A continuity equation for the simulation of the current-voltage curve and the time-dependent properties of dye-sensitized solar cells

A numerical model that simulates the steady-state current-voltage curve and the time-dependent response of a dye-sensitized solar cell with a single continuity equation is derived. It is shown that the inclusion of the multiple-trapping model, the quasi-static approximation and non-linear recombination kinetics leads to a continuity equation for the total electron density in the photoanode with an electron density-dependent diffusion coefficient and a density-dependent pseudo-first order recombination constant. All parameters in the model can be related to quantities accessible experimentally. The required power exponents are taken from impedance spectroscopy measurements at different voltages. The model provides new insights into the physical interpretation of the power exponents. Modeling examples involving a high-efficiency TiO(2)-based dye solar cell and a ZnO-based dye solar cell are presented. It is demonstrated that the model reproduces the transient behavior of the cell under small perturbations. The spatial dependence of the recombination rate and the influence of film thickness and of voltage dependent injection efficiency on cell performance are studied. The implications of the model are discussed in terms of efficiencies potentially attainable in dye-sensitized solar cells and other kinds of solar cells with a diffusional mechanism of charge transport.     

Charge transport versus recombination in dye-sensitized solar cells employing nanocrystalline TiO2 and SnO2 films

We report a comparison of charge transport and recombination dynamics in dye-sensitized solar cells (DSSCs) employing nanocrystalline TiO(2) and SnO(2) films and address the impact of these dynamics upon photovoltaic device efficiency. Transient photovoltage studies of electron transport in the metal oxide film are correlated with transient absorption studies of electron recombination with both oxidized sensitizer dyes and the redox couple. For all three processes, the dynamics are observed to be 2-3 orders of magnitude faster for the SnO(2) electrode. The origins of these faster dynamics are addressed by studies correlating the electron recombination dynamics to dye cations with chronoamperometric studies of film electron density. These studies indicate that the faster recombination dynamics for the SnO(2) electrodes result both from a 100-fold higher electron diffusion constant at matched electron densities, consistent with a lower trap density for this metal oxide relative to TiO(2), and from a 300 mV positive shift of the SnO(2) conduction band/trap states density of states relative to TiO(2). The faster recombination to the redox couple results in an increased dark current for DSSCs employing SnO(2) films, limiting the device open-circuit voltage. The faster recombination dynamics to the dye cation result in a significant reduction in the efficiency of regeneration of the dye ground state by the redox couple, as confirmed by transient absorption studies of this reaction, and in a loss of device short-circuit current and fill factor. The importance of this loss pathway was confirmed by nonideal diode equation analyses of device current-voltage data. The addition of MgO blocking layers is shown to be effective at reducing recombination losses to the redox electrolyte but is found to be unable to retard recombination dynamics to the dye cation sufficiently to allow efficient dye regeneration without resulting in concomitant losses of electron injection efficiency. We conclude that such a large acceleration of electron dynamics within the metal oxide films of DSSCs may in general be detrimental to device efficiency due to the limited rate of dye regeneration by the redox couple and discuss the implications of this conclusion for strategies to optimize device performance.     

Electron transport and recombination in dye-sensitized mesoporous TiO2 probed by photoinduced charge-conductivity modulation spectroscopy with Monte Carlo modeling

We present a combined experimental and theoretical investigation into the charge transport and recombination in dye-sensitized mesoporous TiO2. We electronically probe the photoinduced change in conductivity through in-plane devices while simultaneously optically probing signatures of the charge species. Our quasi-continuous wave technique allows us to build data sets of electron mobility and recombination versus charge density over a wide temperature range. We observe that the charge density dependence of mobility in TiO2 is strong at high temperatures and gradually reduces with reducing temperature, to an extent where at temperatures below 260 K the mobility is almost independent of charge density. The mobility first increases and then decreases with reducing temperature at any given charge density. These observed trends are surprising and consistent with the multiple-trapping model for charge transport only if the trap density-of-states (DoS) is allowed to become less deep and narrower as the temperature reduces. Our recombination measurements and simulations over a broad range of charge density and temperature are also consistent with the above-mentioned varying DoS function when the recombination rate constant is allowed to increase with temperature, itself consistent with a thermally activated charge-transfer process. Further to using the Monte Carlo simulations to model the experimental data, we use the simulations to aid our understanding of the limiting factors to charge transport and recombination. According to our model, we find that the charge recombination is mainly governed by the recombination reaction rate constant and the charge density dependence is mainly a result of the bimolecular nature of the recombination process. The implication to future material design is that if the mobility can be enhanced without increasing the charge density in the film, for instance by reducing the average trap depth, then this will not be at the sacrifice of comparably enhanced recombination and it will greatly increase the charge carrier diffusion lengths in dye-sensitized or mesoscopic solar cells.     

Characterization of nanostructured hybrid and organic solar cells by impedance spectroscopy

We review the application of impedance spectroscopy in dye-sensitized solar cells, quantum dot-sensitized solar cells and organic bulk heterojunction solar cells. We emphasize the interpretation of the impedance parameters for determining the internal features of the device, concerning the carrier distribution, materials properties such as the density of states and/or doping of the semiconductors, and the match of energy levels for photoinduced charge generation and separation. Another central task is the determination of recombination mechanisms from the measured resistances, and the factors governing the device performance by combined analysis of resistances as a function of voltage and current-voltage curves.     

Measuring charge transport from transient photovoltage rise times. A new tool to investigate electron transport in nanoparticle films

Charge transport rate at open-circuit potential (V(oc)) is proposed as a new characterization method for dye-sensitized (DS) and other nanostructured solar cells. At V(oc), charge density is flat and measurable, which simplifies quantitative comparison of transport and charge density. Transport measured at V(oc) also allows meaningful comparison of charge transport rates between different treatments, temperatures, and types of cells. However, in typical DS cells, charge transport rates at V(oc) often cannot be measured by photocurrent transients or modulation techniques due to RC limitations and/or recombination losses. To circumvent this limitation, we show that charge transport at V(oc) can be determined directly from the transient photovoltage rise time using a simple, zero-free-parameter model. This method is not sensitive to RC limitation or recombination losses. In trap limited devices, such as DS cells, the comparison of transport rates between different devices or conditions is only valid when the Fermi level in the limiting conductor is at the same distance from the band edge. We show how to perform such comparisons, correcting for conduction band shifts using the density of states (DOS) distribution determined from the same photovoltage transients. Last we show that the relationship between measured transport rate and measured charge density is consistent with the trap limited transport model.     

Correlation between Energy and Spatial Distribution of Intragap Trap States in the TiO2 Photoanode of Dye‐Sensitized Solar Cells

The energy and spatial distribution of intragap trap states of the TiO₂ photoanode of dye‐sensitized solar cells and their impact on charge recombination were investigated by means of time‐resolved charge extraction (TRCE) and transient photovoltage (TPV). The photoanodes were built from TiO₂ nanospheroids with different aspect ratios, and the TRCE results allowed differentiation of two different types of trap states, that is, deep and shallow ones at the surface and in the bulk of the TiO₂ particles, respectively. These trap states exhibit distinctly different characteristic energy with only a slight variation in the particle size, as derived from the results of the density of states. Analyses of the size‐dependent TPV kinetics revealed that in a moderate photovoltage regime of about 375–625 mV, the dynamics of electron recombination are dominated by shallow trap states in the bulk, which can be well accounted for by the mechanism of multiple‐trap‐limited charge transport.     

Photovoltaic properties of Au/beta-carotene/n-Si organic solar cells

Photovoltaic properties of Au/beta-carotene/n-Si organic solar cells characterized by current-voltage and capacitance-voltage measurements have been investigated. The photocurrent in the reverse direction increases with increasing illumination intensity. The I(sc) increases linearly with light intensity. The I(sc) dependence of light intensity follows a power law I(sc) approximately F(alpha). The exponent alpha was found to be 1.38. This indicates a monomolecular recombination in this device. Au/beta-carotene/n-Si organic solar cells give an open-circuit voltage of 0.316 V and a short-circuit current of 2.33 x 10(-4) A at light intensity of 6 W/m(2). The best conversion efficiency for Au/beta-carotene/n-Si solar cells was found to be 23.3% at a light intensity of 6 W/m(2).     

Ab initio electron propagator calculations in molecular transport junctions: predictions of negative differential resistance

In this work we study current-voltage characteristics in transport molecular junctions with a 1,4-benzene dithiol molecule as a bridge by using different ab initio electron propagator methods such as OVGF and P3 which are both programs in a Gaussian software package. The current-voltage characteristics are calculated for different values of Fermi energy in various basis sets such as 6-311++G(p,d) and cc-pVDZ and are compared with the experimental data. A good agreement is found in almost the entire voltage range. In addition, the results of our calculations indicate that the accuracy of ab initio electron propagator methods is in the range of 0.2-0.3 eV. Since the computational methods are truly ab initio, implying no adjustable parameters, functions, or functionals, the theoretical predictions can be improved only by changing the model of a transport device. The current-voltage characteristics predict peaks, i.e., negative differential resistances, for the various values of Fermi energy. As shown, the origin of the negative differential resistances is related to the voltage dependences of overlap integrals for the active terminal orbitals, expansion coefficients of partial atomic wavefunctions in Dyson orbitals, and the voltage dependences of Dyson poles (ionization potentials). We find that two peak behavior in the current-voltage characteristics can be explained by the anharmonicity of potential energy surfaces. As a result of our studies, we predict that negative differential resistances can be experimentally found by changing a position of Fermi level, i.e., by using different metal electrodes coated by a gold atomic monolayer.     

Determination of rate constants for charge transfer and the distribution of semiconductor and electrolyte electronic energy levels in dye-sensitized solar cells by open-circuit photovoltage decay method

A combination of electron lifetime measurement in nanoparticles as a function of the Fermi level position at high resolution in the potential scale with a new model to describe this dependence provides a powerful tool to study the microscopic processes and parameters governing recombination in dye-sensitized solar cells. This model predicts a behavior divided in three domains for the electron lifetime dependence on open-circuit voltage that is in excellent agreement with the experimental results: a constant lifetime at high photovoltage, related to free electrons; an exponential increase due to internal trapping and detrapping and an inverted parabolla at low photovoltage that corresponds to the density of levels of acceptor electrolyte species, including the Marcus inverted region.     

Oxide thickness and roughness factor as parameters for TiO<Subscript>2</Subscript>-dye sensitized solar cells performance

Oxide surface roughness in connection to oxide thickness has proved to be a key parameter for the performance of a dye sensitised solar cell. In this work, the numerical simulation of the system TiO₂-photo sensitive dye of a dye sensitized TiO₂ solar cell focuses on these two parameters. The steady-state numerical model used is based on the continuity and transport equations for charge species involved in the system, in connection to Poisson’s equation. Light absorbance is set dependent upon TiO₂ porosity and resulting electron density after illumination is derived as a function of the illuminating beam characteristics and material properties. Electron lifetime in the bulk is set dependent upon electron distribution with electron lifetime at the surface taking into consideration surface recombination. An effective dielectric constant dependent also upon the porosity of TiO₂ is used in the model. Results for different values of the TiO₂ thickness and surface roughness leading to optimum values for the cell performance are found in accordance with results reported in the literature.     

锌掺杂对TiO2染料敏化电池光阳极中电荷俘获态分布及电子复合过程的影响

基于瞬态光电压和瞬态光电流技术研究了锌掺杂的TiO2染料敏化太阳能电池中电子复合及传输的动力学行为.通过实验获得了不同阳极掺杂条件下的电子复合时间常数与电子收集时间常数,考察了锌掺杂对电池阳极材料导带能级和电子俘获态的影响.研究结果表明,锌的掺杂在提高TiO2导带能级的同时延长了俘获态电子的复合时间常数,从而大大提高了电池的开路电压.     

Effects of Metal Oxide Modifications on Photoelectrochemical Properties of Mesoporous TiO2 Nanoparticles Electrodes for Dye-Sensitized Solar Cells

Mesoporous TiO₂ (m-TiO₂) nanoparticles were used to prepare the porous film electrodes for dye-sensitized solar cells, and a second metal oxide (MgO, ZnO, Al₂O₃, or NiO) modifi-cation was carried out by dipping the m-TiO₂ electrode into their respective nitrate solution followed by annealing at 500 oC. Experimental results indicated that the above second metal oxide modifications on m-TiO₂ electrode are shown in all cases to act as barrier layer for the interfacial charge transfer processes, but film electron transport and interfacial charge recombination characteristics under applied bias voltage were dependent significantly on the existing states and kinds of these second metal oxides. Those changes based on sec-ond metal oxide modifications showed good correlation with the current-voltage analyses of dye-sensitized solar cell, and all modifications were found to increase the open-circuit photo-voltage in various degrees, while the MgO, ZnO, and NiO modifications result in 23%, 13%, and 6% improvement in cell conversion efficiency, respectively. The above observations indi-cate that controlling the charge transport and recombination is very important to improve the photovoltaic performance of TiO₂-based solar cell.     

Recombination controlled signal transfer through mesoporous TiO2 films

Photocurrent transients were used to investigate electron transport in mesoporous, nanocrystalline TiO2 films immersed into aqueous electrolyte, a regime where recombination cannot be neglected. Laser intensity and potential-dependent measurements show a decreased transient time of the current peak, which is explained by trap filling and electron loss from trap states into the electrolyte. A strongly enhanced recombination is furthermore observed, when the pH of the electrolyte is increased, while the current peak shifts toward longer transient times. Numerical simulations were used to decouple the impact of recombination and trapping on the transient response. We show that enhanced recombination in the absence of trapping accelerates the transfer of a current signal, while increased recombination slows down the transient current in the presence of electron trap sites.     

Scanning tunneling microscopy and spectroscopy for cluster and small particle research

Scanning tunneling microscopy (STM) and spectroscopy (STS) are new methods to investigate atomic arrangements and electronic structures of clusters and small particles of atoms. In this paper we review recent developments in this field, in particular the work from our laboratory. We show studies of single adatoms, small clusters and larger particles of platinum and a trimer of aluminum imaged with atomic resolution on highly-orient ed pyrolytic graphite. We find different isomeric structures for clusters of a specific size. Taking the substrate lattice as reference we determine bond lengths and angles for the clusters. We find that adsorbed Pt-particles have a strong influence on the substrate. Periodic charge density modulations on the graphite lattice surrounding the particles are observed. We also discuss recent STS experiments which showed Coulomb blockade in electron tunneling. A silicon-oxide-graphite tip-junction is used where a mesoscopic insulating area containing trap levels for temporary electron storage is responsible for the blockade of single electron transport. Such an ultra-small insulator capacitor shows large voltage steps in current-voltage characteristics and quantization of the tunneling current.     

Influence of surface area on charge transport and recombination in dye-sensitized TiO2 solar cells

The dependence of the electron transport and recombination dynamics on the internal surface area of mesoporous nanocrystalline TiO2 films in dye-sensitized solar cells was investigated. The internal surface area was varied by altering the average particle size in the films. The scaling of the photoelectron density and the electron diffusion coefficient at short circuit with internal surface area confirms the results of a recent study (Kopidakis, N.; Neale, N. R.; Zhu, K.; van de Lagemaat, J.; Frank, A. J. Appl. Phys. Lett. 2005, 87, 202106) that transport-limiting traps are located predominately on the surfaces of the particles. The recombination current density was found to increase superlinearly (with an exponent of 1.40 +/- 0.12) with the internal surface area. This result is at odds with the expected linear dependence of the recombination current density on the surface area when only the film thickness is increased. The observed scaling of the recombination current density with surface area is consistent with recombination being transport-limited. Evidence is also presented confirming that photoinjected electrons recombine with redox species in the electrolyte via surface states rather than from the TiO2 conduction band.     

Characteristics of high efficiency dye-sensitized solar cells

Impedance spectroscopy was applied to investigate the characteristics of dye-sensitized nanostructured TiO2 solar cells (DSC) with high efficiencies of light to electricity conversion of 11.1% and 10.2%. The different parameters, that is, chemical capacitance, steady-state transport resistance, transient diffusion coefficient, and charge-transfer (recombination) resistance, have been interpreted in a unified and consistent framework, in which an exponential distribution of the localized states in the TiO2 band gap plays a central role. The temperature variation of the chemical diffusion coefficient dependence on the Fermi-level position has been observed consistently with the standard multiple trapping model of electron transport in disordered semiconductors. A Tafel dependence of the recombination resistance dependence on bias potential has been rationalized in terms of the charge transfer from a distribution of surface states using the Marcus model of electron transfer. The current-potential curve of the solar cells has been independently constructed from the impedance parameters, allowing a separate analysis of the contribution of different resistive processes to the overall conversion efficiency.     

Transient absorption studies and numerical modeling of iodine photoreduction by nanocrystalline TiO2 films

We have used transient absorption spectroscopy to study the reaction between photogenerated electrons in a dye-free nanocrystalline titanium dioxide film and an iodine/iodide redox couple. Recombination kinetics was measured by recording the transient optical signal following band gap excitation by a UV laser pulse. In the presence of a methanol hole scavenger in the electrolyte, a long-lived (0.1-1 s) red/infrared absorbance is observed and assigned to photogenerated electrons forming Ti(3+) species. In the presence of iodine and excess iodide in the electrolyte, the signal decays on a millisecond-microsecond time scale, assigned to reduction of the redox couple by photogenerated electrons in the TiO(2). The electron lifetime decreases inversely with increasing iodine concentration, indicating that the back reaction is first order in [I(2)]. No evidence for I(2)(-) is observed, indicating that the reaction mechanism does not involve the formation of I(2)(-) as an intermediate. The shape of the kinetics evolves from monoexponential at low [I(2)] to stretched-exponential as [I(2)] increases. A Monte Carlo continuous-time random walk model is implemented to simulate the kinetics and its [I(2)] dependence and used to address the order of the recombination reaction with respect to electron density, n. The model incorporates the diffusion of oxidized species from the electrolyte toward the TiO(2) surface as well as electron trapping and transport in the TiO(2). In the limit of low [I(2)], the monoexponential kinetics is explained by the recombination reaction being rate limited by the diffusion of the oxidized species in the electrolyte. The stretched-exponential behavior at high [I(2)] can be explained by the reaction being rate limited by the transport of electrons through a distribution of trap states toward reactive sites at the TiO(2)-electrolyte interface, similar to the mechanism proposed previously for the kinetics of electron-dye cation recombination. Such trap-limited recombination can also explain the superlinear dependence of electron recombination rate on electron density, which has been reported elsewhere, without the need for a reaction mechanism that is second order in n. In contrast, a second-order reaction mechanism in a trap-free medium cannot explain the observed kinetics, although a second-order mechanism incorporating electron trapping cannot be conclusively ruled out by the data. We propose that the most likely reaction scheme, that is first order in both [I(2)] and n, is the dissociative reduction of I(2) onto the metal oxide surface, followed by a second electron reduction of the resulting adsorbed iodine radical, and that empirical second-order behavior of the electron lifetime is most likely explained by electron trapping rather than by a second-order recombination mechanism.     

Dependence of the self-bias on the plasma parameters and on the electrode areas in RF plasma reactors

From the current-voltage characteristics for the collisionless sheath the dependence of the self-bias on the plasma parameters (electron temperature, ratio of electron temperatures and electron densities at the two electrodes), on the applied external voltage, and on the ratio of the electrode areas is investigated. Sinusoidal (is well as periodic rectangular and triangular time dependences of the voltage are considered. The integral equation for the self bias voltage is solved numerically. For large external RF voltages in comparison to the floating potential, simple analytical formulas result for the dependence of the bias voltage on the plasma parameters and the dimensions of the electrodes, which can be useful in practice.     

Factors controlling charge recombination under dark and light conditions in dye sensitised solar cells

A simple and powerful approach for assessing the recombination losses in dye sensitised solar cells (DSSCs) across the current voltage curve (j-V) as a function of TiO(2) electron concentration (n) is demonstrated. The total flux of electrons recombining with iodine species in the electrolyte and oxidised dye molecules can be thought of as a recombination current density, defined as j(rec) = j(inj)-j where j(inj) is the current of electrons injected from optically excited dye states and j is the current density collected at cell voltage (V). The electron concentration at any given operating conditions is determined by charge extraction. This allows comparison of factors influencing electron recombination rates at matched n. We show that j(rec) is typically 2-3 times higher under 1 sun equivalent illumination (j(inj) > 0) relative to dark (j(inj) = 0) conditions. This difference was increased by increasing light intensity, electrolyte iodine concentration and electrolyte solvent viscosity. The difference was reduced by increasing the electrolyte iodide concentration and increasing the temperature. These results allowed us to verify a numerical model of complete operational cells (Barnes et al., Phys. Chem. Chem. Phys., DOI: 10.1039/c0cp01554g) and to relate the differences in j(rec) to physical processes in the devices. The difference between j(rec) in the light and dark can be explained by two factors: (1) an increase in the concentration of electron acceptor species (I(3)(-) and/or I(2)) when current is flowing under illumination relative to dark conditions where the current is flowing in the opposite direction, and (2) a non-trivial contribution from electron recombination to oxidised dye molecules under light conditions. More generally, the technique helps to assign the observed relationship between the components, processing and performance of DSSCs to more fundamental physical processes.     

Recombination and transport processes in dye-sensitized solar cells investigated under working conditions

The transport and recombination of electrons in dye-sensitized TiO(2) solar cells were studied by analysis of the current and voltage response to a small square-wave light-intensity modulation. Solar cells were studied under working conditions by using potentiostatic and galvanostatic conditions. An increase in applied voltage, that is, from 0 V toward open-circuit voltage, was found to lead to faster electron transport at low light intensities, while it slowed transport at higher light intensities. This observation seems to be conflicting with the multiple trapping model with diffusive transport. An effective diffusion length at the maximum power point was calculated, and it was shown that it decreases with increasing light intensity.