ELECTRON ENERGY LOSS SPECTROSCOPY: EXPERIMENTAL SET-UP AND METHODS
The development of ultra-high vacuum (UHV) techniques [36, 37] is essential to surface sci-ence. It is common sense that it is essential to keep clean the surface under study, since even a small amount of adsorbate may produce drastic modifications of its intrinsic properties. For this reason, the changes that are undergone by the surface during measurements have to be perfectly controlled. Within the framework of the kinetic theory of gases, the impinging rate ra of a gas on a surface (defined as the number of atomic or molecular collisions per unit area per unit of time) is given by ra = nνaver /4 where n is the number of atoms (or molecules) per unit of volume in the surrounding atmosphere and νaver is their average speed. The gas being considered as ideal 1, n = pgas/kB T where pgas is the pressure of the gas, kB the Boltzmann constant and T the absolute temperature. Since the Maxwell-Boltzmann distribution of species velocity gives νaver = (8kBT /πmgas)1/2 where mgas is the mass of the atom (molecule) of gas, the impinging rate is just a function of gas pressure and tempera-ture ra = Pgas/ 2πkBT mgas. Considering convenient units, the impinging rate expressed in cm−2 • s−1 is given by ra ≈ 2.633 × 1022pgas/ T Mgas where pgas is in mbar, T in K, and Mgas is molecular weight of the gas in gram. To go further in the order of magnitude, let’s assume that all molecules arriving at the surface stick and are incorporated into the surface of the material in the form a monolayer which consists of about 1015.cm−2. In the case of water, a gas which currently appears in the residual atmosphere in UHV systems, it takes less than 3 seconds at a partial pressure of 10−6 mbar at room temperature to cover a bare surface with a full monolayer. This notion of impinging rate is at the origin of a unit of exposure, the so-called Langmuir [36, 37], from the name of the scientist who layed the foundations of surface science and has drawn attention to the concept of surface coverage. A Langmuir corresponds to an exposure of 10−6 torr (1.33 × 10−6 mbar) during one second. As an order of magnitude, it is currently said that an exposure of 1 Langmuir results in the formation of a full monolayer.
Assuming a residual background of water vapour, the above formula shows that it takes at least 8 hours to fully cover the surface at 10−10 mbar. This time, which is suﬃcient to analyse the bare surface or to cover it with a controlled amount of chosen adsorbates, explains why surface science studies are currently performed in UHV conditions corresponding to residual pressures in the low 10−10 or even in the high 10−11 mbar range.
The present work focuses on the reactive properties of rutile single crystal (110) surface towards oxygen, water vapour or both. Experiments have been performed in a UHV system equipped with a High Resolution Electron Energy Loss Spectrometer (HREELS). The UHV system, the sample, its preparation and the electron energy loss technique which is at the heart of the present work are described successively in what follows. drawing of its relevant components.
All experiments have been performed in an UHV system depicted in Fig 2.1. The sys-tem consists of three chambers separated by gate valves: (i) a load-lock, (ii) a preparation chamber and (iii) an analysis chamber housing the HREELS spectrometer (LK2000, LK-Technologies ) which will be described in Sect. 2.3.2. Pressures in all chambers are mea-sured with hot filament Bayard-Alpert gauges (Varian type) calibrated on nitrogen sensitivity.
The preparation chamber is pumped down to a base pressure of 3 × 10−10 mbar after bake-out by a combination (i) of a molecular turbomolecular pump (Leybold, 250 l/s) evacuated by a rotary pump (Alcatel, 10 m3/h), (ii) of a ion pump (Riber, 400 l/s) and (iii) of a titanium sublimation pump (Varian) enclosed into a cold trap. The sample can be transferred and annealed on a compact home-made 5-axis manipulator 2. The sample mounted on Mo-back plate can be heated up to 1500 K either radiatively by a spiral tantalum/tungsten filament or by electron bombardment by applying a negative high voltage to the filament and the wenhelt surrounding it. The sample temperature is measured by an optical pyrometer calibrated once by spotwelding a thermocouple on the sample backplate. An ion gun (Specs, 10/35) equipped with a leak valve is placed in line of sight of the sample and is used to sputter the substrate with Ar+ ions. The preparation chamber is equipped with a four grids LEED-Auger (Low Energy Electron Diﬀraction/Auger spectroscopy, ErLEED from SPECS) apparatus. It allows to check the crystallinity of the sample via the quality of the diﬀraction pattern and also to perform Auger electron spectroscopy (AES) via electronic emission of the sample when excited by an incident electron beam. AES is used to detect surface impurities with a limit of a few percent of monolayer. The principle and theory of LEED and Auger spectroscopy and the method of using retarded field to record Auger data by means of four-grids device is explained in several references [37, 39].
The sample could be transferred by the way of mechanical arm to the main HREELS chamber where a base pressure of < 5.10−11 mbar is maintained thanks to a combined TSP-ion pump (Meca 2000, 400l/s). The sample is hld on a manipulator with 5 degrees of freedom: 3 translations (X,Y,Z), a rotation along the Z direction, and a tilt along X direction. Its head is made out of cooper 3 to allow a fast and eﬃcient cooling by flowing liquid nitrogen. A Au foil is inserted between the Mo support plate on which the sample is firmly clamped and the two side polished TiO2(110) crystal to ensure a good thermal contact while cooling 4. A kapton enclosed heater sandwiched between copper plates on which the sample holder is placed allows the regulation of the sample temperature through a PID regulator between 100 and 550 K. The temperature is monitored by a K-thermocouple clamped on the sample manipulator and cross-checked from the Boltzmann ratio of the loss and gain phonon peaks of TiO2. An ancillary electron gun (Riber) with a focus lens is mounted in line of sight of the sample at an incident angle of 45◦. It is used to bombard the sample with an electron current up to 1µA/cm−2 to create defects at beam energies ranging from 25 to 2000 eV. Finally a tungsten filament is placed in front of the sample at an adjustable distance from 1 to 40 mm. The use of this filament to anneal the surface is discussed in Chap. 4.
Gaz dosers made of a bundle of high aspect ratio (> 40) tubes are mounted in both chambers to increase the local pressure on the sample placed at a distance of around 1 mm . All exposures will be given in Langmuir (L). If not specified, low dosing is done via the back-filling of the vacuum chambers. Both chambers are connected to an ancillary gas pipes manifold. Scientific grade O2 and Ar gases are used while H2O is purified by several freeze-pump cycles.
The TiO2(110) surface and its preparation
Bulk rutile titanium dioxide
Titanium dioxide (TiO2) has several crystal polymorphs among which the major three are: rutile, anatase and brookite. While both rutile and anatase are mainly involved in ap-plication and scientific research field, only the high temperature form i.e. rutile 5 is studied in this work. It has a tetragonal unit cell (space group P42/mnm) which consists of two titanium (Ti) and four oxygen atoms (O) with lattice parameters a = b = 4.548 ˚A and c = 2.953 ˚A. The basic building block is a slightly distorted octahedron formed by one Ti atom with its surrounding six O atoms. Octahedron are stacked with their long axis alter-nating by 90◦ to form the crystal, as shown in Fig 2.2-b. Bond lengths between Ti and O atoms are 1.943 ˚A and 1.988 ˚A for the four-fold symmetric and two-fold symmetric bonds respectively. Rutile TiO2 has a band gap of around 3 eV (see Sect. 3.2.2). This ionocovalent material (Ti:[Ar]3d24s2 / O : [He]2s22p4) has a valence band dominated by O 2p states and its conduction band is mostly derived from Ti 3d orbitals but with some partial hybridization.
Rutile is the archetype of reducible oxide and many of its specific properties are linked to the reduced form TiO2−x that formally corresponds to the reduction of Ti4+ ions into Ti3+. This reduction can result from the formation and ionization of defects, either oxygen vacancies (VO) or titanium interstitials (Tii) which reads in the Kr¨ogerVink notation:
2Ti4+ + 4O2− → Ti3+ +VO•+ 1 O2 + 3O2− → 2Ti3+ +VO+ 1 O2 + 3O2− 2Ti4+ + 4O2− → Ti3+ + Tii••• + O2 + 3O2− → 2Ti3+ + Tii•• + O2 + 3O2− . . . . (2.1)
Reduction which is obtained most of the time through annealing under vacuum can pro-ceed upon the precipitation of defects into crystallographic shear plane up to defined sub-oxides  6. The dominating types of defects in the bulk were studied experimentally by the group of J. Nowotny (see review  and references therein). They have determined the equilibrium constants of the formation of all defects based on a combination of various measurements. The formation of bulk VO seems more favorable in surface science conditions (UHV annealing) than Tii in agreement with ab initio electronic calculations [14, 26, 42–45]. But other authors also introduced the question of interstitial oxygens  or titanium vacan-cies  in the problem.
Figure 2.3: Defect disorder diagram show-ing the eﬀect of oxygen activity at fixed temperature (T = 1273 K) on the concen-tration of ionic and electronic species in TiO2 (From Ref. ).
The diﬀusion mechanism of VO and Tii is very diﬀerent. Oxygen vacancies diﬀuse in a site exchange method. While the most favorable channel for titanium interstitial was supposed to be along the open  direction, latest calculations found it along the  direction  with a barrier lower by 1 eV compared to oxygen vacancies through an interstitialcy mecha-nism (sometimes called as kick-out) mechanism, in which the diﬀusing atom kicks out one of bulk titanium atom and takes its lattice position. This theoretical study agrees with the ex-perimental findings of M.A. Henderson, where the healing of the sputtered TiO2(110) surface is found to proceed through an inward diﬀusion of Ti interstitials upon annealing in vac-uum  or through an outward diﬀusion in oxydative conditions  inducing a regrowth of TiO2−x pacthes on the surface . The activation barrier of Ti diﬀusion has been estimated to 1.0 eV by Z. Zhang et.al  on the basis of electron stimulated desorption measurements performed during annealing in the 360-400 K temperature range. Similar values were reported by another experimental study of oxygen uptake  and by theoretical approaches .
Although reduced rutile is a n-type semiconductor, the mechanism of the electronic con-duction, the localisation of the charges associated to the defects, the charge state of the defect and the major contributions to the observed band gap states are still debated and will be discussed in depth in the forthcoming chapters.
The TiO2(110) surface
The TiO2(110)(1×1) surface is the most energetically stable surface of rutile. It is an archetypal substrate which has drawn an extraordinary scientific interest in the surface science field (see for instance review papers [2–8] or book ) in particular in relation with the photo-catalytic activity of titanium dioxide. It is available as large single crystals, it is a relatively good conductor which allows to use charged probe species and it oﬀers the incredible opportunity to look at the reactivity of point defects at the atomic scale with Scanning Tunnelling Microscopy (STM). The TiO2(110) surface is nearly bulk terminated and non-polar . The auto-compensation criterion requires that formal charges due to cation-derived dangling bonds compensate that from anion-derived dangling bonds in order to obtain a stable surface. Cutting along the dashed line shown in Fig 2.4 ensures that the same number of oxygen-to-titanium bonds are broken as titanium-to-oxygen bonds. As shown in Fig 2.5, the stoichiometric TiO2(110) surface consists of alternating rows of fivefold-coordinated Ti (Ti5c) atoms and protuding twofold-coordinated bridging oxygen (Ob). The Ti atom beneath Ob is sixfold-coordinated (Ti6c), and a row of threefold-coordinated oxygen atoms (O3c) is located between Ti5c and Ob rows. The surface unit cell of TiO2(110) is rectangular with lattice parameters of 2.96 ˚A along the Ob row direction and 6.49 ˚A normal to it. The structure mentioned above ensures that the surface containing twice as many O2− as Ti4+ ions is charge neutral. Along the direction normal to the surface, the spacing between Ti6c planes is 6.49 ˚A.
Figure 2.5: Ball model of the TiO2(110) surface: a) top-view along the  direction; b)side view. Typical defects of the surface are shown in figure: oxygen vacancy Ob-vac, hydroxyl group OHb, titanium insterstitial Tiint and adsorbed oxygen Oad. The notation of defects that will be used hereafter is common in the surface science field.
The most studied defects on the TiO2(110) surface are oxygen vacancies [2–8] that are formed on the Ob row (Ob-vac) (Fig 2.5), and which readily appear in STM as a bright spot in between Ti5c rows. While the exact mechanism of Ob-vac formation is not known, resonant photoemisson and DFT studies have shown that excess charges of two electrons per vacancy fill the unoccupied 3d orbitals of the Ti4+ ions. But the spatial location of this charge is still under investigation. More and more evidences have been reported that those charges are not on the very surface layer but on the subsurface Ti6c atoms with a complex and dynamic distribution among Ti atoms [22, 34, 52–54]. There are many ways to create Ob-vac such as sputtering/annealing and electron bombardment. Sputtering/annealing, the easiest one, produces both Ob-vac and Tiint. Those two defects can hardly be distinguished experimentally through their spectroscopic fingerprints. Interestingly, K. Mitsuhara et al.  have shown that Ob-vac are not created by annealing below 870 K. Electron bombardment creates Ob-vac via the Knotek-Feibelman process . In this process, the incident energetic electron creates a 3p hole in Ti atoms. Since Ti atoms in TiO2 poorly contribute to the valence band, the two electrons that are necessary for Auger hole decay must be provided mostly by O atoms through a inter-atomic Auger decay. After losing their electrons, the surface oxygen atoms become electrically neutral (even become O+ as a result of the double Auger process and share remaining valence electrons with Ti atom) and desorb. The threshold electron energy of 34 eV [56, 57] corresponds to the Ti 3p hole level creation. Several authors reported that electron bombardment only creates Ob-vac and does not rearrange defect distribution beneath the surface layer [11,12,58]. Ob-vac readily react with adsorbed molecules among which water which creates two bridging hydroxyl groups (OHb) per vacancy, one filling the vacancy and the remaining hydrogen sitting on neighbouring bridging oxygen atoms. The reaction with O2 replenishes the vacancies and releases extra-Oad which remains on the Ti5c. Ob-vac, Oad as well as OH groups can diﬀuse along the bridging oxygen row through complex mechanisms. A detailed description of the reaction and diﬀusion mechanisms with temperature of those species on TiO2(110) have been described in details in excellent recent reviews [2–9].
The surface preparation
Initially, several cycles of (i) sputtering with 1 keV Ar+ ions during 10 mins followed (ii) by annealing at T = 1100 K during 20 mins are carried out to obtain a sample with a sharp LEED (1 × 1) pattern and free of contaminants as judged by Auger spectroscopy and also confirmed by the lack of CH stretching frequency in HREELS and a good reflectivity. During this treatment, the sample, which was initially yellow pale, becomes dark blue, reflecting a high conductivity associated to the formation of bulk defects. Those defects eliminate the charging problem when the surface is probed by the low energy electron beam of HREELS.
Several surfaces have been compared throughout this work:
• R-TiO2(110) : the vacuum annealed surface (pristine surface after preparation) or reduced surface with a sizeable concentration of oxygen vacancies 7;
• O-TiO2(110) : a “fully oxydized” surface prepared by annealing in oxygen (5 × 10−6 mbar) at 1100 K for 20 mins after sputtering and also cooled down in oxygen to room temperature (RT). This oxygen treatment is supposed to heal almost all the defects that contribute to the band gap states ;
• E-TiO2(110) : an electron bombarded O-TiO2(110) during 1 hour with a beam energy of 75 eV and a current intensity of ∼ 1µ A/cm−2. This method described in Chap. 4 already used by several authors [11,12,57,59] is supposed to create surface vacancies by electron stimulated desorption of oxygen through the Knotek-Feibelman process ;
• A-TiO2(110) : a surface softly annealed in a controlled way by means of a filament set up in front of the sample 8 (Fig 2.1). Diﬀerent surface temperatures can be achieved as a function of the distance at which the hot filament stands from the surface and of the applied power. The pressure stayed always in the low 10−10 mbar during such a treatment. This method discussed in details in Chap. 4 allows to overcome the thermal equilibrium between the subsurface and the bulk of the sample in contrast to the more classical annealing from the back side. To be sure that no spurious electrons are emitted from the filament 9, some tests leading to the same results in terms of band gap state intensity were performed with a hot filament polarized at an high positive potential (100 eV) and a grounded sample. For grounded filament and sample, no sample current could be detected (below 10 pA).
Table of contents :
1.1 The origin of the bang gap states
1.2 The location of the energy levels of the band gap states
1.3 The nature and transport property of excess electrons
2 Electron Energy Loss Spectroscopy: experimental set-up and methods
2.1 The ultra-high vacuum system
2.2 The TiO2(110) surface and its preparation
2.2.1 Bulk rutile titanium dioxide
2.2.2 The TiO2(110) surface
2.2.3 The surface preparation
2.3 (High Resolution) Electron Energy Loss Spectroscopy
2.3.1 Introduction: basics of EELS
2.3.2 The spectrometer
2.3.3 Electron-surface interaction modes and their cross-section
220.127.116.11 Dipole scattering
18.104.22.168.1 Classical single loss cross section in the dielectric approach
22.214.171.124.2 Semi-classical treatment of multiple losses
126.96.36.199 Impact scattering
3 Dielectric modelling of Electron Energy Loss from TiO2
3.2 Dielectric modelling of EELS from TiO2 : the interplay between carrier excitations, phonons, band gap states and interband transitions
3.2.1 Theoretical reminder about dielectric theory of EELS
188.8.131.52 The single loss probability
184.108.40.206 The sensitivity function and the slit integration
220.127.116.11 Losses from an anisotropic material
18.104.22.168 Losses from a stratified medium
22.214.171.124 Mulitple losses
3.2.2 The dielectric function of TiO2 from far-infrared to ultraviolet
126.96.36.199 Interband transitions
188.8.131.52 The static dielectric function: electron-phonon coupling and polaronic distorsion
184.108.40.206 Defects induced band gap states and optical absorption
220.127.116.11 Excitation due to itinerant motion of carriers: the Drude model
3.2.3 Numerical implementation: the HREELS program
3.2.4 The interplay and screening between reduced TiO2 excitations
18.104.22.168 Effect of dielectric anisotropy
22.214.171.124 Quasi-elastic peak broadening due to carriers
126.96.36.199 Screening of phonons by carrier excitations
188.8.131.52 Screening of phonons by band gap states
3.2.5 Surface versus bulk excitations: the question of depth sensitivity
184.108.40.206 Probing depth in EELS ?
220.127.116.11 A few examples of effects of dielectric function profile
3.3 Resolution enhancement in EELS based on iterative semi-blind Lucy-Richardson algorithm
4 Surface versus bulk contribution to the band gap states in TiO2
4.2 Exposure to oxygen of reduced rutile samples
4.3 Surface annealing
4.3.1 When the hot filament only allows surface annealing
4.3.2 Surface temperature measurements
4.3.3 BGS due to Ti interstitial diffusion for a surface temperature of 420 K
4.3.4 BGS due to a combination of Ti interstitials and oxygen vacancies at various surface temperatures
4.3.5 Toward a defect-free TiO2(110) surface
4.4 How water adsorption can heal BGS associated with surface vacancies ?
4.5 Creation of oxygen vacancies by electron bombardment
4.5.1 Creation of only oxygen vacancies
4.5.2 The limited efficiency of electron bombardment
4.6 Out-of-specular EELS spectra and the profile of excess electrons
4.6.1 BGS recorded from different probing depths
4.6.2 Qualitative description of the profile of excess charges
5 Excess electrons in reducible TiO2 rutile: dual behaviour or coexistence of trapped and free states ?
5.1 Position of the question
5.2 (HR)EELS from reduced TiO2(110) surface
5.2.1 On the existence of carrier excitations
18.104.22.168 Effect of oxygen exposure
22.214.171.124 Quasi-elastic peak: shape and temperature dependence
126.96.36.199 Phonon line shape
5.2.2 The profile of dielectric function for fits
5.3 Bulk and surface excess electrons: dual behavior or coexistence of trapped and free states ?
5.3.1 Bulk excess electrons
5.3.2 Surface excess electrons
7 Annex: Published paper in Rev. Sci. Inst. 86 (2015) 013906