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1 저작자표시 - 비영리 - 변경금지 2.0 대한민국 이용자는아래의조건을따르는경우에한하여자유롭게 이저작물을복제, 배포, 전송, 전시, 공연및방송할수있습니다. 다음과같은조건을따라야합니다 : 저작자표시. 귀하는원저작자를표시하여야합니다. 비영리. 귀하는이저작물을영리목적으로이용할수없습니다. 변경금지. 귀하는이저작물을개작, 변형또는가공할수없습니다. 귀하는, 이저작물의재이용이나배포의경우, 이저작물에적용된이용허락조건을명확하게나타내어야합니다. 저작권자로부터별도의허가를받으면이러한조건들은적용되지않습니다. 저작권법에따른이용자의권리는위의내용에의하여영향을받지않습니다. 이것은이용허락규약 (Legal Code) 을이해하기쉽게요약한것입니다. Disclaimer

2 Charge Transport in Organic Photovoltaic Cells

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4 이학박사 학위논문 Charge Transport in Organic Photovoltaic Cells 유기태양전지에서 전하 전송 연구 2014년 2월 서울대학교 대학원 화학부 물리화학전공 마누엘 슈라더

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6 Johannes-Gutenberg-Universität Mainz Fachbereich Physik Charge Transport in Organic Photovoltaic Cells Dissertation zur Erlangung des akademischen Grades Doktor der Naturwissenschaften (Doctor rerum naturalium) verfasst und vorgelegt von Manuel chrader geb. in Wiesbaden Max-Planck-Institut für Polymerforschung Mainz, Juni 2013

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8 본 논문은 유기 태양 전지의 전하 전송에 대한 심도 있는 이해를 추구하였다. 컴퓨터시뮬레이션을통하여유기 물질에서 전하 전달체의 역학을, 미시적 수 준의양자역학적 과정에서부터 전하 전달체의 이동도를 정량화할 수 있는 거 시적 수준까지재구성하였다. 이다중 스케일적접근 방법에 의하여, 유기 물질 의 화학 구조와 거시적 이동도의 관계 (구조-물성 관계)를 확립하였는데, 이 관 계는 태양광 효율의 개선을 지원하게 된다. 시뮬레이션 모델에는 다음 세 가지 주요구성 요소가포함되어 있다. 첫째는 형태로서, 해당 물질 내에서 분자배 열 모형을 원자 단위로 쪼개어 구성하였다. 둘째는 전하 전송의 호핑 모델로서, 전하이동을 개별 분자사이에서의 연속적인전하 전달반응으로 설명하였다. 마지막은 전하 전달의 비단열 모델로서, 전이율을 다음 세가지파라미터로 설 명하였다: 재구성 에너지, 사이트에너지, 전달 인테그럴. 전하 전송 시뮬레이션은 다이시아노비닐 치환 올리고싸이오펜의 물질적 인 부분과단결정 및 박막과 비정질/스멕틱 메조상의 형태에초점을 맞추었다. 이에따른 일반적결과는, 어셉터-도너-어셉터 순서와 유연한 올리고머주사슬 로구성된 분자구조가 분자의쌍극자모멘텀에 변화를줌으로써사이트에너 지를 변화시킨다는 것이다. 이에너지 측면에서의 무질서는 보통 결정에서 높 으며메조상에서는 더욱 높은 것으로드러났다. 단결정의 경우, 파이스태킹을 갖춘 결정 구조와 그에따른 대규모 전자 전달 인테그럴이 상대적으로 낮은 이 동도로 이어졌다. 이 반직관적인 행동은 에너지 결함이 발생하기 쉬운 전송 경 로의 형성에 기인한것이다. 박막의 경우, 위 추론이 다시 확인됨으로써 실험적 이동도에대한 미시적 이해로이어질 수 있다. 사실, 시뮬레이션결과는측정된 이동도와 태양광 효율 모두와 연관된다. 비정질/스멕틱 계의 경우, 에너지무질 서는올리고머의 길이에따라 증가하는데, 보다스멕틱 질서가커질수록 이동 도가 감소하는 이상 현상을 보인다. 그이유는 스멕틱 층이에너지무질서의 공 간적 상관관계와 충돌하기 때문으로 설명된다. 주요어: 태양전지, 유기, 전하 전송, 이동도, 시뮬레이션, 올리고싸이오펜 학번:

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10 Zusammenfassung Die vorliegende Dissertation dient dazu, das Verständnis des Ladungstransportes in organischen olarzellen zu vertiefen. Mit Hilfe von Computersimulationen wird die Bewegung von Ladungsträgern in organischen Materialien rekonstruiert, und zwar ausgehend von den quantenmechanischen Prozessen auf mikroskopischer Ebene bis hin zur makroskopischen kala, wo Ladungsträgermobilitäten quantifizierbar werden. Auf Grundlage dieses skalenübergreifenden Ansatzes werden Beziehungen zwischen der chemischen truktur organischer Moleküle und der makroskopischen Mobilität hergestellt (truktur-eigenschafts-beziehungen), die zu der Optimierung photovoltaischer Wirkungsgrade beitragen. Das imulationsmodell beinhaltet folgende drei chlüsselkomponenten. Erstens eine Morphologie, d. h. ein atomistisch aufgelöstes Modell der molekularen Anordnung in dem untersuchten Material. Zweitens ein Hüpfmodell des Ladungstransportes, das Ladungswanderung als eine Abfolge von Ladungstransferreaktionen zwischen einzelnen Molekülen beschreibt. Drittens ein nichtadiabatisches Modell des Ladungstransfers, das Übergangsraten durch drei Parameter ausdrückt: Reorganisationsenergien, Lageenergien und Transferintegrale. Die Ladungstransport-imulationen richten sich auf die Materialklasse der dicyanovinyl-substituierten Oligothiophene und umfassen Morphologien von Einkristallen, Dünnschichten sowie amorphen/smektischen Mesophasen. Ein allgemeiner Befund ist, dass die molekulare Architektur, bestehend aus einer Akzeptor-Donor-Akzeptor- equenz und einem flexiblen Oligomergerüst, eine erhebliche Variation molekularer Dipolmomente und damit der Lageenergien bewirkt. Diese energetische Unordnung ist ungewöhnlich hoch in den Kristallen und umso höher in den Mesophasen. Für die Einkristalle wird beobachtet, dass Kristallstrukturen mit ausgeprägter π-tapelung und entsprechend großer Transferintegrale zu verhältnismäßig niedrigen Mobilitäten führen. Dieses Verhalten wird zurückgeführt auf die Ausbildung bevorzugter Transportrichtungen, die anfällig für energetische törungen sind. Für die Dünnschichten bestätigt sich diese Argumentation und liefert ein mikroskopisches Verständnis für experimentelle Mobilitäten. In der Tat korrelieren die imulationsergebnisse sowohl mit gemessenen Mobilitäten als auch mit photovoltaischen Wirkungsgraden. Für die amorphen/smektischen ysteme steigt die energetische Unordnung mit der Oligomerlänge, sie führt aber auch zu einer unerwarteten Mobilitätsabnahme in dem stärker geordneten smektischen Zustand. Als Ursache dafür erweist sich, dass die smektische chichtung der räumlichen Korrelation der energetischen Unordnung entgegensteht.

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12 Abstract This thesis serves to deepen the understanding of charge transport in organic photovoltaic cells. Using computer simulations, the dynamics of charge carriers in organic materials is reconstructed, starting from the quantum mechanical processes on the microscopic level up to the macroscopic scale, where charge carrier mobilities can be quantified. Based on this multiscale approach, relationships between the chemical structure of organic molecules and the macroscopic mobility are established (structure-property relationships), which assist the improvement of photovoltaic efficiencies. The simulation model includes the following three key components. First, a morphology, i.e., an atomistically resolved model of the molecular arrangement within the material of interest. econd, a hopping model of charge transport, describing charge migration as a succession of charge transfer reactions between individual molecules. Third, a nonadiabatic model of charge transfer, expressing transition rates by three parameters: reorganization energies, site energies, and transfer integrals. The charge transport simulations focus on the material class of dicyanovinyl-substituted oligothiophenes and cover morphologies of single crystals, thin films, and amorphous/smectic mesophases. A general result is that the molecular architecture, consisting of an acceptor-donor-acceptor sequence and a flexible oligomer backbone, gives rise to substantial variations of molecular dipole moments and hence of the site energies. This energetic disorder is unusually high in the crystals and even higher in the mesophases. For the single crystals, it is observed that crystal structures with a pronounced π-stacking and correspondingly large transfer integrals lead to relatively low mobilities. This counterintuitive behavior is traced back to the formation of preferred transport directions which are prone to energetic defects. For the thin films, this reasoning can be confirmed and provides a microscopic understanding for experimental mobilities. In fact, the simulation results correlate with both measured mobilities and photovoltaic efficiencies. For the amorphous/smectic systems, the energetic disorder increases with the oligomer length, but also leads to an unexpected mobility reduction in the more ordered smectic state. The reason for this is elucidated by showing that the smectic layering conflicts with the spatial correlations of the energetic disorder. Keywords: solar cell, organic, charge transport, mobility, simulation, oligothiophene tudent number:

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14 Contents Introduction 15 Related Publications 19 Notation 21 I. Background Organic Photovoltaic Cells Electronic tructure of Organic olids Conversion of olar Radiation into Electric Power Power Conversion Efficiency Foundations of Computational Chemistry eparation of Nuclear and Electronic Motions Electronic tructure Theory Hartree-Fock Theory Kohn-ham Density Functional Theory Basis et Approximation II. Methodology Charge Transfer in Molecular ystems Regimes of Charge Transfer Adiabatic Charge Transfer Nonadiabatic Charge Transfer Charge Transfer Rates Bimolecular High-Temperature Nonadiabatic Charge Transfer Further Limits of Nonadiabatic Charge Transfer

15 14 Contents 4. Charge Transport in Organic olids Regimes of Charge Transport Ordered Organic olids Disordered Organic olids Charge Transport imulations in Disordered Organic olids Force Field Morphology Hopping ites Transfer Integrals ite Energies Reorganization Energies Charge Dynamics Macroscopic Observables III. Results Charge Transport imulations in Organic Crystals Dicyanovinyl-ubstituted Oligothiophenes: ingle Crystals Morphological Disorder Charge Transfer Parameters Charge Carrier Mobility Dicyanovinyl-ubstituted Quaterthiophenes: Thin Films Crystal tructure Analysis Charge Carrier Mobility Charge Transport imulations in Organic Mesophases Dicyanovinyl-ubstituted Oligothiophenes: Amorphous/mectic Morphological Disorder Charge Transfer Parameters Charge Carrier Mobility Electric Current Pathways Conclusion and Outlook 151 Bibliography 157

16 Introduction The sun provides more energy to the earth everyhourthanmankindconsumesin an entire year. In fact, the energy resource of terrestrial solar radiation far exceeds that of all other renewable and fossil energy sources combined. 1 Harnessing the immense solar energy resource not only has the potential to accommodate the increasing global energy demand, but also holds promise to reshape the energy sector for environmental sustainability. However, a widespread adoption of photovoltaic electricity generation is only achievable through competitive pricing on the energy market. In fact, conventional inorganic photovoltaic cells, although technologically advanced, are still limited to niche applications due to high costs. The emerging technology of organic photovoltaic cells,incontrast,couldquicklyfindaubiquitousdeploymentsince organic materials offer strong potential for cost reduction. In addition to an inexpensive production, organic solar cells can inherit the advantageous physical properties of organic materials, such as light weight and mechanical flexibility. Although organic photovoltaic technology is still far from the level of maturity required to deliver these promises, the field has recently experienced such a rapid progress that it is currently transitioning from a phase of technology development to industrial production. This dynamic development is the fruit of concerted efforts in several areas, such as synthetic chemistry, producing increasingly fine-tuned organic compounds, and material processing, constantly adapting to the demands of the field. Now that organic photovoltaics is close to first commercialization, the scientific community is more than ever demanded to address the still major challenges ahead. The most critical issues of organic solar cells, as compared to their inorganic counterparts, are their shorter life spans and lower power conversion efficiencies. One of the greatest difficulties in improving such device properties is the widely lacking comprehension of how these properties are linked to the constituent organic compounds. As a result, the chemical synthesis of new or modified compounds is mostly guided by intuitive rather than rational design rules. With the aim of a rational compound design, models relating the chemical structures to macroscopic properties, so-called structure-property

17 16 Introduction relationships, become highly desired. Establishing such relationships is a central concern of this work. This necessitates both a microscopic description of organic photovoltaic cells as well as methods for linking the macroscopic properties to this description. A more detailed discussion on the challenges for improving photovoltaic device properties is provided after introducing the required background on organic photovoltaic cells in Chapter 1. Awindowintothemicroscopicworldofchemicalmatterisopenedbythefieldof computational chemistry, whichprovidesmethodsofcomputersimulation,or,ina sense, a virtual laboratory. Most fundamentally, computational chemistry considers matter as a many-particle system of two different constituents: atomic nuclei and electrons, interacting through the electromagnetic force. Modeling this chemical reality by computer simulations receives its justification and merit from the full understanding of the underlying physical principles. In fact, already in 1929, Dirac realized that the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. 2 Indeed, with the Dirac equation, and certainly today with quantum electrodynamics, well-elaborated theories, accounting for both quantum mechanics and relativity, have been developed. For many chemical systems, these levels of elaboration are not even necessary and one can restrict the description to classical electrodynamics and non-relativistic quantum mechanics, that is, to the chrödinger equation. The second part of the quotation might, due to the ever-increasing processing power of computers, be seen in a different light today. Although certain approximations are indeed required in order to transform an exact quantum mechanical equation of motion from its abstract form into actually tractable expressions (these fundamental approximations include in particular the Born-Oppenheimer approximation, which facilitates a decoupling of the nuclear and electronic motions), the enormous amount of calculation required for solving the resulting expressions has become an increasingly feasible task. As of today, computational chemistry techniques which are solely based on first principles of physics and fundamental approximations, so-called ab initio methods, are applicable to complex systems of microscopic size, such as molecular systems. The background of these foundations of computational chemistry, covering in particular the separation of nuclear and electronic motions, their decoupling by means of the Born-Oppenheimer approximation, as well as ab initio electronic structure theory is discussed in Chapter 2.

18 Introduction 17 One of the most important macroscopic properties of organic photovoltaic cells is their ability to produce an electrical current. The prerequisite for such a current flow is the migration of charge carriers through the organic material. This process is denoted as charge transport and is characterized in terms of the charge carrier mobility. This quantity, which is associated with the average velocity of the charge carriers, can be experimentally measured for a given sample of the organic material. However, when it comes to optimizing the material for an improved mobility, one faces the problem of missing structure-property relationships linking the mobility to the constituent molecules. With the aim of closing this knowledge gap, this work applies computer simulations to reconstruct the macroscopic process of charge transport based on its microscopic origins. These charge transport simulations are based on a model including the following three key components. First, a sufficiently large, but at the same time atomistically resolved model of the organic material, a so-called morphology. To generate such a large-scale material morphology, ab initio methods need to be supplemented by computational chemistry techniques operating on a higher level of approximation. This is achieved by molecular dynamics simulations, where the motion of atoms is governed by classical Newtonian mechanics, calibrated according to ab initio methods. The second ingredient is a model of charge transport which describes charge carrier migration within the morphology as a sequence of charge hops between individual molecules. These microscopic processes of charge movement are referred to as charge transfer reactions and the quantity characterizing their efficiency is the charge transfer rate. uch a rate is influenced by several factors: the electronic structure of the two individual molecules, their relative positions and orientations, but also their environment of surrounding molecules. The third component is an appropriate model of charge transfer, which translates these dependences into a set of tangible parameters, which are accessible by methods of computational chemistry. In some cases, the applicability of ab initio methods may be limited by the large number of molecular pairs for which charge transfer parameters need to be evaluated. The parametrization can then be assisted by semiempirical methods, which are still based on the quantum mechanical level of description, but incorporate certain empirical data to accelerate the computation. Altogether, the simulation of charge transport invokes a hierarchy of methods to scan all the required length and time scales with amanageablecomputationaleffort. Whilethetheoryofchargetransferinmolecular systems is treated in Chapter 3, the complete methodology of charge transport in organic solids is presented in Chapter 4.

19 18 Introduction C60 dcvnt NC NC n Chemical structures of buckminster fullerene (C 60)anddicyanovinyl-substituted oligothiophenes (dcvnt). At present, the most successful materials for building organic photovoltaic cells are compositions of buckminster fullerene (C 60 ) and the novel class of dicyanovinyl-substituted oligothiophenes (dcvnt) or its derivatives. In fact, based on these compounds, an ongoing series of world record power conversion efficiencies has been achieved between 2009 and 2013 by Heliatek GmbH. 3 In addition to these proprietary cells, a wide range of related devices has been published by the collaborating groups of Bäuerle at the Institute of Organic Chemistry II and Advanced Materials in Ulm, Germany, and Leo at the Institute for Applied Photo Physics in Dresden, Germany. In this work, charge transport is studied for a variety of dcvnt material morphologies associated with these devices. A simulation study on single crystals and a further one on thin films are presented in Chapter 5. For single crystals, charge transport is compared for asetoffoursystems:theterthiopheneandquaterthiophene,dcv3tanddcv4t,aswell as two methylated derivatives, dcv3t-m and dcv4t-m. For thin films, charge transport is examined in systems of the bare and methylated quaterthiophenes, dcv4t and dcv4t-m. A simulation study on amorphous and smectic systems of the compound series of thiophene to sexithiophene, dcv1t to dcv6t, is presented in Chapter 6. Parts of the methodology and the results reported in this work (ections ) are the subject of prior publications, listed on Page 19. These studies are presented here in significantly more detail. The background and the methodology (ections ) have been developed based on the textbooks and review articles provided at the beginning of the respective discussions. All chapters of this work employ a notation for symbols summarized on Page Lewis, N.. Toward Cost-Effective olar Energy Use. cience 315 (2007), Dirac, P. A.M. Quantum Mechanics of Many-Electron ystems. Proc. R. oc. London, er. A 123 (1929), Le éguillon, T., and Pfeiffer, M. Efficiency Development. Heliatek,

20 Related Publications In the course of these doctoral studies, the following journal articles were published. The publications on charge transport [1 4] are related to the methodology for charge transport simulations (ection 4.2) and to the results on single crystals (ection 5.1), thin films (ection 5.2), and amorphous/smectic systems (ection 6.1) of dicyanovinylsubstituted oligothiophenes. The independent study on proton transport [5] is not addressed in this thesis. [1] chrader, M., Fitzner, R., Hein, M., Elschner, C., Baumeier, B., Leo, K., Riede, M., Bäuerle, P., and Andrienko, D. Comparative tudy of Microscopic Charge Dynamics in Crystalline Acceptor-ubstituted Oligothiophenes. J. Am. Chem. oc. 134 (2012), [2] chrader, M., Körner,C.,Elschner,C.,andAndrienko,D.ChargeTransport in Amorphous and mectic Mesophases of Dicyanovinyl-ubstituted Oligothiophenes. J. Mater. Chem. 22 (2012), [3] Elschner, C., chrader, M., Fitzner, R., Levin, A. A., Bäuerle, P., Andrienko, D., Leo, K., and Riede, M. Molecular Ordering and Charge Transport in a Dicyanovinyl-ubstituted Quaterthiophene Thin Film. RC Adv. 3 (2013), [4] Rühle, V., Lukyanov, A., May, F., chrader, M., Vehoff,T.,Kirkpatrick,J.,Baumeier, B., and Andrienko, D. Microscopic imulations of Charge Transport in Disordered Organic emiconductors. J. Chem. Theory Comput. 7 (2011), [5] Wehmeyer, C., chrader, M., Andrienko, D., and ebastiani, D. Water-Free Proton Conduction in Hexakis-(p-phosphonatophenyl)benzene Nano-Channels. J. Phys. Chem. C 117 (2013),

21 20 Related Publications

22 Notation Indices n, m electrons a, b nuclei / atoms i, j molecules / sites α, β electronic states +, / i, f adiabatic / diabatic electronic states η, ϑ nuclear states n, m molecular orbitals σ, τ atomic orbitals µ, ν general vector and matrix elements Entity and Pair Properties r n / r electronic coordinates / multi-index p n σ n R a / R R ab P a V a M a z a p a q c a / q n a α c a / α n a Q / P / ω vib electronic momenta electronic spin nuclear coordinates / multi-index nuclear separations nuclear momenta nuclear velocities nuclear masses atomic numbers atomic dipole moments atomic partial charges of charged / neutral site atomic polarizabilities of charged / neutral site reaction coordinate / momentum / eigenfrequency

23 22 Notation r i r ij p i α n i / α c i U n i / U c i U n i / U c i Wi n E int i E elstat i / W c i / E int ij E i / E ij λ ij / λ i J ij ω ij c ij / E elstat ij site coordinates site separations site occupation probabilities site polarizability tensor in neutral / charged state internal site energies in neutral / charged state internal site energies in neutral / charged state, opposite geometry electrostatic site energies in neutral / charged state internal site energies / differences electrostatic site energies / differences site energies / differences reorganization energies / site contributions transfer integrals charge transfer rates edge currents ystem Properties and Observables ρ electron density n number of electrons a number of nuclei / atoms d mass density T temperature F external electric field t time of nuclear motion τ time of charge carrier motion λ / Λ diagonal / off-diagonal dynamic disorder σ / Σ diagonal / off-diagonal static (energetic / electronic) disorder σ / σ eff energetic disorder of neighbor list / reduced neighbor list C E Q µν / Q D µν / D site energy correlation function nematic order tensor charge carrier diffusion tensor µ µν / µ charge carrier mobility tensor

24 Notation 23 Operators Ĥ T nuc V nuc nuc T el / ˆt el (r n ) V el el / ˆv el el (r n, r m ) V nuc el / ˆv nuc el (r n ) Ĥ el (R) Ĥnuc(R) α Θ nuc(r) αβ Ĥ nuc(q) ± / Ĥnuc(Q) i,f Θ + nuc(q) / J if (Q) / J ij Ĥ 1 / Ĥ 2 Ĥ 3 / Ĥ 4 Ĥ hf / Ĥ ks / Ĥ ˆv h (r 1 ) / ˆv x (r 1 ) / ˆv xc (r 1 ) Hamiltonian operator nuclear kinetic energy nuclear-nuclear interaction electronic kinetic energy / for electron n electronic-electronic interaction / for electrons n, m nuclear-electronic interaction / for electron n electronic Hamiltonian operator nuclear Hamiltonian operator nonadiabatic coupling (nonadiabaticity operator) adiabatic / diabatic nuclear Hamiltonian operator nonadiabatic / nondiabatic coupling (transfer integral) equilibrium / phononic Hamiltonian local / nonlocal electron-phonon coupling Hartree-Fock / Kohn-ham / one-particle operator Hartree / exchange / exchange-correlation operator Wave Functions / Eigenstates Ψ(R, r, t) χ αη (R, t) ψ α (r, R) ψ ± (Q) / ψ i,f / ψ i ϕ n i (r 1) / ϕ n i / ϕf i φ τ i (r 1) / φ τ i total wave function nuclear wave functions electronic wave functions adiabatic / diabatic electronic states molecular orbitals / frontier orbitals atomic orbitals Eigenvalues and Potential Energy urfaces E α el (R) U α (R) E el ± (Q) / Ei,f el U ± (Q) / U i,f (Q) ε n i electronic eigenvalues potential energy surface adiabatic / diabatic electronic eigenvalues adiabatic / diabatic potential energy surface molecular orbital energies

25 24 Notation Functionals, Matrices, and Tensors E x [ρ] / E c [ρ] / E xc [ρ] exchange / correlation / exchange-correlation functional Exc b3lyp [ρ] b3lyp exchange-correlation functional T ab / T µ ab / T µν ab multipole interaction tensor / first / second derivative H στ / H one-electron Hamiltonian matrix Hzindo στ / H zindo diag(ε n ) / E C τn / C στ / zindo Hamiltonian matrix molecular orbital energy matrix atomic orbital matrix atomic orbital overlap matrix Photovoltaic Cell Properties and olar Parameters η pce η eqe η ff j / j sc / j mp V / V oc / V mp P solar Φ solar (E) power conversion efficiency external quantum efficiency fill factor current density / at short circuit / for maximum power voltage / at open circuit / for maximum power solar power density solar spectral photon flux density Physical Constants m el e ε 0 c ħ k B electron mass elementary charge vacuum permittivity speed of light Planck constant Boltzmann constant

26 Part I. Background

27

28 Chapter 1. Organic Photovoltaic Cells In contrast to their silicon-based inorganic counterparts, organic photovoltaic cells are manufactured from organic, i.e., carbon-based molecules. Depending on the molecular weight, there is a common classification into organic solar cells produced from polymers and from small molecules. This distinction refers to the processing techniques used for preparing the desired layers of organic molecular solids: while polymers are dissolved in solutions, which are solidified by solvent removal techniques, small molecules are mostly processed by vacuum evaporation or sublimation and subsequent material deposition. However, both types of cells share the same working principle for the photovoltaic power conversion. A third type of functionally different organic solar cells, which is not related to this work, is the class of dye-sensitized solar cells. The following discussion opens with a qualitative insight into the electronic structure of organic molecular solids (ection 1.1). ince organic solids possess relatively weak cohesive intermolecular interactions, their electronic structure can be regarded as a perturbed one of its constituent molecules. Molecules of particular interest are those which comprise π-conjugated systems, since they can enable the desired semiconducting properties of the organic solid. Then, the focus is directed to organic photovoltaic cells and their working principle for the conversion of solar radiation into electrical power (ection 1.2). The power conversion is based on four optical and electronic processes: optical absorption yielding an exciton (a bound electron-hole pair), exciton diffusion, exciton dissociation into free charge carriers, and charge transport towards the electrodes. Finally, the most important metric of a photovoltaic cell the power conversion efficiency is introduced (ection 1.3). After briefly reflecting on the theoretical upper limits for the efficiency, the currently achieved values and challenges for further improvements are discussed. Among the main challenges are the improvement of the light harvesting, the active layer morphologies, but also the fundamental understanding of how the efficiency is linked to the properties of the constituent molecules.

29 28 Chapter 1. Organic Photovoltaic Cells 1.1. Electronic tructure of Organic olids In general, organic solids [6 10] are solid-state materials which are composed of molecules falling within the scope of organic chemistry. These organic molecules are predominantly composed of carbon atoms and exist, due to the versatile bonding capabilities of carbon, in a myriad of architectures. This diversity of compounds is reflected in a wide spectrum of observed solid state order, ranging from the perfect crystalline to the amorphous phase and covering many intermediate forms, such as polycrystalline, semicrystalline, or mesomorphic phases. While most organic solids are insulators, the field of organic photovoltaics is primarily concerned with the subclass of materials acting as (semi)conductors. Thesematerials,capableofcarryinganelectriccurrent, are generally composed of molecules which have electrons delocalized over larger, socalled conjugated systems of the molecular skeleton. Important building blocks for such conjugated systems are aromatic hydrocarbons, such as the polyacenes, i.e., benzene, naphthalene, anthracene, etc., or heterocyclic compounds, such as thiophene, furane, pyrrole, etc., which are depicted in Figure 1.1. To understand the origin of electronic delocalization in conjugated molecules, one can start from the familiar viewpoint of independent electrons, described by individual wave functions, i.e., molecular orbitals. In addition, these molecular orbitals shall be composed as linear combinations of atomic orbitals (mo-lcao). In fact, these concepts constitute electronic structure theories (ection 2.2), which enable one to quantitatively derive the right linear combinations for composing the molecular orbitals. One can then verify that there are indeed delocalized orbitals. For a qualitative understanding, however, the notion of valence bond theory may be illustrative. There, pairs of overlapping atomic valence orbitals give rise to bonding molecular orbitals, i.e., shared electron pairs lead to covalent bonds. This simple picture is accompanied by the Benzene Naphthalene Anthracene Thiophene O Furan H N Pyrrole Figure 1.1. election of basic conjugated organic molecules, acting as building blocks for small molecules, oligomers, or polymers employed in organic electronic devices.

30 1.1. Electronic tructure of Organic olids 29 (a) y x p z -orbital sp2-orbital π-bonding σ-bonding (b) 6p z 2sp2 lumo homo σ π π σ Figure 1.2. (a) Atomic valence orbitals of the carbon atoms in benzene. Overlapping sp 2 -orbitals give rise to σ-bonding, while overlapping p z -orbitals lead to π-bonding. (b) plitting of the energy levels of two atomic sp 2 -orbitals leading to bonding and antibonding molecular σ- and σ -orbitals as well as of six p z -orbitals yielding π- and π -orbitals. Adapted from Reference [11]. idea of hybridization: it allows one to transform each basis of standard (hydrogen-like) atomic orbitals, by intuitive linear combinations, to equivalent bases of so-called hybrid atomic orbitals. Considering carbon, the ground state electron configuration in terms of hydrogen-like atomic orbitals reads 1s 2 2s 2 2p x 2p y with two valence electrons. Hybrid atomic orbitals are, however, derived from the excited electron configuration 1s 2 2s 2p x 2p y 2p z with four valence electrons. This is because the energy expenditure for the excitation is more than compensated by the formation of two additional bonds. Asimplelinearcombinationofthe2s-,2p x -, and 2p y -orbitals leads to three hybrid sp 2 -orbitals, which lie in the xy-plane at angles of 120. The p z -orbital remains unchanged and is perpendicular to the xy-plane. Using the example of benzene, containing six carbon atoms in a hexagonal arrangement, these orbitals are illustrated in Figure 1.2 a. Now, pairs of overlapping atomic sp 2 -orbitals in the xy-plane give rise to molecular σ-orbitals,which are localized between the respective pairs of nuclei. Figure 1.2 b shows how the energy levels of an overlapping pair of sp 2 -orbitals are split into an energetically lower level, corresponding to a bonding σ-orbital, which is doubly occupied, and a higher level, corresponding to an antibonding σ -orbital, which is vacant. Due to the strong overlap of sp 2 -orbitals, the energy splitting and the resulting energetic advantage is large, and therefore the σ-bonding a strong effect. In total, the molecular backbone of the benzene molecule involves twelve sp 2 -orbitals forming the hexagon and a further six linking the hydrogens. The remaining six atomic p z -orbitals are also overlapping, namely above and below the xy-plane, which gives rise to three bonding molecular π-orbitals, which are doubly occupied, and three antibonding π -orbitals, which are empty. Obviously, the three π-orbitals cannot be localized between three pairs of nuclei, since all six pairs of nuclei are equivalent by the molecular symmetry. In fact, the π-orbitals are instead delocalized over the molecular skeleton. As the overlap of the p z -orbitals is weak, their energy splitting is small and

31 30 Chapter 1. Organic Photovoltaic Cells lumo P E dos E E E dos homo P Molecule Ordered olid Disordered olid Figure 1.3. Electronic structure of organic solids: one observes a general shift as well as a slight broadening of the molecular energy levels. While ordered solids show narrow energy bands, disordered solids often exhibit a Gaussian distributed density of states (dos). Adapted from Reference [8]. therefore the mechanism of π-bonding comparatively weak. In many conjugated organic molecules, the highest occupied molecular orbital (homo) is a π-orbital, while the lowest unoccupied molecular orbital (lumo) is a π -orbital. The electronic structure discussed so far refers to isolated organic molecules, as they are encountered in the gas phase. In an organic solid, formed upon condensation of the molecules, the electronic structure changes, since molecules interact with each other. The interaction between molecules, causing their cohesion, is dominated by the van der Waals interaction, providedthemoleculesareneutralandarenotforming ionic bonds. Van der Waals interactions result from fluctuations in the molecular charge distributions: such fluctuating dipole moments polarize adjacent molecules, leading to an induced dipole-dipole attraction. ince these intermolecular interactions are much weaker than the strong covalent binding forces within the molecules, the molecular properties remain largely intact in an organic solid. Thus, the electronic structure of the solid is only a moderately altered one of a free molecule. The main differences are illustrated in Figure 1.3. First, one observes a general shift of the energy levels due to the polarizable environment. The homo and lumo energies, i.e., the ionization potential E ip and electron affinity E ea (in Koopman s approximation), are displaced by the polarization energies P ea and P ip,respectively.therefore,inthe solid, the difference between the ionization potential and electron affinity is usually lowered. econd, the energy levels in the solid are slightly broadened due to the weak overlap of the molecular orbitals. In the case of ordered solids, such as crystalline phases at low temperatures, narrow energy bands can emerge. In analogy to inorganic materials, these bands are sometimes referred to as the valence and conduction bands of the organic solid and the region in between as the band gap. In the case of disordered solids, such as amorphous or mesomorphic phases, the density of states (dos) is often described by Gaussian distributions. Then, the distribution tails extend into the band gap and the band edges are no longer clearly defined.

32 1.2. Conversion of olar Radiation into Electric Power Conversion of olar Radiation into Electric Power Organic photovoltaic cells [12 18] make use of organic solids to convert solar photons into electric voltage and current. A major similarity to inorganic cells, which are mostly based on silicon, is that the photoactive organic materials are semiconductors. Therefore, the photovoltaic effect can be exploited for promoting electrons across the band gap, whichpreventstherapiddecaybacktothegroundstatebyaseriesofphonons, as would occur without the gap. A key difference in organic semiconductors, on the other hand, is that a promoted electron is not free,but instead electrostatically bound to the remaining hole. The bound electron-hole pair is denoted as exciton and therefore organic solar cells sometimes as excitonic solar cells. For the separation of excitons, the most common concept is to use a junction between two different organic semiconductors, which is referred to as a heterojunction. Thisdevicedesignwasfirst proposed in 1986 by Tang in the much-cited Reference [19]. The basic working principle of a heterojunction solar cell involves four optical and electronic processes, which are illustrated in Figure 1.4: optical absorption yielding an exciton, exciton diffusion to the heterojunction, exciton dissociation into free charge carriers, and charge transport to the electrodes. First, upon optical absorption, asolarphotonpromotesanelectronwithinoneof the two different organic semiconductors across the band gap. This is possible since, due to the π-conjugation, organic semiconductors exhibit relatively low band gaps, roughly between 1 and 4 ev, which lies within the spectrum of the solar radiation received on earth. After the photoexcitation, the system rapidly relaxes to the band edges, i.e., dissipates the energy exceeding the band gap via a series of phonons as heat, and finally forms an exciton. The exciton binding energy, that is, the electrostatic interaction energy between the electron and hole, is of the order of 0.1 to 1 ev in organic materials, which is significantly higher than thermal energy at room temperature. As aconsequence,theelectronandholearenot free. Thisstrongelectrostaticattractionis a result of the low dielectric constants, i.e., the weak electrostatic screening of organic materials. In inorganic semiconductors, in comparison, exciton binding energies are of the order of 10 3 ev and photoexcited electrons and holes are free at room temperature. Compared to inorganic materials, organic semiconductors also have significantly higher absorption coefficients. As a consequence, organic photoactive layers can be much thinner. A thickness of the order of 100 nm is usually sufficient to absorb most incident photons whose energy bridges the band gap.

33 32 Chapter 1. Organic Photovoltaic Cells Figure 1.4. Optical and electronic processes taking place in an organic photovoltaic cell: first, optical absorption yielding an exciton; second, exciton diffusion to the heterojunction; third, exciton dissociation into free charge carriers; and fourth, charge transport to the electrodes. econd,exciton diffusion to the heterojunction is required. As an exciton is a neutral quasiparticle, which is not affected by any electric fields, its migration is a purely diffusive process. The diffusion length is determined by the finite lifetime of the exciton and is of the order of 10 nm. Within this length scale, the exciton, traveling within one of the two semiconductors, must reach the interface to the other one, otherwise it is lost due to radiative recombination. In planar heterojunction architectures, where the two semiconductors are arranged in two layers on top of each other, the exciton diffusion length obviously requires thinner layers than are needed for efficient photon absorption (100 nm). It is therefore necessary to find a compromise for the layer thickness. In order to avoid such a trade-off, one can employ bulk heterojunction architectures [20], where the two semiconductors are mixed to an interpenetrating network, as sketched in Figure 1.4. This design allows the interface area to be increased, while at the same time tuning the layer thickness for optimal absorption. Third, exciton dissociation can take place once the exciton has reached the heterojunction of the two semiconductors. The rationale behind this heterojunction, as introduced by Tang, is to provide appropriate energetic steps between the ionization potentials and electron affinities, aligned such as to overcome the exciton binding energy and therefore to facilitate the separation of the electron-hole pair. Figure 1.5 a depicts the required level alignment of the two semiconductors, which are henceforth referred to as the electron donor and acceptor,respectively.theenergydifferencebetweenthe ionization potential of the donor and the electron affinity of the acceptor, E d ip E a ea, must be more than the binding energy lower than the band gap of either material, i.e., E d ip E d ea and E a ip E a ea, provided excitons are generated in both materials. The illustration shows the case where the exciton is formed within the donor: since the energetic step in the electron affinity at the donor-acceptor heterojunction exceeds the binding

34 1.2. Conversion of olar Radiation into Electric Power 33 (a) (b) E E Cathode V Cathode Anode E Donor E Anode Acceptor Figure 1.5. (a) Energy level alignment of a donor-acceptor heterojunction solar cell required to facilitate exciton dissociation into charge carriers. (b) chematic energy diagram of the solar cell under operating conditions leading to drift currents of charge carriers towards the electrodes. energy, the separation of the electron and hole is an energetically favorable process. Therefore, the electron can be transferred from the donor to the acceptor, while the hole remains on the donor. Conversely, if the exciton is formed within the acceptor, the hole can be transferred from the acceptor to the donor, while the electron remains on the acceptor. Fourth, charge transport of the free electron and hole towards their respective electrodes occurs as a result of diffusion and drift [12, 21]. While charge diffusion, similar to the migration of excitons, occurs independently of electric fields, drift currents of the charge carriers are a result of the electric potential gradient inherent in the device. As illustrated in Figure 1.5 b, this potential gradient arises once the anode and cathode are either short-circuited, as indicated by the dashed line, or connected to an external circuit with a voltage drop V. The higher the voltage drop across the external circuit, the lower the internal potential gradient and thus the drift currents. If the voltage drop nearly cancels the internal potential gradient, the migration of electrons and holes is dominated by diffusion currents. Finally, the charge carriers are collected at their respective electrodes, i.e., the electron at the cathode and the hole at the anode. The electrodes, as conductors, are solely characterized by their Fermi levels, or their work functions. In an idealized model, the work function of the cathode matches the electron affinity of the electron acceptor, while the work function of the anode fits to the ionization potential of the donor. In practice, the cathode is often manufactured from aluminum, while the common choice for the anode is indium tin oxide (ito), which is not only conductive, but also transparent for the incident light.

35 34 Chapter 1. Organic Photovoltaic Cells 1.3. Power Conversion Efficiency The power conversion efficiency of any photovoltaic cell [22 24] depends on the device characteristics when operating in an electric circuit. In principle, both inorganic and organic devices generate a photocurrent under illumination, while they exhibit rectifying properties of a diode in the dark. This similarity is because the energetic step in an organic device, due to the heterojunction of two different semiconductors, is essentially similar to the step arising in an inorganic device upon contacting a p-and a n-doped material to a pn-homojunction [14]. As a consequence, any ideal solar cell can be modeled by an equivalent circuit consisting of a currentsourcein parallelwith a diode, as illustrated in Figure 1.6 a. The current-voltage characteristic of a solar cell exposed to light thus corresponds to a shifted diode characteristic, as seen in Figure 1.6 b. If the electrodes of the solar cell are connected, that is, R = 0, no voltage between them can be established and the cell delivers the short-circuit current density j sc.(notethat the current density j is used instead of the current I, since the photocurrent is ideally proportional to the illuminated area.) Conversely, if the electrodes are isolated, that is, R =, no current can flow and the cell develops the open-circuit voltage V oc. This case corresponds to Figure 1.5 a. For any intermediate applied resistance R, the cell generates a voltage V and a current density j = j(v), according to the currentvoltage characteristic, such that R = V/I. This general case corresponds to Figure 1.5b. At any point on the current-voltage characteristic, the electric power density supplied by the solar cell is given by the product of j and V. Thepointmaximizingthisproduct j j dark (a) j j j j (b) Maximum Power V j R V dark V V light V Figure 1.6. (a) Equivalent circuit of an ideal solar cell consisting of a current source in parallel with a diode. Under illumination, the cell generates a current density j and voltage V. (b) Current-voltage characteristic j = j(v). In the light,a shifted characteristic of an ideal diode is encountered.in the dark, the ideal diode characteristic is obtained when a voltage is applied.

36 1.3. Power Conversion Efficiency 35 determines the current density and voltage for maximum power, which are denoted as j mp and V mp.undertheseoperatingconditions,theratioofthemaximumelectric power density and the incident solar power density P solar defines the Power Conversion Efficiency η pce = j mpv mp P solar = η ff j sc V oc P solar. (1.1) Here, the fill factor η ff is introduced to easily reflect the shape of the current-voltage characteristic. It is defined as the quotient of the two rectangular areas in Figure 1.6 b: η ff = j mpv mp j sc V oc. (1.2) Upper Limits for the Efficiency As pointed out by hockley and Queisser [25], atheoreticallimitingefficiencyforanidealsolarcellcanbedeterminedbythreebasic assumptions. First, the device exhibits perfect absorption, i.e., each incident photon produces an exciton, provided the photon energy bridges the optical gap E gap of the absorbing semiconductor (i.e., the electronic gap minus the exciton binding energy). econd, there is no internal device resistance and each electron-hole pair is instantaneously collected at the electrodes if they are short-circuited. With these assumptions, the ideal short-circuit current density simply equals the elementary charge times the number of absorbed photons per time, which can be written as j sc = e E gap deφ solar (E). (1.3) Here, Φ solar is the solar photon flux density in spectral distribution and the lower integration limit reflects the minimum energy of absorbed photons, as shown in Figure 1.8. The third assumption refers to the case where an external resistance is applied to the electrodes and hence charge carriers can no longer be collected instantaneously. In this case, an inevitable process, occurring in addition to absorption, is the spontaneous emission of photons as a result of radiative recombination of electron-hole pairs. By relating generation and recombination rates according to the principle of detailed balance, the current-voltage characteristic of the ideal solar cell (shown in Figure 1.6 b) can be parametrized. With the current-voltage function j(v) at hand, the ideal open-

37 36 Chapter 1. Organic Photovoltaic Cells ev η Figure 1.7. Upper limit of the power conversion efficiency η pce as a function of the optical gap E gap of the absorbing semiconductor and the voltage loss due to exciton dissociation. The values along the abscissa, i.e., for zero voltage loss ( = 0), correspond to the hockley-queisser limit for inorganic photovoltaic cells. Adapted from Reference [26]. E gap ev circuit voltage is defined by the point of vanishing current, which is V(j = 0) 1 e E gap. Although this voltage represents a strict limit for the ideal solar cell, irrespective of its inorganic or organic nature, one can argue more precisely for organic cells. In fact, exciton dissociation in organic devices involves intermediate charge-transfer or chargeseparated states and thus entails further inevitable energy losses. To account for these inherent losses, conceivable as the driving force for exciton dissociation, the considerations of hockley and Queisser can be extended by a voltage loss parameter [26]: V oc = V(j = 0) 1 e. (1.4) With the short-circuit current (1.3) and the open-circuit voltage (1.4), the fill factor (1.2) is, of course, determined and one realizes that the power conversion efficiency (1.1) becomes a function of the optical gap E gap and the voltage loss. This function, shown in Figure 1.7, indicates that the maximum efficiency for a given is achieved for some intermediate gap E gap.thisisbecausetheshort-circuitcurrentgoestozeroforlarge gaps, while the open-circuit voltage vanishes for small gaps. For zero voltage loss, i.e., along the abscissa, the hockley-queisser limit for inorganic solar cells is reproduced, which is 33.7% at an optical gap of 1.34 ev. If the voltage loss is = 0.2 ev, organic cells can theoretically achieve efficiencies slightly above 25% for optical gaps between 1.1 and 1.7 ev [26]. It should be mentioned that these upper limits apply to solar cells with a single absorbing semiconductor and can be surpassed by tandem cells.