem. Rev. 1995, 95, 735–758. (4) Nowotny, M. K.; Sheppard, L. R.; Bak, T.; Nowotny, J. Defect Chemistry of Titanium Dioxide. Application of Defect Engineering in Processing of TiO2-Based Photocatalysts. J. Phys. Chem. C 2008, 112, 5275–5300. (5) Baumard, J. F.; Tani, E. Electrical conductivity and charge compensation in Nb doped TiO2 rutile. J. Chem. Phys. 1977, 67, 857–860. (6) Baumard, J. F.; Tani, E. Thermoelectric power in reduced pure and Nb-doped TiO2 rutile at high temperature. Phys. Status Solidi A 1977, 39, 373–382. (7) Balachandran, U.; Eror, N. G. Electrical conductivity in nonstoichiometric titanium dioxide at elevated temperatures. J. Mater. Sci. 1988, 23, 2676–2682. (8) Nowotny, M. K.; Bak, T.; Nowotny, J. Electrical Properties and Defect Chemistry of TiO2 Single Crystal. I. Electrical Conductivity. J. Phys. Chem. B 2006, 110, 16270–16282. (9) Nowotny, M. K.; Bak, T.; Nowotny, J. Electrical Properties and Defect Chemistry of TiO2 Single Crystal. II. Thermoelectric Power. J. Phys. Chem. B 2006, 110, 16283–16291. (10) Kofstad, P. Nonstoichiometry, Diffusion and Electrical Conductivity in Binary Metal Oxides; Wiley-Interscience: New York, 1972. (11) Jonker, G. H. The application of combined conductivity and Seebeck-effect plots for the analysis of semiconductor properties (Conductivity vs Seebeck coefficient plots for analyzing n-type, p-type and mixed conduction semiconductors transport properties). Philips Res. Rep. 1968, 23, 131–138. (12) Bak, T.; Nowotny, J. Semiconducting Properties of Oxidised and Reduced Polycrystalline TiO2. Jonker Analysis. J. Phys. Chem. C 2011, 115, 97469752 (13) Bak, T.; Nowotny, J.; Nowotny, M. K. Defect Disorder of Titanium Dioxide. J. Phys. Chem. B 2006, 110, 21560–21567. (14) Nowotny, J.; Bak, T.; Burg, T.; Nowotny, M. K.; Sheppard, L. R. Effect of Grain Boundaries on Semiconducting Properties of TiO2 at Elevated Temperatures. J. Phys. Chem. C 2007, 111, 9769–9778. (15) Kr€oger, F. A. The Chemistry of Imperfect Crystals; North Holland: Amsterdam, 1974; Vol. 3. (16) Norby, T. Proton conduction in solids: bulk and interfaces. MRS Bull. 2009, 34, 923–928. (17) Hill, G. J. The effect of hydrogen on the electrical properties of rutile. J. Phys. D: Appl. Phys. 1968, 1, 1151–1162. (18) Peterson, N. L.; Sasaki, J. In Transport in Nonstoichiometry Compounds; Simkovich, G., Stubican, V. S., Eds.; Plenum: New York, 1984; pp 26984. (19) Nowotny, J.; Rekas, M. Defect Structure of Cobalt Monoxide: II, The DebyeH€uckel Model. J. Am. Ceram. Soc. 1989, 72, 1207–1214. (20) Nowotny, J.; Rekas, M. Defect Structure, Electrical Properties and Transport in Barium Titanate. III. Electrical Conductivity, Thermopower and Transport in Single Crystalline BaTiO3. Ceram. Int. 1994, 20, 225–235. (21) Su, M.-Y.; Elsbernd, C. E.; Mason, T. Jonker “Pear” Analysis of Oxide Superconductors. J. Am. Ceram. Soc. 1990, 73, 415–419. (22) Bak, T.; Nowotny, J.; Sorrell, C. C.; Zhou, M. F. Charge transport in CaTiO3: III. Jonker analysis. J. Mater. Sci.: Mater. Electron. 2004, 15, 651–656. 18325



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(23) Nowotny, J.; Radecka, M.; Rekas, M. Semiconducting properties of undoped TiO2. J. Phys. Chem. Solids 1997, 58, 927–937. (24) Bak, T.; Nowotny, J.; Sorrell, C. C.; Zhou, M. F.; Vance, E. R. Charge transport in CaTiO3: I. Electrical conductivity. J. Mater. Sci.: Mater. Electron. 2004, 15, 635–644. (25) Bak, T.; Nowotny, J.; Sorrell, C. C.; Zhou, M. F.; Vance, E. R. Charge transport in CaTiO3: II. Thermoelectric power. J. Mater. Sci.: Mater. Electron. 2004, 15, 645–650. (26) Dhumal, S. Y.; Daulton, T. L.; Jiang, J.; Khomami, B.; Biswas, P. Synthesis of visible lightactive nanostructured TiOx (x < 2) photocatalysts in a flame aerosol reactor. Appl. Catal., B 2009, 86, 145–151. (27) Bennett, J. G.; Sladek, R. J. In Proc.—IEEE Ultrasonics Symposium; de Klerk, J., Ed.; Institute of Electrical and Electronics Engineers, 1974; pp 517518. (28) Rao, C. N. R.; Subba Rao, G. V. Electrical conduction in metal oxides. Phys. Status Solidi A 1970, 1, 597–652. (29) Geraghty, K. G.; Donaghey, L. F. Preparation of suboxides in the TiO system by reactive sputtering. Thin Solid Films 1977, 40, 375–383.

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