Citation for published version (APA): Koster, L. J. A. (2007). Device physics of donor/acceptor-blend solar cells s.n.

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1 University of Groningen Device physics of donor/acceptor-blend solar cells Koster, Lambert IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2007 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Koster, L. J. A. (2007). Device physics of donor/acceptor-blend solar cells s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 CHAPTER ONE Introduction to organic solar cells Summary As the need for renewable energy sources becomes more urgent, photovoltaic energy conversion is attracting more and more attention. In this introductory chapter several aspects of polymer solar cells will be introduced. After discussing the transport of charge in conjugated polymers, the electro-optical processes in bulk heterojunction solar cells are discussed. Finally, an overview of this thesis is given. 1

3 Chapter 1. Introduction to organic solar cells 1.1 Solar energy What can be a more attractive way of producing energy than harvesting it directly from sunlight? The amount of energy that the Earth receives from the sun is enormous: W. As the world energy consumption in 2003 amounted to J, Earth receives enough energy to fulfill the yearly world demand of energy in less than an hour. Not all of that energy reaches the Earth s surface due to absorption and scattering, however, and the photovoltaic conversion of solar energy remains an important challenge. State-of-the-art inorganic solar cells have a record power conversion efficiency of close to 39%, [1] while commerically available solar panels, have a significantly lower efficiency of around 15 20%. Another approach to making solar cells is to use organic materials, such as conjugated polymers. Solar cells based on thin polymer films are particularly attractive because of their ease of processing, mechanical flexibility, and potential for low cost fabrication of large areas. Additionally, their material properties can be tailored by modifying their chemical makeup, resulting in greater customization than traditional solar cells allow. Although significant progress has been made, the efficiency of converting solar energy into electrical power obtained with plastic solar cells still does not warrant commercialization: the most efficient devices have an efficiency of 4-5%. [2] To improve the efficiency of plastic solar cells it is, therefore, crucial to understand what limits their performance. 1.2 Conjugated polymers Since Shirakawa, MacDiarmid, and Heeger demonstrated in 1977 that the conductivity of conjugated polymers can be controlled by doping, [3] a new field has emerged. They were rewarded for their discovery with the Nobel prize in chemistry in These conjugated polymers have been used successfully in, e.g., light-emitting diodes (LEDs) [4,5] and solar cells. [6 8] The insulating properties of most of the industrial plastics available stem from the formation of σ bonds between the constituent carbon atoms. In conjugated polymers, e.g., polyacetylene, the situation is different: In these polymers, the bonds between the carbon atoms that make up the backbone are alternatingly single or double (see Fig. 1.1); this property is called conjugation. In the backbone of a conjugated polymer, each carbon atom binds to only three adjacent atoms, leaving one electron per carbon atom in a p z orbital. The mutual overlap between these p z orbitals results in the formation of π bonds along the conjugated backbone, thereby delocalizing the π electrons along the entire conjugation path. The delocalized π electrons fill up to whole band and, therefore, conjugated polymers are intrinsic semiconductors. The filled π band is called the highest occupied molecular orbital (HOMO) and the empty π* band is called the lowest unoccupied molecular orbital (LUMO). This π system can be excited without the chain, held 2

4 1.3. Transport of charges in conjugated polymers Figure 1.1: In polyacetylene, the bonds between adjacent carbon atoms are alternatingly single or double. together by the σ bonds, falling apart. Therefore, it is possible to promote an electron from the HOMO to the LUMO level upon, for example, light absorption. As the band gap (energy difference between the HOMO and LUMO) of a conjugated system depends on its size, [9] any disturbance of the conjugation along the polymer s backbone will change the local HOMO and LUMO positions. Real conjugated polymers are therefore subject to energetic disorder. The density of states of these systems is often approximated by a Gaussian distribution. [10] 1.3 Transport of charges in conjugated polymers How are charges transported in conjugated polymer films? Since polymers do not have a three dimensional periodical lattice structure, charge transport in polymers cannot be described by standard semiconductor models. As these systems show energetic and spatial disorder, the concept of band conduction of free charge carriers does not apply. In this section, a summary is given of how charge carrier transport in conjugated polymers and akin materials is described theoretically and how it is characterized experimentally. The field of molecularly doped polymers is much older than that of conjugated polymers and valuable insights can be gained from studying this field. As early as in the 1970s the charge transport in molecularly doped polymers was studied by performing time-of-flight (TOF) measurements. In this type of experiment, a sample is sandwiched between two non-injecting electrodes. A short light pulse is used to illuminate one side of the sample through an transparent electrode. Under the action of an applied field, charge carriers of the same electrical polarity as the illuminated electrode will traverse the sample. By monitoring the current flow in the external circuit, the charge carrier mobility can be determined as a function of the applied voltage. In these TOF experiments, the mobility µ of carriers in molecularly doped polymers, can empirically be described by [11 15] µ = µ0 exp(γ F), (1.1) where µ 0 is the zero-field mobility, F is the field strength, and γ is the field activation parameter. Note, that no direct physical contact between the electrodes and the sample is necessary. 3

5 Chapter 1. Introduction to organic solar cells Hopping transport in disordered systems How can the results summarized in Eq. (1.1) be rationalized? As these materials are disordered, the concept of band conduction does not apply. Instead, localized states are formed and charge carriers proceed from one such a state to another (hopping), thereby absorbing or emitting phonons to overcome the energy difference between those states. Conwell [16] and Mott [17] proposed the concept of hopping conduction in 1956 to describe impurity conduction in inorganic semiconductors. Miller and Abrahams calculated that the transition rate W ij for phonon-assisted hopping from an occupied state i with an energy ǫ i to an unoccupied state j with energy ǫ j is described by [18] W ij = ν 0 exp( 2γR ij ) { ( exp ǫ ) j ǫ i k B T ǫ i < ǫ j 1 ǫ i ǫ j, where ν 0 is the attempt-to-jump frequency, R ij is the distance between the states i and j, γ is the inverse localization length, k B is Boltzmann s constant, and T is temperature. The wave function overlap of states i and j is described by the first exponential term in Eq. (1.2), while the second exponential term accounts for the temperature dependence of the phonon density. In his pioneering work, Bässler described the transport in disordered organic systems as a hopping process in a system with both positional and energetic disorder. [10] The hopping rates between sites were assumed to obey Eq. (1.2) and the site energies varied according to a Gaussian distribution with a standard deviation σ. Such a system cannot be solved analytically. By performing Monte Carlo simulations, the following expression for the charge carrier mobility µ was proposed [10] ( ( ) 2 µ = µ e 2σ exp C [ (σ/k B T) 2 Σ 2] ) F Σ 1.5 3k B T ( exp C [ (σ/k B T) ] ) (1.3) F Σ < 1.5, where µ is the mobility in the limit T, C is a constant that is related to the lattice spacing, and Σ describes the positional disorder. Although Eq. (1.3) predicts a functional dependence on field strength similar to Eq. (1.1), the agreement with experiments is limited to high fields. [13] Gartstein and Conwell found that the agreement with experiments could be improved by taking spatial correlations between site energies into account. [19] In this model, the mobility takes the form [20,21] (1.2) [ ( ) ( 2 ( ) 3/2 ) ] 3σ σ qaf µ = µ exp Γ, (1.4) 5k B T k B T σ Since, Eq. (1.3) is an expression which describes the outcome of Monte Carlo simulations, this is a purely mathematical definition of µ and does not mean that it has the physical meaning of the mobility at infinite temperature. At best, it may be interpreted as the mobility if there would be no barriers to hopping at all. 4

6 1.3. Transport of charges in conjugated polymers where q is the elementary charge, a is the intersite spacing, and Γ is the positional disorder of transport sites. This model was successfully used to describe the transport of charges in molecularly doped polymers. [20] Transport in conjugated polymers The stretched exponential dependence on field strength as described by Eq. (1.1) was also observed for conjugated polymers. [22] Subsequently, Eq. (1.4) was also applied successful to explain the charge transport in conjugated polymers [23,24] as well as other organic systems. [25] In the foregoing discussion, only the dependence of the mobility on temperature and field strength was taken into account. When the applied voltage is increased in a TOF experiment, only the field across the sample changes. However, in organic solar cells, as well as organic LEDs, changing the applied voltage does not merely change the field. Due to the nature of the contacts, it influences the charge carrier density as well. Recently, it has been shown that the mobility of charge carriers in conjugated polymers also has an important dependence on charge carrier density. [26 29] Moreover, it was shown that the increase of the mobility with increasing bias voltage (and concomitant increase in carrier density) observed in polymer diodes is, at least for some systems and temperatures, completely due to an increase in charge carrier density. [26] Throughout this thesis, the increase of the mobility with increasing bias voltage is interpreted as an effect of the field only. It should be noted, however, that the polymers used in this thesis show only a rather small dependence of the mobility on bias, suggesting that the influence of either field strength or carrier density for the system described here is quite weak. Additionally, as we will see in chapter 2, the carrier density in solar cells is fairly modest. Several alternative models exist for explaining charge transport; one of them is the so-called polaron model which was first applied to inorganic crystals [30] and later to conjugated polymers. [31] An excess charge carrier in a solid causes a displacement of the atoms in its vicinity thus lowering the total energy of the system. This displacement of atoms results in a potential well for the charge carrier, thereby localizing it. The charge carrier and its concomitant atomic deformation is called a polaron. The transition rate for polaron hopping from site i to site j is given by [32] W ij ( 1 Er T exp (E j E i + E r ) 2 ), (1.5) 4E r k B T where E r is the intramolecular reorganization energy. The resulting charge carrier mobility is of the form [33] [ µ = µ 0 exp E ] r 4k B T (af)2 sinh(af/2kb t). (1.6) 4E r k B T af/2k B T 5

7 Chapter 1. Introduction to organic solar cells The polaron contribution to the activation of the mobility is, as predicted by this model, rather low; it amounts to mev, [33] which is much smaller than the activation due to disorder Measuring the charge carrier mobility When an insulator is contacted by an electrode that can readily inject a sufficiently large number of charge carriers a so-called Ohmic contact and another electrode that can extract these charges, the current flow will be limited by a buildup of space charge. These space-charge-limited (SCL) currents can be used as a simple, yet reliable, tool to determine the mobility in an experimental configuration that is relevant for solar cells. Considering only one charge carrier (either electrons or holes), the SCL current density J SCL flowing across a layer with thickness L is given by [34] J SCL = 9 V2 int εµ 8 L 3, (1.7) where ε is the dielectric constant of the material and V int is the internal voltage drop across the active layer. When the mobility is of the form as given in Eq. (1.1), one can approximate J SCL by [35] JSCL = 9 8 εµ 0e 0.891γ Vint /L V2 int L 3. (1.8) The internal voltage in an actual device is related to the applied voltage V a by V int = V a V bi V Rs, (1.9) where V bi is the built-in voltage which arises from the difference in work function of the bottom and top electrode and V Rs is the voltage drop across the series resistance of the substrate (typically Ω). The built-in voltage is determined from the currentvoltage characteristics as the voltage at which the current-voltage characteristic becomes quadratic, corresponding to the SCL regime. By judiciously choosing the electrode materials, the injection of either carrier type can be suppressed or enhanced, thereby enabling one to selectively assess either the hole or electron mobility. The way to do this, is to make sure that the work function of one of the electrodes is close to the energy level of the transport band under investigation, while there exists a large barrier for injection of the other carrier type into the material. Thus, in order to study the hole transport in conjugated polymers, high work function metals, such as gold and palladium, are used. Conversely, low work function metals can be used as Ohmic contacts for electron injection Conjugated polymers used in this thesis Up to now the photoactive polymers used in this research have not been specified. The polymer poly(2-methoxy-5-(3,7 -dimethyl octyloxy)-p-phenylene vinylene) (MDMO- PPV) had for a long time been the workhorse in polymer photovoltaics. Consequently, its 6

8 1.4. Organic photovoltaics in a nutshell Figure 1.2: The chemical structures of the BEH-PPV, MDMO-PPV, and P3HT. charge transport properties are well documented, making this polymer well suited for modeling purposes. Recently, another polymer has emerged: poly(3-hexylthiophene) (P3HT), which is used in the most efficient polymer solar cells to date. [2] The final polymer considered in this thesis is poly(2,5-bis(2 -ethylhexyloxy)-p-phenylene vinylene) (BEH-PPV). The chemical structure of these polymers is shown in Fig The charge transport in MDMO-PPV has been extensively studied: Typically, the zero field mobility amounts to m 2 /V s. [36] Surprisingly, the hole mobility of MDMO-PPV is enhanced when mixed with 6,6-phenyl C 61 -butyric acid methyl ester (PCBM), as reported by several researchers: [37,38] When 80% (by weight) of this blend consists of PCBM, the hole mobility of the polymer phase is equal to m 2 /V s, an encrease of more than two orders of magnitude as compared to pristine MDMO-PPV. This spectacular behavior of the hole mobility in MDMO-PPV is the main reason for its succes as a donor in BHJ solar cells with PCBM. P3HT is unique in its own right: Padinger et al. observed that solar cells made from P3HT and PCBM showed a great increase in the efficiency upon thermal annealing. [39] Mihailetchi et al. have shown that this enhancement is in part due to an increase in the mobility: [40] In its pristine form the hole mobility amounts to 10 8 m 2 /Vs, see Fig For comparison, Fig. 1.3 also shows the electron mobility of the PCBM phase in these blends. When blended with PCBM, the hole mobility initially decreases, however, upon annealing the hole mobility in the P3HT phase of the blend with PCBM is restored to its pristine value, as depicted in Fig [40] 1.4 Organic photovoltaics in a nutshell The field of organic photovoltaics dates back to 1959 when Kallman and Pope discovered that anthracene can be used to make a solar cell. [41] Their device produced a photovoltage of only 0.2 V and had an extremely low efficiency. Attempts to improve the efficiency solar cells based on a single organic material (a so-called homojunction) were unsuccessful, mainly because of the low dielectric constant of organic materials (typ- In this research, only regio-regular P3HT is used 7

9 Chapter 1. Introduction to organic solar cells 10-7 [m 2 /Vs] 10-9 pristine P3HT holes P3HT:PCBM electrons holes as-cast Annealing Temperature [ o C] Figure 1.3: Electron and hole mobility in P3HT/PCBM blends as a function of annealing temperature, as well as the hole mobility in pristine P3HT. ically, the relative dielectric constant is 2 4). Due to this low dielectric constant, the probability of forming free charge carriers upon light absorption is very low. Instead, strongly bound excitons are formed, with a binding energy of around 0.4 ev in the case of PPV. [42 44] Since these excitons are so strongly bound, the field in a photovoltaic device, which arises from the work function difference between the electrodes, is much too weak to dissociate the excitons. A major advancement was realized by Tang who used two different materials, stacked in layers, to dissociate the excitons. [45] In this so-called heterojunction, an electron donor material (D) and an electron acceptor material (A) are brought together. By carefully matching these materials, electron transfer from the donor to the acceptor, or hole transfer from the acceptor to the donor, is energetically favored. In 1992 Sariciftci et al. demonstrated that ultrafast electron transfer takes place from a conjugated polymer to C 60, showing the great potential of fullerenes as acceptor materials. [46] In order to be dissociated the excitons must be generated in close proximity to the donor/acceptor interface, since the diffusion length is typically 5 7 nm. [47 49] This need limits the part of the active layer that contributes to the photocurrent to a very thin region near the donor/acceptor interface; excitons generated in the remainder of the device are lost. How can the problem of not all excitons reaching the donor/acceptor interface be overcome? In 1995 Yu et al. devised a solution: [7] By intimately mixing both components the interfacial area is greatly increased and the distance excitons have to travel in order to reach the interface is reduced. This device structure is called a bulk heterojunction (BHJ) and has been used extensively since its introduction in An important breakthrough in terms of power conversion efficiency was reached by Shaheen et al. who showed that the solvent used has a profound effect on the morphology and performance of BHJ solar cells. [50] By optimizing the device processing, an efficiency of 2.5% was obtained. Stateof-the-art polymer/fullerene BHJ solar cells have an efficiency of more than 4%. [2] 8

10 1.4. Organic photovoltaics in a nutshell Figure 1.4: Organic photovoltaics in a nutshell: Part (a) shows the process of light absorption by the polymer yielding an exciton which has to diffuse to the donor/acceptor interface. If the exciton reaches this interface, electron transfer to the acceptor phase is energetically favored, as shown in part (b), yielding a Coulombically bound electron-hole pair. The dissociation of the electron-hole pair, either phonon- or field assisted, produces free charge carriers, as depicted in (c). Finally, the free carriers have to be transported through their respective phases to the electrodes in order to be extracted (d). Exciton decay is one possible loss mechanism, see part (e), while geminate recombination of the bound electron-hole pair and bimolecular recombination of free charge carriers (f) are two other possibilities. 9

11 Chapter 1. Introduction to organic solar cells Figure 1.5: Schematic layout of a BHJ solar cell. A part of the active layer is enlarged to illustrate the processes of light absorption and charge transport. The main steps in photovoltaic energy conversion by organic solar cells are depicted in Fig The foremost process is light absorption by the polymer, yielding an exciton which has to diffuse to the donor/acceptor interface. If the exciton reaches this interface, electron transfer to the acceptor phase is energetically favored, resulting in a Coulombically bound electron-hole pair. The dissociation of this electron-hole pair, either phononor field assisted, produces free charge carriers. Finally, the free carriers have to be transported through their respective phases to the electrodes in order to be extracted. Possible loss mechanisms are exciton decay, geminate recombination of bound electron-hole pairs, and bimolecular recombination of free charge carriers. 1.5 Device fabrication and characterization A typical BHJ solar cell has a structure as shown in Fig The active layer is sandwiched between two electrodes, one transparent and one reflecting. The glass substrate is coated with indium-tin-oxide (ITO) which is a transparent conductive electrode with a high work function, suitable to act as an anode. To reduce the roughness of this ITO layer and increase the work function even further, a layer of poly(3,4-ethylene dioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) is spin cast, followed by the active layer. The top electrode usually consists of a low work function metal or lithium fluoride (LiF), topped with a layer of aluminum, all of which are deposited by thermal deposition in vacuum through a shadow mask. In order to determine the performance and electrical characteristics of the photovoltaic devices, current-voltage measurements are performed (positive V a corresponds to positive biasing of the anode), both in dark and under illumination. A typical currentvoltage characteristic of a solar cell under illumination is shown in Fig The current density under illumination at zero applied voltage V a is called the short-circuit current density J sc. The maximum voltage that the cell can supply, i.e., the voltage where the J sc is taken positive throughout this thesis, as is customary. 10

12 1.6. Objective and outline of this thesis JL [A/m 2 ] FF = J L V a max V oc J sc J sc V oc V a [V] Figure 1.6: Typical current-voltage characteristics of a BHJ solar cell showing the V oc, J sc, and FF. The shaded area corresponds to the maximum power that the solar cell can supply. current density under illumination J L is zero is designated as the open-circuit voltage V oc. The fill factor FF is defined as FF = J LV a max V oc J sc, (1.10) relating the maximum power that can be drawn from the device to the open-circuit voltage and short-circuit current. The power conversion efficiency χ is related to these three quantities by χ = J scv oc FF, (1.11) I where I is the incident light intensity. Because of the wavelength and light intensity dependence of the photovoltaic response, the efficiency should be measured under standard test conditions. The conditions include the temperature of the cell (25 C), the light intensity (1000 W/m 2 ) and the spectral distribution of light (air mass 1.5 or AM1.5, which is the spectrum of sunlight after passing through 1.5 times the thickness of the atmosphere). [51] 1.6 Objective and outline of this thesis Although significant progress has been made, the efficiency of current BHJ solar cells still does not warrant commercialization. A lack of understanding makes targeted improvement troublesome. The main theme of this thesis is to introduce a simple model for the electrical characteristics of BHJ solar cells, relating their performance to basic physics and material properties such as charge carrier mobilities. 11

13 Chapter 1. Introduction to organic solar cells The basis of this research is laid down in chapter 2, which describes the MIM model used throughout this thesis. This numerical model describes the generation and transport processes in the BHJ as if occurring in one virtual semiconductor. Drift and diffusion of charge carriers, the effect of charge density on the electric field, bimolecular recombination and a temperature- and field-dependent generation mechanism of free charges are incorporated. From the modeling of current-voltage characteristics, it is found that the bimolecular recombination strength is significantly reduced, and is governed by the slowest charge carrier. Subsequently, the numerical model is successfully applied to experimental data on MDMO-PPV/PCBM solar cells, showing field and carrier density profiles. In chapter 3, two competing models for the open-circuit voltage are introduced: First, a model valid for p-n junctions is examined. By studying the dependency of the opencircuit voltage on light intensity, it is demonstrated that this model does not correctly describe the open-circuit voltage of BHJ solar cells. Within the framework of the MIM model an alternative explanation for the open-circuit voltage is presented. Based on the notion that the quasi-fermi potentials are constant throughout the device, a formula for V oc is derived that consistently describes the open-circuit voltage. Next, the predictions of the MIM model and its relation to other types of solar cells are discussed. One other key parameter of solar cells, the short-circuit current, is the subject of chapter 4. Following the description of some simple analytical expressions for the shortcircuit density, the dependence of the short-circuit current density on incident light intensity is discussed in more detail. A typical feature of polymer/fullerene based solar cells is that the short-circuit current density does not scale exactly linearly with light intensity. Instead, a power law relationship is found given by J sc I α, where α ranges from 0.85 to 1. In this chapter, it is shown that this behavior does not originate from bimolecular recombination but is a consequence of space charge effects. Hybrid organic/inorganic solar cells, as discussed in chapter 5, are an auspicious alternative to polymer/fullerene devices. In this case, an inorganic semiconductor, either titanium dioxide or zinc oxide, is used as the electron acceptor. One way of making these cells is the precursor route: A precursor for the inorganic semiconductor is mixed with the solution of the polymer. Upon spin casting of the active layer in ambient conditions, the precursor reacts with moisture from the air and the inorganic semiconductor is formed. Although promising, this method seems to harm the transport of charge carriers through the active layer. Alternatively, the inorganic semiconductor, in this case zinc oxide, can be formed ex situ. This enables one to better control the reaction conditions and purity of the material. The transport of charge carriers as well as limitations to the efficiency are investigated in detail. In chapter 6, various ways to improve the efficiency of bulk heterojunction solar cells are identified by using the MIM model as outlined in chapter 2. A much pursued way to increase the performance is to increase the amount of photons absorbed by the film by decreasing the band gap of the polymer. Calculations based on the MIM model confirm that this would indeed enhance the performance. However, it is demonstrated that the effect of minimizing the energy loss in the electron transfer from the polymer to the 12

14 1.6. Objective and outline of this thesis fullerene derivative is even more beneficial. By combining these two effects, it turns out that the optimal band gap of the polymer would be 1.9 ev. Ultimately, with balanced charge transport, polymer/fullerene solar cells can reach power conversion efficiencies of 10.8%. Table 1.1: List of symbols and abbreviations used in this thesis. Symbol description A acceptor a electron-hole pair distance α exponent in J sc I α AM1.5 air mass 1.5 BEH-PPV poly(2,5-bis(2 -ethylhexyloxy)-p-phenylene vinylene) BHJ bulk heterojunction D donor D n(p) electron (hole) diffusion coefficient DSSC dye-sensitized solar cell Egap eff effective band gap ε dielectric constant η Poole-Frenkel detrapping parameter F field strength FF fill factor φ n(p) electron (hole) quasi-fermi potential G generation rate of free charge carriers G e h generation rate of bound electron-hole pairs γ field activation parameter of mobility h i grid spacing HOMO highest occupied molecular orbital I incident light intensity ITO indium tin oxide J D current density in dark J L current density under illumination J n(p) electron (hole) current density J ph photogenerated current density J sc short-circuit current density k B Boltzmann s constant k diss electron-hole pair dissociation rate k f electron-hole pair decay rate k r bimolecular recombination rate L active layer thickness LUMO lowest unoccupied molecular orbital MDMO-PPV poly(2-methoxy-5-(3,7 -dimethyl octyloxy)-p-phenylene vinylene) MIM model metal-insulator-metal model µ n(p) electron (hole) mobility n electron density N cv effective density of states of valance and conduction bands nc-zno nanocrystalline zinc oxide n int intrinsic carrier density p hole density P electron-hole pair dissociation probability ψ potential Continued on next page 13

15 Chapter 1. Introduction to organic solar cells Symbol description P3HT poly(3-hexylthiophene) PCBM 6,6-phenyl C 61 -butyric acid methyl ester PEDOT:PSS poly(3,4-ethylene dioxythiophene):poly(styrene sulfonate) Photo-CELIV photoinduced charge carrier extraction in a linearly increasing voltage PPV poly(phenylene vinylene) prec-zno zinc oxide by precursor route q elementary charge R recombination rate of charge carriers S slope of V oc vs. ln(i) SCL space-charge-limited SRH Shockley-Read-Hall σ width of Gaussian distribution energy distribution T absolute temperature TOF time-of-flight U net generation rate of free carriers V 0 compensation voltage V a applied voltage V bi built-in voltage V int internal voltage across active layer V oc open-circuit voltage V t thermal voltage w n(p) electron (hole) drift length x position X density of bound electron-hole pairs χ power conversion efficiency... spatial average 14

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