Many recent advances in metal halide perovskite solar cell (PSC) performance are attributed to surface treatments which passivate interfacial trap states, minimise charge recombination and boost photovoltages. Surprisingly, these photovoltages exceed the cells' built-in potentials, often with large energetic offsets reported between the perovskite and transport layer semiconductor band edges - contradicting standard photovoltaic design principles. Here we show that this tolerance to energetic offsets results from mixed ionic/electronic conduction in the perovskite layer. Combining drift-diffusion simulations with experiments probing the current-voltage performance of PSCs as a function of ion distribution, we demonstrate that electrostatic redistribution of ionic charge reduces surface recombination currents at steady-state, increasing the photovoltage by tens to hundreds of millivolts. Thus, mobile ions can reduce the sensitivity of photovoltage to energetic misalignments at perovskite/transport layer interfaces, benefitting overall efficiency. Building on these insights, we show how photovoltaic design principles are modified to account for mobile ions.

Metal halide perovskite solar cells have gained widespread attention due to their high efficiency and high defect tolerance. The absorbing perovskite layer is as a mixed electron-ion conductor that supports high rates of ion and charge transport at room temperature, but the migration of mobile defects can lead to degradation pathways. We combine experimental observations and drift-diffusion modelling to demonstrate a new framework to interpret surface photovoltage (SPV) measurements in perovskite systems and mixed electronic ionic conductors more generally. We conclude that the SPV in mixed electronic ionic conductors can be understood in terms of the change in electric potential at the surface associated with changes in the net charge within the semiconductor system. We show that by modifying the interfaces of perovskite bilayers, we may control defect migration behaviour throughout the perovskite bulk. Our new framework for SPV has broad implications for developing strategies to improve the stability of perovskite devices by controlling defect accumulation at interfaces. More generally, in mixed electronic conductors our framework provides new insights into the behaviour of mobile defects and their interaction with photoinduced charges, which are foundational to physical mechanisms in memristivity, logic, impedance, sensors and energy storage.

The recent emergence of lead-halide perovskites as active layer materials for thin film semiconductor devices including solar cells, light emitting diodes, and memristors has motivated the development of several new drift-diffusion models that include the effects of both electronic and mobile ionic charge carriers. In this work we introduce Driftfusion, a versatile simulation tool built for modelling one-dimensional ordered semiconductor devices with mixed ionic-electronic conducting layers. Driftfusion enables users to model devices with multiple, distinct, material layers using up to four charge carrier species: electrons and holes plus up to two ionic species. The time-dependent carrier continuity equations are coupled to Poisson's equation enabling transient optoelectronic device measurement protocols to be simulated. In addition to material and device-wide properties, users have direct access to adapt the physical models for carrier transport, generation and recombination. Furthermore, a discrete interlayer interface approach circumvents the requirement for boundary conditions at material interfaces and enables interface-specific properties to be introduced.

Space-charge-limited current (SCLC) measurements are used to estimate charge carrier mobilities and electronic trap densities of semiconductors by analysing the current density-voltage (JV) relationship for unipolar devices predicted by the Mott-Gurney (MG) law. However, the interpretation of SCLC measurements for metal-halide perovskites is problematic due to mobile ionic defects which redistribute to screen electrostatic fields in devices during measurements. To overcome this, an SCLC measurement protocol was recently suggested that minimises ionic charge redistribution by probing the current during millisecond voltage pulses superimposed on a background bias. Here, we use drift-diffusion simulations with mobile ions to assess the validity of the MG law for analysing both the standard and new protocol JV measurements. We simulated idealised perovskite devices with differing mobile ion densities and compared them with simulations and measurements of devices with typical contact materials. We found the validity region for the MG law is limited to perovskites with mobile ion densities lower than the device's equilibrium charge carrier density (<10^17 cm-3 for 400 nm thick methylammonium lead iodide films) and contacts with injection/extraction barriers <=0.1 eV. The latter limitation can be partially overcome by increasing the device thickness, whereas the former limitation cannot. This restricts the range of perovskite layer compositions and viable contact materials that can be reliably analysed with the MG law. Approaches such as estimating trap densities from the apparent voltage onset to trap-free SCLC regime should also be critically reviewed since they rely on the same potentially invalid assumptions as the MG law. Our results demonstrate that extracting meaningful and accurate values for metal halide perovskite material properties from SCLC maybe challenging, or often not possible.

Electric fields arising from the distribution of charge in metal halide perovskite solar cells are critical for understanding the many weird and wonderful optoelectronic properties displayed by these devices. Mobile ionic defects are thought to accumulate at interfaces to screen electric fields within the bulk of the perovskite semiconductor on application of external bias, but tools are needed to directly probe the dynamics of the electric field in this process. Here we show that electroabsorption measurements allow the electric field within the active layer to be tracked as a function of frequency or time. The magnitude of the electroabsorption signal, corresponding to the strength of the electric field in the perovskite layer, falls off for externally applied low frequency voltages or at long times following voltage steps. Our observations are consistent with drift-diffusion simulations, impedance spectroscopy, and transient photocurrent measurements. They indicate charge screening/redistribution on time-scales ranging from 10 ms to 100 s depending on the device interlayer material, perovskite composition, dominant charged defect, and illumination conditions. The method can be performed on typical solar cell structures and has potential to become a routine characterization tool for optimizing hybrid perovskite devices.

The origin of the relationship between fill factor (FF) and light intensity (I) in organic disordered-semiconductor-based solar cells is studied. An analytical model describing the balance between transport and recombination of charge carriers, parameterized with a factor, ${\mathrm{\ensuremath{\Gamma}}}_{m}$, is introduced to understand the FF-I relation, where higher values of ${\mathrm{\ensuremath{\Gamma}}}_{m}$ correlate to larger FFs. Comparing the effects of direct and tail-state-mediated recombination on the FF-I plot, we find that, for low-mobility systems, direct recombination with constant transport mobility can deliver only a negative dependence of ${\mathrm{\ensuremath{\Gamma}}}_{m,\mathrm{dir}}$ on light intensity. By contrast, tail-state-mediated recombination with trapping and detrapping processes can produce a positive ${\mathrm{\ensuremath{\Gamma}}}_{m,t}$ versus sun dependency. The analytical model is validated by numerical drift-diffusion simulations. To further validate our model, two material systems that show opposite FF-I behavior are studied: poly{4,8-bis[5-(2-ethylhexyl)thiophen-2-yl]benzo[1,2-b;4,5-b\ensuremath{'}]dithiophene-2,6-diyl-alt-[4-(2-ethylhexyl)-3-fluorothieno[3,4-b]thiophene)-2-carboxylate-2-6-diyl]} (PTB7-Th):[6,6]-phenyl-${\mathrm{C}}_{71}$-butyric acid methyl ester (${\mathrm{PC}}_{71}$BM) devices show a negative FF-I relation, while PTB7-Th:(5Z,5\ensuremath{'}Z)-5,5\ensuremath{'}-{[7,7\ensuremath{'} -(4,4,9,9-tetraoctyl-4,9-dihydro-s-indaceno[1,2-b:5,6-b\ensuremath{'}]dithiophene-2,7-diyl)bis(benzo[c][1,2,5]thiadiazole-7,4-diyl)]bis(methanylylidene)}bis(3-ethyl-2-thioxothiazolidin-4-one) (O-IDTBR) devices show a positive correlation. Optoelectronic measurements show that the O-IDTBR device presents a higher ideality factor, stronger trapping and detrapping behavior, and a higher density of trap states, relative to the ${\mathrm{PC}}_{71}$BM device, supporting the theoretical model. This work provides a comprehensive understanding of the correlation between FF and light intensity for disordered-semiconductor-based solar cells.

Transient photovoltage (TPV) measurements are frequently used to study recombination processes in thin‐film solar cells by probing the decay of a small optically induced voltage perturbation to infer the charge carrier dynamics of devices at open circuit. However, the validity of this method to probe organic semiconductors has recently come into doubt due to large discrepancies in the reported carrier lifetime values for the same systems and the reporting of unrealistic reaction order values. Herein, the validity of TPV to extract reliable charge carrier lifetimes in thin‐film solar cells is explored through the use of time‐dependent drift‐diffusion simulations and measurements. It is found that in low‐mobility materials, TPV serves primarily as a probe of charge carrier redistribution in the bulk rather than bulk recombination dynamics and that the extracted time constant is highly mobility dependent. To address this shortcoming, transient photocharge, a new technique to measure the charge carrier density during photovoltage decay, is introduced and applied to study the recombination dynamics in a series of (fullerene and nonfullerene) organic solar cell systems. It is shown that using this technique the charge carrier recombination lifetime in the active layer is more accurately determined.

The ideality factor determined by measuring the open circuit voltage (VOC) as function of light intensity is often used as a means to identify the dominant recombination mechanism in solar cells. However, applying this Suns-VOC technique to perovskite cells is problematic since the VOC evolves with time in a way which depends on the previously applied bias (Vpre), the light intensity, and the device architecture/processing. Here we show that the dominant recombination mechanism in two structurally similar CH3NH3PbI3 devices containing either mesoporous Al2O3 or TiO2 layers can be identified from the signature of the transient ideality factor following application of a forward bias, Vpre, to the device in the dark. The transient ideality factor, is measured by monitoring the temporal evolution of VOC at different light intensities. The initial values of the transient ideality were consistent with corresponding photoluminescence vs intensity as well as electroluminescence vs current density measurements. Time-dependent simulations of the measurement on modelled devices, which include the effects of mobile ionic charge, show that Shockley Read Hall (SRH) recombination through deep traps at the charge collection interfaces is dominant in both devices. Using transient photovoltage measurements superimposed on the evolving VOC of bifacial devices we further show that the charge collection interface extends throughout the mesoporous TiO2 layer, consistent with a transient ideality signature corresponding to SRH recombination in the bulk of the film. This information could not be inferred from an ideality factor determined from only steady-state VOC values. The method we have developed will be useful for identifying performance bottlenecks in new variants of perovskite devices by comparison with the transient ideality signatures we have predicted for a range of possible recombination schemes.

Mobile ions in hybrid perovskite semiconductors introduce a new degree of freedom to electronic devices suggesting applications beyond photovoltaics. An intuitive device model describing the interplay between ionic and electronic charge transfer is needed to unlock the full potential of the technology. We describe the perovskite-contact interfaces as transistors which couple ionic charge redistribution to energetic barriers controlling electronic injection and recombination. This reveals an amplification factor between the out of phase electronic current and the ionic current. Our findings suggest a strategy to design thin film electronic components with large, tuneable, capacitor-like and inductor-like characteristics. The resulting simple equivalent circuit model, which we verified with time-dependent drift-diffusion simulations of measured impedance spectra, allows a general description and interpretation of perovskite solar cell behaviour.

Recently Cui et al. reported on the fabrication a p-n homojunction perovskite solar cell (PSC) using stoichiometric control of sequentially-deposited perovskite layers. The authors propose that the junction leads to an enhanced electric field in the perovskite absorber resulting in improved charge separation. In this response to Cui et al. 2019 we show that the experimental data presented in the paper does not directly support this claim. Furthermore, Cui et al.'s thesis is not compatible with the large body of existing literature showing that mobile ionic defects present in methyl-ammonium lead iodide (MAPI) and its derivatives are highly mobile at room temperature. Using drift diffusion device simulations we show that large densities of mobile ionic charge in the system are likely to the screen any beneficial effects of a p-n homojunction.

The development of new flexible and stretchable sensors addresses the demands of upcoming application fields like internet‐of‐things, soft robotics, and health/structure monitoring. However, finding a reliable and robust power source to operate these devices, particularly in off‐the‐grid, maintenance‐free applications, still poses a great challenge. The exploitation of ubiquitous temperature gradients, as the source of energy, can become a practical solution, since the recent discovery of the outstanding thermoelectric properties of a conductive polymer, poly(3,4‐ethylenedioxythiophene)‐poly(styrenesulfonate) (PEDOT:PSS). Unfortunately the use of PEDOT:PSS is currently constrained by its brittleness and limited processability. Herein, PEDOT:PSS is blended with a commercial elastomeric polyurethane (Lycra), to obtain tough and processable self‐standing films. A remarkable strain‐at‐break of ≈700% is achieved for blends with 90 wt% Lycra, after ethylene glycol treatment, without affecting the Seebeck voltage. For the first time the viability of these novel blends as stretchable self‐powered sensors is demonstrated.

Mobile ions in hybrid perovskite semiconductors introduce a new degree of freedom to electronic devices suggesting applications beyond photovoltaics. An intuitive device model describing the interplay between ionic and electronic charge transfer is needed to unlock the full potential of the technology. We describe the perovskite-contact interfaces as transistors which couple ionic charge redistribution to energetic barriers controlling electronic injection and recombination. This reveals an amplification factor between the out of phase electronic current and the ionic current. The resulting simple equivalent circuit model, which we verified with time-dependent drift-diffusion simulations of impedance spectra, allows a general description and interpretation of perovskite solar cell behaviour. Our findings also suggest a strategy to design thin film electronic components with large, tuneable, capacitor-like and inductor-like characteristics.

Mobile ions in hybrid perovskite semiconductors introduce a new degree of freedom to electronic devices suggesting applications beyond photovoltaics. An intuitive device model describing the interplay between ionic and electronic charge transfer is needed to unlock the full potential of the technology. We describe the perovskite-contact interfaces as transistors which couple ionic charge redistribution to energetic barriers controlling electronic injection and recombination. This reveals an amplification factor between the out of phase electronic current and the ionic current. The resulting simple equivalent circuit model, which we verified with time-dependent drift-diffusion simulations of impedance spectra, allows a general description and interpretation of perovskite solar cell behaviour. Our findings also suggest a strategy to design thin film electronic components with large, tuneable, capacitor-like and inductor-like characteristics.

Verification of the “Wiggly Band” model for perovskite solar cells by transients measured at forward bias.

Ion migration has been proposed as a possible cause of photovoltaic current-voltage hysteresis in hybrid perovskite solar cells. A major objection to this hypothesis is that hysteresis can be reduced by changing the interfacial contact materials; however, this is unlikely to significantly influence the behaviour of mobile ionic charge within the perovskite phase. Here, we show that the primary effects of ion migration can be observed regardless of whether the contacts were changed to give devices with or without significant hysteresis. Transient optoelectronic measurements combined with device simulations indicate that electric-field screening, consistent with ion migration, is similar in both high and low hysteresis CH3NH3PbI3 cells. Simulation of the photovoltage and photocurrent transients shows that hysteresis requires the combination of both mobile ionic charge and recombination near the perovskite-contact interfaces. Passivating contact recombination results in higher photogenerated charge concentrations at forward bias which screen the ionic charge, reducing hysteresis.

We investigated the influence of moisture on methylammonium lead iodide perovskite (MAPbI3 ) films and solar cells derived from non-stoichiometric precursor mixtures. We followed both the structural changes under controlled air humidity through in situ X-ray diffraction, and the electronic behavior of devices prepared from these films. A small PbI2 excess in the films improved the stability of the perovskite compared to stoichiometric samples. We assign this to excess PbI2 layers at the perovskite grain boundaries or to the termination of the perovskite crystals with Pb and I. In contrast, the MAI-excess films composed of smaller perovskite crystals showed increased electronic disorder and reduced device performance owing to poor charge collection. Upon exposure to moisture followed by dehydration (so-called solvent annealing), these films recrystallized to form larger, highly oriented crystals with fewer electronic defects and a remarkable improvement in photocurrent and photovoltaic efficiency.