Article pubs.acs.org/JPCA
Electrical Properties and Defect Chemistry of In-Doped TiO2 in Terms of the Jonker Formalism Janusz Nowotny,*,† Tadeusz Bak,† Mihail Ionescu,‡ and Mohammad A. Alim† †
Solar Energy Technologies, School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith, NSW 2751, Australia ‡ Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW 2234, Australia ABSTRACT: The present work considers the semiconducting properties of In-doped TiO2 in terms of the Jonker formalism applied for both electrical conductivity and thermoelectric power data determined simultaneously in equilibrium with the gas phase of controlled oxygen activity. It is shown that the electrical properties of In-doped TiO2 annealed in oxidizing conditions [p(O2) > 10 Pa] can be described by the Jonker formalism very well. However, annealing of In-doped TiO2 in strongly reducing conditions [p(O2) < 10−10 Pa], imposed by the gas phase involving hydrogen, results in a deviation of the experimental data from the Jonker’s theoretical model derived for the Maxwell−Boltzmann statistics. This departure is considered in terms of the effect of hydrogen on the formation of structural domains, which are expected to be entirely different from those of oxidized TiO2 in terms of its electronic properties. It is argued that In-doped TiO2 annealed in the gas phase involving hydrogen exhibits a high concentration of donortype ionic defects, which lead to the formation of high concentration of electrons. The related semiconducting properties are inconsistent with the model of classical semiconductor where the electrons are described by the Maxwell−Boltzmann statistics. It is concluded that strong interactions within the electron gas lead, in consequence, to the behavior resembling correlated transport of electrons. The obtained results suggest that indium incorporation into the rutile structure of TiO2 results in the formation of structural properties that exhibit extraordinary charge transport. and YBaCuO7.7 The most extensive studies have been performed for TiO2, including both single crystal and polycrystalline specimens.3,8,9 These studies indicate that although the semiconducting properties for the TiO2 specimens equilibrated in oxidizing conditions are well-defined, annealing in the gas phase involving hydrogen results in outstanding properties.9 It appears that in the latter case the data are inconsistent with the Jonker theoretical model. The observed departure of the experimental data from the Jonker model for the specimen equilibrated in the gas phase involving hydrogen may be considered in terms of the effect of hydrogen incorporated into the rutile lattice. The effect was initially observed for a pure TiO2 single crystal.9 The aim of the present work is to examine the effect of the gas phase involving hydrogen for TiO2 doped with small amount of trivalent ions, such as indium. The rationale of this approach is to compare the extent of the hydrogen-induced behavior for pure TiO2 and In-doped TiO2. The difference, if any, could provide information on the effect of trivalent ions on the extent of the departure from the Maxwell−Boltzmann statistics of TiO2 annealed in the gas phase involving hydrogen.
1. INTRODUCTION Quantitative assessment of the semiconducting properties using the electrical conductivity as a sole electrical property, which is related to both the concentration and the mobility terms, is difficult. However, the measurements of both electrical conductivity and thermoelectric power may be used in the determination of a range of semiconducting quantities, including the band gap and the mobility terms.1 The transport properties of semiconductors can be derived using the method proposed by Jonker,2 which is based on a combined analysis of both the electrical conductivity and thermoelectric power data. The Jonker formalism may be applied for amphoteric oxide semiconductors using the electrical conductivity and thermoelectric power data determined simultaneously in equilibrium with the gas phase of controlled oxygen activity. The key requirement for the application of the Jonker formalism is that these two electrical properties are determined simultaneously. Although Jonker analysis does not require knowledge of the oxygen activity, the effective use of the formalism proposed by Jonker requires that the data of both electrical properties are available within both nand p-type regimes. Therefore, the Jonker analysis can be applied mainly for the semiconductors described by the experimental data within both n- and p-type regimes. The Jonker analysis has been applied for amphoteric semiconductors, such as TiO2,3 BaTiO3,4 CoO,5 CaTiO3,6 © 2015 American Chemical Society
Received: February 10, 2015 Revised: March 30, 2015 Published: April 1, 2015 4032
DOI: 10.1021/acs.jpca.5b01368 J. Phys. Chem. A 2015, 119, 4032−4040
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The Journal of Physical Chemistry A
The critical quantities of the Jonker formalism, which are represented in Figure 1, include • The extreme left-side point of the “pear-like-curve”, which corresponds to the minimum of the electrical conductivity. Its knowledge is essential for analytical determination of the parameters B and D. The parameter σmin can be determined by isothermal monitoring of both the electrical conductivity and thermoelectric power as a function of oxygen activity, p(O2), within the n−p transition. • The slope of the S vs log σ dependence at the right-hand side of the “pear”, within the regime corresponding to pure n- and p-type regimes, is equal to k ln 10/e. The slope is the consequence of using the Maxwell− Boltzmann statistics for describing the charge carriers in classical semiconductors. • The parameters B and D may be determined graphically from the critical points of the Jonker “pear-like” curve, C, H, G, E, F, N. The parameters B and D may be used for the determination of semiconducting quantities, such as the band gap and the mobility terms, if the transport mechanism is known. When the minimum of the electrical conductivity, related to the n−p transition, is known, then the Jonker equation (1) may also be represented in a linear form (Figure 2):5
The recently reported studies on In-doped TiO2 show that although addition of indium leads to a shift of the n−p transition point toward lower oxygen activity,10−12 the specimen still remains, within the studied range of oxygen activity, an amphoteric semiconductor that is suitable for the application of the Jonker analysis.
2. DEFINITION OF TERMS 2.1. The Jonker Formalism. The classical Jonker formalism applies to the specimens that exhibit the semiconducting properties within both the n- and p-type regimes.2 The Jonker analysis consists of plotting the thermoelectric power data as a function of electrical conductivity data, which are determined isothermally in equilibrium with the gas phase. Application of the Jonker analysis for oxide semiconductors requires that the specimens are annealed in gas phase of different oxygen activities within the n- and p-type regimes. The Jonker formalism is described by the following equation:2 S = ±B 1 −
σmin 2 σ2
−
⎛ k σ ⎜ ln 1± e σmin ⎜⎝
1−
σmin 2 ⎞⎟ +D σ 2 ⎟⎠ (1)
where B=
D=
⎞ k ⎛ Eg + A n + A p⎟ ⎜ 2e ⎝ kT ⎠
μp Npe A p k ln 2e μn Nn e A n
(4)
Y = BX + D (2)
where ⎛ σmin ⎞2 ⎜ ⎟ ⎝ σ ⎠
(5)
k 1±X ln e 1 − X2
(6)
X=± 1− (3)
where Eg is the band gap, An and Ap represent the kinetic terms of electrons and holes, respectively, Nn and Np are the respective densities of states, μn and μp denote the respective mobility terms, k is the Boltzmann constant, e is the elementary charge, σmin is the minimum value of the electrical conductivity, which for symmetric semiconductors corresponds to the n−p transition point, S is thermoelectric power, and σ is the electrical conductivity. The Jonker plot, which is represented by eq 1, has a pear-like shape in the (S − log σ) coordinates. A typical Jonker’s pear-like curve derived for arbitrary quantities is shown in Figure 1.
Y=S+
Figure 2. Schematic representation of the linearized form of the Jonker plot for the determination of parameters B and D of eq 1.
Equation 4 may be used for the determination of parameters B and D by linear regression applied to the experimental data that are transformed accordingly. In most cases, the following inequality applies: σmin ≪ σ (7) Then the component σmin/σ in eq 5 is significantly smaller than unity. The condition (7) will be considered in solution of the Jonker equation (1) (see below).
Figure 1. Jonker formalism represented in graphical terms. The parameters B, D, S, σ, and σmin are explained in the text. 4033
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The Journal of Physical Chemistry A Although derivation of the “pear-like” curve requires knowledge of a wide range of experimental data within both n- and p-type regimes, the linear plot allows the analysis within essentially a narrow range of data in the vicinity of the n− transition point. The critical requirement of the Jonker analysis of oxide semiconductors is that both electrical properties (electrical conductivity and thermoelectric power) correspond to a single phase that is in equilibrium with the gas phase of controlled oxygen activity. 2.2. Effect of Indium on Defect Disorder of TiO2. The predominant ionic defects in pure TiO2 annealed in oxidizing conditions are oxygen vacancies, which are compensated by electrons and titanium vacancies.10 The incorporation of indium into the titanium lattice sites of TiO2 results in the formation of oxygen vacancies. Using the Krö ger−Vink notation,11 the mechanism of indium incorporation into the TiO2 lattice may be represented by the following reaction: In2O3 ↔ 2In′Ti + 3OOx + V •• O
Figure 3. Effect of oxygen activity on the concentration of electronic charge carriers for In-doped TiO2 represented in terms of the Brouwer-type diagram (a) and the related expressions for the concentration of electrons and electron holes (b), where the square brackets denote the concentrations.
(8)
Therefore, the resulting defect disorder is governed by the following charge neutrality: [In′Ti] = 2[V •• O]
(9)
Equations 8 and 9 have the predominant effect on properties of In-doped TiO2 in oxidizing conditions. It has been recently shown12 that the effect of oxygen activity on the concentration of electrons for In-doped TiO2 in strongly reducing conditions is the same as that for pure TiO2 in terms of the slope of the dependence log σ vs log p(O2). This indicates that imposition of strongly reducing conditions results in the formation of oxygen vacancies in excess to their concentration formed as a result of eq 8. Then the simplified charge neutrality is governed by the following equation: n = 2[V •• O]
(10)
The related defect disorder of In-doped TiO2 within strongly reducing and oxidizing conditions is represented by the Brouwer-type defect diagram (Figure 3). As seen, the related concentration of electrons depends on oxygen activity. The p(O2) exponents −1/6 and −1/4 in strongly reducing and oxidizing conditions are reflective of the electronic and ionic charge compensations, respectively. Assuming that the mobility is independent of oxygen activity, the defect disorder may be assessed by isothermal measurements of the electrical conductivity as a function of oxygen activity. The determination of the effect of indium on the semiconducting properties requires alternative approaches, such as the determination of absolute values of the electrical conductivity, when the concentration of indium is low or moderate. An additional complication is that indium may also be incorporated into interstitial sites leading to the formation of donors: x 2In2O3 ↔ 4In••• + 3V⁗ i Ti + 6OO
Figure 4. Isothermal dependence of the electrical conductivity (upper part) and thermoelectric power (lower part) as a function of oxygen activity for In-doped TiO2. The solid lines correspond to the experimental data and the dashed lines represent the extrapolated dependence.
vs oxygen activity is only an indicative approach in the determination of defect disorder for In-doped TiO2. Recent studies of the authors involved the determination of the effect of indium on a range of electrical properties, including the electrical conductivity,12 thermoelectric power,13 the n−p transition point,14 and segregation.15
(11)
Then the charge neutrality is governed by the following condition: ••• 4[V⁗ Ti] = 3[In i ]
(12)
3. BRIEF LITERATURE OVERVIEW It has been shown that oxide semiconductors that exhibit amphoteric properties, such as TiO2,3 BaTiO3,4 CoO,5
Because the effect of indium on the defect disorder of TiO2 is rather complex, the measurement of the electrical conductivity 4034
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Figure 5. Isothermal Jonker plots for In-doped TiO2 represented in the linear form at 1023 K (a), 1073 K (b), 1123 K (c), 1173 K (d), 1223 K (e), and 1273 K (f). The data determined in oxidizing conditions fulfill the linear dependence. The data obtained in the gas phase involving hydrogen, which correspond to X = −1, exhibit a strong deviation from the linearity.
CaTiO3,6 and YBaCuO7,7 can be well described by the Jonker formalism. However, the analysis performed for high purity polycrystalline TiO2 has shown that the semiconducting properties of reduced TiO2 exhibit a departure from the behavior for classical nondegenerated semiconductors that can be described by the Maxwell−Boltzmann statistics of electrons.8 The departure was initially considered in terms of the effect of grain boundaries, which exhibit different semiconducting properties. To understand the effect of grain boundaries, the Jonker analysis was subsequently performed for both polycrystalline specimen and TiO2 single crystal.8,9 This analysis has shown that although TiO2 in oxidizing conditions is described by the Jonker formalism very well, the semiconducting properties in reducing conditions, imposed by argon plus hydrogen (1%), are entirely different. The electrical properties were initially considered in terms of hydrogeninduced larger defect aggregates. The related effects indicate
that hydrogen dissolved in TiO2 lattice results in the formation of structural domains that exhibit outstanding properties. The objective of this work is to perform the Jonker analysis for In-doped TiO2 to assess the effect of indium and the semiconducting properties of the specimens equilibrated in the gas phase involving hydrogen. The ultimate objective is to increase the present level of understanding on the effect of hydrogen on defect disorder of TiO2.
4. EXPERIMENTAL SECTION The details of the processing of In-doped TiO2 and its surface and bulk composition, were reported before.15 The chemical analysis of proton-induced X-ray emission (PIXE) has shown that the bulk content of indium is 0.4 at. %, whereas segregation, determined by secondary ion mass spectrometry (SIMS), results in a substantial enrichment of the surface layer in indium. 4035
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Figure 6. Isothermal Jonker plots for In-doped TiO2 at 1023 K (a), 1073 K (b), 1123 K (c), 1173 K (d), 1223 K (e), and 1273 K (f). The data determined in oxidizing conditions fulfill the pear-type dependence. The data obtained in the gas phase involving hydrogen exhibit a strong deviation from the slope k ln 10/e.
The effect of oxygen activity on the electrical conductivity12 and thermoelectric power13 are considered in terms of the conditions (8), (9), and (11). The related experimental data in both oxidizing [p(O2) > 10 Pa] and reducing [p(O2) < 10−10 Pa] conditions in the temperature range 1023−1273 K are represented in Figure 4. The optical band gap was determined in the reflectance mode using the Agilent Cary 5000 UV−vis spectrophotometer in the wavelength range 200−800 nm. The system baseline was calibrated with polytetrafluoroethylene (PTFE) standard plate on the reference port. The samples were attached to the sample port. The scan rate was 600 nm/min. The samples for the
optical spectra were made by pressing the power at 2 t/m2 into pellets of 12 mm of diameter and 1.5 mm in thickness. The pellets were sintered at 1273 K for 3 h in the gas phase of controlled oxygen activity.
5. RESULTS AND DISCUSSION As seen in Figure 4, the values of the n−p transition points determined by the thermoelectric power, when S = 0, are consistent with the minima of the electrical conductivity. This consistency indicates that the mobility terms of electronic charge carriers are the same (μn = μp) and the studied specimen behaves as a symmetrical semiconductor.12,13 4036
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The Journal of Physical Chemistry A 5.1. Linear Jonker Plots. This section considers the Jonker model in terms of the linear approach that is represented by eq 4. This approach, which is relatively simple, allows a preliminary approach to examine the consistency between the experimental data and the Jonker model. The Jonker plots of both electrical conductivity and thermoelectric power in the range 1023−1273 K are represented in terms of the linear system in Figure 5. The solid lines in Figure 5 represent the best linear fit of the experimental data corresponding to the oxidizing conditions within the n−p transition point. As seen, the experimental data for the specimen annealed in oxidizing conditions exhibit a good linearity. This dependence was used in the determination of the parameters B and D as it is represented in Figure 2. However, as seen from Figure 5, the experimental data for the specimen annealed in the gas phase involving hydrogen do not fall on the same straight line. In this case the group of the experimental data corresponding to X = −1 is consistent with the condition (7) when the following inequality applies: ⎛ σmin ⎞2 ⎜ ⎟ ≪ 1 ⎝ σ ⎠
experimental data and the theoretical Jonker dependence with the slope of k ln 10/e, which is the consequence of using the Maxwell−Boltzmann statistics to describe the charge carriers. To quantify this deviation, we have introduced a factor F, which is defined as the ratio of the experimentally determined slope to the theoretical Jonker slope. The factor F = 1 indicates that the data are in perfect agreement with the Jonker model. The factor F is reflective of the extent of the deviation of the experimental data from the slope associated with the Maxwell− Boltzmann statistics. The smaller the factor F, the stronger is deviation from the slope k ln 10/e. In the first approximation the parameter F is reflective of the interactions within electrons that may be considered in terms of a correlated electron gas.15,16 The determined effect of temperature on the factor F for In-doped TiO2 as well as for pure TiO2 single crystal9 is shown in Figure 8.
(13)
As a consequence, the parameters B and D of the Jonker plot determined using this procedure are reflective only of the TiO2 specimen annealed in oxidizing conditions. The observed departure between the experiment and the theoretical model is limited to the specimens annealed in extremely reducing conditions. As seen, the related experimental data in Figure 5 overlap at X ∼ 1. 5.2. “Pear” Type Jonker Plot. The set of the parameters σmin, B, and D unambiguously identify the Jonker “pear” described by eq 1. The resulting pear-like curves are represented in Figure 6. As seen, the experimental data determined in oxidizing conditions are well described by the Jonker equation. However, the experimental data determined in strongly reducing conditions exhibit a deviation from the Jonker curve in terms of absolute values of thermoelectric power as well as a deviation of the related linear dependence from that expected by the Jonker analysis for a classical semiconductor, where the slope of S vs log σ is k ln 10/e. The deviation of the experimental data in the strongly reducing regime from the Jonker shape is represented schematically in Figure 7 as different slopes of two linear dependencies: the linear dependence represented by the
Figure 8. Effect of temperature on the factor F for pure TiO2 single crystal, reported elsewhere,9 and In-doped TiO2 studied in the present work.
As seen in Figure 8, the deviation for In-doped TiO2 (0.50− 0.57) is much stronger than that for pure TiO2 single crystal (0.67−0.70). So far, little is known on the physical meaning of the factor F. One may expect that the extent of the deviation is reflective of the interactions in the electron gas due to its high density.16,17 The data in Figure 8 indicate that the effect of hydrogen on the interaction-related parameter F is much stronger when indium is present in the TiO2 lattice. This effect suggests that indium has an effect on the properties of the structural domains and the interactions within the electron gas. Therefore, the factor F depends on the structure of these domains and the related statistics of electrons. Better understanding of the effect may lead to processing of such domains with desired properties. The concept of correlated electron gas seems to be related to the effect of hydrogen on deformations of the rutile structure, leading to the formation of structural domains induced by hydrogen incorporation. The electronic properties of these domains are expected to be entirely different from those of the rutile structure. The effect of protons on defect disorder of TiO2 has been extensively studied by Norby et al.18,19 According to Norby, there is a strong affinity between protons and titanium vacancies, which have a tendency to trap protons. The related interactions may lead to the formation of ordered regions and structural domains. So far, little is known about the semi-
Figure 7. Pear-type Jonker plot for of thermoelectric power, S, as a function of log σ for In-doped TiO2 at 1273 K. 4037
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The Journal of Physical Chemistry A conducting properties of these domains and the behavior of the electron gas in these domains. The tendency of titanium vacancies to trap protons is logical because both defects have opposite electric charge. The hypothetical structural domains for pure TiO2 could be considered in terms of the {TiO2H}* structural modules as it is represented in Figure 9.
Figure 10. Effect of temperature on the band gap for In-doped TiO2.
In addition to the effect of indium on the thermal band gap determined using the Jonker eq 2, the present work also obtained the optical band gap for In-doped TiO2 at room temperature from reflectance spectra. These are shown for direct20 and indirect21 transitions in Figure 11.
Figure 9. Schematic representation of the TiO2 lattice showing the hydrogen-containing modules for pure TiO2 (a) and In-doped TiO2 (b).
Figure 11. Reflection spectra for pure and In-doped TiO2 determined assuming the direct (a, b) and indirect (c, d) transitions.
Consequently, the data in Table 1 allows the following points to be made: • Doping of rutile with indium results in a decrease of the band gap from 3.17 to 3.07 eV (direct transitions) or 3.02 to 2.94 eV (indirect transitions). • The difference between the thermal band gap (2.58−2.71 eV) and the optical band gap for In-doped TiO2 determined in this work (3.07−2.94 eV) is substantial.
It appears that annealing of In-doped TiO2 in hydrogen results in the formation of structural domains that exhibit semiconducting properties entirely different than those of oxidized TiO2. As seen in the lower part of Figure 9, replacement of the {TiO2H}* modules with the {InO2H}* modules results in a much stronger effect represented by the parameter F. The studies on the resulting structural properties are underway. Equation 2 of the Jonker formalism may be used for the determination of the thermal band gap, assuming the following expression: Eg = 2eTB − kT (A n + A p)
6. CONCLUSIONS The present work shows that In-doped TiO2 annealed in the gas phase free of hydrogen behaves like the classical semiconductor and its properties are consistent with the Maxwell−Boltzmann statistics. The present work also indicates that In-doped TiO2 is a symmetric semiconductor; i.e., the mobility terms of both electronic charge carriers are the same (μn = μp). Annealing of the In-doped TiO2 specimen in the gas phase including hydrogen results in the departure from the Jonker model. This deviation is considered in terms of the effect of hydrogen on the formation of structural domains in rutile. It appears that the electron gas within the structural domains
(14)
where An and Ap are the kinetic parameters (for electrons and holes, respectively) that depend on the charge transport mechanism. The resulting band gap is shown in Figure 10 as a function of temperature. As seen in Figure 10, depending on the charge transport model, the thermal band gap at room temperature is in the range 2.6−2.7 eV. These values are lower than the optical band gap determined for pure TiO2 (3.07 and 3.17 eV10). 4038
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The Journal of Physical Chemistry A Table 1. Band Gap Determined Using the Jonker Formalism for TiO2 reference
material
approach
3
TiO2−SC
thermal (Jonker analysis)
8
TiO2−PC
thermal (Jonker analysis)
9
TiO2−SC
thermal (Jonker analysis)
conditions
results
985 K < T < 1387 K 10−15 Pa < p(O2) < 105 Pa 1123 K < T < 1273 K 10 Pa < p(O2) < 105 Pa 1073 K < T < 1323 K
TiO2−PC
optical (reflectance spectroscopy)
In−TiO2−PC
optical (reflectance spectroscopy)
thermal (Jonker analysis)
Eg(300 K) = 3.05 eV
300 K
300 K < T < 1273 K
Eg = 2.94 eV (indirect transitions) 2.71 eV < Eg < 1.95 eV
300 K 10−12 Pa < p(O2) < 105 Pa
this work
2.65 eV < Eg < 1.60 eV 2.58 eV < Eg < 1.4 eV Eg = E0 + βT nomenclature PC − poly crystal SC − single crystal p(O2) − oxygen activity Eg − band gap E0 − band gap at T = 0 K β − temperature coefficient of band gap
Eg depends on p(O2)
indium has little effect on Eg
β = 0.8 meV/K (hopping for n + p) β = 1 meV/K (band + hopping models) β = 1.2 meV/K (band model for n + p)
summary Eg(optical) < Eg(thermal) Eg(300 K) ≈ 3 eV
Notes
exhibits interactions typical for the correlated transport of electrons. The behavior seems to be due to high density of electrons. This effect is a result of extremely low oxygen activity, leading to the formation of a high concentration of ionic defects, such as oxygen vacancies and titanium interstitials. It appears that interactions between these defects and protons dissolved in the lattice of rutile are exceptionally strong. It seems that indium ions and indium-induced defects have a crucial role in the formation of larger defect aggregates. The formed structural domains exhibit a high density of electrons resulting in dynamic correlations within the electron gas. Although the effect of hydrogen on the specific properties is not yet clear, it may have a significant impact on the performance of TiO2 in a range of applications, such as solar energy conversion. The present work indicates that indium results in an enhanced effect of hydrogen on the semiconducting properties.
■
TiO2 behaves as a symmetric semiconductor μn = μp β = −0.8 meV K−1
1.8 eV < Eg < 2.06 eV (hopping model) 1.57 eV < Eg < 1.85 eV (hopping + band models) Eg = 3.01 eV (105 Pa) (direct transitions) Eg = 2.91 eV (105 Pa) (indirect transitions) Eg = 2.88 eV (10−12Pa) (direct transitions) Eg = 2.42 eV (10−12 Pa) (indirect transitions) Eg = 3.07 eV (direct transitions)
10 < p(O2) < 105 Pa 22
comments
Eg = 3.09 eV (β = −1.33 mV K−1) Eg(0 K) = 3.09 eV 2.3 eV < Eg < 2.6 eV
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The help of Dr. Wenxian Li in the measurements of the reflection spectra and the support of the University of Western Sydney through the RIF grant is gratefully acknowledged.
■
REFERENCES
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AUTHOR INFORMATION
Corresponding Author
*J. Nowotny. Tel: 61-2-4284-7829. Fax: 61-4620-3711. E-mail: [email protected]. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. 4039
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The Journal of Physical Chemistry A (8) Bak, T.; Nowotny, J. Semiconducting Properties of Oxidized and Reduced Polycrystalline TiO2. Jonker Analysis. J. Phys. Chem. C 2011, 115, 9746−9752. (9) Nowotny, J. Effect of Hydrogen on Semiconducting Properties of TiO2 Single Crystal. Jonker Analysis. J. Phys. Chem. C 2011, 115, 18316−18326. (10) Bak, T.; Nowotny, J.; Sucher, N. J.; Wachsman, E. Effect of Crystal Imperfections on Reactivity and Photoreactivity of TiO2 (Rutile) with Oxygen, Water and Bacteria. J. Phys. Chem. C 2011, 115, 15711−15738. (11) F. A. Kröger The Chemistry of Impefect Crystals; North-Holland: Amsterdam, 1964. (12) Nowotny, J.; Malik, A.; Alim, M. A.; Bak, T.; Atanacio, A. J. Electrical Properties and Defect Chemistry of Indium-Doped TiO2: Electrical Conductivity. ECS J. Solid State Sci. Technol. 2014, 3, P330− P339. (13) Nowotny, J.; Bak, T.; Atanacio, A.; Malik, A.; Alim, M. A. Electrical Properties and Defect Chemistry of Indium-Doped TiO2. Thermoelectric Power. Ionics 2014, DOI: 10.1007/s11581-014-13515. (14) Nowotny, J.; Bak, T.; Alim, M. A. Dual Mechanism of Indium Incorporation into TiO2 (Rutile). J. Phys. Chem. C 2014, 119, 1146− 1154. (15) Atanacio, A. J.; Bak, T.; Nowotny, J. Effect of Indium Segregation on the Surface Versus Bulk Chemistry for IndiumDoped TiO2. ACS Appl. Mater. Interfaces 2012, 4, 6626−6634. (16) Becke, A. D. Correlation Energy of an Inhomogeneous Electron Gas: A Coordinate-Space Model. J. Chem. Phys. 1988, 88, 1053−1062. (17) Gell-Mann, M.; Brueckner, K. A. Correlation Energy of an Electron Gas at High Density. Phys. Rev. 1957, 106, 364. (18) Erdal, S.; Kongshaug, C.; Bjørheim, T. S.; Jalarvo, N.; Haugsrud, R.; Norby, T. Hydration of Rutile TiO2: Thermodynamics and Effects on n-and p-Type Electronic Conduction. J. Phys. Chem. C 2010, 114, 9139−9145. (19) Norby, T. Proton Conduction in Solids: Bulk and Interfaces. MRS Bull. 2009, 34, 923−928. (20) Murphy, A. Band-Gap Determination from Diffuse Reflectance Measurements of Semiconductor Films and Application to Photoelectrochemical Water-Splitting. Sol. Energy Mater. Sol. Cells 2007, 91, 1326−1337. (21) Shao, G. Electronic Structures of Manganese-Doped Rutile TiO2 from First Principles. J. Phys. Chem. C 2008, 112, 18677−18685. (22) Nowotny, J.; Li, W.; Bak, T. Effect of oxygen activity on semiconducting properties of TiO2 (rutile). Ionics 2014, 1−8.
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DOI: 10.1021/acs.jpca.5b01368 J. Phys. Chem. A 2015, 119, 4032−4040
Electrical Properties and Defect Chemistry of In-Doped TiO2 in Terms of the Jonker Formalism Janusz Nowotny,*,† Tadeusz Bak,† Mihail Ionescu,‡ and Mohammad A. Alim† †
Solar Energy Technologies, School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith, NSW 2751, Australia ‡ Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW 2234, Australia ABSTRACT: The present work considers the semiconducting properties of In-doped TiO2 in terms of the Jonker formalism applied for both electrical conductivity and thermoelectric power data determined simultaneously in equilibrium with the gas phase of controlled oxygen activity. It is shown that the electrical properties of In-doped TiO2 annealed in oxidizing conditions [p(O2) > 10 Pa] can be described by the Jonker formalism very well. However, annealing of In-doped TiO2 in strongly reducing conditions [p(O2) < 10−10 Pa], imposed by the gas phase involving hydrogen, results in a deviation of the experimental data from the Jonker’s theoretical model derived for the Maxwell−Boltzmann statistics. This departure is considered in terms of the effect of hydrogen on the formation of structural domains, which are expected to be entirely different from those of oxidized TiO2 in terms of its electronic properties. It is argued that In-doped TiO2 annealed in the gas phase involving hydrogen exhibits a high concentration of donortype ionic defects, which lead to the formation of high concentration of electrons. The related semiconducting properties are inconsistent with the model of classical semiconductor where the electrons are described by the Maxwell−Boltzmann statistics. It is concluded that strong interactions within the electron gas lead, in consequence, to the behavior resembling correlated transport of electrons. The obtained results suggest that indium incorporation into the rutile structure of TiO2 results in the formation of structural properties that exhibit extraordinary charge transport. and YBaCuO7.7 The most extensive studies have been performed for TiO2, including both single crystal and polycrystalline specimens.3,8,9 These studies indicate that although the semiconducting properties for the TiO2 specimens equilibrated in oxidizing conditions are well-defined, annealing in the gas phase involving hydrogen results in outstanding properties.9 It appears that in the latter case the data are inconsistent with the Jonker theoretical model. The observed departure of the experimental data from the Jonker model for the specimen equilibrated in the gas phase involving hydrogen may be considered in terms of the effect of hydrogen incorporated into the rutile lattice. The effect was initially observed for a pure TiO2 single crystal.9 The aim of the present work is to examine the effect of the gas phase involving hydrogen for TiO2 doped with small amount of trivalent ions, such as indium. The rationale of this approach is to compare the extent of the hydrogen-induced behavior for pure TiO2 and In-doped TiO2. The difference, if any, could provide information on the effect of trivalent ions on the extent of the departure from the Maxwell−Boltzmann statistics of TiO2 annealed in the gas phase involving hydrogen.
1. INTRODUCTION Quantitative assessment of the semiconducting properties using the electrical conductivity as a sole electrical property, which is related to both the concentration and the mobility terms, is difficult. However, the measurements of both electrical conductivity and thermoelectric power may be used in the determination of a range of semiconducting quantities, including the band gap and the mobility terms.1 The transport properties of semiconductors can be derived using the method proposed by Jonker,2 which is based on a combined analysis of both the electrical conductivity and thermoelectric power data. The Jonker formalism may be applied for amphoteric oxide semiconductors using the electrical conductivity and thermoelectric power data determined simultaneously in equilibrium with the gas phase of controlled oxygen activity. The key requirement for the application of the Jonker formalism is that these two electrical properties are determined simultaneously. Although Jonker analysis does not require knowledge of the oxygen activity, the effective use of the formalism proposed by Jonker requires that the data of both electrical properties are available within both nand p-type regimes. Therefore, the Jonker analysis can be applied mainly for the semiconductors described by the experimental data within both n- and p-type regimes. The Jonker analysis has been applied for amphoteric semiconductors, such as TiO2,3 BaTiO3,4 CoO,5 CaTiO3,6 © 2015 American Chemical Society
Received: February 10, 2015 Revised: March 30, 2015 Published: April 1, 2015 4032
DOI: 10.1021/acs.jpca.5b01368 J. Phys. Chem. A 2015, 119, 4032−4040
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The critical quantities of the Jonker formalism, which are represented in Figure 1, include • The extreme left-side point of the “pear-like-curve”, which corresponds to the minimum of the electrical conductivity. Its knowledge is essential for analytical determination of the parameters B and D. The parameter σmin can be determined by isothermal monitoring of both the electrical conductivity and thermoelectric power as a function of oxygen activity, p(O2), within the n−p transition. • The slope of the S vs log σ dependence at the right-hand side of the “pear”, within the regime corresponding to pure n- and p-type regimes, is equal to k ln 10/e. The slope is the consequence of using the Maxwell− Boltzmann statistics for describing the charge carriers in classical semiconductors. • The parameters B and D may be determined graphically from the critical points of the Jonker “pear-like” curve, C, H, G, E, F, N. The parameters B and D may be used for the determination of semiconducting quantities, such as the band gap and the mobility terms, if the transport mechanism is known. When the minimum of the electrical conductivity, related to the n−p transition, is known, then the Jonker equation (1) may also be represented in a linear form (Figure 2):5
The recently reported studies on In-doped TiO2 show that although addition of indium leads to a shift of the n−p transition point toward lower oxygen activity,10−12 the specimen still remains, within the studied range of oxygen activity, an amphoteric semiconductor that is suitable for the application of the Jonker analysis.
2. DEFINITION OF TERMS 2.1. The Jonker Formalism. The classical Jonker formalism applies to the specimens that exhibit the semiconducting properties within both the n- and p-type regimes.2 The Jonker analysis consists of plotting the thermoelectric power data as a function of electrical conductivity data, which are determined isothermally in equilibrium with the gas phase. Application of the Jonker analysis for oxide semiconductors requires that the specimens are annealed in gas phase of different oxygen activities within the n- and p-type regimes. The Jonker formalism is described by the following equation:2 S = ±B 1 −
σmin 2 σ2
−
⎛ k σ ⎜ ln 1± e σmin ⎜⎝
1−
σmin 2 ⎞⎟ +D σ 2 ⎟⎠ (1)
where B=
D=
⎞ k ⎛ Eg + A n + A p⎟ ⎜ 2e ⎝ kT ⎠
μp Npe A p k ln 2e μn Nn e A n
(4)
Y = BX + D (2)
where ⎛ σmin ⎞2 ⎜ ⎟ ⎝ σ ⎠
(5)
k 1±X ln e 1 − X2
(6)
X=± 1− (3)
where Eg is the band gap, An and Ap represent the kinetic terms of electrons and holes, respectively, Nn and Np are the respective densities of states, μn and μp denote the respective mobility terms, k is the Boltzmann constant, e is the elementary charge, σmin is the minimum value of the electrical conductivity, which for symmetric semiconductors corresponds to the n−p transition point, S is thermoelectric power, and σ is the electrical conductivity. The Jonker plot, which is represented by eq 1, has a pear-like shape in the (S − log σ) coordinates. A typical Jonker’s pear-like curve derived for arbitrary quantities is shown in Figure 1.
Y=S+
Figure 2. Schematic representation of the linearized form of the Jonker plot for the determination of parameters B and D of eq 1.
Equation 4 may be used for the determination of parameters B and D by linear regression applied to the experimental data that are transformed accordingly. In most cases, the following inequality applies: σmin ≪ σ (7) Then the component σmin/σ in eq 5 is significantly smaller than unity. The condition (7) will be considered in solution of the Jonker equation (1) (see below).
Figure 1. Jonker formalism represented in graphical terms. The parameters B, D, S, σ, and σmin are explained in the text. 4033
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The Journal of Physical Chemistry A Although derivation of the “pear-like” curve requires knowledge of a wide range of experimental data within both n- and p-type regimes, the linear plot allows the analysis within essentially a narrow range of data in the vicinity of the n− transition point. The critical requirement of the Jonker analysis of oxide semiconductors is that both electrical properties (electrical conductivity and thermoelectric power) correspond to a single phase that is in equilibrium with the gas phase of controlled oxygen activity. 2.2. Effect of Indium on Defect Disorder of TiO2. The predominant ionic defects in pure TiO2 annealed in oxidizing conditions are oxygen vacancies, which are compensated by electrons and titanium vacancies.10 The incorporation of indium into the titanium lattice sites of TiO2 results in the formation of oxygen vacancies. Using the Krö ger−Vink notation,11 the mechanism of indium incorporation into the TiO2 lattice may be represented by the following reaction: In2O3 ↔ 2In′Ti + 3OOx + V •• O
Figure 3. Effect of oxygen activity on the concentration of electronic charge carriers for In-doped TiO2 represented in terms of the Brouwer-type diagram (a) and the related expressions for the concentration of electrons and electron holes (b), where the square brackets denote the concentrations.
(8)
Therefore, the resulting defect disorder is governed by the following charge neutrality: [In′Ti] = 2[V •• O]
(9)
Equations 8 and 9 have the predominant effect on properties of In-doped TiO2 in oxidizing conditions. It has been recently shown12 that the effect of oxygen activity on the concentration of electrons for In-doped TiO2 in strongly reducing conditions is the same as that for pure TiO2 in terms of the slope of the dependence log σ vs log p(O2). This indicates that imposition of strongly reducing conditions results in the formation of oxygen vacancies in excess to their concentration formed as a result of eq 8. Then the simplified charge neutrality is governed by the following equation: n = 2[V •• O]
(10)
The related defect disorder of In-doped TiO2 within strongly reducing and oxidizing conditions is represented by the Brouwer-type defect diagram (Figure 3). As seen, the related concentration of electrons depends on oxygen activity. The p(O2) exponents −1/6 and −1/4 in strongly reducing and oxidizing conditions are reflective of the electronic and ionic charge compensations, respectively. Assuming that the mobility is independent of oxygen activity, the defect disorder may be assessed by isothermal measurements of the electrical conductivity as a function of oxygen activity. The determination of the effect of indium on the semiconducting properties requires alternative approaches, such as the determination of absolute values of the electrical conductivity, when the concentration of indium is low or moderate. An additional complication is that indium may also be incorporated into interstitial sites leading to the formation of donors: x 2In2O3 ↔ 4In••• + 3V⁗ i Ti + 6OO
Figure 4. Isothermal dependence of the electrical conductivity (upper part) and thermoelectric power (lower part) as a function of oxygen activity for In-doped TiO2. The solid lines correspond to the experimental data and the dashed lines represent the extrapolated dependence.
vs oxygen activity is only an indicative approach in the determination of defect disorder for In-doped TiO2. Recent studies of the authors involved the determination of the effect of indium on a range of electrical properties, including the electrical conductivity,12 thermoelectric power,13 the n−p transition point,14 and segregation.15
(11)
Then the charge neutrality is governed by the following condition: ••• 4[V⁗ Ti] = 3[In i ]
(12)
3. BRIEF LITERATURE OVERVIEW It has been shown that oxide semiconductors that exhibit amphoteric properties, such as TiO2,3 BaTiO3,4 CoO,5
Because the effect of indium on the defect disorder of TiO2 is rather complex, the measurement of the electrical conductivity 4034
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Figure 5. Isothermal Jonker plots for In-doped TiO2 represented in the linear form at 1023 K (a), 1073 K (b), 1123 K (c), 1173 K (d), 1223 K (e), and 1273 K (f). The data determined in oxidizing conditions fulfill the linear dependence. The data obtained in the gas phase involving hydrogen, which correspond to X = −1, exhibit a strong deviation from the linearity.
CaTiO3,6 and YBaCuO7,7 can be well described by the Jonker formalism. However, the analysis performed for high purity polycrystalline TiO2 has shown that the semiconducting properties of reduced TiO2 exhibit a departure from the behavior for classical nondegenerated semiconductors that can be described by the Maxwell−Boltzmann statistics of electrons.8 The departure was initially considered in terms of the effect of grain boundaries, which exhibit different semiconducting properties. To understand the effect of grain boundaries, the Jonker analysis was subsequently performed for both polycrystalline specimen and TiO2 single crystal.8,9 This analysis has shown that although TiO2 in oxidizing conditions is described by the Jonker formalism very well, the semiconducting properties in reducing conditions, imposed by argon plus hydrogen (1%), are entirely different. The electrical properties were initially considered in terms of hydrogeninduced larger defect aggregates. The related effects indicate
that hydrogen dissolved in TiO2 lattice results in the formation of structural domains that exhibit outstanding properties. The objective of this work is to perform the Jonker analysis for In-doped TiO2 to assess the effect of indium and the semiconducting properties of the specimens equilibrated in the gas phase involving hydrogen. The ultimate objective is to increase the present level of understanding on the effect of hydrogen on defect disorder of TiO2.
4. EXPERIMENTAL SECTION The details of the processing of In-doped TiO2 and its surface and bulk composition, were reported before.15 The chemical analysis of proton-induced X-ray emission (PIXE) has shown that the bulk content of indium is 0.4 at. %, whereas segregation, determined by secondary ion mass spectrometry (SIMS), results in a substantial enrichment of the surface layer in indium. 4035
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Figure 6. Isothermal Jonker plots for In-doped TiO2 at 1023 K (a), 1073 K (b), 1123 K (c), 1173 K (d), 1223 K (e), and 1273 K (f). The data determined in oxidizing conditions fulfill the pear-type dependence. The data obtained in the gas phase involving hydrogen exhibit a strong deviation from the slope k ln 10/e.
The effect of oxygen activity on the electrical conductivity12 and thermoelectric power13 are considered in terms of the conditions (8), (9), and (11). The related experimental data in both oxidizing [p(O2) > 10 Pa] and reducing [p(O2) < 10−10 Pa] conditions in the temperature range 1023−1273 K are represented in Figure 4. The optical band gap was determined in the reflectance mode using the Agilent Cary 5000 UV−vis spectrophotometer in the wavelength range 200−800 nm. The system baseline was calibrated with polytetrafluoroethylene (PTFE) standard plate on the reference port. The samples were attached to the sample port. The scan rate was 600 nm/min. The samples for the
optical spectra were made by pressing the power at 2 t/m2 into pellets of 12 mm of diameter and 1.5 mm in thickness. The pellets were sintered at 1273 K for 3 h in the gas phase of controlled oxygen activity.
5. RESULTS AND DISCUSSION As seen in Figure 4, the values of the n−p transition points determined by the thermoelectric power, when S = 0, are consistent with the minima of the electrical conductivity. This consistency indicates that the mobility terms of electronic charge carriers are the same (μn = μp) and the studied specimen behaves as a symmetrical semiconductor.12,13 4036
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The Journal of Physical Chemistry A 5.1. Linear Jonker Plots. This section considers the Jonker model in terms of the linear approach that is represented by eq 4. This approach, which is relatively simple, allows a preliminary approach to examine the consistency between the experimental data and the Jonker model. The Jonker plots of both electrical conductivity and thermoelectric power in the range 1023−1273 K are represented in terms of the linear system in Figure 5. The solid lines in Figure 5 represent the best linear fit of the experimental data corresponding to the oxidizing conditions within the n−p transition point. As seen, the experimental data for the specimen annealed in oxidizing conditions exhibit a good linearity. This dependence was used in the determination of the parameters B and D as it is represented in Figure 2. However, as seen from Figure 5, the experimental data for the specimen annealed in the gas phase involving hydrogen do not fall on the same straight line. In this case the group of the experimental data corresponding to X = −1 is consistent with the condition (7) when the following inequality applies: ⎛ σmin ⎞2 ⎜ ⎟ ≪ 1 ⎝ σ ⎠
experimental data and the theoretical Jonker dependence with the slope of k ln 10/e, which is the consequence of using the Maxwell−Boltzmann statistics to describe the charge carriers. To quantify this deviation, we have introduced a factor F, which is defined as the ratio of the experimentally determined slope to the theoretical Jonker slope. The factor F = 1 indicates that the data are in perfect agreement with the Jonker model. The factor F is reflective of the extent of the deviation of the experimental data from the slope associated with the Maxwell− Boltzmann statistics. The smaller the factor F, the stronger is deviation from the slope k ln 10/e. In the first approximation the parameter F is reflective of the interactions within electrons that may be considered in terms of a correlated electron gas.15,16 The determined effect of temperature on the factor F for In-doped TiO2 as well as for pure TiO2 single crystal9 is shown in Figure 8.
(13)
As a consequence, the parameters B and D of the Jonker plot determined using this procedure are reflective only of the TiO2 specimen annealed in oxidizing conditions. The observed departure between the experiment and the theoretical model is limited to the specimens annealed in extremely reducing conditions. As seen, the related experimental data in Figure 5 overlap at X ∼ 1. 5.2. “Pear” Type Jonker Plot. The set of the parameters σmin, B, and D unambiguously identify the Jonker “pear” described by eq 1. The resulting pear-like curves are represented in Figure 6. As seen, the experimental data determined in oxidizing conditions are well described by the Jonker equation. However, the experimental data determined in strongly reducing conditions exhibit a deviation from the Jonker curve in terms of absolute values of thermoelectric power as well as a deviation of the related linear dependence from that expected by the Jonker analysis for a classical semiconductor, where the slope of S vs log σ is k ln 10/e. The deviation of the experimental data in the strongly reducing regime from the Jonker shape is represented schematically in Figure 7 as different slopes of two linear dependencies: the linear dependence represented by the
Figure 8. Effect of temperature on the factor F for pure TiO2 single crystal, reported elsewhere,9 and In-doped TiO2 studied in the present work.
As seen in Figure 8, the deviation for In-doped TiO2 (0.50− 0.57) is much stronger than that for pure TiO2 single crystal (0.67−0.70). So far, little is known on the physical meaning of the factor F. One may expect that the extent of the deviation is reflective of the interactions in the electron gas due to its high density.16,17 The data in Figure 8 indicate that the effect of hydrogen on the interaction-related parameter F is much stronger when indium is present in the TiO2 lattice. This effect suggests that indium has an effect on the properties of the structural domains and the interactions within the electron gas. Therefore, the factor F depends on the structure of these domains and the related statistics of electrons. Better understanding of the effect may lead to processing of such domains with desired properties. The concept of correlated electron gas seems to be related to the effect of hydrogen on deformations of the rutile structure, leading to the formation of structural domains induced by hydrogen incorporation. The electronic properties of these domains are expected to be entirely different from those of the rutile structure. The effect of protons on defect disorder of TiO2 has been extensively studied by Norby et al.18,19 According to Norby, there is a strong affinity between protons and titanium vacancies, which have a tendency to trap protons. The related interactions may lead to the formation of ordered regions and structural domains. So far, little is known about the semi-
Figure 7. Pear-type Jonker plot for of thermoelectric power, S, as a function of log σ for In-doped TiO2 at 1273 K. 4037
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The Journal of Physical Chemistry A conducting properties of these domains and the behavior of the electron gas in these domains. The tendency of titanium vacancies to trap protons is logical because both defects have opposite electric charge. The hypothetical structural domains for pure TiO2 could be considered in terms of the {TiO2H}* structural modules as it is represented in Figure 9.
Figure 10. Effect of temperature on the band gap for In-doped TiO2.
In addition to the effect of indium on the thermal band gap determined using the Jonker eq 2, the present work also obtained the optical band gap for In-doped TiO2 at room temperature from reflectance spectra. These are shown for direct20 and indirect21 transitions in Figure 11.
Figure 9. Schematic representation of the TiO2 lattice showing the hydrogen-containing modules for pure TiO2 (a) and In-doped TiO2 (b).
Figure 11. Reflection spectra for pure and In-doped TiO2 determined assuming the direct (a, b) and indirect (c, d) transitions.
Consequently, the data in Table 1 allows the following points to be made: • Doping of rutile with indium results in a decrease of the band gap from 3.17 to 3.07 eV (direct transitions) or 3.02 to 2.94 eV (indirect transitions). • The difference between the thermal band gap (2.58−2.71 eV) and the optical band gap for In-doped TiO2 determined in this work (3.07−2.94 eV) is substantial.
It appears that annealing of In-doped TiO2 in hydrogen results in the formation of structural domains that exhibit semiconducting properties entirely different than those of oxidized TiO2. As seen in the lower part of Figure 9, replacement of the {TiO2H}* modules with the {InO2H}* modules results in a much stronger effect represented by the parameter F. The studies on the resulting structural properties are underway. Equation 2 of the Jonker formalism may be used for the determination of the thermal band gap, assuming the following expression: Eg = 2eTB − kT (A n + A p)
6. CONCLUSIONS The present work shows that In-doped TiO2 annealed in the gas phase free of hydrogen behaves like the classical semiconductor and its properties are consistent with the Maxwell−Boltzmann statistics. The present work also indicates that In-doped TiO2 is a symmetric semiconductor; i.e., the mobility terms of both electronic charge carriers are the same (μn = μp). Annealing of the In-doped TiO2 specimen in the gas phase including hydrogen results in the departure from the Jonker model. This deviation is considered in terms of the effect of hydrogen on the formation of structural domains in rutile. It appears that the electron gas within the structural domains
(14)
where An and Ap are the kinetic parameters (for electrons and holes, respectively) that depend on the charge transport mechanism. The resulting band gap is shown in Figure 10 as a function of temperature. As seen in Figure 10, depending on the charge transport model, the thermal band gap at room temperature is in the range 2.6−2.7 eV. These values are lower than the optical band gap determined for pure TiO2 (3.07 and 3.17 eV10). 4038
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The Journal of Physical Chemistry A Table 1. Band Gap Determined Using the Jonker Formalism for TiO2 reference
material
approach
3
TiO2−SC
thermal (Jonker analysis)
8
TiO2−PC
thermal (Jonker analysis)
9
TiO2−SC
thermal (Jonker analysis)
conditions
results
985 K < T < 1387 K 10−15 Pa < p(O2) < 105 Pa 1123 K < T < 1273 K 10 Pa < p(O2) < 105 Pa 1073 K < T < 1323 K
TiO2−PC
optical (reflectance spectroscopy)
In−TiO2−PC
optical (reflectance spectroscopy)
thermal (Jonker analysis)
Eg(300 K) = 3.05 eV
300 K
300 K < T < 1273 K
Eg = 2.94 eV (indirect transitions) 2.71 eV < Eg < 1.95 eV
300 K 10−12 Pa < p(O2) < 105 Pa
this work
2.65 eV < Eg < 1.60 eV 2.58 eV < Eg < 1.4 eV Eg = E0 + βT nomenclature PC − poly crystal SC − single crystal p(O2) − oxygen activity Eg − band gap E0 − band gap at T = 0 K β − temperature coefficient of band gap
Eg depends on p(O2)
indium has little effect on Eg
β = 0.8 meV/K (hopping for n + p) β = 1 meV/K (band + hopping models) β = 1.2 meV/K (band model for n + p)
summary Eg(optical) < Eg(thermal) Eg(300 K) ≈ 3 eV
Notes
exhibits interactions typical for the correlated transport of electrons. The behavior seems to be due to high density of electrons. This effect is a result of extremely low oxygen activity, leading to the formation of a high concentration of ionic defects, such as oxygen vacancies and titanium interstitials. It appears that interactions between these defects and protons dissolved in the lattice of rutile are exceptionally strong. It seems that indium ions and indium-induced defects have a crucial role in the formation of larger defect aggregates. The formed structural domains exhibit a high density of electrons resulting in dynamic correlations within the electron gas. Although the effect of hydrogen on the specific properties is not yet clear, it may have a significant impact on the performance of TiO2 in a range of applications, such as solar energy conversion. The present work indicates that indium results in an enhanced effect of hydrogen on the semiconducting properties.
■
TiO2 behaves as a symmetric semiconductor μn = μp β = −0.8 meV K−1
1.8 eV < Eg < 2.06 eV (hopping model) 1.57 eV < Eg < 1.85 eV (hopping + band models) Eg = 3.01 eV (105 Pa) (direct transitions) Eg = 2.91 eV (105 Pa) (indirect transitions) Eg = 2.88 eV (10−12Pa) (direct transitions) Eg = 2.42 eV (10−12 Pa) (indirect transitions) Eg = 3.07 eV (direct transitions)
10 < p(O2) < 105 Pa 22
comments
Eg = 3.09 eV (β = −1.33 mV K−1) Eg(0 K) = 3.09 eV 2.3 eV < Eg < 2.6 eV
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The help of Dr. Wenxian Li in the measurements of the reflection spectra and the support of the University of Western Sydney through the RIF grant is gratefully acknowledged.
■
REFERENCES
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AUTHOR INFORMATION
Corresponding Author
*J. Nowotny. Tel: 61-2-4284-7829. Fax: 61-4620-3711. E-mail: [email protected]. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. 4039
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