What is moving in hybrid halide perovskite solar cells?

Organic-inorganic semiconductors, which adopt the perovskite crystal structure, have perturbed the landscape of contemporary photovoltaics research. In this Account, we discuss the internal motion of methylammonium lead iodide (CH$_3$NH$_3$PbI$_3$) and formamidinium lead iodide ([CH(NH$_2$)$_2$]PbI$_3$), covering: (i) molecular rotation-libration in the cuboctahedral cavity; (ii) drift and diffusion of large electron and hole polarons; (iii) transport of charged ionic defects. These processes give rise to a range of properties that are unconventional for photovoltaic materials, including frequency-dependent permittivity, low electron-hole recombination rates, and current-voltage hysteresis. Multi-scale simulations - drawing from electronic structure, ab initio molecular dynamic and Monte Carlo techniques - have been combined with neutron scattering and ultra-fast vibrational spectroscopy to qualify the nature and timescales of the motions. Recent experimental evidence and theoretical models for simultaneous electron transport and ion transport in these materials has been presented, suggesting they are mixed-mode conductors with similarities to metal oxide perovskites developed for battery and fuel cell applications. We expound on the implications of these effects for the photovoltaic action. The temporal behaviour found in hybrid perovskites introduces a sensitivity in materials characterisation to the time and length scale of the measurement, as well as the history of each sample. It also poses significant challenges for accurate materials and device simulations. Herein, we critically discuss the atomistic origin of the dynamic processes.Comment: 29 pages, 3 figure

Ferroelectric Materials for Solar Energy Conversion: Photoferroics Revisited

The application of ferroelectric materials (i.e. solids that exhibit spontaneous electric polarisation) in solar cells has a long and controversial history. This includes the first observations of the anomalous photovoltaic effect (APE) and the bulk photovoltaic effect (BPE). The recent successful application of inorganic and hybrid perovskite structured materials (e.g. BiFeO3, CsSnI3, CH3NH3PbI3) in solar cells emphasises that polar semiconductors can be used in conventional photovoltaic architectures. We review developments in this field, with a particular emphasis on the materials known to display the APE/BPE (e.g. ZnS, CdTe, SbSI), and the theoretical explanation. Critical analysis is complemented with first-principles calculation of the underlying electronic structure. In addition to discussing the implications of a ferroelectric absorber layer, and the solid state theory of polarisation (Berry phase analysis), design principles and opportunities for high-efficiency ferroelectric photovoltaics are presented

Predicting polaron mobility in organic semiconductors with the Feynman variational approach

We extend the Feynman variational approach to the polaron problem \cite{Feynman1955} to the Holstein (lattice) polaron. This new theory shows a discrete transition to small-polarons is observed in the Holstein model. The method can directly used in the FHIP \cite{Feynman1962} mobility theory to calculate dc mobility and complex impedance. We show that we can take matrix elements from electronic structure calculations on real materials, by modelling charge-carrier mobility in crystalline rubrene. Good agreement is found to measurement, in particular the continuous thermal transition in mobility from band-like to thermally-activated, with a minimum in mobility predicted at 140 K.Comment: 8 pages, 6 figure

Spontaneous Octahedral Tilting in the Cubic Inorganic Caesium Halide Perovskites CsSnX3_3 and CsPbX3_3 (X = F, Cl, Br, I)

The local crystal structures of many perovskite-structured materials deviate from the average space group symmetry. We demonstrate, from lattice-dynamics calculations based on quantum chemical force constants, that all the caesium-lead and caesium-tin halide perovskites exhibit vibrational instabilities associated with octahedral titling in their high-temperature cubic phase. Anharmonic double-well potentials are found for zone-boundary phonon modes in all compounds with barriers ranging from 108 to 512 meV. The well depth is correlated with the tolerance factor and the chemistry of the composition, but is not proportional to the imaginary harmonic phonon frequency. We provide quantitative insights into the thermodynamic driving forces and distinguish between dynamic and static disorder based on the potential-energy landscape. A positive band gap deformation (spectral blueshift) accompanies the structural distortion, with implications for understanding the performance of these materials in applications areas including solar cells and light-emitting diodes

Impact of non-parabolic electronic band structure on the optical and transport properties of photovoltaic materials

The effective mass approximation (EMA) models the response to an external perturbation of an electron in a periodic potential as the response of a free electron with a renormalized mass. For semiconductors used in photovoltaic devices, the EMA allows calculation of important material properties from first-principles calculations, including optical properties (e.g., exciton binding energies), defect properties (e.g., donor and acceptor levels), and transport properties (e.g., polaron radii and carrier mobilities). The conduction and valence bands of semiconductors are commonly approximated as parabolic around their extrema, which gives a simple theoretical description but ignores the complexity of real materials. In this work, we use density functional theory to assess the impact of band nonparabolicity on four common thin-film photovoltaic materials - GaAs, CdTe, Cu2ZnSnS4 and CH3NH3PbI3 - at temperatures and carrier densities relevant for real-world applications. First, we calculate the effective mass at the band edges. We compare finite-difference, unweighted least-squares and thermally weighted least-squares approaches. We find that the thermally weighted least-squares method reduces sensitivity to the choice of sampling density. Second, we employ a Kane quasilinear dispersion to quantify the extent of nonparabolicity and compare results from different electronic structure theories to consider the effect of spin-orbit coupling and electron exchange. Finally, we focus on the halide perovskite CH3NH3PbI3 as a model system to assess the impact of nonparabolicity on calculated electron transport and optical properties at high carrier concentrations. We find that at a concentration of 1020cm-3 the optical effective mass increases by a factor of two relative to the low carrier-concentration value, and the polaron mobility decreases by a factor of three. Our work suggests that similar adjustments should be made to the predicted optical and transport properties of other semiconductors with significant band nonparabolicity

The cubic perovskite structure of black formamidinium lead iodide, α-[HC(NH2)2]PbI3, at 298 K

The structure of black formamidinium lead halide, -[HC(NH2)2]PbI3, at 298 K has been refined from high resolution neutron powder diffraction data and found to adopt a cubic perovskite unit cell, a = 6.3620(8) Å. The trigonal planar [HC(NH2)2]+ cations lie in the central mirror plane of the unit cell with the formamidinium cations disordered over 12 possible sites arranged so that the C-H bond is directed into a cube face while the -NH2 groups hydrogen bond (NH…I = 2.75 – 3.00Å) with the iodide atoms of the [PbI3]− framework. High atomic displacement parameters for the formamidinium cation are consistent with rapid molecular rotations at room temperature as evidenced in ab initio molecular dynamic simulations