UNDERSTANDING THE ROLE OF CHARGE MOBILITY AND

RECOMBINATION IN ORGANIC PHOTOVOLTAICS

AN HONORS THESIS SUBMITTED TOTHE DEPARTMENT OF PHYSICS AT STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR THE DEGREE OF

BACHELORS OF SCIENCE WITH HONORS

David LamMay 2015

The undergraduate honors thesis of David Lam was reviewed and approved by the following:

Michael D. McGeheeProfessor, Materials Science and EngineeringThesis Advisor

Patricia R. BurchatProfessor, PhysicsSecond Reader

Abstract

Current organic photovoltaics based on bulk heterojunctions have an active absorbing layer thatis typically only 70 to 100 nm thick. While this results in efficient extraction of photogeneratedcharge carriers, the active layer is too thin for efficient absorption of light. If the active layerwere 300 nm thick, close to 100% of the light would be absorbed. However, when devices aremade with thicker active layers, recombination of charge carriers reduces the overall efficiency ofthe device.

In this project, I conduct an in-depth analysis of the effect of charge mobility and recombina-tion in organic photovoltaics. Using a combination of experiments and a 1D simulation software,Seftos, I explain why bulk heterojunction organic photovoltaics suffer from poor performancewhen made with thick active layers. I experimentally demonstrate charge mobility’s effect onreducing solar cells, then utilize it to extract values of the recombination rate constant for twoorganic photovoltaic systems. These results provide an overview on the role of charge mobilityand recombination in device performance and a road map for designing the next iteration of bulkheterojunction systems.

Parts of this thesis were adopted from a publication currently in review, “Charge-CarrierMobility Requirements for Bulk Heterojunction Solar Cells with High Fill Factor and ExternalQuantum Efficiency > 90%”, of which I was the second author [1].

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Table of Contents

List of Figures iv

List of Tables vi

List of Symbols and Acronyms vii

Acknowledgments ix

Chapter 1Introduction 11.1 An Introduction to Organic Photovoltaics . . . . . . . . . . . . . . . . . . . . . . 11.2 Evaluating Solar Cell Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Factors Limiting Bulk Heterojunction Photovoltaic Performance . . . . . . . . . 41.4 Research Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Chapter 2Understanding Device Performance through Experiments 62.1 Performance of P3HT:PCBM Bulk Heterojunction Cells . . . . . . . . . . . . . . 62.2 Recombination in P3HT:PCBM Bulk Heterojunction Cells . . . . . . . . . . . . . 8

Chapter 3Understanding Device Physics Using Simulation 113.1 Introduction to Seftos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Validation of Seftos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Determining k for P3HT:PCBM and H1:PCBM . . . . . . . . . . . . . . . . . . . 14

3.3.1 P3HT:PCBM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3.2 H1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Chapter 4Discussion 184.1 Charge Mobility and Fill Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2 Recombination in Organic Photovoltaics . . . . . . . . . . . . . . . . . . . . . . . 184.3 Evaluating Organic Photovoltaics with a Device Simulator . . . . . . . . . . . . . 194.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Appendix AExperimental Methods 21A.1 Fabrication of P3HT:PCBM Devices . . . . . . . . . . . . . . . . . . . . . . . . . 21A.2 Solar Cell Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

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A.3 Hole-Only Diode Preparation and Measurements . . . . . . . . . . . . . . . . . . 22A.4 Low Light Intensity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Appendix BSimulation Procedure 23B.1 Simulation Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23B.2 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

B.2.1 LUMO, HOMO and Work Function . . . . . . . . . . . . . . . . . . . . . 28B.2.2 Dielectric Constant and Effective Density of States . . . . . . . . . . . . . 28B.2.3 Optical Generation Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 28B.2.4 Langevin Reduction Factor . . . . . . . . . . . . . . . . . . . . . . . . . . 29B.2.5 Charge Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29B.2.6 Complex Index of Refraction . . . . . . . . . . . . . . . . . . . . . . . . . 29B.2.7 Series Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30B.2.8 Device Stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

B.3 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30B.3.1 Simulator Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30B.3.2 Best Fit Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Bibliography 32

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List of Figures

1.1 An energy-level diagram of exciton splitting. After light is absorbed in the activelayer (by the donor molecule), the exciton diffuses to a heterojunction and splits.Charge is then extracted at the two electrodes. Graphic courtesy of ProfessorMcGehee’s course on solar cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 A schematic of a bulk heterojunction layer. The red lines are polymer chains,while the black dots are fullerene molecules. Graphic courtesy of Jonathan A.Bartelt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 A schematic of a band diagram of an undoped organic semiconductor, as found inOPVs. Because the Fermi level must be constant throughout the device at equilib-rium, a built-in electric field is created, which drives the charge carriers in oppositedirections towards the contacts. Graphic courtesy of Professor McGehee’s courseon solar cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 A current density-voltage curve. Figures of merit include the voltage at open cir-cuit (Voc), the current density at short circuit (Jsc), the power conversion efficiency(PCE), and the fill factor (FF). . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 Chemical structures of the organic molecules used in this thesis. P3HT is a con-jugated polymer while H1 is a small molecule. Both serve as the electron-donorand light absorbing material. The electron-acceptor materials are the fullerenesPC60BM and PC70BM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 JV Curves for roughly 220-nm devices, annealed at 25, 48, 71, 88, 111,and 148. The performance of the device improves as the annealing temperatureincreases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 The electron and hole mobility of a P3HT:PCBM device as a function of annealingtemperature. The hole mobility increases by more than three orders of magnitude,while the electron mobility increases by one and a half orders of magnitude whenthe annealing temperature is increased from 25to 148. . . . . . . . . . . . . . 7

2.3 Plots of FF and PCE vs thickness for devices annealed at 25 (“as cast”), 71,111, and 148. The horizontal error bars represent the minimum and maximumthicknesses for a group of devices, whereas the vertical error bars represent theminimum and maximum PCE and FF for a given group of devices. . . . . . . . . 8

2.4 Current density at short circuit as a function of layer thickness. There are ab-sorption peaks found in the current density, which modulates the PCE despite theincrease in FF at low thicknesses. These calculations are based on the transfer-matrix formalism developed by Burkhard et al. . . . . . . . . . . . . . . . . . . . 9

2.5 A plot of FF as a function of light intensity for devices annealed at various tem-peratures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

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3.1 Simulated (a) and experimental (b) IV curves for ∼220-nm devices annealed at25 (“as cast”), 48, 71, 88, 111, and 148. There is agreement betweensimulated and experimental IV curves as anneal temperature is increased. . . . . 13

3.2 Simulated (a) and experimental (b) plots of FF vs thickness for devices annealedat 25 (“as cast”), 71, 111, and 148. The experimental plot is identical toFigure 2.3(a) and is reproduced for convenience. . . . . . . . . . . . . . . . . . . 13

3.3 Simulated (a) and experimental (b) plots of PCE vs thickness for devices annealedat 25 (“as cast”), 71, 111, and 148. The experimental plot is identical toFigure 2.3(b) and is reproduced for convenience. . . . . . . . . . . . . . . . . . . 14

3.4 Shunt resistance as a function of thickness and anneal temperature. All devicesexhibit a drop of two orders of magnitude in shunt resistance for device thicknessesbelow 100 nm, resulting in lower fill factors than predicted by the simulator.Figure courtesy of Jonathan A. Bartelt. . . . . . . . . . . . . . . . . . . . . . . . 14

3.5 Experimental data on the charge mobility (a) and performance of H1:PCBM asa function of the weight percentage of H1(b). Data provided by our collaboratorsfrom UCSB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.6 Experimental and simulated FF and PCE vs H1 weight percentage. There isstrong agreement in trends for the low and high weight percentage regions, whilein the intermediate region (50% and 60%), there is a deviation. This can be at-tributed to the fact that these two devices have lower recombination rate constantsthan the simulated value, leading to artificially lower values of FF and PCE. . . 17

B.1 The home screen, where the device stack is created and modified. . . . . . . . . . 23B.2 The drift-diffusion tab. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24B.3 The layer properties window, which allows the user to modify the optical and

electrical properties of each layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24B.4 The optical material editor window, which allows the user to enter in the complex

index of refraction as a function of wavelength. . . . . . . . . . . . . . . . . . . . 25B.5 The optical material editor window, which allows the user to enter in the electri-

cal properties of the layer, such as HOMO, LUMO, recombination rate, chargemobility, etc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

B.6 The sweep settings window, which allows the user to sweep across a large varietyof variables, including voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

B.7 The results window, which displays figures of merit and allows the user to generatea results report or view individual generated results for a wide range of electrical(e.g. IV curves, electric fields) and optical (e.g. max photocurrent, absorptionprofile) properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

B.8 Right-clicking on the figure generates a drop-down menu with a save data option. 27B.9 An example of the best fit procedure, done on a 50% H1 device. The residual

between measured and simulated is plotted to see if the residual falls within thetolerance between 0 V and the voltage at open circuit. . . . . . . . . . . . . . . . 31

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List of Tables

2.1 Hole mobility (µh), electron mobility (µe), the active layer thickness (L), andfigures of merit as defined in Section 1.2, for roughly 220-nm devices annealed at25, 48, 71, 88, 111, and 148. . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 Simulated values for the Langevin pre-factor and k for 220-nm thick P3HT:PCBMdevices. The values of k fall in line with literature values and are all within anorder of magnitude of each other, suggesting that k is constant. . . . . . . . . . . 15

3.2 Hole mobility, electron mobility, and figures of merit for ∼100-nm H1:PCBM de-vices made with different H1 concentrations by weight percentage. Data providedby collaborators at UCSB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3 Simulated values for k for 100 nm thick H1:PCBM devices. As with P3HT:PCBM,the values of k all fall within one order of magnitude of the average value. However,the value of k is at least 3 orders of magnitude higher than that of P3HT:PCBM,leading to lower FF despite higher charge mobility. . . . . . . . . . . . . . . . . . 17

4.1 Literature values of the Langevin reduction factor and k for various BHJ systems. 20

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List of Symbols and Acronyms

PV Photovoltaic, page 1

OPV Organic photovoltaic, page 1

HOMO Highest occupied molecular orbital, analogous to the valence band in inorganic semi-conductors, page 1

LUMO Lowest unoccupied molecular orbital, analogous to the conduction band in inorganicsemiconductors, page 1

BHJ Bulk heterojunction, page 1

Voc Voltage at open circuit, when I = 0 mA, page 2

Isc Current at short circuit, when V = 0 V, page 2

Jsc Current density at short circuit, when V = 0 V, page 2

η, PCE Power conversion efficiency, defined as PCE = Power ExtractedPower Incident , page 3

FF Fill factor, defined as FF = PmaxVocIsc

, page 3

EQE External quantum efficiency, defined as EQE = Charge ExtractedPhotons Incident , page 3

q Elementary charge, defined as 1.602× 10−19 coulombs, page 4

IQE Internal quantum efficiency, defined as IQE = Charge ExtractedPhotons Absorbed in Active Layer or IQE =

ηEDηCTηCC, page 4

µh Hole mobility, in units of cm2

V s , page 6

µe Electron mobility, in units of cm2

V s , page 6

k (Bimolecular) recombination rate constant, in units of cm3

s , page 9

n Electron density, in units of cm−3, page 9

p Hole density, in units of cm−3, page 9

γ Langevin pre-factor, page 9

ε0 Permittivity of free space, page 11

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n The real part of the refractive index, page 11

α Absorption coefficient, given by α = 4πκλ , page 11

κ The imaginary part of the refractive index, page 11

εr Relative permittivity, page 12

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Acknowledgments

I would like to thank Professor Michael D. McGehee for providing me with my very first op-portunity to conduct research back in my freshman year. His patience and support for me hasfostered my growth as a researcher, and my academic career would not nearly be as enrichingor rewarding without the opportunity to engage in research as exciting and worthwhile as thework I did in this group. From working on solid-state dye-sensitized solar cells to bulk hetero-junction photovoltaics, I’ve been exposed to a wide range of research and found my true passionin energy-focused research.

I would also like to thank the members of the McGehee group, both past and present. Thankyou to George B., Eric, Jon, Colin, Rachel, Becky, Andrea, Tim, Roong, Aryeh, Billy, William,Dan, Sean, Rohit, Eva, Zach, Jason, Grey, George M., Thomas, and Toby. Everybody in thegroup has gone out of their way to help me and make me feel welcome. From simple experimentalassistance to engaging in long conversations about the direction of my project, every groupmember has been there for me and making sure that I was always equipped to do research. Italso helps that they tolerated having a clumsy undergraduate working in their lab space! Out ofall of the things I’ll miss about Stanford, working in the McGehee group ranks highly on my list.I hope the next group that I join will have as warm and inviting of a group dynamic as this one.

I would like to especially thank Dr. George Y. Margulis for mentoring me through my firstproject with the McGehee group and Jonathan A. Bartelt for supporting me and guiding methrough the majority of this thesis. These two people have served as wonderful mentors to me asI learned how to become a researcher. It is because of them that I feel confident in my abilitiesas a scientist.

Furthermore, I’d like to thank Professor Patricia R. Burchat for being an amazing professor,teacher, and mentor. Taking two physics classes with her really inspired me and pushed metowards finishing the physics major and pursuing my goals to become a professor. Working forher as a teaching assistant in Physics 41 opened my eyes to the depth in the craft of teaching. Iam honored to have Professor Burchat be my second reader.

Finally, I would like to dedicate this thesis to my parents. Without their sacrifice, I wouldnot be here today.

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Chapter 1 |Introduction

One of the critical problems of the twenty-first century is that of rapidly increasing energyconsumption. According to the U.S. Energy Information Administration, in 30 years, energyconsumption in the world will increase by 56% [2]. Solar power offers an excellent option to meetthis demand without increased consumption of fossil fuels. Traditional inorganic photovoltaics(PVs), such as silicon and gallium arsenide, already have high power conversion efficiencies.

In addition to efficiency, cost is another important factor for determining the viability of solarenergy in the larger energy market. The U.S. Department of Energy set an installation costgoal of $0.33/W in order for solar to be competitive with other sources of energy [3]. InorganicPVs require costly purified semiconductors; meeting the cost goal for inorganic PVs is verydifficult. Organic photovoltaics (OPVs), however, can be solution-processed at low temperatureson inexpensive substrates, allowing for inexpensive, large-scale production with wet-processingtechniques like blade-coating and roll-to-roll printing [4]. Thus, OPVs, either as a stand-alonePV technology or as part of a third-generation tandem PV, offer a cost-effective avenue to cleanenergy.

1.1 An Introduction to Organic Photovoltaics

Organic photovoltaics are excitonic solar cells. When an organic semiconducting molecule inan OPV device absorbs an incident photon, an electron from the highest occupied molecularorbital (HOMO) is promoted to the lowest unoccupied molecular orbital (LUMO), similar tothe excitation of an electron from the conduction to valence band in inorganic semiconductors.The resulting excitation creates a bound electron-hole pair called an exciton. An exciton formsbecause the dielectric constant of organic semiconductors are relatively low when compared to in-organic PVs [5]. In OPVs, excitons are dissociated at the interface between an electron-accepting(traditionally a C60 derivative, also known as a fullerene) and electron-donating (traditionally aconjugated polymer or small molecule) material, and the disassociated charges are transportedthrough the active layer of the photovoltaic. These charges are collected at their respective electriccontacts, generating a current and power with an external circuit, demonstrated in Figure 1.1.

Bulk heterojunction (BHJ) solar cells, a type of OPV, are solution-processable with fewmanufacturing steps. Solution-processing has the potential to drastically decrease the cost oflarge-scale production. BHJs eschew a traditional well-defined heterojunction, instead utilizing

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Figure 1.1. An energy-level diagram of exciton splitting. After light is absorbed in the active layer (bythe donor molecule), the exciton diffuses to a heterojunction and splits. Charge is then extracted at thetwo electrodes. Graphic courtesy of Professor McGehee’s course on solar cells.

self-assembly of nanoscale heterojunctions of electron-donating and electron-accepting materials,as shown in Figure 1.2. This self-assembly occurs due to phase separation of the semiconductingpolymer/small molecule and fullerene [6]. When excitons are generated in BHJs, they are disas-sociated at these nanoscale heterojunctions. Then, they are transported through their respectivephases, usually through drift by a built-in electric field, until they are extracted at electricalcontacts, as shown in Figure 1.3. BHJs are a promising approach to meet the U.S. Departmentof Energy’s installation cost goal because of the ease of processing associated with this type ofOPV.

Figure 1.2. A schematic of a bulk heterojunction layer. The red lines are polymer chains, while theblack dots are fullerene molecules. Graphic courtesy of Jonathan A. Bartelt.

1.2 Evaluating Solar Cell Performance

To evaluate the performance of any solar cell, consider a current-voltage curve (IV curve, or JVcurve for current density-voltage), as shown in Figure 1.4. The voltage at open circuit (Voc)occurs when I = 0 mA and the current at short circuit (Isc) when V = 0 V. Equivalently, onecan measure the current density at short circuit (Jsc), which is independent of active area. The

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Figure 1.3. A schematic of a band diagram of an undoped organic semiconductor, as found in OPVs.Because the Fermi level must be constant throughout the device at equilibrium, a built-in electric field iscreated, which drives the charge carriers in opposite directions towards the contacts. Graphic courtesyof Professor McGehee’s course on solar cells.

power conversion efficiency (η, PCE) is given by the formula η = PCE = Power ExtractedPower Incident . For

experiments, solar cells are tested under one sun intensity with a standard solar spectrum at theEarth’s surface (AM1.5G), with Pincident = 100 mW

cm2 .

Figure 1.4. A current density-voltage curve. Figures of merit include the voltage at open circuit (Voc),the current density at short circuit (Jsc), the power conversion efficiency (PCE), and the fill factor (FF).

Finally, the fill factor (FF) is defined by the equation FF = PmaxVocIsc

. The fill factor is a measureof the ideality of the solar cell.

Two other important measures of solar cell performance are the external and internal quantumefficiency. Both are a measure of how many photons are converted into charge carriers in thesolar cell. The external quantum efficiency (EQE) is defined by EQE = Charge Extracted

Photons Incident and is

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a function of the wavelength of the photon. Using this, Isc is related to the EQE using thefollowing formula:

Isc = qA

∫ ∞0

Φp(λ)× EQE(λ) dλ (1.1)

where q is the elementary charge, A is the active device area, and Φp(λ) is the photon flux at agiven wavelength. The EQE is thus a measure of how many charge carriers are generated andcollected for a given intensity of light.

The internal quantum efficiency (IQE) is defined as IQE = Charge ExtractedPhotons Absorbed in Active Layer . The

IQE can be calculated from the EQE by considering the absorption of photons in the active layerand is a measure of how effective charges are collected once photogenerated. This calculationrequires use of a transfer-matrix formalism to take into account interference effects and parasiticabsorption in the various layers of a solar cell stack [7]. More simply, the IQE can be definedas IQE = ηEDηCTηCC, where ηED is the exciton diffusion efficiency, ηCT is the charge transferefficiency and ηCC is the charge collection efficiency.

1.3 Factors Limiting Bulk Heterojunction Photovoltaic Perfor-mance

While BHJs offer a cost-competitive approach, the performance of this PV technology needs to beimproved in order for it to be viable commercially. In order to reach power conversion efficienciesof 15%, the EQE and the FF need to approach 90% and 0.8, respectively. Currently, BHJ solarcells with PCEs approaching 10% and FF of 0.8 have already been reported in literature [8, 9].However, many of these BHJ devices are optimized with a 70 to 100-nm active layer, which resultsin a sub-80% EQE due to insufficient absorption. To increase the EQE to the target goal of 90%,the absorption needs to reach at least 90% in a device with IQE close to 100%, which typicallyoccurs when a BHJ device has a 200-nm thick active layer with a back reflector or 300-nm in asemi-transparent device. However, when devices were made thicker to improve light absorption,the FF decreased, leading to a decline in PCE [10–12]. The drop in FF occurs because chargecarriers must travel a larger distance to reach the electrodes for collection. Furthermore, theelectric field inside the device is governed by the equation E = ∆φm

ql , where ∆φm is the differencein work function between the two contacts, and l is the thickness of the device. As l increases, thebuilt-in electric field decreases, negatively affecting the drift of the charge carriers. Both factorsincrease the recombination in the device, as charges take a longer time to reach the contacts.

Another factor in poor thick active layer device performance is space-charge buildup due tolow or imbalanced-charge carrier mobility [10–13]. The buildup of the charge carrier with thelower mobility leads to screening of the built-in electric field, further decreasing the drift. Recentdevelopments have led to polymers with high hole mobility, on the order of 10−3 cm2

V s , with highfill factor above 0.7, which suggests that increasing hole mobilities in the electron-donor materialcan increase performance of thick active layer devices.

Another issue affecting the development of OPVs is the lack of validated drift-diffusion devicesimulators. While inorganic PV systems have extremely accurate simulators that augment their

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research [14–16], OPV researchers use device simulators and models to a lesser extent. The lack ofdevice simulator usage is due to the complex nature of the morphology of polymer-fullerene blendsin the active layer, as the different materials form different phases with differing compositions.Having access to a device simulator that captures the complex behavior of OPV systems wouldallow researchers to analyze the optical and electrical properties of BHJs, revealing key detailsof the role of charge carrier transport and recombination in BHJ performance.

1.4 Research GoalsIn this thesis, I seek to address the role that charge carrier mobility and recombination play in thepoor fill factor found in thick BHJ devices. I first study the model system Poly(3-hexylthiophene-2,5-diyl):[6,6]-phenyl-C61-butyric acid methyl ester (also known as P3HT:PC60BM, see Fig-ure 1.5(a)), fabricating a large variety of BHJ solar cells with hole mobility ranging from 1.6×10−7

to 3.6×10−4 cm2

V s and thicknesses ranging from 60 to 350 nm. I demonstrate a clear transition inP3HT:PC60BM where charge mobility becomes too low for successful charge extraction, leadingto recombination issues and lower fill factor.

(a) P3HT:PC60BM (b) H1:PC70BM

Figure 1.5. Chemical structures of the organic molecules used in this thesis. P3HT is a conjugatedpolymer while H1 is a small molecule. Both serve as the electron-donor and light absorbing material.The electron-acceptor materials are the fullerenes PC60BM and PC70BM

Afterwards, I use a device simulator for two BHJ systems. I use the experimental datafor P3HT:PC60BM devices to verify a 1D drift-diffusion simulator for organic semiconductors,Seftos [17], by reproducing the data using two fit parameters and measured charge mobility.The second system, p-SIDT(FBTTh2)2:[6,6]-phenyl-C71-butyric acid methyl ester (also knownas H1:PC70BM) contains a small molecule and a fullerene, as shown in Figure 1.5(b). UsingSeftos, I find the recombination rate constant of the two systems. Doing so demonstrates designrules for improving BHJ systems and also validates a valuable tool for gaining important insightsinto BHJ solar cell operations and device physics.

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Chapter 2 |Understanding Device Performance through Experiments

The experiments described in this chapter on the polymer:fullerene system P3HT:PC60BM helpunderline two principal mechanisms for poor device performance in organic photovoltaics: poorcharge mobility and high bimolecular recombination. First, poor charge mobility results indrastically decreased fill factors for thick devices. Second, bimolecular recombination is theprincipal recombination mechanism in the devices. Experimental procedures for the experimentsin this chapter are described in Appendix A.

2.1 Performance of P3HT:PCBM Bulk Heterojunction Cells

Mihailetchi et al. [18] demonstrated that one can tune the charge mobility in P3HT:PCBM bythermally annealing devices after spincasting. To analyze the effect that hole (µh) and electron(µe) mobility has on BHJ devices, I fabricated P3HT:PCBM devices with varying thicknesses,ranging from 60 to 360 nm, and with varying anneal temperatures, annealing the devices for 10minutes either at 25, 48, 71, 88, 111, or 148. More on this experimental procedurecan be found in Section A.1. Each device was tested under illumination by an AM1.5G lampat one sun intensity and the JV curves were measured. Figure 2.1 shows JV curves for roughly220-nm thick devices, annealed at different temperatures.

Figure 2.1. JV Curves for roughly 220-nm devices, annealed at 25, 48, 71, 88, 111, and148. The performance of the device improves as the annealing temperature increases.

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Figure 2.2. The electron and hole mobility of a P3HT:PCBM device as a function of annealing temper-ature. The hole mobility increases by more than three orders of magnitude, while the electron mobilityincreases by one and a half orders of magnitude when the annealing temperature is increased from 25to148.

I then measure the hole mobility of P3HT using hole-only diodes and a space-charge limitedcurrent measurement (as shown in Section A.3) [11]. The electron mobility was extrapolatedfrom measurements done by Mihailetchi et al. [18]. The results of this analysis are shown inFigure 2.2. Both the charge mobility and figures of merit for roughly 220-nm devices are listedin Table 2.1.

Temp. [] µh [ cm2

V s ] µe [ cm2

V s ] L [nm] Voc [V] Jsc [ mAcm2 ] FF PCE [%]

25 1.6× 10−7 1.5× 10−4 205 0.63 3.0 0.30 0.6048 2.0× 10−6 2.5× 10−4 204 0.63 4.9 0.35 1.171 2.3× 10−5 1.0× 10−3 229 0.58 8.7 0.40 2.088 5.5× 10−5 1.5× 10−3 227 0.57 9.3 0.48 2.6111 1.3× 10−4 3.0× 10−3 211 0.56 10.1 0.57 3.2148 3.6× 10−4 5.0× 10−3 197 0.60 10.1 0.69 4.1

Table 2.1. Hole mobility (µh), electron mobility (µe), the active layer thickness (L), and figures ofmerit as defined in Section 1.2, for roughly 220-nm devices annealed at 25, 48, 71, 88, 111,and 148.

Table 2.1 shows that the 25 device performs poorly, with a FF of 0.30 and a PCE below1%. The performance increases as the anneal temperature increases, particularly the FF, andthe 148 device has a FF of 0.69 and a PCE of 4.1%. Since the thicknesses are all approximatelythe same, it is important to note that the performance is not due to higher absorption of light,but rather the differences in charge mobility due to annealing.

I can also analyze device performance as a function of thickness. Figure 2.3 plots the FF andPCE of devices for varying thicknesses and at differing annealing temperatures. Figure 2.3(a)demonstrates three major trends:

1. At low anneal temperatures (25 or “as cast”), the FF is uniformly low for active layerthicknesses above 100 nm, and increases rapidly at thicknesses below 100 nm.

7

2. At intermediate anneal temperatures (71, 111), the FF is low for the thickest devices,but gradually increases and approaches a fill factor of 0.68 at 60 nm.

3. At high anneal temperatures (148), the FF stays relatively constant for the thicknessrange measured, at a FF around 0.7.

(a) FF vs Thickness. (b) PCE vs Thickness.

Figure 2.3. Plots of FF and PCE vs thickness for devices annealed at 25 (“as cast”), 71, 111,and 148. The horizontal error bars represent the minimum and maximum thicknesses for a group ofdevices, whereas the vertical error bars represent the minimum and maximum PCE and FF for a givengroup of devices.

More specifically, for the 25 annealed device, the fill factor starts off at 0.51 for 60 nmand drops sharply above 90 nm, ending up with a constant, low FF of approximately 0.3. Inthe 71 annealed device, the fill factor starts off at 0.66 and drops steeply off after 130 nm,approaching a fill factor of 0.38 at 310 nm. In the 111 annealed device, the fill factor startsclose to that of the 71 annealed device, but maintains a more constant decline in FF, endingin a FF of 0.52 at 290 nm. Finally, the highly annealed device (148) exhibits approximatelyconstant FF for all thicknesses at around 0.7. The PCE trends found in Figure 2.3(b) follow thatof the FF trends modulated by the Jsc, as shown in Figure 2.4 [19].

These trends in FF correlate with the electron and hole mobility data found in Figure 2.2,suggesting a close connection between charge mobility and FF. The increase in charge mobilitycan possibly explain the critical thickness above which devices suffer a large loss in FF and alsoaffects the final FF at large thicknesses.

2.2 Recombination in P3HT:PCBM Bulk Heterojunction Cells

Recombination plays a very important role in understanding the behavior of fill factor in theexperimental devices. Two major types of recombination that occur in the active layer of thebulk photovoltaic are geminate and bimolecular recombination. Geminate recombination refersto the recombination of electron-hole pairs shortly after exciton generation. In this type of

8

Figure 2.4. Current density at short circuit as a function of layer thickness. There are absorption peaksfound in the current density, which modulates the PCE despite the increase in FF at low thicknesses.These calculations are based on the transfer-matrix formalism developed by Burkhard et al.

recombination, the exciton is unable to diffuse to a heterojunction before recombining, or theelectron and hole quickly recombine after they are split at a heterojunction.

Bimolecular recombination occurs when an electron and hole encounter each other on differentmolecules and recombine. Bimolecular recombination is given by the equation:

R = knp (2.1)

where R is the recombination rate, k is the recombination rate constant, and n and p are theelectron and hole densities, respectively. The recombination rate constant can either take theform predicted by Langevin theory:

k = γ × q(µh + µe)ε

(2.2)

where γ is the Langevin pre-factor and ε is the dielectric permittivity (the relative permittivitymultiplied by the permittivity of free space) [17, 20, 21], or be a constant value, independent ofthe charge mobilities.

Langevin theory assumes that every encounter of an electron and hole results in recombina-tion, and the rate of recombination is proportional to how fast the charge carriers meet eachother in the active layer. The Langevin pre-factor γ is an experimentally measured quantity thatdescribes the experimental probability of recombination after a given encounter, where γ = 1 forLangevin theory. Recent experiments [22,23] and simulations [24–26] demonstrate that electronand holes that encounter each other are more likely to separate into free charge-carriers ratherthan recombine. I choose to use the constant recombination rate constant in the rest of thischapter and discuss the differences between assuming a constant recombination rate constantand using a recombination rate constant dependent on mobility in Chapter 4.2.

To verify that bimolecular, as opposed to geminate, recombination is the primary mechanism

9

Figure 2.5. A plot of FF as a function of light intensity for devices annealed at various temperatures.

for decreased FF, I measured the fill factor at low light intensities (see Section A.4 for experi-mental procedure). Because the populations of electrons and holes are largely photogeneratedcarriers, the rate of recombination can be approximated as R ∝ I2 where I is the light intensity.As light intensity incident on the devices is increased, the recombination should increase quadrat-ically, leading to lower fill factors if there is a significant amount of bimolecular recombinationin the devices. Figure 2.5 shows the fill factor plotted as a function of light intensity for 220-nmthick devices with differing anneal temperatures.

For the as-cast devices, although the fill factor gradually increases as light intensity is de-creased, the increase is very modest, suggesting that bimolecular recombination alone is notlimiting the device performance. However, there is an increase in fill factor as light intensitydecreases for the intermediate temperature devices, while the high temperature device seemsto stay constant. These devices seem to converge to roughly the same fill factor at extremelylow light intensities. This result points to bimolecular recombination playing a larger role inthe devices annealed at intermediate temperatures above 25, while bimolecular recombinationdoes not seem to be an issue in devices annealed at 148. In the remainder of this work, I willconsider only bimolecular recombination when discussing recombination in organic photovoltaicsbecause the data in Figure 2.5 shows that bimolecular recombination causes the difference inperformance at one sun between the different devices.

10

Chapter 3 |Understanding Device Physics Using Simulation

In this chapter, I will analyze the two properties discussed in Chapter 2 using a numerical drift-diffusion simulator, providing an effective tool for calculating the recombination rate constantand offering more evidence for a constant k instead of the k predicted by Langevin theory. Amore in-depth explanation of the simulation procedure can be found in Appendix B.

3.1 Introduction to Seftos

Seftos is a 1D numerical drift-diffusion simulator that is offered commercially. It simulates theperformance of a solar cell by first calculating the absorption profile of a multilayer stack [27,28],then calculating the exciton generation profile and their subsequent dissociation. It accomplishesthis by using the transfer matrix model formalism to calculate the absorption in each layer of thestack while accounting for optical inference, as shown in Burkhard et al [19]. Finally, it calculatesthe drift and diffusion of the free charge carriers to the electrodes [17].

In the optical modeling step, the software first considers the optical field intensity within thestack given by the equation

I = 12ε0cn|E|

2 (3.1)

where ε0 is the permittivity of free space, c is the speed of light, and n is the real part of theindex of refraction. Using this equation and by normalizing the incident electric field such thatthe amplitude is 1, the device optical field intensity is shown to be:

I = nn0|Enorm|2I0 (3.2)

where n0 is the index of refraction at the surface of the stack. Equation 3.2 is dependent onwavelength (λ) and position. From this expression of local optical field intensity, the density ofabsorbed photons can be shown to be:

nphotons = αIλ

hc(3.3)

where α stands for the absorption coefficient given by α = 4πκλ , κ is the complex part of the

refractive index and h is Planck’s constant.After determining the profile of photon absorption, electronic modeling of the OPV stack is

11

required for accurate simulations. This is done by solving the following equations that governthe drift-diffusion of charges:

dE(x)dx

= q

εrε0[p(x)− n(x)] (3.4)

Je(x) = qµen(x)E(x) +D(µ, T )dn(x)dx

(3.5)

dn(x)dt

= 1q

dJe(x)dx

− γr(x)p(x)n(x) +G(x) (3.6)

where εr is the relative permittivity, p(x) refers to the hole density, n(x) refers to the electrondensity, and D(µ, T ) is the diffusion coefficient given by D = µkbT

q . γ once again refers tothe Langevin pre-factor, while r(x) is the recombination rate constant predicted by Langevintheory at a specified position and G(x) is the generation rate of charges due to light absorption.Equation 3.4 is Poisson’s equation for one dimension, Equation 3.5 is the current equation forelectrons, and Equation 3.6 is the continuity equation for electrons.

Finally, to determine the electric field, Seftos uses an effective applied voltage Veff = Vappl−Vbi,where Vappl is the experimentally applied voltage and Vbi is the built-in voltage that is determinedfrom the difference in work function between the two electrodes. Veff serves as a constraint todetermine the integration constant when finding the electric field from Equation 3.4.

Using these equations, Seftos simulates the drift and diffusion of charge carriers throughoutthe device and models device performance.

3.2 Validation of SeftosTo validate Seftos, I compare simulated data with experimental data. I use the form of constantrecombination rate constant given by Equation 2.1. I also assume that the splitting of geminatepairs is not dependent on the electric field and that the absorbed photons directly generated freeelectrons and holes, an assumption validated for some systems in recent research [24,29,30].

Using only two fit parameters, k and the series resistance, as shown in Section B.3.1, Isimulated the device performance of a variety of thicknesses and charge mobilities. Figure 3.1compares the IV curves of ∼220-nm devices (listed in Table 2.1) to simulated IV curves. Thereis strong agreement between the two, and the simulator qualitatively captures the behavior ofthe devices as anneal temperature and charge mobility are increased.

Furthermore, FF and PCE trends for devices with varying electron and hole mobility, as shownin Figure 3.2 and Figure 3.3, qualitatively agree. The simulator predicts that the as-cast (25)device will have low fill factor of around 0.4 for all thicknesses. Furthermore, it predicts that thefill factor of the intermediate anneal temperature devices (71, 11) will decrease for increasingthicknesses in a manner similar to what I observe experimentally. Finally, both simulated andexperimental fill factors for the high anneal temperature device (148) demonstrate a high fillfactor that stays either at or above 0.7.

One large difference between the experimental and simulated FF trends for intermediateand high anneal temperature devices is that experimentally, fill factors tend to converge to 0.7,

12

(a) Simulated IV Curves. (b) Experimental IV Curves.

Figure 3.1. Simulated (a) and experimental (b) IV curves for ∼220-nm devices annealed at 25 (“ascast”), 48, 71, 88, 111, and 148. There is agreement between simulated and experimental IVcurves as anneal temperature is increased.

(a) Simulated FF vs Thickness. (b) Experimental FF vs Thickness.

Figure 3.2. Simulated (a) and experimental (b) plots of FF vs thickness for devices annealed at 25 (“ascast”), 71, 111, and 148. The experimental plot is identical to Figure 2.3(a) and is reproduced forconvenience.

while the simulator predicts a fill factor of 0.8. This can be due to the shunt resistance of ourexperimental devices decreasing as I decrease the thickness, as shown in Figure 3.4. I hypothesizethat this is due to pinholes that form in the film at low thicknesses that allow shunt pathwaysto form when the contacts are evaporated on our device. This provides another loss mechanismthat is not accounted for in the simulator. Nevertheless, simulated FF, PCE, and IV curves agreewell qualitatively in reproducing the general trends found experimentally.

It is interesting to note that the device physics of the devices was captured effectively andtrends qualitatively reproduced without inputting the morphology of the BHJ system. This isparticularly important, as it would be nearly impossible to enter in a morphology profile of theactive layer similar to that shown in Figure 1.2, as it is difficult to know the polymer degree ofcrystallinity or the volume fraction of the mixed phase in the BHJ locally. However, by using an

13

(a) Simulated PCE vs Thickness. (b) Experimental PCE vs Thickness.

Figure 3.3. Simulated (a) and experimental (b) plots of PCE vs thickness for devices annealed at25 (“as cast”), 71, 111, and 148. The experimental plot is identical to Figure 2.3(b) and isreproduced for convenience.

Figure 3.4. Shunt resistance as a function of thickness and anneal temperature. All devices exhibit adrop of two orders of magnitude in shunt resistance for device thicknesses below 100 nm, resulting inlower fill factors than predicted by the simulator. Figure courtesy of Jonathan A. Bartelt.

effective medium approach to model both the optical and electrical properties of P3HT:PCBMphotovoltaic devices, the morphology of a BHJ does not have to be considered. Furthermore,although studies have shown that the local, nanoscale charge mobility is much higher than thatmeasured by SCLC measurements and is much more important in determining high internalquantum efficiency [31], this simulation shows that there is some physical importance in theSCLC measured hole and electron mobility, as they help effectively model the devices.

3.3 Determining k for P3HT:PCBM and H1:PCBM

3.3.1 P3HT:PCBM

After validating Seftos, I next try to extract a meaningful value of k by varying fit parametersuntil I simulated IV curves that closely reproduced experimental curves for 220-nm thick devices

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(see Section B.3 for simulation procedure). Table 3.1 provides both the value of γ, the Langevinpre-factor used, as well as the actual value of k.

Anneal Temp [] γ k [10−13 cm3

s ]25 0.008 6.248 0.005 6.571 0.0025 1388 0.0013 10111 0.0025 40148 0.0002 5.5

Literature N/A 1 to 20

Table 3.1. Simulated values for the Langevin pre-factor and k for 220-nm thick P3HT:PCBM devices.The values of k fall in line with literature values and are all within an order of magnitude of each other,suggesting that k is constant.

It is interesting to note that k falls within the same order of magnitude and that it is γ thatdecreases as the hole and electron mobility increase. The simulated values agree with valuesfound in literature [30, 32], demonstrating that the values of k that I extract from simulationagree well with measured results and can be considered meaningful. If Langevin recombinationwere applicable, γ should remain constant and the recombination rate constant should increasewith the sum of the mobilities, µh + µe, which actually increases by a factor of 35 from the25 device to the 148 device. Thus, I conclude that the recombination in these devices is notwell described by the Langevin recombination rate equation.

3.3.2 H1

I now use the device simulator to analyze another organic BHJ system, H1. As mentioned inSection 1.4, H1 is a small molecule designed by collaborators from UC Santa Barbara [33]. Ireceived figures of merit and charge mobilities as a function of the weight percentage of theelectron donating material, H1, from the collaborators, shown in Figure 3.5 and Table 3.2. Alldevices fabricated were roughly 100 nm thick.

H1 [Wt. %] µh [ cm2

V s ] µe [ cm2

V s ] Voc [V] Jsc [ mAcm2 ] FF PCE [%]

8 4.2× 10−7 2.0× 10−3 0.94 4.56 .31 1.412 2.1× 10−6 2.0× 10−3 0.96 7.04 .33 2.316 9.7× 10−6 2.0× 10−3 0.98 8.74 .38 3.320 1.2× 10−5 2.0× 10−3 0.95 9.03 .44 3.830 4.2× 10−5 2.0× 10−3 0.98 9.79 .48 4.640 1.6× 10−4 2.0× 10−3 0.98 9.97 .57 5.650 4.5× 10−4 2.0× 10−3 0.92 10.3 .67 6.360 5.8× 10−4 1.6× 10−3 0.88 10.0 .64 5.670 7.9× 10−4 9.7× 10−4 0.88 8.98 .57 4.580 9.8× 10−4 2.6× 10−4 0.89 8.95 .41 3.390 1.1× 10−3 3.3× 10−6 0.82 2.11 .38 0.66

Table 3.2. Hole mobility, electron mobility, and figures of merit for ∼100-nm H1:PCBM devices madewith different H1 concentrations by weight percentage. Data provided by collaborators at UCSB.

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(a) Hole and electron mobility of H1:PCBM as a func-tion of the weight percentage of H1.

(b) Experimentally measured FF and PCE ofH1:PCBM as a function of the weight percentage ofH1

Figure 3.5. Experimental data on the charge mobility (a) and performance of H1:PCBM as a functionof the weight percentage of H1(b). Data provided by our collaborators from UCSB.

The experimental data shows that the hole mobility increases by three and a half orders ofmagnitude as the concentration of H1 is increased, while the electron mobility drops three ordersof magnitude. As the weight percentage of H1 increases, the Voc decreases, a trend possibly dueto morphology or mixing that needs to be captured in simulations. The best performing deviceoccurs at 50% H1 by weight, with a FF of 0.67 and a PCE of 6.3%.

In order to account for the change in Voc, I include an additional fit parameter by varying theHOMO of the small molecule:fullerene blend. This is justified by noting that the increase in Voccorresponds to an increase in the amount of PCBM in the BHJ, and the Voc levels off at around0.95 V, after the fullerene reaches what might be its limit of miscibility. Further description ofthe fitting procedure can be found in Section B.3.

I first extract the values of k for H1, as found in Table 3.3. The value of k once againfalls within the same order of magnitude instead of changing as the mobility changes, and asidefrom the 20%, 50%, and 60% devices, the recombination rate constant in the devices are above5 × 10−10 cm3

s . The recombination rate constant of H1 will be compared to other OPV systemsin Section 4.2.

16

H1 [Wt. %] k [10−10 cm3

s ]8 1012 7.516 6.220 3.130 1040 9.550 1.860 2.370 9.180 6.490 5.7

Average Value 6.5

Table 3.3. Simulated values for k for 100 nm thick H1:PCBM devices. As with P3HT:PCBM, thevalues of k all fall within one order of magnitude of the average value. However, the value of k is atleast 3 orders of magnitude higher than that of P3HT:PCBM, leading to lower FF despite higher chargemobility.

Using the average value of k calculated and the value of HOMO found during the best fitprocedure, I simulated IV curves for all devices. The experimental and simulated values of FFand PCE are shown in Figure 3.6. This also shows the strong effect that roughly tripling therecombination rate constant from the lowest k to the average k can have on the performance ofH1:PCBM devices. The differences between the recombination rate constant in P3HT:PCBM,H1:PCBM, and other OPV systems and how they impact device performance will be discussedfurther in Section 4.2.

(a) Experimental and simulated FF vs H1 weight per-centage.

(b) Experimental and simulated PCE vs H1 weightpercentage.

Figure 3.6. Experimental and simulated FF and PCE vs H1 weight percentage. There is strongagreement in trends for the low and high weight percentage regions, while in the intermediate region(50% and 60%), there is a deviation. This can be attributed to the fact that these two devices havelower recombination rate constants than the simulated value, leading to artificially lower values of FFand PCE.

17

Chapter 4 |Discussion

4.1 Charge Mobility and Fill Factor

To understand why fill factor increases as the charge mobility increases, first consider the expres-sion for current density J = Je + Jh, given by the sum of the current density due to electronsand holes:

Je = nqµeE (4.1)

Jh = pqµhE (4.2)

J = qE(nµe + pµh) (4.3)

where E is the electric field through the device. From experimental data shown in Chapters 2and 3, while the Jsc of devices may range by an order of magnitude, the hole and electronmobility ranges by several orders of magnitude. As hole and electron mobility decrease in poorerperforming devices, n and p must increase by orders of magnitude in order to drive a comparableamount of current. Another effect of low hole and electron mobility is space-charge build-up, asdiscussed in Section 1.3. A decrease in E corresponds to increased hole and electron densities.

Now consider the expression for bimolecular recombination, assuming k is constant:

R = knp (4.4)

Since the hole and electron density must increase to compensate for reduced hole and electronmobility in order to drive a comparable current density, the recombination increases drastically.The fill factor of the low charge mobility, thick device suffers as a result. This framework allowsus to understand why increasing mobility will lead to better performance, as we maximize thebuilt-in electric field and reduce the carrier density.

4.2 Recombination in Organic Photovoltaics

As discussed in Section 2.2, Langevin theory predicts that the recombination rate constant kshould take the form:

k = γ × q(µh + µe)ε

(4.5)

18

If this form of k is correct, increasing hole and electron mobility may negatively affect ourdevices, as k would increase according to the sum of the mobilities and R would correspondinglyincrease. However, the simulated values of k for both P3HT:PCBM and H1:PCBM are relativelyconstant and certainly do not show a dependence on µh or µe, as predicted by Langevin.

Burke et al. [24] elucidates why Langevin theory might be insufficient in capturing the behaviorof recombination in BHJ systems. He notes that k predicted by Langevin theory, with γ = 1,is effective in predicting the frequency of encounters in disordered material systems, but theLangevin reduction factor γ is used to note that not every encounter of a hole-electron pairresults in recombination. For example, in the P3HT:PCBM devices studied in this thesis, thevalue of γ used for simulations to calculate k ranged from 0.0002 in devices with high mobilityto 0.008 in devices with poor mobility. In contrast, H1:PCBM had values of γ ranging from 0.2to 1. Thus, electron-hole pairs in P3HT:PCBM devices recombine much less per encounter thanin H1:PCBM in this framework.

γ may also provide some information on the mixing or energetic landscape of BHJ systems.Annealing has shown to affect the morphology of P3HT:PCBM, changing the degree of aggre-gation of P3HT from 32% in as-cast devices to 45% in highly annealed devices [34]. Meanwhile,P3HT and H1 differ tremendously; P3HT is a semi-crystalline polymer which forms a three-phasemorphology with a pure polymer and fullerene region sandwiching a mixed region. This mixedregion is critical in providing an energetic offset that drives polymers and fullerenes into the puredomains, decreasing the chance of encounter [11]. While morphological studies have not beendone on H1, it is possible that γ is much higher in H1 due to the fact that it is a small moleculeand may have a different morphology to that of P3HT. Further research needs to be done tounderstand the role that γ plays in BHJ systems.

Finally, it is instructive to compare the values of γ and k found in literature with the valuescalculated in this thesis. Table 4.1 shows the values found in literature. Comparing this table tovalues of γ and k found in Section 3.3, we see that P3HT:PCBM, with γ ranging from 0.0002 to0.008 and k on the order of 10−13 has much higher fill factors due to its lower recombination rateconstant. H1:PCBM, however, has γ much higher than values listed here and a correspondingaverage k = 6.5× 10−10 higher than that of the systems listed below.

Furthermore, the studies done on PCPDTBT, F-PCPDTBT, mono-DPP and bis-DPP allnote that morphological changes occur that decrease the value of γ. It would be interesting tostudy these systems more in-depth to see if there is any direct correlation between γ and themorphology, and if so, how γ can be used to predict the morphology in a bulk heterojunction.

4.3 Evaluating Organic Photovoltaics with a Device Simulator

While Seftos’s use in this thesis was largely limited to validating its ability to capture the devicephysics of various OPV systems without including morphological constraints and extracting ameaningful value of the recombination rate constant k through simulation, it offers other featuresthat will push the field of organic photovoltaics forward. For example, Seftos can generate banddiagrams of OPV devices in various operating conditions (varying the voltage applied across the

19

Molecule γ k [ cm3

s ] FFPDPP-TNT:PC70BM [35] 0.77 2.5× 10−10 N/A

PCPDTBT:PC70BM (0% DIO) [36] 0.20 2.9× 10−11 0.40PCPDTBT:PC70BM (3% DIO) [36] 0.07 2.5× 10−11 0.50F-PCPDTBT:PC70BM (0% DIO) [36] 0.14 1.2× 10−11 0.41F-PCPDTBT:PC70BM (1% DIO) [36] 0.04 1.1× 10−11 0.59F-PCPDTBT:PC70BM (3% DIO) [36] 0.03 1.2× 10−11 0.60mono-DPP:PCBM (3% DIO) [37] 0.11 5.3× 10−11 0.46bis-DPP:PCBM (3% DIO) [37] 0.03 2.6× 10−11 0.62

Table 4.1. Literature values of the Langevin reduction factor and k for various BHJ systems.

device, the intensity of incident light, etc.), a calculation that is not easily done experimentally.The band diagrams can help researchers pinpoint issues such as space-charge build-up or highcarrier densities leading to recombination.

Another valuable use of Seftos is to determine what research goals to strive for in smallmolecule and polymer design. For example, Bartelt et al. uses Seftos in his work [1] to determinethat future researchers should target a charge mobility of 10−2 cm2

V s and a recombination rateconstant less than 10−13 cm3

s in order to reach 15% PCE in BHJ devices. Having a simulatorallows for similar predictions to be made on what properties need to be improved in order toimprove solar cell performance. It also provides a quick and effective method to iteratively testdifferent conditions without worrying about device fabrication issues.

4.4 ConclusionIn this thesis, I use experiment and simulation to analyze how mobility and recombination affectBHJ solar cell performance. I first demonstrate that the fill factor of P3HT:PCBM devices issensitive to both the thickness and hole mobility of the device, showing a large improvement indevices annealed at higher temperatures, especially with thick active layers.

Using this data, I validate a 1-D drift-diffusion simulator, Seftos, by comparing simulatedand experimental IV curves. Afterwards, I use Seftos to extract the values of k for two differentBHJ systems, P3HT:PCBM and H1:PCBM. Simulations show that a constant value of k, insteadof the Langevin picture with k dependent on charge mobility, is a better model of bimolecularrecombination and that increasing the charge mobility will not adversely affect the recombinationrate constant.

Furthermore, by validating Seftos, I show that there is a valuable simulator software thatOPV researchers can utilize in making predictions on which material properties will lead to thegreatest growth in efficiency, as well as diagnose problems and make quantitative estimations ofproperties hard to measure.

The work done in this thesis helps further understanding of the role that charge mobility andrecombination play in having a thick, 300-nm device, with a high FF of 0.8 and possible PCEof 15%. It is vital for OPVs to hit these benchmarks in order to become a major technology intoday’s energy market.

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Appendix A|Experimental Methods

A.1 Fabrication of P3HT:PCBM Devices

ITO patterned glass substrates (Xinyan Technologies LTD, 15Ω ) were cleaned by scrubbing with

a dilute Extran 300 detergent, then ultrasonicated in dilute Extran 300 detergent for 15 min.The substrates were rinsed in deionized water for 5 min, and ultrasonicated in acetone, thenisopropyl alcohol for 15 min, before being rinsed in deionized water for 5 min. Substrates werethen placed in a 115 oven for 30 minutes before exposed to a UV-ozone plasma for 15 minutes.Afterwards, an aqueous solution of PEDOT:PSS (Clevios P VP AI 4083) was spin-cast onto theglass substrates at 4,000 rpm, and then the substrates were thermally annealed at 140 for 10min. The substrates were then transferred to a dry nitrogen glovebox, with less than 5ppm ofO2.

Solutions were prepared in the glovebox with 1 part P3HT (BASF, P-200 batch, 22 kDamolecular weight) and 1 part PC60BM (Nano-C, Batch BJ120703) by weight and dissolved inchloroform (Sigma-Aldrich, 99% purity). Solutions ranged from 10 mg total/mL to 30 mg to-tal/mL for film thicknesses between 60 nm to 350 nm and were allowed to dissolve overnight ona stirplate before being spin-cast at 800 rpm for 45 sec, with a ramp speed of 500 rpm/s. Allthermal annealing took place for 10 minutes and prior to electrode deposition. The electrodesconsisted of 7 nm of calcium (Plasmaterials, 99.5% purity) and 250 nm of aluminum (Kurt J.Lesker, 99.999% purity) and were thermally evaporated at 10−6 torr with a shadow mask thatdefined the active area of the device to 0.1 cm2.

A.2 Solar Cell Characterization

Current-voltage measurements were conducted in a dry nitrogen glovebox and used a Keithley2400 source meter and a Spectra-Physics 91160-1000 solar simulator, which was calibrated usinga NREL certified KG-5 filtered Si photodiode to one sun intensity, AM1.5G.

EQE and absorption measurements were done using a Stanford Research Systems modelSR830 DSP lock-in amplifier, and in the case of absorption, with an integrating sphere. IQEmeasurements were done using the transfer matrix formalism developed by Burkhard et al [19].

Device active layer thicknesses were characterized using a Veeco Dektak profilometer.

21

A.3 Hole-Only Diode Preparation and MeasurementsPreparation for the hole-only diodes are identical to the preparation of solar cells up to electrodedeposition. Instead of calcium and aluminum, 100 nm of gold (Sunshine Minting Inc., 99.99%purity) was evaporated as the top contact. This creates a voltage bias of -0.1 V in the hole-onlydiode.

Hole mobility was calculated by taking the current-voltage measurements in a similar proce-dure detailed in the solar cell characterization section, but placed further into forward bias (12-15V) in order to measure the space charge limited current (SCLC) regime. The hole mobility isextracted by fitting the SCLC regime to the equation:

Jh = 98εrε0µh

(V−Vbi)2

L3 (A.1)

A.4 Low Light Intensity MeasurementsPreparation for the low light intensity devices are identical to the preparation of solar cells. Mea-surements were also done in an identical fashion to the current-voltage measurement procedureoutlined in Section A.2. To reduce the intensity of light, one of several neutral density filterwith different optical densities (Newport, FSQ-ND05, FSQ-ND10, FSQ-ND15, FSQ-ND20) wasplaced between the device and light source. In addition, the power driving the solar simulatorwas reduced, decreasing the intensity.

22

Appendix B|Simulation Procedure

B.1 Simulation OptionsThis section will quickly cover the features offered for OPV researchers in Seftos.

Figure B.1 illustrates the GUI for creating the device stack. The user can add layers andinterfaces, move layers up and down, invert the stack, or remove layers easily using the buttons tothe left of the layer structure schematic. The user can also change the thickness of the layer andselect pre-generated files with parameters for the optical and electrical properties of a given layer.Underneath the layers, the simulator offers the ability to sweep through a set of wavelengths fora given value, change the illumination spectrum or intensity, and modify the electric couplingsettings.

Figure B.1. The home screen, where the device stack is created and modified.

Figure B.2 displays the drift-diffusion options that Seftos offers, which can be selected byclicking on the battery underneath the sun icon shown in Figure B.1. Here, the user can selectthe electrode layers, determine whether the contact between the active layer and electrode is

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ohmic, or change the work function of the electrode. There is also an option to include resistivitythrough the electrode. Furthermore, the user can change the operating conditions of the device(the voltage or temperature) and change how the drift-diffusion solver models the system.

Figure B.2. The drift-diffusion tab.

To modify the properties of each layer, the user clicks the icon of a window with an arrowpointing to the right on the end of each layer. This brings up a screen that looks like the oneshown in Figure B.3.

Figure B.3. The layer properties window, which allows the user to modify the optical and electricalproperties of each layer.

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In order to modify the optical properties of a given layer, the user selects the edit buttonunder the refractive index section. This brings up a window similar to Figure B.4. Here, thecomplex index of refraction can be entered as a function of the wavelength, which helps determinethe propagation of light through the stack.

Figure B.4. The optical material editor window, which allows the user to enter in the complex indexof refraction as a function of wavelength.

To modify the electrical properties of the active layer, the user selects the edit button underthe electrical material section. This brings up a window that is similar to Figure B.5. Here, theuser can set the energy levels of the active layer, modify the dielectric constant and the effectivedensity of states, turn on doping in the layer, set the optical generation efficiency and Langevinreduction factor, and determine the mobility model and values of electron and hole mobility.

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Figure B.5. The optical material editor window, which allows the user to enter in the electricalproperties of the layer, such as HOMO, LUMO, recombination rate, charge mobility, etc.

To determine the sweep settings prior to simulation, the user goes to Simulation settings ->Sweep settings, found in the main menu. This brings up a window as shown in Figure B.6. Whilein this study, I only considered sweeping through the voltage, a large degree of optical, electricaland physical properties can be ranged for each individual layer, such as the thickness of a givenlayer. Furthermore, the sweep settings allow for a linear, logarithmic, or custom sweep.

Figure B.6. The sweep settings window, which allows the user to sweep across a large variety ofvariables, including voltage.

Once all parameters have been sufficiently modified, the user clicks the quick run buttondenoted by a play symbol on the list of icons below the main menu. After the simulation hasbeen completed, a results section appears, as shown in Figure B.7, listing figures of merit. Inaddition, the user can go down to the list of results on the left, selecting generated results suchas IV curves for the device or the electrical field or recombination profile throughout the device.

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Figure B.7. The results window, which displays figures of merit and allows the user to generate aresults report or view individual generated results for a wide range of electrical (e.g. IV curves, electricfields) and optical (e.g. max photocurrent, absorption profile) properties.

In order to save the data for a specific result, such as a IV curve, the user simply right-clickson the figure and selects the option to save visible data, as shown in Figure B.8. This creates atext file that can be used in other data analyzing software.

Figure B.8. Right-clicking on the figure generates a drop-down menu with a save data option.

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B.2 Simulation Parameters

This section describes the parameters that the user can input in Seftos and how the values ofthese parameters were determined.

B.2.1 LUMO, HOMO and Work Function

As explained in Section 1.1, the HOMO refers to the highest occupied molecular orbital andthe LUMO refers to the lowest unoccupied molecular orbital, which determines the energy levelsin the active layer. Seftos uses this information, in conjunction with the work function of theelectrodes, which I assume to make ohmic contact with the active layer, and recombination, todetermine the Voc.

One issue that arises in the analysis of H1 is that the Voc changes as the concentration ofPCBM goes up. This is due to the broadening of energy levels in the mixed region. To accountfor this, the HOMO level is adjusted along with the work function of the hole-collecting contact.

In P3HT:PCBM, I use a LUMO level of 3.7 eV (determined by the fullerene, as shown inliterature [17]) and a HOMO level of 4.9 eV (determined by the polymer [18]). In H1:PCBM, Iuse a LUMO level of 3.9 eV for the fullerene, as found on the website of Sigma-Aldrich, and avariable HOMO level greater than 5.2 eV, the HOMO level of the pure phase small molecule [33].

The work function of the top and bottom contact are matched to the LUMO and HOMO ofthe active layer, respectively.

B.2.2 Dielectric Constant and Effective Density of States

The dielectric constant εr determines the strength of screening and how strongly electrons andholes interact with each other. In organic photovoltaics, the dielectric constant often rangesbetween 3 and 5 in literature [38]. The effective density of states, N0, is also a quantity thatis relatively constant in literature for OPVs [39]. In both P3HT:PCBM and H1:PCBM, we useεr = 3.5 and N0 = 1022

cm3 .

B.2.3 Optical Generation Efficiency

The optical generation efficiency is a measure of the efficiency of generating free charges fromabsorbing light. As shown in Section 1.1, the IQE can be defined as IQE = ηEDηCTηCC, whereηED is the exciton diffusion efficiency, ηCT is the charge transfer efficiency and ηCC is the chargecollection efficiency [7]. The optical generation efficiency is the term ηEDηCT.

To determine the optical generation efficiency in P3HT:PCBM, I divide the IQE by the termηCC. ηCC can be determined by first assuming that in high reverse bias, ηCC = 1. This assumptionis justified because at high reverse biases, there is a large electric field that allows the chargecarriers to quickly drift out of the device before recombination. Then, by comparing a device inhigh reverse bias and at short circuit, I find that the charge collection efficiency at short circuit

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is given by:ηCC, sc = EQEsc

EQEbias(B.1)

From Burkhard et al., EQEbias at 600 nm is roughly 1.05 EQEsc [40]. Using this, along with anexperimentally measured value of IQE, I find the the optical generation efficiency to be 0.793,which successfully reproduces the current density at short circuit.

In H1:PCBM, the optical generation efficiency is used as a fit parameter, because there isinsufficient information to calculate ηCC and the IQE.

B.2.4 Langevin Reduction Factor

As discussed in Sections 2.2 and 4.2, I assume the recombination rate constant to be independentof mobility. However, Seftos assumes recombination to follow the form of Langevin recombina-tion, with a Langevin reduction factor. In simulations where the goal was to calculate therecombination rate constant, the Langevin reduction factor was used as a fit parameter. Then,k was calculated using the usual equation for Langevin recombination:

k = γ × q(µh + µe)ε

(B.2)

In simulations where I assumed a constant k, I first find γ0 corresponding to a device withcharge mobilities µe,0 and µh,0. Then, γ for another device is given by:

γ = γ0µh,0 + µe,0µh + µe

(B.3)

B.2.5 Charge Mobility

Charge mobility characterizes how quickly a charge can move through the active layer. SCLCdiodes are used to measure this, as shown in Section A.3. I assume a constant mobility model.

B.2.6 Complex Index of Refraction

The complex index of refraction is given by n(λ) + ıκ(λ), where n is the index of refraction andκ determines the absorption coefficient, α = 4πκ

λ .The complex index of refraction of a 1:1 P3HT:PCBM blend is found in literature [41] and

measured through ellipsometry. This information is not available for the H1:PCBM blend, soI assume n to be 2.0 and independent of wavelength, which is valid in organic materials, andcalculate κ by first finding the value of the absorption coefficient using the Beer-Lambert lawand measured absorbance A:

I = I0e−αL (B.4)

A = − ln( II0

) = − ln(e−αL) = αL (B.5)

α = A

L(B.6)

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where I is the intensity at a given thickness, I0 is the incident intensity, and L is the thicknessof the device. Then, I set the two expressions of α equal to each other to find that:

κ = λA

4πL (B.7)

B.2.7 Series Resistivity

The series resistance through the active layer is entered in by considering the resistivity of anelectrode, then noting that the resistance is the resistivity times the thickness and divided bythe area of the electrode. This is usually a fit parameter to ensure that the IV curve in forwardbias past Voc agrees with experimental data.

B.2.8 Device Stack

For the P3HT:PCBM simulations, I used a device stack consisting of glass (500 nm), indium-doped tin oxide (115 nm), PEDOT:PSS (35 nm), P3HT:PCBM (50 nm, 100 nm, 150 nm, 220nm, 300 nm, or 375 nm), and aluminum (150 nm). For the H1:PCBM thicknesses, I used thesame structure, but with a layer of H1:PCBM (100 nm) instead of the P3HT:PCBM layer.

B.3 Simulation Procedure

B.3.1 Simulator Verification

To verify the simulator, I used the fit parameters k and series resistance to simulate devices withvarying anneal temperatures and charge mobilities. I first found k and the series resistance forthe as-cast device by iteratively simulating IV sweeps until the simulated curve agreed with theexperimental data. Afterwards, I adjusted the Langevin reduction factor using Equation B.3 tomaintain the same value of k.

To adjust the series resistance through the active layer, I change the series resistivity of thePEDOT layer of fixed thickness. First, the series resistivity through the active layer scales as:

ρP3HT = RA

LP3HT(B.8)

where R is the series resistance and ρ the series resistivity in P3HT:PCBM, A is the active layerarea, which is the same for both P3HT:PCBM and PEDOT, and LP3HT is the thickness ofthe P3HT:PCBM film. To equate the series resistance in the P3HT:PCBM film to the seriesresistance in the PEDOT film, the following equation must hold:

ρPEDOT = ρP3HTLP3HT

LPEDOT(B.9)

Since ρP3HT and LPEDOT do not vary, we can say that ρPEDOT = ρ ∝ LP3HT = L.

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Another trend, only found in P3HT:PCBM, is that the conductivity σ is linear to the sum ofthe charge mobilities µ = µh + µe. This is equivalent to the equation:

σ

µ= σ0

µ0(B.10)

Using the relation σ = 1ρ , the above equation can be rearranged to the form:

ρ = ρ0µ0

µ(B.11)

Thus, series resistance through the film of P3HT:PCBM can be accounted for by changingthe series resistivity through the PEDOT electrode with the relation:

ρ = ρ0µ0

µ

L

L0(B.12)

where L denotes the thickness of the film of P3HT:PCBM and the subscript 0 denotes the originalvalue of mobility or thickness.

B.3.2 Best Fit Procedure

To extract meaningful values of k, I use a best fit procedure to iteratively simulate IV curvesuntil both experimental and simulated curves match with a tolerance of ±0.5 mA

cm2 between 0 Vand Voc. The tolerance, or residual, is defined as Jmeas − Jsimul. An example of this iterativeprocess, done on a 50% H1 device, is shown in Figure B.9.

(a) Simulated and experimental curves plotted to-gether.

(b) A plot of the residual.

Figure B.9. An example of the best fit procedure, done on a 50% H1 device. The residual betweenmeasured and simulated is plotted to see if the residual falls within the tolerance between 0 V and thevoltage at open circuit.

In both P3HT:PCBM and H1:PCBM, the HOMO level, the optical generation efficiency,Langevin reduction factor, and series resistance were fit parameters to ensure a best fit. ForP3HT:PCBM, the HOMO level was changed very slightly, while in H1:PCBM, the HOMO levelvaried significantly, due to the phenomenon described in Section 3.3.2.

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