Theoretical Investigations of Polymer Based Solar Cells
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Theoretical Investigations of Polymer Based Solar Cells Robert S. Echols and Chris E. France California Polytechnic State University, Physics Department, San Luis Obispo, CA 93407 ABSTRACT We investigate the behavior of a polymer blend (M3EH-PPV:CN-ether-PPV) bulk heterojunction solar cell using a numeric model that self-consistently solves Poisson’s equation and the charge continuity equation while incorporating electric field dependent mobilities. We obtain good quantitative agreement with present experimental data for J-V curves and photocurrent action spectra. To reproduce experimental photocurrent action spectra, our model predicts 36% exciton dissociation efficiencies in the bulk of the polymer. We also study the limiting conditions of polymer solar cell development by simulating an ideal solar cell using an AM1.5 global spectrum and assuming all absorbed photons hitting a M3EH-PPV:CN-ether-PPV polymer blend (band gap ~2.0 eV) based solar cell at normal incidence contribute to current. If such a solar cell has 100 nm length, open circuit voltage=0.6 V and 50% fill factor, then the maximum theoretical power conversion efficiency is ηp=5.6%. A similar analysis for a M3EH-PPV:PCBM bulk heterojunction cell yields, ηp=3.5%. These results further highlight the need to develop smaller band gap materials and help explain why the best polymer based solar cells have power conversion efficiencies that remain stuck at about 3%. Our model is used to investigate the important increase in power conversion efficiencies we can expect as lower band gap polymers become available. INTRODUCTION Polymer based solar cells show great promise as a low cost alternative to the traditional silicon based solar cells. In the last decade, device design and material improvements have increased the power conversion efficiencies (ηp) to 3% for polymers blended with the fullerene derivative [6,6]-phenyl-C61 butyric acid methyl ester (PCBM) (for a review see [1]). To improve ηp beyond 3% we need lower band gap polymers to capture more photons from the solar spectrum. These lower band gap polymers are just now becoming available and being investigated [2]. Additional losses include poor charge carrier mobilities, incomplete exciton dissociation, and electron/hole recombination. In the current work we aim to quantify the loss mechanisms in bulk heterojunction polymer based solar cells to further elucidate needed improvements in device design and materials for viable photovoltaics. In the sections that follow we describe our ideal solar cell model and quantify losses due to incomplete absorption. Our detailed model is introduced and used to investigate losses from exciton dissociation inefficiencies and electron/hole recombination. We finish by determining optimal band gaps for an ideal cell limited only by inefficient absorption.
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SIMULATION MODELS Ideal Model To investigate inefficient absorption of polymer based solar cells we have developed the following idealized model. The charge continuity equation governing electrons given
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