THE DEVICE PHYSICS OF ORGANIC SOLAR CELLS A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Timothy M. Burke May 2015 © 2015 by Timothy Matthew Burke. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/mq955kd8880 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Michael McGehee, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Aaron Lindenberg I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Alberto Salleo Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract Organic solar cells are photovoltaic devices that use semiconducting plastics as the active layer rather than traditional inorganic materials such as Silicon. Like any solar cell, their efficiency at producing electricity from sunlight is characterized by three parameters: their short-circuit current (Jsc), open-circuit voltage (Voc) and fill factor (FF ). While the factors that determine each of these parameters are well- understood for established solar technologies, this is not the case for organic solar cells. The short-circuit current is much higher than we would expect given the strong attraction between electrons and holes in organic semiconductors that should lead to fast recombination, preventing the carriers from being collected as current. In contrast, the open-circuit voltage is much lower than we would expect based on the traditional relationship between optical absorption and voltage in inorganic semicon- ductors. Finally, the fill factor is highly variable from device to device and typically gets much worse as the cells are made thicker. In this work we develop a novel and general framework for understanding the short-circuit current, open-circuit voltage and fill factor of organic solar cells. The concept that turns out to unify all three aspects of device operation is the idea that electrons and holes move rapidly enough relative to their lifetimes to equilibrate with each other in the statistical mechanics sense before recombining. Previously, it had been thought that such equilibration was impossible because of the low macroscopic mobilities of charge carriers in organic solar cells. We first show using Kinetic Monte Carlo simulations that the charge carrier mobil- ity is 3-5 orders of magnitude higher on short length scales and immediately after light absorption by comparing simulated results to experimental terahertz spectroscopy iv data. Combining this high mobility with experimental lifetime data fully rationalizes high charge carrier generation efficiency and also explains how carriers can live long enough to be affected by strong inhomogeneities in the energetic landscape of the solar cell, which also improves charge generation. Turning to Voc, we use the same concept of fast carrier motion relative to the re- combination rate to show that recombination proceeds from an equilibrated popula- tion of Charge Transfer states. This simplification permits us to develop an analytical understanding of the open-circuit voltage and explain numerous puzzling Voc trends that have been observed over the years. Finally, we generalize our equilibrium result from open-circuit to explain the entire IV curve and use it to show how the low fill-factor of organic solar cells is not caused, as is often thought, by a voltage dependent carrier generation process but instead by low macroscopic charge carrier mobilities and the presence of dark charge carriers injected during device fabrication. Taken together, these results represent the first complete theory of organic solar cell operation. v Acknowledgments No work is done in isolation. I would like to gratefully acknowledge the collabora- tion and input from both the McGehee and Salleo group memebers, especially Jon Bartelt, Sean Sweetnam and Eric Hoke. I would further like to thank my advisor Mike McGehee for his advice and support during my PhD as well as the love and support of my fiancee, Saumya Sankaran. vi Contents Abstract iv Acknowledgments vi 1 Introduction 1 1.1 What is an Organic Solar Cell . 2 1.2 Basic Solar Cell Device Physics . 4 1.2.1 Electrons, Holes and Quasi-Fermi Levels . 7 1.2.2 Recombination . 9 1.2.3 Quasi-Fermi Levels and Operating Voltage . 10 1.2.4 Maximum Power Point . 11 1.3 Organic Solar Cell Device Physics . 12 1.3.1 Charge Transfer States . 12 1.3.2 Polarons . 12 1.3.3 Energetic Disorder . 13 2 The Short-Circuit Current 15 2.1 Preface . 15 2.2 Current Understanding and Background . 15 2.3 Core Simulation Results . 16 2.4 Conclusion . 27 2.5 KMC Simulation Details . 28 2.6 PL Decay Simulation Details . 28 2.7 Converting Hopping Rates to Mobility Values . 29 vii 2.8 Dependence on Mobility, Lifetime and Morphology . 30 2.9 Dependence of Pesc on Local Mobility and Lifetime . 31 2.10 Dependence of Pesc on Morphology . 33 2.11 The Impact of Energetic Disorder . 35 2.11.1 Simulation Details . 35 2.12 Independence from Bulk Mobility . 38 2.13 Exponential Decay of Photoluminescence . 38 3 The Open-Circuit Voltage 41 3.1 Preface . 41 3.2 Introduction . 41 3.3 Background Information . 42 3.4 The Temperature Dependence of Voc Leads Us Beyond Langevin Theory 47 3.5 Reduced Langevin Recombination Implies Equilibrium . 48 3.6 Equilibrium Simplifies the Understanding of Voc . 52 3.7 Effects of an Energy Cascade in 3-Phase Bulk Heterojunctions . 56 3.8 The Role of Energetic Disorder . 59 3.9 Experimental Observations Explained by the Model . 62 3.10 Explaining the Magnitude of the Voltage Loss . 63 3.11 Opportunities for Improving Voc ..................... 66 3.12 Conclusions . 68 3.13 Experimental Details . 68 3.13.1 Sample Preparation . 68 3.13.2 FTPS measurements . 69 3.14 Why We Expect the CT State Distribution to be Gaussian . 70 3.15 Inhomogeneously Broadened Marcus Theory Absorption . 71 3.16 Relating CT State Density and Chemical Potential . 72 3.17 Defining an Effective Density of CT States . 75 3.18 The Voltage Dependence of τct ...................... 77 3.19 The Low Temperature Limit of Voc ................... 78 3.20 The Light Ideality Factor . 79 viii 3.21 The Langevin Reduction Factor . 80 3.22 CT State Lifetimes . 80 3.23 The Applicability of Chemical Equilibrium to Electrons and Holes . 81 3.24 Deriving our Result Directly From the Canonical Ensemble . 84 4 The Fill Factor 92 4.1 The Myth of the Intrinsic Organic Solar Cell . 93 4.2 Why Dark Carriers Matter . 95 4.3 Methodology . 96 4.4 The Carrier Distribution in an OPV Device . 96 4.5 Recombination Away from Open-Circuit . 99 4.5.1 Classifying Recombination Types . 101 4.6 Using These Results to Understand Organic Solar Cells . 104 4.7 Validating Our Expression Using P3HT:PCBM . 104 4.7.1 Correcting for Series Resistance . 105 4.7.2 Correcting for Shunt Resistance . 108 4.7.3 P3HT:PCBM Data Fits Our Expression . 108 4.7.4 The Photocurrent Term . 114 4.7.5 The Built-in Potential . 115 4.7.6 Photocarrier - Dark Carrier Recombination . 117 4.7.7 Photocarrier - Photocarrier Recombination . 118 4.7.8 Dark - Dark Recombination . 120 4.7.9 Conclusions . 121 4.8 Molecular Weight Variations in PCDTBT . 121 4.9 Apparent Field Dependent Geminate Splitting . 123 4.9.1 Time Delayed Collection Field Measurements . 125 4.10 Conclusion . 129 4.11 Additional Theoretical Background . 130 4.11.1 Properly Counting States in the Presence of Disorder . 130 4.11.2 The Link Between Voltage and Carrier Density . 131 Bibliography 138 ix List of Tables 2.1 Lifetime and mobility values that were required in previous KMC stud- ies to predict 90% geminate splitting at short circuit conditions (field of 105 V/cm). 21 2.2 Literature measurements for local mobility (measured using time re- solved terahertz spectroscopy) and the geminate pair lifetime (mea- sured using transient absorption or transient photoluminescence). 23 2.3 Required local mobilities for 90% field-independent IQE for the speci- fied device morphologies. 27 2.4 Conversion of reported hopping rates into local mobility values. 30 2.5 Extracted escape probabilities for mixed regions between 3.2 and 9.6 nm wide. 33 3.1 Extracted CT state distribution centers and standard deviations with experimental Voc measurements for comparison. All raw data except for RRa P3HT is from literature.[98] . 62 3.2 The potential increases that could be obtained from improvements to each of the material parameters that affects Voc. 66 3.3 Tabulated Langevin Reduction Factors from Literature . 80 3.4 Reported measurements related to the CT state lifetime in literature 81 4.1 Extracted Photocurrent and Short-circuit Currents for PCDTBT:PCBM devices. 123 4.2 Extracted Photocurrent and Short-circuit Currents for p − DTS(FBTTh2)2- PC71BM devices. 125 x List of Figures 1.1 A schematic view of the molecular and energy landscape of a three phase organic solar cell showing the pure and mixed regions as well as the variation in local energy levels among the various phases.