Properties of TiO2 Films: History
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Mariuca Gartner
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Anna Szekeres
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Hermine Stroescu
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Daiana Mitrea
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Maria Covei

For many years, TiO2-based materials and improving their properties in order to expand their application areas have been the focus of numerous research groups. Various innovative approaches have been proposed to improve the photocatalytic and gas-sensing properties of TiO2 nanostructures.

  • titanium dioxide
  • structure and properties
  • photocatalytic applications
  • gas sensors and biosensors

1. Introduction

TiO2 has unique properties that make it very useful in many industrial branches as a material in electrochromic, photovoltaic, and microelectronic devices, gas sensors, photocatalysts, coatings, implants, etc. The effective use of TiO2 for these applications largely depends on its structure (polymorph form, shape, and arrangement of nanocrystallites) and defects (intrinsic defects and extrinsic impurities), which in turn strongly depend on the preparation technologies. Our attention is focused on how dopants (metal or non-metal atoms) affect the properties of TiO2 films.

2. Structural Properties

Among the various crystal phases of titania, the anatase (tetragonal), rutile (tetragonal), and brookite (orthorhombic) phases are of greater importance for different applications. Depending on thermal treatment methods, the phase transition of TiO2 occurs in the order of amorphous to anatase (375 °C), brookite (510 °C), and rutile (650 °C). In the tetragonal crystal structure of anatase (a = b = 0.378 nm, c = 0.95 nm, space group I41/amd) and rutile (a = b = 0.4593 nm, c = 0.2959 nm, space group P42/mnm), the titanium atom is surrounded by six oxygen atoms, and each oxygen atom is surrounded by three titanium atoms [1][2]. Each octahedron shares corners, leading to the formation of (001) planes. Each crystalline phase offers distinctive characteristics that make it suitable for different applications: rutile is preferred for its thermal stability and optical properties, anatase for photocatalytic and surface-area-related applications, while brookite has more limited use due to its relative scarcity and lower stability. From the point of view of gas sensor applications, the rutile and anatase TiO2 crystal forms are of interest and are most intensively investigated. Generated by light illumination of electron–hole pairs in anatase, TiO2 can initiate various photocatalytic reactions, such as the degradation of organic pollutants.
With the increasing demand for nanostructured materials, extensive research has been conducted to develop technologies to obtain nanocrystalline TiO2 structures that would meet the requirements of given applications. It was found that a reduction in particle size improves various TiO2 properties, revealing the superior performance of nanocrystallites. 
By controlling the synthesis parameters, especially pH, temperature, and thermal annealing, various morphologies with improved properties can be achieved. Accordingly, different nanostructures were prepared using synthesis methods [3][4][5][6][7][8][9][10][11] such as the following: classical (for nanorods, nanosheets, nanoflakes, and nanoflowers) or ultrasonic-assisted hydrothermal method (for quantum dots), electrospinning (for nanofibers), dip coating and hydrothermal routes (for nanowires), anodization (for nanotubes), and template-assisted methods (for nanospheres). Using the aforementioned hierarchical structures, an improvement to the different parameters was observed, e.g., an increase in the active surface area, a better charge carrier separation with a smaller recombination rate, etc.
The incorporation of dopants into the TiO2 lattice has a strong impact on the structural properties of TiO2, such as promoting phase transitions and/or changing lattice parameters and generating defects that are activated by external influences (electric field, radiation, etc.).
The growth of specific crystal phases, such as anatase, rutile, or brookite, can be stimulated by certain dopants and, in turn, has a significant effect on the material’s properties. Kondamaredd et al. [12] investigated the effect of doping using tungsten ions (W6+) on a nano-crystalline structure of pristine anatase TiO2 by varying the ion concentration (10, 50, 90, and 120 ppm) using the sol–gel and hydrothermal methods. X-ray diffraction (XRD) analysis pointed out the phase transition from anatase to rutile, which was more pronounced when the concentration of W increased up to 50 ppm. Additionally, certain dopants can alter the phase transition process and thermal stability. For example, certain dopants can slow down phase transitions between anatase and rutile phases, leading to materials with improved phase stability at higher temperatures. Zhu et al. [13] studied the process of phase transition from the anatase form to the rutile form in TiO2 doped with 5 and 7.5% Si by in situ high-temperature XRD. They observed an increase in the phase transition temperature and activation energy while increasing the dopant percentage. This result showed that by introducing Si into the TiO2 lattice, the phase transition of TiO2 from anatase to rutile is inhibited, while the crystal-growth process is controlled by the crystal interface growth. In a recent study, Zhang et al. [14] showed that doping TiO2 with Fe atoms leads to an increase in the temperature of the phase transition from anatase to rutile, while a reduction in Fe3+ to Fe2+ generates oxygen vacancies upon Fe doping, accelerating the phase transition process.
In general, the dopants have different atomic sizes compared to the host atoms, leading to lattice expansion or contraction. Lattice distortion can affect the mechanical properties of the deposited films as well as their electronic structure. For instance, Kayani et al. [15] synthesized V-doped TiO2 thin films with different percentages of V doping (1, 3, 5, 7, and 9 at. wt. %) using the sol–gel technique (the dip-coating method). The incorporation of V ions created defects and distortion in the TiO2 lattice. The increase in the dopant percentage led to a reduction in the degree of crystallinity and crystallite size, and consequently, a decrease in the specific surface area. These modifications are related to the ionic radius of V5+ (0.059 nm) being lower than that of Ti4+ (0.062 nm). An introduction of dopants in the oxide network induces lattice defects such as vacancies, interstitials, and impurities. Although these defects do not cause structural changes, they will create localized energy levels in the oxide band gap, affecting electronic and optical properties, as will be discussed later. For example, Park et al. [16] studied nitrogen-doped TiO2 heterostructures prepared by graft polymerization. The FT-IR spectra showed several absorption bands related to the vibration of N-H, CO, and CN bonds upon polymerization of the grafted poly(methacrylamide) (PMAAm) on TiO2 nanoparticles. With the appropriate thermal treatment, the PMAAm molecules/particles were completely removed, and a uniform N-doped TiO2 with a significantly narrowed band gap was formed. The newly formed N 2p band above the O 2p valence band induced a significant narrowing of the TiO2 band and caused a red shift of the absorption edge in the visible region. Compared to pure TiO2, these N-doped TiO2 heterostructures exhibited improved photocatalytic performance when exposed to visible light, which was attributed to a modification in the electronic band structure of TiO2.
As shown above, the influence of dopants on their structural properties depends on their size, charge, concentration, interaction with the host lattice, etc. By selecting and controlling the type and concentration of dopants, new structural characteristics are developed that can be used for specific applications, ranging from catalysis, sensors, electronics, and energy conversion to medicine and healthcare.

3. Morphological Properties

Nowadays, most of the TiO2 films that have found practical applications have a nanocrystalline structure. Therefore, it is extremely important to understand how (intrinsic and extrinsic) defects affect the morphological properties in order to design TiO2 materials with the desired characteristics for specific applications. The doping of TiO2 films again has a decisive influence on many processes, such as dopant incorporation, crystal growth kinetics, and surface interactions.
The nucleation and growth kinetics of TiO2 nanocrystallites can be altered using dopants. Depending on the type and concentration of dopants, as well as the technology used to deposit doped TiO2, the grown particles will have different sizes and shapes, as the dopants can promote the formation of specific crystal facets, leading to modified particle shapes. For example, in Elmehasseb et al. [17], the effect of doping with N, S, and Zn of sol–gel TiO2 films is expressed by a decrease in the particle sizes, which become smaller (42–70 nm) and less agglomerated compared to those (61–89 nm) observed for pure TiO2. The opposite effect was observed in phosphorus-doped TiO2 films prepared by APCVD at 473 K [18]. The incorporation of P in the film structure caused a drastic change in the structural morphology and increased the electrical conductivity. Scanning electron microscopy (SEM) images visualized the enlarging nanoparticle sizes in the anatase TiO2 structure while increasing the P5+ species in the films. This study showed that it is possible to obtain novel multifunctional materials with an optimal balance between self-cleaning and TCO properties as photocatalytic transparent conductors.
Recently, Asrafuzzaman et al. [19] employed an interesting biogenic method to obtain pure and doped TiO2 nanoparticles from mango leaves. They introduced Cu and Ag transition metals as dopants in concentrations ranging from 0.5% to 2%. A morphological analysis revealed that undoped TiO2 particles had a spherical shape, while both Ag-doped and Cu-doped samples exhibited particle agglomeration. Although the photocatalytic efficiency of doped TiO2 was found to be higher than that of undoped TiO2, minimizing the agglomeration of TiO2 nanoparticles is crucial to further improving the photocatalytic performance.
In some cases, dopants can also influence the growth dynamics of TiO2 crystals. For example, Avilés-García et al. [20] studied co-doping with Mo and W of TiO2 through the evaporation-induced self-assembly (EISA) method. The obtained co-doped TiO2 had smaller crystallite sizes and higher crystallinity than TiO2 with only one dopant.
Dopants can also promote the formation of nanostructures in TiO2 materials, such as nanowires, nanotubes, and nanosheets. These nanostructures have unique morphological properties that are useful for specific applications such as nanoelectronics and energy storage. Several related studies have been reported considering the changes in the morphology of TiO2 structures caused by various factors, such as the technological conditions of different film preparation methods, the type and concentration of the dopants, etc. [18][19][20][21][22][23][24][25].
It is known that dopants are able to influence the surface roughness of doped films. Recently, Bhandarkar et al. [23] studied the effect of the Mn dopant on the properties in TiO2 films. The AFM image of the undoped samples revealed densification when the small crystallites merged together. Analyzing the AFM images, it was shown that the surface roughness values increase with the Mn concentration. Specifically, the undoped TiO2 thin films exhibit the lowest value at 3.2 nm, which rises to 4.1 nm for the sample doped with 8 at.% Mn, which could be attributed to the merging of smaller crystallites.

4. Optical Properties

Optical properties depend on how light propagates in the solid and how much of that light is absorbed in the material. This process depends on the dielectric permittivity of the material, which in turn is determined by the structure of the energy bandgap and the free electrons of TiO2. All the TiO2 polymorphs have high relative permittivity (εox > 30) and refractive index (~1.93 < n < 2.6 at λ = 633 nm), high transparency in the visible spectral range (~80% transmittance), and a wide optical bandgap (Eg > 3 eV). In general, metal oxides with an energy band gap larger than 3 eV have no absorption in the visible range of light. Therefore, TiO2 is a promising candidate among dielectrics as a high refractive index material and transparent coating in multilayer optical systems. However, to exploit the full capacity of Titania in other areas of applications, TiO2 films must be doped with appropriate metal or non-metal atoms. Dopants affect the optical properties of TiO2 by introducing energy levels within the bandgap, which allows visible light to be absorbed and thus changes the oxide’s transparency.
The band gap energy of high-quality pure TiO2 is significantly large and depends on its crystalline phase. Amorphous TiO2 has the widest bandgap, while in crystalline form, the anatase phase has the largest band gap compared with the phases of rutile and brookite, accordingly, Eg ~ 3 eV (rutile) < Eg (brookite) < Eg ~ 3.2 (anatase)< Eg = 3.5 eV (amorphous) [1][3]. The bandgap energy value of each crystalline phase varies with the preparation method and the presence and concentration of the intrinsic/extrinsic defects. From these, it follows that by controlling the TiO2 band gap energy, the optical properties can be engineered.
Over the last decade, a significant number of publications have appeared where different deposition methods have been applied to develop appropriate TiO2 structures for given applications, most of which investigated the role of dopants in controlling the optical properties of the prepared structures [18][24][26][27][28][29][30][31][32][33].
Recently, Lettieri et al. [34] gave a very comprehensive review of the basic knowledge on the charge carrier processes that determine the optical and photophysical properties of intrinsic TiO2, surveying 315 articles on the related research topic. They discuss in detail the elementary photocatalytic processes in an aqueous solution, including the photogeneration of reactive oxygen species (ROS) and the hydrogen evolution reaction for hydrogen (H2) production. In particular, the authors outline the strategies based on highly reduced TiO2 (referred to as “black TiO2”), as well as facet-engineered nanocrystals and heterojunction photocatalysts, where TiO2 is electronically coupled with a different material acting as a co-catalyst.
Extending the light absorption range of TiO2 into the visible region can be achieved by creating localized energy levels within the bandgap, which facilitates the excitation of electrons from the valence band to the dopant-induced energy levels, increasing the material’s light absorption capacity. In [27], the effect of N doping on the structural, optical, electrical, and magnetic properties of epitaxial anatase TiO2 films prepared by the atomic layer deposition (ALD) method has been studied. N doping lowered the bandgap value of 3.23 eV for the undoped film to 3.07 eV, which was attributed to the generation of titanium vacancies by N dopants in an anatase oxide lattice, enhancing p-type conductivity and amplifying room-temperature ferromagnetism in these films.
It has been observed that the V dopant introduced into the TiO2 structure (Eg = 3.08 eV) lowers the bandgap energy to 2.22 eV for TiO2:V and decreases the recombination rate [28]. These TiO2:V structures could be used in applications targeting the visible region of light, such as the successful photodegradation of the Acid Yellow 36 (AY36) dye from textile wastewater. In [29], the doping effect of nitrogen on TiO2 nanotube arrays (TiO2 NTAs) was observed as a bandgap narrowing from 3.16 eV (undoped TiO2 NTAs) to 2.9 and 2.7 eV for N-doped and self-doped TiO2. On the other hand, co-doping was also performed for the same purpose [30], using Mn2+ and Co2+ dopants (Mn-Co-TiO2) for the photocatalytic degradation of enoxacin (ENX) under solar light irradiation. In this case, the calculated Eg values for TiO2, Mn-TiO2, Co-TiO2, and Mn-Co-TiO2 were 2.81, 2.62, 2.50, and 2.10 eV, respectively, as the lower Eg values are for the doped samples [30].
Another example of how the structure and optical properties of TiO2 can be modified is given in [31], where undoped and doped Al+3, Cu+2, and Zn+2 (8 at.% each) TiO2 NPs prepared by green sol–gel synthesis have been studied. TEM micrographs showed high crystallinity and a narrow size distribution of anatase nanocrystallites (3–8 nm) in the undoped and doped samples. UV–Vis–NIR absorption spectra registered a red shift in the absorption edge for doped TiO2 NPs. It has been established that the incorporation of Al+3, Cu+2, and Zn+2 atoms in the TiO2 NPs lattice leads to lattice distortion and generated F+ defect centers and oxygen vacancies, which create intra-band states in the energy band gap and cause the observed reduction in the band gap values.
The above results revealed the specific influence of dopants on the energy band gap of TiO2, varying the dopant’s energy levels, concentration, and synthesis conditions. By selecting and controlling the desired dopants, the absorption edge can be tuned, and thus, the optical properties of TiO2 films can be tailored for a large range of applications, from photocatalysis and solar cells to sensors, light-emitting devices, etc.

5. Electrical Properties

Pure and stoichiometric TiO2 is an insulator at both room and moderate temperatures with an extremely high specific resistivity in the order of 108 Ωcm. It is a wide bandgap semiconductor, and its bandgap energy depends on TiO2 crystalline phases. In stoichiometric TiO2, the almost complete absence of free carriers results in a full valence band and an empty conduction band.
The common feature of TiO2 films prepared by various technological methods is that the obtained films are no longer stoichiometric, as they have a complex defect structure and an increased number of intrinsic defects. These defects can be oxygen vacancies (VO), titanium interstitials (Tiint), titanium vacancies (VTi), or oxygen interstitials (Oint). The predominant defects are oxygen vacancies (VO) and titanium interstitials (Tiint), and both are n-type defects, creating shallow donor states below the conduction band in the TiO2 energy gap. This explains why pure TiO2 is a native n-type semiconductor.
Depending on whether the film is oxygen- or titanium-deficient, it appears as an amphoteric semiconductor and exhibits an n-p transition as an intrinsic property [35][36][37]. This underlines the fact that the O/Ti ratio and defect disorder play an important role in the electrical properties of TiO2 [36]. The dominant type of defect depends on the synthesis conditions, whether the films are prepared under reducing conditions and low temperatures or under oxidizing conditions and high annealing temperatures. It has been shown that the first technological conditions favor the formation of oxygen vacancies, while the second ones favor titanium interstitials [38]. It has been established that oxygen vacancy formation is more favorable in anatase crystal structures than in rutile ones [39]. Double ionized oxygen vacancies (VO2+) create localized donor states in the TiO2 bandgap, about 0.75–1.18 eV below the conduction band (EC), as detected by various measurement methods [33][40][41][42].
By capturing electrons, titanium vacancies (VTi) are the only negatively charged ions, and thus, they are an acceptor-type of intrinsic defects. Although titanium vacancies are the minority, if their number is high enough, they can induce the switch from n-type to p-type TiO2. Wang et al. [43] demonstrated such a transformation in undoped anatase TiO2 films synthesized using a solvothermal method, where they were able to deposit p-type TiO2 films by introducing a large amount of VTi defects, up to 9.5 mol %. In this way, they obtained stable p-type non-stoichiometric TiO2 layers with significantly improved charge mobility and catalytic performance required for photoelectrochemical water splitting, pollutant removal, etc.
Another structural factor that has a strong influence on the electrophysical properties of TiO2 is the boundaries of crystalline grains. Interfaces form at the grain boundaries (GBs) that are in contact, creating electrostatic potential barriers (otherwise known as Schottky barriers), which in turn hinder the flow of the majority carriers and, due to their attractive potential, provide recombination centers for the minority carriers. The trapped charges at the grain boundaries influence the charge carrier transport properties. This effect is well known in polycrystalline semiconductors [44][45][46]. Yan Wang et al. [21] reviewed fourteen methods for the deposition of nanostructured TiO2. Although the materials obtained by these methods have different crystal phases, they all possess large surface areas and good electron transport properties, which allow more intense separation of photo-generated holes and electrons. To utilize the considered technologies, the processes behind the formation of TiO2 nanostructures by these methods are discussed in detail [21].
In most semiconductors, due to the presence of impurities or additives, the grain boundaries are electrically charged and strongly affect the electrical properties of the given structure. For nanostructured semiconductors, such as TiO2, the different charge transport mechanisms can be explained by grain boundaries, heterojunctions, Schottky barriers, or surfaces [47]. When the influence of deep energy levels and interface electric fields is taken into account, the electron transport mechanisms can be characterized via a simple Schottky double barrier model [47].
Depending on the type and degree of crystallinity, the relative dielectric constant (ε) of TiO2 can vary within a wide range of 23–170 [26][48][49]. The large dielectric constant and high resistivity make this material useful in the field of high-k dielectrics for electronics and could be successfully integrated in Si devices. For example, metal–oxide–semiconductor (MOS) structures formed with TiO2 oxides have good Si/TiO2 interface properties (interface state densities are of the order of 1011 cm−2eV−1, which is comparable to those of Si/SiO2), which confirms that TiO2 is a suitable alternative for CMOS applications as a dielectric [50]. Additionally, high-quality TiO2 films, deposited by the sol–gel spin method on Si substrates, had significantly low gate leakage currents in the formed Si MOS devices [51][52]. The study of the electrical characteristics of Si, InAs, and CNT field-effect transistors (FETs) with SiO2, Al2O3, HfO2, La2O3, and TiO2 as gate dielectrics and a detailed comparison of the short-channel parameters show that TiO2 has the best gate dielectric properties [53].
However, the high resistivity and low conductivity of TiO2 are a real drawback for other applications where photo-induced processes are essential, such as photovoltaic cells or photocatalysis. Extensive studies have been conducted to decrease the resistance and increase the conductivity, respectively, by improving the mobility of charge carriers in TiO2 to meet the requirements of each application. Since in the energy bandgap of pure TiO2, almost all charges are compensated, the appearance of energy levels associated with impurities and defects in the structure may contribute significantly to the carrier conduction. Accordingly, to enhance the conductivity of the films, intensive research has been performed in two main directions: (i) the creation of a strong defect disorder introducing intrinsic defects in the TiO2 matrix, and (ii) introducing impurities by doping TiO2 with different metallic or non-metallic atoms. In both directions, intra-band states in the TiO2 bandgap are created, which play an important role in carrier recombination and transport mechanisms. Besides the crystal structure (polymorphic phases, size, and degree of crystallinity) and deposition methods and their conditions, intra-band states are a major factor determining the electrical properties of TiO2.
(i) In defect chemistry, the fabrication of pure and highly non-stoichiometric TiO2 films using various technologies was proposed to improve the transport properties of pure TiO2. Extensive studies have been conducted to tune the properties of TiO2 by creating oxygen deficiency in the TiO2 lattice [27][35][36][40][41][43][54]. Vasu et al. [27] synthesized pure anatase TiO2 films, p-type and n-type by nature, using the atomic layer deposition (ALD) method, but the resulting p-TiO2/n-TiO2 junction showed weak rectification behavior. In order to improve the rectification effect, they were forced to dope the ALD p-TiO2 layer with nitrogen. The N dopants generated VTi defect states, resulting in increased p-type conductivity and the appearance of strong room-temperature ferromagnetism in these films. This and many other experiments confirm that in order to synthesize stable p-type TiO2, acceptor-type impurities must be introduced into the films [24][27][42][55].
Rothschild et al. [54] presented a comparative study on rutile nanocrystalline TiO2 films annealed either in vacuum (reducing condition) or in dry air (oxidizing condition), monitoring in situ the behavior of the conductivity and I–V characteristics as a function of oxygen pressure and temperature. They found that the film annealed at 350 °C in dry air (at 10 mBar) had much higher resistance values and a larger surface potential barrier than that annealed in a vacuum (~4 × 10−6 mbar). In the measured voltage range of (0.01–5 V), the current-voltage (I–V) characteristics of the reduced film were linear, while for the oxidized film, they were non-linear. Such non-linear behaviors of the I–V dependence are associated with charged grain boundaries (GBs) that control the charge transport mechanism. The authors in [54] suggest that potential barriers induced by oxygen chemisorption form at the surface and grain boundaries inside the film that control the charge transport in oxidized films. Vacuum annealing diminishes these barriers and makes the reduced film quite conductive. The observed effects are reversible and suggest that such nanocrystalline TiO2 films may serve as sensors for oxygen and gas sensing [54].
(ii) The introduction of impurities in the TiO2 matrix changes the structure and properties of the films and especially affects their electrical properties. 
The incorporation of dopant atoms into the TiO2 matrix generates defects that are responsible for the appearance of intra-band energy states (shallow or deep) in the TiO2 bandgap. These levels, which trap electrons or holes, act as recombination centers and strongly influence the charge transport properties of doped TiO2 films. If the dopant states give shallow energetic levels, the quasi-Fermi level moves closer to the Ec or Ev band edges, increasing the n-type or p-type conductivity, respectively. If they are deep levels, the quasi-Fermi level moves away from the Ec or Ev edges, respectively, reducing the current and Increasing the specific resistivity of TiO2. From all this, it follows that the current through the film proceeds by trapping and releasing charge carriers from the intra-band levels.
In [33], a comprehensive review of the possible impurities (nearly 40) of TiO2 doping for dye sensitized solar cell (DSSC) applications was performed. The authors emphasize the importance of finding the proper dopants that create shallow levels located close to the Ec band edge. This will avoid the transformation of these levels in recombination centers or their charge causing a large negative shift in the flatband voltage of the device, which would hinder charge injection.
To control the recombination processes and discover the role of shallow and deep levels in TiO2 films, a detailed characterization of their electrical properties, particularly the charge transport mechanism, is required. Therefore, the charge transport through the films prepared by different methods and doped with different types of impurities has been intensively investigated [24][26][31][38][48].
Due to the complex dependence of the structure and properties of TiO2 films on the preparation methods and the type of dopant impurities, the conduction mechanism in TiO2 films could be quite different and must be investigated separately for each specific device. Nevertheless, from the numerous research observations performed on this object [42][49][54][56][57][58][59], the general behavior of electron transport in TiO2 can be described.
Because of the charge compensation effect in TiO2, the contribution of intrinsic free carriers to the conductance is negligible, even at higher temperatures (more than 300 K). Therefore, the observed charge carrier transport in this material mainly occurs through trapping and the release of charges from the energetic levels created in the TiO2 bandgap by intrinsic and/or extrinsic defects. At temperatures higher than 300 K, electronic transport is generally interpreted in terms of thermally activated conduction [56][58]. By lowering the temperature below 300 K, the current proceeds through the variable range hopping (VRH) carrier transport mechanism proposed by Mott [58] and further developed by Efros–Shklovskii (ES) [59]. The second model assumes that at the Fermi energy level (EF), a soft Coulomb gap forms and carrier transport is possible due to different hopping processes that are activated in different temperature ranges [59]. It has been experimentally confirmed that there can be a Mott-type VRH at higher temperatures and an ES-type VRH conduction at lower temperatures [57][60]. In the presence of deep levels in the TiO2 bandgap, the tunneling of charge carriers occurs from the occupied deep levels to the conduction or valence band of the films (trap-assisted tunneling) or to the nearest unoccupied deep levels (inter-trap tunneling) [42][54][56][60]. Inter-trap tunneling prevails when the inter-trap distance is smaller than the charge carrier path from the occupied deep level to the conduction band (Ec) or valence band (Ev).

This entry is adapted from the peer-reviewed paper 10.3390/molecules28237828

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