Photogeneration and dynamics of charge carriers in the conjugated polymer poly(3-hexylthiophene)

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Photogeneration and dynamics of

charge carriers in the conjugated

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Cover: Extended stretched-exponential (Kohlrausch) relaxation formula, in-cluding second-order processes, see Chapter 7.

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Photogeneration and dynamics of

charge carriers in the conjugated

polymer poly(3-hexylthiophene)

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op 5 november 2004 om 13.00 uur

door

Gerald DICKER

Diplomingenieur in de natuurkunde geboren te Gmunden, Oostenrijk

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Dit proefschrift is goedgekeurd door de promotor: Prof. dr. Laurens D. A. Siebbeles

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. dr. L. D. A. Siebbeles Technische Universiteit Delft, promotor

Dr. M. P. de Haas Technische Universiteit Delft, toegevoegd promotor Prof. dr. ir. T. M. Klapwijk Technische Universiteit Delft

Prof. dr. S. J. Picken Technische Universiteit Delft Prof. dr. ir. R. A. J. Janssen Technische Universiteit Eindhoven Prof. dr. ir. P. W. M. Blom Rijksuniversiteit Groningen

Dr. D. M. de Leeuw Philips Natuurkundig Laboratorium

Dr. John M. Warman heeft als begeleider in belangrijke mate aan de tot-standkoming van het proefschrift bijgedragen.

Published and distributed by: DUP Science DUP Science is an imprint of

Delft University Press P.O. Box 98 2600 MG Delft The Netherlands Telephone: +31 15 2785678 Fax: +31 15 2785706 E-mail: info@Library.TUDelft.nl isbn 90-407-2542-X

Keywords: photoconductivity, photoemission, disperse kinetics, conjugated polymer, poly(3-hexylthiophene), thin film, flash-photolysis, pulse-radiolysis, microwave detection

Copyright c 2004 by G. Dicker

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the publisher: Delft University Press.

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Introduction

1.1 Relevance and motivation

Electronic, optoelectronic and solar-energy devices based on organic semicon-ductors are being developed in the R&D departments of multi-national and various start-up companies in the electronic industry sector. Some products are already commercially available and many others are expected to follow [1]. The attractiveness of using organic materials as the active material in semiconductor devices is due to the following properties: low-cost processing, mechanical flexibility, light weight and color-tunability. At present, the most promising applications for organic semiconductors include active full-color displays1_{[2, 3, 4], plastic electronic circuits [5, 6, 7], and solar cells [8].}

Organic semiconductors are made up of molecules which consist mainly of carbon and hydrogen atoms, held together by covalent bonds, and the individual molecules are being held together by van der Waals forces. The molecules in an organic semiconductor can be found arranged in a perfectly regular manner (single-crystal) to completely disordered (amorphous). A spe-cial state of condensed matter is liquid crystallinity, being between that of a crystalline solid and an isotropic liquid. Certain organic semiconductors com-prised of disk-shaped organic molecules have been found to possess such a state.

A very important class of organic semiconductors are conjugated polymers. They consist of chain-like molecules made up of many, tens to thousands, identical repeat units, which have alternating single and double (or triple) bonds between the carbon atoms. The alternating bonds provide the pathway for charge transport along such a chain. The chemical structures of some important conjugated polymers are shown in Fig. 1.1. If hydrocarbon side

1_{see for example www.research.philips.com}

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2 1. Introduction R R _R 2 R1 S R R1 R2 R R PDA PPP PT PPV PF CH3 R1 R1 CH3 R2 R2 MeLPPP S R PTV n n n n n n n

Figure 1.1: Chemical structures of some of the most important conjug-ated polymers, including in the top of the figure a sketch of the singly occu-pied pz-orbitals that provide the pathway for charge transport along a con-jugated chain of carbon atoms. (To each carbon atom a hydrogen atom is bonded but these are not shown for clarity.) PDA = polydiacetylene, PPP = polyparaphenylene, PT = polythiophene, PPV = polyphenylenevinylene, PF = polyfluorene, PTV = polythienylenevinylene, MeLPPP = methyl-substituted ladder-type polyparaphenylene, R = solubilizing side chain.

chains are added to the backbone (denoted as R in Fig. 1.1), conjugated polymers can be dissolved in organic solvents. The solution-processability permits cost-effective production of semiconductor devices.

A very important conjugated polymer is regioregular poly(3-hexylthio-phene) (RR-P3HT) because it has been found to conduct charge at a much higher speed than other conjugated polymers. Field-effect mobilities of up to 0.2 cm2/Vs [9] have been measured, which starts to rival charge transport in amorphous silicon. The chemical structure of RR-P3HT is shown in Fig. 1.2. The term “regioregular” refers to the position of the hexyl side chain, which can be connected to the thiophene ring at two different sites. If it is always connected at the same position (“head-to-tail-head-to-tail” coupling) then it is

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1.1 Relevance and motivation 3 S C6H13 S S C6H13 C6H13 head tail n / 3

Figure 1.2: Chemical structure of head-to-tail-head-to-tail coupled regiore-gular poly(3-hexylthiophene). S S S S S interc hain tr_anspo rt

intrachain tra nsport

Figure 1.3: Sketch of a self-assembled domain in RR-P3HT. Two-dimensional charge transport takes place in the charge-transporting lamella, which extends in the direction of the polymer chain and perpendicular to the planes in which the individual chains lie. The hexyl side chains act as insulators between the charge-transporting lamellea.

capable of forming lamella-like nanometer-sized crystals, in which inter-chain charge transport is much more efficient than between randomly assembled chains. A sketch of the lamellar arrangement is shown in Fig. 1.3. In the ordered lamellar domains of RR-P3HT, appreciable interchain interaction ex-ists, which leads to a splitting of the electronic levels of the individual chains. This introduces new optical absorption bands in the photoinduced absorption [10] as compared to regiorandom P3HT and confirms the delocalization of the charge carriers in two dimensions.

It is not only of fundamental interest but also of technological relevance to unravel the mechanism of charge carrier photogeneration in P3HT. A highly debated issue is whether charge carriers are created directly upon the absorp-tion of a photon or if an intermediate state (exciton) is formed, which can

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sub-4 1. Introduction

sequently decay into an electron-hole pair. The fraction of photons absorbed that lead to the formation of charge carriers is termed the quantum yield of charge carrier photogeneration. The wavelength dependence of the quantum yield gives insight into the mechanism of charge carrier photogeneration and it determines the spectral sensitivity of an optoelectronic device. Further questions arise naturally, such as: Is the quantum yield solely determined by the chemical structure of the polymer and therefore a constant material para-meter or is it also dependent on other factors, such as the molecular order? What is the role of chemical impurities in the charge carrier photogeneration? What are the interactions between the photogenerated species and how do they affect the spectral dependence of the charge carrier yield?

For P3HT, most of the aforementioned issues have not been investigated previously or only data exist that were derived from measurements in device configurations. In such measurements, metallic electrodes and DC electric fields are applied to the polymer layer, which influence the photoconductive properties and complicate the interpretation of the data in terms of the in-trinsic properties of the polymer. In addition, we have shown at the start of this thesis project [11] that electrons photoejected from the polymer surface can make a large contribution to the measured conductivity if no precautions are taken (see Fig. 1.4). Because of these potential complications, consider-able uncertainty existed in the literature as to the spectral dependence, the efficiency, and the limiting factors of intrinsic charge carrier photogeneration in P3HT (and many other conjugated polymers).

In this thesis, we address the above mentioned issues using an electrode-less, high-frequency, low-field technique, the Flash-Photolysis Time-Resolved Microwave Conductivity (FP-TRMC) technique, which circumvents the prob-lems that are associated with conventional DC techniques. The FP-TRMC technique has been used previously to study the optoelectronic properties of molecules in solution. For the present work, the technique has been adapted to the study of polymer thin films. In addition, we perform measurements using the closely related Pulse-Radiolysis Time-Resolved Microwave Conduct-ivity (PR-TRMC) on bulk samples of P3HT. The combination of the results from both measurements allows us to derive absolute values for the photo-generation quantum yield and its activation energy. From an analysis of the charge carrier decay kinetics, we derive a generalized version of the stretched-exponential (Kohlrausch) decay law for the diffusive recombination of charge carriers. Comparison of the decay kinetics observed with PR-TRMC and FP-TRMC, provides further information about the recombination processes of the photogenerated electrons and holes.

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1.2 Principle of π-conjugation 5

polymer light

electron

Figure 1.4: The photoelectron emission artifact in photoconductivity meas-urements. The photocurrent has contributions from the photogenerated charges within the polymer layer and electrons photo-ejected from the poly-mer surface traveling outside the polypoly-mer sample (as sketched). Although the quantum yield of photoemission is low, the photoelectron contribution to the photocurrent can be considerable because of the high gas-phase mobility of the electrons.

1.2 Principle of π-conjugation

Conjugated polymers owe their name to the bonding type between adjacent carbon atoms along the polymer backbone. Let us consider the structurally simplest conjugated polymer, polyacetylene, which consists of a chain of car-bon atoms (see top of Fig. 1.1). The atomic orbitals of the carcar-bon atoms in a conjugated polymer can be considered as hybridized, meaning that the 2s orbital is linearly combined with the 2p orbitals to form new orbitals. In the case of polyacetylene and most other conjugated polymers, the 2s orbital mixes with the 2px and the 2py orbitals to form three energetically equival-ent sp2 _{orbitals, located in the corners of an equilateral triangle. These are} responsible for the so-called σ-bonding to the three neighbors (at least two of which are also carbon atoms). The fourth electron resides in the unaffected 2pzorbital, which is oriented perpendicular to the molecular plane (see top of Fig. 1.1). The 2pzorbitals of all carbon atoms are linearly combined to form the so-called π molecular orbitals, which are delocalized along the polymer chain and are involved in the transport of charge. The π-orbitals are half-filled with electrons since two electrons of opposite spin per carbon atom can be accommodated. On basis of this, an infinitely long chain of polyacetylene would be expected to be a one-dimensional metal, having a half-filled band.

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6 1. Introduction

This is however not observed because of Peierls distortion [12]. As a con-sequence, the bond lengths between neighboring carbon atoms are unequal (indicated as single and double bonds in Fig. 1.1) and the band is split into a fully occupied, π, valence band and an empty, π∗, conduction band with an energy gap of 1.5 eV between them.

1.3 Historical development of conjugated

poly-mers

In its pristine form, polyacetylene is nonconducting because the bandgap is too large for thermal excitations of electrons from the valence to the conduction band. In 1976, Alan MacDiarmid, Hideki Shirakawa, and Alan J. Heeger discovered that polymers can be chemically doped to reach the metallic state [13], for which they were awarded the Nobel Prize in Chemistry in 2000. The metallic state was shown originally for polyacetylene by exposing it to iodine. Chemical doping is achieved by a redox-reaction whereby electrons are transferred from polyacetylene to iodine, or in solid state terminology, holes are injected into the valence band of polyacetylene, thereby creating a half-filled band at high doping levels, and hence metallic conductivity.

The first conducting polymers, including polyacetylene, were neither pro-cessable nor chemically stable in atmospheric conditions. Industrial interest rose when environmentally stable conjugated polymers were synthesized that could be processed from solution. Solution processability is usually achieved by introducing alkyl or alkoxy side chains. A thin film can then be made by spinning the polymer solution on a substrate. After evaporation of the solvent, a homogeneous thin film remains on the substrate.

A real boost to the field of conjugated polymers was the demonstration of the first polymer light-emitting diode (LED) [14] in 1990 by Richard Friend and co-workers. The active layer of this device was PPV, which was obtained by in-situ conversion of a solution-processable precursor. In such a device, the generation of light is achieved by the radiative recombination of electrons and holes injected into the polymer. Holes are injected from an electrode consisting of a metal whose workfunction matches the energetic position of the valence band of the polymer. Likewise, electrons are injected from another electrode whose workfunction matches the energetic position of the conduction band of the polymer.

The reverse process, efficient conversion of light into electricity, requires the addition of an electron-accepting molecule with appropriate energy levels. This was shown for a mixture of a PPV-derivative and buckminsterfullerene (C60) [15]. Upon the absorption of light by PPV, an ultrafast electron trans-fer (within 50 fs) to C60 takes place. Under appropriate mixing conditions,

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1.4 Charge carrier generation 7

interpenetrating networks are formed, such that the electron is transported away along the C60network and the hole along the PPV network [16].

By exciting a fluorescent conjugated polymer (PPV) in a microcavity using high laser intensities, optically driven laser activity was shown in 1996 [17]. This is a pre-requisite for developing (electrically driven) solid-state lasers based on conjugated polymers. The realization of such a laser still remains a challenge to the field.

In digital electronic circuits, field-effect transistors (FETs) are used as logical switches. By varying the voltage at the gate contact, the current between the source and drain contacts can be switched on and off. The development of electronic circuits based on conjugated polymers started with the first demonstration of the field effect in polyacetylene in 1983 [18] and the first working polymer FET in 1986 [19], which contained polythiophene. The polythiophene layer in this device was obtained by in-situ electrochemical polymerization and a charge carrier mobility of only 10−5 cm2_{/Vs was found.} A major breakthrough [20] was the demonstration of an FET with a high charge carrier mobility, of 0.045 cm2/Vs, based on solution-cast RR-P3HT. An integrated optoelectronic device consisting of an RR-P3HT FET and an MEH-PPV LED was subsequently fabricated [21]. The high charge carrier mobility in RR-P3HT is ascribed to the self-ordering properties, resulting in nanometer-sized lamellea, as sketched in Fig. 1.3. The two-dimensional nature of charge transport [22, 10] within these lamellea was investigated using various spectroscopic techniques. In the meantime, the performance of FETs based on RR-P3HT was further improved, with a current record mobility of 0.2 cm2_{/Vs [9].}

A recent breakthrough [23] in the development of CMOS (complimentary metal-oxide-semiconductor) electronic circuits was the discovery of ambipolar charge transport in polymer FETs. One type of ambipolar FET is based on an interpenetrating network of a hole transporting polymer (PPV derivative) and an electron transporting molecule (C60derivative). Another type of ambipolar FET consists of a single polymer, with a narrow bandgap, in which both holes and electrons are mobile.

1.4 Charge carrier generation

A defect-free, chemically pure conjugated polymer would contain almost no free charge carriers at room temperature since the energetic gap between the valence band and the conduction band is typically a hundred times the thermal energy and thermal excitation of electrons into the conduction band is therefore negligible. The charge carriers present in a conjugated polymer are almost entirely due to chemical impurities that lead to doping, whereby an electron is transferred from the polymer to the impurity or defect site,

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8 1. Introduction

S D

G I

P

Figure 1.5: Sketch of a (bottom-contact) polymer field-effect transistor. P = polymer, S = source, D = drain, I = insulator, G = gate.

leaving behind a mobile hole on the backbone of the conjugated polymer (p-type doping).

In an atmospheric environment, oxygen diffuses into the polymer and a (reversible) electron transfer from the polymer to oxygen can occur, thereby further increasing the hole doping concentration. As was shown by Heeger et al. using iodine [13], this hole doping concentration can be increased to reach a metallic state. This is termed ‘chemical doping’ and the number of charge carriers created is determined by the amount of electron accepting molecules added to the polymer. The dopant concentration can be further controlled by applying a voltage difference between the polymer and a counter electrode (e.g. Li) in an electrochemical cell (electrochemical doping).

For semiconductor applications, a variable conductivity is required. This is realized in a field-effect transistor [24] (see Fig. 1.5). Charges are injected into the polymer from the source (S) and drain (D) contacts, which ideally form ohmic contacts with the polymer. The number of charges injected at the S-P and D-P interfaces is controlled by the gate (G) voltage (= field-effect). If a negative voltage is applied at the gate, holes are injected and accumulated at the polymer-insulator (P-I) interface (= conductive channel). A voltage drop across source and drain will now result in an increased source-drain current through the channel.

Charge carriers in a conjugated polymer can also be generated by the absorption of light. There existed some controversy in the literature [25] as to whether free charge carriers are generated immediately upon the absorption of a photon. Most experiments confirm that this is not the case [26, 27]. Instead, an excited state (exciton) is formed with electron and hole being close to each other (on the same molecule or on adjacent molecules) and only much less than one percent of the excitons decay into charge carriers in most conjugated polymers. Typically, the electrical current generated by the absorption of light is measured in a thin-film device configuration (Fig. 1.6), consisting of two electrodes between which the polymer layer is sandwiched. The presence of electrodes and DC electric fields generally enhances the photogeneration yield in such devices [28, 29].

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ex-1.4 Charge carrier generation 9 L P CB E F E F H L H VB P

Figure 1.6: Left: Sketch of a sandwich DC photocurrent setup consisting of a transparent low-workfunction electrode (L), the polymer layer (P), and a high-workfunction electrode (H). The diode is reversely biased and the current generated by the absorption of light (entering from the left) is measured. Right: Simplified band structure diagram. EF= Fermi level of the metal, CB = conduction band of the polymer, VB = valence band of the polymer. Upon the absorption of a photon, an electron-hole pair (or an exciton) is formed. The electric field drags the electron to the anode and the hole to the cathode. Since in most conjugated polymers, the electron is trapped or immobile and would therefore not reach the anode, only a thin layer close to the anode is photoactive. If illumination is carried out from the cathode (right-hand) side, only weakly absorbed light, capable of penetrating to the photoactive layer, generates a photocurrent.

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10 1. Introduction CB VB (a) CB VB (b) (1) (2)

Figure 1.7: Double-quantum processes occurring at high laser intensities. (a) Sequential excitation of an exciton. (b) Exciton annihilation, whereby the energy of the annihilated (left) exciton leads to a highly excited state of the other exciton (1) or is dissipated (2). Note that the band structure diagrams shown are idealized representations.

cited states or from the sequential excitation of an excited state by a second photon can influence the charge carrier yield. These effects will be shown to have a pronounced effect on the photoemission and bulk photogeneration of charges in RR-P3HT in Chapters 3, 4 and 6. In Fig. 1.7, these processes are schematically depicted.

In addition to the aforementioned processes, chemical impurities can play a role in the photogeneration of charges. If an exciton is formed in the vicinity of an electron accepting impurity, this can lead to charge transfer of the electron to the acceptor, leaving behind a mobile hole on the polymer chain, see Fig. 1.8 (a). In (b) is shown the neutralization of a hole on encounter with a negatively charged impurity, which will be discussed in the next subsection

CB VB A (a) (b) CB VB

A-Figure 1.8: The role of an electron accepting impurity in the generation and decay of charge carriers. (a) Exciton dissociation by electron transfer. (b) Hole recombination at an occupied acceptor site. Note that the band structure diagrams shown are idealized representations.

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1.5 Charge carrier recombination 11

and analyzed in Chapter 7.

Charge carriers in a conjugated polymer can also be formed by inelastic col-lisions of a highly energetic charged particle passing through the sample. This is exploited in the pulse-radiolysis technique, described in the next chapter. With this technique, electrons of an energy of several MeV (β-particles) im-pinge on the sample. On passing through, the incident electron loses energy by inelastic collisions with the bound electrons of the polymer. Upon colli-sion, an electron can be removed from the polymer chain and thermalizes at a certain distance, leaving behind a hole on the chain.

1.5 Charge carrier recombination

The electron-hole pair formed in an ionization process can either recombine geminately or escape the coulomb potential to form free, independent charge carriers. The probability of escape, φ, is given by the initial separation dis-tance, r, the dielectric constant of the medium, r, and the temperature, T . In hydrocarbon liquids and organic single crystals, the escape from geminate recombination at zero electric field is given by [30, 31]

φ = e−rc/r _(1.1)

whereby rcis the coulombic capture radius, the distance at which the thermal energy of the electron equals its coulombic potential energy, i.e.

e2 4πrc0r

= kBT. (1.2)

Conjugated polymers are disordered, consisting of sites with different ener-gies. Electron transfer to an adjacent site that is lower in energy can therefore increase the yield of geminate escape. In RR-P3HT charge transporting lamel-lae are formed by self assembly (see Fig. 1.3). If the electron thermalizes in another lamella than its sibling hole, the intervening side chains will hinder in-terlamellar back recombination, thereby increasing the probability of escape. It can therefore be expected that the escape yield in RR-P3HT will be greater than predicted by Eq. (1.1).

A hole that has escaped geminate recombination, may undergo random diffusion. On encounter with an electron stemming from another ionization process, bimolecular (Langevin [32]) recombination occurs, whereby electron and hole recombine by the emission of energy quanta (photon and/or phon-ons). The bimolecular recombination can be described by

dnh

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12 1. Introduction

where γ is the bimolecular recombination rate coefficient and ne and nh are the electron and hole concentrations, respectively. In hydrocarbon liquids and organic crystals [31], γ is related to the charge carrier drift mobility, µ, via

γ = eµ/0r (1.4)

Due to disorder, the mobility in RR-P3HT is time-dependent, following a power-law, tβ−1 (0 < β < 1), as discussed in the next section. Because of relation (1.4), the same time dependence results for γ and we show in Chapter 7 that bimolecular recombination in RR-P3HT is correctly described by a power-law time dependence of γ.

As stated earlier, conjugated polymers usually contain electron accepting impurities. Depending on the temperature and the energetic position of the impurity level in the bandgap, a certain amount of acceptors is occupied by electrons, i.e. negatively charged. A negatively charged acceptor is a recom-bination site for holes, see Fig. 1.8 (b). In Chapter 7, we find that this is the most important recombination process for free holes in RR-P3HT at a sufficiently low hole surplus.

1.6 Charge carrier transport

The charge carrier drift mobility, µ, is defined as the average drift velocity, hvi, per unit electric field strength, E,

µ = hvi/E. (1.5)

The charge carrier drift mobility is appropriately measured in a time-of-flight (TOF) experiment. This is similar to a DC photocurrent setup, as depicted in Fig. 1.6, except that the distance between anode and cathode is much larger than the photon penetration depth. Using a short light pulse, a sheet of charge carriers is generated near one electrode. The charge carriers are subsequently dragged to the counter electrode by the electric field, leading to a displacement current. After traversing the sample, the carriers arrive at the counter electrode, where they are neutralized. The “time of flight,” τ , is connected to the drift velocity, hvi, and the sample thickness, d, via

hvi = d/τ (1.6)

and with Eq. (1.5) the drift mobility is obtained.

In single-crystals of covalently bonded semiconductors, like silicon or ger-manium, charge carriers are delocalized in the crystal. This is due to the periodic structure of the crystal. Electrons can be described by Bloch wave functions with energies that can take values within allowed bands. The width

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1.6 Charge carrier transport 13

of an energy band determines the effective mass, m∗, of a charge carrier and consequently the mobility, via

µ = eτ

m∗, (1.7)

where τ is the average time-interval between scattering events of the charge carrier with phonons according to the Drude model [33]. In germanium, the width of the valence band is ≈ 3 eV and the hole mobility is 1900 cm2_/Vs at room temperature [24]. In Ge, the hole scatters on average every 100 nm in intervals of τ ≈ 10−13 s at room temperature [31]. As the temperature is decreased, the number of phonons decreases and consequently the mobility increases, following a power-law [31],

µ ∝ 1/Tn, (1.8)

with n > 1.

The same charge transport model can be applied to molecular single crys-tals, like anthracene, at room temperature and below. However, due to the much weaker, van-der-Waals interactions between the building blocks (mo-lecules) of the crystal, the bandwidth is only of the order of 0.1 - 0.5 eV [34] and the charge carrier mobilities are ≈ 1 cm2_{/Vs. Most interestingly,} the band-transport model fails above a certain temperature, depending on the crystallographic direction. At this transition point, the mobility becomes independent of temperature in a small temperature range and then increases with temperature. In the high temperature range, charge transport is de-scribed by hopping of localized charge carriers from site to site. The temper-ature dependence of the mobility for hopping transport is given by

µ ∝ e−Ea/kBT_, _(1.9)

where Ea is an activation energy. The most striking experimental difference between band-like transport and hopping transport is the decrease of mobility with temperature in the former case and the increase of mobility with temper-ature in the latter case. In band transport, the phonons disturb the wave-like motion of the charge carriers, while in hopping transport, the phonons provide the energy necessary to hop from site to site.

The DC drift mobility over macroscopic distances in conjugated polymers is found to be temperature-activated, which is characteristic for hopping trans-port. This is mainly due to energetic and structural disorder. The charge carriers are localized in the conjugated segments. The segments are separ-ated by physical or chemical defects, providing a potential barrier or trap. To overcome the defect, tunneling is required or thermal energy in the form of phonons has to be supplied to the charge carrier. In conjugated polymers, the

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14 1. Introduction

most efficient transport pathway is along the conjugated backbone. The band-width along the chain direction in a perfect, defect-free conjugated polymer is comparable with that for germanium [35]. This result indicates that along a perfect polymer chain, band-like transport with a high-mobility can be ex-pected [36, 37]. Indeed, for the structurally best ordered conjugated polymer, single-crystalline polydiacetylene, charge carrier mobilities of a few cm2/Vs have been measured along the backbone [38], which is higher than in some organic single-crystals at room temperature. (Note that the extremely high value for the charge carrier mobility in polydiacetylene reported by Donovan et al. [39] could be due to the photoelectron emission artifact [11].)

RR-P3HT consists of two-dimensional domains, as shown in Fig. 1.3. In these domains, charge carriers delocalize in two dimensions [10] – along the chain and perpendicular to it. It can be hypothesized that in a perfect lamella of macroscopic dimension, two-dimensional, band-like transport can occur at low temperatures. However, to date, RR-P3HT could not be produced in the form of a single-crystal. Rather, it consists of ordered and amorphous regions, resulting in a disordered energy landscape. A sketch of a possible energy landscape in non-ideal RR-P3HT is given in Fig. 1.9.

The disorder in conjugated polymers has important consequences for the charge transport properties. The drift mobility of pulse-generated excess charge carriers, as measured by TOF, is usually time-dependent, following a power-law [40],

µ ∝ tβ−1, (1.10)

with 0 < β < 1. This is observed in many disordered materials, includ-ing amorphous silicon [41]. Consequently, because of the time-dependence, the drift mobility of excess charges is no material parameter in this class of semiconductors. Several theories have been developed to explain the time-dependence of µ, including continuous-time random-walk [41], multiple trap-ping [42] and hoptrap-ping [43]. Qualitatively, the decay of the drift mobility can be understood as follows. At time zero, charge carriers are injected at sites independent of the site energy. As time proceeds, the charge carriers will visit other sites, some of which are lower in energy (or confined by higher barriers) than the initial site. Once a particle has reached a site with lower energy (or higher barriers), it will reside there longer on average since thermal hopping to another site becomes increasingly difficult. As a net effect, the mean en-ergy of the ensemble decreases (or the average potential barrier to overcome increases) with time, resulting in a smaller average drift mobility.

After an excitation pulse, the charge carriers produced decay by trapping or recombination with time-dependent rate constants that are proportional to the mobility given by Eq. (1.10) (see Chapter 7). After disappearance of the excess charge carriers, the conductivity in real RR-P3HT is however non-zero,

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1.6 Charge carrier transport 15 “CB” “VB” large domain small domain domain boundary amorphous region trapped electron

Figure 1.9: Sketch of an energy landscape in a conjugated polymer consisting of relatively ordered domains and amorphous regions.

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16 1. Introduction

but a background conductivity remains, which is given by

σ0= en0µ0, (1.11)

whereby n0 is the equilibrium concentration of holes stemming from the im-purity electron acceptors and µ0 is their average mobility, which is time-independent after the thermodynamic equilibrium has been established. Due to disorder in the solid, µ0has a frequency dependence that is different from the prediction by the Drude model. In the Drude model, the (real part of the) mobility decreases with the frequency of the external electric field, while it is generally observed in disordered materials that the mobility increases with frequency. In the high frequency limit, it is universally observed in disordered solids that (the real part of) µ0 follows a power law [44, 45, 26],

µ0∝ ωn, (1.12)

with n of the order of 1. The increase of the mobility with frequency can be understood qualitatively as follows: At sufficiently high frequencies, the region that the charge carriers visit within one frequency cycle is smaller than a typical domain size and the mobility measured reflects the mobility within the well-ordered, well-conducting domains. At lower frequencies, charge transport must extend over longer distances and is limited by potential barriers and defects, resulting in a net decrease of the measured mobility.

In hopping transport, energy barriers have to be overcome by the charge carriers. In DC photoconductivity and time-of-flight experiments, relatively high DC electric fields are present. The field alters the energy landscape, whereby the energy required to escape a trap, or to overcome a barrier, is reduced. From this follows that the charge carrier mobility is electric-field (E) dependent [31], increasing with field strength. This problem was originally treated for an electron to escape the coulomb potential of a trapped hole (Poole-Frenkel model [31]). The Poole-Frenkel mobility is given by

µ = µ0eeβ √

E/kBT_, _(1.13)

where µ0 is the zero-field mobility and β = (e/πr0)1/2. It has been found that this model describes very well the electric field dependence of the mobility in conjugated polymers. Recently [46], it has been found in RR-P3HT that β can become negative at high temperatures, leading to a decrease of mobility with field strength. (Note that at higher temperatures, the mobility was always found to be higher than at lower temperatures and only the field dependence changed.) This is associated with the interplay of energetic versus positional disorder. At higher temperatures, positional disorder (= random variation of inter-site distances) is more important than energetic disorder since charge carriers have enough energy to overcome the potential barriers.

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1.7 Scope of this thesis 17

However, due to positional disorder, faster routes as well as dead ends are encountered by the carriers executing their random walk. For a charge carrier entering a dead end aligned in the field direction, it is much harder at a high field to jump backwards and find an alternative pathway to the sink. Therefore, the drift mobility decreases at higher fields.

In field-effect transistor measurements (see Fig. 1.5), it is observed that the field-effect mobility, µF E, is strongly dependent on the gate-induced dop-ing concentration in the conductive channel [47]. The field-effect mobility increases with the doping concentration. This can be understood as follows: As the doping concentration is increased, the lowest lying traps and sites are filled up with charge carriers. The charge carriers that are responsible for the current between source and drain can now take advantage of the higher lying sites, which show less variation in site energy, leading to an increase in the field-effect mobility.

In this thesis, an alternative technique is used to study charge transport. The differences with the aforementioned techniques are summarized as fol-lows. In the present technique, no electrodes or DC electric fields are present, which could enhance the dissociation of excited states. Charge carriers are detected by the absorption of microwaves at GHz frequencies. Due to the high-frequency of detection, the mobility obtained reflects transport in the well-ordered domains, whereas in TOF experiments, the mobility refers to transport over macroscopic distances. The electric field strength is orders of magnitude smaller than in typical DC device configurations and therefore electric-field dependent transport effects can be excluded in the present work. The transient doping level, introduced by pulsed irradiation of the sample, is negligible compared to the gate-induced doping in field-effect measurements, and consequently, no doping effects on the mobility are expected to occur.

1.7 Scope of this thesis

In this work, the Flash-Photolysis Time-Resolved Microwave Conductivity (FP-TRMC) is used to study the photoconductive properties of poly(3-hexyl-thiophene) (P3HT) thin films and the Pulse-Radiolysis Time-Resolved Mi-crowave Conductivity (PR-TRMC) is used to study bulk P3HT. With the PR-TRMC technique, both the background conductivity and the transient conductivity generated by a high-energy electron pulse are studied.

The principles of the experimental techniques are described in Chapter 2, while further details can be found in the experimental sections of the sub-sequent chapters. In Chapter 3, the quantum yield and the photon energy dependence of the photoelectron emission in RR-P3HT are obtained. In Chapter 4, we focus on the photoconductivity within the polymer. We obtain the photon energy dependence and activation energy of the quantum yield

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18 1. Introduction

of charge carrier photogeneration. The importance of molecular order in the photogeneration of charge carriers is examined in Chapter 5. In Chapter 6, we clarify the source of the sublinear depedence of the charge carrier yield on laser intensity and discuss its pronounced effect on the spectral dependence of the photoconductance. In Chapter 7, the PR-TRMC technique is used to measure the GHz charge carrier mobility and the recombination dynamics of charge carriers in the presence of electron-accepting impurities. We derive a generalized version of the stretched-exponential (Kohlrausch) decay law and provide a connection between the charge carrier dynamics in TOF experi-ments and PR-TRMC experiexperi-ments. In Chapter 8, we investigate the decay dynamics of the photoconductivity. We find that it differs from the decay dynamics found in the PR-TRMC experiment and derive a semi-empirical model.

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Chapter 2

Generation and

electrodeless detection of

charge carriers

In this work, the conductive properties of P3HT were investigated using mi-crowaves. Three types of microwave experiments were performed: steady-state (background) conductivity, time-resolved conductivity upon pulsed ion-ization with high-energy electrons (PR-TRMC), and time-resolved photocon-ductivity (FP-TRMC) using a laser as the excitation source. Upon passing through a weakly conducting medium, a microwave will be phase-shifted and attenuated. Phase shift and attenuation are described by the real part and the imaginary part of the dielectric function, (ω), respectively, where ω denotes the radian frequency of the wave. The real part, <[(ω)] = r(ω), is also called the relative dielectric constant. In general, both bound and mobile charges contribute to the real part and to the imaginary part of (ω). However, if no permanent dipoles are present (e.g. no water molecules in the medium) and when the frequency of the electromagnetic field is far off resonance from an electronic or vibrational transition, then, the imaginary part is entirely due to the conductivity, σ, of the mobile charges, according to =[(ω)] = −σ/ω0. In this thesis, only σ and pulse-induced changes of σ, ∆σ, are investigated. In the first section of this chapter, the general principle of microwave conduct-ivity measurements is explained. In the second section, an outline is given of the Pulse-Radiolysis Time-Resolved Microwave Conductivity (PR-TRMC), and in the third section, the Flash-Photolysis Time-Resolved Microwave Con-ductivity (FP-TRMC) is briefly explained. In this chapter, only the most relevant equations are cited and a mere overview of the detection equipment is given. For derivations of the equations and technical details, the interested

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20 2. Generation and electrodeless detection of charge carriers

reader is referred to previously published theses and extensive articles by the Radiation Chemistry Department, see e.g. refs. [48, 49, 50, 51]. Additional details regarding the analysis of the experimental data can be found in the experimental sections of the following chapters.

2.1 Microwave measurement of the

conductiv-ity

The propagation of electromagnetic waves through a medium is described classically by Maxwell’s equations [52], where the quantities have their usual meanings. ~ ∇ · ~D(~r, t) = ρ(~r, t) (2.1) ~ ∇ × ~H(~r, t) −∂ ~D ∂t (~r, t) = ~j(~r, t) (2.2) ~ ∇ · ~B(~r, t) = 0 (2.3) ~ ∇ × ~E(~r, t) +∂ ~B ∂t (~r, t) = 0 (2.4)

In this set of equations, the first is Coulomb’s law, the second is Ampere’s law generalized to time-dependent fields, the third one states the absence of magnetic monopoles, and the last equation is Faraday’s law. In a conducting homogeneous medium with linear response and no space charge, the following constitutive relations hold:

ρ(~r, t) = 0 (2.5) ~j(~r, t) = σ ~E(~r, t) (2.6) ~ D(~r, t) = 0(r− iσ/ω0) ~E(~r, t) (2.7) ~ B(~r, t) = µ0µrH(~~ r, t) (2.8)

Inserting these relations into Maxwell’s equations and performing vector al-gebra, the Maxwell equations reduce to two separate wave equations, one for the electric field, ~E(~r, t), and one for the magnetic field, ~H(~r, t). For electro-magnetic fields that are periodic in time, complex quantities are conveniently used. Because of the periodicity, the wave equations can be solved separately in space and time. Since any field pattern can be constructed by linear (Four-ier) combinations of plane waves that are solutions to the Maxwell equations, a plane wave ansatz is made.

Determination of the conductivity, σ, of a sample is carried out by meas-uring the electromagnetic power, P , dissipated in it. Waveguides are used, in which the electromagnetic wave propagates from the source to the sample,

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2.1 Microwave measurement of the conductivity 21 ax Ey b y Ey z0 z Ey

Figure 2.1: Spatial dependences of the electric field strength, Ey, of the TE1,0 mode in a rectangular waveguide. Upper left: Ey(x, y0, z0) with 0 ≤ y0≤ b. Upper right: Ey(a/2, y, z0), Lower figure: Ey(a/2, y0, z).

which is contained in a piece of the waveguide. After passing through the sample, the wave is guided to a detector. The waveguides used in this work are of rectangular cross-section, with dimensions a and b in x- and y-direction, respectively. The z-direction is the propagation direction of the wave. Be-cause of the geometrical shape of the waveguide, several restrictions exist for the propagation of electromagnetic waves inside the waveguide. The inner surface of the waveguide is an equipotential. As a consequence, the trans-verse electromagnetic (TEM) wave, with both ~E and ~H being perpendicular (transverse) to the propagation direction, cannot exist. Because of continu-ity, there can exist no tangential electric field component on the surface of the – highly conducting – waveguide, and no magnetic field component per-pendicular to the surface. Under these conditions, the solutions of the wave equations in the waveguide can be split into two categories. One set of solu-tions of this eigenvalue problem are the transverse magnetic (TM) waves (with Hz = 0 everywhere) and the others are the transverse electric (TE) waves (with Ez= 0 everywhere).

Each set of solutions contains a spectrum of eigenvalues and corresponding eigenfunctions, which form an orthogonal set. These different solutions are called the modes of the waveguide. Each mode has a characteristic cut-off frequency, below which it cannot propagate in the waveguide (“It does not

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22 2. Generation and electrodeless detection of charge carriers x=a x=0 z Ey Ey

Figure 2.2: Three-dimensional plot of the (x, z)-dependence of the electric field strength, Ey, of the TE1,0 mode in a rectangular waveguide.

fit in the waveguide.”) At the lowest possible frequencies, only one mode of propagation can exist (the dominant mode). At higher frequencies, increas-ingly more modes, with different phase velocities, can exist. For time-resolved measurements of the conductivity it is therefore essential that only one mode, which can only be the dominant mode, is present in the waveguide. The lower limit of the operating frequency range is therefore given by the cut-off frequency of the dominant mode and the higher limit by the onset (cut-off frequency) of the second-lowest mode. The lowest mode in a rectangular wave-guide with a > b is the TE1,0 mode, meaning that one half wavelength fits in the x-direction and none in the y-direction. The electric field is polarized in the y-direction (Ex = Ez = 0). The x, y, and z-dependences of the electric field are shown in Fig. 2.1 and in Fig. 2.2 is shown a three-dimensional plot of the (x, z)-dependence. The TE1,0 wave can be written as

Ey(x, z) = E0sin(πx/a)eiωt−γ1,0z (2.9) with the complex propagation constant [53]

γ1,0= p

(π/a)2_{+ iωµ}

0µr(σ + iω0r). (2.10) In the case of nonconducting media (σ = 0), γ1,0 is real (and no wave can propagate) when the frequency is smaller than the cut-off frequency, fc, given as

fc= 1/2a √

µ0µr0r. (2.11)

For X-band wave guides (a = 22.9 mm, b = 10.2 mm) filled with air, the cut-off frequency of the TE1,0 mode is fc = 6.6 GHz. The second highest mode, TE2,0, has a cut-off frequency which is twice that of the TE1,0mode. The X-band waveguide is therefore operated between these frequencies. The Q-X-band

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2.1 Microwave measurement of the conductivity 23 y x z γ γ d1 d2 1 2

Figure 2.3: Sketch of the reflection cell containing sample material, shown in light gray. The microwaves enter and exit at the left-hand side of the cell and are reflected at the air/sample (z = d1) and sample/end-plate (z = d2) boundaries. The propagation constant for the TE1,0 mode in air is denoted as γ1 and in the sample material as γ2.

waveguide (a = 7.1 mm, b = 3.6 mm) has accordingly a cut-off frequency of 21.1 GHz.

The conductivity of a bulk sample in the present technique is measured by filling a reflection cell with the sample material, as shown in Fig. 2.3. The reflection cell is short-circuited at the end and the conductivity of the sample is obtained by comparing the microwave power reflected from the empty cell, Pr0, with the microwave power reflected from the filled cell, Pr. This ratio is related to the complex reflection coefficient, Γ, via

Pr/Pr0= Γ(d1)Γ∗(d1), (2.12) where Γ∗ denotes the complex conjugate of Γ. A plot of Pr/Pr0 versus fre-quency is shown in Fig. 7.1 for two different samples of commercially available RR-P3HT. The occurrence of maxima and minima is due to the similarity of the wavelength of the microwave with the length of the sample volume, leading to constructive and destructive interferences due to reflections at the sample/air boundary. The complex reflection coefficient, Γ, can be related to the propagation constants of the media using transmission-line theory [53],

Γ(d1) = γ1 γ2tanh[γ2(d2− d1)] − 1 γ1 γ2tanh[γ2(d2− d1)] + 1 . (2.13)

A custom-made computer fit program was used to fit the frequency depend-ence of Pr/Pr0 according to Eq. (2.12) with Γ from Eq. (2.13) and γ from Eq. (2.10). (In the fit program also losses in the waveguide walls due to the skin effect are included but omitted in the discussion here.) The fits are shown as the smooth lines in Fig. 7.1, whereby for the RR-P3HT powder the ma-terial parameters r = 1.8, µr = 1, d2− d1 = 1.0 cm were used, with the conductivity, σ, as the free fit parameter.

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2.2 Pulse-radiolysis time-resolved microwave

conductivity

In the previous section, we have described the measurement of the background (or dark) conductivity. In this section, we describe the measurement of the transient change of the conductivity due to the interaction of a short pulse of high-energy electrons with the sample material. The measurement cell, containing the sample material, is irradiated with a single pulse of 3 MeV electrons from a van-de-Graaff accelerator. A basic sketch of the experimental setup is shown in Fig. 2.4. To allow high-energy electrons to penetrate into the sample material, the top wall of the copper measurement cell is only 0.4 mm thick. The penetration depth of the 3 MeV electrons produced by the van-de-Graaff accelerator in materials of density 1 g/cm3 _{is ca. 15 mm} [54], i.e. much larger than the sample thickness of b = 3.6 mm (Q-band), and the Gaussian half-width of the beam cross section is larger than the lateral dimensions of the sample. Energy deposition and ionization within the sample is therefore close to uniform. Energy transfer from high-energy electrons to the medium occurs in discrete events, both via excitations and ionizations, along the track of the primary electron. A large fraction of the energy transfer events results in ionization of the molecules and the formation of secondary electrons, which will lose their energy via excitation of electronic transitions and will eventually become thermalized. For an organic material of density 1 g/cm3_{, the individual ionization events are separated by 100 - 200 nm,} with an average energy of 20 - 40 eV transfered to each secondary electron. The average thermalization distance of the secondary electrons is typically 5 - 10 nm from the sibling hole [55] for the present class of materials. For more details on the energy deposition by high-energy electrons, see Chapter 7.

The free electrons and holes generated in the sample lead to a change in the conductivity, ∆σ, and a decrease of the microwave power reflected from the cell, ∆Pr. The conductivity change, ∆σ, is obtained analogous to the background conductivity, σ, in the previous section. The frequency dependence of ∆Pr(t)/Pr is obtained from a series of pulses. The maxima, ∆Pr(t0)/Pr, reached at the end of each pulse, are plotted against frequency and ∆σ(t0) is obtained from a fit using Eq. (2.12) with Eqs. (2.13) and (2.10) and the substitutions P0

r → Pr, Pr → ∆Pr and σ → ∆σ. It was found [48] that, for small values of ∆σ, the change in the microwave power is proportional to ∆σ and therefore a sensitivity parameter, A(ω), can be defined that directly relates the change of microwave power to the change in conductivity,

∆Pr(t) Pr = P ∆σ r (t) − Pr Pr ≈ −A(ω)∆σ(t). (2.14)

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high-2.3 Flash-photolysis time-resolved microwave conductivity 25

electron pulse from van-de-Graaff accelerator circulator microwave source microwave detector microwave cell

Figure 2.4: Schematic representation of the Pulse-Radiolysis Time-Resolved Microwave Conductivity (PR-TRMC) experiment.

energy electron pulse, whose length can be varied between 0.3 and 50 ns, provided that the conductivity decay is much slower than the pulse length. The end-of-pulse conductivity can be related to the mobility of the charge carriers with the knowledge of the ionization yield per pulse. The conduct-ivity transients are recorded using an oscilloscope and from the dependence of the shape of the transients on temperature, radiation dose and impurity concentration, conclusions about the charge carrier dynamics can be drawn, see Chapter 7.

2.3 Flash-photolysis time-resolved microwave

conductivity

In the Flash-Photolysis Time-Resolved Microwave Conductivity (FP-TRMC), the electron accelerator is replaced by a laser (see Fig. 2.5) capable of pro-ducing 3 ns pulses with tunable photon energy, matching the electronic ab-sorption band of P3HT. Charge carriers are generated as a consequence of electronic excitations by the strongly absorbed photons. The photons have a penetration depth of typically less than 1 micrometer and therefore thin films, spin-coated or drop-cast, on quartz substrates are investigated instead of bulk material. The film is placed at a position of maximum electric field strength within the microwave cell, as shown in Fig. 3.1. Because of the much smaller volume in which a conductivity change is generated as compared to

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26 2. Generation and electrodeless detection of charge carriers measurement cell filters circulator microwave source intensity meter Nd:YAG laser microwave detector

Figure 2.5: Sketch of the Flash-Photolysis Time-Resolved Microwave (FP-TRMC) experiment.

the PR-TRMC technique, where bulk samples are used, considerably less mi-crowave power is absorbed and the signal-to-noise ratio of ∆Pr(t)/Pris much smaller. To overcome this problem, an iris is inserted at a position of minimal electric field strength, as shown in Fig. 3.1. In transmission-line theory, the circular iris can be described as an inductive obstacle and is treated as such when deriving a relationship between the microwave power absorbed in the cavity and the conductivity of the thin film.

Alternatively, the iris can be viewed as a partially reflecting mirror for the microwaves and the measurement cell can be regarded as a resonant cavity. In a resonant cavity, only those frequencies are allowed for which the bound-ary conditions, namely no tangential electric field component on the inner waveguide surfaces, are fulfilled. In other words, there have to be nodes at the boundaries, which is fulfilled if the cavity length, d, equals integer mul-tiples of half wavelengths. For the TE1,0,n mode, the eigenfrequencies of the resonant cavity are given by

f1,0,n= 1 2π√0rµ0µr r π a 2 +nπ d 2 . (2.15)

In the FP-TRMC experiment, X-band waveguides are used (a = 22.9 mm), and the length of the cavity is d = 48 mm. For n = 2 (see Fig. 3.1), resonance occurs at ca. 9 GHz in an air-filled resonator.

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2.3 Flash-photolysis time-resolved microwave conductivity 27 1.0 0.8 0.6 0.4 0.2 0.0 Pr / P i frequency f0 FWHM R₀

Figure 2.6: Resonance curve of a microwave cavity. Pr/Pi is the ratio of reflected to incident microwave power.

The eigenfrequency spectrum of an iris-coupled resonant cavity consists of allowed frequency bands centered at the resonance frequencies. The width of the bands is determined mainly by the diameter of the iris and is a measure of the “quality” of the cavity. The (loaded) quality factor is given by

Ql= 2πf0/FWHM, (2.16)

where FWHM is the full width at half maximum (FWHM) of the resonance frequency band. A plot of such a resonance curve, given as the ratio of reflected over incident power, is shown in Fig. 2.6. Due to multiple reflections of the microwave within the cavity, the detected transient microwave signal is the result of a convolution of the response function of the cavity with the conductivity change in the sample contained in the cavity. The delta-response function of a cavity is governed by an exponential function, with a rise time, τ , at the resonance frequency given as

τ = Ql/πf0 (2.17)

in the present setup [51]. Two different irises of diameter 9.6 or 7.4 mm were used in this work. The respective cavity parameters were Ql ≈ 500 or 1000 and τ ≈ 20 or 40 ns.

At resonance, the change of the microwave power reflected from the cell due the photoexcitation has been derived [56] to be related to the change in

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the conductivity of a homogeneously filled cavity via ∆Pr Pr (f0) = − Ql(1 + 1/ √ R0) πf00r ∆σ, (2.18)

where R0 is the ratio of the reflected to the incident power level at the res-onance frequency, R0 = Pr(f0)/Pi, see Fig. 2.6. In the present FP-TRMC experiments, a thin film of thickness L, placed at a position z0 of maximum electric field strength (see Fig. 3.1) is investigated instead of a completely filled cavity. Therefore, Eq. (2.18) has to be adjusted accordingly. The cor-rection factor is obtained by comparing the microwave power absorbed in the thin film to the microwave power absorbed by the completely filled cell with the same conductivity. The absorbed microwave power is proportional to the volume integral over the square of the electric field strength,

∆P = 1 2

Z Z Z

∆σE2dx dy dz. (2.19)

Since the x- and y-dimensions remain unchanged, only the z-dependence has to be considered. The z-dependence of E is given by a sine-function. Com-parison of the sine-squared integral over the whole cavity length, d, with the integral over the film positioned at z0 gives the correction factor

∆Pfilm ∆Pfull = Rz0+L z0 sin 2_{[2πz/d] dz} Rd 0 sin 2_{[2πz/d] dz} = L d/2, (2.20) (for L d).

In addition, because of the strong absorption of the photons in the film, a z-dependence of ∆σ within the film results. Therefore, the obtained conduct-ivity from Eq. (2.18) (with the factor (2.20)) is to be seen as an average over the film thickness, h∆σi. For films that are thinner than the optical penetra-tion depth of the laser beam, h∆σi is a useful quantity. However, it has no meaning for films that are much thicker than the light penetration depth. It is therefore useful to change from the spatially dependent conductivity to the bulk conductance, G, of the film. These are related via

∆G = h∆σiaL

b (2.21)

and we finally obtain ∆Pr Pr = −2Ql(1 + 1/ √ R0) πf00rda/b ∆G = −K∆G. (2.22)

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Chapter 3

Photoemission of electrons

from the polymer surface

The photoconductivity of an optically dense layer of regioregular poly(3-hexylthiophene) has been measured using the time-resolved microwave con-ductivity technique for photon energies up to 5 eV. The effects of the gaseous environment and of irradiation from the polymer (front) or substrate (back) side of the sample have been studied. For back-side irradiation or front-side irradiation with an electron attaching gas mixture, the same intensity-normalized photoconductivity is found. Considerably larger photoconduct-ivity transients are observed on front-side irradiation with a non-attaching gas. This additional photoconductivity is attributed to photoelectron emis-sion into the gas phase. The quantum yield for photoelectron emisemis-sion at 5 eV is estimated to be ca. 10−7 per incident photon. The bulk photoconductivity is insensitive to the charge imbalance caused by photoejection of electrons. The onset of photoelectron emission is found to be close to 3 eV and increases by more than a factor of 5 in going from 4 eV to 5 eV. (This chapter is an extended and revised version of ref. [57].)

3.1 Introduction

In a previous publication [11], we have demonstrated how electrons, photo-ejected into the gas phase, can make a substantial contribution to the overall photoconductivity of conjugated polymer films. We have suggested that this effect may play a role in the interpretation of data obtained from conventional DC photoconductivity setups which also probe the solid/gas interfacial region, e.g. refs. [39, 58, 59, 60]. It is now realized that special experimental care has

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30 3. Photoemission of electrons from the polymer surface

to be taken in order to eliminate artifacts arising from such highly mobile gas phase electrons [61].

If a gaseous environment consisting of CO2 + 10% SF6 at atmospheric pressure is used, the contribution of gas phase electrons to the overall pho-toconductivity can be suppressed. Free electrons in such a gas mixture are rapidly thermalized by energy transfer to CO2and subsequently attach to SF6 forming heavy, relatively immobile, negative ions. Similar gas mixtures are used to prevent electrical discharges in high-voltage transformers and particle accelerators. Alternatively, the occurrence of photoelectron emission can be avoided by choosing a suitable sample- and/or measurement cell-geometry. For instance, the polymer can be covered with an appropriate transparent layer which functions as a barrier towards electron escape into the gas phase. These two measures are fundamentally different from each other. In the first case, electrons are removed from the bulk polymer leaving a surplus of holes in the film. In the second case, electron ejection from the film is suppressed and the concentration of positive and negative charge carriers in the bulk remains equal. In this report, we compare the effects of these dif-ferent methods of photoelectron suppression on the photoconductivity of a polythiophene film on a quartz substrate.

3.2 Experimental

The polymer used was regioregular Head-to-Tail-Head-to-Tail coupled poly(3-n-hexylthiophene) (P3HT) with a degree of regioregularity of 92%. The weight-average molecular weight (Mw) was 12.8 kg/mol (D = 1.4) corres-ponding to 55 monomer units per chain. A polymer film was prepared by drop-casting ca. 0.1 ml of a highly concentrated toluene solution (50 g/l) onto a 12 × 25 mm2_{, 1 mm thick supracil quartz plate in air at room temperature.} The sample was optically dense in the wavelength range investigated. After the photoconductivity measurements, 3 scratches were made in the film and the thickness was determined to be 16 ± 1 µm using a Tencor Instruments Alpha-Step 200 profilometer.

The quartz plate was placed in a microwave resonant cavity at a position of maximum electric field strength, as illustrated in Fig. 3.1. A grating in the back-wall of the cavity was covered and vacuum-sealed with a supracil quartz window. The iris coupling hole of the cavity was vacuum-sealed with Kapton foil. The cavity could be attached to a vacuum line via a stopcock and evacuated down to a pressure of less than 10−4 mbar. After evacuation, the cavity was filled with either 20 torr CO2 or atmospheric pressure of a 10:1 CO2:SF6 mixture.

The sample was illuminated with 3 ns FWHM pulses from a Coherent “Infinity/OPO” laser. The laser beam was shaped to a rectangle with

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di-3.3 Results and discussion 31

laser

quartz

window iris X-band waveguide

polymer film quartz substrate

gas inlet

microwaves laser

quartz

window iris X-band waveguide

polymer film quartz substrate

gas inlet

microwaves

Figure 3.1: Schematic representation of the microwave resonant cavity con-taining a thin-layer sample (not to scale). The sinusoidally varying dashed lines represent the standing-wave pattern of the microwave electric field.

mensions closely matching the 12 × 25 mm2cross-section of the sample. The intensity distribution over the cross-section of the beam was uniform and free of hot-spots. Because of the grating, the illuminated area of the film was only 1.6 cm2. The pulse energy was measured using a Coherent “Labmaster” power meter to monitor a small fraction of the incident beam reflected by a quartz plate. The laser intensity could be attenuated using neutral density filters. For all of the measurements in this paper, the pulse-integrated incid-ent photon flux was 3 × 1014_photons/cm2_{. The signal-to-noise ratio could be} improved by signal averaging transients from up to 30 single pulses.

Changes in the conductivity of the sample on flash-photolysis were mon-itored as changes in the microwave power reflected by the cavity at resonance (ca. 9 GHz) using microwave circuitry and detection equipment which has been fully described elsewhere [62, 49]. For the small (ca. 1 ppm) changes in power, P , observed ∆P/P is directly proportional to N µ, where N is the number and µ the mobility of the charge carriers in the film, respectively. The electric field strength at the position of the sample was ca. 100 V/cm and the electric field vector was parallel to the surface of the sample. The overall time-response of detection of ca. 40 ns was controlled mainly by the loaded quality factor of the cavity, QL.

3.3 Results and discussion

For the purposes of the present experiments, a particularly (ca. 16 µm) thick film of P3HT on a quartz substrate was prepared with the intention that all photons with wavelengths much shorter than the absorption onset at ca. 690 nm (1.8 eV) would be completely absorbed within the polymer layer.

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32 3. Photoemission of electrons from the polymer surface

polymer

quartz

polymer

Figure 3.2: Sketch of the two illumination geometries. Left: Front-side illumination, with the possibility of electron photoemission. Right: Back-side illumination. The ejection of electrons is suppressed by the quartz substrate in this case. Since all photons get absorbed in a submicron thick layer close to the quartz/polymer interface, the electron emission at the polymer/gas interface is negligible.

Since the photon penetration depth is only a few hundred nanometers at most, photoelectron emission at the polymer/gas interface on irradiation of the sample from the substrate (back) side can be excluded and the photo-conductivity should be insensitive to the gaseous environment in the cell. On the other hand, the occurrence of photoelectron emission on irradiation from the polymer (front) side should be apparent as a dependence of the photo-conductivity on the gaseous environment. The illumination geometries are depicted for clarity in Fig. 3.2.

The expected difference in sensitivity to the gaseous environment between front-side and back-side irradiation of the sample is illustrated by the photo-conductivity transients in Fig. 3.3. In the latter (right-hand side of figure), a complete lack of sensitivity to the nature of the gas is evident as expec-ted. In the former (left-hand side of figure), a substantial reduction in the conductivity is seen on going from 20 torr of the non-attaching gas CO2 to 1 atmosphere of a 10:1 CO2:SF6 mixture, in which electrons attach within a few picoseconds to form molecular negative ions with mobilities, µ(M−)G, many orders of magnitude lower than that of electrons. The reduction in the photoconductivity signal is therefore direct evidence for the occurrence of photoelectron emission into the gas phase. As shown previously, even larger effects of the gaseous medium are observed for low electron collision frequency, high electron mobility gases such as N2 or Ar [11].

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3.3 Results and discussion 33 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ηΣµ (10 -3cm 2/Vs) 400 300 200 100 0 time (ns) 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ηΣµ (10 -3 cm 2 /Vs) 400 300 200 100 0 time (ns)

Figure 3.3: Microwave photoconductivity signals of an optically dense P3HT film obtained from front-side illumination (left-hand side) and back-side illu-mination (right-hand side). Dashed line: cavity filled with 20 torr CO2, full line: cavity filled with 1 atm CO2 / 10% SF6. The laser photon energy was 5 eV and the pulse-integrated photon flux was 3 × 1014_/cm2_.

CO2 is used as the non-attaching gas in the present study because it thermalizes electrons rapidly (within a few nanoseconds at 20 torr) [63]. This allows one to use the thermal value of the electron mobility in the gas phase, µ(e−₎

G, for a quantitative evaluation of the photoelectron emission data. For CO2, the value of the real, in-phase component of µ(e−)G is related to the momentum transfer collision frequency, νm, and the radian frequency of the electric field, ω, by

µ(e−)G=

e

mνm(1 + ω2/ν2m)

, (3.1)

with e and m the charge and mass of the electron, respectively. From the value of νm/N = 1.0 × 10−7 cm−3/s (with N the gas density) [64] and ω = 5.7 × 1010_s−1_{, the maximum value of µ(e}−₎

Gis determined to be 1.5 × 104cm2/Vs at a pressure, P , of ca. 20 torr.

For comparison, the zero frequency (DC) value of µ(e−)G is 5.3 × 105/ P cm2/Vs, for P in torr or 2.7 × 104 cm2/Vs at 20 torr. For typical electrode spacings of ca. 100 µm and a voltage of 100 V in DC experiments, the drift or draw-out time of electrons with this mobility would be a few tens of pico-seconds. In the present work, the electrons are not removed by the rapidly oscillating electric field but do still appear to decay on a (sub)nanosecond timescale. This is attributed to rapid geminate recombination with holes at the polymer/gas interface. Because of the limited time-response of the resonant-cavity detection system, this process could not be accurately

Photogeneration and dynamics of charge carriers in the conjugated polymer poly(3-hexylthiophene)

Photogeneration and dynamics of

charge carriers in the conjugated

Photogeneration and dynamics of

charge carriers in the conjugated

polymer poly(3-hexylthiophene)

PROEFSCHRIFT

Gerald DICKER

Contents

Chapter 1

Introduction

1.1

Relevance and motivation

1.2

Principle of π-conjugation

1.3

Historical development of conjugated

poly-mers

1.4

Charge carrier generation

1.5

Charge carrier recombination

1.6

Charge carrier transport

1.7

Scope of this thesis

Chapter 2

Generation and

electrodeless detection of

charge carriers

2.1

Microwave measurement of the

conductiv-ity

2.2

Pulse-radiolysis time-resolved microwave

conductivity

2.3

Flash-photolysis time-resolved microwave

conductivity

Chapter 3

Photoemission of electrons

from the polymer surface

3.1

Introduction

3.2

Experimental

3.3

Results and discussion