Multiscale Modeling and Simulation of Organic Solar Cells

In this article, we continue our mathematical study of organic solar cells (OSCs) and propose a two-scale (micro- and macro-scale) model of heterojunction OSCs with interface geometries characterized by an arbitrarily complex morphology. The microscale model consists of a system of partial and ordinary differential equations in an heterogeneous domain, that provides a full description of excitation/transport phenomena occurring in the bulk regions and dissociation/recombination processes occurring in a thin material slab across the interface. The macroscale model is obtained by a micro-to-macro scale transition that consists of averaging the mass balance equations in the normal direction across the interface thickness, giving rise to nonlinear transmission conditions that are parametrized by the interfacial width. These conditions account in a lumped manner for the volumetric dissociation/recombination phenomena occurring in the thin slab and depend locally on the electric field magnitude and orientation. Using the macroscale model in two spatial dimensions, device structures with complex interface morphologies, for which existing data are available, are numerically investigated showing that, if the electric field orientation relative to the interface is taken into due account, the device performance is determined not only by the total interface length but also by its shape

Theory and simulation of quantum photovoltaic devices based on the non-equilibrium Green's function formalism

This article reviews the application of the non-equilibrium Green's function formalism to the simulation of novel photovoltaic devices utilizing quantum confinement effects in low dimensional absorber structures. It covers well-known aspects of the fundamental NEGF theory for a system of interacting electrons, photons and phonons with relevance for the simulation of optoelectronic devices and introduces at the same time new approaches to the theoretical description of the elementary processes of photovoltaic device operation, such as photogeneration via coherent excitonic absorption, phonon-mediated indirect optical transitions or non-radiative recombination via defect states. While the description of the theoretical framework is kept as general as possible, two specific prototypical quantum photovoltaic devices, a single quantum well photodiode and a silicon-oxide based superlattice absorber, are used to illustrated the kind of unique insight that numerical simulations based on the theory are able to provide.Comment: 20 pages, 10 figures; invited review pape

Quantum-kinetic perspective on photovoltaic device operation in nanostructure-based solar cells

The implementation of a wide range of novel concepts for next-generation high-efficiency solar cells is based on nanostructures with configuration-tunable optoelectronic properties. On the other hand, effective nano-optical light-trapping concepts enable the use of ultra-thin absorber architectures. In both cases, the local density of electronic and optical states deviates strongly from that in a homogeneous bulk material. At the same time, non-local and coherent phenomena like tunneling or ballistic transport become increasingly relevant. As a consequence, the semi-classical, diffusive bulk picture conventionally assumed may no longer be appropriate to describe the physical processes of generation, transport, and recombination governing the photovoltaic operation of such devices. In this review, we provide a quantum-kinetic perspective on photovoltaic device operation that reaches beyond the limits of the standard simulation models for bulk solar cells. Deviations from bulk physics are assessed in ultra-thin film and nanostructure-based solar cell architectures by comparing the predictions of the semi-classical models for key physical quantities such as absorption coefficients, emission spectra, generation and recombination rates as well as potentials, densities and currents with the corresponding properties as given by a more fundamental description based on non-equilibrium quantum statistical mechanics. This advanced approach, while paving the way to a comprehensive quantum theory of photovoltaics, bridges simulations at microscopic material and macroscopic device levels by providing the charge carrier dynamics at the mesoscale.Comment: 22 pages, 8 figures; review article based on an invited talk at the MRS Spring Meeting 2017 in Phoeni

PV Parameter Identification using Reduced I-V Data

In this paper, possibility and accuracy of using reduced I-V data in PV parameter identification are discussed. Based on the linear identification method proposed in [1], six I-V points are used instead of the whole I-V curve to identify the PV parameters. The maximum power point (MPP) is then estimated using the identified I-V and P-V characteristics. Validation is done by using different sets of six points on the I-V curve. Experiment results show that the accurate curve fitting (with low RMSE and MPE) and good estimation of MPP can be achieved

Impact of different time series aggregation methods on optimal energy system design

Modelling renewable energy systems is a computationally-demanding task due to the high fluctuation of supply and demand time series. To reduce the scale of these, this paper discusses different methods for their aggregation into typical periods. Each aggregation method is applied to a different type of energy system model, making the methods fairly incomparable. To overcome this, the different aggregation methods are first extended so that they can be applied to all types of multidimensional time series and then compared by applying them to different energy system configurations and analyzing their impact on the cost optimal design. It was found that regardless of the method, time series aggregation allows for significantly reduced computational resources. Nevertheless, averaged values lead to underestimation of the real system cost in comparison to the use of representative periods from the original time series. The aggregation method itself, e.g. k means clustering, plays a minor role. More significant is the system considered: Energy systems utilizing centralized resources require fewer typical periods for a feasible system design in comparison to systems with a higher share of renewable feed-in. Furthermore, for energy systems based on seasonal storage, currently existing models integration of typical periods is not suitable

Analytical and Numerical Study of Photocurrent Transients in Organic Polymer Solar Cells

This article is an attempt to provide a self consistent picture, including existence analysis and numerical solution algorithms, of the mathematical problems arising from modeling photocurrent transients in Organic-polymer Solar Cells (OSCs). The mathematical model for OSCs consists of a system of nonlinear diffusion-reaction partial differential equations (PDEs) with electrostatic convection, coupled to a kinetic ordinary differential equation (ODE). We propose a suitable reformulation of the model that allows us to prove the existence of a solution in both stationary and transient conditions and to better highlight the role of exciton dynamics in determining the device turn-on time. For the numerical treatment of the problem, we carry out a temporal semi-discretization using an implicit adaptive method, and the resulting sequence of differential subproblems is linearized using the Newton-Raphson method with inexact evaluation of the Jacobian. Then, we use exponentially fitted finite elements for the spatial discretization, and we carry out a thorough validation of the computational model by extensively investigating the impact of the model parameters on photocurrent transient times.Comment: 20 pages, 11 figure

Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells

We report a model describing the molecular orientation disorder in CH3NH3PbI3, solving a classical Hamiltonian parametrised with electronic structure calculations, with the nature of the motions informed by ab-initio molecular dynamics. We investigate the temperature and static electric field dependence of the equilibrium ferroelectric (molecular) domain structure and resulting polarisability. A rich domain structure of twinned molecular dipoles is observed, strongly varying as a function of temperature and applied electric field. We propose that the internal electrical fields associated with microscopic polarisation domains contribute to hysteretic anomalies in the current--voltage response of hybrid organic-inorganic perovskite solar cells due to variations in electron-hole recombination in the bulk.Comment: 10 pages; 4 figures, 2 SI figure