Particle Consolidation and Electron Transport in Anatase TiO₂ Nanocrystal Films

Abstract

A sequence of chemical vapor synthesis and thermal annealing in defined gas atmospheres was used to prepare phase-pure anatase TiO₂ nanocrystal powders featuring clean surfaces and a narrow particle size distribution with a median particle diameter of 14.5 ± 0.5 nm. Random networks of these nanocrystals were immobilized from aqueous dispersions onto conducting substrates and are introduced as model systems for electronic conductivity studies. Thermal annealing of the immobilized films at 100 °C < T < 450 °C in air was performed to generate particle-particle contacts upon virtual preservation of the structural properties of the nanoparticle films. The distribution of electrochemically active electronic states as well as the dependence of the electronic conductivity on the Fermi level position in the semiconductor films was studied in aqueous electrolytes in situ using electrochemical methods. An exponential distribution of surface states is observed to remain unchanged upon sintering. However, capacitive peaks corresponding to deep electron traps in the nanoparticle films shift positive on the potential scale evidencing an increase of the trapping energy upon progressive thermal annealing. These peaks are attributed to trap states at particle-particle interfaces in the random nanocrystal network (i.e. at grain boundaries). In the potential region, where the capacitive peaks are detected, we observe an exponential conductivity variation by up to 5 orders of magnitude. The potential range featuring the exponential conductivity variation shifts positive by up to 0.15 V when increasing the sintering temperature from 100 °C to 450 °C. Importantly, all films approach a potential- and sintering-temperature-independent maximum conductivity of ~10^-4Ω^-1cm^-1 at more negative potentials. Based on these results we introduce a qualitative model, which highlights the detrimental impact of electron traps located on particle-particle interfaces on the electronic conductivity in random semiconductor nanoparticle networks.

1. Introduction

Materials based on metal oxide nanocrystal networks are essential for many applications ranging from photovoltaics^1,2 and photocatalysis³ to electrochromic windows⁴ and sensors.⁵ Furthermore, nanocrystal films are investigated as transparent conducting materials.^6,7 In many of these applications electron transport through the nanocrystal network governs the material or device performance and is therefore subject to study and optimization. However, the design and realization of conducting or semiconducting metal oxide nanocrystal films face several processing- and characterization-related difficulties. On the one hand, numerous wet-chemical as well as vapor-phase-based synthesis routes yielding nanocrystals of defined size, shape and composition are available. However, control of particle assembly and particle consolidation upon conservation of the desired primary particles’ properties is challenging.^8–10 For colloidal semiconductor oxide nanocrystals ligand exchange processes followed by thermal annealing steps have to be performed to remove non-conductive organic ligands.^5,7,11

Plasma-synthesized semiconductor oxide nanocrystal films have successfully been used as model systems to systematically study the impact of inter-particle contact area and carrier density on the electronic conductivity.^12,13 However, technologically relevant metal oxide nanocrystal networks are more frequently prepared from particle powders obtained by high-throughput methods in the gas-phase such as flame aerosol syntheses. Typically, these powders are used as a precursor material for particle slurries and yield – following their immobilization and sintering – mesoporous nanoparticle films and electrodes. Particle powders from flame aerosol syntheses are typically characterized by varying and often undefined degrees of aggregation.^14–16 A prominent example in the field of photocatalysis and photoelectrocatalysis³ is commercial Aeroxide TiO₂ P25 powder, which is prepared from TiCl₄ in a hydrogen flame and consists mainly of nanoparticle aggregates.¹⁵ Electron transport in porous films prepared from TiO₂ P25 powder has been studied mainly due to the technological relevance of the material and in spite of its complexity with regard to the crystal structure (P25 consists of a mixture of the rutile and the anatase modification), the particle morphology and the microstructure.^17,18 The studies aimed at elucidating the dependence of electron diffusion in these films on different processing conditions (during e.g. electrophoretic deposition, particle compaction or sintering of the films) and revealed the importance of particle ordering, coordination number between particles and their interconnection by conductive particle contacts.

However, semiconductor oxide particle powders featuring broad property distribution functions complicate the elucidation of the interplay between microscopic and macroscopic film properties and are therefore less suitable for the preparation of model systems for conductivity studies on nanocrystal films. One difficulty results from the huge number of nanoparticles forming the network. As an example, a 5 µm thick mesoporous film consisting of nanoparticles with a diameter of 15 nm contains roughly 10¹⁴ particles per 1 cm² of projected film area and particle / particle interfaces in the same order of magnitude. Characterization methods (e.g. macroscopic conductivity measurements) based on the evaluation of signals, which result from the response of the whole film, integrate over all the particles and interfaces present in the studied system. To establish firm relationships between morphological film properties and macroscopic response, narrow property distributions are therefore desirable but difficult to achieve. A systematic and independent tuning of some of the relevant film properties results even more difficult. The stepwise built-up of particle-particle interfaces during sintering, for instance, often comes along with a change in the surface composition of the oxide and / or a modification of the particle or pore morphology. One way to circumvent the difficulties arising from structural complexity is to address charge transport through single particle-particle interfaces. For nanostructured films this strategy has been successful in some cases.¹⁹

Random semiconductor oxide nanoparticle networks feature not only high geometric but also high energetic disorder, which both determine the mechanism of charge transport in these materials. In semiconductor oxide nanoparticle electrodes electron transport is assumed to occur mainly by diffusion due the fact that the particles are too small to sustain internal electrical fields and due to the screening effect of the surrounding electrolyte used in many applications.²⁰ Electron diffusion in these systems takes place as a consequence of successive trapping and detrapping events involving sites with a distribution of trap energies.²¹ Important insights into the details of charge transport in these systems have been provided in this context by theoretical modelling on different levels of sophistication. Several studies have highlighted that traps at the semiconductor / electrolyte interface govern electron transport in nanoparticle electrodes.^22,23 The origin of these traps, however, as well as the impact of interparticle grain boundaries are still under investigation.^24–31

The objective of this work is to establish random networks of anatase TiO₂ nanocrystals, which have been produced by chemical vapor synthesis, processed in the gas phase and immobilized from aqueous particle suspensions, as model systems for the study of electronic conductivity in semiconductor oxide nanoparticle electrodes. Sintering of the immobilized films at different temperatures has been performed to generate particle-particle contacts upon virtual preservation of the structural properties of the nanoparticle films. Electrochemistry was used to study in situ the distribution of electrochemically active electronic states as well as the dependence of the electronic conductivity on the accumulated electron charge density (i.e. Fermi level) in semiconductor films sintered at different temperatures.

2. Experimental Section

2.1. Chemicals

Titanium(IV) isopropoxide (99.999 %), perchloric acid (70 % w/w in water) and methanol (MeOH, ≥ 99.8 %) were purchased from Sigma Aldrich and used without further purification. Ultrapure water (18 MΩ cm) was obtained by a Milli-Q water purification system (Merck Millipore).

2.2. Electrode preparation

Anatase TiO₂ nanocrystals were prepared by metal organic chemical vapor synthesis (MOCVS) based on the decomposition of titanium (IV) isopropoxide at T = 1073 K in a hot wall reactor system.^32,33 For purification, the obtained powder samples were subjected to thermal treatment under high vacuum conditions (p < 10^-5 mbar). First, the powder sample was heated to T = 873 K using a rate of r ≤ 5 K min^-1. Subsequent oxidation with O₂ at this temperature was applied to remove organic remnants from the precursor material and to guarantee the stoichiometric composition of the oxide. Such post-synthesis treatment eliminates organic remnants as evidenced by IR spectroscopy.³⁴ The resulting particle powder was used as the precursor for slurry preparation. The TiO₂ nanoparticle powder (0.150 g) was ground in ultrapure water (Milipore, 18.2 MΩ cm, 1.30 mL) in the absence of any additives to avoid the adsorption of organic molecules on the high surface area material. The carbon content of dry and water-treated anatase TiO₂ nanocrystal samples resulting from the adsorption of ubiquitous carbon-containing species during sample handling in ambient air and in water was estimated in a previous study to correspond to ~ 0.3 % of a monolayer at the surface of the nanoparticles.³⁵

The non-stabilized slurry was spread by doctor blading onto fluorine doped tin oxide (FTO) coated glass (Pilkington TEC 8, resistance 8 Ω/□) or on interdigitated gold electrodes (IDE, DropSens, G-IDEAU5). The TiO₂ nanoparticle films were heated in air with a rate of 10 °C·min^-1 to the final sintering temperature 100 °C ≤ T ≤ 450 °C, where they were annealed for t _sintering = 1 h.

2.3. Structural characterization

Top view and cross sectional images of TiO₂ films were acquired by scanning electron microscopy (SEM, Zeiss Gemini Ultra 55 microscope). X-ray diffraction (XRD) studies were carried out on a Bruker AXS D8 Advance diffractometer using Cu K_α radiation as source (λ = 154.06 pm). The average crystallite domain size was extracted from a full profile analysis of measured Bragg peaks using the Rietveld method. The latter was necessary due to an overlap of Bragg peaks from the anatase TiO₂ phase and the cassiterite SnO₂ (FTO) phase (Figure S1). The intrinsic peak shape of the Bragg peaks was modelled with the fundamental parameter approach. The crystallite size broadening then was handled by allowing a Lorentzian-type component convolution. For every sintering temperature three independently prepared films were investigated. To study whether a previous sintering at lower temperatures impacts on the average crystallite domain size, we performed consecutive thermal annealing steps on one single electrode at increasing sintering temperatures between 100 °C and 450 °C (ΔT = 50 ° C, t _sintering = 1 h at every sintering temperature). However, the average crystallite domain size following sintering at a defined temperature did not depend on the sintering history at lower temperatures.

The size distribution of individual particles was derived from the analysis of transmission electron microscopy (TEM) images. The images were acquired on a JEOL JEM F200 TEM, which is equipped with a cold field emission source, using a TVIPS F216 2k by 2k CMOS camera. The accelerating voltage was set at 200 kV during the measurement. For related measurements the nanoparticle powder samples were scratched from the glass substrate and cast on a lacey carbon grid.

Nitrogen physisorption experiments were performed to study the impact of the sintering temperature on the specific surface area of TiO₂ nanocrystal ensembles. For this purpose, we investigated nanoparticle powders instead of nanoparticle films in order to provide the sample amount necessary for reliable sorption measurements. To mimic processing conditions during electrode preparation as closely as possible, we spread the aqueous TiO₂ nanoparticle slurry on glass slides and dried the resulting films in air. Following an additional sintering step at 200 °C, 300 °C or 450 °C, the nanoparticle films were removed from the glass slide and transferred to a quartz glass tube for nitrogen sorption measurements. Samples were degassed under vacuum at 200 °C for 1 h and measured on an ASAP 2420 (Micrometrics Instrument) at 77 K. The specific surface area was calculated using the algorithm developed by Brunauer Emmett and Teller (BET).³⁶

2.4. Cyclic voltammetry, chronoamperometry and impedance spectroscopy using TiO₂ films deposited on FTO

All electrochemical measurements were conducted using a computer-controlled Autolab PGSTAT302N potentiostat featuring a response analyzer module (FRA2, Metrohm). Measurements were performed in 1 M MeOH / 0.1 M HClO₄ aqueous solution using the TiO₂ films deposited on FTO as the working electrode, a platinum wire as the counter electrode and a Ag/AgCl (3 M KCl) (BasInc) reference electrode (three electrode configuration).

Cyclic voltammetry and chronoamperometry were performed in nitrogen-purged electrolyte. Cyclic voltammograms (CVs) were measured in a potential range -0.6 V ≤ E _Ag/AgCl ≤ 0.6 V with a scan rate of 0.02 Vs^-1. Electron accumulation and electron extraction were studied by chronoamperometry upon the application of different potential steps. Electron accumulation was investigated by measuring the current upon a stepwise decrease of the applied potential from E _Ag/AgCl = 0.14 V to -0.40 V (potential step E = 0.02 V; waiting time at each potential: 100 s). After polarization at E _Ag/AgCl = -0.40 V for 100 s the potential was stepped back progressively to the starting potential (E _Ag/AgCl = 0.14 V).

Electrochemical impedance spectroscopy (EIS) measurements were performed in oxygen-purged electrolyte. Impedance spectra were acquired with an amplitude of 5 mV and frequencies between 10 kHz and 10 mHz and were fitted using the Zview software (Scribner) by means of an equivalent circuit (Figure S3) described by Bisquert.³⁷

The transport resistance R _t inside the TiO₂ film was extracted by spectra fitting and was used to calculate the film conductivity σ

$$\sigma =\frac{d}{R_t\cdot A\cdot \left(1-P\right)}$$ (Equation 1)

where d, A and P represent the thickness, the geometrical area and the porosity of the films, respectively.³⁷

The electrode porosity P was estimated from the TiO₂ mass (as measured by a Sartorius R160P Analytical Balance) and the apparent film volume V = d · A (where the average film thickness d was determined by scanning electron microscopy from electrode cross sections). An average porosity of 71 ± 5 % was calculated for all TiO₂ films. The TiO₂ film thickness on FTO is very inhomogeneous due to the omission of paste formulation (see above) and accounts for 5 ± 3 µm (Figure S4). The geometrical surface area A of the different electrodes was 2.1 ± 0.1 cm².

2.5. Conductivity of TiO₂ films deposited on interdigitated gold electrodes

Conductivity measurements were also performed using interdigitated gold electrodes (IDEs) immobilized on a glass substrate in a coplanar source-drain configuration. The two gold electrodes are separated from each other by a non-conducting gap with a gap width of t = 5 µm and a gap length of L = 340 cm.

The non-stabilized anatase TiO₂ nanoparticle slurry was spread by doctor blading onto the interdigitated gold electrode and the resulting film was sintered at temperatures 100 °C ≤ T ≤ 300 °C. The resulting TiO₂ film thickness was determined from cross sectional views by SEM and accounts for d = 10 ± 3 µm (Figure S4). The maximum sintering temperature of TiO₂ films deposited on IDEs is limited by the de-wetting of the gold films on the glass substrate at T > 300 °C. After deposition and sintering the TiO₂ film forms two gold supported nanocrystalline electrodes, which are electrically contacted by the TiO₂ layer present in the gap between the two gold contacts.

The two independent gold electrodes were operated as two working electrodes (WE1 and WE2) in a four electrode configuration using a computer-controlled Autolab PGSTAT302N potentiostat featuring a bi-potentiostat module (Metrohm). A platinum wire served as the counter electrode, an Ag/AgCl (3 M KCl) (BasInc) electrode as the reference and nitrogen-purged 1 M MeOH / 0.1 M HClO₄ aqueous solution as the electrolyte.

2.5.1. Determination of the thin film conductivity upon external electrode polarization in the dark

The set-up described above was used to study the transport resistance (R _t) of the TiO₂ film, which bridges the gap between the Au electrodes, as a function of its charging state. Following a previously reported approach by Bisquert et al.,³⁸ we measured the direct current flowing in response to a small bias from WE2 to WE1 at different working electrode potentials (Figure S5). Specifically, the following experimental steps were performed:

1. Simultaneous variation of the working electrodes’ potential (potentiodynamic measurements, v = 0.02 Vs^-1, E ^WE1 = E ^WE2) in the potential range $0.2V\ge E_{Ag/AgCl}^{WE1}=E_{Ag/AgCl}^{WE2}\ge -0.4V$ and acquisition of the CV for WE1. This CV features capacitive currents associated with the chemical capacitance of the nanocrystalline electrode WE1. At potentials E _Ag/AgCl < - 0.4 V high faradaic currents due to electrolyte reduction at uncovered Au surfaces were detected, thus limiting the accessible potential range.

2. Application of a small bias between the two working electrodes (ΔE = E ^WE2 – E ^WE1 = -0.01 V) and simultaneous variation (v = 0.02 Vs^-1) of both electrode potentials. The CV of WE1 was acquired in the potential range $0.2V\ge E_{Ag/AgCl}^{WE1}\ge -0.4V$. This CV features thus in addition to capacitive currents (associated with the chemical capacitance of the nanocrystalline electrode WE1) a contribution due to the current flow from WE2 across the gap to WE1.

3. Calculation of the difference ΔI ^WE1 between the current $I_{\Delta E=0V}^{WE1}$ measured for WE1 in the absence of a bias (i.e. ΔE = 0 V, CV acquired in experimental step a.) and the current $I_{\Delta E=-0.01V}^{WE1}$ measured when applying a bias ΔE = -0.01 V between WE1 and WE2 (CV acquired in experimental step b.)..I ^WE1 thus corresponds to the direct current flowing from WE2 across the gap to WE1 in the experimental step b. The transport resistance R _t was then calculated as

   $$R_t=\frac{\Delta E}{\Delta I^{WE1}}$$ (Equation 2)

   By using different potential differences ΔE between the two working electrodes the validity of Ohm’s Law under the conditions used was verified.
4. The conductivity σ of the TiO₂ films deposited on the IDEs was finally calculated by

   $$\sigma =\frac{t}{R_t\cdot L\cdot d\cdot \left(1-p\right)}$$ (Equation 3)

   where t, L, d and P represent the width and the length of the gap between the interdigitated gold electrodes, the TiO₂ film thickness and the porosity of the film, respectively.

Alternatively and to exclude kinetic effects resulting from the slow population of trap states in the potentiodynamic experiments, we measured the stabilized direct current flow between the two working electrodes (in response to a bias ΔE _WE2-WE1 = -0.01 V) also at static potentials (potentiostatic measurement).³⁹ Again, transport resistance R _t was calculated by applying Ohm’s law (Equation 2) and the conductivity was calculated by using Equation 3.

2.5.2. Determination of the thin film conductivity upon UV-induced band gap excitation

We used the same electrode geometry as described above (i.e. TiO₂ films deposited on IDEs), however, this time the working electrode WE1 was operated at open circuit (Figure S6). Electrode polarization at open circuit was induced by UV light exposure of the TiO₂ film from the electrolyte side and the open circuit photopotential for WE1 was measured with respect to the Ag/AgCl (3 M KCl) reference electrode. While WE1 was operated at open circuit, the potential of the second working electrode (WE2) was controlled by the bipotentiostat, which was programmed to assure a small bias ΔE = E ^WE2 – E ^WE1 = -0.01 V throughout the whole experiment. The direct current between the two working electrodes and the open circuit photopotential for WE1 were then measured simultaneously as a function of light exposure time (Figure S6). Transport resistance R _t was calculated by applying Ohm’s law (Equation 2) and the conductivity was calculated by using Equation 3. The conductivity was finally represented as a function of the open circuit photopotential of the working electrode WE1 (Figure S6).

A 1000 W Xe-discharge arc lamp (LOT QuantumDesign) was equipped with a water filter to remove IR light. The light irradiance (P = 4 mWcm^-2 and P = 400 mWcm^-2) was measured with a bolometer (International Light, IL1400A).

3. Results and discussion

3.1. Structural properties of anatase TiO₂ nanoparticle electrodes

TiO₂ nanoparticle powders, which were prepared by metal organic chemical vapor synthesis and purified by thermal annealing at high vacuum conditions and in oxygen atmosphere, consist of isolated (i.e. non-aggregated), irregularly shaped nanocrystals with sizes between 10 and 20 nm and a specific surface area of 120 m²g^-1.^34,35,40 The particles were dispersed in ultrapure water, spread onto glass slides and the resulting films were dried in air. Particle ensembles were recovered by scratching them from the substrate and were then characterized by TEM (Figure 1 and Table 1) yielding particle sizes between 8 – 25 nm and a median diameter d _TEM = 14.5 ± 0.5 nm (Figure 1a,b). Importantly, annealing of the particle films at 450 °C in air prior to particle detachment from the substrate does not result in a significant change of the particle morphology or size distribution (Figure 1c,d). Annealing-induced particle coarsening can thus be excluded and films obtained at different sintering temperatures below 450 °C consist of particle ensembles with uniform particle properties in terms of size and morphology. The specific surface area of the particle ensemble decreases from 120 m²g^-1 for the vapor-phase synthesized nanoparticle powder to ~90 m²g^-1 for nanoparticle aggregates obtained after nanoparticle dispersion in water, drying and thermal annealing at 200 °C or 450 °C in air (Table 1). The decrease in the specific surface area indicates the formation of contact areas between primary particles and the formation of particle aggregates upon preservation of the primary particle size (as evidenced by TEM).

Figure 1.

Transmission electron micrographs (a, c) of anatase TiO₂ nanoparticle aggregates. A nanoparticle powder obtained by metal organic chemical vapor synthesis was used to prepare an aqueous particle slurry, which was extended on a glass substrate and dried at room temperature (a, b) or, alternatively, thermally annealed for 1 h at 450 °C (c, d). Particle aggregates were recovered by scratching the film from the glass substrate and were immobilized on a lacey carbon grid for TEM analysis. (b, d) Size distribution of primary particles as determined from transmission electron micrographs. 250 particles were analyzed for each sample.

Table 1.

Crystal phase, specific surface area and nanocrystal size of anatase TiO₂ nanoparticle ensembles sintered at different temperatures. X-ray diffraction (XRD) was performed on TiO₂ nanoparticle electrodes. The crystallite domain size d_XRD was obtained by full pattern profile analysis and Rietveld refinement of X-ray diffraction patterns. Nitrogen physisorption experiments and transmission electron microscopy (TEM) were performed on TiO₂ nanoparticle aggregates. The specific surface area was obtained from nitrogen physisorption experiments applying the BET algorithm. The primary particle size d_TEM corresponds to the median nanoparticle diameter as deduced from the primary particle size distribution functions (Figure 1b and d).

Sintering temperature / °C	Crystal phase	Specific surface area / m2 g-1	dXRD / nm	dTEM / nm
pristine	anatase	-	15 ± 1	14.5 ± 0.5
100	anatase	-	14 ± 1	-
150	anatase	-	15 ± 1	-
200	anatase	89 ± 2	15 ± 1	-
250	anatase	-	14 ± 1	-
300	anatase	89 ± 6	15 ± 1	-
400	anatase	-	14 ± 1	-
450	anatase	90 ± 10	16 ± 1	14.5 ± 0.5

Top view and cross sectional microscopy images of electrodes prepared from non-stabilized TiO₂ slurries reveal inhomogeneous and partially cracked nanoparticle films featuring aggregates with sizes up to 30 µm and a mean film thickness of 5 µm (FTO coated glass substrates) and 10 µm (IDEs), respectively (Figure S4). Single aggregates are significantly larger than the separation between the interdigitated gold electrodes (t = 5 µm) thus bridging the nonconductive gap between the gold tracks. The microstructural inhomogeneity of TiO₂ nanoparticle films results from the omission of paste formulation (i.e. addition of surface active agents such as e.g. acetylacetone or Triton X).⁴¹ To exclude microstructural differences between different electrodes as the reason for the observed sintering-induced changes of their electronic and electrochemical properties, which will be discussed in the following, we used for all electrochemical methods (except electrochemical impedance spectroscopy) the following approach. On the one hand, we studied for each substrate (i.e. FTO covered glass and IDEs) the electronic and electrochemical properties of various TiO₂ electrodes, whose processing chain deviated only in the last step i.e. the final sintering, which was performed at different temperatures. On the other hand, we investigated for one single electrode the impact of sintering temperature on the electrode properties. For this purpose, the nanoparticle film was sintered at 100 °C prior to electrochemical measurements. After electrochemical characterization, the electrode was extensively washed with ultrapure water, dried and then sintered at a higher temperature followed again by an electrochemical characterization step. This sequence was repeated up to the final sintering temperature (i.e. 300 °C for films deposited on IDEs and 450 °C for those deposited on FTO coated glass). Importantly, for both processing / characterization approaches the same trends were observed (see below). For the electrochemical impedance study a new electrode was prepared for each sintering temperature.

Despite poor microstructural definition, structural characterization highlights some unique features of anatase TiO₂ nanoparticle electrodes:

• Due to the high-vacuum processing of the precursor powder and the use of non-stabilized aqueous slurries for electrode preparation, anatase TiO₂ nanoparticle ensembles feature clean oxide surfaces independent from sintering temperature. With respect to chemical surface composition sintering temperature is expected to change the degree of surface hydration and hydroxylation, which is however of limited relevance for the electrochemical characterization after electrode transfer into an aqueous electrolyte.

• The use of a powder consisting of isolated (i.e. non-aggregated) nanoparticles as the precursor for the particle slurry allows for a stepwise build-up of particle-particle contacts in the immobilized films upon thermal annealing. The impact of nanoparticle consolidation on electronic and electrochemical film properties can therefore be studied in a systematic way as a function of sintering temperature. Such an analysis is unfeasible if precursor powders of undefined aggregation state are used.

• Structural characterization furthermore evidences that the consolidation of the random nanoparticle network takes place upon preservation of the crystal structure and the primary particle size.

Such a control of electrode characteristics is difficult to achieve by other preparation methods. Particle systems prepared by flame spray pyrolysis for instance are typically aggregated and feature surface residues.⁴² Wet chemical approaches toward nanoparticle dispersions often yield inorganic nanocrystals featuring at their surface ligands for colloidal stabilization. In such a case thermal annealing leads not only to particle consolidation, but furthermore to significant changes in surface composition.

In contrast, sintering temperature is expected to influence primarily the structural and energetic properties of particle-particle contacts in the case of anatase TiO₂ nanoparticle electrodes prepared from vapor-phase grown powders, while crystal structure, primary particle size and surface composition remain unchanged. Due to their unique characteristics we introduce these electrodes as suitable model systems for the investigation of nanocrystal consolidation and electronic conductivity in random nanoparticle films. Related model systems are extremely difficult to establish.

3.2. Impact of sintering temperature on the capacitive behavior of anatase TiO₂ nanoparticle electrodes

Cyclic voltammograms of anatase TiO₂ electrodes were recorded in 0.1 M HClO₄ aqueous electrolyte (Figure 2a). Capacitive currents at potentials E _Ag/AgCl < -0.2 V are detected both for pristine (i.e. non-sintered) and for sintered films in line with previous studies on anatase TiO₂ electrodes.^43–45 While for a pristine electrode capacitive currents are very low, we observe a significant increase upon thermal annealing at only 100 °C. Importantly, capacitive currents do not further increase upon sintering at higher temperatures up to 450 °C (Figure 2a).

Figure 2.

a) Cyclic voltammograms of a pristine (i.e. a non-sintered) TiO₂ film deposited on FTO coated glass and of a TiO₂ film sintered first at 100 °C and then at 450 °C. b) Magnification of the onset of capacitive currents both for the positive-going (anodic) and the negative-going (cathodic) branch of cyclic voltammograms for electrodes sintered at 150 °C, 300 °C and 450 °C. c) Logarithmic representation of the capacitive currents in the accumulation region for electrodes sintered at 150 °C, 300 °C and 450 °C. Data obtained from cathodic and anodic voltammetric scans are represented using different y-axis for better conspicuity. Electrolyte: 1 M MeOH / 0.1 M HClO₄ aqueous solution purged with N₂; v = 0.02 Vs^-1.

Capacitive currents in mesoporous anatase TiO₂ electrodes have previously been attributed to the population / depopulation of electronic states in the band gap of the semiconductor compensated by proton adsorption at the oxide surface.⁴³ The corresponding accumulated charge has been associated with the density of electrochemically active band gap states in anatase TiO₂ ⁴⁶ and was shown to scale linearly with the internal area of the semiconductor / electrolyte interface.⁴⁷ Consequently, anatase TiO₂ nanoparticle electrodes thermally annealed at temperatures between 100 °C and at 450 °C feature the same electrochemically active surface area. As nitrogen sorption measurements yield comparable specific surface areas for particle ensembles annealed at 200 °C, 300 °C and 450 °C (Table 1) and the primary particle size is independent from sintering temperature in the range 100 °C ≤ T ≤ 450 °C, we conclude that annealing at a temperature as low as 100 °C imparts to the electrodes sufficient conductivity to electrochemically access – at least at sufficiently negative potentials – the whole nanoparticle network.

For mesoporous anatase TiO₂ the presence of a broad exponential distribution of states below the conduction band edge has been demonstrated in the accumulation region both by cyclic voltammetry and by electrochemical impedance spectroscopy and was proposed to be connected to surface states. The chemical capacitance C_μ associated with such an exponential distribution of band-gap states depends exponentially on potential E:^44,45

$$C_{\mu }=\frac{\alpha e^2{\Theta }_{t}d}{\kappa T}\left(\frac{\alpha e\left(E_C-E\right)}{\kappa T}\right)$$ (Equation 4)

where e is the elemenatry charge, Θ_t the electrode total volume density of traps, d the film thickness κ the Boltzmann constant and E_C is the potential corresponding to the bottom conduction band edge. α is the trap distribution parameter which defines the broadening of the exponential distribution.

In addition, a narrow distribution of deep trap states has typically been reported giving rise to a pair of capacitive peaks at more positive potentials.^44,48,49

The CVs of anatase TiO₂ electrodes sintered at 100 °C ≤ T ≤ 450 °C contain both contributions (Figures 2 and 3). The position of the capacitive peaks resulting from the narrow distribution of deep trap states shifts toward more positive potentials with increasing sintering temperature, concretely from E _Ag/AgCl = -0.20 V at 150 °C to -0.15 V at 250 °C and -0.05 V at 450 °C (Figure 2b,c). Importantly, these voltammetric peaks are at least partially reversible i.e. anodic and cathodic branches of the CVs contain the narrow contribution, which is slightly broadened in the positive-going (i.e. anodic) branch. At potentials more negative than the capacitive peak we observe for all sintering temperatures an additional capacitive contribution, which increases exponentially toward more negative potentials (Figure 2). Importantly, this exponential current extends towards more positive potentials in the anodic scan, i.e. once electrons have been accumulated in the film at a sufficiently negative potential. Very similar observations have been made for TiO₂ films deposited on interdigitated gold electrodes (Figure S7).

Figure 3.

a) Cyclic voltammograms of an anatase TiO₂ film deposited on FTO coated glass and sintered sequentially at 150 °C (black, solid line) and at 450 °C (red, dotted line). Electrolyte: N₂-purged 1 M MeOH / 0.1 M HClO₄ aqueous solution; v = 0.02 Vs^-1 b) Film capacitance as determined for the same electrodes by electron accumulation-extraction experiments: In the accumulation step, the electrode was polarized for 100 s at E _Ag/AgCl = -0.4 V. Then the electrode potential was stepped (∆E = 0.02 V) towards more positive potentials. For every potential step the extracted charge was determined by charge integration for 100 s. The chemical capacitance (symbols) was calculated by referring the extracted charge to ∆E. Capacitance data represented by solid and dotted lines were calculated from the anodic branches of the cyclic voltammograms in Figure 3a. Electrolyte: N₂-purged 1 M MeOH / 0.1 M HClO₄ aqueous solution.

At fast scan rates it is possible that not all of the deep traps in a mesoporous film are equilibrated with the Fermi level of the conducting substrate. This is the reason why even large perturbation techniques such as cyclic voltammetry may yield for deep trap states only apparent chemical capacitances.^49,50 Therefore, we performed charging and discharging measurements using extremely long lasting perturbations in the potential range featuring the capacitive peaks (Figure 3). We measured the capacitive currents upon stepping the electrode potential from E _Ag/AgCl = -0.4 V (charge accumulation) in potential steps ΔE = 0.02 V to E _Ag/AgCl = 0.14 V (charge extraction). After every step the potential was kept constant for 100 s and the extracted charge density associated with each potential step was determined by integration of the resulting currents. To obtain the chemical capacitance associated with the deep traps the charge was referred to ΔE. Importantly, resulting data resemble capacitance data extracted from the CVs (solid and dotted lines in Figure 3b). These were determined by dividing the capacitive current density j of the anodic branches of the CVs (Figure 3a) by the scan rate v = 20 mV·s^-1.⁴⁵ The chemical capacitance values obtained this way are consistent with capacitance values determined by other techniques.⁵¹

From the total charge extracted upon stepping the electrode potential from E _Ag/AgCl = -0.30 V to -0.10 V (150 µC·cm^-2, Figure 3b) we estimate (using the electrode mass and the average value of the particle size) the number of electrons associated with the narrow distribution of deep trap states to be 11 ± 3 electrons per anatase TiO₂ nanoparticle for an electrode sintered at 150 °C. However, due to the overlap of the exponential current and the discrete peak this number constitutes only an upper limit and includes furthermore electrons associated with the currents attributed to an exponential distribution of states. A reliable assessment of a possible change of the number of electrons in deep traps upon sintering at higher temperatures is therefore not feasible.

The coplanar source-drain configuration (Figure S5) was used to measure the electronic conductivity of an anatase TiO₂ nanoparticle film upon electrochemical gating, i.e. upon varying the charge carrier density and thus the Fermi level in the mesoporous film by changing the electrochemical potential.⁵² For this purpose a single electrode was subjected to consecutive steps of thermal annealing at temperatures between 100 °C and 300 °C. The potential dependence of the electronic conductivity (Figure 4a) features two distinct regions after electrode sintering at the highest temperature (i.e. 300 °C) in line with previous studies.^38,53,54 At potentials close to the onset potential for charge accumulation (Figures 2 and 3) we observe an exponential increase of the electronic conductivity towards more negative potentials (i.e. upon electrochemical charge accumulation, Figure 4a). For the electrode sintered at 300 °C the conductivity increases between E _Ag/AgCl = -0.10 V and -0.25 V from ~10^-7 Ω^-1cm^-1 by almost 3 orders of magnitude with a variation of ~70 mV per decade in line with previous studies.^38,55 The conductivity variation has previously been interpreted in terms of a progressive displacement of the Fermi level towards the conduction band.³⁸ At more negative potentials the film approaches a potential-independent, maximum conductivity of ~10^-4 Ω^-1cm^-1. This saturation behavior has been related to a state of Fermi level pinning.^38,52

Figure 4.

Electronic conductivity of anatase TiO₂ nanoparticle films annealed at different temperatures. The potential-dependence of the conductivity was determined upon electrochemical (a, c) or photochemical (b) polarization of the TiO₂ film deposited on interdigitated gold electrodes (coplanar source-drain configuration) (a, b) or on fluorine-doped tin oxide covered glass (c). The conductivity in (a) was calculated from the direct current between the two interdigitated electrodes in response to a small bias ∆E = -0.01 V. The TiO₂ film was polarized by linearly changing the electrode potential (v = 0.02 Vs^-1) of the interdigitated electrodes during a cathodic and an anodic voltammetric scan. The conductivity profiles calculated from the anodic scans are represented (as lines) also in (b) and (c) for comparison. Conductivity data represented by symbols in (b) have been calculated from the direct current between the two interdigitated electrodes upon exposure of the TiO₂ film to polychromatic UV/Vis light (P = 400 mWcm^-2, except data points represented by stars, which have been determined at P = 4 mWcm^-2). The working electrode WE1 was operated at open circuit, while, simultaneously, the potential of the second working electrode (WE2) was controlled by the bipotentiostat, which was programmed to assure a small bias ∆E = E ^WE2 – E ^WE1 = -0.01 V throughout the whole experiment. In this case the conductivity is represented as a function of the open circuit photopotential measured for the working electrode WE1. Conductivity data represented by symbols in (c) have been calculated from the transport resistance as extracted from electrochemical impedance spectra (Figure 5). Electrolyte: 1 M MeOH / 0.1 M HClO₄ aqueous solution purged with N₂ (a, b) or O₂ (c).

The electronic conductivity (Figure 4a) was determined from the current flowing between the source and drain contacts of the interdigitated electrode (Figure S5) while linearly scanning the potential of the TiO₂ electrode from more negative to more positive potentials (anodic scan of the cyclic voltammogram / electron extraction, Figures 3a and S7) and back (cathodic scan / electron accumulation, Figures 3a and S7). Importantly we find for the film sintered at 300 °C that the conductivity at a given electrode potential does not depend on the scan direction. This observation points to a fast and reversible charge accumulation / charge extraction in the studied potential range.

The electrode behavior changes significantly at lower annealing temperatures. First, a negative displacement of the conductivity profiles on the potential axis is observed (Figure 4a). The potential region featuring the exponential conductivity variation shifts negative by ~30 mV when decreasing the sintering temperature from 300 °C to 250 °C (Figure 4a). Even more pronounced shifts are observed at lower sintering temperatures. While the plateau region is thus reached at more negative potentials, it has to be emphasized that the value of the limiting conductivity remains unchanged as may be seen in the conductivity profiles for an electrode sintered at 300 °C, 250 °C and 200 °C, respectively (Figure 4a). The limited potential window due to electrolyte reduction at uncovered Au surfaces at potentials E _Ag/AgCl < -0.40 V avoids observation of the maximum conductivity in the case of electrode annealing at T ≤ 150 °C. The shift of the conductivity profiles towards more positive potentials upon increasing annealing temperatures seems to be associated with the positive shift of the onset potential for electrochemical charge accumulation as manifested in the corresponding CVs (Figures 2, 3 and S7) by the displacement of the pair of capacitive peaks associated with deep trap states. Importantly, the voltammetric responses of electrodes sintered at different temperatures significantly deviate from each other near the onset potential of charge accumulation (i.e. at more positive potentials), while they converge at more negative potentials. Interestingly, the electronic conductivity also approaches a constant plateau at sufficiently negative potentials independent from the thermal annealing temperature.

While for a defined annealing temperature in the range T ≥ 250 °C almost congruent conductivity profiles are obtained independent of the scan direction, significant deviations between the anodic and cathodic scans are observed for annealing temperatures T ≤ 200 °C. More specifically, the anodic scan yields a higher conductivity than the cathodic scan at more positive potentials. At more negative potentials, however, both conductivity profiles converge. This behavior is reminiscent of the charge accumulation / charge extraction behavior of the electrodes as studied by cyclic voltammetry (Figure 2c). Especially for those films thermally annealed at low temperatures a pronounced difference between the cathodic and anodic branches of the CV is observed. Concretely, the exponential current extends towards more positive potentials in the anodic scan (Figure 2c). This observation points to a slow charge accumulation / charge extraction in the studied potential range for films annealed at low temperatures. The difference in the charging kinetics for electrodes annealed at different temperatures is clearly demonstrated by potential step experiments (Figure S8). For this purpose, charge accumulation was induced by stepping the electrode potential from E _Ag/AgCl = 0.6 V to different potentials in the accumulation regime (-0.1 V ≥ E _Ag/AgCl ≥ -0.4 V) while measuring the transient currents. Importantly, we do not observe a significant difference in the charging kinetics at E _Ag/AgCl = -0.4 V for a film annealed alternatively at 150 °C or 450 °C, respectively (Figure S8a). However, major differences are observed for these films upon charging at more positive potentials, specifically near the onset potential of electron accumulation (Figure S8b-d).

Additional potentiostatic measurements were performed at selected electrode potentials to exclude that kinetic effects resulting from the slow population of trap states distort the conductivity values as determined by potentiodynamic measurements. The conductivity values as determined by the two independent methods for one TiO₂ nanoparticle film annealed first at 100 °C and then at 250 °C are represented in Figure S9. The perfect agreement between the two different data sets allows to exclude a major impact of slow trap population kinetics on the conductivity determination by potentiodynamic experiments, when using a scan rate v = 0.02 V s^-1.

We furthermore determined the film conductivity upon band gap excitation (see Section 2.5.2) to circumvent problems associated with different charging / discharging kinetics and to assure that the whole cross section of the mesoporous films equally contributes to charge transport. This can be achieved upon UV exposure at open circuit conditions as under these conditions electron accumulation in the film is not triggered by electron injection from the conducting substrate, but by the photogeneration of charge carriers within the nanocrystals throughout the random particle network. A hole acceptor (1 M MeOH) was added to the electrolyte in order to efficiently scavenge photogenerated holes and to facilitate electron accumulation in the mesoporous films. The working electrode WE1 was operated at open circuit, while, simultaneously, the potential of the second working electrode (WE2) was controlled by the bipotentiostat, which was programmed to assure a small bias ΔE = E ^WE2 – E ^WE1 = -0.01 V throughout the whole experiment (Figure S6). The conductivity was then determined by measuring the direct current between the two interdigitated electrodes upon exposure of the TiO₂ film to polychromatic UV/Vis light. The conductivity is represented in Figure 4b as a function of the open circuit photopotential, which was measured for WE1 simultaneously. Importantly, there is a perfect match (in the common potential range) between the conductivity profiles determined (i) from the anodic scans following electrochemical charge accumulation in the dark and (ii) upon light-induced charge accumulation (Figure 4b). This coincidence is perfectly in line with previous IR-spectroelectrochemical experiments showing that under appropriate conditions the electrode potential determines the Fermi level throughout the mesoporous film and thus the occupation of band gap states, independent from the type of external perturbation, i.e., application of a bias voltage or electrode exposure to photons exceeding the semiconductor band gap at open circuit.⁵⁶

Working at open circuit conditions furthermore allows extending the potential window to more negative potentials (Figure 4b). These data clearly show that for all annealing temperatures in the range 100 °C ≤ T ≤ 300 °C the same limiting conductivity is reached at low potentials (i.e. σ~10^-4Ω^-1cm^-1).

Single frequency impedance measurements were performed at 10 mHz and 10 kHz for an electrode sintered at 100 °C and at 450 °C and evidence a strong frequency dispersion of the interfacial impedance (Figure S10). To study interfacial processes in more detail we performed wide-frequency-range (10 mHz – 10 kHz) electrochemical impedance spectroscopic (EIS) measurements. Characteristic impedance spectra of anatase TiO₂ electrodes thermally annealed at 450 °C, 300 °C and 100 °C are represented in Figure 5 as a function of the applied dc potential (-0.35 V ≤ E _Ag/AgCl ≤ -0.05 V). The complex plane plots (Nyquist plots) of an electrode annealed at 450 °C feature two domains of frequency behavior: a semicircle at low frequencies and a high frequency straight line, which are separated by an elbow (Figure 5, top line). This impedance behavior is analogous to the one of similar types of electrodes reported earlier.³⁷

Figure 5.

Electrochemical impedance spectra (symbols) and best fit (lines) of porous TiO₂ electrodes at different dc potentials. Electrolyte: O₂ purged 1 M MeOH / 0.1 M HClO₄ aqueous solution.

For electrodes annealed at lower temperatures (T = 300 °C and 100 °C, Figure 5, middle and bottom line) the small signal ac response resembles the shape described above only at sufficiently negative potentials (i.e. E _Ag/AgCl = -0.35 V and -0.20 V for the electrode annealed at 300 °C as well as E _Ag/AgCl = -0.35 V for the electrode annealed at 100 °C). However, at more positive potentials the two clearly separated domains of frequency behavior (high frequency straight line and low frequency arc) merge for low annealing temperatures resulting in an asymmetric and clearly depressed arc. The potential, at which this change of the signal envelope is observed, shifts with decreasing annealing temperature towards more negative potentials (Figure 5).

The well-established transmission line model (Figure S3)^57,58 can be applied to comprehensively extract from EIS measurements information on electron dynamics in mesoporous TiO₂ films, particularly electron transport resistance (R _t) as well as chemical capacitance (Q) and charge transfer resistance (R _ct) at the TiO₂ / electrolyte. The distributed capacitive element, Q (F s^1-n) typically shows some frequency dispersion and can be described by a constant phase element with exponent n.^57,58 While the low frequency arc in the impedance spectra can be related to chemical capacitance and charge transfer resistance distributed at the TiO₂ / electrolyte interface, the straight line at high frequencies can be associated with electron diffusion through the mesoporous film. The capacitance Y ₀ relates to the interface between the FTO substrate and the electrolyte and has been described in detail.⁵⁹

We used the transmission line equivalent circuit shown in Figure S3 to fit the experimental impedance spectra in Figure 5. The fitting values R _t, R _ct, Q and n are shown in Figure S11. R _t and Q show an exponential dependence on the applied potential in agreement with previous reports.³⁷ The annealing temperature has only a minor impact on the charge transfer resistance R _ct (Figure 6b). The capacitive element Q shows an annealing temperature independence only at potentials E _Ag/AgCl ≤ -0.20 V, but differs at more positive potentials. This behavior resembles capacitance data extracted from the CVs (solid and dotted lines in Figure 3b), which highlight an annealing temperature-independent capacitance at more negative potentials in addition to a positive shift of capacitive peaks at more positive potentials for increasing annealing temperatures. Such defined peaks, however, are not resolved in the potential-dependence of Q (Figures 6c and S11). The capacitive element can be fitted with an exponential function (Figure S12) to estimate the trap distribution parameter, which takes values between 0.25 and 0.35 in line with previous reports and indicating that the capacitance is associated with an exponential distribution of band gap states.⁴³ The values of the trap distribution parameter are virtually independent from sintering temperature (Table S1). The frequency dispersion of the distributed capacitive element as described by the exponent n of the constant phase element depends both on potential and annealing temperature (Figures 6d and S11). While for the most negative potentials n takes values near to 1, indicating that Q can be considered as an almost ideal capacitor, a significant decrease of n is observed at more positive potentials. This decrease is less pronounced for electrodes annealed at 450 °C, but significant for electrodes annealed at lower temperatures. The lower the annealing temperature, the lower are the values of n at positive potentials (e.g. n ~ 0.4 at E _Ag/AgCl = 0.05 V for an electrode annealed at 100 °C, Figure 6d).

Figure 6.

Comparison of the best fit values of R_t, R_ct, Q and n extracted from electrochemical impedance spectra of porous TiO₂ electrodes sintered at 100 °C and 450 °C, respectively (Figure 5). The equivalent circuit in Figure S3 was used to fit the experimental impedance spectra.

The fitting parameter showing the most significant dependence on annealing temperature over the whole potential range studied is the transport resistance R _t (Figure 6a). When increasing the annealing temperature from 100 °C to 450 °C a displacement of the transport resistance curve towards more positive potentials (by ~ 0.1 V) is observed in the semi-logarithmic plot. Only at the most negative potential (E _Ag/AgCl = -0.35 V) the R _t values determined for different sintering temperatures tend to converge (Figure S11). The potential-dependent electronic conductivity profiles were calculated from the transport resistance (as extracted by EIS for anatase TiO₂ nanoparticle films on FTO substrates) and are represented as semilogarithmic plots in Figure 4c. For films sintered at T ≥ 200 °C, these profiles perfectly match (in the common potential range) the conductivity profiles determined from IDEs upon electrochemical charge accumulation in the dark and upon light-induced charge accumulation at open circuit (Figure 4b). The close match observed for high sintering temperatures between the conductivity data extracted from EIS analysis (using TiO₂ films deposited on FTO substrates) and the data obtained from the coplanar source-drain configuration (i.e. using TiO₂ films deposited on interdigitated gold electrodes) is remarkable. It indicates that differences in the sample configuration do not significantly affect the characteristic conductivity profiles. Furthermore, while a possible diffusion of gold from the interdigitated electrodes into the porous TiO₂ layer upon sintering can not be fully excluded, we can thus rule out any significant impact on the electronic conductivity of the TiO₂ films. Deviations are observed at sintering temperatures T ≤ 150 °C. Conductivity profiles were fitted with an exponential function in the linear range of the semilogarithmic plots (Figure S13) to quantify the dependence of conductivity on electrode potential. The fitting parameter α_σ is virtually independent from sintering temperature and takes values between 0.6 and 0.8 (Table S1) corresponding to slopes of σ between ~ 70 – 100 mV per decade.

4. General discussion: Impact of particle consolidation on electronic conductivity

The specific surface area of vapor phase-grown and purified anatase TiO₂ nanoparticle powders is substantially depleted from 120 m²g^-1 to 90 m²g^-1 upon particle dispersion in ultrapure water, immobilization and subsequent water removal in air at T = 200 °C. An increase of the annealing temperature (200 °C ≤ T ≤ 450 °C) does not induce any further significant reduction of the specific surface area (Table 1). After annealing the size of the nanocrystals in the particle networks resembles the nanocrystal size in the original powder (d _TEM = 14.5 ± 0.5 nm). The loss of the specific surface area upon preservation of the nanocrystal size thus results from powder consolidation and the formation of contact areas between the particles. No measurable change of the total contact area is observed upon increasing the annealing temperature in the investigated temperature range. When deposited on conducting substrates and used as electrodes in an acidic aqueous electrolyte, electrons can be electrochemically accumulated in the nanoparticle films upon application of an external bias. The charge accumulated at E _Ag/AgCl ≤ -0.4 V (Figures 2a and 3), which was previously shown to scale linearly with the electrochemically active surface area of TiO₂ nanocrystal electrodes,⁴⁷ does not depend on sintering temperature in the range 100 °C ≤ T ≤ 450 °C. Electrochemical data thus substantiate the conclusion of an annealing temperature-independent internal surface area of random nanoparticle networks as drawn from gas sorption experiments.

While the structural properties of the films remain virtually unchanged upon thermal annealing in the investigated temperature range, significant changes of the electronic film properties are observed. Most importantly, sintering temperature strongly impacts on the potential-dependence of the electronic conductivity, σ. The potential range featuring an exponential increase of σ when E becomes more negative (i.e. the linear region in the semilogarithmic plot), shifts positive with increasing sintering temperature (Figure 4). At more negative potentials, however, the conductivity of all films reaches an annealing temperature-independent saturation value. These observations shall be discussed in the following on the basis of the distribution of electrochemically active states, which is extracted from the analysis of the capacitive response of the electrodes investigated.

The conductivity and the capacitive current (as recorded by cyclic voltammetry) of anatase TiO₂ nanoparticle electrodes sintered at 100 °C and at 450 °C, respectively, are represented on a common potential scale in Figure 7a and b. At potentials E _Ag/AgCl ≤ -0.4 V capacitive currents are virtually identical for both electrodes. In this potential range, furthermore, both electrodes exhibit comparable and constant values of electronic conductivity (σ ~ 10^-4 Ω^-1cm^-1). However, at more positive potentials (i.e. at E _Ag/AgCl > -0.4 V), major differences in the potential-dependence of both the conductivity and the capacitive current are observed for electrodes sintered at different temperatures. Upon increasing the sintering temperature a positive displacement by ~0.15 V (along the E-axis) of the linear region in the semilogarithmic representation of σ vs E is observed (Figure 7a) and is accompanied by a positive shift (by the same magnitude) of the capacitive peaks associated with deep traps in the lnj vs. E plot (Figure 7b). This observation suggests that the population of deep trap states is directly related with the pronounced conductivity change at more positive potentials.

Figure 7.

Potential-dependence of (a) the electrical conductivity, (b) capacitive currents and (c) the density of states (as estimated from capacitive currents) for anatase TiO₂ nanoparticle films sintered at 100 °C and at 450 °C, respectively. I-III: Schemes highlighting the interplay between the population of surface and grain boundary trap states and the electronic conductivity.

The location of the conduction band edge of similar anatase TiO₂ nanoparticle electrodes in 0.1 M HClO₄ aqueous solution has previously been estimated at E _Ag/AgCl = -0.7 V.⁶⁰ Charge accumulation upon electrode polarization at potentials more positive than E _Ag/AgCl = -0.6 V (Figures 2, 3 and 7b) can thus mainly be associated with the population of states located in the band gap of TiO₂. In the absence of significant band unpinning the Fermi level within the band gap can be controlled by varying the electrode potential.⁴⁵ Consequently, electron accumulation under Fermi level control renders possible the sampling of band gap states as a function of their energy and the deduction of the density of electrochemically active states (DOS), which is proportional to the capacitance as e.g. calculated from capacitive currents (Figure 3b) or extracted from the fitting of impedance spectra (Figure 6c).^44,45 The DOS of anatase TiO₂ nanocrystal electrodes (Figure 7c) is in line with previous reports on similar types of electrodes^43,44 and contains as a dominant feature an exponential distribution of localized states in the band gap just below the conduction band edge (shallow traps). The origin of these states has not conclusively been resolved so far. However, a quantum mechanical investigation of electronic states in anatase TiO₂ nanocrystals has revealed that under-coordinated surface Ti atoms give rise to an approximately exponential distribution of states below the conduction band.^27,61 Apart from the exponential distribution of shallow traps an additional distinct peak of much lower intensity contributes to the DOS of anatase TiO₂ nanocrystal electrodes at more positive potentials (Figure 7c). This contribution is associated with the filling and depopulation of a narrow distribution of deep trap states.⁵⁰ Previous studies indicate that these trap states are associated with interparticle grain boundaries.^47,49,62 Quantum mechanical calculations have revealed that even defect- and impurity-free grain boundaries between TiO₂ crystals contain Ti sites, which act as electron traps.^28,30

Voltammograms of anatase TiO₂ nanocrystal electrodes (Figure 7b) clearly evidence that the sintering temperature (in the investigated temperature range) has no significant qualitative or quantitative impact on the exponential distribution of shallow traps. This is in line with the observation of a sintering temperature-independent internal surface area of the nanocrystal network. Importantly, nanocrystals have been thermally annealed at 600 °C under high vacuum conditions and in oxygen atmosphere prior to dispersion in water and immobilization. This high temperature pretreatment may explain the invariance of the concentration and the energetic distribution of surface Ti sites upon immobilization and sintering at T ≤ 450 °C.

Voltammograms, however, reveal a sintering temperature-dependent energy of the narrow distribution of deep traps – the higher the sintering temperature, the deeper the corresponding traps. Adhering to the assignment of deep traps to sites at the interparticle grain boundary, this observation implies a sintering-induced modification of particle-particle interfaces, which may be facilitated by the presence of adsorbed water.³⁵ The atomic origin of the increase of trapping energies upon sintering is unknown so far. However, for defect- and impurity-free grain boundaries it was found that trap states are associated with local perturbations of the electrostatic potential resulting from undercoordination of Ti sites, topological disruption and strain.²⁸ It is feasible that the on-site electrostatic potentials of trap states at the grain boundary experience major modifications upon thermal energy input. Sintering may also come along with a change of the concentration of grain boundary trap states. An experimental validation of such a change is however hampered by the overlap of capacitive currents (Figures 2 and 3) resulting from surface traps and from traps at the particle-particle interface. A significant change of the particle-particle contact area, however, can be excluded – in the range of sintering temperatures studied – based on the results of sorption measurements (Table 1) and cyclic voltammetry (Figure 1), respectively.

Importantly, the analysis of the density of electrochemically active states reveals that the variation of the sintering temperature allows for a relative displacement on the energy (and potential) scale of the narrow distribution of deep traps with respect to the invariant exponential distribution of surface traps (Figure 7c). This opens up the possibility to exploit the impact of deep traps on electron transport in these films.

Electronic transport is by orders of magnitude slower in nanocrystal films than in bulk materials due to the broad distribution of localized states causing electrons to be almost permanently localized. Consequently, transport occurs upon thermal activation of carriers to a band of extended states or by hopping via localized states.⁶³ Slow thermally activated transport is also common in amorphous TiO₂ films.⁶⁴ For nanocrystal films, transport coefficients are found to depend strongly on the Fermi level (or the carrier concentration) in the film. The classical multiple trapping model considers electron transport in the conduction band of the semiconductor, which is slowed down by a sequence of trapping and detrapping events involving localized states in the band gap. For an exponential distribution of localized states the multiple trapping model predicts an exponential dependence of the diffusion coefficient, D _n, on the Fermi level position (i.e. the electrochemical potential of the electrons), E _F

$$D_n=\frac{N_C}{\alpha N_L}{D}_0\exp \left[\frac{\left(1-\alpha \right)\left(E_C-E_F\right)}{\kappa T}\right]$$ (Equation 5)

where D ₀ is the diffusion coefficient of free electrons at the transport level, N_L the total density of localized states, N_C the effective density of conduction band states, α the trap distribution parameter and E_C is the potential corresponding to the lower edge of the conduction band. In the absence of band unpinning (i.e. at a fixed conduction band edge) the diffusion coefficient depends thus exponentially on electrode potential, E. The electronic conductivity can be written as⁶³

$$\sigma =D_n{C}_{\mu }$$ (Equation 6)

Bearing in mind the exponential dependence of C _µ, the multiple trapping model predicts thus for an exponential distribution of trap states a variation of σ with electrode potential by $\exp \left(-\frac{eE}{\kappa T}\right)$ corresponding to 60 mV per decade.⁶⁵ However, the fitting parameter α_σ takes values < 1 (Table S1) corresponding to a variation of ~ 70 – 100 mV per decade, which is inconsistent with the predicted value. Hence, the multiple trapping model predicts the correct potential dependence, but not with the correct slope. However, it must be taken into account that the multiple trapping model is based on the ideal situation of non-interacting electrons. Departures from non-ideality may take place, specially at high electrons concentrations or low values of the dielectric constant.^66–68

The multiple trapping model furthermore predicts – as a consequence of trap saturation – a constant diffusion coefficient once the Fermi level approaches the conduction band. The direct experimental determination of this value will be prevented by band edge shifts (i.e. band unpinning) once the film approaches a quasi-metallic state.⁵² Indeed, conductivity saturation was observed in a previous study and attributed to band unpinning.³⁸ Such conductivity saturation is observed independent from sintering temperature also in the present study (Figure 7a), however, capacitive currents (Figure 7b) allow to exclude band unpinning as the main reason for such a behavior. More concretely, we observe that the conductivity increase (Figure 7a) ceases once the narrow distribution corresponding to deep traps has been populated. While at more negative potentials conductivity remains virtually constant (Figure 7a) we still observe an exponentially increasing capacitive current (Figure 7b) corresponding to the filling of the exponential density of band gap states (Figure 7c). This observation is in line with a conduction band edge position E_Ag/AgCl ^~-0.7V ⁶⁰ and highlights the possibility of a homogeneous displacement of the semiconductor Fermi level with respect to the conduction band in the studied potential range (i.e. E_Ag/AgCl > -0.6V) and thus the absence of significant band unpinning.

While previous studies located transport-limiting traps in nanoparticle films mainly at the TiO₂ particle surface,^22,23 results of the present study point to a strong impact on electronic conductivity of a narrow distribution of deep traps, which is presumably located at particle-particle interfaces.^28,62,69 A qualitative interpretation of our results is schematized in Figure 7 (I-III) and is based on the following experimental results (Figure 7a-c): the potential-dependences (a) of the electronic conductivity, (b) of capacitive currents and (c) of the density of states (DOS) estimated therefrom. When the conducting substrate is polarized at potentials more positive than the onset potential for the population of grain boundary traps (i.e.E > E ₁) there is no equilibration between the Fermi level of the substrate and the Fermi level of the nanoparticle film. However, once the demarcation level is passed upon lowering the electrode potential, electrons are transferred from the conducting substrate to the semiconductor giving rise (i) to a steadily increasing capacitive current and (ii) to an increasing conductivity. The onset of the capacitive currents and of the conductivity increase is observed – independent from sintering temperature – once grain boundary traps start to be populated, i.e. at E = E ₁ (Figure 7 I → II), as evidenced by the capacitive peaks in the CVs. (Figure 7b). The population of these states lowers the interfacial resistance at the particle-particle contact⁷⁰ allowing for the population of exponentially distributed surface states all across the film and thus for the equilibration of the Fermi level of the mesoporous film with the Fermi level of the conductive substrate (the electrode potential) once all grain boundary traps are fully populated, i.e. at E = E ₂ (Figure 7 II). At potentials E < E ₂ the Fermi level in the semiconductor can be controlled via the electrode potential allowing for a progressive and homogeneous displacement of the Fermi level towards the conduction band throughout the mesoporous film. Accordingly, exponentially increasing capacitive currents resulting from the population of an exponential distribution of surface states (with a trap distribution parameter, α = 0.25 − 0.35) are observed. The progressive displacement of the Fermi level towards the conduction band will lead to a continuous increase of the concentration of free conduction band electrons. Surprisingly, conductivity data clearly highlight an almost invariant maximum conductivity σ(E ₂) = σ_max at potentials E < E ₂ i.e. once all grain boundary traps are filled. The observation of an invariant conductivity in spite of an increasing concentration of free conduction band electrons clearly points to the limitation of charge transport in the mesoporous films by inter-particle charge transfer (Figure 7 II). Importantly, the potential E ₂ at which the maximum conductivity σ(E ₂) = σ_max is reached depends on the energy of the grain boundary trap states and thus on sintering temperature.

The relative energetic position between deep traps at the grain boundary and exponentially distributed surface traps (Figure 7c) determines, furthermore, the behavior of the films upon electrochemical charge extraction. Once the electrode potential is stepped back to a sufficiently positive potential E > E ₁, electrons populating the exponential distribution of surface states can be fully extracted only from those electrodes, where grain boundary traps are energetically located at or below the distribution of surface states (i.e. electrodes sintered at high temperatures, Figure 7c). In this case electron transport across the particle-particle interface can be sustained until all surface traps are depopulated. However, if the grain boundary traps lie energetically within the exponential distribution of surface traps (as in the case of electrodes sintered at low temperatures, Figure 7c), one fraction of the electrons trapped in surface states – namely electrons populating the deepest traps – will remain in the film due to the fact that electron transport across the particle-particle interface ceases once all grain boundary traps are depopulated. Accordingly, for these electrodes the conduction band will be more strongly populated than prior to charge accumulation / extraction giving rise to an increased σ’ (E ₁ > E ₁ conductivity (Figure 7 III) as observed in the corresponding conductivity profiles (Figure 4a).

Finally, our conclusions concerning the strong impact of grain boundary traps on electron dynamics in nanoparticle films are qualitatively in line with previous experimental studies on structurally and compositionally less defined systems. Increased diffusion coefficients and diffusion lengths in TiO₂ nanoparticle-based photoanodes were observed when the annealing temperature of the films was increased from 150 °C to 450 °C.⁷¹ An up to 6-fold increase of the diffusion coefficient was attributed to a change of the charge-trap density at the grain boundaries and to neck growth between particles. Using cyclic voltammetry a narrow distribution of deep trap states located at particle-particle interfaces was detected and the contribution of the traps to the slow-down of transport and to the acceleration of recombination of photogenerated charges was demonstrated.^47,49,62,69 In the absence of surface recombination, a clear correlation between the population of these deep trap states and the photocurrent rise time was observed.⁶² In the potential range where deep traps were fully depopulated, slow photocurrent responses could be associated with the rate of the filling of deep trap levels. A combination of quantum chemical calculations and kinetic Monte Carlo simulations allowed to rationalize the corresponding trap filling mechanism.²⁸ Perturbations in electrostatic potential at grain boundaries give rise to high concentrations of strong electron trapping sites, which hamper electron transport between the TiO₂ particles. Consequently, electron transit times across the boundary were found to be up to five orders of magnitude slower than in the bulk crystal as electrons trapped in Ti sites at the grain boundary face a high activation barrier to escape. However, upon occupation of the deepest traps the average trapping time of electrons decreases as they can follow alternative diffusion paths characterized by lower activation energies. This gives rise to a reduction of the transit time by up to five orders of magnitude.²⁸ An electrochemical way to induce such a trap filling effect consists in the (reversible) bias-induced charge accumulation as exploited in the present study, a chemical way would be the introduction of n-type dopants providing excess electrons to fill deep trap states. A special case is the decoration of grain boundaries by hydrogen. In this context it was shown in a combined electrochemical and quantum chemical study that the energetics of deep traps at grain boundaries can be modified via an (transient) electrochemical doping (i.e. the incorporation of electron / proton pairs), leading to a reduction in trap concentration, a modification of electron trapping properties and, consequently, a large enhancement of photoelectrode performance.³⁰ In the present study we clearly demonstrate that nanoparticle sintering constitutes an alternative way to modify the energy and – possibly – the concentration of trap states located at particle-particle interfaces, which significantly impacts the macroscopic film conductivity. The corresponding impact on the photochemical and the photoelectrochemical performance of the electrodes will be addressed in an upcoming study.

In a more general vein, this study highlights the capability of electrochemical methods for tracking dynamic processes in nanoparticle-based films in situ. In addition, reliable structure-property relationships can be established for these inherently complex systems by a comprehensive electrochemical approach if structurally and compositionally well-defined model systems are available.

5. Conclusions

Using random networks of anatase TiO₂ nanocrystals as model systems for conductivity studies we have reached the following conclusions:

• (i)Thermal annealing in the temperature range 100 °C ≤ T ≤ 450 °C does not induce significant changes of particle size, crystallite domain size, specific surface area and electrochemically active surface area of the investigated nanoparticle electrodes.
• (ii)Thermal annealing in this temperature range results in the significant modification of the distribution of electrochemically active states as determined by cyclic voltammetry or impedance spectroscopy. While an exponential distribution of surface states remains invariant, we observe a positive shift on the potential scale of capacitive peaks attributed to deep trap states at the particle-particle interface (i.e. at grain boundaries).
• (iii)Population of the grain boundary traps leads to an increase of the electronic conductivity by up to 5 orders of magnitude. The onset potential of the conductivity increase shifts positive upon increasing annealing temperature in line with the displacement of the pair of capacitive peaks associated with deep trap states. The electronic conductivity approaches a constant plateau once all grain boundary traps have been populated (i.e. at sufficiently negative potentials). This maximum conductivity does not depend on thermal annealing temperature.
• (iv)Once all grain boundary traps are filled an exponentially increasing capacitive current is observed upon scanning the electrode potential further in the negative direction. This current is associated with the population of an exponential distribution of surface states in the absence of significant band unpinning. The progressive displacement of the Fermi level towards the conduction band leads to a continuous increase of the concentration of free conduction band electrons. The observation of an invariant conductivity in spite of an increasing concentration of free conduction band electrons clearly points to the limitation of charge transport in the mesoporous films by inter-particle charge transfer even at negative potentials.

Supplementary Material

X-ray diffraction patterns, the equivalent circuit used for fitting impedance spectra, scanning electron micrographs of anatase TiO₂ nanoparticle electrodes, schematic representations of the coplanar configuration based on interdigitated gold electrodes, cyclic voltammograms of an anatase TiO₂film deposited on interdigitated gold electrodes, current transients and additional data extracted from impedance measurements. This material is available free of charge via the Internet at http://pubs.acs.org.