Self-doped TiO2 Research Articles

Blue Ti3+ self-doped TiO2 nanosheets with rich {001} facets for photocatalytic performance

The as-prepared BT1.5TNs exhibits superior photocatalytic performance for RhB degradation due to Ti3+ doping.

Facile preparation of Ti3+ self-doped TiO2 nanoparticles and their dramatic visible photocatalytic activity for the fast treatment of highly concentrated Cr(vi) effluent

An efficient visible photocatalyst which is suitable for the rapid removal of highly concentrated Cr(vi) for environmental therapy.

A novel 3DOM Ti3+ self-doped TiO2 for photocatalytic removal of NO

A novel three dimensionally ordered macroporous (3DOM) Ti3+ self-doped TiO2 with an ordered distribution of macropores in the diameter of 270 nm is synthesized by a facile colloidal polystyrene template sol-gel and ice-water quenching method. The performance of photocatalytic removal of NO from continuous air flow with visible light irradiation show 3DOM Ti3+ self-doped TiO2 has enhanced efficiency under visible light irradiation. The improved photocatalytic efficiency could contribute to the presence of Ti3+ doping induced by ice-water quenching and the 3DOM structure with a large specific surface area.

Assembly of surface-defect single-crystalline strontium titanate nanocubes acting as molecular bricks onto surface-defect single-crystalline titanium dioxide (B) nanorods for efficient visible-light-driven photocatalytic performance

Ti3+ self-doped single-crystalline SrTiO3−x nanocubes acting as molecular bricks are successfully assembled onto Ti3+ self-doping single-crystalline TiO2−x(B) nanorods through an effortless two-step hydrothermal process coupled with an in situ solid-state chemical reduction method. SrTiO3−x nanocubes act as molecular bricks, which are uniformly assembled onto the surface of TiO2−x(B) nanorods due to lattice matching. The band gap of the resultant SrTiO3−x/TiO2−x(B) sample is ∼2.97 eV, which exhibits excellent photocatalytic performance for the reduction of Cr(VI) and hydrogen production under visible light. The apparent rate constant k value for the photocatalytic reaction of SrTiO3−x/TiO2−x(B) for Cr(VI) reduction is ∼8 times higher than that of white TiO2(B). The photocatalytic hydrogen production rate for SrTiO3−x/TiO2−x(B) is ∼160.2 μmol g−1 h−1, which is ∼5 times higher than that of white TiO2(B). The enhanced photocatalytic activity can be considered to be caused by a synergetic effect of heterojunction formation and the introduction of Ti3+ self-doping, which can not only facilitate the separation of photogenerated charge carriers between TiO2−x(B) and SrTiO3−x, but also broaden the photoresponse from the UV to visible-light region.

Enhanced visible-light activation of persulfate by Ti3+ self-doped TiO2/graphene nanocomposite for the rapid and efficient degradation of micropollutants in water.

In this study, a novel TiO2-x/rGO-PS-Vis process was developed, which utilizes the TiO2-x/rGO (Ti3+ and oxygen vacancies self-doped TiO2 coupled with reduced graphene oxide) nanocomposite as a promising and efficient activator of persulfate (PS) for the enhanced oxidation of micropollutants under visible -light irradiation. TiO2-x/rGO exhibited a significantly high activity for PS activation to produce more sulfate radicals (SO4-) and hydroxyl radicals (OH). Therefore, almost 100% BPA (10 mg/L) and 80% TOC can be removed just within 12 min with 1.0 g/L TiO2-x/rGO and 2 mM PS under visible light. Moreover, it was found that many other typical micropollutants, such as phenol, acetaminophen and sulfamethoxazole can also be effectively degraded by this process. Electron paramagnetic resonance (EPR) and radical quenching experiments indicated that both SO4- and OH contribute to the degradation of organics, and the radical process was the main degradation pathway. In addition, the effects of PS concentration, catalyst dosage, initial solution pH and inorganic anions were investigated systematically. Experiments carried out in the real background of water matrix with low-concentration of BPA indicated that the proposed TiO2-x/rGO-PS-Vis process has strong non-selective photo-oxidative ability for the removal of micropollutants in water.

Ti3+ self-doping in bulk of rutile TiO2 for enhanced photocatalysis

A facile method, by sintering commercially available TiO2 in inert gas at high temperature, was used to obtain Ti3+ self-doping blue rutile TiO2 ceramic powder. Our results indicate that Ti3+ ions exist in bulk of TiO2 and the reduced TiO2 exhibits enhanced visible-light absorption. The reduced TiO2 possesses superior photocatalytic ability in photodegradation of methylene blue under Xe light illumination. Moreover, the reduced TiO2 exhibits good stability even after 12 months. This method provides an economical and universally applicable way to synthesize commercially available TiO2 powder with high and stable photocatalytic performance, which may have the promise for solar applications.

Defective black Ti3+ self-doped TiO2 and reduced graphene oxide composite nanoparticles for boosting visible-light driven photocatalytic and photoelectrochemical activity

We present a facile and environmentally friendly way to successfully build partially reduced titanium dioxide nanoparticles integrated with reduced graphene oxide composite nanosheets (RGO/TiO2−x) through an environmental solvothermal method at relatively low temperature. The Ti3+ self-doping of TiO2−x is conducive to enhance its visible light absorption, and the existence of RGO as the electron receiver makes the electrons on TiO2−x transport better to its surface, effectively promoting the separation of electrons and holes. Experiments on photocatalytic degradation of methylene blue dye and phenol colorless organic pollutant by visible light demonstrate that the RGO/TiO2−x assemblies exhibit the highest photocatalytic activity, and that methylene blue solution concentration of used in the experiment is 40 mg L−1, which was more higher than the concentration (10 mg L−1) used in many of reported articles. Compared to the pure TiO2 and TiO2−x, the photodegradation efficiency of methylene blue and phenol can be increased to 100% within 120 min and 150 min under visible light. Moreover, the mineralization rates of MB, such as the total organic carbon (TOC) degradation rate, can reach to 75.7%, 86.6% and 89.4% for m-RGO/TiO2−x, respectively. And the reaction efficiency of RGO/TiO2−x is basically not much changed after 4th cycles, suggesting its excellent photocatalytic stability.

A novel single-mode microwave assisted synthesis of metal oxide as visible-light photocatalyst

Visible-light photocatalyst titanium dioxide (TiO2) was successfully prepared via a novel and facile single-mode microwave assisted synthesis process. In this one-step synthesis, Ti as target material selectively oxidizes in magnetic field throughout rapid heating, whose process requires less energy consumption and short time. In obtained TiO2, self-doping of Ti3+ was confirmed, which makes TiO2 perform sufficient light absorption in visible region with wavelength above 400 nm. Such Ti3+ self-doped TiO2 exhibits much narrower optical bandgap (2.14 eV) with compared stoichiometric TiO2 (3.0–3.2 eV). The synthesized TiO2 also shows superior photocatalytic activity to commercially available TiO2 towards the degradation of Rhodamine B under visible light irradiation.

Enhanced photocatalytic hydrogen evolution activity of carbon and nitrogen self-doped TiO2 hollow sphere with the creation of oxygen vacancy and Ti3+

Introducing oxygen vacancies and Ti3+ into TiO2 is thought to be an effective method of increasing the utilization of sunlight and promoting the efficiency of electron transfer. In this work, novel carbon and nitrogen self-doped TiO2 hollow spheres (CNTH) with oxygen vacancies and Ti3+ were synthesized by a one-pot hydrothermal strategy in H2OC2H5OHHFH2O2 mixed solution with TiCN as a precursor of anatase TiO2 and self-doping source of N and C. The presence of oxygen vacancies and Ti3+ in the resulting CNTH photocatalyst was supported by electron paramagnetic resonance (EPR) and X-ray absorption near-edge structure spectroscopy (XANES). X-ray photoelectron spectroscopy (XPS) analysis showed that the C and N atoms were successfully self-doped into TiO2 lattice, which resulted in the CNTH materials exhibiting the enhanced absorption in the UV–visible region with a clear red shift at the absorption edges. The electronic structure of CNTH was examined by first-principle density functional theory (DFT) calculations, which further confirmed the optical properties of CNTH for the enhanced visible-light absorption properties and the red-shift phenomenon of the absorption edges. The resulting CNTH photocatalyst showed enhanced visible-light photocatalytic activity for H2 production. The enhanced activity of CNTH was due to the introduction of C and N self-doping and the existence of oxygen vacancies and Ti3+. The former can promote the photocatalytic reactions of the photogeneration electrons and holes on CNTH under visible-light irradiation, while the latter create more active sites and prolong the life time of electrons and holes by their donor states.

Surface characteristics of a dental implant modified by low energy oxygen ion implantation

The good biocompatibility of Titanium-based medical device is related to the thin oxide layer (titanium dioxide, TiO2) formed on the surface. In this study, Plasma Immersion Ion Implantation (PIII) method and Optical Emission Spectrometer (OES) were used to produce oxidized surface in order to study the influence of plasma composition on surface composition. The result of OES showed that higher electron temperature, more metastable argon atom and oxygen ion content facilitate the formation of TiO2 top surface. The treated implant surfaces possessed higher content Ti2O3, lower contact angle. When the atomic percentage of Ti2O3 is similar to the TiO2, the contact angle is close to zero, which could attribute to the photocatalytic activity of self-doped TiO2−x. It generates more hydroxyl groups under visible light, causing a decrease in contact angle. But release of titanium ions was found in some solutions. It is believed that the TiO2−x produced by low energy oxygen ion implant has super hydrophilic properties, which indicates the potential for improved implant osseointegration in vivo.

Protonated g-C3N4/Ti3+ self-doped TiO2 nanocomposite films: Room-temperature preparation, hydrophilicity, and application for photocatalytic NOx removal

Fabrication of photocatalysis films with good adhesion, hydrophilicity, and high activity on substrates at room temperature is essential for their application in air pollution control. Herein, functionalized transparent composite films containing ultrathin protonated g-C3N4 (pCN) nanosheets and Ti3+ self-doped TiO2 nanoparticles (pCN/TiO2) were fabricated on glass at room temperature. Thickness of the films measures 80 nm with surface roughness of 7.16 nm. The adhesion ability was attributed to the viscosity of TiO2 sol, which served as “chemical glue” in the films. The high photo-induced hydrophilicity demonstrated their self-cleaning potential. pCN/TiO2 films showed remarkably high visible-light-driven activity in terms of NO removal in a continuous-flow mode. Photoelectrochemical tests demonstrated the superior charge separation efficiency of pCN/TiO2 films compared with that of pristine TiO2. As identified by electron spin resonance spectra, O2− and OH radicals were the key reactive species involved in NO removal. The possible mechanism for photocatalytic NO oxidation was proposed. Potential cytotoxicity of pCN/TiO2 films was evaluated by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide assay to ensure the biosecurity. This work provides a facile route to fabricate nanocomposite films under ambient temperature. The nanocomposite films were characterized by photo-induced hydrophilicity, high NO removal efficiency, and good biocompatibility, showing its potential in large-scale application.

Electrochemical Peroxodisulfate (PDS) Generation on a Self-Doped TiO2 Nanotube Array Electrode

Peroxodisulfate (PDS, S2O82–) is one of the strong oxidants (E°[S2O82–/HSO4–] = 2.12 VNHE), which is widely used for radical polymerization or wastewater treatment. In electrochemical PDS generation, its efficiency highly depends on the •OH generating electrode materials. A boron-doped diamond (BDD) used in electrochemical PDS generation is very expensive prompting the need for new electrode materials for PDS generation. This study reports the self-doped TiO2 nanotube array electrodes (blue and black TNAs) for PDS generation which are cheap and effective for generating a significant amount of •OH and comparable to BDD electrodes. Blue and black TNA electrodes were excellent for PDS generation exhibiting high current efficiencies for PDS generation (46% and 22%, respectively). Similar to the BDD electrode, it was also confirmed that •OH was the key precursor to the PDS generation on the self-doped TNA electrodes from the linear relationship between the PDS generation rate and •OH generation.

One-pot topotactic synthesis of Ti3+ self-doped 3D TiO2 hollow nanoboxes with enhanced visible light response

Ti3+ self-doped anatase three-dimensional (3D) TiO2 hollow nanoboxes were synthesized via a topological transformation process involving template participation by a facile one-pot hydrothermal treatment with an ethanol solution of zinc powder and TiOF2. It is worth noting that the 3D TiO2 hollow nanoboxes are assembled from six single-crystal nanosheets and have dominant exposure of the {001} facets. It is found from EPR spectra that adding zinc powder is an environment-friendly and effective strategy to introduce Ti3+ and oxygen vacancy (Ov) into the bulk of 3D hollow nanoboxes rather than the surface, which is responsible for their enhanced visible photocatalytic properties. The photocatalytic activity was evaluated by measuring the formation rate of hydroxide free radicals using 7-hydroxycoumarin as a probe. The sample prepared with zinc/TiOF2 mass ratio of 0.25 exhibited the highest RhB photodegradation activity under visible-light irradiation with a degradation rate of 96%, which is 4.0-times higher than that of pure TiO2. The results suggest a novel approach to construct in-situ 3D hierarchical TiO2 hollow nanoboxes doped with Ti3+ and Ov without introducing any impurity elements for superior visible-light photocatalytic activity.

Photocatalytic activity and mechanism of bisphenol a removal over TiO2−x/rGO nanocomposite driven by visible light

In the present study, Ti3+ and oxygen vacancies (Ti3+/Ov) self-doped TiO2 and coupled with a reduced graphene oxide (rGO) nanocomposite (TiO2−x/rGO) was successfully synthesized via a facile hydrothermal-calcination method for the efficient degradation of bisphenol A (BPA) under visible light. The results of XPS, ERP and TEM analyses revealed that the presence of Ti3+/Ov in the lattice of TiO2−x/rGO leads to the narrowed band gap and enhanced visible light harvesting. The chemical bonds (TiOC) between TiO2−x and rGO act as the channel for electron transfer, consequently resulting in the efficient charge separation, which was investigated and confirmed by such methods as PL spectra and time-resolved PL spectra. In addition, the coupling of TiO2−x and rGO could strongly suppress the aggregation of TiO2−x particles and therefore improve the adsorption of organic pollutants. For the synergistic effect of the three preeminent features mentioned above, TiO2−x/rGO exhibited a 6.16-, 2.92- and 2.55-fold faster reaction rate for BPA degradation than that of pristine TiO2, TiO2/rGO and TiO2−x, respectively. Moreover, the effects of the initial substrate concentration, initial solution pH, catalyst dosage and inorganic anions on BPA removal were also investigated in depth. EPR measurements indicated that ·O2− as the major oxidizing species, is responsible for the degradation of BPA. Next, the feasible pathway of BPA degradation by TiO2−x/rGO was proposed based on the analysis of intermediate products. Finally, the mechanism of the enhanced photocatalytic performance by TiO2−x/rGO under visible light was discussed. Based on these results, the TiO2−x/rGO nanocomposite could be an efficient and promising photocatalyst for the degradation of organic pollutants in water.

Self-doped TiO2 nanowires in TiO2-B single phase, TiO2-B/anatase and TiO2-anatase/rutile heterojunctions demonstrating individual superiority in photocatalytic activity under visible and UV light

TiO2 nanowires possess structurally well-defined physical and chemical properties related to their dimensional confinements. However, the obscure phase transformation mechanism and the wide optical band gap of TiO2 nanowires limit their wide applications as a photocatalytic material, particularly under the visible solar spectrum. The present investigation deals with the systematic synthesis of TiO2 nanowires with their different phases e.g., TiO2-B, anatase and rutile, by the hydrothermal technique and subsequent thermal annealing in vacuum at different temperatures, and probing on their characteristic photocatalytic performances. Pure single phase TiO2-B nanowires of high crystallinity have been obtained at TA = 600 °C in which the oxygen vacancies generated via reduction of Ti4+ centers to Ti3+ facilitate enhancing absorption of visible light by virtue of their reduced optical band gaps. In addition, large surface area out of their porous structures provides enhanced adsorptive and reactive sites and accelerates the photocatalytic activity in the visible region, extending a photodegradation efficiency of RhB to ∼88% with a rate constant ∼0.013 min−1. Purely rutile phase of TiO2 formed at TA = 900 °C, exhibiting an intermediate band gap, demonstrates moderate degradation efficiency, ∼55% under visible light and ∼45% under UV exposure on RhB. However, the TiO2-B/anatase heterostructured nanowires grown by partial phase transformation at TA = 700 °C, exhibit a significantly enhanced UV photocatalytic ability by virtue of their wide optical band gaps. Migration of photogenerated holes from the anatase to the TiO2-B facilitated by the differences in two distinct phases reduces the charge recombination and enhances the photocatalytic activity with a high degradation efficiency ∼96% and a rate constant ∼0.058 min−1 under the UV light exposure. The self-transformed TiO2 heterostructured nanowires grown on thermal annealing are significantly promising for advanced photocatalytic applications, by virtue of controllable optical band gap, high porosity and self-doping characteristics.

Reagentless Detection of Low-Molecular-Weight Triamterene Using Self-Doped TiO2 Nanotubes.

TiO2 nanotube electrodes were self-doped by electrochemical cathodic polarization, potentially converting Ti4+ into Ti3+, and thereby increasing both the normalized conductance and capacitance of the electrodes. One-hundred (from 19.2 ± 0.1 μF cm-2 to 1.9 ± 0.1 mF cm-2 for SD-TNT) and two-fold (from ∼6.2 to ∼14.4 mS cm-2) concomitant increases in capacitance and conductance, respectively, were achieved in self-doped TiO2 nanotubes; this was compared with the results for their undoped counterparts. The increases in the capacitance and conductance indicate that the Ti3+ states enhance the density of the electronic states; this is attributed to an existing relationship between the conductance and capacitance for nanoscale structures built on macroscopic electrodes. The ratio between the conductance and capacitance was used to detect and quantify, in a reagentless manner, the triamterene (TRT) diuretic by designing an appropriate doping level of TiO2 nanotubes. The sensitivity was improved when using immittance spectroscopy (Patil et al. Anal. Chem. 2015, 87, 944-950; Bedatty Fernandes et al. Anal. Chem. 2015, 87, 12137-12144) (2.4 × 106 % decade-1) compared to cyclic voltammetry (5.8 × 105 % decade-1). Furthermore, a higher linear range from 0.5 to 100 μmol L-1 (5.0 to 100 μmol L-1 for cyclic voltammetry measurements) and a lower limit-of-detection of approximately 0.2 μmol L-1 were achieved by using immittance function methodology (better than the 4.1 μmol L-1 obtained by using cyclic voltammetry).

Fabrication of IrO2 decorated vertical aligned self-doped TiO2 nanotube arrays for oxygen evolution in water electrolysis

To fabricate effective and stable OER electrode in water electrolysis, self-doped TiO2 nanotube arrays which has a higher electrical conductivity than pristine TiO2 nanotube arrays was used as the support for loading IrO2. The self-doped TNTA was fabricated by a simple electrochemical reduction of TNTA in neutral electrolyte solution, and then IrO2 nano particles were deposited by pulse electro-deposition method. The cyclic voltammetric behavior, electrical conductivity and micro structure of self-doped TNTA prepared at different reduction potential were characterized to obtain an optimal performance, and self-doped TNTA prepared under −1.9 V (vs. Ag/AgCl) shows the best electrochemical performance. After depositing IrO2, the OER activity and stability of new electrodes were also determined. Due to the enhanced electrical conductivity of support, the mass activity of IrO2/self-doped TNTA are 50 times higher than IrO2/TNTA. The OER stability of new electrode was evaluated under constant current of 5 mA/cm2, IrO2/TNTA and IrO2/Ti were also tested for comparison. A higher stability of IrO2/self-doped TNTA electrode is observed than the other two electrodes, and XPS studies indicate a lower oxidation state of Ir in IrO2/self-doped TNTA, this shows a possible interactions between IrO2 and the new support.

IrO2 Decorated Self-Doped TiO2 Nanotube Arrays: A Binder-Free and More Stable Electrode for Oxygen Evolution Reaction in Acid Condition

The effective, stable and low cost anodic catalyst or electrode for OER is still a big challenge for water electrolysis in acid condition. Many efforts were devoted to develop suitable supports for depositing Ir and Ru metal or oxides to obtain an enhanced activity or stability for OER. In this work, self-doped TiO2 nanotube arrays (sTNTA) which has a higher electrical conductivity than TNTA was chosen as the support, it was fabricated by a simple electrochemical reduction of TNTA in neutral electrolyte. Then IrO2 nano particles were deposited on it by electrochemical pulse deposition method to form an OER electrode. The cyclic voltammetric behavior, electrical conductivity and micro structure of sTNTA prepared under different reduction potential were characterized to obtain an optimal performance for depositing IrO2, the OER activity and stability of new electrode were also determined. The obtained sTNTA shows an increased current in CV test than TNTA, which is due to the increased carrier density. As the reduction potential move to more negative level (from -1.5V to -1.9V vs. Ag/AgCl), the carrier density was found increased for 3 order of magnitudes, and XPS characterization confirm the existence of Ti3+ which formed in electrochemical reduction process, and sTNTA prepared under -1.9V shows the best electrochemical performance. After depositing IrO2, IrO2/sTNTA exhibited higher OER activity than IrO2/TNTA, according to the CV and EIS test, this can be ascribed to the enhanced electrical conductivity of support, which results in more active sites and lower charge transfer resistance of the electrode. The OER stability of IrO2/sTNTA was tested under constant current of 5mA/cm2, IrO2/TNTA and IrO2/Ti which prepared by electrochemical deposition on Ti foil were also tested for comparison. A higher stability of IrO2/sTNTA electrode was observed than the other two electrodes, and this may be due to the interaction between the IrO2 and sTNTA. XPS studies show a clear peak shift of Ir4f in IrO2/sTNTA, indicating a possible lower valence of Iridium, and such lower oxidation state of Iridium may be response for the enhanced OER stability. In summary, our studies have demonstrated the possibility of self-doped TNTA as a potential anodic support for OER. Comparing with the TNTA, the high electrical conductivity of sTNTA facilitate the charge transfer rate and thus improve the OER activity. Additionally, a higher OER stability was observed for IrO2/sTNTA electrode, and this may be due to possible catalyst-support interactions between IrO2 and self-doped TNTA. Figure 1

Visible light driven photocatalytic decomposition of penicillin G by Ti 3+ self-doped TiO 2 nano-catalyst through response surface methodology

Abstract In present study, Ti3+ self-doped TiO2 (r-TiO2) nano-catalyst was successfully fabricated by one-step solution reduction treatment in the presence of potassium borohydride. The self-doping process can induce the generation of Ti3+ and oxygen vacancy (Ov) to form a new energy level in the forbidden band of TiO2. Moreover, physicochemical properties of the resulting samples were studied by series of techniques. Results suggest that r-TiO2 nano-catalyst exhibits remarkable enhancement of visible light harvesting and higher charge separation efficiency. In order to investigate the influence factors on degradation of penicillin G (PENG), the experimental design was made using central composite method (CCD) of response surface methodology (RSM). For this purpose, the r-TiO2 dosage, PENG concentration and initial pH value were selected as critical parameters. Results indicate the r-TiO2 dosage and initial pH possess higher influences. Besides, the highest photocatalytic efficiency of PENG (98.3%) can be obtained under the optimal conditions of r-TiO2 dosage 50 mg, PENG concentration 100 mg/L and initial pH 5.5, respectively.

Bi plasmon-enhanced mesoporous Bi2MoO6/Ti3+ self-doped TiO2 microsphere heterojunctions as efficient visible-light-driven photocatalysts

Bi plasmon-enhanced mesoporous Bi2MoO6/Ti3+ self-doped TiO2 microsphere heterojunctions (Bi-BMO/TiO2-x) have been synthesized by a mild hydrothermal method combined with an in situ solid-state chemical reduction process, and subsequently annealed at 400 °C in N2 atmosphere. The prepared Bi-BMO/TiO2-x photocatalysts are characterized by X-ray diffraction, N2 adsorption, scanning electron microscopy, transmission electron microscopy, and X-ray photoelectron spectroscopy. The results reveal that Ti3+ self-doped TiO2 is loaded on surface of mesoporous Bi2MoO6 microsphere efficiently and metallic Bi is produced for surface plasmon resonance (SPR). Under visible-light irradiation, the heterojunctions photocatalyst shows excellent photodegradation and photoelectrochemical properties of ∼95% for phenol removal rate and 20 μA/cm2 for photocurrent density, respectively, which is several times higher than that of single component. Moreover, it also has high photocatalytic oxygen production with a rate of 134 μmol h-1 g-1. The enhanced photocatalytic activities are mainly attributed to the existence of Ti3+ self-doping and heterojunction structure, which narrow the band gap to extend photoresponse to visible light region. Another reason is the influence of SPR of metallic Bi. They all promote the spatial separation and transfer of photogenerated charge carriers.