Doping of TiO₂ for sensitized solar cells

Abstract

This review gives a detailed summary and evaluation of the use of TiO₂ doping to improve the performance of dye sensitized solar cells. Doping has a major effect on the band structure and trap states of TiO₂, which in turn affect important properties such as the conduction band energy, charge transport, recombination and collection. The defect states of TiO₂ are highly dependent on the synthesis method and thus the effect of doping may vary for different synthesis techniques, making it difficult to compare the suitability of different dopants. High-throughput methods may be employed to achieve a rough prediction on the suitability of dopants for a specific synthesis method. It was however found that nearly every employed dopant can be used to increase device performance, indicating that the improvement is not so much caused by the dopant itself, as by the defects it eliminates from TiO₂. Furthermore, with the field shifting from dye sensitized solar cells to perovskite solar cells, the role doping can play to further advance this emerging field is also discussed.

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Bart Roose

Bart Roose graduated in chemistry from the Radboud University Nijmegen in 2013. He then went on with his doctoral research in the group of Prof. Ullrich Steiner at the University of Cambridge and the Adolphe Merkle Institute in Fribourg, Switzerland. His research interests include nanostructured metal oxides, doping of metal oxides and sensitized solar cells.

Sandeep Pathak

Sandeep Pathak gained his PhD at the University of Cambridge, UK in 2011, working on High Temperature Superconductors with Prof. David Cardwell. He spent two years at the Clarendon Laboratory (University of Oxford, UK) with Prof. Henry Snaith as a post doc working on Dye-Sensitized Solar Cells. He then joined Prof. Ullrich Steiner at Cavendish Laboratory (University of Cambridge, UK) and continued to work on photovoltaic devices as research associate. He moved back to Clarendon Laboratory (Oxford University, UK) to work with Prof. Henry Snaith, as a senior research associate in October 2013 and since then his research activities remained focussed on the perovskite solar cells. His current research work predominantly involves development of new material structures for perovskite solar cells. Subsequently, understanding their photo-physical properties and controlling the physical processes occurring at the electronic interfaces.

Ullrich Steiner

Ullrich (Ulli) Steiner studied physics at the University of Konstanz, Germany. He gained his PhD in 1993, working with Prof. J Klein and Prof. G. Schatz at the Weizmann Institute, Israel. After post-doc positions at the Weizmann Institute and the Institute Charles Sadron, France, he returned to Konstanz where he finished his Habilitation in 1998. He joined the faculty of the University of Groningen as full professor in 1999 and became the John Humphrey Plummer Professor of Physics of Materials at the University of Cambridge in 2004. Since 2014, he holds the chair of Soft Matter Physics at the Adolphe Merkle Institute in Switzerland.

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1 Introduction

To keep up with the future demand for energy it will be necessary to deploy clean, renewable sources on a massive scale.^1,2 One promising option is the large scale application of photovoltaic devices, which generate electricity directly from sun light.³ This has so far been limited because of the high cost associated with the production of these devices.^2,4,5 In the last decades many new photovoltaic technologies have been developed, promising low cost, high-throughput processing which will pave the way to affordable renewable energy.^1,2,5,6 One of the leading candidates is the dye sensitized solar cell (DSSC),^7–9 in particular the perovskite-based solar cell, which is closely related to devices employing organic dyes.^10–13 Perovskite solar cells currently have a NREL certified record efficiency of more than 20%,⁶ with a marked upward trend. This is in the efficiency range needed for commercially viable applications.¹⁴

Major challenges remain however in scaling up the fabrication from the laboratory to industrial production,^15,16 addressing toxicity issues,^17–19 reducing hysteresis^17,20,21 and in particular regarding the achievement of sufficiently high device lifetimes.^13,20 The control over the device properties and how they can be reliably achieved requires a better understanding of the underlying chemistry and physics. Ever since the first report of DSSCs, best performing devices have relied on titanium dioxide (TiO₂) as nanostructured electron transporting layer and/or hole blocking layer.^22,23 Extensive research has been done to control the morphology of the TiO₂ with the aim of maximizing the dye–TiO₂ interface area and light absorption.^24–26 With the recent optimization of dyes, hole-conductors and device architectures the focus has shifted to controlling the electronic properties of TiO₂. Mesoporous TiO₂ is full of lattice defects that arise during synthesis, resulting in a multitude of electronic sub-band gap states that are able to trap charges.^8,9

Here we discuss how these defects affect the electronic properties of TiO₂ and how they can be influenced by doping, that is by deliberately introducing impurities into TiO₂. In photocatalytic materials this is a well known method to increase the spectral response and promote the separation of charges.^27–29 From these studies it is evident that not only the type of dopant is important but also where the dopant is situated in the TiO₂-lattice. Another way to control recombination processes is to cover TiO₂ with a thin layer of insulating oxide,³⁰ this is however outside the scope of this review.

First the general working principle of DSSCs and the properties of TiO₂ are elucidated. This is followed by a detailed overview of results that have been achieved so far using different dopants and doping techniques. Then, we assess what can be learned from these doping studies and how doping can be implemented to achieve better performance in perovskite solar cells. Finally, the tools that can be used to investigate the (electronic) properties of TiO₂ and the effects of doping are summarized.

2 Working principle of DSSCs

The first working example of a DSSC was reported by O'Regan and Grätzel in 1991.⁷ The same device architecture is still employed today and consists of the following components (top to bottom of Fig. 1a):

Fig. 1 (a) Schematic of DSSC device architecture, consisting of (top to bottom): transparent conducting oxide (TCO) coated glass; continuous metal oxide hole blocking layer (HBL); electron conductor coated with dye; liquid electrolyte or solid-state hole transporting material (HTM); metal back electrode. Upon the absorption of light, electrons and holes are created, which are transported through the respective transporting materials to the electrodes. (b) Charge transport in a DSSC: upon absorption of light by the dye, an electron is excited from the HOMO to the LUMO, injected into the CB of the electron conductor (TiO₂) and transported to the TCO electrode. The dye is regenerated by oxidation of iodide to tri-iodide. In the case of a sold-state HTM, the hole is transported through the HTM to the electrode.

• Transparent conducting oxide (TCO) coated glass. Typical TCOs are tin-doped indium oxide (ITO) and fluorine-doped tin oxide (FTO).

• Hole blocking layer (HBL), a continuous layer of a metal oxide that prevents holes from reaching the TCO, shorting the device.

• Electron transporting material consisting of a mesoporous metal oxide, which is usually TiO₂. Several other metal oxides such as SnO₂,³¹ ZnO^32,33 and SrTiO₃³⁴ have also been explored, but none of them perform as well as TiO₂.

• Dye adsorbed to the mesoporous metal oxide, which is responsible for absorbing light. Because the adsorbed dye usually consists of only a monolayer, a several micrometer thick mesoporous layer is needed to provide sufficient surface area to absorb most of the light.

• Liquid electrolyte or solid-state hole transporting material (HTM), which is infiltrated into the mesoporous layer. Liquid electrolytes often contain the iodide/triiodide redox couple. A problem using liquid electrolytes is the possible leakage of the corrosive fluid. Solid-state HTMs do not suffer from this problem but feature lower device efficiencies. A typical HTM is 2,2′,7,7′-tetrakis(N,N′-di-p-methoxyphenylamine)-9,9′-spirobifluorene (spiro-OMeTAD).

• Back contact consisting of a metal electrode.

When the device is illuminated the dye is excited, promoting electrons from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). This excited state injects electrons into the conduction band (CB) of TiO₂, which diffuse through the mesoporous scaffold to the TCO. The holes are transferred from the HOMO of the dye to the HTM and from there to the back electrode (Fig. 1b).

The three important quantities governing the efficiency of a solar cell are the short circuit current J_SC, the open circuit voltage V_OC and the fill factor FF. J_SC is the current through the device in the absence of a net voltage, that is for a short-circuited device. It is highly dependent on light absorption and charge collection efficiency. V_OC is the voltage across the device in the absence of a net current. It depends on the energy difference between the Fermi levels (E_F) of the TiO₂ CB and HTM valence band (VB) or HOMO, and on recombination processes. The fill factor quantifies the power that can be delivered by the device. It is defined by dividing the maximum power output by J_SC × V_OC. Its magnitude depends on series and shunt resistances in the device. A low series resistance and high shunt resistance minimize internal losses, thereby maximizing the power output of the device.

To obtain maximum efficiencies, it is important to match the CB of TiO₂ to the LUMO of the dye so that the potential difference is sufficiently large for electron injection, while keeping the difference between the CB of TiO₂ and the VB of the HTM as large as possible to maximize V_OC.

3 TiO₂

The large band gap, suitable band edge levels for charge injection and extraction, the long lifetime of excited electrons, exceptional resistance to photo corrosion, non-toxicity and low cost have made TiO₂ a popular material for solar energy applications.^27–29

TiO₂ occurs naturally in three crystalline forms; anatase (tetragonal), rutile (tetragonal) and brookite (orthorhombic). For DSSCs, anatase is the most commonly used phase due to its superior charge transport. The tetragonal anatase crystal structure is made up of a chain of distorted TiO₆ octahedrons, which results in a unit cell containing four Ti atoms (at positions [0,0,0], [½,½,½], [0,½,¼] and [½,0,¾]) and eight O atoms^26,35,36 (Fig. 2).

Fig. 2 The anatase unit cell; titanium atoms are grey, oxygen atoms are red. Oxygen atoms form a distorted octahedron with a titanium atom at the center, which is clearly illustrated for the central titanium atom.

TiO₂ prepared by sol–gel processes is amorphous and annealing at elevated temperatures is required to achieve the desired crystal structure. The crystallization temperature is limited by the anatase–rutile transition. Since rutile is the thermodynamically most stable polymorph of TiO₂ at all temperatures, the anatase to rutile transition temperature depends sensitively on preparation conditions. Because of their different band structures, mixed phases of anatase and rutile generally cause the trapping of charge carriers and promote recombination processes. They are mostly undesirable in DSSC electrodes, although there are some studies suggesting a small amount of rutile nanoparticles can enhance device performance.^37–39 DSSCs employing rutile TiO₂ generally suffer from a lower CB compared to anatase, leading to a lower V_OC. In addition, reduced dye adsorption and charge transport lower the obtainable J_SC.^40–42 Because of these complications, rutile is not frequently used in DSSCs, although there are some examples which are discussed in Section 4.^43,44

The band gap of n-type semiconducting single-crystal anatase TiO₂ is approximately 3.2 eV and the resistivity is 10¹⁵ Ω cm.⁴⁵ The lower edge of the CB is made up of vacant Ti⁴⁺ 3d bands and the upper edge of the VB is made up of filled O²⁻ 2p bands.⁴⁶ Bulk oxygen vacancies, titanium interstitials and reduced crystal surfaces generate shallow electron traps that can enhance the conductivity of TiO₂. Of particular interest here is the occurrence of Ti³⁺ species, which form a band roughly 0.5 eV below the TiO₂ CB. These defects act as n-type dopants, increasing the number of free electrons in the TiO₂ and hence the conductivity and current. At the same time defects can act as charge traps and are therefore recombination centers, having a negative effect on device performance.^45,47

The number of defects can be influenced by moderately heating the device or by placing it in an inert atmosphere.⁴⁸ Furthermore, it was discovered that the number of traps can be reversibly changed by oxygen exposure or deprivation, indicating oxygen can adsorb onto TiO₂ defects and by doing so passivate trap states. A further remarkable observation is that UV irradiation causes the desorption of oxygen from these defects. Under exposure to air, oxygen release is counterbalanced by oxygen adsorption from the atmosphere. DSSCs are however typically protected from moisture and dye degradation by air-free encapsulation. The lack of oxygen inside the encapsulated device upsets the desorption–adsorption balance, leading to an increase in trap states and deterioration of device properties. This again is reversible upon breaking the seal and exposure to oxygen.^49–51

Because of its many defects and the resulting sub-band gap states in TiO₂, electron transport is complex and hard to investigate. In devices, this is particularly difficult because parameters relating to one device property can not be studied individually without significantly changing other material properties. There is however strong theoretical and experimental evidence indicating that charge transport in TiO₂ proceeds by detrapping from sub-band gap states. These states lie deep in the tail of the density of states (DOS), from which electrons can be detrapped into the CB, according to the multiple-trapping model for charge transport.⁸ The occupation of sub-band gap states at energy E_A can be found through the Fermi–Dirac distribution function

and the density of carriers at the energy E_A is n_A = N_AF_A, where N_A is the total number of available trap sites at this energy. From this, the density of electrons in the CB (n_CB) can be derived as a function of the position of the quasi-Fermi level for electrons (E_Fn),

n_CB = N_CBe^{(E_Fn−E_CB)/k_BT} (2)

Considering electron transport takes place only in the CB, the conductivity of the film is given by

σ = n_CBeμ, (3)

where μ is the electron mobility. Generally, a higher TiO₂ conductivity means a higher current output from the device. From the equations above it is apparent that the conductivity of the film is determined by the probability of the electrons being in the CB, which increases as the quasi-Fermi level approaches the CB. This means that any modification that eliminates deep trap states will increase the conductivity of the film.⁸

To be able to effectively modify the trap states it is important to know where the traps are located. Different studies have suggested traps are located either in the bulk,⁵² at inter-particle grain boundaries⁵³ or at the surface of the particles.^54,55 Bulk defects do not seem to play a major role⁵⁶ and it should be noted that charge recombination is an interfacial process.⁵⁷ But because of the difficulty to experimentally distinguish between boundary or surface defects it is still unclear were exactly the traps are located⁸ and it can not be excluded that both traps at the grain boundaries and at the TiO₂ surface play an equally important role. Furthermore the synthesis method heavily affects defect locations and type. This makes it difficult to effectively modify the TiO₂ structure. It is understood that weakly reducing synthesis conditions and low annealing temperatures favor the formation of oxygen vacancies, whereas more reducing synthesis conditions and high annealing temperatures favor titanium interstitials as main defects.^26,45

This combination of factors leads to the complex situation where shallow traps are essential for charge transport and can actually improve conductivity, but at the same time, deep traps lower the quasi-Fermi level and decrease conductivity. The voltage of the device, which is defined as the energy difference between the quasi-Fermi levels of TiO₂ and the HTM, is also affected by the trap states, with less deep traps resulting in a higher open circuit voltage. Furthermore, traps can act as recombination sites for electrons and holes,²⁶ which leads to a decrease in both current and voltage.

At the interface between TiO₂ and the HTM, band bending occurs due to the formation of a space charge region, implying that the CB in the bulk and at the surface do not have the same energy. The space charge region provides an electric field that separates electrons and holes. An external voltage can cancel out band bending and eliminate the space charge region. This specific voltage is called the flat-band potential V_FB.⁵⁸ Because trap states are predominantly located on the TiO₂ surface they have a large influence on V_FB and thereby on the separation efficiency of electrons and holes. When V_FB is negatively shifted (indicating an upward shift of the conduction band and the Fermi level), the injection of electrons from the dye into TiO₂ will become less efficient and a loss in current occurs. The reverse is also true and some defects make injection more efficient by positively shifting V_FB, causing a downward shift of the conduction band and Fermi level. With so many interconnected processes it is clear that devising a method to improve the electronic properties of TiO₂ is not trivial.

TiO₂ nanostructures for DSSCs can be synthesized in several ways, the most common methods discussed in this review are:

• Sol–gel synthesis. The sol–gel method is a versatile process that can be employed to make nanoparticles of ceramic materials. A colloidal suspension (sol) is made by hydrolyzing and polymerizing metal oxide precursors. The precursor typically is an inorganic metal salt or a metal organic compound. Frequently used precursors for TiO₂ are titanium tetrachloride (TiCl₄) and titanium isopropoxide (TTIP). When the polymerization is complete and the solvent has evaporated, the sol forms a gel. Heat treatment will transform the gel into the desired TiO₂ nanoparticle.²⁶

• Hydrothermal synthesis. For the hydrothermal method a titanium precursor (TTIP) is mixed with water and a peptizer (HNO₃) after which the mixture is treated in an autoclave at elevated temperatures and pressures. After autoclaving the mixture is calcined to obtain TiO₂ nanoparticles.²⁶

• Solvothermal synthesis. The solvothermal method is similar to the hydrothermal method, with the exception that the used solvent is non-aqueous. By choosing high boiling point solvents it is possible to achieve much higher temperatures, increasing the control over the particle formation.²⁶

• Flame spray pyrolysis. For flame spray pyrolysis (FSP) titanium precursor is dissolved in a solvent to generate a source solution. This solution is vaporized using a spray nozzle onto a substrate which is kept at elevated temperatures (300–500 °C). During spraying the solvent evaporates due to the elevated temperature and nanoparticles are formed.⁵⁹

• Anodization. TiO₂ nanotubes can be grown directly from titanium metal by applying a potential to a metal foil in a fluoride containing electrolyte solution. The tube length and diameter can be controlled through the anodization time and potential, electrolyte composition and pH. The amorphous nanotubes are then annealed at elevated temperatures to achieve crystalline TiO₂ nanotubes.^25,26,60

• Micelle method. With the help of surfactants, micelles of TiO₂ precursor are formed in solution. Upon heat treatment these are converted to TiO₂ nanoparticles.²⁶

• Direct oxidation. Titanium can be treated with oxidising agents to yield TiO₂ nanostructures,⁶¹ similar to anodization.

• Sonochemical synthesis. Applying ultrasound to a solution can cause intense local heating, high pressures and enormous heating and cooling rates. This can be used to synthesize TiO₂ nanoparticles with high aspect ratios.^26,62

• Microwave synthesis. Electromagnetic radiation can be used to heat up dielectrics to form nanostructures. A major advantage is the fast processing times due to the rapid heat transfer.⁶³

• Electrospinning. An electrical charge is used to draw fibres from a solution, resulting in TiO₂ nanostructures with high aspect ratios.⁶⁴

Compact TiO₂ films for electron blocking layers are synthesized through the following methods:

• Spin coating. A solution of TiO₂ precursor is spin coated on a substrate to form a thin layer of compact TiO₂.⁶⁵

• Spray pyrolysis. This method is similar to that described for the synthesis of TiO₂ nanoparticles, with the exception that the particles form a dense layer on the substrate.⁶⁶

• Atomic layer deposition. A substrate is alternatingly exposed to a TiO₂ precursor and H₂O, resulting in the deposition of atomically thick layers. The thickness of the layer can accurately be controlled through the number of cycles.⁶⁷

• Thermal oxidation. A thin layer of titanium is deposited by sputtering or evaporation and subsequently heated to high temperatures in the presence of oxygen to oxidize the film which forms a compact TiO₂ layer.⁶⁸

• Electrochemical deposition. A compact layer of TiO₂ can be deposited from a TiO₂ precursor solution by electrochemical deposition. The layer is subsequently crystallized by heating.⁶⁹

• Pulsed laser deposition. For pulsed laser deposition a TiO₂ precursor is pressed to form a disk which is used as a laser target. The laser vaporizes the target and the vapor condenses on the substrate forming a thin layer.^70,71

4 Doping

An effective way of modifying the electronic properties of TiO₂ is doping,⁷² the deliberate insertion of impurities into the TiO₂-lattice. In silicon solar cells, doping is a frequently used method to improve conductivity. Here the effect can mainly be ascribed to the increase in free charges and thus conductivity, by the donation of electrons for dopants with a valency higher than that of the native material (n-type doping), or holes for dopants with a lower valency (p-type doping). In the case of TiO₂ the mechanism is much more complicated due to the defect ridden nature of TiO₂ and doping mainly affects the trap states and electronic structure of TiO₂, which is illustrated by the improvements that are made by doping with elements of equal valency as the host TiO₂ ions.⁷³ Doping can be achieved by either replacing the Ti⁴⁺ cation or the O²⁻ anion. Cationic dopants are typically metals, whereas anionic dopants are non-metals. Since the lower edge of the CB is made up of Ti⁴⁺ 3d bands, replacing Ti⁴⁺ by a different cation is thus expected to heavily affect the CB structure. The upper edge of the VB consists of O²⁻ 2p bands and replacing O²⁻ by a different anion affects the VB energy.

The atomic radius of the dopant should not differ much from the ion it replaces to prevent lattice distortion, introducing new defects that may hamper device performance.

Because dye molecules anchor to Ti atoms,⁷⁴ the replacement of Ti with another cation also affects dye adsorption due to different binding strengths between the dye and the dopant, or because the dopant induces oxygen vacancies.⁷⁵ Dopants often inhibit the growth rate of the TiO₂ nanoparticles, resulting in smaller particles.⁷⁶ This is in many cases beneficial since assemblies made from smaller particles have a larger surface area per volume of mesoporous TiO₂ compared to large particle assemblies. The increased surface area accommodates more dye, leading to higher light absorption and current densities. The main advantage of high light absorption is that thinner films can be used in photovoltaic devices, resulting in a reduction of recombination, which benefits both J_SC and V_OC.

Morphology is a further factor that influences the properties of TiO₂. One-dimensional structures such as nanotubes have superior charge transport over nanoparticle assemblies, but have less surface area and thus adsorb less dye.⁷⁷ This implies that one-dimensional structures will benefit more from dopants that increase dye adsorption, whereas nanoparticle assemblies will benefit more from doping that leads to increased charge transport. The dopant source can also influence the effectiveness of doping and it has been shown that organic sources lead to better performances than inorganic salts.⁷⁸ Furthermore, doping influences the anatase to rutile phase transition.⁷⁹ The above factors complicate the study of the effect of doping on the electronic properties of TiO₂ as it is hard to distinguish and quantify whether an improvement is caused by increased absorption or electronic effects.

The dopant can be introduced into the TiO₂-lattice in a number of ways:

• The most common method is simply mixing a dopant precursor with the TiO₂ precursor solution. This method can be employed in the sol–gel, hydrothermal, solvothermal, spray pyrolysis, atomic layer deposition, electrochemical deposition, sonochemical, microwave and electrospinning methods.³⁵

• For pulsed laser deposition a dopant precursor is mixed with the titanium precursor and pressed to form a disk that can be used as a target for the laser.^70,71

• By immersing the final TiO₂-structure into an electrolyte solution containing the dopant and applying a voltage to electrochemically dope the TiO₂.⁸⁰

• For anodization and thermal oxidation, a Ti-dopant alloy can be used.^25,60

The dopants can be grouped into separate categories that share common electronic configurations. These are (earth)alkali metals (Section 4.1), metalloids (Section 4.2), non-metals (Section 4.3), transition metals (Section 4.4), post-transition metals (Section 4.5) and lanthanides (Section 4.6).

In some cases co-doping with two or more dopants is applied to further increase device performance. Each dopant can separately enhance device properties.⁸¹ One dopant can reinforce the effect of the other dopant,⁸² or one dopant may counteract some of the detrimental effects caused by the other dopant.⁸³

4.1 (Earth)alkali metals

The outer electron shell of the metals in this group consists of s electrons which can be easily donated,⁸⁴ making these metals interesting cationic dopants for TiO₂. The earth-alkali metals that have been used for TiO₂ doping are lithium,^85,86 magnesium^87–90 and calcium.^91–93

4.1.1 Lithium. Using electrochemical impedance spectroscopy (EIS) and Hall effect measurements, it was found that Li⁺-doping increases conductivity and charge densities in TiO₂, resulting in an increased J_SC. Fourier transform infrared (FTIR) spectroscopy indicated Li⁺ is incorporated interstitially. It is suggested the observed V_OC increase arises from a negative V_FB shift, increasing E_F and CB (Fig. 3b).⁸⁵

Fig. 3 The effect of TiO₂ doping on the CB and E_F. The doping induced states are shown in red. (a) In pristine TiO₂, electrons are transported by ‘hopping’ from shallow trap to shallow trap until they reach the electrode. The shallow trap density will thus influence electron transport rate and J_SC. Deep traps can permanently trap electrons and act as recombination sites, affecting V_OC. Another important factor determining V_OC is E_F, as V_OC is defined as the difference between E_F of TiO₂ and the HTM. (b) Doping can decrease the deep trap density, resulting in an upward shift of E_F and thus an increase of V_OC. The elimination of deep traps retards recombination and boosts the V_OC even further. Because the CB is shifted towards the LUMO of the absorber, the driving force for electron injection is lowered, in combination with a decreased trap density and the related electron transport, lowering J_SC. (c) When doping contributes to the formation of deep traps, the conduction band and E_F are shifted downwards. In combination with enhanced recombination through the deep trap states V_OC decreases. Because of the larger offset between the CB and the absorber LUMO, electron injection is improved and the higher trap density causes an increase in electron transport, resulting in an enhanced J_SC. Ideally, the dopant eliminates deep traps while introducing new states close to CB, enhancing both V_OC and J_SC through decreased recombination and increased electron transport.

To investigate the effect of particle size on doping, three different sized particles (22, 14 and 6 nm) were synthesized. In large particles bulk doping was dominant, while small particles exhibited mainly surface doping, as confirmed by X-ray diffraction (XRD). For the larger two particle sizes Li⁺-doping decreased device efficiencies, while efficiencies increased for the smallest particle size. The loss in efficiency is ascribed to the formation of Ti³⁺ species in the bulk that permanently trap electrons and decrease photocurrents. The enhanced efficiency for the smallest particle size is attributed to the Li⁺ ions at the surface acting as temporary electron traps, which increases the electron lifetime and reduces recombination (EIS). V_OC increases for all sizes caused by a band edge shift instigated by surface Li⁺ adsorption.⁸⁶ The fact that doped small particles yield less efficient devices compared to undoped large particles (generally a decrease in particle size results in an increase in dye adsorption and efficiency) is an indication that several factors are playing a role, not only Li⁺-doping. The large particles were obtained from commercial sources and contained substantial amounts of rutile, while the small particles were synthesized using a hydrothermal method and were pure anatase. This results in different TiO₂ particles that will not react similarly to doping.

In addition, Li⁺ ions from the electrolyte can adsorb onto and intercalate into TiO₂, resulting in a positive shift of the CB (Fig. 3c) and reduced recombination.^94,95

4.1.2 Magnesium. A high V_OC of up to 1.2 V was reached by doping TiO₂ with Mg²⁺.^87,88 A more detailed study showed Mg²⁺ is introduced substitutionally and decreases particle size. UV/Vis absorption spectroscopy showed a widening of the band gap indicating an upward shift of CB. This leads to an increase in V_OC, but because of decreased electron injection and lifetime J_SC is reduced.⁸⁹

Zn/Mg co-doped devices showed no effect on the optical band gap or V_OC. There is a positive shift in V_FB, indicating a lowering in E_F and CB (Fig. 3c), and an increase in recombination sites, which might be compensated by faster electron transport. The faster transport, in combination with enhanced electron injection due to the shift of CB resulted in a marked increase in J_SC.⁹⁰

4.1.3 Calcium. Doping TiO₂ with Ca²⁺ was shown to drastically improve J_SC, but this was accompanied by a loss in V_OC. Mott–Schottky plots showed a positive shift of V_FB (Fig. 3c) and an increased carrier density, which is associated with increased electron injection and higher J_SC, but at a loss in V_OC. Intensity-modulated photo current spectroscopy (IMPS) showed an increased electron mobility, which further increased J_SC.⁹¹ Other studies showed similar increases in J_SC. By using a low doping concentration V_OC was unaffected⁹² or even improved by reducing the recombination rate.⁹³

4.2 Metalloids

The elements that belong to the metalloid group have properties that lie between metals and non-metals, offering the possibility to combine the positive doping effects of metals and non-metals.⁹⁶ Metalloids regularly used for doping are boron,^97–100 silicon,¹⁰¹ germanium¹⁰² and antimony.^83,103

4.2.1 Boron. Scanning electron microscopy (SEM) and XRD showed an increase in TiO₂ crystallinity upon B³⁺-doping, which is beneficial for electron transport. X-ray photoelectron spectroscopy (XPS) indicated that B³⁺ is incorporated both substitutionally and interstitially. Interstitial doping has been reported to be accompanied by a blue shift of the UV/Vis absorption spectrum¹⁰⁴ and an increase in oxygen vacancies,¹⁰⁵ which was confirmed by UV/Vis and electron paramagnetic resonance (EPR) spectroscopy. EIS showed an increase in electron recombination, which compensates the negatively shifted V_FB (Fig. 3b) and leaves V_OC unchanged. J_SC is increased due to the increased electron transport.^97–99 Another study also reported improved crystallinity and interstitial doping for TiO₂ nanotubes. However, a red shifted absorption spectrum was also reported in this study and although recombination was retarded, a lower V_OC was observed. A shift in V_FB allowed for better charge injection, which in combination with improved crystallinity led to increased J_SC.¹⁰⁰

4.2.2 Silicon. XRD showed increased crystallinity for Si⁴⁺ doped TiO₂, which should have a positive effect on electron transport and recombination.¹⁰¹

4.2.3 Germanium. XRD and gas absorption surface area analysis (BET) indicate a decrease in particle size and an increase in surface area upon Ge⁴⁺ doping of TiO₂, resulting in higher values of J_SC. V_FB shows a negative shift (Fig. 3b), which results in an increase in V_OC.¹⁰² Electron injection is probably reduced by this shift in V_FB, limiting J_SC.

4.2.4 Antimony. The introduction of Sb³⁺ into TiO₂ did not affect the particle size, as measured by XRD. UV/Vis absorption spectroscopy showed a small decrease in band gap and V_FB was shifted positively (Fig. 3c), resulting in a reduction of V_OC, which is in part compensated by reduced recombination. Despite a decrease in electron density and lifetime, the charge collection efficiency increased due to faster electron transport. Together with enhanced electron injection due to a lower V_FB, the faster electron transport resulted in increased J_SC.¹⁰³ This trend was confirmed by a second study, which also showed that the drop in V_OC can be compensated by co-doping with Cr³⁺, due to electron transfer from Sb to Cr, preventing the formation of oxygen vacancies and Ti³⁺ species.⁸³

4.3 Non-metals

Characteristic properties of non-metals are high ionization energies and high electro negativity. Because of these properties non-metals usually gain electrons when reacting with other compounds, forming covalent bonds. Among the non-metals are the only anionic dopants, which have a strong influence on the VB. Non-metal dopants are carbon,^99,106,107 nitrogen,^{82,98,99,107–143} fluorine,^{99,141,144–147} sulphur^{82,118,120,128} and iodine.¹⁴⁸

4.3.1 Carbon. Carbon was mainly incorporated interstitially, as measured by XPS, and resulted in a red shift in the UV/Vis spectrum. This is indicative of narrowing of the band gap, resulting in an increase in J_SC.¹⁰⁶ IMPS and intensity-modulated photovoltage spectroscopy (IMVS) showed increased transport rates and electron lifetimes, further contributing to increased values of J_SC and V_OC.^99,107

4.3.2 Nitrogen. Nitrogen doping usually causes a red shift of the absorption band edge^82,108–119 instigated by a positive shift of V_FB (Fig. 3c), which improves electron injection.¹²⁰ Increased dye adsorption resulted in higher J_SC values. XPS studies showed that N³⁻ was introduced both substitutionally (replacing oxygen) and interstitially,¹²¹ which was confirmed by EPR.¹²² The introduction of N³⁻ distorts the lattice and was reported to lower charge transport.^123,124 Most studies have however report increased charge transport rates^{107,125–132} and/or longer lifetimes,^99,133–143 leading to an increase in J_SC and V_OC.

Negative shifts in V_FB (Fig. 3b) have been reported for Boron co-doped TiO₂, in combination with retarded recombination leading to a marked increase in V_OC.^98,99

4.3.3 Fluorine. Fluorine-doping reduced the interfacial resistance between the TiO₂ blocking layer and FTO, significantly improving J_SC.¹⁴⁴ In mesoporous TiO₂ a decreased defect density was found, while crystallinity increased and the formation of brookite was inhibited. Improved crystallinity led to an increase in J_SC.¹⁴⁵I–V curves in the dark showed a decrease in parasitic resistances, leading to a marked increase in FF. EIS showed prolonged electron lifetimes, indicating that recombination was retarded, resulting in an increase in V_OC.^99,146,147 Co-doping with Nb⁵⁺, Sn⁴⁺, Sb³⁺ or Ta⁵⁺ resulted in a further increase in electron transport and decrease in recombination.¹⁴⁷ A positive shift of V_FB (Fig. 3c) was reported to enhance electron injection while recombination was reduced.¹⁴¹

4.3.4 Sulphur. Sulphur is often used as a co-dopant for N-doping to further decrease the band gap energy and increase light absorption.^{82,118,120,128}

4.3.5 Iodine. Doping of TiO₂ with I⁵⁺ can enhance light absorption and decrease recombination.^149,150 Dye adsorption studies showed that the amount of adsorbed dye is not significantly changed. UV/Vis spectroscopy showed a distinct absorption red shift upon doping, indicating a decrease in the band gap energy. This leads to more efficient electron injection and higher J_SC. EIS evidenced a decreased recombination rate, resulting in a higher V_OC.¹⁴⁸ DFT calculations predict that I⁵⁺ doping can improve conductivity, V_OC and light absorption.¹⁵¹

4.4 Transition metals

The incorporation of transition metals into TiO₂ gives rise to the formation of a wide range of new energy levels close to the CB arising from their partially filled d-orbitals. This makes transition metals suitable materials to tune the CB structure. The transition metals discussed here are scandium,¹⁵² vanadium,^153–155 chromium,^83,156–159 manganese,^160–162 iron,^163,164 cobalt,^160,162 nickel,^165–167 copper,^162,168,169 zinc,^{90,126,130,161,170–178} yttrium,^179–181 zirconium,^{102,140,182–184} niobium,^{44,60,70,71,102,154,185–191} molybdenum,¹⁶⁶ silver,¹⁹² tantalum^{43,59,154,193–197} and tungsten.^{64,81,174,198–202}

4.4.1 Scandium. Sc³⁺ is an interesting dopant because of its similar size compared to Ti⁴⁺. It creates a ‘solid solution’, where Sc³⁺ embedding gives rise to defect sites. Synchrotron scattering measurements showed substitutional incorporation of Sc³⁺ with a minimal distortion of the TiO₂-lattice. BET and pore size and volume analysis (BJH) showed surface area and porosity were not affected in the relevant concentration range and dye adsorption was unchanged. V_FB was shifted negatively (Fig. 3b), which was confirmed by widening of the band gap. This should result in a V_OC increase, but lower J_SC through reduction of electron injection. A lowering of V_OC was however observed, possibly due to an increase in series resistance. Carrier density and transport rate decreased, but electron lifetime increased, resulting in an increase in J_SC.¹⁵²

4.4.2 Vanadium. A gradient with decreasing V⁵⁺ doping was generated by the sequential deposition of differently doped TiO₂ nanoparticles, which enhanced electron transport. A gradual red shift in UV/Vis absorption spectra with increasing doping concentration indicated a positive shift in V_FB (Fig. 3c). In the used device architecture the layered structure formed a graded pathway along which electrons can be transferred to the electrode (Fig. 4). This led to an increase of the electron transfer rate and decreased recombination, leading to higher J_SC and V_OC.¹⁵³ The V_FB shift was also found in a different study through Mott–Schottky plots. IMPS and EIS showed an increase in transport rate which further enhanced J_SC.^154,155

Fig. 4 Schematic diagram of the energy levels for V-doped TiO₂ DSSCs, showing the gradient induced by the different V⁵⁺ doping levels. Reprinted with permission from ref. 153. Copyright 2011 American Chemical Society.

4.4.3 Chromium. Cr³⁺ doping of TiO₂ led to a clear red shift in the UV/Vis absorption spectrum, evidencing a decrease in band gap and VB shift, which resulted in a slightly lower value of V_OC. Although dye adsorption is not affected, Cr³⁺ doping seems to influence the TiO₂ crystal structure, as a clear rutile peak was detected in the XRD spectrum. EIS shows a decrease in charge transfer resistance and open-circuit voltage decay (OCVD), and an increase in electron lifetime, which led to higher values of J_SC. It was suggested that the reason for the better conductivity is an increase in free charges injected by Cr³⁺ doping.¹⁵⁶

For the high Cr³⁺ doping concentration of 3 at% rutile formation was inhibited, but some brookite formed instead, and the dye adsorption was increased. The optical band gap was decreased, increasing electron injection efficiency, at the expense of a V_OC reduction.¹⁵⁷ The exact role of mixed crystal phases remains poorly understood.

At very high Cr³⁺ doping concentrations of ∼10%, TiO₂ behaves as a p-type semiconductor, as confirmed by measuring the Hall effect. The introduction of Cr³⁺ into TiO₂ causes E_F to move towards the VB. This made it possible to construct a TiO₂ based p–n homojunction. Because of the diode like character, recombination is repressed, leading to an increase in J_SC and efficiency.^158,159

A high-throughput testing of dopants showed that Cr co-doped with Sb resulted in a massive increase in J_SC and a small decrease in V_OC. It is suggested that this is caused by an electron transfer from Sb to Cr, which prevents the formation of oxygen vacancies and Ti³⁺ species.⁸³

4.4.4 Manganese. It was shown that Mn²⁺ doping can reduce particle size (XRD) and increase surface area (BET), but because of a positive shift of V_FB (Fig. 3c) and the introduction of a large number of recombination sites due to a high doping concentration, V_OC, J_SC and efficiency decreased.¹⁶⁰ A separate study did not show a reduction in particle size. But because of the positive shift of V_FB, J_SC was enhanced, resulting in a slightly higher efficiency.^161,162

4.4.5 Iron. Fe³⁺-doping was reported to reduce the trap density and charge recombination, while improving dye adsorption, resulting in drastically improved values of J_SC.¹⁶³

At high concentrations (∼10%) of Fe³⁺, TiO₂ behaves as a p-type semiconductor. The introduction of Fe³⁺ into TiO₂ caused E_F to move towards the VB. This made it possible to construct a TiO₂ based p–n homojunction. Because of the diode like character, recombination was reduced.¹⁶⁴

4.4.6 Cobalt. Cobalt doping of TiO₂ was shown to drastically deteriorate DSSC performance due to the formation of sub-band gap states that reduce V_OC and act as recombination centres, as evidenced by UV/Vis absorption spectroscopy and EIS.^160,162 The used doping concentration in ref. 160 was however rather high at 12.6 at%. Doping at these high concentrations is likely to give rise to massive lattice distortions and accompanying defects. Low doping of 0.2 at% in ref. 162 showed a much more modest decrease in efficiency.

4.4.7 Nickel. Ni²⁺-doping was shown to enhance the crystallinity of electrospun TiO₂ nanowires, enhancing charge mobility. A Mott–Schottky plot showed a negative shift of V_FB (Fig. 3b), which in combination with reduced recombination leads to improved V_OC.¹⁶⁵

Separate studies found that Ni²⁺ doping decreased particle size, resulting in an increase in J_SC. The decreased band gap indicates a positive shift of V_FB (Fig. 3c). The V_OC loss was compensated by a reduced recombination rate.^166,167

4.4.8 Copper. Surface doping of TiO₂ with Cu²⁺ drastically increased both J_SC and V_OC. The increase in V_OC is caused by a negative shift of V_FB (Fig. 3b) due to the interaction of Cu²⁺ with defect states. OCVD showed that recombination was suppressed resulting in improved J_SC. Cu²⁺ doping also seems to improve the electron transfer from the dye to the electron conductor by providing an alternative route for electrons from the dye into TiO₂.¹⁶⁸

Other studies confirmed the negative shift of V_FB and showed a similar increase in V_OC. Despite an increase in adsorption, J_SC decreased drastically, caused by less efficient electron injection and a redox reaction of Cu with the electrolyte.^162,169

4.4.9 Zinc. Because of the similar ion sizes of Ti⁴⁺ and Zn²⁺, lattice distortion is small when inserting Zn²⁺ into the TiO₂-lattice, which was confirmed by XRD. Zn²⁺-doping was shown to increase both J_SC and V_OC.¹⁷⁰V_FB was negatively shifted (Fig. 3b), while recombination increased, resulting in a slight increase in V_OC. The electron density and transport rate were increased, leading to higher values of J_SC.^171,172 By reducing recombination and increasing surface area and dye adsorption a massive increase in efficiency could be achieved,^173,174 but the negative shift of V_FB can lead to severely decreased electron injection and J_SC.¹⁷⁵

In contrast, other studies reported a positively shifted V_FB (Fig. 3c) and reduced recombination, while electron densities and transport were increased as well.^{90,126,130,161,176,178} Zn²⁺ doping was also shown to inhibit the anatase–rutile phase transformation, increasing device performance.¹⁷⁷

The discrepancy in V_FB shift can be explained by the close proximity of the CB of ZnO and TiO₂.²⁰³ Slight variations in synthesis protocols might result in the Zn²⁺ impurity energies being either below or above the CB of TiO₂, resulting in a positive or negative shift of V_FB respectively.

4.4.10 Yttrium. Previous studies have shown that Y³⁺-doping does not affect the optical band gap,⁴¹ which suggests that J_SC could be improved without suffering a loss in V_OC. Mott–Schottky plots showed that Y³⁺-doping can negatively shift V_FB (Fig. 3b) leading to improved values of V_OC. In addition J_SC was significantly enhanced, which was attributed to up-conversion. Incident photon to current efficiency (IPCE) however showed an improvement for the entire optical spectrum which suggests additional effects play a role in improving J_SC.^179,180

In another study the interstitial incorporation of Y³⁺ into the TiO₂-lattice was confirmed by XRD. The surface area of mesoporous assemblies was slightly increased, increasing dye adsorption. Contrary to previous literature, UV/Vis absorption spectroscopy showed a marked decrease of the band gap and an increase in conductivity. Charge extraction measurements showed no change in trap density and the energy distribution below the CB. Photovoltage decay measurements showed an increase in electron lifetime, but this comes at a loss in the transport rate. The increase in V_OC seems to be a result of a reduction in recombination, compensating the positive V_FB shift (Fig. 3c). J_SC increased due to better electron injection and collection efficiencies. In addition, no TiCl₄ treatment of the TiO₂ scaffold was needed simplifying device manufacture.¹⁸¹

4.4.11 Zirconium. The CB of ZrO₂ is located ∼0.7 eV above the CB of TiO₂. From this it can be expected that doping TiO₂ with Zr⁴⁺ will shift the CB upwards.

Zr⁴⁺-doping proved to decrease particle size, resulting in an increased surface area of nanoparticle assemblies and dye adsorption. The band gap was indeed found to be increased, indicating a negative shift of V_FB (Fig. 3b). These factors contributed to increased values of J_SC and V_OC.¹⁸² Additional research found that the recombination rate was hardly affected and that the improved V_OC was purely caused by the CB shift.¹⁸³ Other studies reported much higher,^102,184 or lower recombination rates upon doping.¹⁴⁰

4.4.12 Niobium. Niobium is probably the most studied cationic dopant for TiO₂ in DSSCs because of promising optical and electronic properties.²⁰⁴ Even for this well studied system, there are some discrepancies between different reports, which indicates that the effect of the doping is strongly dependent on the type of defects induced by the TiO₂ synthesis method.

Initial attempts were not very successful as a positive shift of V_FB (Fig. 3c) and a decrease in dye adsorption led to poor device efficiencies,¹⁰² although charge mobility was increased.¹⁸⁵

In further studies a Nb⁵⁺ doped HBL deposited via pulsed laser deposition showed an increase in J_SC, but a minute loss in V_OC. EIS showed slightly more current leakage for the doped compact layer, leading to a lower V_OC. But in addition the resistivity between the HBL and mesoporous TiO₂ dropped, leading to more efficient electron transfer between the two layers and thus a higher J_SC.⁷⁰ Optimization of the deposition protocol prevented leakage and led to an increase in V_OC.⁷¹

A novel water soluble Nb⁵⁺-precursor made it possible to evenly distribute Nb⁵⁺ ions throughout anatase TiO₂, resulting in more efficient devices. XRD showed an increase in crystallite size, but dye adsorption remained largely unchanged, indicating that the particle size was not affected. This means there are less grain boundaries in the material, or the particles were bigger and Nb⁵⁺ increased the dye concentration,²⁰⁵ improving in both cases the conductivity of the material. UV/Vis absorption showed a decreased band gap and positively shifted V_FB, resulting in more efficient electron injection at the expense of a lower V_OC. EIS confirmed the drop in resistivity between TiO₂ particles and showed that doping reduced recombination, in part compensating the loss in V_OC by the shift of V_FB.¹⁸⁶ Another study showed a positive shift of V_FB by a Mott–Schottky plot and an increased transport rate by IMPS,¹⁵⁴ resulting in a lower V_OC but higher J_SC.

A similar trend was found for devices doped with 2.5 mol% Nb⁵⁺. Interestingly, V_OC increased for these low concentrations, caused by a decrease of oxygen vacancies and recombination. As the doping concentration increases, the CB is lowered, enhancing electron injection and J_SC.¹⁸⁷ EIS showed an increase in electron lifetime at low concentrations, but for higher doping concentrations shorter electron lifetimes were observed. This explains the observed V_OC trend. The transport rate was increased leading to a higher J_SC.¹⁸⁸ It was found that the drop in V_OC could be prevented by adding a hole conductor co-adsorbant, which drastically decreased recombination.¹⁸⁹

It also proved to be possible to prevent a loss in V_OC by lowering the doping concentration (<0.5 mol%). Smaller particles and a larger surface area led to increased dye adsorption. Charge extraction measurements showed a downward shift of the trap states, lowering the CB and V_OC. Transient studies showed longer electron lifetimes, but a lower transport rate, resulting in an overall higher charge collection efficiency. Reduced recombination compensated for the loss in V_OC due to the shifted CB, resulting in a device with better J_SC and V_OC, drastically improving efficiency.¹⁹⁰ Similar electronic properties were found for Nb⁵⁺ doped TiO₂ nanotubes⁶⁰ and rutile nanorods.⁴⁴

A recent study showed an increase in both J_SC and V_OC. A decrease in recombination was observed through EIS and transient photo current and is responsible for the improved V_OC.¹⁹¹

These results seem to suggest that it is only possible to improve J_SC without negatively affecting V_OC when the TiO₂ is relatively defect free. In low-defect TiO₂, a small amount of Nb⁵⁺ is needed to passivate oxygen defects and reduce recombination. This implies that only few Nb⁵⁺ sub-band gap states are formed and the effect of these states on V_OC is compensated by a reduction in recombination, while they increase J_SC by enhancing electron injection. For lower quality TiO₂ much higher doping concentrations are needed to reduce recombination and improve electron injection, resulting in more sub-band gap states, which lowers V_OC more than can be compensated through recombination suppression.

4.4.13 Molybdenum. Mo⁶⁺-doping proved to effectively decrease particle size (XRD) and band gap (UV/Vis absorption). Due to the increased surface area, an increase in J_SC was observed. Although a V_OC loss might be expected as a result of the smaller band gap, the reduced recombination rate resulted in a much enhanced V_OC.¹⁶⁶

4.4.14 Silver. Calculations have predicted that doping with Ag⁺ can heavily affect the optic and electronic properties of TiO₂.²⁰⁶ XRD evidenced the inhibition of rutile formation. Reduced charge transfer resistance due to enhanced charge transport results in higher J_SC. Increased charge lifetime indicates recombination is suppressed, resulting in higher V_OC (EIS).¹⁹²

4.4.15 Tantalum. XRD showed particle size was not affected by incorporation of Ta⁵⁺. V_FB was shifted positively (Fig. 3c), resulting in a lower V_OC but enhanced electron injection. The electron density and transport rate were also increased, leading to an improved J_SC.^{154,193–195} Interestingly, the opposite behaviour was found for Ta⁵⁺ doped rutile nanowires.⁴³ An explanation can be found in a different study where anodized Ta⁵⁺-doped TiO₂ nanotubes were annealed at 450 °C and 550 °C, inducing different defects and mixtures of crystal phases. The devices annealed at 450 °C showed characteristics similar to ref. 193, whereas the devices annealed at 550 °C contained a larger fraction of rutile and characteristics were more similar to ref. 43 suggesting the difference is largely caused by the rutile content.¹⁹⁷ The CB of rutile has been reported to be approximately 0.2 V lower than the CB of anatase.²⁰⁷ When Ta⁵⁺ induces defects in this 0.2 V wide range it will have opposite effects on the electronic properties. This is probably also true for anatase TiO₂ that is synthesized by different methods and as a result has a different distribution of defect states, varying the position of CB.

Other studies found both J_SC and V_OC were increased, which was attributed to increased dye adsorption,¹⁹⁶ Mott–Schottky plots showed a negative shift of V_FB (Fig. 3b). V_OC was further enhanced by suppressed recombination (EIS, IMVS).^59,197

4.4.16 Tungsten. XRD showed W⁶⁺ insertion results in smaller particles and thus mesoporous assemblies with bigger surface areas. An increase in J_SC was found, although dye adsorption was unchanged. The electron lifetime was greatly enhanced indicating a reduction in recombination.^81,174 A more detailed study shows a similar trend in device performance. V_FB was shown to be positively shifted (Fig. 3c), improving electron injection but at the cost of lowering V_OC. IMPS showed a decrease in electron diffusion, IMVS an increase in electron lifetime and thus a decrease in recombination, compensating for the lower CB.¹⁹⁸ This was further confirmed by DFT calculations,¹⁹⁹ EIS^200,201 and OCVD.²⁰²

One study reported a blue shift of the absorption band edge (UV/Vis absorption) for electrospun nanowires, indicating a negative shift in V_FB (Fig. 3b), which in combination with longer electron lifetimes led to a marked increase in V_OC. An increase in dye adsorption caused J_SC to improve as well.⁶⁴

4.5 Post-transition metals

In the periodic table the post-transition metals are located between the transition metals and the metalloids. As such, post-transition metals have some non-metal properties, showing covalent bonding effects. The investigated post-transition metals are aluminum,^{51,80,81,208–210} gallium,¹⁸¹ indium^83,211 and tin.^73,78,83,147

4.5.1 Aluminum. Aluminum is a group III metal with good optical quality, low resistivity and high conductance.²¹² This makes Al³⁺ an interesting candidate for doping.

In Al³⁺ doped TiO₂ improved values of V_OC were reported, with largely unaffected J_SC. XPS studies showed a decrease in Ti³⁺ defects, which was accompanied by a decrease in recombination. This resulted in a higher V_OC, but reduced J_SC. Higher dye loading in mesoporous Al³⁺-doped TiO₂ compensated this loss and photo currents for doped and undoped samples were comparable.⁸¹ The increase in V_OC might also be caused by a negative shift of V_FB (Fig. 3b) as was evidenced by UV/Vis absorption spectroscopy.²⁰⁸ A decrease in the number of trap states was also shown by photo-thermal deflection spectroscopy (PDS). Additionally it was shown that by decreasing the number of trap states the device is much less sensitive to UV instigated oxygen desorption, leading to significantly longer device lifetimes.⁵¹ Another study found that V_FB was slightly negatively shifted upon Al³⁺-doping due to an increase in trap density, but this was compensated by an increase in current caused by longer electron lifetimes. XPS studies showed no change in the Ti³⁺ concentration with Al³⁺-doping. In this study there is no clear evidence that Al³⁺ dopes into the TiO₂-lattice. It is more likely that islands of Al₂O₃ were formed on the TiO₂ surface, which may acts as a blocking layer, increasing electron lifetime.⁸⁰ For 20% Al³⁺ doped TiO₂ it was found that Al³⁺ substituted both into the TiO₂-lattice and formed a separate Al₂O₃ phase. Substitutional Al³⁺ eliminated deep traps by substituting Ti³⁺, resulting in a higher V_OC. A larger surface area of the mesoporous electrode and better charge injection resulted in a larger J_SC, while the Al₂O₃ phase acted as a blocking layer, preventing charge recombination.²⁰⁹

Al-doping was shown to inhibit the formation of rutile, leading to a decreased band gap and enhancing J_SC through improved electron injection. A larger surface area of the nanoparticle assembly and higher anatase content further improved J_SC. Reduced recombination rate partially compensated the loss in V_OC due to the band gap reduction.²¹⁰

4.5.2 Gallium. Previous studies have shown that Ga³⁺-doping does not affect the TiO₂ optical band gap,²¹³ which suggests that J_SC can be improved without suffering a loss in V_OC.

The incorporation of Ga³⁺ into the TiO₂-lattice was confirmed by XRD. A Rietveld analysis showed that Ga³⁺ substitutes Ti⁴⁺ in the TiO₂-lattice. The surface area and porosity of nanoporous electrodes were slightly increased, allowing an increase in dye adsorption. XPS showed an increase in oxygen vacancies upon Ga³⁺-doping. Despite the increase in oxygen vacancies, a drop in resistivity was measured. Charge extraction measurements showed no change in the trap density and energy distribution below the CB. Photovoltage decay measurements showed an increase in electron lifetime, but this came at a loss in the transport rate. The increase in V_OC seemed to be a result of a reduction in recombination, rather than a shift of the CB. In addition, no TiCl₄ treatment of the mesoporous scaffold was needed.¹⁸¹

4.5.3 Indium. Although most studies focus on the doping of the mesoporous TiO₂ structure, doping of the HBL can also lead to a marked increase in performance. It was shown that the transmittance of a In³⁺-doped HBL was higher than that of pristine TiO₂. This allows more photons into the active layer, leading to an increase in absorption and J_SC. The observed negative shift in V_FB (Fig. 3b) of the HBL will also result in a shift in V_FB of the mesoporous TiO₂, leading to a higher V_OC. A decrease in dark current and a higher onset potential is an indication that the In³⁺ doped HBL prevents recombination more effectively, which is supported by a longer electron lifetime as measured by EIS and OCVD. The V_FB shift and reduced recombination led to a higher V_OC.²¹¹

A high throughput screening of 35 elements showed that In³⁺ was one of the most promising dopants (along with Sb and Sn). This study similarly found a negative shift for V_FB.⁸³

4.5.4 Tin. The particle size and dye adsorption were not affected by Sn⁴⁺-doping. V_FB was negatively shifted (Fig. 3b), resulting in an increase in V_OC, which was limited by increased recombination because the Sn⁴⁺-ions acted as recombination centers. The increase in electron density and faster transport led to a higher electron collection efficiency and J_SC.^73,78,83,147

4.6 Lanthanides

Because of their 4f bands, lanthanides provide interesting optic and electronic properties,²¹⁴ such as up-conversion, photoluminescence or down-conversion,^215,216 making it possible to harvest photons that are outside the absorption region of most dyes (400–800 nm). Although there are some reports that show effective up- or down-conversion,^216–218 these processes are not yet very efficient in DSCCs, and their exact role in improving device efficiencies is unclear. Because many optical conversion studies do not consider the effect of doping on the electron transport rate and lifetime, the exact contribution of conversion is hard to quantify. Lanthanides that have been used to dope TiO₂ are lanthanum,^219–221 cerium,^222,223 neodymium,²²⁴ samarium,^225,226 europium,^{225,227–230} erbium,^{229,231–236} thulium^237,238 and ytterbium.^{231,232,234–239}

4.6.1 Lanthanum. Lanthanum is an interesting element because of its high binding strength to oxygen. When La³⁺ is doped into TiO₂, it will scavenge oxygen and induce vacancies on the surface.²⁴⁰ XRD and BET analyses showed that the particle size and the mesoporous surface area were largely unaffected by doping, but the dye adsorption was significantly increased. This can be explained by an increase in oxygen vacancies, which has been reported to increase dye loading.⁷⁵ This theory has been confirmed by EPR analysis, which showed a strong correlation between density of oxygen vacancies, dye loading and device efficiency.^219,220

A post-treatment with an acidic La³⁺ solution was shown to drastically increase J_SC although no La³⁺ was detected in the final particles and no morphology change was observed. An increase in electron density, combined with a down-shifted CB and increased dye adsorption was responsible for the increase in J_SC.²²¹

4.6.2 Cerium. It is known that Ce induces unoccupied 4f states just under the TiO₂ CB.²⁴¹ This may enlarge the driving force for electron injection from the dye into TiO₂.

The crystallite size and dye adsorption capability were not significantly changed upon doping. XPS showed that both Ce³⁺ and Ce⁴⁺ were present and the VB was unaffected. The UV/Vis absorption spectrum showed a red-shift, which indicated that Ce indeed induces unoccupied 4f states just under the TiO₂ CB. This was confirmed by cyclic voltammetry. Charge extraction and EIS measurements showed an increase in the electron density and capacitance due to enhanced electron injection, resulting in a higher J_SC, but caused a loss in V_OC.²²² A follow up study showed that the dopant acted solely as a surface trap state and therefore it was possible to counteract some of the adverse effects of Ce-doping by a TiCl₄ treatment.²²³

4.6.3 Neodymium. UV/Vis absorption spectroscopy indicated narrowing of the band gap upon Nd³⁺-doping. This suggests a downward shift of the CB, which would explain the reduced V_OC. The amount of adsorbed dye was unaffected, but due to enhanced electron injection and reduced recombination, J_SC saw a marked increase.²²⁴

4.6.4 Samarium. Sm³⁺-doping decreased the anatase particle size and increased dye adsorption. In combination with down-conversion this led to an improved J_SC.²²⁵ Another study showed an additional improvement in V_OC, which was suggested to be the result of p-type doping and recombination reduction.²²⁶

4.6.5 Europium. Due to the 4f bands of Eu³⁺ it is possible to achieve down-conversion with Eu³⁺ doped TiO₂.²¹⁸ A second important effect is a shift of the CB. It was found that dye adsorption increased upon doping. IPCE shows an absorption increase for the entire optical spectrum, with a new peak around 260 nm caused by down-conversion, leading to an increase in J_SC.^225,227 Other studies reported a negative shift of V_FB (Fig. 3b), leading to a higher V_OC.^228–230

4.6.6 Erbium. Er³⁺ has energy bands inside the band gap of TiO₂ which are expected to promote up-conversion. An increase in J_SC was found, which was attributed to up-conversion, but doping effects likely play a big role as the IPCE over the whole spectrum is increased (Fig. 5). V_OC was increased due to a negative shift of V_FB (Fig. 3b).^{229,231–234} EIS showed a drop in resistivity, indicating an improvement in conductivity and reduced recombination, further contributing to enhanced values of J_SC and V_OC.²³⁵ The absorption edge was found to be red-shifted indicating a downward shift of CB, although this was probably caused by the fluorine co-dopant.²³⁶

Fig. 5 IPCE of Eu³⁺/Er³⁺-doped TiO₂ DSSCs in light range of 300−800 nm. Although some of the increased IPCE above 700 nm can be ascribed to up-conversion, the drastic improvement for the whole spectrum suggests doping plays a more important role. Reprinted with permission from ref. 229. Copyright 2013 John Wiley & Sons, Inc.

4.6.7 Thulium. The observed up-conversion improved J_SC and an increase in V_OC suggested an upward shift of the CB.^237,238

4.6.8 Ytterbium. No significant change in particle size was observed upon Yb³⁺-doping. Dark current measurements show decreased recombination, which explains an increase in V_OC.²³⁹ Later studies report that due to up-conversion, Yb³⁺ doping can enhance the J_SC. It was also suggested that the increased V_OC was due to a negative V_FB shift (Fig. 3b).^{231,232,234–238}

4.7 Summary

In short, doping can affect five different properties of anatase TiO₂.

• Flat-band potential. V_FB can be shifted either positively or negatively; a positive shift is indicative of a downward shift of the CB and E_F while a negative V_FB shift indicates an upward shift of CB and E_F. A positive shift of V_FB makes electron injection easier, increasing J_SC. Because of a smaller difference between E_F of TiO₂ and the HTM V_OC is decreased. A negative shift of V_FB will have the opposite effect on J_SC and V_OC (Fig. 3).

• Recombination rate. A decrease in the number of defect states usually enhances the electron lifetime and reduce recombination rate, resulting in an increase in V_OC. Because of the dependence on trap states for electron transport based on the trap-detrap mechanism, this can however lead to a decrease in electron mobility and J_SC.

• Electron transport rate. An increase in shallow trap states can lead to enhanced electron mobility and thus a higher J_SC. Simultaneously the introduced trap states can promote recombination which leads to a decreased V_OC (Fig. 3).

• Dye adsorption. The dopant can change the growth rate of TiO₂ particles resulting in differently sized particles, affecting the amount of adsorbed dye and number of grain boundaries. Additionally, the dopant may affect dye adsorption by a change in binding affinity of the dye to the doped surface.

• Phase transition. Doping can inhibit the anatase-to-rutile phase transition, reducing rutile instigated charge recombination.

The main contributions for improving TiO₂ properties in DSSCs are summarized for each element in Table 1. This illustrates that the doping of TiO₂ with the aim to improve DSSC performance is not trivial. The correct balance between the CB energy, charge transport and recombination rate has to be found to obtain an optimally working device. It is important that the energy levels introduced by the dopant are located close to the CB to prevent these levels from becoming recombination centers or causing a large negative shift in V_FB, inhibiting charge injection. The best results are obtained for TiO₂ with few deep trap states. In this case, the properties of TiO₂ can be further improved by low-concentration doping, preventing the dopant from causing new trap states that give rise to detrimental effects such as increased recombination or decreased electron injection.

Table 1 Dopants and their main contribution to the improvement of DSSCs

Dopant	Comments	V FB pos.	V FB neg.	Recombination	Transport	Absorption
Lithium			85 and 86	86	85
Magnesium			89			89
	Zn co-doped	90			90
Calcium		91–93		92 and 93	91–93
Boron			97		97
	Nanotubes	100		100	100
	N co-doped		98 and 99	98 and 99
Silicon				101	101
Germanium			102			102
Antimony		103			103
	Cr co-doped	83		83	83
	F co-doped			147	147
Carbon		99, 106 and 107		99 and 107	99 and 107
Nitrogen		99 and 107–117		133–143	107 and 125–127	108–117
		119 and 121			129–132	119 and 121
		123–127
		129–142
	S co-doped	82 and 118				82 and 118
		120 and 128				120 and 128
	B co-doped		98 and 99	98 and 99
	Solid HTM	122				122
Fluorine		141		99 and 141	145 and 147
				146 and 147
	Nb/Sn/Sb/Ta co-doped			147	147
	Er co-doped	236
	HBL				144
Sulphur	N co-doped	82 and 118				82 and 118
		120 and 128				120 and 128
Iodine		148		148
Scandium			152	152
Vanadium		153–155		153	153–155
Chromium		156 and 157		156, 158 and 159	156	157
	Sb co-doped	83		83	83
Manganese		161 and 162				160
Iron				163 and 164		163
Cobalt	Detrimental
Nickel		166 and 167		166 and 167		166 and 167
	Nanowires		165	165	165
Copper			162, 168 and 169	168	168	162 and 169
Zinc		126, 130 and 161	172–175	173 and 174	126 and 130	173, 174 and 177
		176 and 178			161 and 172
					176 and 178
	N co-doped		171		171
	Mg co-doped	90			90
Yttrium		181		181		181
	Co-doped		179 and 180			179 and 180
Zirconium			102 and 140	140		182
			182–184
Niobium		154 and 186–188		186 and 187	154 and 185–189	190
		189–191		189–191	205
	HBL				70 and 71
	Nanotubes	60		60
	r-Nanorods	44		44
Molybdenum		166		166		166
Silver				192	192
Tantalum		154 and 193–195			154 and 193–195	196
	FSP		59	59
	Nanotubes		197	197
	r-Nanowires		43	43
Tungsten		198		81, 174 and 198
				200–202
	Nanowires		64	64		64
Aluminum			80, 208 and 209	80, 81 and 209		81 and 209
	Phase stab.	210		210
	Solid		51		51
Gallium				181		181
Indium			83
	HBL		211	211		211
Tin			73, 78 and 83		73, 78 and 83
	F co-doped			147	147
Lanthanum		221				219–221
Cerium					222 and 223
Neodymium		224		224
Samarium				226		225 and 226
Europium			228–230			225 and 227–230
Erbium			229 and 231–234	235		229 and 231–234
	F co-doped	236
Thulium			237 and 238			237 and 238
Ytterbium			231 and 232	239		231 and 232
			234–238			234–238

---

Because of the strong dependence of TiO₂ electronic properties on the fabrication protocol it is difficult to compare the effect of different dopants. This complicates the choice of dopant, particularly since opposite changes in device properties were found in many studies, employing the same dopant. For the moment, this means that for each synthesis method the ideal dopant and doping concentration has to be found by trial and error. High-throughput methods can be of significant help here, drastically cutting back the time needed to optimize each system.⁸³

5 Outlook: perovskite solar cells

With the recent emergence of perovskite solar cells (PSCs) it will be interesting to see which lessons can be learned from DSSCs. Due to the high optical density and charge transport of perovskites, much thinner devices can be constructed and the influence of TiO₂ surface area is much reduced. Because of the instability of perovskite in liquid electrolytes²² only solid HTMs are used. The high charge transport through the perovskite allows the construction of devices without mesoporous layer,¹¹ but it is presently difficult to produce pinhole free films,²⁴² limiting device performance. Mesoporous structures help wetting of the substrate and prevent the formation of pinholes.^12,13 Similar to DSSCs, most PSCs rely on a hole blocking layer of TiO₂.¹⁰ This implies that the electronic properties of TiO₂ are also important, both as compact and mesoporous layers, and similar to dye-sensitised solar cells doping will be important for performance enhancements in PSCs. So far, Mg,²⁴³ Nb,^244,245 Y,^246,247 Al⁵¹ and Zr²⁴⁸ doping of TiO₂ have been employed in perovskite solar cells.

Similar to Mg-doping in DSSCs,^87–89V_OC was improved in PSCs with a Mg-doped HBL, due to a higher CB energy and reduced recombination.²⁴³ Nb-doping resulted in improved electron injection and transport, resulting in higher J_SC.^244,245

In the case of Y-doping a small negative shift of V_FB was observed and recombination is slightly reduced. The main reason for the improvement in device performance was increased perovskite loading, leading to a marked increase in J_SC.²⁴⁶ A separate study found increased electron transport led to higher J_SC for a planar device with doped HBL.²⁴⁷

Al-doping was shown to reduce the number of oxygen vacancies and the associated deep trap states, effectively reducing recombination and increasing conductivity of the film. This led to an overall increase in J_SC. Additionally, it was shown that the long-term stability in inert atmosphere was significantly enhanced. This was ascribed to the elimination of oxygen defects by Al-doping. UV radiation causes the desorption of oxygen and in an inert atmosphere, where adsorbed oxygen can not be replenished, this leads to the emergence of oxygen vacancies that act as deep trap states, deteriorating device performance (Fig. 6). By reducing the number of traps through Al-doping this deterioration effect is much less profound.⁵¹

Fig. 6 Schematic of Ti(III) trap passivation, doping and oxygen adsorption. (a) Oxygen defects in the lattice give rise to Ti(III) defects that form deep electronic traps. (b) Al substitution at the Ti(III) sites passivates these defects. (c) In the presence of oxygen, ionisation of Ti(III) gives rise to O² superoxide which passivates the trap sites. (d) Photoexcited holes neutralise and desorb O2, activating Ti(III), which (e) enables charge recombination. Reprinted with permission from ref. 51. Copyright 2014 John Wiley & Sons, Inc.

A major problem in PSCs is hysteresis; the performance of the device depends strongly on how the measurement is performed. Typically the performance is much better sweeping from high to low voltages (forward bias) than vice versa, making it difficult to define the true power conversion efficiency. The precise mechanism causing hysteresis is yet unknown, although there are several hypotheses on the origin of hysteresis, such as the ferroelectric polarization,^21,249,250 ion migration^21,251 or deep trap states.²¹ Trap states at the interface of perovskite and charge conducting material may play an important role. These trap states get filled under forward bias measurements, resulting in good contacts and high efficiency devices. Under short-circuit conditions the traps may empty, resulting in a poor device performance until the trap states are filled again.^21,251–255 It was shown that by passivating interfacial traps, hysteresis could be drastically reduced, while overall device performance was improved.²⁵⁶ By doping TiO₂ with Zr⁴⁺ hysteresis was decreased, while at the same time the CB was shifted upward and recombination was decreased, leading to an increase in V_OC.²⁴⁸ This result suggests that doping can play an important role by decreasing surface trap states and reducing hysteresis.

Overall, it is likely that doping of TiO₂ may play an important role in improving efficiencies of PSCs. Doping can shift the CB, increase charge transport and reduce recombination. In addition, it may prolong device lifetimes, increase perovskite loading and play an important role in reducing hysteresis.

6 Techniques

There are several techniques that can give information on the effects of doping on the structural and electronic properties of TiO₂. This section discusses the most common techniques and the information that can be extracted from the measurements.

6.1 Computational modelling

Computational modelling can be used to predict and design material properties. Density functional theory (DFT) has become a popular method due to its low computational cost, making it possible to quickly screen dopants for their suitability to increase TiO₂ properties.^151,199 However, caution must be taken as the band gap is often underestimated, leading to inaccurate predictions.²⁵⁷

6.2 Morphological studies

To gain insight in the structure of (doped) TiO₂ several techniques can be employed. Electron microscopy offers the possibility to image nanostructures, from X-ray diffraction average particle size and dopant distribution can be determined and surface analysis quantifies the effect of doping on surface area and dye adsorption.

6.2.1 Electron microscopy. Electron microscopy makes it possible to visualize and characterize nanostructures. Scanning electron microscopy (SEM) is generally used to study the surface topography and to measure the average particle size and film thickness. The latter can also be measured by a profilometer. If equipped with an energy dispersive X-ray (EDX) spectrometer, the distribution of elements in the film can also be mapped. Transmission electron microscopy (TEM) yields a higher resolution than SEM, but requires extremely thin samples, which makes TEM less well suited for topographic investigations. Atomic resolution allows to image the TiO₂ lattice and typically gives a better measurement of the average crystallite size.

6.2.2 X-ray diffraction. X-ray diffraction (XRD) is a precise method to determine the crystal structure of TiO₂. It is routinely used to determine the crystal structure and the presence of impurity phases. A typical XRD spectrum of anatase TiO₂ is shown in Fig. 7 with the Miller indices (hkl) of the different peaks. The Rietveld refinement method allows a more detailed analysis of XRD spectra by using a least squares fit to approximate the measured profile.²⁵⁸ This way it is possible to determine the average crystallite size D by using the Scherrer formula^259,260where K is a dimensionless shape factor which is dependent on the shape of the particle (0.9 for spherical particles), λ is the wavelength of the X-rays, β is the full width half-maximum (FWHM) after subtracting the instrumental line broadening and θ is the Bragg angle. It is important to note that β and θ are in radians, whereas the instrumental output is usually in degrees. Furthermore, the inter-planar spacing d_hkl can be calculated with Bragg's law²⁶¹and using this interplanar spacing the lattice parameters a and c can be calculated using the Bragg formula for a tetragonal (a = b) lattice¹⁶²The change of the individual lattice parameters on doping can be determined by calculating the distortion degree of the lattice using²⁶² Vegard's law provides an empirical method to assess the successful incorporation of a dopant. It states that there is a linear relation between the lattice distortion and the concentration of dopant. It requires that the crystal retains it lattice structure and the dopant and matrix form a solid solution.²⁶³

Fig. 7 X-ray diffraction spectrum of anatase TiO₂. Each peak is labeled with the corresponding Miller indices (hkl).

6.2.3 Dye adsorption. The amount of dye adsorbed on the TiO₂ surface is typically a good measure to determine how many photons will be absorbed. Dye adsorption depends on the porosity of the mesoporous TiO₂, which can be measured by gas adsorption. Gas adsorption isotherms are typically analyzed by the Brunauer–Emmett–Teller (BET) theory²⁶⁴ that yields the specific surface area of the material or by the Barrett–Joyner–Halenda (BJH)²⁶⁵ analysis, which yields the pore size distribution. Doping however often affects the adsorption of the dye to TiO₂ (i.e. the dye affinity) implying differing the amounts of adsorbed dye for samples with the same surface area. In a more direct measurement, the dye can be desorbed from TiO₂ using a non-reactive solvent. By comparing the UV-vis absorption of the extracted solvent to reference spectra, the amount of adsorbed dye can be estimated. A combination of the two methods can be used to calculate the average dye density.

6.3 Spectroscopic techniques

By studying the interaction between light and matter the electronic structure of the material can be determined. The band gap, presence of defect states and material composition can be found through these methods.

6.3.1 UV/Vis spectroscopy. The main use for UV/Vis spectroscopy in TiO₂ doping studies is to obtain the direct and indirect band gap by determining the position of the absorption band edge. Absorption and reflectance are recorded in the range of 300–800 nm. Absorption and the direct band gap E_g are related through²⁶⁶

αE = C(E − E_g)^1/2, (8)

where α is the absorption coefficient, E the photon energy and C a proportionality constant. Sample reflectance can be converted to the Kubelka–Munk function,²⁶⁷ which is equivalent to the absorption coefficient in eqn (8) Using a Tauc plot (Fig. 8)^89,268 it is possible to extract the direct and indirect band gap. In a Tauc plot (F(R)E)^1/r is plotted versus E, where r = ½ for the direct band gap and r = 2 for the indirect band gap. Extrapolation of the linear regime gives the band gap energy.

Fig. 8 Determination of the indirect band gap energy for a TiO₂ film and a Mg²⁺-doped TiO₂ film from the plot of (αE)^½versus the excitation energy, hγ (α is the absorption coefficient, E is hγ, h is Plancks constant, and γ is the photon frequency). The indirect band gap energy is given by the intersect of the extrapolated linear regime with the x-axis. Reprinted with permission from ref. 89. Copyright 2011 American Chemical Society.

6.3.2 X-ray photoelectron spectroscopy. In X-ray photoelectron spectroscopy (XPS) the sample is irradiated with X-rays and the number of escaping electrons and their energy are measured to gain information about the elemental composition and electronic state of the elements. For example, it is possible to quantify the amount of dopant in the sample and the Ti³⁺ to Ti⁴⁺ ratio.⁸¹

6.3.3 FTIR spectroscopy. Fourier transform infrared (FTIR) spectroscopy measures optical absorption in a wide spectral range (4400–4000 cm⁻¹) and gives information about atomic bond vibrations. The intensity and position of the peaks of stretching vibrations of Ti–O–Ti and Ti–O bonds give information about the interaction between TiO₂ and the dopant since they are related to the number and strength of Ti–O bonds. By doping into interstitial sites the dopant directly decreases the number of Ti–O bonds. The size, electron affinity and valency of the dopant also influences the strength and orientation of neighbouring Ti–O bonds.

6.3.4 Raman spectroscopy. Raman spectroscopy is used to find rotational, vibrational and other low-frequency modes in a system. A laser beam interacts with the samples modes, resulting in an up- or down-shift of the photon energy. Each material has a distinct spectrum which allows the identification of impurity phases. Dopants alter the modes and in this way it is possible to measure the effect of the dopant on the TiO₂ crystal lattice. Raman spectroscopy is particularly useful to detect the formation of oxygen vacancies.²⁶⁹

6.3.5 Material composition. Several methods are able to determine the amount of dopant in TiO₂ with great precision such as EDX spectroscopy,¹⁶⁹ XPS spectroscopy,⁸¹ mass spectroscopy¹⁸⁷ or neutron activation analysis,²⁷⁰ which make use of unique “fingerprint” measurement spectra obtained upon sample irradiation.

6.4 Electromagnetic measurements

The interaction between magnetic fields and free charges in the sample makes it possible to determine the type of conduction, carrier concentration and detect trap states.

6.4.1 Hall effect measurement. When a magnetic field is applied on a current-carrying semiconductor, the charge carriers experience a force perpendicular to the magnetic field and the current. This is called the Hall effect, by measuring the strength of this effect the type of conduction (p- or n-type) and the carrier concentration are determined.^271,272

6.4.2 Electron paramagnetic resonance analysis. In electron paramagnetic resonance analysis (EPR) the spins of unpaired electrons are excited by microwave radiation in a magnetic field. This makes it possible to detect trapped electrons, which are unpaired, and the corresponding trap states.^220,273 The technique is similar to nuclear magnetic resonance analysis (NMR) with the exception that in NMR nuclear spins are excited.

6.5 (Photo-)electrochemical measurements

By simulating real world conditions the performance of the solar cell can be predicted through the determination of the photovoltaic properties such as short circuit current density J_SC, open circuit voltage V_OC and fill factor FF.

A wide range of measurements where the sample is subjected to periodic optical or electronic perturbations provide information about the concentration, diffusion length and lifetime of electrons, CB position, density of trap states as well as transport and recombination processes. They include transient and decay measurements, electrochemical impedance spectroscopy (EIS), intensity modulated photo current spectroscopy (IMPS), intensity modulated photovoltage spectroscopy (IMVS) and open circuit voltage decay (OCVD).^9,274

6.5.1 Photovoltaic properties. The power conversion efficiency of a solar cell is determined by measuring the current density as a function of applied voltage characteristics under illumination. The illumination spectrum and intensity should approximate that of the sun. To this end, a standardized light source of 100 mW cm⁻² AM 1.5 solar simulator is used. From the photo current–voltage (I–V) curve (Fig. 9) J_SC, V_OC and FF are extracted. J_SC is the current in the absence of a net voltage, V_OC is the voltage in the absence of net current and FF is a measure for the “squareness” of the curve and is a good indication for the resistances in the device. FF is determined by dividing the maximum power output P_max of the device by J_SC × V_OC. Parasitic resistances in the device lower FF; for low voltages shunt resistances are dominating, while for high voltages the series resistance is important. These are revealed by I–V curves measured in the dark. Under dark conditions, a solar cell behaves as an ideal diode, and deviations from the ideal diode behaviour arise from injected current leakage.

Fig. 9 Typical I–V curve for DSSCs. Short circuit current density J_SC is given by the intersect with the y-axis and open circuit voltage V_OC by the intersect with the x-axis. Fill factor FF can be calculated from .

The quantum efficiency is defined as the ratio of incident photons of a certain energy to the charges collected. The external quantum efficiency (EQE) considers all the incident photons including those that are transmitted and reflected, whereas internal quantum efficiency (IQE) only takes the absorbed photons into account. From this, a correlation between the energy of the photon and the probability of charge collection can be found.

Lastly, the stability of the device can be tested by measuring the device efficiency over a long period of time.

6.5.2 Electrochemical impedance spectroscopy. By perturbing an applied voltage with a small sine wave modulation the impedance can be found through the sinusoidal current response. Impedance can be defined as the frequency domain ratio of the voltage with respect to the current and is a complex value. The resulting function can be visualised with a Nyquist plot, where the real part of the function is plotted on the x-axis and the imaginary part on the y-axis. The system can be described by an equivalent circuit consisting of parallel and series connected elements (Fig. 10). From this charge transfer and transport processes and capacitance can be extracted.^9,274,275

Fig. 10 EIS spectra of TiO₂ and Sn-doped TiO₂ DSSCs. The inset shows the equivalent circuit that was used to find the electron lifetime and capacitance. Reprinted with permission from ref. 73. Copyright 2012 American Chemical Society.

6.5.3 Electron transport. Because electron transport and recombination processes respond non-linearly to different light intensities they can be studied using a small perturbation of light modulated onto a higher constant light intensity. The output can again be visualised with a Nyquist plot. In IMPS a sinusoidal modulation of light intensity is applied and the photo current is measured as a function of this modulation.²⁷⁶ The photo current response τ_pc depends on both the electron transport and recombination.⁵⁴ Under short-circuit conditions, the electron lifetime τ_n is usually much larger than the transport time τ_tr, implying τ_pc ≈ τ_tr.⁹

The chemical diffusion coefficient D_n can be derived from the transport time

where d is the thickness of the TiO₂ layer and C is a constant which depends on the absorption coefficient and direction of illumination.²⁷⁷

6.5.4 Electron lifetime. The measurement of the electron lifetime is similar to the electron transport, but the open circuit potential rather than the photo current is measured. Under these conditions, photo-generated electrons are not extracted and will eventually recombine with holes. Using a small intensity modulation, the response time of the potential corresponds to the electron lifetime τ_n.²⁷⁸

An alternative is the OCVD method, where V_OC is measured as a function of time after the light source is switched off.²⁷⁹ The electron lifetime is calculated from the slope of the transient as

The advantage of this method is that the electron lifetime can be determined for a wide potential range in just one measurement.

A third method is time-dependent charge extraction,²⁸⁰ where the lifetime is given by

Q(t) is the extracted charge after decay in the dark for the time t, assuming recombination follows first-order kinetics.

IMVS and OCVD give similar values, while charge extraction usually gives a value that is about 4 times higher.²⁸⁰ This can be explained by the fact that the former methods are based on the recombination of photo induced excess charges, whereas the latter method gives an average lifetime for all the electrons in the TiO₂.⁹

6.5.5 Electron concentration. The electron concentration can be measured through charge extraction methods, where the current is integrated over time after the light has been switched off.²⁸¹

Alternatively the capacity is measured.²⁸² An open-circuit potential is established by a bias illumination after which a light pulse is applied. The resulting voltage rise is measured, while the transient photo current is measured separately under short-circuit conditions to calculate the injected charge. The capacity is given by the ratio of injected charge and voltage change.

Lastly, the electron concentration can be estimated from the slope of a Mott–Schottky plot (Section 6.5.6).

6.5.6 Flat-band potential. The flat-band potential V_FB can be derived from a Mott–Schottky plot, where the capacitance of the space charge region is measured as a function of voltage under depletion conditions. For a fit of the linear part of the curve, V_FB and electron density are given by the axis-intersect and the slope of the fit respectively (Fig. 11).^193,283 The flat-band potential is usually referenced to a standardized electrode. A negative shift is indicative of an upward shift of CB, whereas a positive shift indicates a downward shift of CB.

Fig. 11 Mott–Schottky plots for TiO₂ and TaTiO₂.¹⁹³V_FB is given by the intersect of the extrapolated linear regime with the x-axis, the electron density by the slope. Reprinted with permission from ref. 283. Copyright 2007 American Chemical Society.

6.5.7 Charge collection efficiency. The charge collection efficiency η_CC is an important parameter as it combines the results of electron transport and lifetime studies, enabling to find the ideal balance between the two. η_CC is given by²⁸⁴provided τ_tr and τ_n are measured at the same quasi-Fermi level.

A similar parameter is the electron diffusion length

which is the average diffusion distance of electrons before they recombine with holes.

Acknowledgements

This work was supported by the Swiss National Science Foundation under the program NRP70 number 153990 and the European Community's Seventh Framework Programme (FP7/2007–2013) under grant agreement nr. 310184 of the CARINHYPH project.

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