# Nonstoichiometry inTiO2−y Studied by Ion Beam Methods and Photoelectron Spectroscopy

Authors: K. Zakrzewska
Journal: Advances in Materials Science and Engineering
 (2012)

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## Abstract

This paper treats a problem of nonstoichiometry inTiO2−y 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 y in the bulk and at the surface of TiO2−y layers. The critical review of these experimental methods is given. Defect structure responsible for the electrical resistivity of rutile TiO2 is discussed.


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## Body

## 1. Introduction

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 ofTiO2 in hazardous environments, hardness, high refractive index, and many other remarkable features.Titanium dioxideTiO2 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 [1].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,TiO2 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 [2]. 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 [1]) 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 [3].Much work has been devoted to the nonstoichiometric rutileTiO2-y, both in the structural aspects related to the nature of defects [4, 5] and in the subsequent physical [6, 7] and thermodynamic properties [8]. 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 TiO2-y extending it to a value as high as y≅0.1 at 1170–1270 K [8]. Later experimental evidence [9] suggests that the homogeneity range is much narrower (y≅0.008 at 1270 K).The structure of defects responsible for the electronic conduction in rutile and anataseTiO2 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 [10], titanium interstitials [11, 12], or a combination of these two defects [13]. 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 [14].It should be pointed out that there exists a significant controversy between two different approaches to the problem of defects in rutile. Some authors [4] 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 (TiO2) 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 [5]. Magnéli phases constitute a homologous series with the general formula TijO2j-1, where j is related by j=1/y to a deviation from stoichiometry y (TiO2-y).Phase diagram of Ti–O system [1] indicates that the region of 0.1≤y≤0.25 contains stable ordered phases TijO2j-1 with 4≤j≤10. For smaller departures from stoichiometry y<0.1 (10<j<16) the concentration of the shear planes defects decreases and their mutual interaction becomes weaker. For a very small departure from stoichiometry, y≅0.001, corresponding to j>1000, formation of isolated shear planes in equilibrium with point defects was proposed [15]. 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 [17] and TEM [18].The experimental results of tracer diffusion [12], chemical diffusion [11], and thermogravimetric measurements [19] indicate titanium interstitials as the majority point defects in oxygen-deficient TiO2-y. Works in favour of oxygen vacancies are also numerous. The computer simulation of the defect chemistry of rutile TiO2 has been carried out as well [20].This issue in the case of anatase has been only quite recently brought up [21, 22]. Na-Phattalung et al. [21] 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. [22] 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 stoichiometryy in TiO2-y 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 [23].


## 2. Electrical Conductivity and Point Defect Structure ofTiO2-y

The departure from stoichiometryy may be expressed within the ideal mass action law as a function of the oxygen partial pressure pO2:(1)y∝pO2-1/my,
where my yields information on the nature of the defect structure [24].The following types of defects: doublyVO•• and singly VO• ionized oxygen vacancies as well as titanium interstitials Tii3+ and Tii4+ are usually taken into account. Theoretically predicted values of my associated with the specific point defect are listed in Table 1. When dealing with the structure of point defects, the Kröger-Vink notation [25] is used.Table 1
Theoretical analysis of point defects formation inTiO2-y.
Majority defectReaction of formationTheoretical value ofmyDoubly ionized oxygen vacancyVO••OOx⟷12O2(g)+VO••+2e′6Singly ionized oxygen vacancyVO•OOx⟷12O2(g)+VO•+e′4Titanium interstitialTii4+TiTix+2OOx⟷Tii4++4e′+O2(g)5Titanium interstitialTii3+TiTix+2OOx⟷Tii3++3e′+O2(g)4The electrical conductivity of titanium dioxide is a function of the temperature,T, and oxygen partial pressure, pO2. The latter is a consequence of the relation between the departure from stoichiometry y and pO2 given by (1).The temperature dependence of the carrier concentration and conductivity for nonstoichiometricTiO2-y involves the activation energy Ea 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 Eg and a measurable value of the electrical conductivity can be observed even at room temperature for nonstoichiometric TiO2-y.The experimental evidence shows that at high oxygen partial pressurespO2, close to 0.1 MPa and below 1200 K, TiO2 exhibits an n-p-type transition [3, 26, 27].In the n-type regime, the electrical conductivityσ of TiO2-y is affected by the oxygen partial pressure pO2(2)σ∝pO2-1/mσ.This is due to the fact that the electron concentrationne is a function of pO2(3)ne∝pO2-1/mn,
which results from the relationship between ne and the departure from stoichiometry y. When the mobility of charge carriers is independent of the oxygen partial pressure, then mn=mσ.The coefficientsmy, mn, and mσ 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 y, ne, or σ, respectively, as a function of oxygen partial pressure pO2. As shown in Figure 1, the slope of σ(pO2) dependence plotted in the double logarithmic coordinate system yields the coefficient mσ. 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.Figure 1
Electrical conductivityσ measured at 1250 K as a function of the oxygen partial pressure pO2 for a thin film of TiO2-y. The results of σ and Seebeck coefficient Q concern rutile single crystal.In practice, the electrical measurements inTiO2 over the temperature range of 1070–1370 K reveal [14] that the slope of logσ against logpO2 is different under different regimes of oxygen activities. Therefore, the parameter mσ associated with the majority defect, changes when pO2 is varied. At low oxygen partial pressures mσ close to 5 is obtained which can be accounted for by titanium interstitials, Tii4+. Over the intermediate range of pO2, mσ=6 and doubly ionized oxygen vacancies VO•• are postulated. Finally, at high pO2 the value close to 4 is observed, corresponding to either singly ionized oxygen vacancy defect, VO•, or interstitial titanium,Tii3+.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 VTi//// associated with oxygen vacancy VO••. Both models give the same dependence of concentration of electrons (ne) and that of holes (nh) on pO2:(4)ne∝pO2-1/4,nh∝pO21/4.The p-type conductivity inTiO2 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 [26]. 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 VTi////. The results of these models are quite different. The extrinsic disorder yields the concentration of holes independent of the pO2 [26]. The Schottky model gives [26](5)nh∝pO21/5.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 ofpO2≤105 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 ofmσ 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 mσ=4 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 inTiO2-y.In fact, the coexistence of divalent oxygen vacancies with tri- and tetravalent titanium interstitials has been proposed [13].


## 3. Nonstoichiometric Thin Films ofTiO2-y

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 TiO2 thin films, such as sol-gel process [35], atomic layer epitaxy (ALE) [36], pulsed laser deposition [37], and filtered arc deposition (FAD) [38]. Excellent reviews, covering both the growth techniques applied to deposition of TiO2 coatings as well as the film morphology and optical properties, have been published [39].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 y of TiO2-y 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. [44] and another given by Löbl et al. [47]. The work of Pawlewicz et al. [44] suggests that the phase composition is controlled by the substrate temperature and oxygen partial pressure pO2.According to the diagram of Löbl et al. [47] (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.Figure 2
Phase composition diagram after Löbl et al. [47] modified to include the results obtained for TiO2 thin films discussed in this work; Sd: deposition rate of thin films.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 anataseTiO2 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 Stoichiometryy in Thin Films of TiO2-y

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 (y in the formula TiO2-y). 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, typically4He++ [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 [58]. 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 [54]. 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 E0=2.012 MeV or 1.96 MeV. The detector was placed at the scattering angle Θ=165°.The XPS was studied at the Surface Spectroscopy Laboratory, AGH University of Science and Technology. Multitechnique setup of VSW Scientific Instruments was used.


#### 3.2.1. RBS

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 [52] of particles with atomic mass m at nuclei of the atomic mass M.The energyE1 of the ionized particle scattered at the sample surface is related to the incident energy E0 by the laws of conservation of momentum and energy as [52, 53](6)E1=KME0,
with the kinematic recoil factor KM(7)KM=(mcos⁡Θ+M2-m2sin⁡2Θm+M)2.Hence, for a given scattering geometry, the detected energy of ions scattered from the surface is a simple function of the atomic massM 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.Figure 3
Comparison between the experimental RBS spectra of aTiO2-y thin film deposited by rf sputtering on different substrates: thermally oxidized Si wafer (Si/SiO2) and carbon foil C.The energy differenceΔE 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 ΔE of the signal is proportional to the film thickness d [52]:(8)ΔE=[S]d,
where [S] is the energy loss that depends on KM and on the energy loss per unit path length dE/dz in a given material [52].Equation (8) can be used to determine the thickness of layers. This is shown in Figure 3, where two experimental RBS spectra of TiO2-y 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 TiO2-y 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[S] in (8) depends on the material density ρmat. Therefore, if the layer thickness is known independently and ΔE is derived from the RBS spectrum, then [S] can be used to calculate the energy loss per unit length dE/dz from(9)[S]TiTiO2=KTidEdz|inTiO2+1|cos⁡Θ|dEdz|outTiO2.The energy loss factor[S]TiTiO2 of TiO2 for scattering from Ti is composed of two terms: KTi(dE/dz)|inTiO2 that represents the energy loss of particles on their inward path and (1/|cosΘ|)(dE/dz)|outTiO2 that corresponds to the outgoing factor.The energy lossdE/dz is, in turn, related to the number of atoms nTi in the cubic centimetre and through it to the material density ρmat. This relation is expressed by the stopping cross-section εstop defined as(10)εstop=1nTidEdz=MNA1ρmatdEdz,
where nTi is the number of target atoms per unit volume, M is their atomic mass, and NA is the Avogadro number.The stopping cross section described by (10) expresses the energy loss based on the number of atoms per square centimetre.The values ofεstop are tabulated for all elements [53, 59, 60] while for compounds such as TiO2 the stopping cross section εTiO2 is given as a sum of the elemental contributions:(11)εTiO2=εTi+2εO.Densityρmat can be found from (10) when the energy loss dE/dz 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 TiO2-y 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 Table2. The lowest values of  ρmat correspond to the density of the amorphous TiO2 [38], slightly higher ρmat 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).Table 2
Summary of the microanalysis ofTiO2-y by RBS and NRA; Sd: deposition rate, d: film thickness, NO: surface number of oxygen atoms, NTi: surface number of titanium atoms, ρmat: film density; calculated density of anatase ρA=3.864 g/cm3 and calculated density of rutile ρR=4.250 g/cm3 according to [1].
Sample/substrateDeposition methodTime (sec)Sd (nm/s)d (nm)NO×1017 (at/cm2) from NRANO×1017 (at/cm2) from RBSNTi×1017 (at/cm2) from RBSρmat (g/cm3) from RBSNa1/Cdc magnetron sputtering411.4358–603.253.031.583.17–3.39Na2/Cdc magnetron sputtering481.1754–583.363.201.523.67–3.94Na3/Cdc magnetron sputtering570.9852–583.413.09–3.221.433.67–4.09Na4/Cdc magnetron sputtering720.7654–563.162.791.403.22–3.33Na5/Cdc magnetron sputtering950.5450–522.532.69–2.741.313.15–3.27Na6/Cdc magnetron sputtering1430.2332–342.452.481.163.35–4.60M50/Crf sputtering27500.0250–603.542.931.573.27–3.92M50/Si/ SiO2rf sputtering27500.0250–607.95—1.63.27–3.92WO_1/Sirf sputtering150000.0230017—9.133.7The quantitative RBS microanalysis yields the number of atomsX per square centimetre of the target, NX, either from the height or from the area of the corresponding peak [52]. The area AX under the peak is proportional to the total number of atoms NX per unit area and to the differential scattering cross section dσ/dΩ. The absolute value of NX requires a careful calibration, and therefore the procedure adopted in this work is based on the following formula:(12)NX=NrefAXAref(dσ/dΩ)refqref(dσ/dΩ)XqX,
where the subscripts ref denote a reference sample (Bi implanted into Si) of the known concentration Nref. The integrated charge q of the incident beam is usually the same for the reference sample and the studied material, qref=qX. 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 (NTi),(ii)
surface number of oxygen atoms in at/cm2 (NO),(iii)
the atomic ratio O/Ti related to the departure from stoichiometryy,(iv)
film density (ρmat),for a series ofTiO2-y deposited by plasma emission controlled dc-pulsed reactive magnetron sputtering and by rf reactive sputtering at different growth rates Sd (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 Figure3) indicate that the samples are homogeneous and are not contaminated by foreign species. The amount of build-in argon is negligible.


#### 3.2.2. NRA

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 Z, like oxygen (Z=8), where RBS loses sensitivity due to the Z2 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 ofTiO2-y. The 16O(d,p)17O* 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 Figure4. Apart from the basic reaction 16O(d,p)17O* used for oxygen determination, two other nuclear reactions, 16O(d,p)17O and 12C(d,p)13C, take place. The large peak in Figure 4(c) is related to the 12C(d,p)13C reaction in the carbon substrate.The NRA spectra of (a) Ta2O5 reference sample; (b) TiO2-y thin film deposited on thermally oxidized Si wafer (Si/SiO2) and (c) TiO2-y on carbon foil C. The nuclear reactions corresponding to three peaks in the spectra are indicated.
(a)
Ta2O5 reference(b)
TiO2-y on Si/SiO2(c)
TiO2-y on CIn order to perform the quantitative analysis, only the area of the peak of16O(d,p)17O* 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.Table2 lists the results of the RBS and NRA analysis. Figure 5 gives the atomic ratio O/Ti for a series of TiO2-y obtained by reactive sputtering as a function of the sputtering rate Sd. There is a fairly good agreement between the surface number of oxygen atoms NO 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 Sd and the surface number of titanium atoms NTi 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 Sd and yields in a consequence larger content of Ti in the film. It is interesting to note that neither NO (Table 2) nor O/Ti (Figure 5) follow the systematic dependence on Sd. For the intermediate Sd 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 NO and the film density ρmat. 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.Figure 5
Atomic ratio of O/Ti, as determined by RBS and NRA, for two sets (I, II) ofTiO2-y thin films deposited by sputtering at different growth rates Sd. Sets I and II have different film thickness, I: 100–130 nm, II: 30–60 nm. The solid line is a guide to the eye.


#### 3.2.3. XPS

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 Ti2p3/2 [64]. 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 [65]. 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. [68] 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 CX 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 AX is then divided by the respective relative sensitivity factors SX [73, 74] according to the formula:(13)CX=100AX/SX∑iAi/Si,
where the summation is extended over all elements in the sample.In this work the sensitivity factorsSX were assumed to be equal to the corresponding normalized photoelectric cross-sections SC1s=1, SO1s=2.93, and  STi2p=7.91 [75].Figure6 shows a survey spectrum of a TiO2-y thin film deposited by sputtering. The spectrum contains the most prominent 2p3/2 and 2p1/2 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 6
Typical overall XPS spectrum for aTiO2-y thin film deposited by reactive sputtering onto Si wafer.The binding energies of Ti2p3/2 and O 1s core levels are listed in Table 3. The detailed analysis of the oxygen and titanium XPS peaks is presented in Figures 7 and 8.Table 3
Binding energies of Ti2p3/2 and O 1s states for TiO2-y thin films deposited by reactive sputtering as compared to the literature data.
Binding energy (eV)ReferenceOIIOITi4+Ti3+Ti2+Ti0531.9529.7458.5455.8453.5Reactive sputteringSd=0.23 nm/s531.9530.0458.6456.3453.9Reactive sputteringSd=1.82 nm/s——459.0457.5455.3453.9[68]532.0530.3459.4457.9455.4454.2[63]532.4530.1458.5456.7455.9—[62]——458.5456.3—453.8[70]——458.5456.8455.0—[71]—529.5457.9456.6——[67]Binding energy shifts (eV) relative to Ti4+0.0−2.7−5.0Reactive sputteringSd=0.23 nm/s0.0−2.3−4.7Reactive sputteringSd=1.82 nm/s0.0−1.9−3.5−5.3[66]0.0−1.5−3.8−4.7[65]0.0−1.5−3.5−5.1[68]Figure 7
Fit of Ti2p XPS spectrum for thin films of TiO2-y obtained at (a) Sd=1.82 nm/s and (b) Sd=0.23 nm/s. Three components of each fit 1, 2, 3 correspond to different oxidation states of titanium.Figure 8
Fit of O 1s XPS peak for aTiO2-y thin film deposited by reactive sputtering onto Si wafer at Sd=0.23 nm/s.Figure7 shows Ti 2p doublet measured in thin films deposited under oxidizing conditions controlled by sputtering rate Sd. Two limiting cases are shown: Sd=1.82 nm/s that yields substoichiometric oxides and Sd=0.23 nm/s that corresponds to overoxidized conditions. The measured Ti 2p 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+ [68]. Almost symmetrical shape of Ti 2p peak is observed in the case of samples obtained at Sd<1.5 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 Sd=1.82 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 2p3/2 photoelectron peak have been calculated, and the results of the quantitative analysis are listed in Table 4.Table 4
Relative contributions (%) to the Ti2p3/2 and O 1s XPS lines from the different oxidation states for TiO2-y thin films deposited by the reactive sputtering.
Sd (nm/s)OIIOIOII/(OI+OII)Ti4+Ti3+/Ti2+Ti01.8219810.1975.410.514.10.8815850.1591.55.13.40.2313870.1391.94.73.4The assignment of each of the three components forming Ti2p 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 (Table3). 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 (atSd<1.5 nm/s). The presence of small amounts of Ti3+ or Ti2+ in the films that are not completely oxidized (Sd=1.82 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 [69]. High-energy component has been assigned to oxygen bonded to Ti+3 (O–Ti3+) [62]. 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 [62] 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 Sd=1.82 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. [78] 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 OII/(OI+OII) as a measure of the porosity it may be concluded that TiO2-y 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 Ti2p 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 [65].


## 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. [44] and another given by Löbl et al. [47]. The work of Pawlewicz et al. [44] suggests that the phase composition is controlled by the substrate temperature and oxygen partial pressure pO2.According to the diagram of Löbl et al. [47] (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.Figure 2
Phase composition diagram after Löbl et al. [47] modified to include the results obtained for TiO2 thin films discussed in this work; Sd: deposition rate of thin films.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 anataseTiO2 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 Stoichiometryy in Thin Films of TiO2-y

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 (y in the formula TiO2-y). 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, typically4He++ [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 [58]. 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 [54]. 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 E0=2.012 MeV or 1.96 MeV. The detector was placed at the scattering angle Θ=165°.The XPS was studied at the Surface Spectroscopy Laboratory, AGH University of Science and Technology. Multitechnique setup of VSW Scientific Instruments was used.


### 3.2.1. RBS

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 [52] of particles with atomic mass m at nuclei of the atomic mass M.The energyE1 of the ionized particle scattered at the sample surface is related to the incident energy E0 by the laws of conservation of momentum and energy as [52, 53](6)E1=KME0,
with the kinematic recoil factor KM(7)KM=(mcos⁡Θ+M2-m2sin⁡2Θm+M)2.Hence, for a given scattering geometry, the detected energy of ions scattered from the surface is a simple function of the atomic massM 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.Figure 3
Comparison between the experimental RBS spectra of aTiO2-y thin film deposited by rf sputtering on different substrates: thermally oxidized Si wafer (Si/SiO2) and carbon foil C.The energy differenceΔE 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 ΔE of the signal is proportional to the film thickness d [52]:(8)ΔE=[S]d,
where [S] is the energy loss that depends on KM and on the energy loss per unit path length dE/dz in a given material [52].Equation (8) can be used to determine the thickness of layers. This is shown in Figure 3, where two experimental RBS spectra of TiO2-y 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 TiO2-y 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[S] in (8) depends on the material density ρmat. Therefore, if the layer thickness is known independently and ΔE is derived from the RBS spectrum, then [S] can be used to calculate the energy loss per unit length dE/dz from(9)[S]TiTiO2=KTidEdz|inTiO2+1|cos⁡Θ|dEdz|outTiO2.The energy loss factor[S]TiTiO2 of TiO2 for scattering from Ti is composed of two terms: KTi(dE/dz)|inTiO2 that represents the energy loss of particles on their inward path and (1/|cosΘ|)(dE/dz)|outTiO2 that corresponds to the outgoing factor.The energy lossdE/dz is, in turn, related to the number of atoms nTi in the cubic centimetre and through it to the material density ρmat. This relation is expressed by the stopping cross-section εstop defined as(10)εstop=1nTidEdz=MNA1ρmatdEdz,
where nTi is the number of target atoms per unit volume, M is their atomic mass, and NA is the Avogadro number.The stopping cross section described by (10) expresses the energy loss based on the number of atoms per square centimetre.The values ofεstop are tabulated for all elements [53, 59, 60] while for compounds such as TiO2 the stopping cross section εTiO2 is given as a sum of the elemental contributions:(11)εTiO2=εTi+2εO.Densityρmat can be found from (10) when the energy loss dE/dz 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 TiO2-y 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 Table2. The lowest values of  ρmat correspond to the density of the amorphous TiO2 [38], slightly higher ρmat 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).Table 2
Summary of the microanalysis ofTiO2-y by RBS and NRA; Sd: deposition rate, d: film thickness, NO: surface number of oxygen atoms, NTi: surface number of titanium atoms, ρmat: film density; calculated density of anatase ρA=3.864 g/cm3 and calculated density of rutile ρR=4.250 g/cm3 according to [1].
Sample/substrateDeposition methodTime (sec)Sd (nm/s)d (nm)NO×1017 (at/cm2) from NRANO×1017 (at/cm2) from RBSNTi×1017 (at/cm2) from RBSρmat (g/cm3) from RBSNa1/Cdc magnetron sputtering411.4358–603.253.031.583.17–3.39Na2/Cdc magnetron sputtering481.1754–583.363.201.523.67–3.94Na3/Cdc magnetron sputtering570.9852–583.413.09–3.221.433.67–4.09Na4/Cdc magnetron sputtering720.7654–563.162.791.403.22–3.33Na5/Cdc magnetron sputtering950.5450–522.532.69–2.741.313.15–3.27Na6/Cdc magnetron sputtering1430.2332–342.452.481.163.35–4.60M50/Crf sputtering27500.0250–603.542.931.573.27–3.92M50/Si/ SiO2rf sputtering27500.0250–607.95—1.63.27–3.92WO_1/Sirf sputtering150000.0230017—9.133.7The quantitative RBS microanalysis yields the number of atomsX per square centimetre of the target, NX, either from the height or from the area of the corresponding peak [52]. The area AX under the peak is proportional to the total number of atoms NX per unit area and to the differential scattering cross section dσ/dΩ. The absolute value of NX requires a careful calibration, and therefore the procedure adopted in this work is based on the following formula:(12)NX=NrefAXAref(dσ/dΩ)refqref(dσ/dΩ)XqX,
where the subscripts ref denote a reference sample (Bi implanted into Si) of the known concentration Nref. The integrated charge q of the incident beam is usually the same for the reference sample and the studied material, qref=qX. 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 (NTi),(ii)
surface number of oxygen atoms in at/cm2 (NO),(iii)
the atomic ratio O/Ti related to the departure from stoichiometryy,(iv)
film density (ρmat),for a series ofTiO2-y deposited by plasma emission controlled dc-pulsed reactive magnetron sputtering and by rf reactive sputtering at different growth rates Sd (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 Figure3) indicate that the samples are homogeneous and are not contaminated by foreign species. The amount of build-in argon is negligible.


### 3.2.2. NRA

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 Z, like oxygen (Z=8), where RBS loses sensitivity due to the Z2 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 ofTiO2-y. The 16O(d,p)17O* 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 Figure4. Apart from the basic reaction 16O(d,p)17O* used for oxygen determination, two other nuclear reactions, 16O(d,p)17O and 12C(d,p)13C, take place. The large peak in Figure 4(c) is related to the 12C(d,p)13C reaction in the carbon substrate.The NRA spectra of (a) Ta2O5 reference sample; (b) TiO2-y thin film deposited on thermally oxidized Si wafer (Si/SiO2) and (c) TiO2-y on carbon foil C. The nuclear reactions corresponding to three peaks in the spectra are indicated.
(a)
Ta2O5 reference(b)
TiO2-y on Si/SiO2(c)
TiO2-y on CIn order to perform the quantitative analysis, only the area of the peak of16O(d,p)17O* 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.Table2 lists the results of the RBS and NRA analysis. Figure 5 gives the atomic ratio O/Ti for a series of TiO2-y obtained by reactive sputtering as a function of the sputtering rate Sd. There is a fairly good agreement between the surface number of oxygen atoms NO 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 Sd and the surface number of titanium atoms NTi 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 Sd and yields in a consequence larger content of Ti in the film. It is interesting to note that neither NO (Table 2) nor O/Ti (Figure 5) follow the systematic dependence on Sd. For the intermediate Sd 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 NO and the film density ρmat. 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.Figure 5
Atomic ratio of O/Ti, as determined by RBS and NRA, for two sets (I, II) ofTiO2-y thin films deposited by sputtering at different growth rates Sd. Sets I and II have different film thickness, I: 100–130 nm, II: 30–60 nm. The solid line is a guide to the eye.


### 3.2.3. XPS

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 Ti2p3/2 [64]. 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 [65]. 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. [68] 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 CX 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 AX is then divided by the respective relative sensitivity factors SX [73, 74] according to the formula:(13)CX=100AX/SX∑iAi/Si,
where the summation is extended over all elements in the sample.In this work the sensitivity factorsSX were assumed to be equal to the corresponding normalized photoelectric cross-sections SC1s=1, SO1s=2.93, and  STi2p=7.91 [75].Figure6 shows a survey spectrum of a TiO2-y thin film deposited by sputtering. The spectrum contains the most prominent 2p3/2 and 2p1/2 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 6
Typical overall XPS spectrum for aTiO2-y thin film deposited by reactive sputtering onto Si wafer.The binding energies of Ti2p3/2 and O 1s core levels are listed in Table 3. The detailed analysis of the oxygen and titanium XPS peaks is presented in Figures 7 and 8.Table 3
Binding energies of Ti2p3/2 and O 1s states for TiO2-y thin films deposited by reactive sputtering as compared to the literature data.
Binding energy (eV)ReferenceOIIOITi4+Ti3+Ti2+Ti0531.9529.7458.5455.8453.5Reactive sputteringSd=0.23 nm/s531.9530.0458.6456.3453.9Reactive sputteringSd=1.82 nm/s——459.0457.5455.3453.9[68]532.0530.3459.4457.9455.4454.2[63]532.4530.1458.5456.7455.9—[62]——458.5456.3—453.8[70]——458.5456.8455.0—[71]—529.5457.9456.6——[67]Binding energy shifts (eV) relative to Ti4+0.0−2.7−5.0Reactive sputteringSd=0.23 nm/s0.0−2.3−4.7Reactive sputteringSd=1.82 nm/s0.0−1.9−3.5−5.3[66]0.0−1.5−3.8−4.7[65]0.0−1.5−3.5−5.1[68]Figure 7
Fit of Ti2p XPS spectrum for thin films of TiO2-y obtained at (a) Sd=1.82 nm/s and (b) Sd=0.23 nm/s. Three components of each fit 1, 2, 3 correspond to different oxidation states of titanium.Figure 8
Fit of O 1s XPS peak for aTiO2-y thin film deposited by reactive sputtering onto Si wafer at Sd=0.23 nm/s.Figure7 shows Ti 2p doublet measured in thin films deposited under oxidizing conditions controlled by sputtering rate Sd. Two limiting cases are shown: Sd=1.82 nm/s that yields substoichiometric oxides and Sd=0.23 nm/s that corresponds to overoxidized conditions. The measured Ti 2p 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+ [68]. Almost symmetrical shape of Ti 2p peak is observed in the case of samples obtained at Sd<1.5 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 Sd=1.82 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 2p3/2 photoelectron peak have been calculated, and the results of the quantitative analysis are listed in Table 4.Table 4
Relative contributions (%) to the Ti2p3/2 and O 1s XPS lines from the different oxidation states for TiO2-y thin films deposited by the reactive sputtering.
Sd (nm/s)OIIOIOII/(OI+OII)Ti4+Ti3+/Ti2+Ti01.8219810.1975.410.514.10.8815850.1591.55.13.40.2313870.1391.94.73.4The assignment of each of the three components forming Ti2p 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 (Table3). 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 (atSd<1.5 nm/s). The presence of small amounts of Ti3+ or Ti2+ in the films that are not completely oxidized (Sd=1.82 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 [69]. High-energy component has been assigned to oxygen bonded to Ti+3 (O–Ti3+) [62]. 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 [62] 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 Sd=1.82 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. [78] 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 OII/(OI+OII) as a measure of the porosity it may be concluded that TiO2-y 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 Ti2p 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 [65].


## 3.2.1. RBS

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 [52] of particles with atomic mass m at nuclei of the atomic mass M.The energyE1 of the ionized particle scattered at the sample surface is related to the incident energy E0 by the laws of conservation of momentum and energy as [52, 53](6)E1=KME0,
with the kinematic recoil factor KM(7)KM=(mcos⁡Θ+M2-m2sin⁡2Θm+M)2.Hence, for a given scattering geometry, the detected energy of ions scattered from the surface is a simple function of the atomic massM 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.Figure 3
Comparison between the experimental RBS spectra of aTiO2-y thin film deposited by rf sputtering on different substrates: thermally oxidized Si wafer (Si/SiO2) and carbon foil C.The energy differenceΔE 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 ΔE of the signal is proportional to the film thickness d [52]:(8)ΔE=[S]d,
where [S] is the energy loss that depends on KM and on the energy loss per unit path length dE/dz in a given material [52].Equation (8) can be used to determine the thickness of layers. This is shown in Figure 3, where two experimental RBS spectra of TiO2-y 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 TiO2-y 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[S] in (8) depends on the material density ρmat. Therefore, if the layer thickness is known independently and ΔE is derived from the RBS spectrum, then [S] can be used to calculate the energy loss per unit length dE/dz from(9)[S]TiTiO2=KTidEdz|inTiO2+1|cos⁡Θ|dEdz|outTiO2.The energy loss factor[S]TiTiO2 of TiO2 for scattering from Ti is composed of two terms: KTi(dE/dz)|inTiO2 that represents the energy loss of particles on their inward path and (1/|cosΘ|)(dE/dz)|outTiO2 that corresponds to the outgoing factor.The energy lossdE/dz is, in turn, related to the number of atoms nTi in the cubic centimetre and through it to the material density ρmat. This relation is expressed by the stopping cross-section εstop defined as(10)εstop=1nTidEdz=MNA1ρmatdEdz,
where nTi is the number of target atoms per unit volume, M is their atomic mass, and NA is the Avogadro number.The stopping cross section described by (10) expresses the energy loss based on the number of atoms per square centimetre.The values ofεstop are tabulated for all elements [53, 59, 60] while for compounds such as TiO2 the stopping cross section εTiO2 is given as a sum of the elemental contributions:(11)εTiO2=εTi+2εO.Densityρmat can be found from (10) when the energy loss dE/dz 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 TiO2-y 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 Table2. The lowest values of  ρmat correspond to the density of the amorphous TiO2 [38], slightly higher ρmat 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).Table 2
Summary of the microanalysis ofTiO2-y by RBS and NRA; Sd: deposition rate, d: film thickness, NO: surface number of oxygen atoms, NTi: surface number of titanium atoms, ρmat: film density; calculated density of anatase ρA=3.864 g/cm3 and calculated density of rutile ρR=4.250 g/cm3 according to [1].
Sample/substrateDeposition methodTime (sec)Sd (nm/s)d (nm)NO×1017 (at/cm2) from NRANO×1017 (at/cm2) from RBSNTi×1017 (at/cm2) from RBSρmat (g/cm3) from RBSNa1/Cdc magnetron sputtering411.4358–603.253.031.583.17–3.39Na2/Cdc magnetron sputtering481.1754–583.363.201.523.67–3.94Na3/Cdc magnetron sputtering570.9852–583.413.09–3.221.433.67–4.09Na4/Cdc magnetron sputtering720.7654–563.162.791.403.22–3.33Na5/Cdc magnetron sputtering950.5450–522.532.69–2.741.313.15–3.27Na6/Cdc magnetron sputtering1430.2332–342.452.481.163.35–4.60M50/Crf sputtering27500.0250–603.542.931.573.27–3.92M50/Si/ SiO2rf sputtering27500.0250–607.95—1.63.27–3.92WO_1/Sirf sputtering150000.0230017—9.133.7The quantitative RBS microanalysis yields the number of atomsX per square centimetre of the target, NX, either from the height or from the area of the corresponding peak [52]. The area AX under the peak is proportional to the total number of atoms NX per unit area and to the differential scattering cross section dσ/dΩ. The absolute value of NX requires a careful calibration, and therefore the procedure adopted in this work is based on the following formula:(12)NX=NrefAXAref(dσ/dΩ)refqref(dσ/dΩ)XqX,
where the subscripts ref denote a reference sample (Bi implanted into Si) of the known concentration Nref. The integrated charge q of the incident beam is usually the same for the reference sample and the studied material, qref=qX. 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 (NTi),(ii)
surface number of oxygen atoms in at/cm2 (NO),(iii)
the atomic ratio O/Ti related to the departure from stoichiometryy,(iv)
film density (ρmat),for a series ofTiO2-y deposited by plasma emission controlled dc-pulsed reactive magnetron sputtering and by rf reactive sputtering at different growth rates Sd (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 Figure3) indicate that the samples are homogeneous and are not contaminated by foreign species. The amount of build-in argon is negligible.


## 3.2.2. NRA

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 Z, like oxygen (Z=8), where RBS loses sensitivity due to the Z2 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 ofTiO2-y. The 16O(d,p)17O* 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 Figure4. Apart from the basic reaction 16O(d,p)17O* used for oxygen determination, two other nuclear reactions, 16O(d,p)17O and 12C(d,p)13C, take place. The large peak in Figure 4(c) is related to the 12C(d,p)13C reaction in the carbon substrate.The NRA spectra of (a) Ta2O5 reference sample; (b) TiO2-y thin film deposited on thermally oxidized Si wafer (Si/SiO2) and (c) TiO2-y on carbon foil C. The nuclear reactions corresponding to three peaks in the spectra are indicated.
(a)
Ta2O5 reference(b)
TiO2-y on Si/SiO2(c)
TiO2-y on CIn order to perform the quantitative analysis, only the area of the peak of16O(d,p)17O* 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.Table2 lists the results of the RBS and NRA analysis. Figure 5 gives the atomic ratio O/Ti for a series of TiO2-y obtained by reactive sputtering as a function of the sputtering rate Sd. There is a fairly good agreement between the surface number of oxygen atoms NO 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 Sd and the surface number of titanium atoms NTi 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 Sd and yields in a consequence larger content of Ti in the film. It is interesting to note that neither NO (Table 2) nor O/Ti (Figure 5) follow the systematic dependence on Sd. For the intermediate Sd 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 NO and the film density ρmat. 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.Figure 5
Atomic ratio of O/Ti, as determined by RBS and NRA, for two sets (I, II) ofTiO2-y thin films deposited by sputtering at different growth rates Sd. Sets I and II have different film thickness, I: 100–130 nm, II: 30–60 nm. The solid line is a guide to the eye.


## 3.2.3. XPS

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 Ti2p3/2 [64]. 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 [65]. 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. [68] 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 CX 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 AX is then divided by the respective relative sensitivity factors SX [73, 74] according to the formula:(13)CX=100AX/SX∑iAi/Si,
where the summation is extended over all elements in the sample.In this work the sensitivity factorsSX were assumed to be equal to the corresponding normalized photoelectric cross-sections SC1s=1, SO1s=2.93, and  STi2p=7.91 [75].Figure6 shows a survey spectrum of a TiO2-y thin film deposited by sputtering. The spectrum contains the most prominent 2p3/2 and 2p1/2 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 6
Typical overall XPS spectrum for aTiO2-y thin film deposited by reactive sputtering onto Si wafer.The binding energies of Ti2p3/2 and O 1s core levels are listed in Table 3. The detailed analysis of the oxygen and titanium XPS peaks is presented in Figures 7 and 8.Table 3
Binding energies of Ti2p3/2 and O 1s states for TiO2-y thin films deposited by reactive sputtering as compared to the literature data.
Binding energy (eV)ReferenceOIIOITi4+Ti3+Ti2+Ti0531.9529.7458.5455.8453.5Reactive sputteringSd=0.23 nm/s531.9530.0458.6456.3453.9Reactive sputteringSd=1.82 nm/s——459.0457.5455.3453.9[68]532.0530.3459.4457.9455.4454.2[63]532.4530.1458.5456.7455.9—[62]——458.5456.3—453.8[70]——458.5456.8455.0—[71]—529.5457.9456.6——[67]Binding energy shifts (eV) relative to Ti4+0.0−2.7−5.0Reactive sputteringSd=0.23 nm/s0.0−2.3−4.7Reactive sputteringSd=1.82 nm/s0.0−1.9−3.5−5.3[66]0.0−1.5−3.8−4.7[65]0.0−1.5−3.5−5.1[68]Figure 7
Fit of Ti2p XPS spectrum for thin films of TiO2-y obtained at (a) Sd=1.82 nm/s and (b) Sd=0.23 nm/s. Three components of each fit 1, 2, 3 correspond to different oxidation states of titanium.Figure 8
Fit of O 1s XPS peak for aTiO2-y thin film deposited by reactive sputtering onto Si wafer at Sd=0.23 nm/s.Figure7 shows Ti 2p doublet measured in thin films deposited under oxidizing conditions controlled by sputtering rate Sd. Two limiting cases are shown: Sd=1.82 nm/s that yields substoichiometric oxides and Sd=0.23 nm/s that corresponds to overoxidized conditions. The measured Ti 2p 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+ [68]. Almost symmetrical shape of Ti 2p peak is observed in the case of samples obtained at Sd<1.5 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 Sd=1.82 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 2p3/2 photoelectron peak have been calculated, and the results of the quantitative analysis are listed in Table 4.Table 4
Relative contributions (%) to the Ti2p3/2 and O 1s XPS lines from the different oxidation states for TiO2-y thin films deposited by the reactive sputtering.
Sd (nm/s)OIIOIOII/(OI+OII)Ti4+Ti3+/Ti2+Ti01.8219810.1975.410.514.10.8815850.1591.55.13.40.2313870.1391.94.73.4The assignment of each of the three components forming Ti2p 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 (Table3). 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 (atSd<1.5 nm/s). The presence of small amounts of Ti3+ or Ti2+ in the films that are not completely oxidized (Sd=1.82 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 [69]. High-energy component has been assigned to oxygen bonded to Ti+3 (O–Ti3+) [62]. 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 [62] 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 Sd=1.82 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. [78] 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 OII/(OI+OII) as a measure of the porosity it may be concluded that TiO2-y 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 Ti2p 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 [65].


## 4. Discussion

The summary of the quantitative analysis is given in Table5 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 [61]. 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.Table 5
Atomic ratio O/Ti determined by four different analytical methods described in this work forTiO2-y thin films obtained under controllable conditions; electron microprobe EMP was performed with X-ray microanalyzer ARL SEMQ at beam parameters: 10 kV and 0.5 μA; beam diameter on the sample 5 μm.
Analytical methodO/TiSd=1.46 nm/sSd=0.23 nm/sEMP1.871.92XPS2.472.44RBS1.932.11NRA2.062.14Ion beam techniques, RBS and NRA are better suited for determination of oxygen nonstoichiometryy in thin films of TiO2-y.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 1μm thick [52]. On the other hand, Rutherford backscattering RBS provides information on the composition profile in depth in a nondestructive way [53]. 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 [79].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 inTiO2-y 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 resistivityρ as a function of the sputtering rate Sd is shown in Figure 9 for nonstoichiometric thin films of TiO2-y obtained by reactive sputtering. It demonstrates the existing correlation between the electrical resistivity and film composition.Figure 9
Electrical resistivityρ at room temperature and the atomic ratio of O/Ti versus deposition rate Sd for TiO2-y thin films prepared by reactive sputtering. Lines are guides to the eye.For fully oxidized samples, that is, at the lowest value of growth ratesSd the electrical resistance exceeds the limit of measurement. At Sd>1.5 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 stoichiometryy, TiO2-y thin films become more conducting. The close relationship between ρ and y indicates that oxygen nonstoichiometry is the source of electrons in the conduction band of titanium dioxide thin films.


## 5. Conclusions

The importance of ion beam techniques in the determination of oxygen nonstoichiometry in reactively sputteredTiO2-y has been discussed in this review paper. The following detailed conclusions can be formulated:(i)
chemical composition ofTiO2-y thin films deposited by reactive sputtering from Ti target is close to stoichiometric but a controlled departure from stoichiometry y can be reached at a specific deposition rate;(ii)
departure from stoichiometry over the range of-0.2<y<0.2 has been found by RBS and NRA techniques while XPS, which is a typical surface analysis, yields y as high as 0.5;(iii)
film densityρmat 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, NO;(iv)
close relationship between the electrical resistivity and the deviation from stoichiometryy 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 makeTiO2-y based oxides into reliable and commercially viable electronic devices.



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