University of Groningen

Device physics of donor/acceptor-blend solar cellsKoster, Lambert

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CHAPTER

ONE

Introduction to organic solar cells

Summary

As the need for renewable energy sources becomes more urgent, photovoltaic en-ergy conversion is attracting more and more attention. In this introductory chapterseveral aspects of polymer solar cells will be introduced. After discussing the transportof charge in conjugated polymers, the electro-optical processes in bulk heterojunctionsolar cells are discussed. Finally, an overview of this thesis is given.

1

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 fromsunlight? The amount of energy that the Earth receives from the sun is enormous: 1.75× 1017 W. As the world energy consumption in 2003 amounted to 4.4 × 1020 J, Earth re-ceives 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, how-ever, 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 to39%, [1] while commerically available solar panels, have a significantly lower efficiencyof around 15–20%.

Another approach to making solar cells is to use organic materials, such as conju-gated polymers. Solar cells based on thin polymer films are particularly attractive be-cause of their ease of processing, mechanical flexibility, and potential for low cost fab-rication of large areas. Additionally, their material properties can be tailored by mod-ifying their chemical makeup, resulting in greater customization than traditional solarcells allow. Although significant progress has been made, the efficiency of convertingsolar energy into electrical power obtained with plastic solar cells still does not warrantcommercialization: the most efficient devices have an efficiency of 4-5%. [2] To improvethe efficiency of plastic solar cells it is, therefore, crucial to understand what limits theirperformance.

1.2 Conjugated polymers

Since Shirakawa, MacDiarmid, and Heeger demonstrated in 1977 that the conductivityof conjugated polymers can be controlled by doping, [3] a new field has emerged. Theywere rewarded for their discovery with the Nobel prize in chemistry in 2000. These con-jugated 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 theformation of σ bonds between the constituent carbon atoms. In conjugated polymers,e.g., polyacetylene, the situation is different: In these polymers, the bonds between thecarbon 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 car-bon atom binds to only three adjacent atoms, leaving one electron per carbon atom ina pz orbital. The mutual overlap between these pz orbitals results in the formation ofπ bonds along the conjugated backbone, thereby delocalizing the π electrons along theentire 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 highestoccupied molecular orbital (HOMO) and the empty π* band is called the lowest unoc-cupied molecular orbital (LUMO). This π system can be excited without the chain, held

2

1.3. Transport of charges in conjugated polymers

Figure 1.1: In polyacetylene, the bonds between adjacent carbon atoms are alternatingly single ordouble.

together by the σ bonds, falling apart. Therefore, it is possible to promote an electronfrom the HOMO to the LUMO level upon, for example, light absorption.

As the band gap (energy difference between the HOMO and LUMO) of a conjugatedsystem depends on its size, [9] any disturbance of the conjugation along the polymer’sbackbone will change the local HOMO and LUMO positions. Real conjugated polymersare therefore subject to energetic disorder. The density of states of these systems is oftenapproximated 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 havea three dimensional periodical lattice structure, charge transport in polymers cannot bedescribed by standard semiconductor models. As these systems show energetic andspatial disorder, the concept of band conduction of free charge carriers does not apply. Inthis section, a summary is given of how charge carrier transport in conjugated polymersand akin materials is described theoretically and how it is characterized experimentally.

The field of molecularly doped polymers is much older than that of conjugated poly-mers and valuable insights can be gained from studying this field. As early as in the1970s the charge transport in molecularly doped polymers was studied by performingtime-of-flight (TOF) measurements. In this type of experiment, a sample is sandwichedbetween two non-injecting electrodes.∗ A short light pulse is used to illuminate one sideof 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 traversethe sample. By monitoring the current flow in the external circuit, the charge carrier mo-bility 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 describedby [11–15]

µ = µ0 exp(γ√

F), (1.1)

where µ0 is the zero-field mobility, F is the field strength, and γ is the field activationparameter.

∗Note, that no direct physical contact between the electrodes and the sample is necessary.

3

Chapter 1. Introduction to organic solar cells

1.3.1 Hopping transport in disordered systems

How can the results summarized in Eq. (1.1) be rationalized? As these materials aredisordered, the concept of band conduction does not apply. Instead, localized states areformed and charge carriers proceed from one such a state to another (hopping), therebyabsorbing 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 de-scribe impurity conduction in inorganic semiconductors. Miller and Abrahams calcu-lated that the transition rate Wij for phonon-assisted hopping from an occupied state i

with an energy ǫi to an unoccupied state j with energy ǫj is described by [18]

Wij = ν0 exp(−2γRij)

exp(

− ǫj−ǫi

kBT

)

ǫi < ǫj

1 ǫi ≥ ǫj,(1.2)

where ν0 is the attempt-to-jump frequency, Rij is the distance between the states i andj, γ is the inverse localization length, kB is Boltzmann’s constant, and T is temperature.The wave function overlap of states i and j is described by the first exponential term inEq. (1.2), while the second exponential term accounts for the temperature dependence ofthe phonon density.

In his pioneering work, Bassler described the transport in disordered organic systemsas a hopping process in a system with both positional and energetic disorder. [10] Thehopping rates between sites were assumed to obey Eq. (1.2) and the site energies variedaccording to a Gaussian distribution with a standard deviation σ. Such a system cannotbe solved analytically. By performing Monte Carlo simulations, the following expressionfor the charge carrier mobility µ was proposed [10]

µ = µ∞e−(

2σ3kBT

)2

exp(

C[

(σ/kBT)2 − Σ2]√

F)

Σ ≥ 1.5

exp(

C[

(σ/kBT)2 − 2.25]√

F)

Σ < 1.5,(1.3)

where µ∞ is the mobility in the limit T → ∞,∗ C is a constant that is related to the latticespacing, and Σ describes the positional disorder.

Although Eq. (1.3) predicts a functional dependence on field strength similar toEq. (1.1), the agreement with experiments is limited to high fields. [13] Gartstein and Con-well found that the agreement with experiments could be improved by taking spatialcorrelations between site energies into account. [19] In this model, the mobility takes theform [20,21]

µ = µ∞ exp

[

−(

3σ

5kBT

)2

+ 0.78

(

(

σ

kBT

)3/2

− Γ

)

√

qaF

σ

]

, (1.4)

∗Since, Eq. (1.3) is an expression which describes the outcome of Monte Carlo simulations, this is a purelymathematical definition of µ∞ and does not mean that it has the physical meaning of the mobility at infinitetemperature. At best, it may be interpreted as the mobility if there would be no barriers to hopping at all.

4

1.3. Transport of charges in conjugated polymers

where q is the elementary charge, a is the intersite spacing, and Γ is the positional dis-order of transport sites. This model was successfully used to describe the transport ofcharges in molecularly doped polymers. [20]

1.3.2 Transport in conjugated polymers

The stretched exponential dependence on field strength as described by Eq. (1.1) was alsoobserved for conjugated polymers. [22] Subsequently, Eq. (1.4) was also applied success-ful to explain the charge transport in conjugated polymers [23,24] as well as other organicsystems. [25]

In the foregoing discussion, only the dependence of the mobility on temperature andfield strength was taken into account. When the applied voltage is increased in a TOFexperiment, 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 animportant dependence on charge carrier density. [26–29] Moreover, it was shown that theincrease of the mobility with increasing bias voltage (and concomitant increase in carrierdensity) 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 isinterpreted as an effect of the field only. It should be noted, however, that the polymersused in this thesis show only a rather small dependence of the mobility on bias, suggest-ing that the influence of either field strength or carrier density for the system describedhere is quite weak. Additionally, as we will see in chapter 2, the carrier density in solarcells is fairly modest.

Several alternative models exist for explaining charge transport; one of them is theso-called polaron model which was first applied to inorganic crystals [30] and later toconjugated polymers. [31] An excess charge carrier in a solid causes a displacement of theatoms in its vicinity thus lowering the total energy of the system. This displacement ofatoms results in a potential well for the charge carrier, thereby localizing it. The chargecarrier 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]

Wij ∝1√ErT

exp

(

−(Ej − Ei + Er)2

4ErkBT

)

, (1.5)

where Er is the intramolecular reorganization energy. The resulting charge carrier mo-bility is of the form [33]

µ = µ0 exp

[

− Er

4kBT− (aF)2

4ErkBT

]

sinh(aF/2kBt)

aF/2kBT. (1.6)

5

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 25–75 meV, [33] which is much smaller than the activation dueto disorder.

1.3.3 Measuring the charge carrier mobility

When an insulator is contacted by an electrode that can readily inject a sufficiently largenumber of charge carriers — a so-called Ohmic contact — and another electrode thatcan 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 todetermine the mobility in an experimental configuration that is relevant for solar cells.Considering only one charge carrier (either electrons or holes), the SCL current densityJSCL flowing across a layer with thickness L is given by [34]

JSCL =9

8εµ

V2int

L3, (1.7)

where ε is the dielectric constant of the material and Vint is the internal voltage dropacross the active layer. When the mobility is of the form as given in Eq. (1.1), one canapproximate JSCL by [35]

JSCL =9

8εµ0e0.891γ

√Vint/L V2

int

L3. (1.8)

The internal voltage in an actual device is related to the applied voltage Va by

Vint = Va − Vbi − VRs, (1.9)

where Vbi is the built-in voltage which arises from the difference in work function ofthe bottom and top electrode and VRs is the voltage drop across the series resistance ofthe substrate (typically 30–40 Ω). The built-in voltage is determined from the current-voltage characteristics as the voltage at which the current-voltage characteristic becomesquadratic, corresponding to the SCL regime.

By judiciously choosing the electrode materials, the injection of either carrier type canbe suppressed or enhanced, thereby enabling one to selectively assess either the hole orelectron mobility. The way to do this, is to make sure that the work function of one of theelectrodes is close to the energy level of the transport band under investigation, whilethere 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 usedas Ohmic contacts for electron injection.

1.3.4 Conjugated polymers used in this thesis

Up to now the photoactive polymers used in this research have not been specified. Thepolymer 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

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 formodeling purposes. Recently, another polymer has emerged: poly(3-hexylthiophene)(P3HT),∗ which is used in the most efficient polymer solar cells to date. [2] The finalpolymer considered in this thesis is poly(2,5-bis(2’-ethylhexyloxy)-p-phenylene viny-lene) (BEH-PPV). The chemical structure of these polymers is shown in Fig. 1.2.

The charge transport in MDMO-PPV has been extensively studied: Typically, thezero field mobility amounts to 5 × 10−11 m2/V s. [36] Surprisingly, the hole mobility ofMDMO-PPV is enhanced when mixed with 6,6-phenyl C61-butyric acid methyl ester

(PCBM), as reported by several researchers: [37,38] When 80% (by weight) of this blendconsists of PCBM, the hole mobility of the polymer phase is equal to 2 × 10−8 m2/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 itssucces as a donor in BHJ solar cells with PCBM.

P3HT is unique in its own right: Padinger et al. observed that solar cells made fromP3HT 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 themobility: [40] In its pristine form the hole mobility amounts to 10−8 m2/Vs, see Fig. 1.3.For comparison, Fig. 1.3 also shows the electron mobility of the PCBM phase in theseblends. When blended with PCBM, the hole mobility initially decreases, however, uponannealing the hole mobility in the P3HT phase of the blend with PCBM is restored to itspristine value, as depicted in Fig. 1.3. [40]

1.4 Organic photovoltaics in a nutshell

The field of organic photovoltaics dates back to 1959 when Kallman and Pope discov-ered that anthracene can be used to make a solar cell. [41] Their device produced a pho-tovoltage of only 0.2 V and had an extremely low efficiency. Attempts to improve theefficiency solar cells based on a single organic material (a so-called homojunction) wereunsuccessful, mainly because of the low dielectric constant of organic materials (typ-

∗In this research, only regio-regular P3HT is used

7

Chapter 1. Introduction to organic solar cells

20 40 60 80 100 120 140 160

10-11

10-9

10-7

pristine P3HT holes

P3HT:PCBM electrons holes

as-cast

[m2 /V

s]

Annealing Temperature [oC]

Figure 1.3: Electron and hole mobility in P3HT/PCBM blends as a function of annealing temper-ature, as well as the hole mobility in pristine P3HT.

ically, the relative dielectric constant is 2–4). Due to this low dielectric constant, theprobability 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 caseof PPV. [42–44] Since these excitons are so strongly bound, the field in a photovoltaic de-vice, which arises from the work function difference between the electrodes, is much tooweak 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 elec-tron donor material (D) and an electron acceptor material (A) are brought together. Bycarefully matching these materials, electron transfer from the donor to the acceptor, orhole transfer from the acceptor to the donor, is energetically favored. In 1992 Sariciftciet al. demonstrated that ultrafast electron transfer takes place from a conjugated poly-mer to C60, showing the great potential of fullerenes as acceptor materials. [46] In order tobe dissociated the excitons must be generated in close proximity to the donor/acceptorinterface, since the diffusion length is typically 5–7 nm. [47–49] This need limits the partof the active layer that contributes to the photocurrent to a very thin region near thedonor/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 beovercome? In 1995 Yu et al. devised a solution: [7] By intimately mixing both componentsthe interfacial area is greatly increased and the distance excitons have to travel in order toreach the interface is reduced. This device structure is called a bulk heterojunction (BHJ)and has been used extensively since its introduction in 1995. An important breakthroughin terms of power conversion efficiency was reached by Shaheen et al. who showed thatthe solvent used has a profound effect on the morphology and performance of BHJ solarcells. [50] By optimizing the device processing, an efficiency of 2.5% was obtained. State-of-the-art polymer/fullerene BHJ solar cells have an efficiency of more than 4%. [2]

8

1.4. Organic photovoltaics in a nutshell

Figure 1.4: Organic photovoltaics in a nutshell: Part (a) shows the process of light absorptionby the polymer yielding an exciton which has to diffuse to the donor/acceptor interface. If theexciton reaches this interface, electron transfer to the acceptor phase is energetically favored, asshown in part (b), yielding a Coulombically bound electron-hole pair. The dissociation of theelectron-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 electrodesin order to be extracted (d). Exciton decay is one possible loss mechanism, see part (e), whilegeminate recombination of the bound electron-hole pair and bimolecular recombination of freecharge carriers (f) are two other possibilities.

9

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 illustratethe processes of light absorption and charge transport.

The main steps in photovoltaic energy conversion by organic solar cells are depictedin Fig. 1.4. The foremost process is light absorption by the polymer, yielding an excitonwhich 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 Coulombi-cally bound electron-hole pair. The dissociation of this electron-hole pair, either phonon-or field assisted, produces free charge carriers. Finally, the free carriers have to be trans-ported through their respective phases to the electrodes in order to be extracted. Possi-ble loss mechanisms are exciton decay, geminate recombination of bound electron-holepairs, 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. 1.5. The active layer is sand-wiched between two electrodes, one transparent and one reflecting. The glass substrateis coated with indium-tin-oxide (ITO) which is a transparent conductive electrode witha high work function, suitable to act as an anode. To reduce the roughness of this ITOlayer and increase the work function even further, a layer of poly(3,4-ethylene dioxythio-phene):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 invacuum through a shadow mask.

In order to determine the performance and electrical characteristics of the photo-voltaic devices, current-voltage measurements are performed (positive Va correspondsto positive biasing of the anode), both in dark and under illumination. A typical current-voltage characteristic of a solar cell under illumination is shown in Fig. 1.6. The currentdensity under illumination at zero applied voltage Va is called the short-circuit currentdensity Jsc.∗ The maximum voltage that the cell can supply, i.e., the voltage where the

∗ Jsc is taken positive throughout this thesis, as is customary.

10

1.6. Objective and outline of this thesis

0.0 0.3 0.6 0.9

-60

-30

0

30

JscVoc

Voc

Jsc

J L [A

/m2 ]

Va [V]

FF = |JL Va|max

Figure 1.6: Typical current-voltage characteristics of a BHJ solar cell showing the Voc, Jsc, and FF.The shaded area corresponds to the maximum power that the solar cell can supply.

current density under illumination JL is zero is designated as the open-circuit voltageVoc. The fill factor FF is defined as

FF =|JLVa|max

Voc Jsc, (1.10)

relating the maximum power that can be drawn from the device to the open-circuit volt-age and short-circuit current. The power conversion efficiency χ is related to these threequantities by

χ =JscVocFF

I, (1.11)

where I is the incident light intensity. Because of the wavelength and light intensitydependence of the photovoltaic response, the efficiency should be measured under stan-dard test conditions. The conditions include the temperature of the cell (25°C), the lightintensity (1000 W/m2) 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 theatmosphere). [51]

1.6 Objective and outline of this thesis

Although significant progress has been made, the efficiency of current BHJ solar cellsstill does not warrant commercialization. A lack of understanding makes targeted im-provement troublesome. The main theme of this thesis is to introduce a simple model forthe electrical characteristics of BHJ solar cells, relating their performance to basic physicsand material properties such as charge carrier mobilities.

11

Chapter 1. Introduction to organic solar cells

The basis of this research is laid down in chapter 2, which describes the MIM modelused throughout this thesis. This numerical model describes the generation and trans-port processes in the BHJ as if occurring in one virtual semiconductor. Drift and diffusionof charge carriers, the effect of charge density on the electric field, bimolecular recom-bination and a temperature- and field-dependent generation mechanism of free chargesare incorporated. From the modeling of current-voltage characteristics, it is found thatthe bimolecular recombination strength is significantly reduced, and is governed by theslowest charge carrier. Subsequently, the numerical model is successfully applied to ex-perimental data on MDMO-PPV/PCBM solar cells, showing field and carrier densityprofiles.

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 open-circuit voltage on light intensity, it is demonstrated that this model does not correctlydescribe the open-circuit voltage of BHJ solar cells. Within the framework of the MIMmodel an alternative explanation for the open-circuit voltage is presented. Based on thenotion that the quasi-Fermi potentials are constant throughout the device, a formula forVoc is derived that consistently describes the open-circuit voltage. Next, the predictionsof 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 chap-ter 4. Following the description of some simple analytical expressions for the short-circuit density, the dependence of the short-circuit current density on incident light in-tensity is discussed in more detail. A typical feature of polymer/fullerene based solarcells is that the short-circuit current density does not scale exactly linearly with light in-tensity. Instead, a power law relationship is found given by Jsc ∝ Iα, where α rangesfrom 0.85 to 1. In this chapter, it is shown that this behavior does not originate frombimolecular recombination but is a consequence of space charge effects.

Hybrid organic/inorganic solar cells, as discussed in chapter 5, are an auspicious al-ternative to polymer/fullerene devices. In this case, an inorganic semiconductor, eithertitanium dioxide or zinc oxide, is used as the electron acceptor. One way of makingthese cells is the precursor route: A precursor for the inorganic semiconductor is mixedwith the solution of the polymer. Upon spin casting of the active layer in ambient condi-tions, the precursor reacts with moisture from the air and the inorganic semiconductor isformed. Although promising, this method seems to harm the transport of charge carri-ers through the active layer. Alternatively, the inorganic semiconductor, in this case zincoxide, can be formed ex situ. This enables one to better control the reaction conditionsand purity of the material. The transport of charge carriers as well as limitations to theefficiency are investigated in detail.

In chapter 6, various ways to improve the efficiency of bulk heterojunction solar cellsare identified by using the MIM model as outlined in chapter 2. A much pursued way toincrease the performance is to increase the amount of photons absorbed by the film bydecreasing the band gap of the polymer. Calculations based on the MIM model confirmthat this would indeed enhance the performance. However, it is demonstrated that theeffect of minimizing the energy loss in the electron transfer from the polymer to the

12

1.6. Objective and outline of this thesis

fullerene derivative is even more beneficial. By combining these two effects, it turns outthat the optimal band gap of the polymer would be 1.9 eV. Ultimately, with balancedcharge transport, polymer/fullerene solar cells can reach power conversion efficienciesof 10.8%.

Table 1.1: List of symbols and abbreviations used in this thesis.

Symbol description

A acceptora electron-hole pair distanceα exponent in Jsc ∝ Iα

AM1.5 air mass 1.5BEH-PPV poly(2,5-bis(2’-ethylhexyloxy)-p-phenylene vinylene)BHJ bulk heterojunctionD donorDn(p) electron (hole) diffusion coefficient

DSSC dye-sensitized solar cell

Eeffgap effective band gap

ε dielectric constantη Poole-Frenkel detrapping parameterF field strengthFF fill factorφn(p) electron (hole) quasi-Fermi potential

G generation rate of free charge carriersGe−h generation rate of bound electron-hole pairsγ field activation parameter of mobilityhi grid spacingHOMO highest occupied molecular orbitalI incident light intensityITO indium tin oxideJD current density in darkJL current density under illuminationJn(p) electron (hole) current density

Jph photogenerated current densityJsc short-circuit current densitykB Boltzmann’s constantkdiss electron-hole pair dissociation ratek f electron-hole pair decay ratekr bimolecular recombination rateL active layer thicknessLUMO lowest unoccupied molecular orbitalMDMO-PPV poly(2-methoxy-5-(3’,7’-dimethyl octyloxy)-p-phenylene vinylene)MIM model metal-insulator-metal modelµn(p) electron (hole) mobility

n electron densityNcv effective density of states of valance and conduction bandsnc-ZnO nanocrystalline zinc oxidenint intrinsic carrier densityp hole densityP electron-hole pair dissociation probabilityψ potential

Continued on next page

13

Chapter 1. Introduction to organic solar cells

Symbol descriptionP3HT poly(3-hexylthiophene)PCBM 6,6-phenyl C61-butyric acid methyl esterPEDOT:PSS poly(3,4-ethylene dioxythiophene):poly(styrene sulfonate)Photo-CELIV photoinduced charge carrier extraction in a linearly increasing voltagePPV poly(phenylene vinylene)prec-ZnO zinc oxide by precursor routeq elementary chargeR recombination rate of charge carriersS slope of Voc vs. ln(I)SCL space-charge-limitedSRH Shockley-Read-Hallσ width of Gaussian distribution energy distributionT absolute temperatureTOF time-of-flightU net generation rate of free carriersV0 compensation voltageVa applied voltageVbi built-in voltageVint internal voltage across active layerVoc open-circuit voltageVt thermal voltagewn(p) electron (hole) drift length

x positionX density of bound electron-hole pairsχ power conversion efficiency〈. . .〉 spatial average

14

References chapter 1

References

[1] M. A. Green, K. Emery, D. L. King, Y. Hishikawa, and W. Warta, Prog. Photovoltaics 14, 455(2006).

[2] G. Li, V. Shrotriya, J. Huang, Y. Yao, T. Moriarty, K. Emery, and Y. Yang, Nature Mater. 4, 864(2005).

[3] C. K. Chiang, C. R. Fincher Jr., Y. W. Park, A. J. Heeger, H. Shirakawa, E. J. Louis, S. C. Gau,and A. G. MacDiarmid, Phys. Rev. Lett. 39, 1098 (1977).

[4] J. H. Burroughes, D. D. C. Bradly, A. R. Brown, R. N. Marks, K. McKay, R. H. Friend, P. L. Burn,and A. B. Holmes, Nature 347, 539 (1990).

[5] R. H. Friend, R. W. Gymer, A. B. Holmes, J. H. Burroughes, R. N. Marks, C. Taliani,D. D. C. Bradly, D. A. Dos Santos, J. L. Bredas, M. Logdlund, and W. R. Salaneck, Nature397, 121 (1999).

[6] N. S. Sariciftci, D. Braun, C. Zhang, V. I. Srdanov, A. J. Heeger, G. Stucky, and F. Wudl,Appl. Phys. Lett. 62, 585 (1993).

[7] G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, Science 270, 1789 (1995).

[8] J. J. M. Halls, C. A. Walsh, N. C. Greenham, E. A. Marseglia, R. H. Friend, S. C. Moratti, andA. B. Holmes, Nature 376, 498 (1995).

[9] R. Hoffmann, C. Janiak, and C. Kollmar, Macromolecules 24, 3725 (1991).

[10] H. Bassler, Phys. Status Solidi B 175, 15 (1993).

[11] D. M. Pai, J. Chem. Phys. 52, 2285 (1970).

[12] W. D. Gill, J. Appl. Phys. 43, 5033 (1972).

[13] L. B. Schein, A. Peled, D. Glatz, J. Appl. Phys. 66, 686 (1989).

[14] P. M. Borsenberger, J. Appl. Phys. 68, 6263 (1990).

[15] M. A. Abkowitz, Phil. Mag. B 65, 817 (1992).

[16] E. M. Conwell, Phys. Rev. 103, 51 (1956).

[17] N. F. Mott, Can. J. Phys. 34, 1356 (1956).

[18] A. Miller and E. Abrahams, Phys. Rev. 120, 345 (1960).

[19] Y. N. Gartstein and E. M. Conwell, Chem. Phys. Lett. 245, 351 (1995).

[20] D. H. Dunlap, P. E. Parris, and V. M. Kenkre, Phys. Rev. Lett. 77, 542 (1996).

[21] S. V. Novikov, D. H. Dunlap, V. M. Kenkre, P. E. Parris, and A. V. Vannikov, Phys. Rev. Lett. 81,4472 (1998).

15

Chapter 1. Introduction to organic solar cells

[22] P. W. M. Blom, M. J. M. de Jong, and M. G. van Munster, Phys. Rev. B 55, 656 (1997).

[23] H. C. F. Martens, P. W. M. Blom, and H. F. M. Schoo, Phys. Rev. B 61, 7489 (2000).

[24] P. W. M. Blom and M. C. J. M. Vissenberg, Mater. Sci. Eng. 27, 53 (2000).

[25] V. D. Mihailetchi, J. K. J. van Duren, P. W. M. Blom, J. C. Hummelen, R. A. J. Janssen,J. M. Kroon, M. T. Rispens, W. J. H. Verhees, and M. M. Wienk, Adv. Funct. Mater. 13, 43(2003).

[26] C. Tanase, E. J. Meijer, P. W. M. Blom, and D. M. de Leeuw, Phys. Rev. Lett. 91, 216601 (2003).

[27] C. Tanase, P. W. M. Blom, and D. M. de Leeuw, Phys. Rev. Lett. 70, 193202 (2004).

[28] C. Tanase, P. W. M. Blom, D. M. de Leeuw, and E. J. Meijer, Phys. Status Solidi A 201, 1236(2004).

[29] W. F. Pasveer, J. Cottaar, C. Tanase, R. Coehoorn, P. A. Bobbert, P. W. M. Blom, D. M. de Leeuw,and M. A. J. Michels, Phys. Rev. Lett. 94, 206601 (2005).

[30] J. Yamashita and T. Kurosawa, J. Phys. Chem. Solids 5, 34 (1958).

[31] K. Fesser, A. R. Bishop, and D. K. Campbell, Phys. Rev. B 27, 4804 (1983).

[32] R. A. Marcus, J. Chem. Phys. 81, 4494 (1984).

[33] K. Seki and M. Tachiya, Phys. Rev. B 65, 14305 (2001).

[34] M. A. Lampert and P. Mark, Current injection in solids, (Academic Press, New York, 1970).

[35] P. N. Murgatroyd, J. Phys. D 3, 151 (1970).

[36] P. W. M. Blom, M. J. M. de Jong, and J. J. M. Vleggaar, Appl. Phys. Lett. 68, 3308 (1996).

[37] C. Melzer, E. Koop, V. D. Mihailetchi, P. W. M. Blom, Adv. Funct. Mater. 14, 865 (2004).

[38] S. M. Tuladhar, D. Poplavskyy, S. A. Choulis, J. R. Durrant, D. D. C. Bradley, and J. Nelson,Adv. Funct. Mater. 15, 1171 (2005).

[39] F. Padinger, R. S. Rittberger, and N. S. Sariciftci, Adv. Funct. Mater. 13, 85 (2003).

[40] V. D. Mihailetchi, H. Xie, B. de Boer, L. J. A. Koster, and P. W. M. Blom, Adv. Funct. Mater. 16,599 (2006).

[41] H. Kallmann and M. Pope, J. Chem. Phys. 30, 585 (1959).

[42] P. Gomes da Costa and E. M. Conwell, Phys. Rev. B 48, 1993 (1993).

[43] R. N. Marks, J. J. M. Halls, D. D. C. Bradley, R. H. Friend, and A. B. Holmes, J. Phys.: Con-dens. Matter 6, 1379 (1994).

[44] S. Barth and H. Bassler, Phys. Rev. Lett. 79, 4445 (1997).

16

References chapter 1

[45] C. W. Tang, Appl. Phys. Lett. 48, 183 (1986).

[46] N. S. Sariciftci, L. Smilowitz, A. J. Heeger, and F. Wudl, Science 258, 1474 (1992).

[47] J. J. M. Halls, K. Pichler, R. H. Friend, S. C. Moratti, and A. B. Holmes, Appl. Phys. Lett. 68,3120 (1996).

[48] D. E. Markov, C. Tanase, P. W. M. Blom, J. Wildeman, Phys. Rev. B 72, 045217 (2005).

[49] D. E. Markov, E. Amsterdam, P. W. M. Blom, A. B. Sieval, and J. C. Hummelen, J. Phys. Chem.A 109, 5266 (2005).

[50] S. E. Shaheen, C. J. Brabec, N. S. Sariciftci, F. Padinger, T. Fromherz, J. C. Hummelen,Appl. Phys. Lett. 78, 841 (2001).

[51] J. M. Kroon, M. M. Wienk, W. J. H. Verhees, and J. C. Hummelen, Thin Solid Films 403–404,223 (2002).

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