Predictive Mechanistic Model for the Electrical Impedance and Intensity-Modulated Photocurrent and Photovoltage Spectroscopic Responses of an Organic Bulk Heterojunction Solar Cell

Ying Ting Set, Erik Birgersson, and Joachim Luther

Phys. Rev. Applied 5, 054002 – Published 3 May 2016

Abstract

We develop a predictive and mechanistic model for the intensity-modulated photocurrent spectroscopic (IMPS), intensity-modulated photovoltage spectroscopic (IMVS), and electrical impedance spectroscopic (EIS) responses of organic bulk heterojunction (BHJ) solar cells. Unlike the dominant analytical framework—equivalent circuit analysis—the model uses physical parameters that directly reflect the device’s fundamental electronic mechanisms, eliminating the ambiguity associated with interpreting phenomenological parameters. Formulated in the frequency domain, the model is a computationally efficient tool for extracting parameters from the measured spectra. With a set of physical parameters representing a device, we predict the device’s spectra (a) in techniques employing different methods of perturbing a device and (b) at different bias voltages and illumination intensities. The predicted spectra show good agreement with the measured ones. By quantifying the device’s internal electric field and charge carrier concentration and relating them to the spectra, we determine that the IMPS responses at the short-circuit condition and the IMVS responses at the open-circuit condition directly reflect the charge carrier extraction and recombination, respectively. Furthermore, the EIS response indicates the device’s recombination time scale at different bias voltages.

Received 23 December 2015

DOI:https://doi.org/10.1103/PhysRevApplied.5.054002

Physics Subject Headings (PhySH)

Photoconductivity

Organic semiconductors Solar cells

Spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ying Ting Set^1,2,*, Erik Birgersson¹, and Joachim Luther³

¹Solar Energy Research Institute of Singapore (SERIS), National University of Singapore, 7 Engineering Drive 1, Singapore 117574, Singapore
²Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117585, Singapore
³Fraunhofer Institute for Solar Energy Systems (ISE), Heidenhofstrasse 2, 79110 Freiburg, Germany

^*setyingting@nus.edu.sg; setyingting@gmail.com

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Vol. 5, Iss. 5 — May 2016

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Images

Figure 1
Steady-state current-density voltage ( $j − V_{a}$ ) curves at different illumination intensities: $P_{0} = 1$ sun (solid line) and 10% above or below that level (dotted line). Frequency-resolved techniques subject a BHJ device to a small-signal harmonic perturbation (sinusoids) about a steady state (symbols). IMPS and IMVS spectroscopy vary the illumination intensity to perturb the device along the $j$ axis and $V_{a}$ axis, respectively, whereas the EIS varies the bias voltage to perturb the device along the $j − V_{a}$ curve.
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Figure 2
(a) Nyquist and (b) Bode magnitude and phase plots of the IMPS transfer functions of BHJ devices: time-domain (solid squares) and frequency-domain model predictions (solid line).
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Figure 3
(a) IMPS Nyquist responses, (b) the characteristic frequencies for IMPS (solid line), and the bulk electric field strengths (dashed line) of BHJ devices at the short-circuit condition under different illumination intensities, $P_{0}$ : experiments (symbols) and model predictions (lines). (a) $P_{0} = 0.5$ (solid squares), 0.75 (solid down triangles), and 1 (solid circles) sun. (b) Data for training (solid diamonds) and testing (solid triangles) model parameters. The symbols and error bars indicate the means and standard deviations of the $f_{c}^{IMPS}$ of three BHJ devices, respectively.
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Figure 4
(a) IMVS Nyquist responses, (b) the characteristic frequencies for IMVS (solid line), and the bulk electron concentration (dashed line) of BHJ devices at the open-circuit condition under different illumination intensities, $P_{0}$ : experiments (symbols) and model predictions (lines). (a) $P_{0} = 0.5$ (solid squares), 0.75 (solid down triangles), and 1 (solid circles) sun. (b) Data for training (solid diamonds) and testing (solid triangles) model parameters. The symbols and error bars indicate the means and standard deviations of the $f_{c}^{IMVS}$ of three BHJ devices, respectively.
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Figure 5
(a) EIS Nyquist responses, (b) EIS characteristic frequencies (solid line), and bulk electron concentration (dashed line) of BHJ devices at different bias voltage $V_{a}$ and under $P_{0} = 1$ sun: experiments (symbols) and model predictions (lines). (a) $V_{a} = 0.2$ (solid squares), 0.3 (solid down triangles), and 0.4 (solid circles) V. (b) Data for training (solid diamonds) and testing (solid triangles) model parameters. The symbols and error bars indicate the means and standard deviations of the $f_{c}^{EIS}$ of three BHJ devices, respectively.
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