- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Materials Science and Engineering
Volume 2012 (2012), Article ID 826873, 13 pages
Nonstoichiometry in Studied by Ion Beam Methods and Photoelectron Spectroscopy
Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, AGH University of Science and Technology, 30 Mickiewicza Avenue, 30-059 Kraków, Poland
Received 7 July 2011; Revised 30 August 2011; Accepted 1 September 2011
Academic Editor: Adam Georg Balogh
Copyright © 2012 K. Zakrzewska. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper treats a problem of nonstoichiometry in thin films deposited by reactive sputtering at controlled sputtering rates. Ion beam techniques, Rutherford backscattering (RBS), and nuclear reaction analysis (NRA) along with X-ray photoelectron spectroscopy have been applied to determine a deviation from stoichiometry in the bulk and at the surface of layers. The critical review of these experimental methods is given. Defect structure responsible for the electrical resistivity of rutile is discussed.
Titanium dioxide is considered as one of the most important materials from the point of view of both fundamental properties and applications. These applications rely on excellent chemical stability of in hazardous environments, hardness, high refractive index, and many other remarkable features.
Titanium dioxide exists in three polymorphic forms: brookite, rutile, and anatase. Anatase and brookite as metastable phases transform irreversibly into rutile over the temperature range of 973 K–1173 K .
Rutile is a high-temperature, stable phase, thus it is not surprising that this particular polymorphic form has been the most thoroughly investigated. The majority of crystal growth techniques yield titanium dioxide in the rutile phase. Moreover, in many devices (e.g., gas sensors) that operate at high temperatures, is already converted into rutile.
Recently, less common anatase has gained a considerable scientific importance thanks to a significant role it plays in photocatalytic, photovoltaic, and photoelectrochemical applications of titanium dioxide . Some basic physical parameters such as the bandgap, effective mass, and mobility of charge carriers, assumed earlier to be the same as in rutile, in fact were found to differ considerably in the case of anatase.
Titanium dioxide due to its wide band gap (3.0 eV for rutile and 3.2 eV for anatase ) should be treated as an insulator. However, when equilibrated in an atmosphere of low oxygen activity, it becomes an oxygen-deficient semiconductor due to the electronic disorder related to nonstoichiometry .
Much work has been devoted to the nonstoichiometric rutile , both in the structural aspects related to the nature of defects [4, 5] and in the subsequent physical [6, 7] and thermodynamic properties . However, there is still a disagreement as to the extent of nonstoichiometry and the mechanism by which it is accommodated in rutile. It is generally believed that titania can support large deviations from stoichiometry. Earlier investigations overestimated the homogeneity range of extending it to a value as high as at 1170–1270 K . Later experimental evidence  suggests that the homogeneity range is much narrower ( at 1270 K).
The structure of defects responsible for the electronic conduction in rutile and anatase is still a subject of discussion in spite of numerous studies devoted to this topic and the varied experimental techniques used to determine it. It is often assumed that oxygen deficiency could be accommodated by point defects: oxygen vacancies , titanium interstitials [11, 12], or a combination of these two defects . Ionization of these defects provides electrons necessary for the electrical conduction. Which particular defect is responsible for the electrical conductivity is largely affected by the conditions of experiment. The majority of defects switch their role when scanning over the temperature and oxygen partial pressure ranges as shown in .
It should be pointed out that there exists a significant controversy between two different approaches to the problem of defects in rutile. Some authors  claim that even for an extremely small departure from the ideal composition, nonstoichiometry is accommodated mainly by a crystallographic shear plane mechanism while the point defects model may be applied very close to the stoichiometric composition only.
Randomly distributed point defects of low density, present when the deviation from stoichiometry is small, become ordered as their concentration and interaction between them increase. In rutile () this ordering takes a form of planar defects, that is, crystallographic shear (CS) planes. The planar defects, when numerous enough, order to form new compounds with distinct compositions and structures known as Magnéli phases . Magnéli phases constitute a homologous series with the general formula , where is related by to a deviation from stoichiometry ().
Phase diagram of Ti–O system  indicates that the region of contains stable ordered phases with . For smaller departures from stoichiometry () the concentration of the shear planes defects decreases and their mutual interaction becomes weaker. For a very small departure from stoichiometry, , corresponding to , formation of isolated shear planes in equilibrium with point defects was proposed . This is described as a Wadsley defect.
A detailed description of the mechanism of nucleation, growth, and aggregation of the shear planes CS is beyond the scope of this work but may be found in numerous papers devoted to this problem [4, 5, 16]. Existence of such defects in single crystals has been confirmed experimentally by STM  and TEM .
The experimental results of tracer diffusion , chemical diffusion , and thermogravimetric measurements  indicate titanium interstitials as the majority point defects in oxygen-deficient . Works in favour of oxygen vacancies are also numerous. The computer simulation of the defect chemistry of rutile has been carried out as well .
This issue in the case of anatase has been only quite recently brought up [21, 22]. Na-Phattalung et al.  performing first-principle calculations have found that the formation energy of oxygen vacancies is higher than that of titanium interstitials. Thus, in undoped samples, titanium interstitials should be the leading donors while postgrowth formation of oxygen vacancies is also possible upon heating.
A transition from predominant oxygen vacancies to titanium interstitials in anatase has been reported by Weibel et al.  on the basis of the measurements of the electrical resistivity in dense anatase ceramics. This transition has been observed upon the temperature increase and/or the oxygen partial pressure decrease. Hence, it could be concluded that the formation of titanium interstitials was more favourable in anatase in comparison to rutile due to lower density of anatase than that of rutile.
The aim of this work is to review the problem of experimental techniques best suited to the determination of deviation from stoichiometry in thin films. Thin films were deposited by rf and dc magnetron sputtering technique. The sputtering conditions are well defined in such a sense that the substrate temperature and sputtering rate were continuously controlled as described in detail in .
2. Electrical Conductivity and Point Defect Structure of
The departure from stoichiometry may be expressed within the ideal mass action law as a function of the oxygen partial pressure : where yields information on the nature of the defect structure .
The following types of defects: doubly and singly ionized oxygen vacancies as well as titanium interstitials and are usually taken into account. Theoretically predicted values of associated with the specific point defect are listed in Table 1. When dealing with the structure of point defects, the Kröger-Vink notation  is used.
The electrical conductivity of titanium dioxide is a function of the temperature, , and oxygen partial pressure, . The latter is a consequence of the relation between the departure from stoichiometry and given by (1).
The temperature dependence of the carrier concentration and conductivity for nonstoichiometric involves the activation energy of the conduction process, associated with ionization of certain neutral defects. As oxygen vacancies usually form shallow donor levels, their activation energy is much smaller than the forbidden band gap and a measurable value of the electrical conductivity can be observed even at room temperature for nonstoichiometric .
In the n-type regime, the electrical conductivity σ of is affected by the oxygen partial pressure
This is due to the fact that the electron concentration is a function of which results from the relationship between and the departure from stoichiometry . When the mobility of charge carriers is independent of the oxygen partial pressure, then .
The coefficients , , and can be calculated from the appropriate models of point defects. Experimentally, they can be determined from the relations given by (1), (2), or (3) by measuring , , or , respectively, as a function of oxygen partial pressure . As shown in Figure 1, the slope of dependence plotted in the double logarithmic coordinate system yields the coefficient . According to the analysis presented in Table 1, it should be possible on this basis to discriminate between different types of defects and determine the majority defect mechanism.
In practice, the electrical measurements in over the temperature range of 1070–1370 K reveal  that the slope of σ against is different under different regimes of oxygen activities. Therefore, the parameter associated with the majority defect, changes when is varied. At low oxygen partial pressures close to 5 is obtained which can be accounted for by titanium interstitials, . Over the intermediate range of , and doubly ionized oxygen vacancies are postulated. Finally, at high the value close to 4 is observed, corresponding to either singly ionized oxygen vacancy defect, , or interstitial titanium,.
In the n-p-type transition region, two competitive defect models have been proposed [26, 27]. One is related to the extrinsic disorder and assumes that the acceptor-type impurities are always present in TiO2. The second model considers the Schottky-type defect comprising the titanium vacancy associated with oxygen vacancy . Both models give the same dependence of concentration of electrons () and that of holes () on :
The p-type conductivity in is predicted to occur under very high partial pressure of oxygen. The same two models: extrinsic disorder and Schottky-type defect are discussed in this case . The former assumes that the concentration of holes is much larger than that of oxygen vacancies. The latter requires the concentration of holes to be compensated by . The results of these models are quite different. The extrinsic disorder yields the concentration of holes independent of the . The Schottky model gives 
The arguments leading to the relation described above assume a quite unrealistic situation in which only one type of defect is present. In practice, under the experimental conditions of Pa the dependence given by (4) is observed instead.
The following comments to the analysis presented above should be taken into account.(i)Unambiguous assignment of the majority defect on the basis of is difficult to make because frequently the same value of this parameter corresponds to more than one type of defect. This is the case for related to the singly ionized oxygen vacancy or the titanium interstitial.(ii)Different types of majority defects predominate over different ranges of oxygen partial pressure. (iii) One should expect the combination of point defects rather than a single defect to be present in .
In fact, the coexistence of divalent oxygen vacancies with tri- and tetravalent titanium interstitials has been proposed .
3. Nonstoichiometric Thin Films of
A variety of deposition techniques including chemical (CVD) [28–31] and physical vapour deposition (PVD) [32–34] have been reported for titanium dioxide thin films. One should mention here growth techniques successfully applied in the elaboration of thin films, such as sol-gel process , atomic layer epitaxy (ALE) , pulsed laser deposition , and filtered arc deposition (FAD) . Excellent reviews, covering both the growth techniques applied to deposition of coatings as well as the film morphology and optical properties, have been published .
Among the PVD techniques, the most important from the point of view of mass production is the sputter deposition in its multiple forms [32–34]. From all of these forms, only the reactive process, that is, the sputtering of the metallic target in oxidizing atmosphere was chosen in this work. The reason for that is the simple preparation procedure and a low cost of the target. Moreover, reactive sputtering provides thin films that are dense and uniform in thickness. It is relatively easy to control the film stoichiometry in the reactive sputtering.
The problem of nonstoichiometry is especially important in the case of thin films deposited by high-rate sputtering sources such as magnetrons. Here an uncontrollable switching between two stable modes: reactive and metallic, is likely to occur causing an abrupt change in the oxidation state of the target surface followed by modification of sputtering rate [40–43]. This affects not only a departure from stoichiometry of deposited thin films but the microstructure and related film properties as well.
Microstructure understood as an ensemble of physical features such as phase composition, density, porosity, roughness, and grain size is generally accepted to be the most important factor affecting the behaviour of specific devices based on thin films. This is true for gas sensors as well as for photonic and optoelectronic devices in which the electrical and optical properties of thin films are responsible for device performance. Stability of the electrical and optical responses is directly related to the microstructure changes during device operation. The control over the material microstructure is in most cases the prerequisite condition for the successful application of thin films.
3.1. Crystallographic Properties of Thin Films
It is well known that the occurrence of anatase and rutile phases in thin films depends significantly on the method and conditions of the deposition process [44–47]. There were attempts to create phase composition diagrams for thin films defining the experimental conditions under which the anatase or rutile form prevailed. The most important seem to be two such diagrams: one proposed by Pawlewicz et al.  and another given by Löbl et al. . The work of Pawlewicz et al.  suggests that the phase composition is controlled by the substrate temperature and oxygen partial pressure .
According to the diagram of Löbl et al.  (see Figure 2) modified to show the properties of the films prepared for the purposes of this work, the substrate temperature and the energy of particles impinging on the substrate, but not directly the oxygen partial pressure, are the relevant parameters that determine the film structure. The nucleation of rutile is favoured by the increasing energy transfer to the growing film and by the presence of Ti in the vapour phase.
The conclusions drawn from the above results are, however, by no means universal. As the parameters of the technological importance change from one preparation technique to another, the conditions of anatase and rutile growth should be reexamined for each particular case. For the purposes of this work, such an analysis has been performed [23, 34, 48–51] and the results can be summarized as follows.(i)Thin films grow as a mixture of amorphous, anatase, and rutile polymorphic forms with a varying contribution that depends on the substrate temperature and deposition rate related to oxygen partial pressure and oxidation state of the sputtered target. Low substrate temperature, low deposition rate, and oxidizing atmosphere result in anatase small crystals embedded in the amorphous background.(ii)The contribution from the anatase increases with the increasing substrate temperature up to 720 K and is typical for rf sputtering at relatively low sputtering rate.(iii) Dc magnetron sputtering at higher deposition rates yields anatase/rutile mixture. Rutile content increases with the sputtering rate under oxygen-deficient atmosphere.
3.2. Determination of the Departure from Stoichiometry in Thin Films of
Among many methods used to determine the chemical composition of a thin film, only some of them are sensitive enough to small negative or positive deviation from ideal stoichiometric composition ( in the formula ). These methods of microanalysis comprise Rutherford backscattering (RBS), analysis by nuclear reactions (NRA), and X-ray photoelectron spectroscopy (XPS). Traditionally employed methods of chemical analysis of elements such as electron microprobe (EMP) or energy-dispersive spectroscopy (EDS) have been used in this work but with a moderate success as they are not particularly destined for determination of oxygen nonstoichiometry.
Both RBS and NRA use the same experimental configuration that consists of an analyzed sample placed in a monoenergetic beam of protons, deuterons, or helium ions, typically 4He++ [52–57]. Particles coming from the bombarded sample as a result of the interaction of the beam and the elements in the sample are detected and analyzed. In the case of RBS, it is the energy of the backscattered particles that dissipated their incident energy by elastic (Rutherford) collisions, while for NRA, the energy of the reaction products is analyzed. XPS is a method that makes use of the X-ray radiation to excite electrons from the core levels of atoms . Kinetic energy of the photoelectrons measured directly in XPS is related to their binding energy in atoms, which in turn is sensitive to the atom environment. The chemical shift in the binding energy forms a basis for the identification of elements and their oxidation states in the specific chemical compounds.
RBS and NRA measurements were carried out at a beam line of the 2 MeV Van de Graaff accelerator being at the disposition of GIP (Groupe de Physique des Solides) at Ecole Normale Supérieure, in collaboration with LOS (Laboratoire d’Optique des Solides) Université P. et M. Curie, Paris 6, France, described in detail in . The energy of particles was measured with a silicon surface-barrier detector and the signals were analyzed with a multichannel analyzer. Complementary RBS measurements were performed at California Institute of Technology CalTech, USA. In this work, the RBS experiments were done mostly with alpha particles 4He++ of the incident energy MeV or 1.96 MeV. The detector was placed at the scattering angle °.
The XPS was studied at the Surface Spectroscopy Laboratory, AGH University of Science and Technology. Multitechnique setup of VSW Scientific Instruments was used.
Microanalysis by Rutherford backscattering (RBS) provides the ability to distinguish the atomic masses of elements and their distribution in depth as a function of the detected energy [52–56]. It is a nondestructive method, the most suitable in the case of heavy nuclei on light substrates. Typically silicon and carbon are used as substrates.
In the energy domain of the order of 2 MeV, only Coulomb interactions are responsible for the elastic scattering  of particles with atomic mass at nuclei of the atomic mass .
Hence, for a given scattering geometry, the detected energy of ions scattered from the surface is a simple function of the atomic mass of sample atom.
Equations (6) and (7) allow us to establish the position of the higher energy (leading) edge of the RBS spectrum as indicated by arrows in Figure 3. The leading edge can be further used for the identification of elements constituting the sample.
The energy difference between the position of the high and low energy edges represents the amount of energy lost by the beam on inward and outward passage through a layer. The total width of the signal is proportional to the film thickness : where is the energy loss that depends on and on the energy loss per unit path length in a given material .
Equation (8) can be used to determine the thickness of layers. This is shown in Figure 3, where two experimental RBS spectra of obtained by rf sputtering are shown. One sample was deposited on carbon foil thus enabling to observe clearly O peak (the atomic mass of carbon is smaller than that of oxygen). Simultaneously, the thin film was deposited onto Si wafer thermally oxidized to form a thin layer of SiO2. Thickness of this layer of about 160 nm was calculated from the width of the step shown on the Si edge in the RBS spectrum. The error in the evaluation of the thickness is determined by the energy resolution of the detector and amounts to 10–20 nm in this case.
However, one should keep in mind that the factor in (8) depends on the material density . Therefore, if the layer thickness is known independently and is derived from the RBS spectrum, then can be used to calculate the energy loss per unit length from
The energy loss factor of for scattering from Ti is composed of two terms: that represents the energy loss of particles on their inward path and that corresponds to the outgoing factor.
The energy loss is, in turn, related to the number of atoms in the cubic centimetre and through it to the material density . This relation is expressed by the stopping cross-section defined as where is the number of target atoms per unit volume, is their atomic mass, and is the Avogadro number.
The stopping cross section described by (10) expresses the energy loss based on the number of atoms per square centimetre.
Density can be found from (10) when the energy loss is known from (9) and the stopping cross section is calculated from (11). This procedure has been adopted for determination of the density of the deposited thin films of as there is no reason to assume the density equal to that of the bulk rutile or anatase. The film thickness can be taken from the profilometry and ellipsometry. The error in thickness determination is the major source of the inaccuracy of the estimated values of the density.
The results of the analysis are given in Table 2. The lowest values of correspond to the density of the amorphous TiO2 , slightly higher is obtained for the mixture of anatase and rutile. The samples, the results of which are presented in Table 2, do not contain a single phase of the most elevated density (rutile).
The quantitative RBS microanalysis yields the number of atoms per square centimetre of the target, , either from the height or from the area of the corresponding peak . The area under the peak is proportional to the total number of atoms per unit area and to the differential scattering cross section . The absolute value of requires a careful calibration, and therefore the procedure adopted in this work is based on the following formula: where the subscripts denote a reference sample (Bi implanted into Si) of the known concentration . The integrated charge of the incident beam is usually the same for the reference sample and the studied material, . This procedure entails a systematic error in the calculated atomic concentrations of the order of 5%.
The RBS technique was applied to determine the following:(i)surface number of titanium atoms in at/cm2 (),(ii)surface number of oxygen atoms in at/cm2 (), (iii) the atomic ratio O/Ti related to the departure from stoichiometry , (iv) film density (),
for a series of deposited by plasma emission controlled dc-pulsed reactive magnetron sputtering and by rf reactive sputtering at different growth rates (see Table 2). Oxygen can be best analyzed by RBS when the samples are deposited on C foil.
The obtained RBS spectra (e.g., in Figure 3) indicate that the samples are homogeneous and are not contaminated by foreign species. The amount of build-in argon is negligible.
Two basic advantages of nuclear reactions with respect to the RBS are that they provide background-free detection of light elements on heavier substrates and that they allow a perfect discrimination between two isotopes of the same element [54, 57]. Nuclear reaction analysis (NRA) is a complementary technique used for elements with low atomic number , like oxygen (), where RBS loses sensitivity due to the dependence of the cross section. Nuclear reactions are induced by charged particles such as protons and deuterons. The observed reaction products could be the charged particles that are detected and analyzed with the same apparatus as for RBS. Detailed information on this technique may be found in reviews [54, 57].
In this work, NRA was applied to determine oxygen concentration in thin films of . The reaction produced by a deuteron beam with the incident energy of 850 keV was analyzed at an angle of 150°.
Typical NRA spectra of thin oxide films are shown in Figure 4. Apart from the basic reaction used for oxygen determination, two other nuclear reactions, and , take place. The large peak in Figure 4(c) is related to the reaction in the carbon substrate.
In order to perform the quantitative analysis, only the area of the peak of is taken into account. It is then compared to the corresponding peak area of a reference sample (Ta2O5 thin film) of the known oxygen content.
Table 2 lists the results of the RBS and NRA analysis. Figure 5 gives the atomic ratio O/Ti for a series of obtained by reactive sputtering as a function of the sputtering rate . There is a fairly good agreement between the surface number of oxygen atoms determined from NRA and RBS (Table 2). However, one should keep in mind that NRA is much more sensitive to oxygen than RBS. Systematic dependence between the sputtering rate and the surface number of titanium atoms is observed for a given set of samples (Na) deposited by dc magnetron sputtering (Table 2). For the purpose of keeping the same thickness for a whole set of samples, the time of deposition was adjusted accordingly. Metallic mode of deposition results in higher and yields in a consequence larger content of Ti in the film. It is interesting to note that neither (Table 2) nor O/Ti (Figure 5) follow the systematic dependence on . For the intermediate one observes a maximum in O/Ti that corresponds to the maximum in the film density derived from the RBS measurements (Table 2). The general feeling is that there is a strong correlation between the oxygen content and the film density . This may be due to the amorphous nature of very thin films of TiO2. Changes in the film density in thicker samples are due to the systematic variation in anatase/rutile ratio as a function of the sputtering rate.
X-ray photoelectron spectra (XPS) were recorded using a VSW Scientific Instruments electron spectrometer fitted with a dual anode MgKα (1253.6 eV) and AlKα (1486.6 eV) as a source of X-ray radiation. The anode was operated at 200 W (10 kV, 20 mA). The XPS/AES chamber was equipped with a hemispherical analyzer HA150 (diameter 150 cm) at a constant pass energy of 22 eV and a multichannel detector (18 channels, 1.8 kV operating voltage). The photoelectrons were collected at a constant take-off angle. The binding energy shifts due to the surface charging were corrected assuming the C 1s XPS peak at 285.0 eV [61–63]. The position of C 1s line served as an internal standard for calibration of the binding energy scale.
The depth of XPS analysis is limited by the length of the escape path of the photoelectrons, which in turn amounts to about 2 nm for Ti . Taking into account a monolayer thickness of TiO2 to be 0.22 nm it was estimated that only 10% of the total emission resulted from the surface atoms . Therefore, not only the surface is probed by XPS but the subsurface layers are as well.
The objective of the XPS studies in TiO2 is usually twofold. Primarily, it of great interest to establish the oxidation state of Ti ions. Not only Ti4+ related to TiO2 but also lower oxidation states due to the presence of titanium suboxides have been reported in the literature [63, 65–72]. The first detailed study by Carley et al.  devoted to the step-by step oxidation of Ti metal provided evidence for intermediate oxidation states Ti2+ and Ti3+. As to the second objective of the XPS investigations, it is of equal importance to establish the relative surface composition of elements as well as to monitor the evolution of the O/Ti atomic surface ratio with deposition parameters. This requires the quantitative analysis of XPS spectra preceded by smoothing, deconvolution, and fitting of the relevant peaks. The corresponding peak area is then divided by the respective relative sensitivity factors [73, 74] according to the formula: where the summation is extended over all elements in the sample.
In this work the sensitivity factors were assumed to be equal to the corresponding normalized photoelectric cross-sections , , and .
Figure 6 shows a survey spectrum of a thin film deposited by sputtering. The spectrum contains the most prominent and lines of Ti, O 1s and C 1s at standard positions. The carbon contamination is almost impossible to avoid [73, 76]. Fortunately, it is usually limited to the film-air interface.
Figure 7 shows Ti doublet measured in thin films deposited under oxidizing conditions controlled by sputtering rate . Two limiting cases are shown: nm/s that yields substoichiometric oxides and nm/s that corresponds to overoxidized conditions. The measured Ti doublet is shifted by approximately 5 eV towards higher binding energy as compared with the metal. The binding energy shift of this value indicates that both films contain titanium at the highest oxidation state Ti4+ . Almost symmetrical shape of Ti peak is observed in the case of samples obtained at nm/s. Formally, however, apart from Ti4+ related to TiO2, one can expect at least Ti3+ and Ti2+ oxidation states as a result of the deviation from stoichiometry already discussed in this work. The substantial contributions from lower oxidation states (Ti3+ or Ti2+ and Ti0) are seen for the samples obtained at nm/s which indicates the largest oxygen deficiency. Therefore, the experimental spectra have been refined assuming a three-component structure with each component assigned to a different oxidation state, as shown in Figure 7. The relative contributions to the Ti photoelectron peak have been calculated, and the results of the quantitative analysis are listed in Table 4.
The assignment of each of the three components forming Ti XPS peak is difficult to make, especially because in the literature there is a large scatter of binding energies of Ti3+ and Ti2+ (see Table 3). The charging effects in thin insulating films complicate the problem.
In this work, the relative shifts of each of the fitted components have been compared to those observed in the literature (Table 3). The highest and the lowest energy components have been assigned to Ti4+ and Ti0, respectively, while the intermediate component has the energy shift relative to TiO2 that falls in between that of Ti3+ and Ti2+. Therefore, Ti3+ and Ti2+ cannot be resolved without ambiguity.
In conclusion, the contributions from the lower oxidation states of Ti can be neglected in samples obtained with the sufficient amount oxygen in the sputtering process (at nm/s). The presence of small amounts of Ti3+ or Ti2+ in the films that are not completely oxidized ( nm/s) cannot be excluded.
Oxygen O 1s lines are asymmetrical in all studied samples which suggest that oxygen occurs in two different chemical states at least. The O 1s line could be resolved into two contributions: OI and OII (see Figure 8 and Table 4).
The binding energy of OI state matches the literature value [63, 74] and corresponds to oxygen that occupies the normal lattice sites in the TiO2 structure. Thus, the OI state represents bulk oxygen. The OII state of higher binding energy could not be classified unambiguously. It is often assumed that oxygen in the surface state is responsible for the high-energy component of the asymmetrical O 1s line . High-energy component has been assigned to oxygen bonded to Ti+3 (O–Ti3+) . However, the most probable is the argument involving the presence of hydroxyl species (OH) that are easily formed at the surface of oxide films [62, 77]. It was suggested  that OH-group chemisorption takes place on unsaturated Ti-sites such as Ti3+. This interpretation has been assumed in this work to account for the OII component of XPS O 1s peak. The presence of OH–Ti3+ species at the surface is supported by the observation that the intensity of OII component increases for samples obtained at nm/s (19% of the total O 1s peak area). This effect is accompanied by a significant contribution from the low-energy component to Ti 2p peak.
Meng et al.  have attributed the presence of OII component to the porosity, on the account of the fact that it is related to the moisture that accumulates mainly in the pores or empty columns of the material. Using the ratio of as a measure of the porosity it may be concluded that thin films with the largest deviation from stoichiometry are more porous than the stoichiometric films (see Table 4).
The observed general trend in the substoichiometric films that the O 1s high-energy and Ti low-energy components are formed is associated with a defect formation. The electronic charge transfer from the anion (oxygen) to the cation (titanium) increases the binding energies of oxygen, but decreases the binding energy of the titanium core electrons .
The summary of the quantitative analysis is given in Table 5 that compares the O/Ti atomic ratio obtained from XPS with other methods. X-ray electron microprobe (EMP) underestimates the results, but it is the method that generates the largest error as far as the oxygen content is concerned. This is due to the lack of an appropriate oxygen standard for this method. On the contrary, XPS yields the highest values for O/Ti of all the methods employed in this study. The values of O/Ti from XPS, listed in Table 5, have been obtained when integrating the area of OI component of the O 1s peak, only. The area of OII component that corresponds to oxygen bound in OH− was not taken into account. And even in this case, the resulting values of O/Ti are much higher than those expected for a perfectly stoichiometric composition. This does not remain in accordance with the literature reports that indicate the defective surface of TiO2 . The result obtained here suggests rather that the tendency to oxidation is great for the surfaces containing titanium. The exposed surface is easily oxidized. The possible systematic error in O/Ti determination from XPS could result from the relative sensitivity factors.
Ion beam techniques, RBS and NRA are better suited for determination of oxygen nonstoichiometry in thin films of .
The results of all methods discussed in this review differ as they all have their specific capabilities and limitations with respect to the material system studied. For instance, nuclear reaction microanalysis (NRA) allows for a very fast determination of the absolute total amounts of light elements in thin films up to 1 μm thick . On the other hand, Rutherford backscattering RBS provides information on the composition profile in depth in a nondestructive way . The analysis of XPS is limited to the first (of the order of five) atomic layers close to the sample surface because of the small mean escape depth of the photoelectrons .
Film composition and particularly oxygen nonstoichiometry, microstructure, and surface morphology are closely related to the sputtering conditions and in a consequence affect the electrical properties.
Systematic changes in the anatase and rutile contribution in thin films can be accounted for by the modification of the oxidation state of the sputtered Ti target and the film deposition rate. Structure dominated by anatase grains embedded in the amorphous background seems to be a result of specific growth conditions such as a low sputtering rate of the oxidized target surface. Oxygen nonstoichiometry created at high sputtering rates promotes rutile growth.
High activation energy is required for anatase-rutile formation. This transformation involves an overall contraction of the oxygen sublattice and a movement of ions so that a cooperative rearrangement of Ti4+ and O2- occurs. Hence, it is proposed that the removal of some oxygen ions, which generates lattice vacancies, accelerates this transformation.
The electrical resistivity ρ as a function of the sputtering rate is shown in Figure 9 for nonstoichiometric thin films of obtained by reactive sputtering. It demonstrates the existing correlation between the electrical resistivity and film composition.
For fully oxidized samples, that is, at the lowest value of growth rates the electrical resistance exceeds the limit of measurement. At nm/s the electrical resistivity decreases to such a level that it becomes measurable even at room temperature.
As expected, with the decreasing O/Ti, that is, for increasing deviation from the oxygen stoichiometry , thin films become more conducting. The close relationship between ρ and indicates that oxygen nonstoichiometry is the source of electrons in the conduction band of titanium dioxide thin films.
The importance of ion beam techniques in the determination of oxygen nonstoichiometry in reactively sputtered has been discussed in this review paper. The following detailed conclusions can be formulated:(i)chemical composition of thin films deposited by reactive sputtering from Ti target is close to stoichiometric but a controlled departure from stoichiometry can be reached at a specific deposition rate;(ii)departure from stoichiometry over the range of has been found by RBS and NRA techniques while XPS, which is a typical surface analysis, yields as high as 0.5;(iii) film density determined from RBS measurement remains in accordance with the progressive evolution from amorphous, anatase to rutile phase and is related to the film nonstoichiometry through the surface number of oxygen atoms, ;(iv) close relationship between the electrical resistivity and the deviation from stoichiometry indicates that the oxygen deficit is a source of electrons in the conduction band.
It should be pointed out that general understanding of the problem of nonstoichiometry and its influence on the material properties is an imperative in order to make based oxides into reliable and commercially viable electronic devices.
Special thanks are due to M. Radecka from the Department of Inorganic Chemistry, Faculty of Materials Science and Ceramics, AGH-UST for invaluable scientific contribution and fruitful discussions. The author is grateful to A. Brudnik from Department of Electronics, Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, AGH-UST for preparation of dc magnetron sputtered samples; A. Brunet-Bruneau for the RBS and NRA measurements at the Laboratoire d’Optique des Solides, Universite P. et M. Curie, Paris 6, France; E. Kolawa for the RBS measurements performed at CalTech, Pasadena, USA; K. Kowalski, for XPS at the Surface Spectroscopy Laboratory, AGH-UST, Kraków, Poland. Finally, financial support from the Polish Ministry of Science and Higher Education under AGH-University of Science and Technology Grant no. 220.127.116.114 (statutory project) is acknowledged.
- L. Börnstein, “Numerical data and functional relationships in science and technology,” in Semiconductors, O. Madelung, Ed., vol. 17, pp. 133–149, Springer, Berlin, Germany, 1983.
- M. A. Henderson, “A surface science perspective on TiO2 photocatalysis,” Surface Science Reports, vol. 66, pp. 185–298, 2011.
- U. Balachandran and N. G. Eror, “Electrical conductivity in non-stoichiometric titanium dioxide at elevated temperatures,” Journal of Materials Science, vol. 23, no. 8, pp. 2676–2682, 1988.
- J. S. Anderson, “Shear Structures and non-stoicheiometry,” in Surface and Defect Properties of Solids, M. W. Roberts and J. M. Thomas, Eds., p. 1, The Chemical Society, London, UK, 1972.
- J. S. Anderson and B. G. Hyde, “On possible role of dislocations in generating ordered and disordered shear structures,” Journal of Physics and Chemistry of Solids, vol. 28, no. 8, pp. 1393–1396, 1967.
- J. F. Baumard and F. Gervais, “Plasmon and polar optical phonons in reduced rutile ,” Physical Review B, vol. 15, no. 4, pp. 2316–2323, 1977.
- J. F. Baumard, D. Panis, and A. M. Anthony, “A study of TiO system between Ti3O5 and TiO2 at high temperature by means of electrical resistivity,” Journal of Solid State Chemistry, vol. 20, no. 1, pp. 43–51, 1977.
- R. N. Blumenthal and D. H. Whitmore, “Thermodynamic study of phase equilibria in the titanium-oxygen system within the TiO1.95-TiO2 region,” Journal of the Electrochemical Society, vol. 110, pp. 92–93, 1963.
- J. S. Anderson and A. S. Khan, “Equilibria of intermediate oxides in the titanium-oxygen system,” Journal of the Less-Common Metals, vol. 22, no. 2, pp. 219–223, 1970.
- P. Kofstad, “Thermogravimetric studies of the defect structure of rutile (TiO2),” Journal of Physics and Chemistry of Solids, vol. 23, no. 11, pp. 1579–1586, 1962.
- N. Ait-Younes, F. Millot, and P. Gerdanian, “Isothermal transport in . Part II. Chemical diffusion in ,” Solid State Ionics, vol. 12, no. C, pp. 437–442, 1984.
- K. Hoshino, N. L. Peterson, and C. L. Wiley, “Diffusion and point defects in ,” Journal of Physics and Chemistry of Solids, vol. 46, no. 12, pp. 1397–1411, 1985.
- P. Kofstad, “Note on the defect structure of rutile (TiO2),” Journal of the Less-Common Metals, vol. 13, no. 6, pp. 635–638, 1967.
- M. Radecka and M. Rekas, “Effect of high-temperature treatment on n-p transition in titania,” Journal of the American Ceramic Society, vol. 85, no. 2, pp. 346–354, 2002.
- S. Mrowec, “Extended defects in transition metals oxides,” Revue Internationale des Hautes Temperatures et des Refractaires, vol. 14, pp. 225–242, 1977.
- L. A. Bursill and M. G. Blanchin, “Structure of cation interstitial defects in nonstoichiometric rutile,” Journal de Physique. Lettres, vol. 44, no. 4, pp. L165–L170, 1983.
- G. S. Rohrer, V. E. Henrich, and D. A. Bonnell, “Structure of the reduced TiO2(110) surface determined by scanning tunneling microscopy,” Science, vol. 250, no. 4985, pp. 1239–1241, 1990.
- M. Reece and R. Morrell, “Electron microscope study of non-stoichiometric titania,” Journal of Materials Science, vol. 26, no. 20, pp. 5566–5574, 1991.
- R. T. Dirstine and C. J. Rosa, “Defect structure and related thermodynamic properties of nonstoichiometric rutile () and Nb2O5 doped rutile. II. The defect structure of TiO2 solid solution containing 0.1–3.0 mole % Nb2O5 and partial molar properties for oxygen solution at 1273 K,” Zeitschrift fuer Metallkunde, vol. 70, no. 5, pp. 322–329, 1979.
- C. R. A. Catlow and R. James, “Disorder in ,” Proceedings of the Royal Society of London Series A, vol. 384, pp. 157–173, 1982.
- S. Na-Phattalung, M. F. Smith, K. Kim et al., “First-principles study of native defects in anatase TiO2,” Physical Review B, vol. 73, no. 12, Article ID 125205, pp. 1–6, 2006.
- A. Weibel, R. Bouchet, and P. Knauth, “Electrical properties and defect chemistry of anatase (TiO2),” Solid State Ionics, vol. 177, no. 3-4, pp. 229–236, 2006.
- M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapiński, and S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of thin films,” Applied Surface Science, vol. 65-66, pp. 227–234, 1993.
- F. Millot, M. G. Blanchin, R. Tétot et al., “High temperature nonstoichiometric rutile ,” Progress in Solid State Chemistry, vol. 17, no. 4, pp. 263–293, 1987.
- F. A. Kröger, The Chemistry of Imperfect Crystals, North Holland, Amsterdam, The Netherlands, 1964.
- J. Nowotny, M. Radecka, and M. Rekas, “Semiconducting properties of undoped TiO2,” Journal of Physics and Chemistry of Solids, vol. 58, no. 6, pp. 927–937, 1997.
- J. Nowotny, M. Radecka, M. Rekas, S. Sugihara, E. R. Vance, and W. Weppner, “Electronic and ionic conductivity of TiO2 single crystal within the n-p transition range,” Ceramics International, vol. 24, no. 8, pp. 571–577, 1998.
- S. C. Huang, T. F. Lin, S. Y. Lu, and K. S. Chou, “Morphology of and surface modification by TiO2 deposits on a porous ceramic substrate,” Journal of Materials Science, vol. 34, no. 17, pp. 4293–4304, 1999.
- K. Nishida, K. Morisawa, A. Hiraki, S. Muraishi, and T. Katoda, “In-situ monitoring of PE-CVD growth of TiO2 films with laser Raman spectroscopy,” Applied Surface Science, vol. 159, pp. 143–148, 2000.
- H. Sun, C. Wang, S. Pang et al., “Photocatalytic TiO2 films prepared by chemical vapor deposition at atmosphere pressure,” Journal of Non-Crystalline Solids, vol. 354, no. 12-13, pp. 1440–1443, 2008.
- M. L. Hitchman and F. Tian, “Studies of TiO2 thin films prepared by chemical vapour deposition for photocatalytic and photoelectrocatalytic degradation of 4-chlorophenol,” Journal of Electroanalytical Chemistry, vol. 538-539, pp. 165–172, 2002.
- S. Chaiyakun, A. Pokaipisit, P. Limsuwan, and B. Ngotawornchai, “Growth and characterization of nanostructured anatase phase TiO2 thin films prepared by DC reactive unbalanced magnetron sputtering,” Applied Physics A, vol. 95, no. 2, pp. 579–587, 2009.
- A. Brudnik, H. Czternastek, K. Zakrzewska, and M. Jachimowski, “Plasma-emission-controlled d.c. magnetron sputtering of thin films,” Thin Solid Films, vol. 199, no. 1, pp. 45–58, 1991.
- K. Zakrzewska, A. Brudnik, M. Radecka, and W. Posadowski, “Reactively sputtered thin films with plasma-emission-controlled departure from stoichiometry,” Thin Solid Films, vol. 343-344, no. 1-2, pp. 152–155, 1999.
- Z. Zainal and C. Y. Lee, “Properties and photoelectrocatalytic behaviour of sol-gel derived TiO2 thin films,” Journal of Sol-Gel Science and Technology, vol. 37, no. 1, pp. 19–25, 2006.
- A. Turković, “Grazing-incidence SAXS/WAXD on nanosized TiO2 films obtained by ALE,” Materials Science and Engineering B, vol. 75, no. 1, pp. 85–91, 2000.
- M. F. Brunella, M. V. Diamanti, M. P. Pedeferri, F. D. Fonzo, C. S. Casari, and A. L. Bassi, “Photocatalytic behavior of different titanium dioxide layers,” Thin Solid Films, vol. 515, no. 16, pp. 6309–6313, 2007.
- A. Bendavid, P. J. Martin, and H. Takikawa, “Deposition and modification of titanium dioxide thin films by filtered arc deposition,” Thin Solid Films, vol. 360, no. 1-2, pp. 241–249, 2000.
- P. J. Martin, “Ion-based methods for optical thin film deposition,” Journal of Materials Science, vol. 21, no. 1, pp. 1–25, 1986.
- M. C. Marchi, S. A. Bilmes, C. T. M. Ribeiro, E. A. Ochoa, M. Kleinke, and F. Alvarez, “A comprehensive study of the influence of the stoichiometry on the physical properties of films prepared by ion beam deposition,” Journal of Applied Physics, vol. 108, no. 6, Article ID 064912, 2010.
- S. H. Mohamed, O. Kappertz, T. P. Leervad Pedersen, R. Drese, and M. Wuttig, “Properties of coatings prepared by dc magnetron sputtering,” Physica Status Solidi A, vol. 198, no. 1, pp. 224–237, 2003.
- A. G. Spencer and R. P. Howson, “Dynamic control of reactive magnetron sputtering: a theoretical analysis,” Thin Solid Films, vol. 186, no. 1, pp. 129–136, 1990.
- E. Kinbara, E. Kusano, and S. Baba, “ film formation process by reactive sputtering,” Journal of Vacuum Science, vol. 10, pp. 1483–1487, 1992.
- W. T. Pawlewicz, P. M. Martin, D. D. Hays, and I. B. Mann, “Recent development in reactively sputtered optical thin films,” Proceedings of SPIE-The International Society for Optical Engineering, vol. 325, pp. 105–116, 1982.
- D. Wicaksana, A. Kobayashi, and A. Kinbara, “Process effects on structural properties of TiO2 thin films by reactive sputtering,” Journal of Vacuum Science and Technology A, vol. 10, pp. 1479–1482, 1992.
- M. H. Suhail, G. M. Rao, and S. Mohan, “Dc reactive magnetron sputtering of titanium-structural and optical characterization of TiO2 films,” Journal of Applied Physics, vol. 71, no. 3, pp. 1421–1427, 1992.
- P. Löbl, M. Huppertz, and D. Mergel, “Nucleation and growth in TiO2 films prepared by sputtering and evaporation,” Thin Solid Films, vol. 251, no. 1, pp. 72–79, 1994.
- K. Zakrzewska, A. Brudnik, E. Kusior, M. Radecka, and A. Kowal, “Microstructure of thin films reactively sputtered by dc magnetron,” in Surface Engineering: in Materials Science I, S. Seal, N. B. Dahotre, J. J. Moore, and B. Mishra, Eds., pp. 163–173, The Minerals, Metals & Materials Society, 2000.
- M. Radecka, M. Rekas, and K. Zakrzewska, “Titanium dioxide in photoelectrolysis of water,” Trends in Inorganic Chemistry, Review, vol. 9, pp. 81–125, 2006.
- A. Brudnik, A. Gorzkowska-Sobaś, E. Pamuła, M. Radecka, and K. Zakrzewska, “Thin film TiO2 photoanodes for water photolysis prepared by dc magnetron sputtering,” Journal of Power Sources, vol. 173, no. 2, pp. 774–780, 2007.
- M. Radecka, M. Rekas, A. Trenczek-Zajac, and K. Zakrzewska, “Importance of the band gap energy and flat band potential for application of modified TiO2 photoanodes in water photolysis,” Journal of Power Sources, vol. 181, no. 1, pp. 46–55, 2008.
- W. K. Chu, J. W. Mayer, M.-A. Nicolet, T. M. Buck, G. Amsel, and F. Eisen, “Principles and applications of ion beam techniques for the analysis of solids and thin films,” Thin Solid Films, vol. 17, no. 1, pp. 1–41, 1973.
- W. K. Chu, J. W. Mayer, and M.-A. Nicolet, Backscattering Spectrometry, Academic Press, London, UK, 1978.
- F. Abel, “Impurity analysis in solids by direct observation of nuclear reactions and elastic scattering,” Bulletin de la Societe Francaise de Mineralogie et de Cristallographie, vol. 95, pp. 658–669, 1972.
- P. Mazzoldi and G. Della Mea, “The use of nuclear techniques for the analysis of thin films on glass,” Thin Solid Films, vol. 77, no. 1–3, pp. 181–194, 1981.
- D. J. Oostra, “RBS and ERD analysis in materials research of thin films,” Philips Journal of Research, vol. 47, no. 3–5, pp. 315–326, 1993.
- G. Amsel, J. P. Nadai, E. D'Artemare, D. David, E. Girard, and J. Moulin, “Microanalysis by the direct observation of nuclear reactions using a 2 MeV Van de Graaff,” Nuclear Instruments and Methods, vol. 92, no. 4, pp. 481–498, 1971.
- D. Briggs and M. P. Seah, Eds., Practical Surface Analysis, vol. 1, Wiley, Chichester, UK, 2nd edition, 1990.
- J. F. Ziegler and W. K. Chu, “Stopping cross sections and backscattering factors for 4He ions in matter,” Atomic Data and Nuclear Data Tables, vol. 13, no. 5, pp. 463–489, 1974.
- R. Zanoni, G. Righini, A. Montenero et al., “Surface composition of alkali-doped TiO2 films for sensors investigated by XPS,” Sensors and Actuators B, vol. 25, no. 1–3, pp. 886–888, 1995.
- P. M. Kumar, S. Badrinarayanan, and M. Sastry, “Nanocrystalline TiO2 studied by optical, FTIR and X-ray photoelectron spectroscopy: correlation to presence of surface states,” Thin Solid Films, vol. 358, no. 1, pp. 122–130, 2000.
- E. McCafferty and J. P. Wightman, “An X-ray photoelectron spectroscopy sputter profile study of the native air-formed oxide film on titanium,” Applied Surface Science, vol. 143, no. 1, pp. 92–100, 1999.
- M. P. Seah and W. A. Dench, “Quantitative electron spectroscopy of surfaces: a standard data base for electron inelastic mean free paths in solids,” Surface and Interface Analysis, vol. 1, no. 1, pp. 2–11, 1979.
- W. Göpel, J. A. Anderson, D. Frankel et al., “Surface defects of TiO2(110): a combined XPS, XAES and ELS study,” Surface Science, vol. 139, no. 2-3, pp. 333–346, 1984.
- N. R. Armstrong and R. K. Quinn, “Auger and X-ray photoelectron spectroscopic and electrochemical characterization of titanium thin film electrodes,” Surface Science, vol. 67, no. 2, pp. 451–468, 1977.
- D. J. Dwyer, S. D. Cameron, and J. Gland, “Surface modification of platinum by titanium dioxide overlayers: a case of simple site blocking,” Surface Science, vol. 159, no. 2-3, pp. 430–442, 1985.
- A. F. Carley, P. R. Chalker, J. C. Riviere, and M. W. Roberts, “The identification and characterisation of mixed oxidation states at oxidised titanium surfaces by analysis of X-ray photoelectron spectra,” Journal of the Chemical Society, Faraday Transactions 1, vol. 83, no. 2, pp. 351–370, 1987.
- G. Rocker and W. Göpel, “Titanium overlayers on TiO2(110),” Surface Science, vol. 181, no. 3, pp. 530–558, 1987.
- C. da Fonseca, S. Boudin, and M. da Cunha Belo, “Characterisation of titanium passivation films by in situ ac impedance measurements and XPS analysis,” Journal of Electroanalytical Chemistry, vol. 379, no. 1-2, pp. 173–180, 1994.
- M. Sasase, K. Miyake, I. Takano, and S. Isobe, “Photocurrent performance of films prepared by Ar+ ion beam-assisted reactive deposition method,” Thin Solid Films, vol. 269, no. 1-2, pp. 36–40, 1995.
- F. Zhang, S. Jin, Y. Mao, Z. Zheng, Y. Chen, and X. Liu, “Surface characterization of titanium oxide films synthesized by ion beam enhanced deposition,” Thin Solid Films, vol. 310, no. 1-2, pp. 29–33, 1997.
- J. H. Scofield, “Hartree-Slater subshell photoionization cross-sections at 1254 and 1487 eV,” Journal of Electron Spectroscopy and Related Phenomena, vol. 8, no. 2, pp. 129–137, 1976.
- C. D. Wagner, W. M. Riggs, L. E. Davis, J. F. Moulder, and G. E. Mullenberg, Handbook of X-Ray Photoelectron Spectroscopy, Elmer Corp., Eden Prairie, MN, USA, 1979.
- C. D. Wagner, “Appendix 5,” in Practical Surface Analysis, D. Briggs and M. P. Seah, Eds., vol. 1, Wiley, Chichester, UK, 2nd edition, 1990.
- L. J. Meng and M. P. dos Santos, “Investigations of titanium oxide films deposited by d.c. reactive magnetron sputtering in different sputtering pressures,” Thin Solid Films, vol. 226, no. 1, pp. 22–29, 1993.
- K. Zakrzewska, S. Skrzypek, and J. Stoch, “Structure and composition of transparent conducting CdIn2O4 thin films,” in Proceedings of the 12th International Congress on X-ray Optics and Microanalysis, (ICXOM '89), S. Jasienska and L. J. Maksymowicz, Eds., vol. 2, pp. 876–879, Cracow, Poland, August, 1989.
- Li-Jian Meng, C. P. Moreira de Sá, and M. P. dos Santos, “Study of porosity of titanium oxide films by X-ray photoelectron spectroscopy and IR transmittance,” Thin Solid Films, vol. 239, no. 1, pp. 117–122, 1994.
- C. J. Powell, “Attenuation lengths of low-energy electrons in solids,” Surface Science, vol. 44, no. 1, pp. 29–46, 1974.