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Nonequilibrium drift-diffusion model for organic semiconductor devices
Linköping University, Department of Physics, Chemistry and Biology, Complex Materials and Devices. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Biomolecular and Organic Electronics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Physics, Chemistry and Biology, Complex Materials and Devices. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7104-7127
2016 (English)In: PHYSICAL REVIEW B, ISSN 2469-9950, Vol. 94, no 3, article id 035205Article in journal (Refereed) Published
Abstract [en]

Two prevailing formalisms are currently used to model charge transport in organic semiconductor devices. Drift-diffusion calculations, on the one hand, are time effective but assume local thermodynamic equilibrium, which is not always realistic. Kinetic Monte Carlo models, on the other hand, do not require this assumption but are computationally expensive. Here, we present a nonequilibrium drift-diffusion model that bridges this gap by fusing the established multiple trap and release formalism with the drift-diffusion transport equation. For a prototypical photovoltaic system the model is shown to quantitatively describe, with a single set of parameters, experiments probing (1) temperature-dependent steady-state charge transport-space-charge limited currents, and (2) time-resolved charge transport and relaxation of nonequilibrated photocreated charges. Moreover, the outputs of the developed kinetic drift-diffusion model are an order of magnitude, or more, faster to compute and in good agreement with kinetic Monte Carlo calculations.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC , 2016. Vol. 94, no 3, article id 035205
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:liu:diva-131516DOI: 10.1103/PhysRevB.94.035205ISI: 000381482700003OAI: oai:DiVA.org:liu-131516DiVA, id: diva2:974402
Available from: 2016-09-26 Created: 2016-09-23 Last updated: 2018-09-10
In thesis
1. Effects of Energetic Disorder on the Optoelectronic Properties of Organic Solar Cells
Open this publication in new window or tab >>Effects of Energetic Disorder on the Optoelectronic Properties of Organic Solar Cells
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Organic photovoltaics (OPVs) is a promising low-cost and environmental-friendly technology currently achieving 12-14% power conversion efficiency. Despite the extensive focus of the research community over the last years, critical mechanisms defining the performance of OPVs are still topics of debate. While energetic disorder is known to be characteristic of organic semiconductors in general, its potential role in OPV has received surprisingly little attention. In this thesis we investigate some aspects of the relation between energetic disorder and several optoelectronic properties of OPV.

Charge carrier mobility is a key parameter in characterizing the performance of organic semiconductors. Analyzing the temperature dependence of the mobility is also an oftenused method to obtain (estimates for) the energetic disorder in the HOMO and LUMO levels of an organic semiconductor material. Different formalisms to extract and analyze mobilities from space charge limited conductivity (SCLC) experiments are reviewed. Surprisingly, the Murgatroyd-Gill analytical model in combination with the Gaussian disorder model in the Boltzmann limit yields similar mobilities and energetic disorders as a more elaborate drift-diffusion model with parametrized mobility functionals. Common analysis and measurement errors are discussed. All the models are incorporated in an automated analysis freeware tool.

The open circuit voltage (Voc) has attracted considerable interest as the large difference between Voc and the bandgap is the main loss mechanism in bulk heterojunction OPVs. Surprisingly, in ternary devices composed of two donors and one acceptor, the Voc is not pinned to the shallowest HOMO but demonstrates a continuous tunability between the binary extremities. We show that this phenomenon can be explained with an equilibrium model where Voc is defined as the splitting of the quasi-Fermi levels of the photo-created holes and electrons in a common density of states accounting for the stoichiometry, i.e. the ratio of the donor materials and the broadening by Gaussian disorder. Evaluating the PCE, it is found that ternary devices do not offer advantages over binary unless the fill factor (FF) is increased at intermediate compositions, as a result of improved transport/recombination upon material blending.

Stressing the importance of material intermixing to improve the performance, we found that the presence of an acceptor may drastically alter the mobility and energetic disorder of the donor and vice versa. The effect of different acceptors was studied in a ternary onedonor- two-acceptors system, where the unpredictable variability with composition of the energetic disorder in the HOMO and the LUMO explained the almost linear tunability of Voc. Designing binary OPVs based on the design rule that the energetic disorder can be reduced upon material blending, as we observed, can yield a relative PCE improvement of at least 20%.

CT states currently play a key role in evaluating the performance of OPVs and CTelectroluminescence (CT-EL) is assumed to stem from the recombination of thermalized electron-hole pairs. The varying width of the CT-EL peak for different material combinations is intuitively expected to reflect the energetic disorder of the effective HOMO and LUMO. We employ kinetic Monte Carlo (kMC) CT-EL simulations, using independently measured disorder parameters as input, to calculate the ground-to-ground state (0-0) transition spectrum. Including the vibronic broadening according to the Franck Condon principle, we reproduce the width and current dependence of the measured CT-EL peak for a large number of donor-acceptor combinations. The fitted dominant phonon modes compare well with the values measured using the spectral line narrowing technique. Importantly, the calculations show that CT-EL originates from a narrow, non-thermalized subset of all available CT states, which can be understood by considering the kinetic microscopic process with which electron-hole pairs meet and recombine.

Despite electron-hole pairs being strongly bound in organic materials, the charge separation process following photo-excitation is found to be extremely efficient and independent of the excitation energy. However, at low photon energies where the charges are excited deep in the tail of the DOS, it is intuitively expected for the extraction yield to be quenched. Internal Quantum Efficiency (IQE) experiments for different material systems show both inefficient and efficient charge dissociation for excitation close to the CT energy. This finding is explained by kinetic Monte Carlo simulations accounting for a varying degree of e-h delocalization, where strongly bound localized CT pairs (< 2nm distance) are doomed to recombine at low excitation energies while extended delocalization over 3-5nm yields an increased and energy-independent IQE. Using a single material parameter set, the experimental CT electroluminescence and absorption spectra are reproduced by the same kMC model by accounting for the vibronic progression of the calculated 0-0 transition. In contrast to CT-EL, CT-absorption probes the complete CT manifold.

Charge transport in organic solar cells is currently modelled as either an equilibrium or a non-equilibrium process. The former is described by drift-diffusion (DD) equations, which can be calculated quickly but assume local thermal equilibrium of the charge carriers with the lattice. The latter is described by kMC models, that are time-consuming but treat the charge carriers individually and can probe all relevant time and energy scales. A hybrid model that makes use of the multiple trap and release (MTR) concept in combination with the DD equations is shown to describe both steady-state space charge limited conductivity experiments and non-equilibrium time-resolved transport experiments using a single parameter set. For the investigated simulations, the DD-MTR model is in good agreement with kMC and ~10 times faster.

Steady-state mobilities from DD equations have been argued to be exclusively relevant for operating OPVs while charge carrier thermalization and non-equilibrium time-dependent mobilities (although acknowledged) can be disregarded. This conclusion, based on transient photocurrent experiments with μs time resolution, is not complete. We show that non-equilibrium kMC simulations can describe the extraction of charge carriers from subps to 100 μs timescales with a single parameter set. The majority of the fast charge carriers, mostly non-thermalized electrons, are extracted at time scales below the resolution of the experiment. In other words, the experiment resolves only the slower fraction of the charges, predominantly holes.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 60
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1943
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Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-150998 (URN)10.3384/diss.diva-150998 (DOI)9789176852712 (ISBN)
Public defence
2018-09-13, Schrödinger (E324), Fysikhuset, Campus Valla, Linköping, 10:15 (English)
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Available from: 2018-09-10 Created: 2018-09-10 Last updated: 2019-10-09Bibliographically approved

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