Semiconducting Properties of Oxidized and Reduced Polycrystalline

ARTICLE pubs.acs.org/JPCC

Semiconducting Properties of Oxidized and Reduced Polycrystalline TiO2. Jonker Analysis Tadeusz Bak and Janusz Nowotny* Solar Energy Technologies, University of Western Sydney, Locked Bag 1797, Penrith NSW 2751, Australia ABSTRACT: The present work considers semiconducting properties of polycrystalline TiO2 in terms of the formalism proposed by Jonker. It is shown that the linearized form of the Janker equation can be successfully applied for systems with sparse experimental data. The results of the analysis indicate different semiconducting properties of oxidized and reduced TiO2. The determined band gap of oxidized TiO2 varies between 2.32 eV at 1123 K and 3.72 eV at 1323 K. The data determined in reduced conditions (1013 Pa < p(O2) < 105 Pa) can not be well described by the Jonker formalism.

1. INTRODUCTION The interest in photocatalytic properties of rutile (TiO2) is increasing.13 Awareness is growing that several properties of rutile, such as semiconducting properties and diffusion of lattice species are determined by defect disorder.4 Therefore, knowledge of defect disorder models may be used to predict the defectrelated properties. Electrical properties, such as electrical conductivity and thermoelectric power, have been commonly used for the characterization of defect disorder and the related semiconducting properties of metal oxides.4,5 The electrical conductivity data determined in equilibrium (at elevated temperatures) as a function of oxygen activity, p(O2), may be used for derivation of defect disorder models where either the mobility terms remains independent of p(O2) or their changes with p(O2) are known. The thermoelectric power data determined in equilibrium as a function of oxygen activity may also be used for derivation of defect disorder models. The latter data are independent of the mobility terms. Both electrical conductivity and thermoelectric power data may be analyzed using the method proposed by Jonker.6 The advantage of this analysis is that knowledge of oxygen activity related to these two properties is not required, if they were determined simultaneously. Accordingly, the Jonker analysis eliminates any error resulting from the determination of the oxygen activity. Moreover, the Jonker analysis may be used to determine the semiconducting properties, such as band gap and the mobility terms. The electrical properties of polycrystalline rutile (TiO2), including electrical conductivity7 and thermoelectric power8 as a function of oxygen activity have been already reported. These data were used for the determination of defect disorder of TiO2.5 The purpose of the present work is to determine semiconducting properties of both oxidized and reduced rutile phase in terms of the Jonker analysis. The ultimate aim of this work is to understand the effect of oxidation on the semiconducting properties. r 2011 American Chemical Society

2. DEFINITION OF TERMS 2.1. Nonstoichiometry and Defect Disorder of Titanium Dioxide. Titanium dioxide is a nonstoichiometric compound. Its

nonstoichiometry, which is closely related to oxygen activity, may be imposed by the gas phase of controlled oxygen activity, p(O2). TiO2 has been commonly considered as an oxygen-deficient oxide that can be represented by the formula TiO2x (where the apparent oxygen deficit is caused by the real oxygen deficit and the real excess of metal4). Recent studies have shown, however, that TiO2 can exhibit a deficit in both oxygen and cation sublattices. Therefore, titanium dioxide can be better represented by the formula Ti1(xO2y.5,7,8 2.2. Electrical Conductivity. The concentration of point defects, including electronic defects, is determined by oxygen activity, p(O2). The effect of oxygen activity on the defect-related properties of TiO2, such as electrical conductivity, is reported elsewhere.7 Electrical conductivity is closely related to the concentration of electronic charge carriers, which are formed as a result of (i) reaction between the TiO2 lattice and oxygen in the gas phase, and (ii) intrinsic ionization. The associated defect equilibria, derived according to the Kr€ogerVink notation,9 and the associated equilibrium constants are shown in Table 1. The effect of p(O2) on electrical conductivity of oxide semiconductors, such as TiO2, may be described by the following relation: σ ¼ const pðO2 Þ1=mσ

ð1Þ

where σ is electrical conductivity and the parameter mσ is the parameter that is closely related to defect disorder.4,7 Therefore 1 D log σ ¼ mσ D log pðO2 Þ

ð2Þ

Received: February 15, 2011 Revised: March 28, 2011 Published: April 26, 2011 9746

dx.doi.org/10.1021/jp201515u | J. Phys. Chem. C 2011, 115, 9746–9752

The Journal of Physical Chemistry C

ARTICLE

Table 1. Defect Reactions and the Related Equilibrium Constants for TiO2.5 reaction 1

0

•• O O h VO þ 2e þ 1/2O2

4

þ Ti Ti þ Ti Ti O2 h 2O O

5

nil h e þ h

2 3

2O O 2O O

0

0 h Ti••• i þ 3e þ O2 0 h Ti•••• þ 4e þ O2 i 0000 þ VTi þ 4h• •

ΔH0 [kJ/mol]

constant 0

2 1/2 K1 = [V•• O][e ] p(O2) 0

3 K2 = [Ti••• i ][e ] p(O2) 0

4 K3 = [Ti•••• i ][e ] p(O2) 0000

K4 = [VTi ][h•]4p(O2) 1 0

Ki = [e ][h•]

ΔS0 [J/mol]

493.1

106.5

879.2

190.8

1025.8

238.3

354.5

202.1

222.1

44.6

ln K = ΔS0/R ΔH0/RT

Jonker plot, which exhibits a pear-like shape, is described by the following formula: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! σ2min k σ σ2 þD 1 ( 1 min S ¼ ( B 1 2 ln e σmin σ σ2 ð4Þ The width and the position of the Jonker plot is determined by the parameters B, D, and the minimum of electrical conductivity, σmin. These parameters can be determined graphically from the characteristic points of the Jonker plot and are expressed as k Eg þ An þ Ap B¼ ð5Þ 2e kT and Figure 1. Schematic representation of the Jonker plot of thermoelectric power as a function of electrical conductivity (determined simultaneously) for arbitrarily chosen parameters σmin, B, and D of the Jonker equation.6

The log σ versus log p(O2) dependence for amphoteric oxide semiconductors (that exhibits np transition), involves two linear dependences of opposite slopes, which intersect at the np transition point that correspond to the minimum of electrical conductivity (when mobilities of both charge carriers are equal).7 2.3. Thermoelectric Power. Thermoelectric power may be directly related to the concentration of electronic charge carriers,4,8 while the electrical conductivity data depends on both the concentration and the mobility terms. Therefore, combined measurements of both thermoelectric power and electrical conductivity can be used for the determination of the mobility terms. When electrical properties are controlled by one type of charge carriers, then the dependence of thermoelectric power on oxygen activity, p(O2), may be used for the verification of defect disorder models of metal oxides:8 1 k DS ¼ mS e D log pðO2 Þ

D¼

ð6Þ

where Eg is the band gap, An and Ap are the kinetic terms, Nn and Np are densities of states, and μn and μp are the mobilities of charge carriers. The subscripts “n” and “p” correspond to electrons and electron holes, respectively. Other symbols have their traditional meaning. The relationship between S and σ, expressed by eq 4, is the basic relationship of the Jonker analysis. Therefore, the Jonker formalism allows the determination of the key semiconducting quantities, including the band gap and the mobility terms. The determination of semiconducting quantities in eqs 5 and 6 is possible when the number of experimental points and their distribution allow one to draw the entire shape of the pear-like dependence. It means that the measured data should cover both n- and p-type regime, close to the np transition point as well as far from it. Otherwise the determination of the parameters B and D results in a significant error. However, such graphical analysis is cumbersome and hard to automate. Equation 4 may be transformed into a linear form:10,11

ð3Þ

where S is thermoelectric power, mS is the reciprocal of the p(O2) exponent of thermoelectric power, e denotes elementary charge, and k is the Boltzmann constant. The characteristic point of the S versus p(O2) dependence is when S = 0. This point corresponds to the np transition, assuming that the kinetic constants are equal. 2.4. Jonker Formalism. The Jonker analysis is based on the joint analysis of both thermoelectric power and electrical conductivity determined in the same thermodynamic conditions. A typical Jonker plot of S as a function of log σ, for arbitrarily chosen parameters B, D, and σmin, is shown in Figure 1.6 The

A k μp Np e p ln 2e μn Nn eAn

Y ¼ BX þ D

ð7Þ

using the transformation X Y

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σmin 2 ¼ ( 1 σ k 1þX ¼ S þ ln pffiffiffiffiffiffiffiffiffiffiffiffiffi e 1 X2

ð8Þ

The sign of X is positive for S g 0. Employing the simple leastsquares analysis, the parameters B and D may be determined from the linear dependence of the transformed experimental data (see Figure 2). In order to perform the transformation 8 the 9747

dx.doi.org/10.1021/jp201515u |J. Phys. Chem. C 2011, 115, 9746–9752


Figure 2. Schematic representation of the linearized Jonker plot.10

parameter σmin must be known. It can be deduced by interpolation from isothermal log σ vs log p(O2) plots. Therefore, application of the linear analysis requires only the knowledge of experimental data within the np transition regime. Data corresponding to deep n- and p-type regime (σ .σmin), due to the nature of transformation (eq 8), converge into single points at X = 1 and X = 1, respectively. Nevertheless, all these points should obey the same linear relationship. Correct quantitative assessment of semiconducting properties of metal oxides in terms of the formalism proposed by Jonker6 requires that the following conditions are met: • The applied p(O2) range corresponds to a single phase regime. If this condition is not met, the experimental data can not be described by a single pear-like Jonker curve. In other words, the concept of Jonker analysis is based on the assumption that the electronic structure and transport mechanism does not change. • Both the electrical conductivity and thermoelectric power data points correspond to the same p(O2) and, therefore, should be determined simultaneously. • Both the electrical conductivity and thermoelectric power are measured in the gas/solid equilibrium. As seen in eq 4, σmin is the parameter in the Jonker equation. Therefore, the Jonker formalism may be applied when the minimum of electrical conductivity is known. Consequently, the Jonker analysis can be applied for amphoteric oxides, which in the experimental range of oxygen activities exhibit both n- and p-type properties. The results of Jonker analysis were reported for CoO,11 BaTiO3,12 oxide superconductors,13 CaTiO3,14 as well as for TiO2.10 The former study of semiconducting properties of undoped TiO2,10 determined in the temperature range 9851166 K, has shown that the experimental data do not follow very well the linear dependence 7. Particularly: • While the data determined in oxidized conditions obey the linearity relatively well, the scatter of data is substantial. • The data determined in reduced conditions exhibit a clear departure from the linear behavior. The observed discrepancy indicates that reduced TiO2 may exhibit different semiconducting properties than the oxidized specimen. This effect could also be related to the presence of impurities. Therefore, this study was performed on a high-purity specimen of rutile.

3. EXPERIMENTAL SECTION 3.1. Specimen. High-purity polycrystalline TiO2 was prepared from high-purity (99.999%) titanium isopropoxide.

ARTICLE

Figure 3. Scanning electron micrograph of the ceramic specimen of pure TiO2.7

Figure 4. Sample holder of the high-temperature Seebeck probe.7

Deionized water, in the amount required by the reaction, was slowly added into the titanium isopropoxide/ethanol mixture leading to precipitation of TiO2. The powder was uniaxially pressed into pellets (∼4 mm thick and 20 mm in diameter) at 200 MPa, with 1 min hold time, and sintered in air at 1423 K for 12 h. The chemical analysis was performed using inductively coupled plasma mass spectrometry (ICP/MS). The total concentration of acceptor-type cation impurities and anions (mostly chlorine) was 34 ppm and 20 ppm, respectively. The scanning electron micrograph of the sintered specimen in Figure 3 shows that the specimen exhibits high density, and is free of intergranular precipitates. The X-ray diffraction (XRD) studies confirmed that the specimen was of the rutile polymorph. The properties of specimens are reported elsewhere in detail.7 3.2. Equipment. Both electrical conductivity and thermoelectric power were determined simultaneously using the hightemperature Seebeck probe.7 The sample holder of the probe is shown in Figure 4. The external (current) probes were formed of platinum plates attached to both sides of the rectangular-shaped specimen (2 mm 3 mm 10 mm). A spring mechanism, located outside the high temperature zone, was used to maintain good galvanic contact between the Pt electrodes and the specimen. Voltage electrodes were formed of two Pt wires wrapped around the specimen and welded to the connecting wires. The distance between these electrodes was 7 mm. The sample holder was placed in an alumina tube, which was connected to the gas flow system allowing the gas of controlled oxygen activity to flow through the reaction chamber. The probe was positioned inside a 9748



ARTICLE

Figure 5. Effect of oxygen activity on electrical conductivity for high purity polycrystalline TiO2.7

horizontal tube furnace. The details of the experimental setup are reported elsewhere.7,15 3.3. Experimental Procedure. Required oxygen activity, p(O2), in the reaction chamber was imposed by an argon and oxygen mixture, of appropriate composition, flowing with a flow rate 100 mL/min. The p(O2) in the lower range was imposed using the mixtures of hydrogen and water vapor. The oxygen activities were determined with a zirconia-based electrochemical oxygen probe. The measurements of electrical conductivity and thermoelectric power were taken during both oxidation and reduction experiments, after the equilibrium was established. The electrical conductivity was measured within the DC current range 10 nA to 1 mA (applied voltage below 5 V). In these conditions, the sample exhibits ohmic behavior. The thermoelectric voltages were taken along the temperature gradient of two different polarities (signs): ΔT and ΔT in the range (5 K. Both electrical conductivity and thermoelectric power data were determined simultaneously using a single data acquisition program. The details of the measurements of the electrical conductivity and thermoelectric power are reported in refs 7 and 8, respectively. The studies were performed in the temperature range 11231323 K. The lowest temperature in this work is higher than that in the previous study (985 K10) because the data at 985 K may not correspond to equilibrium conditions.

4. RESULTS 4.1. Electrical Conductivity. The effect of oxygen activity on the electrical conductivity of TiO2 in the temperature range 11231323 K within the entire studied p(O2) regime is shown in Figure 5, where the solid lines represent the best approximation of the experimental data, and the dashed lines represent the interpolated dependencies. As seen, the observed effect of p(O2) on electrical conductivity depends on the p(O2) regime. The minima of the log σ versus log p(O2) dependencies are related, in the first approximation, to the np transition points, which are marked in Figure 5 by the dashed line. These data, showing both n- (left side of the transition line) and p-type (right side of the transition line) behaviors, indicate the presence of acceptor-type intrinsic defects (titanium vacancies), responsible for p-type properties. Increasing temperature results in a shift in the p(O2)

Figure 6. Effect of oxygen activity on thermoelectric power for high purity polycrystalline TiO28.

corresponding to the np transition point toward higher p(O2) values. There is a clear tendency for the slope, 1/mσ, to change from about 1/6 in reduced conditions to 1/4 in oxidized conditions. These data were discussed in terms of the related defect disorder models.7 4.2. Thermoelectric Power. As seen in Figure 6, the slope of S versus log p(O2) in reduced conditions, which is slightly lower than 1/6, is consistent with the slope of log σ versus log p(O2). At higher p(O2) levels, data deviate from the 1/6 linearity. This deviation increases with the increase of p(O2) due to the increasing effect of minority charge carriers (electron holes). Their influence ultimately leads to the np transition, which is revealed in the high-p(O2) range (change to positive values of thermoelectric power). These data are discussed in more details in ref 8. The consistency of the slopes 1/mσ and 1/mS indicates that the effect of oxygen activity on the changes of both electrical properties is mostly determined by the concentration term, while the effect of the mobility term is negligible. 4.3. Jonker Analysis. According to Figures 5 and 6, the obtained experimental data correspond to n-type and np transition regimes. Consequently, there are no experimental points that would belong to the upper branch of Jonker’s “pear’’ (see Figure 1). This lack of data prevents the graphical determination of parameters σmin, B, and D. It is still possible, however, to use the linearized form 7, with the parameter σmin estimated from Figure 5. The results of the analysis are presented in Figures 712, where the solid lines represents the best fit to the experimental data.

5. DISCUSSION As seen in Figures 712, experimental data is relatively well described by the linear dependence in the Regime I, which 9749



ARTICLE

Figure 7. Linearized Jonker plot for high purity polycrystalline TiO2 at 1123 K.






correspond to oxidizing conditions. The departure from linearity is observed at all temperatures except 1173 K, where the data for reduced TiO2 is not available. Moreover, the points

corresponding to reduced TiO2 (Regime II) do not converge into a single Y value at X = 1. This indicates that they do not line-up with the theoretical slope k/e. The difference between the 9750



ARTICLE

Figure 14. Effect of temperature on the band gap for high purity polycrystalline TiO2.

Figure 13. Isothermal plots of thermoelectric power as a function of log σ (Jonker “pears’’) for high-purity polycrystalline TiO2.

Table 2. Effect of Temperature on the Band Gap for Polycrystalline TiO2 According to Jonker Analysis temperature, T [K]

band gap, Eg [eV]

1123

2.32

1173

2.37

1223

2.38

1248

2.03

1273

2.60

1323

3.72

two regimes suggests that semiconducting properties of oxidized and reduced TiO2 are different. The above effects are better visible on classical Jonker plots. Figure 13 shows the “pears’’ drawn using parameters σmin, B, and D calculated from the corresponding linear dependencies in Figures 712. As seen, the data for reduced TiO2 can not be described by the same Jonker plot that is consistent with the data for oxidized TiO2. The reason for the difference in semiconducting properties of oxidized (Regime I) and reduced (Regime II) TiO2 is not clear at this stage. One possible explanation is the presence of proton defects16 in reduced TiO2, as in the present experiments the low p(O2) conditions were achieved using hydrogen/water vapour mixtures, while the gas phase in oxidizing conditions was composed of argon and oxygen. Therefore, in the later case the gas/solid reactions were limited to oxygen incorporation or evolvement only. However, the gas/solid system in reducing conditions was more complex, as the gas phase included hydrogen and water vapour. Most likely hydrogen is incorporated into the TiO2 lattice in such conditions,

resulting in the formation of a solid solution. Apparently, the semiconducting properties of this solid solution are different from those of TiO2 that is hydrogen-free. One should also remember, that Jonker analysis is applicable to nondegenerated semiconductors only, i.e., charge carries must obey the MaxwellBoltzmann statistics. However, concentrations of point and electronic defects in reduced TiO2 are high; therefore it is reasonable to expect a deviation from the model of noninteracting electrons and the beginning of the shift toward metallic-like properties. These hypotheses require further verification. The band gap values determined from the Jonker analysis for TiO2 equilibrated in oxidized conditions (Regime I only) in the range 11231323 K are collected in Table 2. The calculations were performed assuming hopping mechanism of charge transport for both electrons and electron holes (An = 0 and Ap = 0).10 The effect of temperature on the band gap determined in this work is shown in Figure 14. The band gap remains within a reasonable range 2.02.6 eV, except the data at 1323 K, where Eg = 3.72 eV. This substantial discrepancy seems to be related to inaccurate determination of the np transition point which, at that temperature, lies at the experimental limit of the oxygen activity that can be imposed in our setup. As seen, the temperature coefficient of the band gap, β, within the temperature range 11231323 K is 0.4 meV/K. For comparison, taking into account that the band gap values at 1200 and 300 K are equal to 2.35 eV (interpolated from values determined in this work) and 3.05 eV,7 respectively, the temperature coefficient of the band gap is β = 0.8 meV/K. The former value is strongly affected by a substantial scatter of data (Figure 14); the later, however, seems to be more reliable due to much wider temperature range. On the other hand, the value reported by Baumard and Tani in the temperature range 2731573 K is β = 0.66 meV/K,17 which is smaller than that obtained here. The difference is probably related to the effect of impurities. According to the analysis provided by Baumard and Tani,17 their sample contained twice more acceptor-type impurities than the sample examined in this work.

6. CONCLUSIONS The experimental data of both electrical conductivity and thermoelectric power data determined in this work for high-purity 9751



ARTICLE

polycrystalline TiO2 (11231323 K) can be described in terms of the Jonker-type formalism only for the data determined in oxidized conditions. It is shown that semiconducting properties of reduced TiO2 are different. The reasons for the observed difference is not clear. At high temperatures (11231273 K) the band gap of oxidized TiO2 remains in the range 2.32.6 eV, except for that at 1323 K (Eg = 3.72 eV).

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ 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) Kofstad, P. Nonstoichiometry, Diffusion and Electrical Conductivity in Binary Metal Oxides; WileyInterscience: New York, 1972. (5) 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. (6) 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. (7) Nowotny, J.; Bak, T.; Burg, T. Electrical Properties of Polycrystalline TiO2 at Elevated Temperatures. Electrical Conductivity. Phys. Status Solidi B 2007, 244, 2037–2054. (8) Nowotny, J.; Bak, T.; Burg, T. Electrical Properties of Polycrystalline TiO2: Thermoelectric Power. Ionics 2007, 13, 155–162. (9) Kr€oger, F. A. The Chemistry of Imperfect Crystals; North Holland: Amsterdam, 1974; Vol. 3. (10) Nowotny, J.; Radecka, M.; Rekas, M. Semiconducting Properties of Undoped TiO2. J. Phys. Chem. Solids 1997, 58, 927–937. (11) Nowotny, J.; Rekas, M. Defect Structure of Cobalt Monoxide: II, The DebyeH€uckel Model. J. Am. Ceram. Soc. 1989, 72, 1207–1214. (12) 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. (13) Su, M.-Y.; Elsbernd, C. E.; Mason, T. Jonker “Pear” Analysis of Oxide Superconductors. J. Am. Ceram. Soc. 1990, 73, 415–419. (14) 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. (15) Nowotny, J. In Handbook of Solid State Electrochemistry; Gellings, P. J., Bouwmeester, H. J. M., Eds.; CRC Press: Boca Raton, FL, 1997; pp 121160. (16) Nowotny, J.; Norby, T.; Bak, T. Reactivity between Titanium Dioxide and Water at Elevated Temperatures. J. Phys. Chem. C 2010, 114, 18215–18221. (17) 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.

9752


Semiconducting Properties of Oxidized and Reduced Polycrystalline

Recommend Documents