Overscreening and Underscreening in Solid-Electrolyte Grain Boundary Space-Charge Layers.

Polycrystalline solids can exhibit material properties that differ significantly from those of equivalent single-crystal samples, in part, because of a spontaneous redistribution of mobile point defects into so-called space-charge regions adjacent to grain boundaries. The general analytical form of these space-charge regions is known only in the dilute limit, where defect-defect correlations can be neglected. Using kinetic Monte Carlo simulations of a three-dimensional Coulomb lattice gas, we show that grain boundary space-charge regions in nondilute solid electrolytes exhibit overscreening-damped oscillatory space-charge profiles-and underscreening-decay lengths that are longer than the corresponding Debye length and that increase with increasing defect-defect interaction strength. Overscreening and underscreening are known phenomena in concentrated liquid electrolytes, and the observation of functionally analogous behavior in solid electrolyte space-charge regions suggests that the same underlying physics drives behavior in both classes of systems. We therefore expect theoretical approaches developed to study nondilute liquid electrolytes to be equally applicable to future studies of solid electrolytes.

Simulating morphologies of organic semiconductors by exploiting low-frequency vibrational modes.

Generating morphologies of amorphous organic materials represents a significant computational challenge and severely limits the size of systems that can be studied. Furthermore, the dynamical evolution of a film at high density occurs on time scales impractical to simulate dynamically, limiting the number of independent states that can be generated. This is a problem in glassy systems as well as protein and polymeric systems. To overcome this problem, we identify rigid sections in molecules and construct an elastic network between them. Using normal mode analysis, we calculate the lowest frequency eigenmodes for the network and displace rigid sections along the low-frequency modes. The system undergoes fast structural relaxation, which allows us to generate many structurally independent approximations to a final atomistic morphology rapidly without force-field parameterization. Using these states as high-density starting configurations, we find equilibrium structures through short molecular dynamics simulations that show close agreement with other atomistic molecular dynamics studies. This method provides a convenient alternative for simulating morphologies of large molecular systems without access to high-performance computing facilities.

Monte carlo studies of electronic processes in dye-sensitized solar cells.

This topic reviews random walk Monte Carlo simulation models of charge transport in DSSC. The main electron transport approaches used are covered. Monte Carlo methods and results are explained, addressing the continuous time random walk model developed for transport in disordered materials in the context of the large number of trap states present in the electron transporting material. Multiple timescale MC models developed to look at the morphology dependence of electron transport are described. The concluding section looks at future applications of these methods and the related MC models for polymer blend cells.

Influence of ionizing dopants on charge transport in organic semiconductors.

Ionizing chemical dopants are widely used in organic semiconductors to enhance the charge transport properties by increasing the number of mobile charge carriers. However, together with mobile charges, chemical doping produces anion-cation pairs in the organic matrix. In this work we use experimental and computational analysis to study the influence of these ionic species on the charge transport. We show that the anion-cation pairs introduced upon doping have a detrimental, doping-level dependent effect on charge mobility. For doping levels of 0.02-0.05% molar ratio with respect to the molecular organic semiconductor, the increase in conductivity from the extra mobile charges is partially cancelled by a reduction in charge mobility from traps introduced by the anion-cation pairs. As the doping concentration increases, anion-cation pairs start to overlap, resulting in a comparatively smoother potential landscape, which increases the charge mobility to values closer to the undoped semiconductor. This result has a significant, practical impact, as it shows the need to dope at or slightly above a threshold level, which depends on the specific host-dopant combination.

Motional Narrowing Effects in the Excited State Spin Populations of Mn-Doped Hybrid Perovskites.

Spin-orbit coupling in the electronic states of solution-processed hybrid metal halide perovskites forms complex spin-textures in the band structures and allows for optical manipulation of the excited state spin-polarizations. Here, we report that motional narrowing acts on the photoexcited spin-polarization in CH3NH3PbBr3 thin films, which are doped at percentage-level with Mn2+ ions. Using ultrafast circularly polarized broadband transient absorption spectroscopy at cryogenic temperatures, we investigate the spin population dynamics in these doped hybrid perovskites and find that spin relaxation lifetimes are increased by a factor of 3 compared to those of undoped materials. Using quantitative analysis of the photoexcitation cooling processes, we reveal increased carrier scattering rates in the doped perovskites as the fundamental mechanism driving spin-polarization-maintaining motional narrowing. Our work reports transition-metal doping as a concept to extend spin lifetimes of hybrid perovskites.

Ionic Accumulation as a Diagnostic Tool in Perovskite Solar Cells: Characterizing Band Alignment with Rapid Voltage Pulses.

Despite record-breaking devices, interfaces in perovskite solar cells are still poorly understood, inhibiting further progress. Their mixed ionic-electronic nature results in compositional variations at the interfaces, depending on the history of externally applied biases. This makes it difficult to measure the band energy alignment of charge extraction layers accurately. As a result, the field often resorts to a trial-and-error process to optimize these interfaces. Current approaches are typically carried out in a vacuum and on incomplete cells, hence values may not reflect those found in working devices. To address this, a pulsed measurement technique characterizing the electrostatic potential energy drop across the perovskite layer in a functioning device is developed. This method reconstructs the current-voltage (JV) curve for a range of stabilization biases, holding the ion distribution "static" during subsequent rapid voltage pulses. Two different regimes are observed: at low biases, the reconstructed JV curve is "s-shaped", whereas, at high biases, typical diode-shaped curves are returned. Using drift-diffusion simulations, it is demonstrated that the intersection of the two regimes reflects the band offsets at the interfaces. This approach effectively allows measurements of interfacial energy level alignment in a complete device under illumination and without the need for expensive vacuum equipment.

3D-to-2D Transition of Anion Vacancy Mobility in CsPbBr3 under Hydrostatic Pressure.

Anion vacancy migration in the orthorhombic Pnma phase of the lead-halide perovskite CsPbBr3 under hydrostatic pressure is studied computationally. Density functional theory calculations are used to determine transition states, activation enthalpies, and attempt frequencies for vacancies to hop between nearby lattice sites, under pressure in the range 0.0-2.0 GPa. The resulting data are used to parametrize a kinetic model of vacancy migration under the influence of an electric field, which is solved in the steady state to determine the anion vacancy mobility tensor as a function of pressure. It is found that the mobility tensor becomes increasingly anisotropic with increasing pressure, such that at 2.0 GPa, the mobility within the (010) lattice plane is 3 orders of magnitude greater than the mobility normal to it. The results demonstrate the potentially significant influence of pressure, and by extension, other forms of stress, on defect migration in lead-halide perovskites.

Bicontinuous minimal surface nanostructures for polymer blend solar cells.

This paper presents the first examination of the potential for bicontinuous structures such as the gyroid structure to produce high efficiency solar cells based on conjugated polymers. The solar cell characteristics are predicted by a simulation model that shows how the morphology influences device performance through integration of all the processes occurring in organic photocells in a specified morphology. In bicontinuous phases, the surface defining the interface between the electron and hole transporting phases divides the volume into two disjoint subvolumes. Exciton loss is reduced because the interface at which charge separation occurs permeates the device so excitons have only a short distance to reach the interface. As each of the component phases is connected, charges will be able to reach the electrodes more easily. In simulations of the current-voltage characteristics of organic cells with gyroid, disordered blend and vertical rod (rods normal to the electrodes) morphologies, we find that gyroids have a lower than anticipated performance advantage over disordered blends, and that vertical rods are superior. These results are explored thoroughly, with geminate recombination, i.e. recombination of charges originating from the same exciton, identified as the primary source of loss. Thus, if an appropriate materials choice could reduce geminate recombination, gyroids show great promise for future research and applications.

Simulation of loss mechanisms in organic solar cells: A description of the mesoscopic Monte Carlo technique and an evaluation of the first reaction method.

In this letter we evaluate the accuracy of the first reaction method (FRM) as commonly used to reduce the computational complexity of mesoscale Monte Carlo simulations of geminate recombination and the performance of organic photovoltaic devices. A wide range of carrier mobilities, degrees of energetic disorder, and applied electric field are considered. For the ranges of energetic disorder relevant for most polyfluorene, polythiophene, and alkoxy poly(phenylene vinylene) materials used in organic photovoltaics, the geminate separation efficiency predicted by the FRM agrees with the exact model to better than 2%. We additionally comment on the effects of equilibration on low-field geminate separation efficiency, and in doing so emphasize the importance of the energy at which geminate carriers are created upon their subsequent behavior.

Identification of recombination losses and charge collection efficiency in a perovskite solar cell by comparing impedance response to a drift-diffusion model.

Interpreting the impedance response of perovskite solar cells (PSCs) is significantly more challenging than for most other photovoltaics. This is for a variety of reasons, of which the most significant are the mixed ionic-electronic conduction properties of metal halide perovskites and the difficulty in fabricating stable, and reproducible, devices. Experimental studies, conducted on a variety of PSCs, produce a variety of impedance spectra shapes. However, they all possess common features, the most noteworthy of which is that they have at least two features, at high and low frequency, with different characteristic responses to temperature, illumination and electrical bias. The impedance response has commonly been analyzed in terms of sophisticated equivalent circuits that can be hard to relate to the underlying physics and which complicates the extraction of efficiency-determining parameters. In this paper we show that, by a combination of experiment and drift-diffusion (DD) modelling of the ion and charge carrier transport and recombination within the cell, the main features of common impedance spectra are well reproduced by the DD simulation. Based on this comparison, we show that the high frequency response contains all the key information relating to the steady-state performance of a PSC, i.e. it is a signature of the recombination mechanisms and provides a measure of charge collection efficiency. Moreover, steady-state performance is significantly affected by the distribution of mobile ionic charge within the perovskite layer. Comparison between the electrical properties of different devices should therefore be made using high frequency impedance measurements performed in the steady-state voltage regime in which the cell is expected to operate.

Putting the Squeeze on Lead Iodide Perovskites: Pressure-Induced Effects To Tune Their Structural and Optoelectronic Behavior.

Lattice compression through hydrostatic pressure has emerged as an effective means of tuning the structural and optoelectronic properties of hybrid halide perovskites. In addition to external pressure, the local strain present in solution-processed thin films also causes significant heterogeneity in their photophysical properties. However, an atomistic understanding of structural changes of hybrid perovskites under pressure and their effects on the electronic landscape is required. Here, we use high level ab initio simulation techniques to explore the effect of lattice compression on the formamidinium (FA) lead iodide compound, FA1-x Cs x PbI3 (x = 0, 0.25). We show that, in response to applied pressure, the Pb-I bonds shorten, the PbI6 octahedra tilt anisotropically, and the rotational dynamics of the FA+ molecular cation are partially suppressed. Because of these structural distortions, the compressed perovskites exhibit band gaps that are narrower (red-shifted) and indirect with spin-split band edges. Furthermore, the shallow defect levels of intrinsic iodide defects transform to deep-level states with lattice compression. This work highlights the use of hydrostatic pressure as a powerful tool for systematically modifying the photovoltaic performance of halide perovskites.

Dye-sensitized solar cells based on oriented TiO2 nanotube arrays: transport, trapping, and transfer of electrons.

Dye-sensitized solar cells fabricated using ordered arrays of titania nanotubes (tube lengths 5, 10, and 20 microm) grown on titanium have been characterized by a range of experimental methods. The collection efficiency for photoinjected electrons in the cells is close to 100% under short circuit conditions, even for a 20 microm thick nanotube array. Transport, trapping, and back transfer of electrons in the nanotube cells have been studied in detail by a range of complementary experimental techniques. Analysis of the experimental results has shown that the electron diffusion length (which depends on the diffusion coefficient and lifetime of the photoinjected electrons) is of the order of 100 microm in the titania nanotube cells. This is consistent with the observation that the collection efficiency for electrons is close to 100%, even for the thickest (20 microm) nanotube films used in the study. The study revealed a substantial discrepancy between the shapes of the electron trap distributions measured experimentally using charge extraction techniques and those inferred indirectly from transient current and voltage measurements. The discrepancy is resolved by introduction of a numerical factor to account for non-ideal thermodynamic behavior of free electrons in the nanostructured titania.

Analysis of photovoltage decay transients in dye-sensitized solar cells.

It is shown that application of the so-called quasi-static approximation greatly simplifies the theoretical treatment of the open circuit photovoltage decay of dye-sensitized nanostructured solar cells (DSCs), since it removes the need to treat the kinetics of trapping and detrapping explicitly and leads to a straightforward analytical solution in the case of an exponential trap distribution. To identify the conditions under which the quasi-static approach is valid, transients calculated using the quasi-static approximation are compared with the results of numerical calculations that treat trapping and detrapping of electrons explicitly. The application of the quasi-static approach to derive the rate constant for the back-reaction of electrons from experimental photovoltage decay data is illustrated for an optimized DSC.

Interpretation of apparent activation energies for electron transport in dye-sensitized nanocrystalline solar cells.

Electron transport in dye-sensitized nanocrystalline solar cells appears to be a slow diffusion-controlled process. Values of the apparent electron diffusion coefficient are many orders of magnitude smaller than those reported for bulk anatase. The slow transport of electrons has been attributed to multiple trapping (MT) at energy levels distributed exponentially in the band gap of the nanocrystalline oxide. In the MT model, release of immobile electrons from occupied traps to the conduction band is a thermally activated process, and it might therefore be expected that the apparent electron diffusion coefficient should depend strongly on temperature. In fact, rather small activation energies (0.1-0.25 eV) have been derived from time and frequency resolved measurements of the short circuit photocurrent. It is shown that the MT model can give rise to such anomalously low apparent activation energies as a consequence of the boundary conditions imposed by the short circuit condition and the quasi-static relationship between changes in the densities of free and trapped electrons. This conclusion has been confirmed by exact numerical solutions of the time-dependent generation/collection problem for periodic excitation that provide a good fit to experimental data.

Utilizing Energy Transfer in Binary and Ternary Bulk Heterojunction Organic Solar Cells.

Energy transfer has been identified as an important process in ternary organic solar cells. Here, we develop kinetic Monte Carlo (KMC) models to assess the impact of energy transfer in ternary and binary bulk heterojunction systems. We used fluorescence and absorption spectroscopy to determine the energy disorder and Förster radii for poly(3-hexylthiophene-2,5-diyl), [6,6]-phenyl-C61-butyric acid methyl ester, 4-bis[4-(N,N-diisobutylamino)-2,6-dihydroxyphenyl]squaraine (DIBSq), and poly(2,5-thiophene-alt-4,9-bis(2-hexyldecyl)-4,9-dihydrodithieno[3,2-c:3',2'-h][1,5]naphthyridine-5,10-dione). Heterogeneous energy transfer is found to be crucial in the exciton dissociation process of both binary and ternary organic semiconductor systems. Circumstances favoring energy transfer across interfaces allow relaxation of the electronic energy level requirements, meaning that a cascade structure is not required for efficient ternary organic solar cells. We explain how energy transfer can be exploited to eliminate additional energy losses in ternary bulk heterojunction solar cells, thus increasing their open-circuit voltage without loss in short-circuit current. In particular, we show that it is important that the DIBSq is located at the electron donor-acceptor interface; otherwise charge carriers will be trapped in the DIBSq domain or excitons in the DIBSq domains will not be able to dissociate efficiently at an interface. KMC modeling shows that only small amounts of DIBSq (<5% by weight) are needed to achieve substantial performance improvements due to long-range energy transfer.

Grain morphology and trapping effects on electron transport in dye-sensitized nanocrystalline solar cells.

We have examined the combined effects of grain morphology and electron trapping on the transient response of photoelectrons moving through the TiO2 grains in a dye-sensitized nanocrystalline solar cell using a multi-time-scale random walk Monte Carlo model. Our use of a multi-time-scale approach enables us to simulate transport for electrons moving through spherical connected grains in a three-dimensional (3D) voided network and look at the effect of the size of interparticle boundaries on carrier dynamics. We can also address similar times to those over which measurements are taken, namely, 0.1 ms. These times are long because of deep traps in the TiO2 grains. The grains have 2-fold connectivity in one dimension (linear chains) or 4-fold or 6-fold connectivity in three dimensions and traps with an exponential distribution of energies. Photoelectrons are generated by a light pulse of short duration. The spatial distribution of the photogenerated electron density from this pulse either has a uniform profile or is peaked on the electrolyte side. We show that the constrictions at the grain necks slow the electrons, making trapping more likely and hence further delaying their passage to the extracting electrode. By comparing our results for 4-fold and 6-fold coordinated particles on a cubic lattice with 2-fold coordinated particles on linear chains, we show that transport is slowed in the former case due to the additional paths available to the electrons in the 3D network. We also find that the charge and current transients cannot be fit to an analytical solution of the continuum equations with an effective diffusion coefficient even at long times. Therefore, caution must be exercised when attempting to fit experimental transient data with an effective diffusion coefficient.

Dynamic Monte Carlo simulation for highly efficient polymer blend photovoltaics.

We developed a model system for blend polymers with electron-donating and -accepting compounds. It is found that the optimal energy conversion efficiency can be achieved when the feature size is around 10 nm. The first reaction method is used to describe the key processes (e.g., the generation, the diffusion, the dissociation at the interface for the excitons, the drift, the injection from the electrodes, and the collection by the electrodes for the charge carries) in the organic solar cell by the dynamic Monte Carlo simulation. Our simulations indicate that a 5% power conversion efficiency (PCE) is reachable with an optimum combination of charge mobility and morphology. The parameters used in this model study correspond to a blend of novel polymers (bis(thienylenevinylene)-substituted polythiophene and poly(perylene diimide-alt-dithienothiophene)), which features a broad absorption and a high mobility. The I-V curves are well-reproduced by our simulations, and the PCE for the polymer blend can reach up to 2.2%, which is higher than the experimental value (>1%), one of the best available experimental results up to now for the all-polymer solar cells. In addition, the dependency of PCE on the charge mobility and the material structure are also investigated.

Two-dimensional simulations of bulk heterojunction solar cell characteristics.

We present a two-dimensional model of a bulk heterojunction solar cell in which we include the effects of optical interference, exciton diffusion, charge separation via the formation of polaron pairs, and charge transport in two separate interpenetrating phases. Our model shows that the current is increased by an order of magnitude with a full optical model compared to assuming that absorbed photons have a Lambertian profile, and depends much more strongly on applied bias when dissociation via polaron pairs is considered. We find a power efficiency at solar intensities of 1-3% depending on the morphology, and show that the fill factor decreases from 40% at low intensities to 20% at solar intensities because of the increase in the open circuit voltage and decreases much more rapidly at higher intensities due to the decrease in the power efficiency.

Predictive study of charge transport in disordered semiconducting polymers.

We present a theoretical study of charge transport in disordered semiconducting polymers that relates the charge mobility to the chemical structure and the physical morphology in a novel multiscale approach. Our studies, focusing on poly(9,9-dioctylfluorene) (PFO), show that the charge mobility is dominated by pathways with the highest interchain charge-transfer rates. We also find that disorder is not always detrimental to charge transport. We find good agreement with experimental time-of-flight mobility data in highly aligned PFO films.

Dynamical Monte Carlo modelling of organic solar cells: the dependence of internal quantum efficiency on morphology.

We present a dynamical Monte Carlo study of the dependence of the internal quantum efficiency (IQE) of an organic bulk heterojunction solar cell on the device morphology. The IQE is found to be strongly sensitive to the scale of phase separation in the morphology, with a peak at approximately 20 nm for the PFB/F8BT system studied. An ordered, checkered morphology exhibits a peak IQE 1.5 times higher than a disordered blend.