Eindhoven University of Technology

MASTER

The fill factorrecombination vs. extraction in organic solar cells

del Carmen Pérez, I.

Award date:2014

Link to publication

DisclaimerThis document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Studenttheses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the documentas presented in the repository. The required complexity or quality of research of student theses may vary by program, and the requiredminimum study period may vary in duration.

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

Technische Universiteit Eindhoven Rijksuniversiteit Groningen

Department of Applied Physics Photophysics and OptoElectronics group

The fill factor: Recombination vs. extraction

in organic solar cells

Irene del Carmen Pérez, June 2014

Supervisors:

ir. Davide Bartesaghi

dr. L. Jan Anton Koster

prof.dr.ir. Rene Janssen

1

Abstract

In this research we investigate the fill factor of polymer:fullerene bulk heterojunction

solar cells through a novel approach. We relate the fill factor with the ratio between the

rate of bimolecular recombination of free charge carriers and the extraction of free

carriers at the electrode, which we define as θ. The parameter θ depends on the

properties of the material and the device; i.e., in the mobilities of single and double

carrier devices. Through computational simulations [20] we found a trend for the FF-θ

curve. We fabricate organic solar cells (OSCs) and single carrier devices. Then we

collect experimental values of θ and FF to confirm the predicted FF-θ trend. The key

experiment is the measurement of the current-voltage curve (J-V) curves for both

devices without illumination and for the OSCs under illumination. We characterize the

OSCs by their dependency to the light intensity and their thickness, at three different

temperatures. We successfully confirm the predicted trend, assuming bimolecular

recombination as the dominant mechanism that determines the FF. We discuss

deviations to the predicted FF-θ trend and we propose that they are caused by the

presence of trap assisted recombination of free charges.

2

Contents

ABSTRACT ................................................................................................................. 1

INTRODUCTION ......................................................................................................... 4

1.1 THIS THESIS ............................................................................................................ 5

THEORY ..................................................................................................................... 7

PART I: ELECTRICAL CONDUCTION THROUGH ORGANIC MATERIALS ................... 7

2.1 CONJUGATED POLYMERS ............................................................................................. 7

2.2 THE MOBILE CHARGE CARRIERS ................................................................................... 9

2.3 THE HOPPING MECHANISM ......................................................................................... 10

PART II: ORGANIC PHOTOVOLTAIC DEVICES ........................................................ 11

2.4 HOW TO INDUCE A CURRENT THROUGH AN ORGANIC SEMICONDUCTOR ......................... 11

2.5 CHARGE CARRIER MOBILITY ....................................................................................... 12

2.6 ORGANIC SOLAR CELL DEVICE .................................................................................... 14

2.7 DEVICE CHARACTERISTICS OF AN ORGANIC SOLAR CELL .............................................. 16

2.8 THE SHORT CIRCUIT CURRENT AND OPEN CIRCUIT VOLTAGE ......................................... 19

PART III: CHARGE CARRIER RECOMBINATION IN OSC DEVICES .......................... 20

2.9 BIMOLECULAR RECOMBINATION .................................................................................. 20

2.10 TRAP-ASSISTED RECOMBINATION ............................................................................. 21

2.11 THE PARAMETER Θ (RECOMBINATION VS. EXTRACTION) ............................................ 23

OBJECTIVE .............................................................................................................. 26

METHODS ................................................................................................................ 28

4.1 MATERIALS ........................................................................................................ 28

4.1.A FULLERENES .......................................................................................................... 28

4.1.B POLYMERS ............................................................................................................. 28

4.1.C PEDOT:PSS ........................................................................................................ 30

4.2 DEVICE FABRICATION ....................................................................................... 30

4.3 THE EXPERIMENTS ........................................................................................... 32

3

RESULTS ................................................................................................................. 34

5. 1 CHARACTERIZATION OF THE ORGANIC SOLAR CELLS .................................. 34

5.1.A J-VINT CURVES WITHOUT ILLUMINATION .................................................................... 35

5.1.B J-V CURVES OF SINGLE CARRIER DEVICES ............................................................... 36

5.1.C J-V CURVES UNDER ILLUMINATION .......................................................................... 37

5.1.D JSC, VOC AND FF ANALYSIS ...................................................................................... 38

5. 2 THE FILL FACTOR AS A FUNCTION OF PARAMETERS ..................................... 41

5.3 IDENTIFYING RECOMBINATION ........................................................................ 43

5.3.A FURTHER ANALYSIS ................................................................................................ 46

5.3.A THE FILL FACTOR AND DEGRADATION ....................................................................... 48

CONCLUSIONS ........................................................................................................ 51

6.1 OUTLOOK ............................................................................................................. 52

APPENDIX .................................................................................................................. 53

A.2 HOLE MOBILITIES ΜH (M2/VS) ..................................................................................... 54

A.3 ELECTRON MOBILITIES ΜE (M2/VS) .............................................................................. 54

A.4 SHORT CIRCUIT CURRENT, OPEN CIRCUIT VOLTAGE AND POWER CONVERSION

EFFICIENCY (PCE) AT 1 SUN. .......................................................................................... 55

REFERENCES.......................................................................................................... 59

ACKNOWLEDGMENTS ............................................................................................ 63

4

Introduction In this chapter we discuss the importance of organic electronic research nowadays

and define the goal of this thesis.

In the classical era it was thought that humans are different from the rest of the animals

because they are social (Aristoteles). Nowadays it is known that animals behave and

organize in many social ways [34]. Thus, why are humans special if compared to the rest

of the species? An interesting statement is to describe the modern human as the

electronic animal. A day without being surrounded by electronic devices - or electricity -

is considered as an adventure or a game, but certainly not as a common day. For

centuries, people have been transforming the nature that surrounds us into the present

world. A remarkable consequence of this transformation is pollution. Indeed, the human

is also the polluting animal. An actual challenge as a global community is to change our

polluting energy sources to renewable ones. Harvesting energy from solar radiation is

one of these modern renewable technologies. Solar light can be converted into electricity

by the photovoltaic effect, which is the functioning principle of a solar cell device.

Most of the electrical currents that flow inside electronic devices are transported through

inorganic semiconductors. For a long time, organic materials were thought to be

electrically insulating, since the band-gap of most organic substances is too large to

allow electrical conduction [49]. The development of photo-conductive organic materials,

which are mainly based on carbon and hydrogen atoms, emerged in the middle of the

last century [47]. In 1977, Heeger, MacDiarmid and Shirakawa [9] demonstrated that it is

possible to have conduction of charges in polymers. Their discovery gave birth to the

field of organic electronics.

Organic materials have unique advantages. They have mechanical flexibility, so they do

not break easily like inorganic semiconductor crystals. It is relatively simple to process

them, thereby they are cheap to produce and manufacture. They have chemical

tunability, this means that the chemical properties can be controlled by changing a side-

1

5

group of an organic molecule [29]. Despite these advantages, organic electronics does

not compete yet with conventional electronics, due to the poor efficiency and short

lifetime of organic-based devices. It is worth noting that advanced techniques like optical

or quantum computing also aim to compete with conventional electronics [31].

Nonetheless, organic materials are promising low-cost candidates for replacing

conventional semiconductors and lighting technologies. A fundamental understanding of

the electrical conduction in organic materials is a challenge that requires an

interdisciplinary scientific attitude.

Nowadays there are organic-semiconductor devices like organic light-emitting diodes

(OLEDs), organic photovoltaic cells (OPVs), organic field effect transistors (OFETs) and

new hybrid organic-inorganic devices. It is possible that these devices will never reach

the efficiency of inorganic electronic devices, but this does not necessarily imply that

they cannot be used for commercial applications. To compete with inorganic technology,

further improvement of organic solar cells is necessary; this requires a thorough and

fundamental understanding of the loss mechanisms taking place.

1.1 This thesis

The motivation of this thesis is to investigate the fill factor of polymer:fullerene bulk

heterojunction solar cells through a novel method. The idea is to prove the dependence

of the fill factor on properties of the materials and the device. The fill factor FF is the ratio

of maximum obtainable power to the product of the open-circuit voltage and short-circuit

current. The fill factor describes the efficiency of the solar cell. A fundamental

understanding of the FF as a function of parameters that depend on the material and the

device properties has not been achieved yet.

It is our goal to confirm the dependency of the fill factor on a variable we define as θ.

The parameter θ is defined as the ratio between the rate of recombination of free charge

carriers and the extraction of free carriers at the electrodes. Recombination is a loss

mechanism in solar cells. The parameter θ only takes into account bimolecular

6

recombination [26, 59]. We consider that the recombination of charges in organic solar

cells whose FF-θ curves follows the expected trend is dominated by the bimolecular

mechanism described by Langevin.

In summary, the questions that this thesis aims to answer are the following:

Can the fill factor be determined by properties of the materials and the device?

Can the relation between the fill factor and θ identify what is the dominant

recombination mechanism occurring in organic solar cells?

7

Theory This chapter gives the basic theoretical background required for understanding

electrical conduction in organic semiconductors and particularly in organic solar cells.

The process of bimolecular recombination of free charge carriers is explained and the parameter

θ, which will serve for the analysis of the fill factor, is introduced.

PART I: ELECTRICAL CONDUCTION THROUGH ORGANIC MATERIALS

2.1 Conjugated polymers

Conjugated polymers are sequences of carbon (C) atoms with hydrogen (H) atoms

attached to this sequence. Nitrogen, oxygen, sulfur or other atoms can be also attached

to this sequence. The atom sequence along the chain alternates between single and

double bounds; it is of the type C=C-C=C- . Each carbon atom has four valence

electrons, three of them form in-plane bonds and the last one occupies an out-of-plane

orbital, which is delocalized. The electrons that are strongly localized are strongly bound,

which prevents their movement. Conduction in the molecule occurs due to the

delocalized electrons, by an effect called π-conjugation. The out-of-plane electronic

orbital of an atom can overlap with the out-of-plane electronic orbitals of another

delocalized neighbor atom, forming a π-bond. The overlap between neighboring π-

bonds will form an extended array, leading to a delocalized molecular orbital, a π band

[49], along which the delocalized π electrons can smear out around adjacent carbon

atoms

2

8

Figure 2.1: σ- and π-bonds in an ethene molecule. The σ-bonds represent strongly bounded

states while the π-bonds are formed by electrons that were delocalized. Figure taken from [62].

The complete π-electron system will be formed by a set of bonding and anti-bonding

orbitals. Electrons in the bonding states lower their energy and the ones in the anti-

bonding states increase their energy. Hence, the bonding orbitals are energetically

favored and are generally filled. The highest occupied molecular orbital (HOMO)

corresponds to the highest level of the filled π band. The lowest unoccupied molecular

orbital (LUMO) corresponds to the bottom of the empty π* band. There is a forbidden

energy gap between the HOMO and the LUMO, typically ranging from ~1 to ~4 eV [14,

16]. Thus, conjugated polymers are intrinsic semiconductors. The range of the energy

gap allows the organic material to interact with light in the visible spectrum. This fact

combined with the property of charge transport make organic optoelectronic devices

feasible.

Any distortion in the conjugation, like chain distortion or chemical defects, changes the

positions of the local HOMO and LUMO levels. In consequence, the energy of

conjugated polymers has a disordered topology; the polymers have multiple conjugated

segments with different conjugation lengths. Thus, these materials do not present an

electronic band structure. Actually the charge transport in conjugated polymers occurs

via hopping between localized states. It is often assumed that the density of states

(DOS) of each band has a Gaussian distribution in energy, with σ the width of this

spread [16].

CC

H

H

Hσ-bond

π-bondσ-bond

H

π-bond

σ-bond

σ-bondσ-bond

9

Figure 2.2: Energy landscape of conjugated polymers. A Gaussian and an exponential function

are used to describe the energy distribution. The charge transport occurs via hopping between

localized states. The probability of each hop depends on both the difference in energy ΔE and

distance R. A trap is depicted as a level of low energy. Figure adapted from [62].

In this thesis, conjugated polymers and fullerene derivatives are used to fabricate

polymer:fullerene bulk heterojunction solar cells. Fullerenes are small molecules

composed entirely by carbon [29]. They have closed geometrical hollow forms, like

hollow spheres, ellipsoids or tubes. Conduction in fullerenes also occurs due to

conjugation and hopping transport .

2.2 The mobile charge carriers

A model that explains the charge transport in conjugated polymers is the polaron model

[12]. This model has its origin in the strong coupling of electronic and geometric structure

in the conjugated segments. A polaron can be referred to as positive or negative, as it is

correlated to a hole or an electron. While charge carriers move, they locally distort the

host material. Once the charge is present, the molecule or polymer segment will change

its conformation. In consequence, the lattice is polarized due to the charge. This

polarization acts as a potential well that limits the movement of the charge, decreasing

the mobility of the charge carrier. The carrier and distortion caused by it are considered

a quasi-particle called ‘polaron’.

10

2.3 The hopping mechanism

Due to the energetic and geometric disorder in the organic molecules, there are

localized states that block the flow of free charge carriers through the semiconductor [19,

49]. In order to continue flowing in the semiconductor, charge carriers need to overcome

this blockage. This occurs through ‘hopping’; charge carriers hop between localized

states with different conjugation lengths (figure 2.2). A hop upward in energy requires

the absorption of a phonon, while a downward hop releases a phonon [11, 42]. Hopping

occurs with a certain rate that depends on the distance and energy difference between

the states, the overlap of the electronic wave functions and the available thermal energy

[2].

A description for the transition rates for hopping of charge carriers between sites is found

in the work of Miller and Abrahams [39]. The typical hopping distance of charges in

organic semiconductors is 1-2 nm [1]. In some cases, sites with very low lying energy

levels can be present in the device. Charges which hop to these sites can be trapped [4]:

the probability of hopping away from these site is very small. Charge traps had been

related to intrinsic defects, to impurities remaining from the synthesis and/or

contamination from the environment. Despite that the origin of traps remains unclear, it

is likely that traps have a common origin and are extrinsic in nature [45]. A trap site is

shown in figure 2.2.

In semiconductor devices, the application of a bias voltage to the organic material

influences the hopping from one to another localized state, as will be explained in the

next section.

11

PART II: ORGANIC PHOTOVOLTAIC DEVICES

2.4 How to induce a current through an organic semiconductor

Organic semiconductor devices consist of an organic active layer with semiconductor

properties, sandwiched between two electrodes. This structure is going to be referred to

in the following as ‘device’. To induce a current through the organic semiconductor,

charge carriers must first be injected or photogenerated, and later transported through

the semiconductor. Injection and photogeneration corresponds to the functioning

principle of organic light emitting diodes and organic solar cells, respectively.

The electrodes of the device allow the application of a bias voltage through the organic

polymer. The energy diagrams for zero and non-zero applied voltage are presented in

the next figures.

Figure 2.3: (a) Energy diagram of an organic semiconductor with no applied bias voltage,

showing the electron (hole) injection barrier ϕe(h) and electrode work function Φe(h) (b) The energy

diagram of the device with applied forward bias voltage V equal to the built-in voltage Vbi, showing

the transport of electrons and positive charges (holes). Figure taken from [62].

At zero voltage, the work functions of the electrodes Φ usually do not match with the

upper and lower levels of energy (HOMO and LUMO), as it is illustrated in figure 2.3.a.

To facilitate the charge injection or extraction, the metal work functions must match the

LUMO or HOMO of the organic semiconductor, for electron or hole injection/extraction

respectively.

12

Once the layers of the device are connected (figure 2.3.b) the charge carriers arrange

themselveselectrons flow from high to low Fermi energy areas [54]. This causes an

internal electric field to arise and a difference between Φh and Φe that defines a built-in

voltage Vbi. To allow charge carriers to gain the ability to move through the device, the

Vbi must be overcome. This occurs when a voltage is applied on the device, which

imposes an electric field that reduces the internal electric field. In this way, electrons and

holes are transported across the active layer. The diffusion of charges contributes to the

total current. For an even higher bias, the electric field changes sign and now assists

carriers to enter the material. This is known as drift.

2.5 Charge carrier mobility

In a semiconductor, charge transport is essentially characterized in terms of the charge-

carrier mobility (µc), given by

, (2.1)

where is the drift velocity of charges and E the applied electric field. Mobilities in

organic semiconductors are generally much lower than in inorganic semiconductors.

This is principally due to the irregular nature of hopping transport and to the low relative

dielectric constants, which has typical values of 2-4 [16]. In addition, the dependence of

the mobility on temperature and electric field also exhibits different behavior [14].

The mobility can be determined experimentally, by measuring the current. When

applying a voltage, a current will flow through the semiconductor device. When an

electrode injects more charge carriers into a material than the space between the

electrode and counter-electrode can accept, the current is limited by the build-up of

space charge [19]. The built-up of space charge will create an electric field which

reduces the rate of charge carrier emission from the respective electrode, giving rise to a

space charge limited current (SCLC).

13

The build-up of space charge limits the current of single carrier devices, i.e., devices in

which only electrons or holes are injected. The SCLC density follows the Mott-Gurney

law [40], given by

(2.2)

where ε is the electrical permittivity of the material, L the thickness of the active layer, Vint

the internal voltage drop across the active layer, and µp and µn the hole and electron

mobilities. The internal voltage in a device Vint is related to the applied voltage Va by

, (2.3)

where VRs is the voltage drop across the series resistance of the substrate.

Thus, by measuring the current density-voltage (J-V) curve and fitting this curve with

equation (2.2) it is experimentally possible to find the value of the mobility in

semiconductor devices. Below the built-in voltage the current will be dominated by

diffusion of charge carriers, and above the built-in voltage the current will be space

charge limited, dominated by drift. In equation (2.2) a constant mobility is assumed.

An empirical description of the mobility of carriers in molecularly doped polymers is given

by [49]

√ , (2.4)

where is the zero-field mobility, E is the electric field strength, and the electric field

activation parameter. Using this experimental field dependency for the mobility, it is

possible to approximate JSCL by [44]

√

(2.5)

We neglect the dependency of the mobility on the density of charge carriers in our

devices; we consider the E to be dominant.

14

2.6 Organic solar cell device

An organic solar cell (OSC) is a device that absorbs light to generate charge carriers

inside the device and produce electricity by extracting these carriers through an external

circuit. This functioning principle is known as the photovoltaic effect. The OSC consists

of a nanostructured blend of two materials, an electron donor and an electron acceptor,

sandwiched between Ohmic electrodes.

The OSC will absorb the irradiated photon only if its energy has the same or higher

value than the forbidden energy gap between HOMO and LUMO of the electron donor or

electron acceptor. The absorbed photon promotes an electron from the HOMO to the

LUMO, leaving a hole behind in the HOMO. The electron in the LUMO and the hole in

the HOMO are initially strongly bound; exchange interactions will start to play a role and

the wave functions of the electron and hole will overlap. Consequently, the electron and

hole create a quasiparticle called exciton [19].

Figure 2.4: Schematic energy-band diagram of a bulk-heterojunction organic solar cell. The solid

lines represent the energy levels of the donor, while the dashed lines represent the energy levels

of the acceptor. A photon is absorbed by the donor material leading to the formation of an

exciton. This will dissociate when it reaches the donor-acceptor interface, forming an electron-

hole pair, which also dissociates into free charges. The free electrons and holes are transported

through the LUMO of the acceptor and the HOMO of the donor, respectively. Finally, the free

charges are extracted at the electrodes. Figure taken from [58].

15

An exciton can follow two routes, either it recombines to the ground state or it

dissociates into an electron-hole pair (e-h). An e-h pair can reside on adjacent molecules

or in chain segments. [29]. Recombination implies the loss of charge carriers; it is a loss

mechanism in solar cells. The dissociation of an exciton into an e-h pair only occurs at

the donor-acceptor interface, where the energy offset between the two materials

facilitates the reduction of the binding energy. The exciton can only reach the donor-

acceptor interface when its distance to that interface is equal or smaller than the exciton

diffusion length, which is typically around 10 nm in organic semiconductors [33].

Excitons generated at distances longer than ~10 nm from the interface are generally lost

by intrinsic decay. It is worth to notice that the exciton binding energy is high due to the

low values of the dielectric constant (2-4) [14]. This hinders the dissociation of the

exciton.

After exciton dissociation, the e-h pair may still be Coulombically bound in a charge-

transfer state [50]. Once the charge-transfer excitons are separated into free charge

carriers, the charges are transported to the electrodes. This process is assisted by the

built-in electric field, induced by the built-in voltage due the difference in work function

between the electrodes. Holes and electrons are then collected by the anode and

cathode, respectively, respectively, and driven into the external circuit, producing an

electrical current.

A major advancement was realized when the donor/acceptor were intimately mixed. This

greatly increased the interfacial area and reduced the distance that excitons have to

travel in order to reach the interface. This device structure is called a bulk heterojunction

(BHJ) and has been used extensively since its introduction in 1995 [15, 63]. Its use

facilitates exciton dissociation, consequently, charge generation takes place everywhere

in the active layer [4].

16

2.7 Device characteristics of an organic solar cell

Without illumination, the OSC behaves as a diode and the dark current density JD is

described by the classical Shockley diode equation [53]:

(2.6)

where Js is the (reverse bias) saturation current at negative bias, q is the elementary

charge, V the voltage across the active layer, KB is Boltzmann’s constant, T is

temperature and η is the ideality factor. The (J-V) curve of an OSC without illumination,

as well as of an OLED, shows three discernable regimes. These are indicated in the

next figure.

Figure 2.5: J-V curve of an OSC without illumination. The three different regions represent the

different behaviors of the curve. Image adapted from [62].

Region 1: The current starts with a slow increase, which is attributed to parasitical

currents between the electrodes, referred to as leakage current [54]. For an ideal device,

the diffusion part of the JV-curve could be traced back to zero bias. In practice however,

there is always a leakage current characterized by an Ohmic resistance, that is inherent

to the fabrication of the device. The leakage current density varies linearly with voltage,

J~V. In our experiments we try to minimize the presence of leakage current.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

1E-4

1E-3

0.01

0.1

1

10

J~V

31

J~(V-Vbi)p

J (

A/m

^2)

Voltage (V)

J~eqV/KbT

2

17

Region 2: The current presents a sudden rise, in accordance to the diode equation (2.6).

Therefore, the current density is an exponential function of the applied bias voltage (J ~

exp (

). This regime is diffusion dominated and the voltages are below the built-in

voltage.

Region 3: This region starts at the built-in voltage Vbi and continues to higher voltages.

The current is drift dominated and increases slower than in the previous region. The

current density is described by a power law and a built-in voltage as: An

exponent equal to 2 is expected for a space-charge limited device, according to equation

(2.2). This equation assumes trap-free transport. In the case that traps exist in the

device, trapped charges can be released when the bias voltage rises and the electric

field is increased, leading to a stronger voltage dependence. In consequence, a higher

value for p is expected, around p ~ 2.8 [6].

Under illumination, the current density JL is usually described by

(2.7)

where Jph is the photogenerated current density.

To understand the performance and efficiency of a solar cell, the curve of the current

density-voltage (J-V) measurement under illumination is analyzed in the region between

zero voltage and zero current density under illumination JL. This is represented in figure

2.6. The intersection of the J-V curve with the voltage and current density axes are the

open circuit voltage Voc and the short-circuit current density Jsc..

18

Figure 2.6. Typical current density-voltage characteristic of a BHJ OSC. The parameters short-

circuit current density Jsc, open-circuit voltage Voc, maximum power point MPP and fill factor FF

are indicated. The shaded rectangle corresponds to the maximum power output that the OSC can

supply. A graphic definition of the FF is indicated. Figure adapted from [23].

The power generated by the solar cell, is the product of the voltage and the

corresponding current. In an ideal device all the photogenerated charge carriers will be

extracted from the device. The maximum power generated in this case is represented in

figure 2.6 as a rectangle, which is the product Jsc.Voc . In real devices recombination

plays a role, therefore not all the photogenerated charge carriers are extracted from the

device. The ratio between the maximum power generated by the real cell and the power

that an ideal device (with the same Jsc and Voc) would generate is called fill factor FF,

expressed as

; (2.8)

The power-conversion efficiency of the OSC can be expressed as

(2.9)

where I is the incident light intensity. In the standard test condition, light intensity is set to

1000 W/m2, the temperature of the cell at 295 K and the spectral distribution of the light

is given by the air mass (AM) 1.5 spectrum. The AM1.5 spectrum is the spectrum of

sunlight passing through 1.5 times the thickness of the atmosphere.

19

2.8 The short circuit current and open circuit voltage

The analysis of the short circuit current and open circuit voltage is the focus of several

research studies in organic solar cells. We are interested in the relation of these two

factors with the light intensity.

For an ideal solar cell it is assumed that the photogenerated current density Jph is

voltage-independent, meaning that Jph = Jsc at any applied voltage. In polymer:fullerene

OSC devices, the short circuit current exhibits a power law behavior with respect to light

intensity, thus

, (2.10)

with 0.75 < α < 1 [22]. The exponents depends on the mobility of electrons and holes,

and on the strength of the charge carrier recombination. When both charge carriers have

similar mobilities and the bimolecular recombination is weak, α will be close to 1.

At the open circuit voltage Voc there is no current extraction and all the photogenerated

charge carriers recombine or diffuse out of the device. In consequence, the Voc is limited

by the amount of recombination that is present in the device. Less recombination leads

to a higher value of Voc. In the absence of traps, where Langevin recombination is the

dominant recombination process, Voc can be expressed by an equation derived by

Koster et al., [21], where

(2.11)

with P the dissociation probability of bound e-h pairs, Egap the energy gap between the

HOMO of the donor and the LUMO of the acceptor, kR the bimolecular recombination

coefficient, Ncv the effective density of states, and G the generation rate of bound e-h

pairs.

The generation rate G is proportional to the light intensity in this equation, directly

connecting Voc to the light intensity.

20

PART III: CHARGE CARRIER RECOMBINATION IN OSC DEVICES

2.9 Bimolecular recombination

Charge carrier recombination is a loss process in a solar cell, though it is a desired

process for an OLED because it results in the emission of photons. The electron and

hole concentrations in OSCs are lower than in OLEDs. The positive result of this is that

the bimolecular recombination in solar cells is weaker than in OLEDs, because the

bimolecular recombination rate is proportional to the carrier concentrations, in

accordance to

,

(2.12)

with kR the bimolecular recombination coefficient, n and p the electron and hole

concentrations, respectively, and ni the intrinsic carrier concentration of electrons and

holes given by ni2 = Ncv exp[-Egap/kT]. In pristine organic semiconductors, bimolecular

recombination is of the Langevin type, i.e., it is proportional to the diffusion of the two

charge carriers, electrons and holes, towards each other in their mutual Coulomb field

[26]. This behavior is characteristic of materials in which the mean free path of the

charge carriers is smaller than the critical Coulombic capture distance, which is

approximately rc ~18.5 nm [1]. Organic semiconductors enter in this category because

the typical hopping distance is between 1 and 10 nm [8]. Therefore, the bimolecular

recombination coefficient is given by the Langevin expression

, (2.13)

with µn and µp the electron and hole mobilities, respectively.

In organic bulk-heterojunction solar cells, however, bimolecular recombination often

deviates from the Langevin picture; recombination rates are smaller than predicted by

the Langevin formula. In some cases, the reduction can be up to several orders of

magnitude. For example, the recombination strength in a solar cell based on poly(3-

21

hexylthiophene) (P3HT) and [6,6]-phenyl-C60-butyric acid methyl ester (PCBM) was

measured to be reduced by 3 orders of magnitude [17]. While such slow carrier

recombination is beneficial for the performance of organic solar cells, its origin remains

unclear. To obtain a more accurate value of the bimolecular recombination rate, a

prefactor γpre is added to the Langevin equation, giving

( ) (2.14)

with kR the total bimolecular recombination strength. In a double-carrier device, electrons

and holes are present at the same time. The effective double carrier µD can be obtained

by fitting the dark current of OSCs with equation (2.3). A recent study of Wetzelaer et al.

[59] derives an expression for the Langevin prefactor γpre that depends on easily

accessible experimental quantities, i.e., the hole, electron and double-carrier currents.

This is given by

. (2.15)

The prefactor has been derived defining the double carrier current as subjected to two

phenomena: charge recombination and charge neutralization [46]. In the bimolecular

recombination process two charges of opposite sign annihilate. In charge neutralization

these oppositely charged carriers coexist in the film. Neutralization leads to an

enhancement of current because the total amount of charge in the layer can exceed the

net space charge.

2.10 Trap-assisted recombination

Trapped charges can also take part in the recombination process. A charge carrier is

trapped when it is located in an isolated site within the energy band gap. Traps can be

originated from imperfections or impurities in the crystal structure. A mobile carrier of

opposite sign can meet the trapped carrier and subsequently recombine due to their

Coulombic interaction. A description of this process is given by the Shockley-Read-Hall

(SRH) statistics [53]. The presence of SRH recombination has been identified in all-

22

polymer solar cells, OLED and polymer:fullerene solar cells with intentionally added

impurities [25, 32]. In organic semiconductors, electron transport is frequently hindered

by trapping. Thus recombination occurs between free holes and trapped electrons.

Trap-assisted recombination can be non radiative and it actually yields to the release of

a phonon.

Recombination of holes by trapped electrons implies four steps: 1) The electron is

captured by a neutral center with a rate governed by a capture coefficient Cn. 2) This

trapped electron can subsequently be excited back to the conduction band or 3) is being

captured by a hole governed by a capture coefficient Cp. 4) Another option is that an

electron is captured from the valence band by a neutral center, which is a generation

process. In their work, SRH calculated the total trap-assisted recombination rate by

assuming thermal equilibrium between the four processes, which requires the rate of

capture and the rate of emission to be equal. Recombination of electrons by trapped

holes occurs in a similar manner.

The result of the recombination of holes by trapped electrons and vice versa is the well-

known SRH recombination rate is , with

(2.16)

where Cn denotes the probability per unit time that an electron in the conduction band

will be captured for the case that the trap is empty and able to capture an electron.

Correspondingly, Cp indicates the probability per unit time that a hole will be captured

when a trap is filled with an electron and able to capture the hole. Nt is the density of

electron traps.

Bimolecular recombination can be differentiated from trap-assisted recombination by

analyzing the slope of the Voc–ln(I) curve (equation 2.15)). A slope ~kT/q is expected

when only bimolecular recombination acts in the device, and a slope > kT/q when the

dominant recombination mechanism is trap-assisted [21]. In such a case, the

bimolecular strength will be the sum of the Langevin and SRH recombination strengths,

[60].

23

2.11 The parameter θ (Recombination vs. extraction)

We analyze the ratio between the rates of bimolecular recombination and extraction of

free charge carriers at the electrodes. We define the parameter as

, (2.17)

where the rates of extraction and recombination are equal to the inverse of the time of

transit (ttr) and recombination (trec). We arbitrarily defined terms that appear in the

derivation of θ, in order to provide a better understanding of the relation between FF and

θ, which indeed is the focus of this research.

When a bias is applied, charges are moving inside the device under the influence of an

electric field E. Assuming that one charge carrier is slower than the other, the effective

velocity of charges can be expressed in a similar fashion to the drift velocity of single

charge carriers (equation (2.1)), but taking into account the whole movement of charges

inside the device. Thus,

, (2.18)

where μeff is the effective mobility. For convenience, we define the effective mobility as a

function of the minimum and maximum mobilities in the following manner:

. (2.19)

The transit time that a charge requires to cross the whole thickness L of the active layer

is defined as

, (2.20)

24

where the relation and equation (2.18) have been used. Assuming we have

good Ohmic contacts, we define the internal voltage as

, (2.21)

we attribute 0.4 V to the band bending at the Ohmic contact.

The recombination time can be expressed as

, (2.22)

where γpre is the Langevin prefactor given in equation (2.13), and n and p the density of

carriers. It is assumed that holes are the slowest carriers. We include another prefactor

in the bimolecular recombination time, which hinges on the density of carriers n and p.

We obtain

√

. (2.23)

When the density of charge carriers is dominated by extraction, it can be expressed as

, (2.24)

where G is the generation rate of charge carriers. The factor G can be calculated by

considering the simple case that all photogenerated carriers are extracted, thus the

recombination of charge carriers is negligible. The photoconduction of an OSC is

assumed to occur without injection of charges at the contacts and with a uniform electric

field distribution. Goodman and Rose [13] derived an expression for G in the described

case, which is given by

. (2.25)

25

In this derivation, only the drift of charge carriers is taken into account and the

contribution of diffusion is neglected. We substitute equation (2.24) into equation (2.23)

twice, for n and p respectively, and we obtain

√

√

. (2.26)

Finally, we substitute equation (2.26) and (2.20) into equation (2.18). It is found that is

equal to

(2.27)

26

Objective This research investigates the fill factor as a function of the bimolecular

recombination/extraction ratio in polymer:fullerene bulk-heterojunction solar cells.

This research proposes a novel manner to investigate OSCs, through the analysis of the

fill factor FF. A fundamental understanding of the FF as a function of parameters that

depend on the material and the device properties has not been achieved yet. Our

objective is to determine how the FF depends on certain variables, expressed together

in the parameter θ (equation (2.27)). Computational simulations [20] of FF-θ curves

have been done by this research group. We have found a well-defined trend shown in

figure 3.1. The range of the simulations is given in table 3.1.

Figure 3.1: FF- θ curve for computational simulations.

3

10-6

10-4

10-2

100

102

104

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

FF

27

Table 3.1: Range of the computational simulations performed on polymer:fullerene bulk

heterojunction solar cells

Thickness 60 - 260 nm

Generation rate 1e25 - 1e28 m-3s-1

μn 1e-10 - 4e-7 m2/Vs

μp 1e - 10-4e-7 m2/Vs

γpre 1e-3 - 1

HOMO-LUMO 1.0 -1.4 eV

The present research aims for collecting experimental data points to the FF- θ curve

shown in figure 3.1. We consider that the given trend given in this plot has a universal

character. Due to the definition of θ, it is clear that this trend identifies the dominant

presence of bimolecular recombination of free charge carries acting on organic solar

cells. The FF-θ curve shows three regimes:

1) For lower values of θ, the fill factor reaches its higher values. In this case there is

a high extraction and a low recombination rate. The FF-θ curve is flat.

2) For middle values of θ, the fill factor has values between 0.4 and 0.7. While θ

increases the FF is reduced. The extraction rate balances the bimolecular

recombination rate.

3) For higher values θ, the fill factor shows its lowest values. There is a high

bimolecular recombination rate and a low extraction rate. The FF-θ curve is flat.

The OSCs to be considered are polymer:fullerene bulk heterojunction solar cells. The

fullerenes selected to fabricate of the solar cells are PC60BM and PC70BM. The polymers

used are P3HT, PDPP5T and PTB7. Their chemical structure are presented in the next

section. Polymeric-donor/PCBM devices have a high efficiency, due to an ultrafast

charge transfer of electrons from the polymer to the PCBM [33]. To obtain values of θ

and FF, the key experiment is the measurement of the current-voltage (J-V) curves.

28

Methods This section presents the device layout and fabrication method for the devices used

in this research. Furthermore, the experiments to be performed are described.

The experiments are performed on fullerene:polymer bulk heterojunction solar cells and

single carrier devices. In order to obtain values of θ and FF, we need to: 1) Characterize

the device by measuring the Voc, Jsc and FF . 2) Calculate the mobilities of double and

single charge carriers for each device. The key experiment is the measurement of the

current-voltage (J-V) curves. This enables us to characterize the device and calculate

the mobility of charge carriers, either of double or single carriers, by fitting the (J-V)

curve with equation (2.2) or equation (2.5), in case that the influence of the electric field

in the mobility cannot be neglected.

4.1 MATERIALS

4.1.a Fullerenes

The fullerene derivatives selected for this investigation were the derivatives are the [6,6]-

phenyl-C60-butyric acid methyl ester (PCBM) and its homologous with a 70-atom carbon

buckyball (PC70BM). These fullerene derivatives are used as acceptor material. The

advantage over other fullerenes is that PCBM is soluble in chlorobenzene and

chloroform [44], which allows for solution processable donor/acceptor blends. This

material is particularly interesting for us because it shows trap-free electron transport as

well as relatively high free electron mobility [35].

4.1.b Polymers

Conjugated polymers serve as donors in the OSC devices. The donor polymers need to

exhibit [63]: a) A low bandgap for efficient light absorption. b) A proper energy level

mismatch with the LUMO of the acceptor. c) Effective π-π overlap between polymer

4

29

backbones. d) Optimized enegy difference between the HOMO of the donor polymer and

the LUMO of the acceptor.

a) b)

Figure 4.1: Chemical structure of a) PC60BM and b) PC70BM.

The polymers selected for this study are:

a) Poly(3-hexylthiophene -2,5-diyl) (P3HT).

b) Diketopyrrolopyrrole-quinquethiophene alternating copolymer (PDPP5T).

c) Poly[4,8-bis[(2-ethylhexyl)oxy]benzo[1,2-b:4,5-bA]dithiophene-2,6-diyl][3-

fluoro-2-[(2-ethylhexyl)carbonyl]thieno[3,4-b]-thiophenediyl] (PTB7).

a) b) c)

Figure 4.2: Chemical structure of a) P3HT, b) PDPP5T and c) PTB7.

30

4.1.c PEDOT:PSS

A conjugated polymer poly(3,4-ethylenedioxythiophene) (PEDOT) is mixed with

poly(styrenesulfonate) (PSS), forming a highly conductive and transparent organic

semiconducting material with a work function of 5.0-5.2eV, the PEDOT:PSS. It is used to

improve the hole injection current and provides a better bonding between the hole-

extracting contact and polymer layer, consequently improving the surface properties.

Due to the PSS, the material is soluble in water and can be processed by spincoating or

printing. In our experiments, low-ohmic PEDOT:PSS from HC Starck (Al4083) was used.

4.2 DEVICE FABRICATION

The donor and acceptor are chosen such that electron transfer from donor to acceptor –

or hole transfer from acceptor to donor – is energetically favorable. The electron

transport takes place through the LUMO of the acceptor, while the hole transport takes

place through the HOMO of the donor. It is assumed that the electrodes are ohmic

contacts. On the other hand, single carrier devices - devices with a dominant type of

carrier - can be created by selecting appropriate injecting and blocking contacts. The

electrodes are chosen such that the carriers of one sign are blocked by employing an

injection barrier. This is achieved by the energy mismatch between the electrode and the

active layer. Therefore, electron transport can be distinguished from hole transport. The

experiments are performed on fullerene:polymer bulk heterojunction solar cells and

single carrier devices. In the OSCs, the active layer consists of a donor-acceptor blend.

The architecture of the solar cell devices is described in figure 4.1. The device contains

six layers placed on top of each other. The first layer of the device is the bottom

electrode. It consists of an indium tin oxide (ITO) layer, which allows the absorption of

light because it is a transparent layer. PEDOT:PSS is subsequently spin coated on the

ITO layer. The devices are then transported into an atmosphere of nitrogen where the

contamination of water and oxygen is less than 1 ppm. Inside the glove box,

polymer:fullerene layers are spin coated. By means of thermal evaporation, a thin layer

31

of lithium fluoride (LiF) is deposited. This layer acts as a buffer between the organic layer

and the top electrode, and it improves electron injection/extraction. Finally the top

contact, which consists of an aluminum (Al) layer is deposited. The PEDOT:PSS and the

top contact are connected by pinholes. This is unwanted because it results in shorts and

it leads a leakage current (region 1 in figure 2.5), which is characterized by an Ohmic

resistance. For a more detailed description of the fabrication of the devices, refer to [18].

a) b)

c)

Figure 4.3.a: General layout of the organic solar cell used in the experiments. Figure 4.3.b:

Diagram of the energy levels of a PDPP5T: PC70BM organic solar cell. Figure 4.3.c: Energy

diagram of an organic semiconductor at zero bias voltage. Shown are the built-in energy eVbi , the

electron and hole injection barrier φe and φh respectively, the electrode work functions ϕe and ϕh,

the LUMO, HOMO and the vacuum level energy.

The next tables show the electrodes used for single carriers and solar cells, and the

selected active layers. We use the following abbreviations: Pd: Palladium, Cr:

32

Chromium, Au: Gold, CB: Chlorobenzene: CF: Chloroform, oDCB:

Orthodichlorobenzene, Dio: Diiodooctane.

Table 4.1: Architecture of the devices Table 4.2: Selected active layers

In addition, we tested PBT7:PC70BM OSCs using calcium as the top contact.

4.3 THE EXPERIMENTS

The key measurement to be performed on solar cells and single carrier is the

measurement of the current-voltage (J-V) curve. For OSCs, the measurements occur in

dark and under illumination.

- Organic solar cell devices

After the fabrication of the devices, the samples are placed in a sealed container and

transported to the glovebox in the measurement room. The sample is placed in a sealed

sample holder, where two electrodes are put in contact with the sample, forming an

electrical circuit. In this holder the electron quantum efficiency (EQE) measurement is

performed. This was used to calibrate the solar simulator at 1000 W/m2 [52]. Later, the

sample is returned to the glovebox and placed in the solar simulator set up. This set up

consists of a sample holder with electrodes, which can be illuminated with a

Device Bottom contact Top contact

Solar cell

ITO

PEDOT:PSS LiF/Al

Electron

only Al LiF/Al

Hole only

Cr/Au

PEDOT:PSS Pd/Au

Active layers

1) P3HT:PC[60]BM , 1:1 Solvent: CB.

2) P3HT:PC70BM , 1:1 Solvent: CF.

3) PDPP5T:PC70BM , 1:1 and 1:2

Solvent: CF and oDCB 5% volume as a co-

solvent (Abbreviation used: CF/oDCB).

4) PBT7:PC70BM , 1:1.5

Solvent: CB, oDCB and CB and Dio 3%

volume as a co-solvent (Abbreviation used:

CB/Dio).

33

Steuernaugel SolarConstant 1200 metal halide lamp. The temperature of the sample

can be controlled through a liquid nitrogen cooling system. Finally, the J-V curve

measurements can be initiated, using a computer-controlled Keithley source meter.

- Single carrier devices

The measurement is done in a similar manner than the OSC but it does not incorporate

the illumination of the sample. Inside the glovebox, the sample is placed in a sealed

sample holder, where two electrodes form an electrical circuit. The J-V curve

measurements are done using a computer-controlled Keithley source meter.

The mobility of the single and double carriers without illumination (dark currents) can be

calculated by fitting the J-V curves with the Mott Gurney law (equation (2.3)), which

describes space charge limited currents (SCLCs). When the influence of the electric field

cannot be neglected, the fit is done using equation (2.5). To calculate the internal

voltage inside the device Vint (equation 2.4), the Vbi and VRs are estimated for each

measurement using a protocol described in the recent work of Blakesley et al. [3]. The

thickness of the device is measured inside the clean room at temperature. The samples

are carefully scratched and the thickness is measured using a DektaK 6M profilometer.

In order to collect a considerable amount of data points to verify the relation between the

fill factor and the parameter θ, we vary in our experiments:

The composition of the active layer.

The device thickness L, by changing the velocity at which the polymer:fullerene

solution is spin cast.

The generation rate G, by changing the intensity of the light using neutral density

filters, this yields an intensity variation of three orders of magnitude (from 2 to

1000 W/m2).

The charge mobilities (µ) of the devices. These vary by changing the temperature

in which the measurements take place (215 K, 255 K and 295 K). For systems

using P3HT as a polymer, the mobilities vary by thermal annealing the devices at

different temperatures (typically 60 oC and 120oC) [38].

34

Results The OSCs are characterized as a function of the light intensity. The fill factor is

plotted as a function of θ. The utility of the FF vs. θ plot to identify loss

mechanisms in the OSC is discussed.

The crucial calculation to obtain values of θ is the calculus of the mobility of the electron,

hole and double carriers in a polymer:fullerene bulk heterojunction device. For this the

current-voltage (J-V) curves of the single carriers and the solar cells without illumination

are measured and fitted with equation (2.2) or, if the electric field dependence of the

mobility cannot be neglected, we use equation (2.5).

The current-voltage (J-V) curves of organic solar cells are measured without illumination

and at different light intensities, at three different temperatures. To describe the OSCs,

we plot Jsc, Voc and the FF as a function of the light intensity. Single carrier devices are

also measured at three different temperatures.

5. 1 CHARACTERIZATION OF THE ORGANIC SOLAR CELLS

As an example of the characterization of an OSC, the following analysis shows the

results obtained for a PDPP5T: PC70BM 1:1 (solvent: CF/oDCB) device, 178 nm thick

(figure 5.1 to 5.5).

The OSCs are measured from high to low light intensities. Due to the fast degradation

observed for PTB7 devices after being exposed to light, we have repeated the

experiment, measuring from low to high light intensities. This is defined as “method 2”.

For PTB7:PC70BM using CB/Dio as a solvent, we tested different solute concentrations

without changing the polymer:fullerene ratio.

In the following we will refer to each polymer:fullerene solar cell only by the name of its

polymer.

5

35

5.1.a J-Vint curves without illumination

The double carrier mobilities are found, in all cases, by fitting the JD-V curves with the

Mott Gurney law (equation (2.2)). The internal voltage is calculated for each

measurement. For this, the built-in voltage Vbi and the voltage drop across the series

resistance of the substrate VRs are estimated using the protocol described by Blakesley

[3]. For each JD- V curve, a table with the results of the resistance, Vbi and the mobility

for each temperature is presented. This is shown in figure 5.1 and table 5.1.

Table 5.1: Values of the resistance and

the built-in voltage used to calculated

Vint. The mobilities of the double carriers

obtained with the fitted curves are

included.

Figure 5.1: : JD-V curve of a PDPP5T device.

The absolute value of JD is plotted.

As expected, the JD-V curves decrease with lower temperatures. Hence the mobilities

reduce in value with lower temperatures. The Vbi shifts to higher voltages while the

temperature is reduced.

T

(K)

R

(Ω)

Vbi

(V)

μD

(m2/Vs)

295 35 0.52 5.20E-07

255 24 0.54 1.50E-07

215 20 0.68 4.60E-08

0 1 2 3 4 5

10-2

10-1

100

101

102

103

104

295 K

255 K

215 K

Fits

JD

(A

/m2)

V (V)

36

5.1.b J-V curves of single carrier devices

The mobilities of single carriers are calculated in a similar manner to those of the dark

currents. They show a dependency on the electric field, so equation (2.5) is used for the

fit. The results show a slightly higher electron mobility compared to the hole mobility.

Nonetheless the difference between the two is not large enough to give rise to a space

charge limited photocurrent, as is described in Mihailetchi et al. [37]. We show an

example of an electron only device, PDPP5T: PC70BM 1:1 (solvent: CF/oDCB), 292 nm

thick.

Table 5.2: Values the obtained mobilities at

different temperatures in figure 5.2 and the

values of γ used to calculate Vint.

Figure 5.2: J-V curve of an electron only PDPP5T device.

The relation between μe and temperature is evaluated in the next figure. The plot shows

a linear behavior in a semi-logarithmic scale, in agreement with the investigation of

Cracium et al. [10]. A similar analysis was done to the hole mobility.

Figure 5.3: μe-1/T curve. The data belongs to figure 5.2.

T (K) μe (m2/Vs) γ (m/V)

295 1.10E-08 -1.30E-04

255 1.40E-09 7.00E-05

215 9.20E-11 2.80E-04 0 1 2 3 4 5

10-4

10-3

10-2

10-1

100

101

102

J (

A/m

2)

295 K

255 K

215 K

Fits

V (V)

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8

1E-10

1E-9

1E-8

e (

m2/V

s)

1/T (1/K)

37

5.1.c J-V curves under illumination

The J-V curves under illumination show the typical behavior of OSC devices. The curves

decrease their values while the light faints and the temperature decreases.

a) b)

c)

Figure 5.3: J-V curves of solar cells of PDPP5T devices under illumination with different light

intensities, for different temperatures.

From figure 5.3 we qualitatively observe how Voc, Jsc and FF behave as a function of the

light intensity and of the temperature. Voc and Jsc decrease when the light intensity

-0.2 0.0 0.2 0.4 0.6

-1.5x102

-1.2x102

-9.0x101

-6.0x101

-3.0x101

0.0

3.0x101

1000

780

620

490

340

250

150

91

43

25

14

J (

A/m

2)

V (V)

295 K

I (W/m2)

-0.2 0.0 0.2 0.4 0.6

-1.2x102

-9.0x101

-6.0x101

-3.0x101

0.0

3.0x101

1000

780

620

490

340

250

91

43

25

14

J (

A/m

2)

V (V)

255 K

I (W/m2)

0.0 0.2 0.4 0.6

-7x101

-6x101

-5x101

-4x101

-3x101

-2x101

-1x101

0

1x101

2x101

1000

780

620

490

340

250

150

91

43

25

14

J (

A/m

2)

V (V)

215 K

I (W/m2)

38

diminishes. When the temperature is lower, Voc increases and Jsc decreases. The FF is

also decreasing when the measurements are performed at low temperature, but it

follows the opposite trend with light intensity: reducing the incident power enhances the

fill factor of the solar cell.

5.1.d Jsc, Voc and FF analysis

Figure 5.4 and 5.5 show the Jsc and Voc dependency on the intensity of the light. The Jsc

shows a power-law dependency on the intensity of the light, in agreement with equation

(equation (2.10)). The exponent is determined by the slope of the double-logarithmic

plot (figure 5.5). An exponent close to one is found for all the PDPP5T samples; a sub-

linear behavior is observed only at low temperatures and high light intensity, due to

bimolecular recombination losses.

Figure 5.4: a) Jsc-vs. I curve of a Figure 5.5: Voc vs. I curve of a

PDPP5T device. PDPP5T device.

Figure 5.5 shows that the Voc as a function of the logarithm of the light intensity follows a

linear trend. This linear trend can be expressed as where Vt is the thermal

voltage, i.e., Vt= KBT/q. The slope of figure 5.5, let us call it s, can be expressed as the

slope of equation (2.11), as

. PDPP5T devices have a slope s* ~kT/q, thus

we assume that bimolecular recombination is the dominant mechanism [21].

1 10 100 1000

0,3

0,4

0,5

0,6

0,7

295 K

255 K

215 K

Fits

Voc

I (W/m2)

Voc

vs. I

1 10 100 1000

0,1

1

10

100

295 K

255 K

215 K

Fits

Jsc

vs. I

Jsc (A

/m2)

I (W/m2)

39

For P3HT devices slopes were s* ~1.25kT/q for devices annealed at 140 oC, in

agreement with previous results [25, 27]. This implies the presence of a lower-order

recombination mechanism in P3HT devices.

The slopes of PTB7 devices do not vary significantly with respect to the solvent used to

fabricate the device. We found a remarkable difference between the slopes and s*

when these are calculated in a regime of high (between 100 and 1000 W/m2) or low

(between 2 and 100 W/m2) light intensities. At high light intensities s* ~kT/q and at low

light intensities s*~1.4kT/q. This indicates that traps are assisting the recombination. A

concise description is given in section 5.3.

Figure 5.6 shows the dependency of the FF on the intensity of the light, in a logarithmic

scale. After being annealed, the P3HT:PCBM devices have higher values of FFs. We

present one result per device, corresponding to: a) PDPP5T:PC70BM device mentioned

at the beginning of this chapter, b) PTB7:PC70BM 1:1.5 device, solvent CB/Dio, 118 nm

thick, and c) P3HT:PC70BM 1:1 device, solvent CF, 237 nm thick. The sample was

annealed at 140 oC.

Figure 5.6.a: FF vs. I curve. Figure 5.6.b: FF vs. I curve.

Example of a PDPP5T:PC70BM device. Example of a PTB7:PC70BM device.

1 10 100 1000

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

FF

I (W/m2)

295 K

255 K

215 K

PDPP5T:70PCBM

1 10 100 1000

0.48

0.52

0.56

0.60

0.64

0.68

0.72

PTB7:70PCBM

295 K

255 K

215 K

FF

I (W/m2)

295 K

255 K

215 K

40

Figure 5.6.c: FF vs. I curve. Example of a P3HT:PC70BM device.

In general, the FF increases when the intensity of the light decreases. For PDPP5T

devices the FF dependency with I is almost linear at all light intensities. The decrease of

the FF at very low light intensities is caused by the presence of a leakage current. For

P3HT and PTB7 devices, the FF stops increasing at low light intensities. We will discuss

this in more depth in section 5.3.

PTB7 devices measured at 215 K show a steeper slope at light intensities between 100

to 1000 W/m2. At lower temperatures, the generation rate and the recombination rate

balance in a different manner at 215 K, giving rise to a steeper FF vs. I trend. In addition,

PTB7 devices degrade fast when they are exposed to light. It is possible that at 215 K

devices are already degraded and therefore show a different behavior.

The thickness of PDPP5T devices varied between 80 to 240 nm. It was found that the

Voc increases as a function of thickness, the FF decreases and the Jsc presents an

oscillatory behavior. There is destructive interference between the incident and the

reflected light near the aluminum cathode; this causes oscillatory behavior in the light

absorption and consequently in the Jsc dependence of the active layer thickness [24].

1 10 100 1000

0.56

0.58

0.60

0.62

0.64

0.66

0.68

0.70

0.72

FF

I (W/m2)

295 K

255 K

215 K

P3HT:70PCBM

41

5. 2 THE FILL FACTOR AS A FUNCTION OF PARAMETERS

The results presented in figure 5.7 confirm the relation between θ and the FF predicted

by numerical simulations (figure 3.1). The data belongs to measurements at different

light intensities and at different temperatures. The measurements were performed

starting from high to low light intensities (method 1). PTB7 devices measured using

method 2 are included1.

The data in figure 5.7 includes the measurements at all light intensities. Data points at

the lowest light intensities that shown leakage behaviors were not included. For PTB7

devices using CB as a solvent, the data points measured at low light intensities (2 to 50

W/m2) were excluded2. The highest efficiencies - higher values of FF - of PTB7 devices

were given by devices using CB/Dio as solvent.

Figure 5.7: FF vs θ. The experimental points are classified according to the active layer material.

1 A comparison between the two methods is given in section 5.3. 2 The results of data points at low light intensities are shown in section 5.3, figure 5.10.

10-5

10-3

10-1

101

103

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

PDPP5T

PTB7

FF

42

The influence of annealing in P3HT devices is represented in the next figure. It is known

that annealing optimizes the efficiency of the devices [22], in consequence the fill

factors increase as it is manifest in figure 5.8.

Figure 5.8: FF vs. I curve. Annealing dependence of P3HT: PC70BM devices.

To support our findings, we plotted published data from other researchers, Lenes et al.

[27] and Kniepert (to be published). The trend we predicted is successfully corroborated.

Figure 5.9: FF vs θ. Data from Lenes [27] and Kniepert (to be published).

10-8

10-6

10-4

10-2

100

102

104

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

MDMO/PCBM [27]

P3HT/PCBM

P3HT/PCBM - as cast

FF

10-7

10-5

10-3

10-1

101

103

0,2

0,3

0,4

0,5

0,6

0,7

0,8

Not

annealed

60 oC

120 oC

Annealing temperature:

140 oC

120 oC

60 oC

Not annealed

FF

140 oC

43

Our conclusion is striking: the fill factor can be investigated as a function of the

bimolecular recombination/extraction ratio θ, assuming bimolecular recombination as the

dominant loss mechanism. In the following we discuss deviations from the predicted

trend.

5.3 IDENTIFYING RECOMBINATION

The next figure shows the behavior of PTB7 devices using CB as a solvent. It is evident

that at low light intensities (between 2 to 50 W/m2) the experimental points deviate from

the predicted trend. The figure shows the higher FFs obtained when devices are

measured from low to high intensities (method 2). Also, it is noticeable how devices

show lower values of FFs at lower temperatures.

Figure 5.10: FF vs. I curve for PTB7 devices using CB as a solvent, including the measurements

at all light intensities.

To explain this deviation from our theory we have to consider the occurrence of trap-

assisted SRH recombination. Since θ is defined for the case of bimolecular

recombination, if another recombination mechanism comes into play and becomes the

dominant recombination mechanism we expect to observe a deviation from the predicted

trend. Other results of PTB7 devices deviated from the expected trend at low light

10-7

10-5

10-3

10-1

101

0,3

0,4

0,5

0,6

0,7

295 K

215 K

255 K

Light intensity:

90 to 1000 W/m2

Light intensity:

2 to 50 W/m2

295 K (Method 2)

295 K

255 K

215 K

FF

295 K

44

intensities. These are: a) PTB7 using oDCB as a solvent, in case that it is measured

using method 1 (from high to low intensities)3 and b) PTB7 using CB/Dio as a solvent,

PTB7 14mg/ml, measured at 215 K.

We recognize two behaviors of the OSCs, depending on the range of light intensity used

for the measurement. This statement is obvious in the FF vs. I trend presented in figure

5.5. This motivated us to analyze the slopes of Voc as a function of the light intensity in

two steps, first for light intensities between 2 and 100 W/m2 and second for intensities

between 100 and 1000 W/m2. At low light intensities all devices show higher values of

slopes s*. The next table shows results of slopes obtained for Jsc vs. I and Voc vs. I for

different OSCs at 295 K.

Table 5.3: Values of slopes obtained for Voc vs. I for different PTB7 devices at 295 K.

s*

PTB7 devices

100-1000

(W/m2)

2-100

(W/m2)

Method 1

CB 1.25 1.55

oDCB 1.2 1.62

CB/Dio

(PTB7 10 mg/ml) 1.23 1.53

CB/Dio 3%

(PTB7 14 mg/ml) 1.25 1.59

Method 2

CB 0.97 1.54

oDCB 0.98 1.41

CB/Dio

(PTB7 10 mg) 1 1.3

CB/Dio

(PTB7 14 mg) 0.96 1.56

3 The results of a PTB7 device, solvent oDCB, measured with method 2 is shown in figure 5.11.

45

At high light intensities the slope s* ~1.23kT/q when devices are measured using

method 1, and s* ~kT/q when are measured with method 2. There is not a noteworthy

difference of slope values with respect to the solvent use. The results indicate that all

devices are dominated by bimolecular recombination at high light intensities, but not at

low light intensities. This does not elucidate the deviating behavior of devices using CB

as a solvent. An additional research must be done to explain the assistance of traps in

the recombination process.

It is worth noting that the FF-θ curves of PTB7 devices show similar trends for different

solvents. This is presented in figure 5.11. Nonetheless, the lower power conversion

efficiency of CB devices in comparison with the rest of PTB7 devices leads to the FF-θ

trend to be located in a different region of the FF-θ curve.

Figure 5.11: FF-θ curves of PTB7 devices of four different solvents, measured at all light

intensities. The measurements were done at room temperature.

Let us analyze the behavior of the data points at the lowest light intensities in figure 5.11.

For oDCB and CB/Dio devices, there is a deviation from the expected trend. We

ascribed this deviation to leakage. For CB devices, instead of leakage we attribute the

deviation to the occurrence of trap-assisted SRH recombination.

10-5

10-4

10-3

10-2

10-1

100

0,4

0,5

0,6

0,7

0,8

Solvents:

Dio/CB 3%, PTB7 10 mg/ml

Dio/CB 3%, PTB7 14 mg/ml

oDCB

CB

FF

46

5.3.a Further analysis

To confirm the dominance of bimolecular recombination we can examine the bias-

dependence of the electroluminescence (EL) and its quantum efficiency.

For all solar cells, weak luminescence could be detected [57]. The experiment consists

in placing a photodiode detector in a sample holder, preventing the exposition of the

sample to any external light. The electrical measurements are conducted in a controlled

nitrogen atmosphere in dark, using a computer-controlled Keithley source meter.

Luminescence can be expressed by the photodiode signal Iphotodiode.

The ratio between the luminescence and the current without illumination Id of an organic

solar cell device is defined as the electroluminescence quantum efficiency, i.e.

.

Recombination is present in the luminescence (L) as well as in the current. Both of these

parameters depend on voltage. When the ELeff is calculated, the voltage dependency

cancels exclusively when either of the two recombination channels is present. Each type

of recombination has its own voltage dependency. Bimolecular recombination has a

quadratic density dependence, while trap-assisted recombination has a linear density

dependence. Therefore, when both recombinations are present in the device, the EL

efficiency shows a voltage dependency, due to the discrepancy in voltage dependencies

of both recombination processes [61].

Figure 5.12 shows the preliminary results of the ELeff of PTB7 OSC devices. These

measurements were performed before irradiating light over the samples. For PTB7

devices using CB as solvent, it is observed that the luminescence reaches higher values

than the rest of the blends. The EL efficiency presents a voltage dependency, which is

more pronounced at 215 K. The ELeff of oDCB devices show a minor voltage

dependency than for CB devices. The ELeff -V curves of CB/Dio devices show an almost

constant slope, which is assumed as voltage independent.

47

a) b)

Figure 5.12: ELeff -V curves obtained for PTB7:PC70BM solar cell devices.

- A research by Kuik et al. [25] confirms that P3HT devices annealed at 140 oC show

a voltage-dependent efficiency of the luminescence of the charge-transfer state. This

implies the presence of a lower-order recombination mechanism. This is in agreement

with the slopes of Voc vs ln(I) found, which are larger than kT/q, at high and low light

intensities. In addition, at low light intensities P3HT devices presented in figure 5.8,

specifically annealed at 120 oC and not annealed, have a FF vs θ. trend with a similar

behavior that PTB7/CB devices in figure 5.10. It is known that for P3HT:PCBM solar

cells SRH recombination is important al low charge density, that is, at low light intensities

[25]. This implies the presence of a lower-order recombination mechanism in P3HT

devices.

- It is worth noting that the luminescence ideality factor can bring information about the

dominant recombination mechanism acting on OSCs. At the onset of

electroluminescence, the emission shows an exponential dependence on voltage

according to ). Therefore, the slope of the exponential is determined by

the ideality factor, which can be directly obtained by numerical differentiation according

to (

)

. For polymer:fullerene bulk-heterojunction solar cells, this is expected

to be when bimolecular recombination acts in the device, and when trap-

assisted recombination dominates. Nevertheless, values of have been found to

systems were trap-assisted recombination is completely absent, but there is an

1 2 3 4 5

0,0

3,0x10-8

6,0x10-8

9,0x10-8

1,2x10-7

EL e

ffic

iency (

a.u

.)

V (V)

Solvent: CB

295 k

255 k

215 k

1 2 3 4

0

3x10-9

6x10-9

9x10-9

1x10-8

Solvent:

oDCB

CB/Dio 3%, PTB7 14mg/ml

CB/Dio 3%, PTB7 10mg/ml

EL

effic

ien

cy (

a.u

.)

V (V)

48

enhanced diffusion due to violation of the Einstein relation [60]. Therefore, the value of

cannot bring conclusive information about the presence of absence of trap-assisted

recombination.

- A definitive statement about the absence or presence of trap-assisted recombination

cannot be made because recombination via trap states is usually nonradiative [61].

5.3.a The fill factor and degradation

PTB7 devices are known for having a poor photochemical stability [56]. During our

experiments we found that PTB7 devices degrade when they are exposed to light. We

verified this statement by irradiating light to electron and hole only PTB7 devices. Both

devices showed reduced values of current vs. voltage after being exposed to light. To

solve this drawback, we measured devices starting from low to high light intensities,

which has been previously defined as method 2.

We measured a PTB7 device once during three consecutive days. The device was

measured using method 2. Figure 5.13 shows the relation between the intensity of the

light and the Jsc, Voc and the FF of a PTB7:PC70BM 1:1.5 device, solvent CB/Dio, PTB7

16 mg/ml, 136 nm thick, at 295 K.

a) b) c)

Figure 5.13.a: Jsc-vs. I curve. Figure 5.13.b: Voc vs. I curve. Figure 5.13.c: FF-vs. I curve.

A PTB7 device was measured during three consecutive days.

1 10 100 1000

0,60

0,62

0,64

0,66

0,68

0,70

0,72

0,74

0,76

FF

I (W/m2)

Day 1

Day 2

Day 3

1 10 100 1000

0.50

0.55

0.60

0.65

0.70

0.75

Voc (V

)

I (W/m2)

Day 1

Day 2

Day 3

1 10 100 1000

0,1

1

10

100

Jsc (A

/m2)

I (W/m2)

Day 1

Day 2

Day 3

49

Figure 5.13 shows that the fill factor is indeed the parameter that better represents the

degradation of the device. Actually, the slopes obtained during the three consecutive

days ( =1.02, 1.03 and 0.88 respectively)4 and (s* =0.92, 1.08 and 0.98 respectively) do

not present a significant change. When the sample is measured for the first time it shows

a zig zag behavior that disappears when the sample is measured again.

Devices measured with method 2 showed higher values of FFs and power efficiencies

than the same devices measured with method 1. To clarify this discrepancy, we

compare results of PTB7 devices using CB/Dio as a solvent, measured with the two

mentioned methods. The experiments were done at room temperature. Different solution

concentrations were tested. This is shown in figure 5.14.

a) b)

Figure 5.14.a: Jsc-vs. I curves. Figure 5.14.b: Voc vs. I curves. Four different concentrations of

PTB7 and two different methods of measurement are presented. The measurements are

performed at room temperature.

Figure 5.14.a shows that the Jsc-vs. I curves do not change their behavior with respect to

the method or the concentration employed. In figure 5.14.b we observe that the Voc vs. I

curves do change according to the method of measurement, not due to the

concentration. Taking into account light intensities between 100 – 1000 W/m2, a slope s*

4 The given slopes and s* correspond to light intensities between 100 and 1000 W/m2.

10 100 1000

1

10

100

PTB7 concentration

Method 1:

14 mg/ml

10 mg/ml

Method 2:

16 mg/ml

7 mg/ml

Jsc (A

/m2)

I (W/m2)

1 10 100 1000

0,50

0,55

0,60

0,65

0,70

0,75

PTB7 concentration

Method 1:

14 mg/ml

10 mg/ml

Method 2:

16 mg/ml

7 mg/ml

Vo

c (V

)

I (W/m2)

50

~1.23 is obtained for devices measured with method 1 and s* ~0.92 with method 2. This

suggests that a loss mechanism competing with bimolecular recombination is acting on

devices measured from high to low intensities.

The FF vs. I curves given in figure 5.14.c show the most notorious difference. When we

measure with method 2 the values of the fill factor increase. Also, the FF vs. I trend is

steeper between 100 to 1000 W/m2 and irregular at low light intensities.

c)

Figure 5.14.c: FF vs. I curves. Four different concentrations of PTB7 and two different methods of

measurement are presented. The legend shows that the thicknesses of the devices are similar.

All the measurements are performed at room temperature.

The concentration of PTB7 affects the device performance when samples are measured

with method 1. In this case, devices fabricated using a concentration of 10 mg/ml of

PTB7 showed the optimal performance. Their values of current, Voc, FF and the power of

the cells were higher than for the rest of the devices, even from devices using a

concentration of 7 mg/ml of PTB7. Figure 5.14.c demonstrates that the concentration of

PTB7 used does not affect the performance of the device when it is measured using

method 2.

1 10 100 1000

0.58

0.60

0.62

0.64

0.66

0.68

0.70

0.72

0.74

0.76

PTB7 concentration

Method 1:

14 mg/ml (117 nm)

10 mg/ml (114 nm)

Method 2:

16 mg/ml (135 nm)

7 mg/ml (117 nm)

FF

I (W/m2)

51

Conclusions In this chapter the main conclusions are described. The future research steps are

presented in the outlook.

This research proves that the fill factor of polymer:fullerene bulk heterojunction

OSCs can be investigated as a function of the bimolecular

recombination/extraction ratio θ. Computational simulations performed by this

group predicted a particular trend in the FF-θ curve. Experimental results

successfully reproduced this trend.

The predicted trend of FF-θ curve represents the dominance of bimolecular

recombination over any other recombination mechanism acting on OSCs. The

FF-θ curve seems as a promising method to identify and understand efficiency

and recombination in organic solar cells. For instance, this must lead to further

optimization of the devices.

PTB7:PC70BM devices using CB as a solvent showed two behaviors, at low and

high light intensity, i.e., the results match the expected trend at high light

intensities and it deviates from it at low intensities. This fact is not in

disagreement with our theory. It simply expresses the presence of another

recombination mechanism acting on the devices. We consider that traps are

assisting the recombination of free charges at low light intensities.

An organic solar cell can have a different behavior according to the regime of

light intensity used for the measurements. This difference is notorious in the

values of slopes of Voc vs. ln(I). For PTB7:PC70BM devices, the difference is

remarkable. For high light intensities, the slope s* ~kT/q and s*>1.4kT/q at low

light intensities. These results apply when the measurements are performed

starting from low to high light intensities. Otherwise, also at high light intensities

s*>1.4kT/q.

6

52

6.1 Outlook

Our next step is to investigate how the morphology of OSCs can influence

bimolecular recombination. The FF-θ curve will be used to identify the dominant

recombination process.

The parameter θ can serve as an example to investigate and derive a similar

parameter, which describes the dominance of trap assisted recombination. In this

way, we will be able to identify a particular trend in the FF- θ curve for a lower

order of recombination. In addition, it is needed to identify which are the common

characteristics of OSCs devices that make them be dominated by one

recombination mechanism or the other.

The instability of the PTB7:PC70BM devices contrasts with their high efficiencies.

It is needed to provide an explanation of the fast degradation of PTB7:PC70BM

devices and its relation to recombination. The challenge is to unifying efficiency,

stability and process for the same device.

Other methods to identify bimolecular recombination in organic solar cells must

be investigated; this can require an interdisciplinary effort. In order to have a

complete understanding of the recombination mechanisms acting on organic

solar cells, it is needed to investigate other recombination processes in

polymer:fullerene OSCs, like exciton recombination, geminate polaron pairs

recombination and surface recombination.

53

Appendix

A.1 Double carrier mobilities μD (m2/Vs)

PTB7 :PC70BM 1:1.5

(*): Devices measured with method 2.

Solvent: CB (m2/Vs)

T 124 nm 136 nm (*) 177 nm

295 K 5.00E-07 3.20E-07 5.00E-07

255 k 1.50E-07 X 1.50E-07

215 k 4.50E-08 X 4.50E-08

Solvent: CB/Dio PTB7 14 mg/ml (m2/Vs)

T 78 nm 117 nm 121 nm 158 nm

295 K 1.20E-07 4.30E-07 4.50E-07 3.90E-07

255 k 6.50E-08 1.50E-07 1.00E-07 1.20E-07

215 k 2.20E-08 5.80E-08 4.00E-08 2.80E-08

Solvent: CB/Dio PTB7 10 mg/ml (m2/Vs)

T 101 nm (*) 114 nm 116 nm

295 K 4.20E-07 4.30E-07 6.00E-07

255 k x 2.30E-07 2.20E-07

215 k x 5.00E-08 4.00E-08

Solvent: CB (m2/Vs)

T 84 nm (*) 116 nm

295 K 2.40E-07 5.00E-07

255 k X 2.50E-07

215 k X 7.00E-08

54

PDPP5T:PC70BM, 1:1

(m2/Vs)

T 81 nm 94 nm 107 nm 117 nm 127 nm 147 nm (ratio 1:1.5) 178 nm 203 nm

295 K 5.2E-07 6.4E-07 X 5.0E-07 6.0E-07 3.5E-06 5.0E-07 3.8E-07

255 k 4.6E-07 4.6E-07 3.6E-07 2.0E-07 2.0E-07 1.6E-06 1.7E-07 1.2E-07

215 k 1.4E-07 2.0E-08 9.8E-08 4.0E-08 5.7E-08 9.8E-08 4.6E-08 2.6E-08

A.2 Hole mobilities μh (m2/Vs)

PTB7:PC70BM, 1:1.5

CB/Dio

(m2/Vs)

CB/Dio

(m2/Vs)

CB

(m2/Vs)

oDCB

(m2/Vs)

T PTB7 10 mg/ml PTB7 14 mg/ml

295 k 1.00E-08 6.00E-08 5.40E-08 3.80E-08

255 k 5.00E-09 1.40E-08 1.10E-08 1.40E-08

215 k 8.00E-10 1.00E-09 3.10E-09 3.80E-09

PDP5T :PC70BM, 1:1

A.3 Electron mobilities μe (m2/Vs)

PTB7 :PC70BM CB/Dio

(m2/Vs)

CB/Dio

(m2/Vs)

CB

(m2/Vs)

oDCB

(m2/Vs)

T PTB7 10mg/ml PTB7 14mg/ml

295 k 1.00E-08 1.00E-08 8.00E-08 5.20E-08

255 k 9.00E-09 7.00E-09 3.60E-08 3.40E-08

215 k 5.00E-09 2.00E-09 1.50E-08 1.40E-08

T h (m2/Vs)

295 K 2.70E-07

255 k 8.80E-08

215 k 1.40E-08

55

PDDP5T :PC70BM, 1:1

A.4 Jsc, Voc, FF at 1 Sun.

The value of Jsc measured at room temperature in the solar simulator set up was

approximately 10% higher than the value of Jsc measured in the EQE set up. We do not

perform measurements in the EQE set up at different temperatures. Therefore, we show

the measurements obtained in the solar simulator.

PTB7 :PC70BM, 1:1.5

Solvent: CB, thickness 124 nm.

T Joc (A/m2) Voc (V) FF

295 K 103.9 0.757 0.512

255 k 88.4 0.802 0.472

215 k 67.6 0.858 0.408

Solvent: oDCB, thickness 116 nm.

T Joc (A/m2) Voc (V) FF

295 K 133.6 0.741 0.576

255 k 121.8 0.794 0.499

215 k 99.4 0.857 0.419

T e (m2/Vs)

295 K 1.10E-08

255 k 1.40E-09

215 k 9.20E-11

56

Solvent: CB/Dio, PTB7 16 mg/ml, thickness 117 nm (*).

T Joc (A/m2) Voc (V) FF

295 K 148.6 0.722 0.669

255 k 143.9 0.775 0.62

215 k 134.1 0.832 0.475

Solvent: CB/Dio, PTB7 14 mg/ml, thickness 121 nm.

T Joc (A/m2) Voc (V) FF

295 K 143.1 0.701 0.636

255 k 129.13 0.742 0.49

215 k 117.55 0.812 0.425

Solvent: CB/Dio, PTB7 10 mg/ml, thickness 116 nm.

T Joc (A/m2) Voc (V) FF

295 K 151.7 0.708 0.677

255 k 143.9 0.771 0.623

215 k 131.2 0.826 0.494

Solvent: CB/Dio, PTB7 7 mg/ml, thickness 135 nm (*).

T Joc (A/m2) Voc (V) FF

295 K 153.8 0.714 0.682

255 k 147.5 0.77 0.622

215 k 130.2 0.825 0.457

57

PDP5T :PC70BM, 1:1

T: 295 K

Thickness (nm) Joc (A/m2) Voc (V) FF

81 67.9 0.533 0.582

94 78.4 0.536 0.589

107 141.7 0.565 0.576

117 137.8 0.553 0.482

127 130.44 0.556 0.46

147 (ratio 1:1.5) 175.1 0.537 0.659

178 107 0.543 0.377

203 79 0.566 0.352

T: 255 K

Thickness (nm) Joc (A/m2) Voc (V) FF

81 63.29 0.586 0.557

94 74.2 0.589 0.561

107 130.7 0.621 0.527

117 122 0.605 0.462

127 116 0.603 0.454

147 (ratio 1:1.5) 164.1 0.595 0.639

178 92 0.592 0.355

203 65.6 0.624 0.315

58

T: 215 K

Thicness (nm) Joc (A/m2) Voc (V) FF

81 59.2 0.64 0.513

94 68.4 0.638 0.521

107 115.1 0.678 0.472

117 93.400 0.660 0.394

127 85.7 0.66 0.393

147 (ratio 1:1.5) 151.22 0.654 0.529

178 61.8 0.647 0.301

203 36.81 0.675 0.286

59

References

[1] U. Albrecht and H. Bässler, Chem. Phys. 199, 207 (1995).

[2] H. Bässler, Charge transport in disordered organic photoconductors, Physical Status Solidi B,

Volume 175, Pages 15-56 (1993).

[3] J. C. Blakesley, F. Castro, W. Kylberg, G. F. A. Dibb, C. Arantes, R. Valaski, M. Cremona, J.

S. Kim and J. Kim, Organic Electronics, Volume 15, 1263 (June 2014).

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

[5] P. W. M. Blom, V. D. Mihailetchi, L. J. A. Koster, and D. E. Markov, Adv. Mater. 19, 1551

(2007).

[6] P. A. Bobbert, T. D. Nguyen, F. W. A. van Oost, B. Koopmans, and M. Wohlgenannt, Phys.

Rev. Lett. 102, 156604 (2007).

[7] C.L. Braun, J. Chem. Phys. 80, 4157 (1984).

[8] J. J. Brondijk, W. S. C. Roelofs, S.G. J. Mathijssen, A. Shehu, T. Cramer, F. Biscarini, P. W.

M. Blom and D. M. de Leeuw, Phys. Rev. Lett. 109, 056601 (2012).

[9] 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).

[10] N.I. Cracium, J. Wilderman and P.W.M. Blom, Phys. Rev. Lett. 100, 056601 (2008).

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

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

[13] A. M. Goodman and A. Rose, J. Appl. Phys. 42, 2823 (1971).

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

[15] R. N. Hall, Phys. Rev. 83, 228 (1951); ibid. 87, 387 (1952).

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

60

[17] G. Juška, K. Arlauskas, J. Stuchlik, and R. Österbacka, J. Non-Cryst. Solids 352, 1167

(2006).

[18] N. J. van der Kaap, Electron-transport layers in organic light-emitting diodes, Master’s thesis,

University of Groningen (2011).

[19] K. C. Kao and W. Hwang, Electrical Transport in Solids l, Pergamon Press, Oxford, U.K.

(1981).

[20] L. J. A. Koster, E. C. P. Smits, V. D. Mihailetchi and P. W. M. Blom, Phys. Rev. B 72, 085205

(2005).

[21] L. J. A. Koster, V. D. Mihailetchi, R. Ramaker, and P. W. M. Blom, Appl. Phys. Lett. 86,

123509 (2005).

[22] L. J. A. Koster, V. D. Mihailetchi, H. Xie and P. W. M. Blom, Appl. Phys. Lett. 87, 2 (2005).

[23] L. J. A. Koster, Device physics of donor/acceptor-blend solar cells, PhD thesis, University of

Groningen, The Netherlands (2006).

[24] J.D. Kotlarksi, Optical and electrical modeling of polymer:fullerene bulk heterojunction solar

cells, PhD thesis, pages 61-62, University of Groningen, The Netherlands (2012).

[25] M. Kuik, L. J. A. Koster, G. A. H. Wetzelaer, and P. W. M. Blom, Phys. Rev. Lett. 107,

256805 (2011).

[26] P. Langevin, Ann. Chim. Phys. 28, 433 (1903).

[27] M. Lenes, L. J. A. Koster, V. D. Mihailetchi and P. W. M. Blom, Appl. Phys. Lett. 88, 24

(2006).

[28] M. Lenes, S. W. Shelton, A. B. Sieval, D. F. Kronholm, J. C. Hummelen, and P. W. M. Blom,

Adv. Funct. Mater. 19, 3002 (2009).

[29] D. R. Lide and ed., CRC Handbook of Chemistry and Physics (86th ed.), Boca Raton, U.S.A.

(2005).

[30] Y. Liang, Z. Xu, J. Xia, S.T. Tsai, Y. Wu, G. Li, C. Ray and L. Yu, Adv. Mater. 2010, 22,

E135-E138 (2010).

[31] L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press

(1995).

61

[32] M. M. Mandoc, F. B. Kooistra, J. C. Hummelen, B. de Boer, and P. W. M. Blom, Appl. Phys.

Lett. 91, 263505 (2007).

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

[34] T. McGlynn, Nat. Edu. Know. 3, 10 (2010).

[35] 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).

[36] V. D. Mihailetchi, L. J. A. Koster, J. C. Hummelen and P. W. M. Blom, Phys. Rev. Lett. 93,

216601 (2004).

[37] V. D. Mihailetchi, J. Wildeman and P. W. M. Blom, Phys. Rev. Lett. 94, 126602 (2004).

[38] V. D. Mihailetchi, H. Xie, B. de Boer, L. J. A. Koster and P. W. M. Blom, Adv. Funct. Mater.

16, 699-7 (2006).

[39] A. Miller and E. Abrahams, Phys. Rev. 120, 745 (1960).

[40] N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals, Oxford University Press,

London, U.K. (1940).

[41] N. F. Mott, Canadian J. Phys. 34, 1356 (1956).

[42] N. F. Mott, Electronic processes in non-crystalline materials, Oxford University Press,

London, U.K. (1979).

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

[44] C. R. Newman, C. D. Frisbie, J. L. Bedras, P. C. Ewbank and K. R. Mann, Chem. Mater. 16,

4436 (2004).

[45] H. T. Nicolai, M. Kuik, G. A. H. Wetzelaer, B. de Boer, C. Campbell, C. Risko, J. L. Brédas

and P. W. M. Blom, Nat. Mater. 11, 882 (2012).

[46] R. H. Parmenter and W. Ruppel, J. Appl. Phys. 30, 1548 (1959).

[47] D. M. Pai and B.E. Spingett, Rev. Mod. Phys. 65, 163 (1993).

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

[49] M.C. Petty, Molecular electronics: from principles to practice, Wily-Interscience, Weinheim,

Germany D, (2008).

62

[50] C. Piliego and M.A. Loi, J. Mater. Chem. 22, 4141 (2012).

[51] A. Pivrikas, G. Juška, R. Österbacka, W. Westerling, M. Viliunas, K. Arlauskas and H. Stubb,

Phys. Rev. B. 71, 125205. (2005).

[52] V. Shrotriya, G. Li, Y. Yao, T. Moriarty, K. Emery and Y. Yang, Adv. Funct. Mater. 16, 2016–

2023 (2006).

[53] W. Shockley and W. T. Read, Phys. Rev. 87, 835(1952).

[54] S.M. Sze, Physics of semiconductor devices, Wily-Interscience, Weinheim, Germany (1981).

[55] W. Shockley and W. T. X. Read, Phys. Rev. 87, 835 (1952).

[56] Y. W. Soon , H. Cho , J. Low , H. Bronstein , I. McCulloch and J. R. Durrant, Chem.

Commun. 49, 1291-1293 (2013).

[57] K. Tvingstedt, K. Vandewal, A. Gadisa, F. Zhang, J. Manca, and O. Inganas, J., Am. Chem.

Soc. 131, 11819 (2009).

[58] G. J. A. Wetzelaer, Charge transport and recombination in Organic-Semiconductor Diodes,

PhD thesis, University of Groningen, The Netherlands (2014).

[59] G-J. A. Wetzelaer, Van der Kaap, N. J., Koster, L., and P.W. Blom, Adv. Energy Mater. 3,

Issue 9, 1130 (2013).

[60] G. A. H. Wetzelaer, M. Kuik, M. Lenes, and P. W. M. Blom, Appl. Phys. Lett. 99, 153506

(2011).

[61] G. A. H. Wetzelaer, M. Kuik, H. T. Nicolai, and P. W. M. Blom, Phys. Rev. B 83, 165204

(2011).

[62] S. H. W. Wouters, Magnetic field effects in the current and electro-luminescence of OLEDs.

Expanding our view, Master’s thesis, Eindhoven University of Technology (2012).

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

63

Acknowledgments

First of all, dear reader, if you enjoyed reading this thesis, then you should join me in

thanking my supervisors Jan Anton Koster, Rene Jansen and Davide Bartesaghi, for their

constant and inconstant supervision, for doing and not doing the dirty work, which finally resulted in a

pleasant lecture for you. I particularly appreciate the opportunity that Jan Anton gave me to be part of his

team, his elegance and precision for talking; Davide for his patience and the friendship we developed and

Rene for his facility to smile (also, what a mastery of the detail!).

As any common person, I thank my parents, family and friends even if they did not do anything

with respect to this experimental work (well, Bart did, he gave me a hole to fall into every time I go to

Eindhoven). (Of course, Conchita 1- Cadivi 0). Anyway, distracting me from work is also part of the work.

I want to thank all that people in science that beyond all the (**) make me remember

that Physics is beautiful and it worth the shame. In Eindhoven, Paul van del Schoot (god

damn yeah), Kees Flipse and Bert Koopmans.

Ms. Mirjam Hagoort and Ms. Patricia Veling from the international office of the TU/e must be

definitely included. Last year I honestly thought I was not going to make it if it wouldn’t be for their support.

Now you have no doubts of how (ridiculously) thick the word ‘bureaucracy’ can be!

I thank Gert Jan Antonius Wetzelaer for writing such a cool thesis, moreover, that children’s story

we wrote in the air during our lunch breaks made me very happy.

Finally I want to thank my beloved boyfriend Wout, for obvious reasons. Also, for the not so obvious ones.

To begin with, his gravity attracted me to Groningen. To end, his gravity will push me away from Groningen.

This master project helped me to keep in touch with a different reality than the one we are living

now in my native land. I dedicate this thesis to my university, la simón. To all those students who

have been arrested or are currently in jail, those teachers who blablabla and well, this is the part I must be

poetic and say something positive about the future. Blank space. Latin America is so wonderful!. People

fight this situation with a very light and satirical sense of humor. Also, I dedicate this thesis to that

crazy little thing inside me that forced me to change my life and start studying physics, when I did not

have neither the qualities or the … naivety?. But that is another story. Let us better print one less page, you

know, save a sheet, save a tree, save the world.