Electron transport in organic single-crystal transistors

Thesis

Reference

Electron transport in organic single-crystal transistors

MINDER, Nikolas Aron

Abstract

In this thesis we experimentally study the intrinsic charge transport properties in n-channel organic field-effect transistors and its disorder-induced suppression. We observe that certain molecular and crystal structures are beneficial for minimizing the disorder experienced by charge carriers and thus for studying the microscopic charge transport mechanisms of organic semiconductors in a field-effect configuration. Experiments on perylene derivatives show that disorder can be suppressed by attaching longer core substituents – thereby reducing potential fluctuations in the transistor channel and increasing the mobility in the activated regime – without altering the intrinsic transport properties. We further explore the influence of the dielectric environment on the charge transport properties using polymer gate dielectrics as well as electric-double layer gating with ionic liquids. In our field-effect transistors, we further observe an extremely low gate bias stress effect, i.e., the degradation of the source-drain current upon prolonged application of a gate bias potential.

MINDER, Nikolas Aron. Electron transport in organic single-crystal transistors . Thèse de doctorat : Univ. Genève, 2014, no. Sc. 4633

URN : urn:nbn:ch:unige-349185

DOI : 10.13097/archive-ouverte/unige:34918

Available at:

http://archive-ouverte.unige.ch/unige:34918

Disclaimer: layout of this document may differ from the published version.

1 / 1

GENÈVE

Atelier d’impression ReproMail 2014

THÈSE

Electron transport in organic single-crystal transistors

Nikolas A. Minder

DPMC and GAP Professeur Alberto F. Morpurgo

de Californie, États-Unis

Thèse N° 4633 par

présentée à la Faculté des sciences de l’Université de Genève

pour obtenir le grade de Docteur ès sciences, mention physique

UNIVERSIT ´E DE GEN `EVE DPMC and GAP

FACULT ´E DES SCIENCES Professeur Alberto F. Morpurgo

Electron transport in organic single-crystal transistors

TH` ESE

pr´ esent´ ee ` a la Facult´ e des sciences de l’Universit´ e de Gen` eve pour obtenir le grade de Docteur ` es sciences, mention physique

par

Nikolas A. Minder de Californie, ´ Etats-Unis

Th` ese N

4633

GEN `EVE

Atelier d’impression ReproMail 2014

Acknowledgements

Acquiring my PhD has been a great experience during which I had the privilege of collaborating with many brilliant scientists and build great friendships. I want to thank everyone in and outside the University of Geneva contributing to achieving this thesis.

First, I would like to thank Prof. Alberto Morpurgo for giving me the opportunity to do a PhD with him. I learned a lot from his profound un- derstanding of physics and his ability of sharing it. Alberto created a very stimulating work environment by constantly improving the research facilities as well as by attracting – and collaborating with – many highly competent and inspiring researchers. He always took the time to discuss results and think about their interpretation and I am highly impressed by his deep commitment to research. I am also deeply grateful to Prof. Yoshihiro Iwasa (Tokyo), Prof.

Sergio Ciuchi (L’Aquila) and Prof. Dirk van der Marel (Geneva) for their key role of evaluating this thesis as members of the dissertation committee and for stimulating discussions. I also want to thank Antonio Facchetti for the great collaboration on several projects and for all his great effort in synthesizing the molecular semiconductors we used for our studies and am also grateful to Simone Fratini, Sergio Ciuchi, Mario Barra and Antonio Cassinese for good collaborations.

A very special thanks goes to all members of the Quantum Electronics Group for their support in my everyday work as well as for all the great times spent together. Especially Ignacio Guti´errez, Nuno Couto and Alexandre Fer- reira who accompanied me during my entire PhD time, and also Sandra Sopic, Dong Keun Ki, Anya Grushina, Sanghyun Jo, Fabio Deon, Davide Costanzo and Yulia Krupskaya who joined in along the way. Of course this also goes for all former members of the group - Hangxing Xie, Masaki Nakano, Shimpei Ono, Benjamin Sac´ep´e, Jeroen Oostinga, Flavia Viola Di Girolamo, Daniele Braga, Christophe Caillier and Seif Ben Khelil as well as many friends and colleagues from other groups - Benedikt Ziegler, Edward Coutureau, Pavlo Zubko, Simone Fratini, Siony McKeown, Iaroslav Gaponenk, Marta Gibert, Alexandre Fˆete, St´ephanie Fernandez, Raoul Scherwitzl, Claudia Cancellieri, Yulia Lisunova, C´edric Blaser, Iris Crassee, Alberto de la Torre, Renan Villar- real, Anna Maria Novello, Fran¸cois Bianco, Giorgio Mondonico, Florin Buta,

iii

Marco Bonura, Tomer Barnea and many others. It has been great working with all of you and also sharing awesome times barbecuing, playing beach volleyball, swimming in the Rhˆone, going kart racing, hiking up the Sal`eve, relaxing at the lake or bar hopping in New York (above 40th street due to Hurricane Sandy).

I also want to thank Michel Decroux, Carmine Senatore, Stefano Gariglio, Ivan Maggio-Aprile, Enrico Giannini and Vincenzo Fontana for the good co- operation in teaching the travaux pratiques. Furthermore, I am grateful for many interesting discussions at conferences and workshops, amongst others with Vitaly Podzorov, Daniel Frisbie, Wei Xie, Alberto Salleo, Yoshi Iwasa, Jun Takeya, Christian Sch¨onenberger, Michel Calame, Bertram Batlogg, Roger H¨ausermann, Thomas Mathis, Tobias Morf, Kristin Willa, and Frank Ort- mann. Further I thank Christophe Berthod for doing a great job in teaching many-body physics in a very clear way and I would also like to acknowl- edge technical assistance by Gregory Manfrini, Marco Lopes, Mehdi Brandt, G´eraldine Cravotto, S´ebastian Muller, Sandro D’Aleo, Spiros Zanos, J´erˆome Cadoret, Daniel Chablaix and Bernard Guipet, the members of the admin- istration Denise Borjon, Marie-Anne Gervais, Nathalie Chaduiron, Nathalie Buret, Fabienne Hartmeier, and the MaNEP team.

Finally I want to thank my family and my friends from outside the Univer- sity of Geneva for their great moral support while I was working towards my PhD, which has been an immense help. I will start this non-comprehensive list by thanking my parents Kathy and Peter, Mirjam, Barbara, Christine and Daniel, Thomas and Anna, Pascal, Jenny, Feli and Dominik, Emy, Olga, Christelle, Heinrich and Monika, Dominik, Tom and Nora, Bj¨orn and Anja, G´eraldine, P¨adi and Sandra, P¨adi and Sue, Christian, Dominikus and Lisa, Jelena, Oren, Rick and Martha, Sarah and Will, Katherine, Devan, Scott and Denise, Karen and Jake, Ann, Susan, Harry, Emily and Owen, Vick, Michael, Ryan and Adam, Nancy, Bill and Cassie, Sebastian and Pamela, Andreia, Barney, the producers of the Big Bang Theory, and everyone who has morally supported me during this interesting journey.

R´ esum´ e

L’´electronique organique est un domaine en ´evolution rapide de l’´electronique appliqu´ee. Le terme organique est dˆu au fait que les ´el´ements constitutifs sont `a base de carbone, synth´etis´es par la chimie organique. Le grand int´erˆet pour l’´electronique organique provient des propri´et´es des mat´eriaux uniques de ses composantes: des semi-conducteurs de petites mol´ecules ou des polym`eres organiques. Leur flexibilit´e, transparence, adaptabilit´e `a un large ´eventail

´electronique et surtout leur poids l´eger sont de forts atouts. En outre, la capacit´e `a grande ´echelle et au traitement `a basse temp´erature, ainsi que leur faible coˆut font des semi-conducteurs organiques candidats id´eaux pour les dispositifs (opto-)´electroniques. Un des domaines d’application promet- teur pour les semi-conducteurs organiques est la diode ´electroluminescente or- ganique (OLED), utilis´ee dans les appareils ´electroniques portables avec ´ecrans OLED, ou encore dans de nombreuses applications ´electroniques organiques qui se d´eveloppent activement, y compris des cellules photovoltaque organiques (OPV), des capteurs du gaz et de pression ou des puces de radio-identification (RFID).

Alors que les applications ´electroniques `a base de composantes organiques reposent souvent sur la fabrication de couches minces de semi-conducteurs or- ganiques en grande surface, ces films poly-cristallines contiennent des joints de grains, des d´efauts et des impuret´es et par cons´equent le transport de charge est domin´ee par le d´esordre structurel - masquant les propri´et´es intrins`eques de transport lui-mˆeme. L’´etude des m´ecanismes de transport de charge micro- scopiques des semi-conducteurs organiques et les processus limitant le trans- port intrins`eque n´ecessitent des monocristaux hautement ordonn´es de petites mol´ecules organiques. En particulier, l’´etude des propri´et´es de transport de charge en temp´erature peut r´ev´eler des m´ecanismes supprimant les perfor- mances des semi-conducteurs organiques.

Contrairement aux semi-conducteurs inorganiques conventionnels, les semi- conducteurs organiques ont typiquement une largeur de bande plus faible, ce qui augmente l’effet des sources de d´esordre sur les propri´et´es de transport

´electronique. Dans des transistors organiques `a effet de champ (OFETs), o`u les propri´et´es de transport ont lieu `a l’interface entre les solides mol´eculaires or- ganiques et un di´electrique de grille, il existe plusieurs sources de d´esordre qui

v

peuvent agir comme des pi`eges `a charges et ainsi d´egrader leur mobilit´e. No- tamment pour les transistors organiques domin´es par la conduction ´electronique (canal n), il existe plusieurs groupes chimiques capables de pi´eger les charges, expliquant la faible performance des OFETs `a canal n par rapport `a ceux domin´es par la conduction des trous (canal p).

Une grande partie de cette th`ese est consacr´ee `a l’´etude des propri´et´es de transport de charge intrins`eques des OFETs `a canal n et la suppression de la performance par le d´esordre. Nous d´ecrivons nos mesures en temp´erature et d’effet Hall sur des OFETs canal n de haute qualit´e et mettons en ´evidence le transport dit type de bande . Grˆace `a une analyse quantitative de nos mesures de transistors avec diff´erents di´electriques, nous proposons une rela- tion entra la structure et les propri´et´es favorisant l’apparition de transport de type bande dans des OFETs. La validit´e de ces pr´edictions est confirm´ee par des mesures de transport de charge `a diff´erentes temp´eratures sur deux d´eriv´es mol´eculaires. Ces mesures montrent que le d´esordre peut ˆetre supprim´e par la fixation de longs substituants sur les parties conjugu´ees des mol´ecules (entre lesquelles le transport de charge a lieu), conduisant `a une r´eduction des fluc- tuations de potentiel dans le canal du transistor et augmentent la r´egion de temp´eratures dans laquelle le transport de type de bande a lieu.

Une partie importante de cette th`ese se focalise sur les applications abor- dant les diff´erents aspects du fonctionnement d’appareil `a basse tension et leur stabilit´e op´erationnel. Le premier est ´etudi´e par des OFETs `a double-couche

´

electrique en utilisant des liquides ioniques `a temp´erature ambiante. Lors de l’application d’une diff´erence de potentiel entre deux ´electrodes au travers d’un ´electrolyte, il existe une accumulation d’ions de charge oppos´ee aux in- terfaces des ´electrodes, formant ainsi une double-couche ´electrique. Une forte chute de potentiel apparaˆıt au niveau des deux surfaces, tandis que le poten- tiel reste constant dans l’´electrolyte. Les champs ´electriques ´elev´es malgr´e des tensions comparativement faibles peuvent ainsi accumuler une haute densit´e de porteurs de charge dans les semi-conducteurs. Les mesures sur plusieurs transistors organiques `a canal n avec des liquides ioniques montrent une con- ductance tr`es ´elev´e `a des tensions faibles. De plus, la mobilit´e des OFETs ne se d´egrade pas de faon significative par rapport aux valeurs mesur´ees sans liq- uides ioniques. Ces r´esultats sont donc prometteurs pour un fonctionnement

`

a haute performance d’OFETs organiques `a faible tension.

La stabilit´e op´erationnelle des transistors organiques `a canal n est adress´ee par les mesures de stress de polarisation de grille. Dans des OFETs de canal n compos´es de polym`eres fluor´es comme di´electriques de grille, nous constatons que la d´egradation lors d’un fonctionnement prolong´e du dispositif est environ deux ordres de grandeur plus faible que dans les meilleurs OFETs `a canal p.

vii Ceci est remarquable pour les transistors organiques `a canal n, et s’av`ere ˆetre un r´esultat tr`es prometteur.

En r´esum´e, les r´esultats pr´esent´es dans cette th`ese soulignent l’importance d’´etudier les propri´et´es de transport de charge intrins`eques des semi-conducteurs organiques. Ceci est important pour faire avancer notre compr´ehension fon- damentale des m´ecanismes microscopiques de transport de charge dans les semi-conducteurs organiques. En outre, une meilleure compr´ehension des m´ecanismes microscopiques contribue `a am´eliorer les applications ´electroniques organiques.

Contents

Acknowledgements iii

R´esum´e v

1 Introduction to organic electronics 1

1.1 Organic electronic applications . . . 2

1.2 Organic molecular crystals . . . 4

1.3 Thesis outline . . . 6

2 Electronic properties of organic semiconductors and charge transport in organic molecular crystals 9 2.1 Electronic properties of organic molecular solids . . . 10

2.1.1 π-conjuated molecules . . . 10

2.1.2 Organic molecular crystals . . . 11

2.1.3 Electronic structure of organic molecular crystals . . . . 14

2.2 Differences between organic and inorganic semiconductors . . . 15

2.2.1 Small bandwidth materials . . . 16

2.2.2 Implications of a small bandwidth . . . 16

2.3 Organic field-effect transistors . . . 17

2.3.1 Current-voltage characteristics of FETs . . . 18

2.3.2 Electron versus hole channel devices . . . 22

2.3.3 Non-idealities in organic field-effect transistors . . . 23

2.4 Electrolyte gating . . . 25

2.4.1 Electric double-layer gating using ionic liquids . . . 26

2.4.2 Ionic liquid-gating of organic FETs . . . 29

2.5 Charge transport at the surface of highly ordered organic semi- conductors . . . 30

2.5.1 Bandlike transport in organic FETs . . . 32

2.5.2 Intrinsic charge transport in organic semiconductors . . 35

2.5.3 Extrinsic disorder in organic field-effect transistors . . . 39

2.5.4 Phenomenological mobility edge model for characteriza- tion of disorder . . . 41

ix

3 Experimental techniques 45

3.1 Single crystal growth . . . 45

3.2 Device fabrication . . . 47

3.2.1 Fabrication of air-gap stamps . . . 47

3.2.2 Fabrication of Cytop/PMMA substrates . . . 50

3.3 Crystal lamination . . . 50

4 Band-like electron transport in organic transistors and impli- cation of the molecular structure for performance optimiza- tion 53 4.1 Introduction . . . 54

4.2 Observation of band-like electron transport . . . 55

4.3 Gate dielectric: correlations between dipolar disorder and trans- port . . . 60

4.4 Influence of the molecular structure . . . 61

4.5 Conclusions . . . 63

5 Tailoring the molecular structure to suppress extrinsic disor- der in organic transistors 67 5.1 Introduction . . . 67

5.2 Influence of the side chain length . . . 69

5.3 Microscopic estimates of potential fluctuations . . . 78

5.4 Other possible mechanisms . . . 80

5.5 Conclusions . . . 83

6 High-performancen-type organic field-effect transistors with ionic liquid gates 85 6.1 Introduction . . . 85

6.2 Ionic liquid gating ofn-type OFETs . . . 87

6.3 Conclusions . . . 91

7 Very low bias stress inn-type organic single crystal transistors 93 7.1 Introduction . . . 94

7.2 Bias stress inn-channel devices . . . 94

7.3 Influence of the exposure to air . . . 99

7.4 Conclusions . . . 101

References 102

List of publications 119

1

Introduction to organic electronics

Also known as plastic electronics, organic electronics is a rapidly evolving field of applied electronics. The term organic is due to the fact that the constituent components are carbon-based, synthesized by organic chemistry.

Organic electronics has its origin in the discovery of electrical conductivity of chemically doped polyacetylene¹ in 1977 [1] – a discovery for which Alan J.

Heeger, Alan MacDiarmid and Hideki Shirakawa were awarded with the Nobel prize in chemistry in 2000. However, it was not until 1987, when Koezukaet al. demonstrated the first organic field-effect transistor (FET) based on the π-conjugated polymer polythiophene [2], that research on organic semicon- ductorsreally kicked off. Nowadays, a vast number of organic semiconductors – polymers as well as small molecules – are used in electronic applications and their electrical conductivity is commonly controlled by electric field-effect modulation.

Although being strongly driven by today’s demand for permanent advance- ments in consumer electronics, the field of organic electronics has strongly ben- efited from vast basic research on the fundamental properties of its constituent materials. Even though organic semiconductors have much in common with conventional inorganic semiconductors, there are several – in some cases major – differences between the two. Despite substantial research efforts on organic semiconductors, there are today still several open questions on the exact nature

1which, being a plastic, had always been regarded as electrically insulating

1

of charge transport in these materials. With this thesis, we aim to contribute to the understanding of the intrinsic charge transport mechanisms on the surface of highly ordered organic semiconductors as well as the mechanisms which pre- vent intrinsic transport. In particular, we conducted experimental studies of the (temperature-dependent) mobility in electron-transporting single-crystal field-effect transistors with the goal of understanding the microscopic mecha- nisms which lead to localization of charge carriers and hinder charge transport.

1.1 Organic electronic applications

The large interest in organic semiconductors arises from the unique material properties – including flexibility, transparency, electronic tunability, and light weight. Furthermore, the ability for large-scale and low-temperature process- ability, and their low cost make organic semiconductors ideal candidates for (opto-)electronic devices, where a high switching rate is not a major require- ment. One of the promising fields of application for organic semiconductors is organic light-emitting devices (OLEDs) [3]. Examples are display devices, as shown in Figure 1.1, which benefit from the flexibility and transparency of the organic semiconductors and at the same time do not require the same processing power as for example single-crystalline Silicon integrated circuits.

Organic small molecules or polymers can be patterned onto large area plastic (and even paper) substrates by large-scale ink-jet printing, roll-to-roll manufacturing or thermal evaporation, which reduces not only the processing temperature, but also the weight and cost of these devices. At the time of writing this thesis, there are several commercially available products which implement organic electronics, such as portable electronic devices with active matrix OLED displays or 55” OLED televisions.

Other examples of organic electronic applications which are being actively developed include organic photovoltaic (OPV) cells [4], gas [5, 6] and pres- sure sensors [7], radio frequency identification (RFID) tags [8], organic light- emitting field-effect transistors [9], or organic microprocessors (in 2012, an 8-Bit, 40 Hz organic microprocessor was demonstrated [10]). Although or- ganic semiconductors are used complementary to inorganic semiconductors employed in high-speed microprocessors, the performance of organic semicon- ductors has progressed significantly: The field-effect mobility µ_{F ET} – a key parameter in determining the switching speed of transistors – has increased by several orders of magnitude since the first organic FET [2] (10⁻⁶cm²/Vs) and nowadays reaches values on the order of 10 cm²/Vs in the best and highest pu- rity devices. With this, it has surpassed the mobility of amorphous silicon (∼

0.5 cm²/Vs), a material commonly employed in thin film transistors (TFTs)

1.1. Organic electronic applications 3

Figure 1.1: Organic semiconductors allow for large-area production of electronic applica- tions, for instance by roll-to-roll coating onto plastic or paper substrates (panels on the left).

Devices using OLED technology are today’s most advanced organic electronics applications, with commercially available display devices (top center and panels on the right) which take advantage of the flexibility and transparency and small device thickness of organic semi- conductors. Other interesting applications for organic semiconductors are flexible, low-cost photovoltaic cells (bottom center).

used in liquid crystal displays (LCDs) and therefore a direct ”competitor” of organic semiconductors.

Besides the switching speed of transistors, an important characteristic for applications is a good long-term stability – one of the major issues with organic semiconductor devices, especially when they are exposed to oxygen and hu- midity (such as for gas sensors), or UV radiation (as in OPV cells). Therefore, much effort is devoted to understanding the origin(s) of device degradation and preventing the degradation of the electrical characteristics (see section 2.3.3).

By exposing organic devices to ambient oxidants or sunlight, the chemical com- position of the constituent materials can change, resulting in a degradation of their electrical performance under operation [11]. Figure 1.2 shows the number of days after which the FET mobility degrades in air to 80 % of the initial value (T₈₀) for several commonly used hole-channel organic semiconductors.

Issues with degradation of the device performance are even more pro- nounced in electron-conducting (as opposed to hole-conducting) organic semi- conductors, which are indispensable for implementation of low power consump- tion complementary metal-oxide-semiconductor (CMOS) integrated circuits.

Figure 1.2: Duration for mobility to degrade in air to 80 % of the initial value (T80) versus initial mobility for various hole-transporting organic semiconductors. Adapted from Ref.

[12].

During the first two decades of research on organic semiconductors, mainly hole-conducting (p-channel) organic semiconductors were investigated, which is one of the reasons why many electron-conducting (n-channel) semiconduc- tors still suffer from low mobility and stability (see section 2.3.2). Only re- cently, high-performancen-type organic semiconductors have been developed [13,14]. The issues of performance enhancement and stability of electron con- ducting organic semiconductors are two main topics of this thesis which were investigated by fundamental studies of electron-conducting organic molecular crystals.

1.2 Organic molecular crystals

Since organic electronic applications rely on large-area fabrication of thin films of organic semiconductors, most of the research work is also devoted to the study of organic TFTs, deposited onto substrates either from solution or from gas phase. In organic molecular TFTs, the constituent molecules do not have a perfectly periodic arrangement as in a single crystal but are polycrystalline, containing grain boundaries, defects and impurities. Consequently, charge transport in these systems is dominated by structural disorder – masking the intrinsic charge transport properties – which is one of the reasons why knowl- edge of the microscopic mechanisms governing charge transport in organic FETs has so far been limited.

1.2. Organic molecular crystals 5 The intrinsic properties of organic semiconductors are studied by probing single crystals of organic small molecules. In the early 1980s, Norbert Karl and coworkers used the time-of-flight (TOF) method to study thebulk carrier drift mobility in single crystals of highly purified small molecules [15,16]. By studying the temperature-dependence of the mobilityµ(T), they observed a strong increase when lowering the temperature and found that the mobility follows a power-law dependenceµ(T)∝T⁻ⁿ, similar to what is observed in inorganic semiconductors. The fact that the mobility increases with decreasing temperature suggests that charge carriers are not strongly localized on single molecules (moving by occasionally hopping from one molecule to the next), but form extended states over several molecules at lowT. This was an important observation at a time when organic semiconductors suffered from extremely low mobility values and were regarded as highly disordered materials.

Considering the fact that in many semiconductor devices, such as TFTs, charge transport takes place at interfaces with other materials [17], thesurface charge transport properties of organic molecular crystals are of interest. As opposed to the bulk of the crystal, transport at the surface is affected by a higher degree of disorder – both due to a higher density of defects at the surface as well as disorder originating from the dielectric environment at the interface with the gate insulator. Around the turn of the century,vapor phase transport (VPT) – a method for growing single crystals from powder of small molecules – was used to grow high-purity organic molecular crystals [18,19], paving the way for numerous studies of intrinsic charge transport properties in OFETs [17,20,21].

One material which can easily be grown into nearly perfect single crystals and has proven extremely useful is rubrene, a small molecule organic semi- conductor which reproducibly shows room temperature hole mobility values in FETs up to ∼20 cm²/Vs [22]. Rubrene was the first material for which a negative dµ/dT [22], as well as the Hall effect [23, 24] were observed in organic single crystal FETs. This observation showed that charge transport on the surface of organic molecular crystals is not dominated by incoherent, thermally activated hopping between strongly localized states, but by diffusive transport in delocalized states [23].

Given that organic semiconductors are small bandwidth materials and the carrier mean free path at room temperature is on the order of the lat- tice spacing [25, 26], applying band theory used to describe conventional semiconductors is not justified and appropriate models need to be developed which correctly describe charge transport in OFETs. However, studying high- performance single crystal OFETs is not only useful for determining the micro- scopic charge transport mechanisms, it also helps determining the ”intrinsic

limit” of organic semiconductor devices. Fundamental research on organic molecular crystals is therefore indispensible to identify mechanisms which can improve the performance of organic electronic devices.

1.3 Thesis outline

This thesis focuses on electronic transport in n-type FET devices of single crystals from organic molecular semiconductors with the aim to further the understanding of the microscopic charge transport mechanisms on the surface of highly ordered molecular semiconductors. In chapter 2, we describe the electronic properties of small π-conjugated molecules and molecular crystals and discuss the differences between organic and inorganic semiconductors.

Since field-effect transistors are an important tool to probe the charge transport mechanisms in organic semiconductors, we introduce the working mechanism of FETs in general and electric double-layer transistors gated by ionic liquids. Furthermore, we give an overview of the experimental observa- tions of ”band-like” transport in OFETs as well as the historical development of various models aiming to describe charge transport in organic molecular crystals. We then discuss the influence of disorder on charge transport and describe a phenomenological model used in chapters 4 and 5 to quantify dis- order in high-performance OFETs.

Important aspects of device fabrication useful for reproducing the experi- mental measurements described in this thesis are discussed in chapter 3. We describe the vapor phase transport method for single crystal growth, substrate fabrication, as well the method used for lamination of single crystals onto the substrates.

In chapter 4, we present experimental evidence for band-like electron trans- port inn-channel single-crystal FETs. Through a quantitative analysis of our measurements, together with results on different p-channel organic transis- tors, we suggest a structure-property relation between the molecular structure / crystal packing and the occurrence of band-like transport in OFETs. We test the validity of these predictions in chapter 5 by extensive temperature- dependent charge transport measurements on two perylene derivatives. We find that disorder can be suppressed by attaching long substituents to the π-conjugated molecular cores, which leads to a reduction of potential fluctua- tions in the transistor channel and increases the temperature range over which band-like transport occurs.

Our measurements on ionic liquid gating ofn-channel FETs is presented in chapter 6. We find that the field-effect mobility in our devices remains remarkably high and – for a considerable fraction of the devices – does not

1.3. Thesis outline 7 degrade as compared to the FET mobility measured in air. These results are promising for low-voltage operation of high-performancen-type organic FETs.

In chapter 7, we study the bias stress effects inn-channel single-crystal FETs on fluoropolymer gate dielectrics. We find that the current degradation in vacuum, resulting from a shift of the threshold voltage, is extraordinarily low in our devices – two orders of magnitude lower than in the best p-channel organic FETs. In air, the bias stress-induced current degradation is, although higher than in vacuum, still extremely low. This is remarkable forn-channel organic transistors, which commonly show substantial device degradation in air, and is a promising result for organic electronic applications.

2

Electronic properties of organic semiconductors and charge transport in organic molecular crystals

In this chapter, we discuss some general concepts useful for understanding the charge transport properties in organic semiconductors. We introduce the electronic properties ofπ-conjugated organic molecules and molecular solids, discuss the characteristics of conventional field-effect transistors (FETs) as well as electric double-layer gated FETs, and give an overview of the charge trans- port mechanisms and the influence of disorder in organic molecular crystals.

Finally, we discuss a phenomenological mobility edge model used in chapters 4 and 5 for characterizing energetic disorder in high-performance single-crystal FETs.

Althoughπ-conjugated polymers are interesting for organic electronic ap- plications, thin films of semiconducting polymers are typically highly disor- dered, masking the intrinsic transport properties. Therefore, this thesis focuses on single crystals of small conjugated molecules – exhibiting highest possible degree of molecular ordering – to study the fundamental charge transport mechanisms in organic semiconductors. Extensive reviews on semiconducting polymers can be found for instance in Refs. [27] or [28].

9

2.1 Electronic properties of organic molecular solids

In this section, we introduce the basic concepts of organic semiconductors, such as π-conjugation in organic molecules, the molecular arrangement in organic molecular crystals and the formation of energy bands in organic molecular solids.

2.1.1 π-conjuated molecules

Carbon, the main element of organic semiconductors, has four valence elec- trons and hence can bond up to four different atoms. The electronic ground state configuration of an isolated carbon atom is 1s²2s²2p², while in chemically bonded carbon, the 2s and 2porbitals can hybridize and form either sp, sp², or sp³ configurations, depending on the number of p-orbitals involved in hy- bridization. In organic semiconductors, the carbon atoms aresp² hybridized, which means that they have three coplanarsp²orbitals and one perpendicular p_z orbital. The overlap of the atoms three sp²-hybridized orbitals with the sp²orsorbitals of three neighboring atoms results in three planarσcovalent bonds, while the overlap of thep_z-orbital with that of one neighboring atom leads to an additional π-bond – thus forming a double bond between those two neighboring atoms. A system of connected sp²-hybridized carbon atoms has an alternating sequence of single (σ) and double (σandπ) bonds. Such a system is calledπ-conjugated and the electrons in theπ-bonds aredelocalized over the whole conjugated part of the molecule.

Since the orbital overlap betweensp²hybridized orbitals is larger than that of thepz-orbitals, electrons in σbonds are much deeper in energy than those in π bonds. σbonds are mainly responsible for the chemical bonding of the atoms. π-electrons on the other hand are shallower in energy and determine the low-energy electronic properties, such as the energy levels of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). Forπ-conjugated molecules, the difference between the HOMO and LUMO levels (the molecule’s HOMO-LUMO-gap) is a few electron volts (eV) and consequently, conjugated molecules and molecular solids typically absorb or luminesce electromagnetic radiation in the visible spectral region [29].

Theσand πbonds are shown schematically in Figure 2.1a,b for the case of benzene – the simplest example of anaromatic molecule. Benzene, a cyclic molecule containing six carbon and hydrogen atoms, is the basic building block of most molecular semiconductors whoseπ-conjugated cores are composed of several aromatic (or heterocyclic) rings. As shown in Figure 2.1c, the positions of the single and double bonds can be interchanged, leading to two distinct but

2.1. Electronic properties of organic molecular solids 11 degenerate electronic configurations. The electronic structure of the molecule in the ground state is a linear combination of these resonant structures. To indicate the delocalized nature of the electrons across theπ-conjugated system, the benzene ring is often represented by a circle inside the hexagon of carbon- carbonσ-bonds, as shown in Figure 2.1d.

a

c

b

d

Figure 2.1: Schematic representation of the isosurfaces ofσ (a) andπ bonds (b) in the benzene molecule, the main building block of molecular semiconductors (from Ref. [29]).

The two resonance Kekul´e structures of benzene (c) are often represented by a circle inside the hexagon of carbon-carbonσ-bonds (d), emphasizing the delocalized nature of theπ- electrons.

Of the virtually unlimited amount of possible conjugated molecules, a small selection of some of the widely studied molecules are shown in Figure 2.2: The class of molecules which historically has probably attracted most attention in the field of organic electronics – both experimentally and theoretically – are the linear polyacenes, consisting of linearly arranged benzene rings. More recently, research has focused on molecules with side groups attached to theπ- conjugated core. PDIF-CN2[30], ann-channel molecular semiconductor which has been an inherent part of this thesis has cyano (C≡N), dicarboximide, and fluorocarbon groups attached to the π-conjugated perylene core. Rubrene – a derivative of tetracene with four phenyl groups attached to the two central benzene rings – has since its re-discovery for organic semiconductors in 2003 [31] proven extremely successful.

2.1.2 Organic molecular crystals

A crystal is ”a body that is formed by the solidification of a chemical element, a compound, or a mixture and has a regularly repeating internal arrange- ment of its atoms and often external plane faces” [32]. There are metallic,

a b

c

N N

O

O O O

C N

CH2C

3F F 7

7C

3CH

2

N C

Figure 2.2: Examples of organic molecular semiconductors. The linear polyacenes (a) consist of a number of linearly arranged benzene rings. Shown here are (from top to bot- tom) benzene, naphthalene, anthracene, tetracene, and pentacene, which exhibits good hole conduction in polycrystalline thin films. PDIF-CN2 (b), one of the main molecular semi- conductors studied in this thesis, shows good electron transport properties in single crystals as well thermally evaporated thin films. The molecular semiconductor which reproducibly shows the highest hole mobility is rubrene (c). This it why rubrene is often used for studying the intrinsic charge transport mechanisms in organic molecular crystals.

ionic, covalent, and molecular crystals, depending on the bonding mechanism.

Molecular crystals are held together by weak (compared to theintramolecular covalent bonds)intermolecular van der Waals (vdW) and electrostatic (multi- pole) forces. This weak interaction between molecules has vast implications on the physical properties of organic molecular crystals, such as the mechanical (e.g.: low melting point, high thermal expansion) or electronic properties as discussed below.

The molecular arrangement in a crystal is determined by the interplay of attractive and repulsive interactions between the molecules. A large attractive contribution of the vdW dispersion force comes from interactions of fluctuat- ing/instantaneous dipoles (due to the motion of electrons in theπ-conjugated system) with induced dipoles on neighboring molecules. Consequently, vdW dispersion interactions favor high π-π orbital overlap and therefore parallel face-to-face configuration of molecules (”π-stacking”).

However, the distribution of π-electrons in conjugated molecules is such that there is a high electron density above and below the molecular plane, which results in negative net charges outside of the molecular plane and gives π-conjugated molecules a permanent quadrupole moment. Due to attractive interactions between the negatively charged π-electron clouds with the pos- itively charged edges of neighboring molecules, quadrupole interactions fa- vor anedge-to-face orientation (while a face-to-face packing leads to repulsive

2.1. Electronic properties of organic molecular solids 13

quadrupole interactions).

a b

Figure 2.3: Examples of two common molecular packing motifs in organic molecular crys- tals. The crystal structure of PDIF-CN2 (a), viewed along the unit cell diagonal, reveals how the nearest neighbor molecules in thea-bplane are shifted to the side in the slip-stacked face-to-face packing motif (adapted from Ref. [30]). The crystal structure of rubrene (b), viewed along thecaxis, is an example of a herringbone structure, where the next-nearest neighbors in thea-b plane are oriented differently (from Ref. [33]). Due to the different orbital overlap along theaandbaxes, the charge transport properties in herringbone-type molecular crystals are usually highly anisotropic, as discussed in section 2.5.2

The crystal structure essentially depends on which of the two interac- tions dominates. In small conjugated molecules such as benzene, quadrupole interactions dominate, while van der Waals dispersion interactions – being proportional to the orbital overlap – become increasingly important with in- creasing size of the molecule. Generally, the molecules form densely packed two-dimensional layers perpendicular (or somewhat tilted) to the long axis of the molecule. For most molecular semiconductors, the 2D layers are nei- ther perfectly π-stacked nor edge-to-face orientated. Two common packing motifs of molecular semiconductors are a slip-stacked face-to-face molecular packing (as for PDIF-CN₂, see Figure 2.3a) or a herringbone structure (such as for rubrene, see Figure 2.3b). An extensive overview on crystal packing of molecular semiconductors is given in Ref. [34].

As discussed below, a high orbital overlap between neighboring molecules is beneficial for charge transport as it maximizes the transfer integral [35].

However, engineering of molecular semiconductors with high orbital overlap is challenging and predictions of the precise crystal structure are extremely diffi- cult [36]. Additionally, since the intermolecular interaction energies are weak,

several molecular crystals form polymorph structures and therefore the orbital overlap in crystalline molecular semiconductors can depend on the growth con- ditions [37,38].

2.1.3 Electronic structure of organic molecular crystals

As mentioned in section 2.1.1, the energy levels relevant for the low-energy electronic properties of isolated molecules are the HOMO and LUMO levels.

In a crystal, intermolecular interactions lead to energy level splitting and give rise to energy bands: the HOMO and LUMO levels of all molecules in the crystal hybridize into HOMO and LUMO bands, or – to adopt the terminology used for inorganic semiconductors – valence band (VB) and conduction band (CB), as illustrated in Figure 2.4.

Figure 2.4: Illustration of the formation of HOMO and LUMO bands (valence and con- duction bands) by the interaction of a large number of (ethylene) molecules. From Ref.

[39]

The bandwidthW is proportional to the orbital overlap of the molecules and therefore depends crucially on the orientation of the molecules in the crystal [38]. Knowing the crystal structure, it is possible to predict the band structure of organic molecular crystals. This is commonly done by performing ab initio calculations of the intermolecular electronic coupling and the reorga- nization energy (energy relaxation upon adding a charge carrier to a molecule) within the framework of density functional theory (DFT) [33,40–43].

The photoemission spectrum (Figure 2.5a), measured at 75 K on a 100 nm thickin situ grown crystalline pentacene film shows the dispersion of the two (because crystalline pentacene has two non-equivalent molecules per unit cell)

2.2 Differences between organic and inorganic semicond. 15 branches of the VB [44]. The estimated bandwidth (extracted at theM point) isW = 450±15 meV. A similar bandwidthW ≈400 meV is extracted from

2.0 1.5 1.0 0.5 0.0

10 5

0

Γ Y Γ

Binding energy (eV)

k_// (nm^-1)

a b

Figure 2.5:Photoemission spectroscopy measurements on two typical organic semiconduc- tors. (a) Density plot of the second derivative of the photoemission spectrum of a crystalline pentacene film, recorded at 75 K, along different paths in the Brillouin zone. The dots rep- resent the peak positions of the individual spectra, while the full line is the calculated band dispersion without disorder and coupling to molecular vibrations [43]. The width of the valence band (extracted at theM point) isW = 450±15 meV. Adapted from Ref. [44].

(b) Second derivative of the photoelectron spectrum of a rubrene single crystal recorded at RT. The width of the valence band dispersion is approximately 400 meV and the effective mass of the holes, estimated at the Γ points, is 0.65(±0.1)m₀. Adapted from Ref. [45].

.

photoelectron spectroscopy measurements on rubrene single crystals at room temperature (Figure 2.5b) [45]. The hole effective mass, estimated at the Γ points within the tight-binding approximation, ism^∗_h= 0.65(±0.1)m0.

2.2 Differences between organic and inorganic semiconductors

Organic semiconductors are different in many aspects from their inorganic counterparts. Inorganic semiconductors are ionic or covalent crystals, which discriminates them substantially from predominantly vdW-bonded organic molecular crystals. While organic semiconductors differ in several aspects (e.g., in their chemical or mechanical properties) from inorganic semiconduc- tors, the focus in this section lies in the differences in electronic properties between organic and inorganic semiconductors. An important implication of the distinct type of bonding in organic and inorganic crystals is the compa-

rably weak intermolecular transfer integral t in organic semiconductors and therefore lower bandwidth, whose impacts are discussed in this section.

2.2.1 Small bandwidth materials

In commonly encountered inorganic semiconductors, such as for example sil- icon, bandwidths are typically on the order of 10 eV, while we have seen in section 2.1 that W ∼ 0.5 eV in crystalline molecular semiconductors. The small bandwidth in organic semiconductors is due to the lowπ-πorbital over- lap of adjacent molecules, which reduces the probability of an electron hopping from one molecule to the next. This process is typically characterized by a hopping or transfer integral t, which is proportional to the bandwidth¹ and is direction-dependent (leading to anisotropic charge transport properties in many molecular crystals).

If one could think of charge carriers in organic semiconductors in terms of heavy quasiparticles,² the small bandwidth in organic semiconductors would imply a much larger effective massm^∗than in inorganic semiconductors. Since the mobility is proportional to 1/m^∗, the smallW qualitatively explains why the mobility in organic semiconductors is roughly one order of magnitude smaller than in inorganic semiconductors. The ratio of the bandwidth of silicon divided by the bandwidth of rubrene (WSi/Wrub) is approximately _{0.5 eV}^{10 eV} = 20, which is almost identical to the ratio of the RT hole mobilities µ^RT_Si /µ^RT_rub ≈

450 cm²/Vs

20 cm²/Vs = 22.5.

A small bandwidth also implies a high density of states (DOS), since a large number of states is distributed over a small energy window, which enhances the impact of disorder on the charge transport properties. The density of surface statesN_2D in the band of an organic crystal can be estimated by taking one state per molecule distributed in energy over the bandwidth of the valence band: N2D= (a²W)⁻¹. For rubrene,a= 7.2 ˚A andN2D≈4·10¹⁴cm⁻²eV⁻¹. For comparison, the density of surface atoms in Si along the (100) orientation is 6.8·10¹⁴ cm⁻² [46], son2D≈7·10¹³cm⁻²eV⁻¹.

2.2.2 Implications of a small bandwidth

An important consequence of the small bandwidth is that organic semicon- ductors are sensitive to a number of interactions whose energy scales are too small to be relevant for large-bandwidth inorganic semiconductors. An exam- ple are polaronic effects (i.e., the tendency of charge carriers to localize due to

1In a 1-D tight-binding approximation,W= 4t.

2Strictly speaking, application of band theory is not justified due to the small mean free path in the relevant temperature range.

2.3. Organic field-effect transistors 17 their polarization of the environment): the polaron binding energy in organic semiconductors can easily be on the order of 0.1 eV [47], which can have a significant influence on charge transport. Using high-kdielectric materials as gate insulators leads to the formation ofFr¨ohlich polarons – quasiparticles of charge carriers dressed by ionic polarization clouds in the dielectric medium [48,49]. The magnitude of these interactions can correspond to a significant fraction of the bandwidth, in which case it has a large influence on charge localization in organic molecular crystals. In large-bandwidth semiconductors on the other hand, the energies associated with polaronic effects are small compared to the bandwidth and can be treated perturbatively [50].

More generally, an implication of the small bandwidth in organic semi- conductors is thatdisorder has a significant influence on charge transport in OMCs. Intermolecular interactions with sources of disorder locally modulate the energy levels, which leads to a broadening of the DOS (creating a ”band tail”) and effectively enhances localization of the charge carriers. An important source of disorder in organic crystals is thermal fluctuations of the molecules (”dynamic disorder”) as will be discussed in section 2.5. This causes fluctu- ations of the hopping integrals which, around room temperature (RT), are comparable to their average valuehti[51] and greatly affect charge transport.

In actual devices, static disorder (crystal defects, or any kind of impurities) is often induced by the substrate or during device fabrication. Even in high- quality single crystals there can be charged impurities introduced during device fabrication, especially on the surfaces where they strongly affect the charge carriers in the FET channel: charged or charge polarized impurities on the crystal surface evoke electrostatic interactions with the charge carriers in the channel, which are spatially separated by only a few nanometers. The Coulomb interaction energy can easily be tens of meV, such that these impurities act as charge traps or scattering centers for the field-induced carriers. A well-studied example of disorder encountered in organic field-effect transistors (see section 2.3) is the substrate-induceddipolar disorder, where randomly oriented static dipoles of the monomer units in organic polymers (used as gate insulators) cause potential fluctuations at the interface with an organic semiconductor, which broaden the DOS and thereby reduce the carrier mobility [52,53].

The implications of all these mechanisms on charge transport are discussed in more detail in section 2.5.3.

2.3 Organic field-effect transistors

In organic crystals, the bandgapEgis typically on the order of 2-3 eV – large compared to W – and chemical doping, as it is commonly done in inorganic

semiconductors, often leads to suppression of the carrier mobility [54,55] due to increased impurity scattering.³ A way to introduce carriers (and modulate the carrier density) is byelectrostatic doping through application of an electric field – which is why field-effect transistors represent a powerful tool to study organic semiconductors. In this section, we will discuss the basics of (organic) FETs with a focus onn-channel (electron conducting) devices.

2.3.1 Current-voltage characteristics of FETs

FETs are the basic building blocks of integrated circuits such as microproces- sors. As shown in Figure 2.6, they consist of a metallic gate electrode and an insulating material separating the semiconductor from the gate, which is why they are also called MISFETs (metal-insulator-semiconductor field-effect tran- sistors) or MOSFETs, if the insulator is an oxide. Besides the gate contact, FETs have source and drain electrodes for injecting and extracting current.

Applying a potential difference VGS between gate and source contacts gen- erates an electric field across the insulator, which attracts charge carriers in the semiconductor to the interface with the dielectric and forms a conductive channel.

Gate

V

I

Insulator Semiconductor

V

E

Drain + + + + + + + + + + + + + + + + + + + + Source

Figure 2.6: Illustration of the FET geometry and charge accumulation in the transistor channel: Application of a gate-source biasVGS creates an electric fieldE~ in the gate insu- lator, attracting charges to the surface of the semiconductor at the interface with the gate dielectric. The charge density is proportional toE, and therefore to~ VGS. Application of a drain-source bias VDS leads to a flow of charge carriers between the drain and source electrodes.

This geometry resembles a parallel-plate capacitor and the field-induced

3However, chemical doping of organic semiconductors has also lead to the emergence of superconductive states [56,57].

2.3. Organic field-effect transistors 19 charge densitynat the interface is given by

n= C_i

e (V_GS−V_{T h}) (2.1)

where the capacitance per unit areaC_i=/d_ins depends on the permittivity and thickness d_ins of the gate dielectric, e is the electron charge, and the threshold voltageV_{T h} is the voltage required to form the conducting channel between source and drain electrodes. The formation of the channel is accom- panied by a modification of the energy bands: applying a potential difference between gate and source contacts shifts the energy levels of the semiconductor at the interface with the gate dielectric with respect to the energy levels of the metal contacts. Thereby, charge is accumulated at the interface, which leads to bending of the energy bands.

Figure 2.7 schematically shows the band bendingperpendicular to the semi- conductor/dielectric interface (FET channel) for the ideal case of an undoped semiconductor, whose Fermi level lies in the middle of the HOMO-LUMO gap.

If the Fermi level of the semiconductor is different from the work function of the gate metal (Figure 2.7a), a potentialVF B needs to be applied to the gate electrode in order to recover flat bands in the semiconductor, where no charge is accumulated (Figure 2.7b). Increasing VGS > VF B bends the HOMO and LUMO bands down and leads to electron accumulation in the LUMO band (Figure 2.7c), whileV_GS< V_{F B} leads to depletion of electrons and accumula- tion of holes in the HOMO band (Figure 2.7d).

After aligning the LUMO (HOMO) band with the energy levels of the drain and source contacts, applying a voltage bias V_DS between drain and source leads to an electron (hole) current. This drain-source currentI_DS can be modulated by changing the gate-source potential V_GS, which controls the electron (hole) concentration in the FET channel (and therefore the channel resistance).

FETs are characterized by two types of I−V characteristics, either by measuringIDS vs. VDS for constantVGS(”output characteristics”) orIDS vs.

VGS for constant VDS (”transfer characteristics”). In the linear regime (i.e., when|VGS−VT h| ≥ |VDS|), the current in an ideal FET is given by [58]

I_DS^lin =W

LµVDSCi

(VGS−VT h)−VDS

2

. (2.2)

Here,W andLare the width and length of the FET channel and the mobility µ describes how fast charge carriers move in the FET channel (the unit of µis m²/V·s). WhenVDS →(VGS−VT h), the gate electric field at the drain

VGS = V

a

VGS > V

FB V

GS < V

c d

--- --- -- --

+ ++ +++++

e·V

GS

E

z

e·V

GS

VGS = 0 V

LUMO

EF

S I

M

b

HOMO

e·V

FB

+

Figure 2.7: Band diagrams of a metal-insulator-semiconductor (M-I-S) device perpendic- ular to the semiconductor/dielectric interface. If the Fermi level of the semiconductor is different from the work function of the gate metal (a), a potential differenceVGS =VF B

needs to be applied between source and gate contacts (b) in order to restore flat bands in the semiconductor, compensating for the difference in the metal work function and the semiconductor Fermi energy. Application ofVGS > VF Bbends the bands down and leads to accumulation of electrons in LUMO band (c), whileVGS < VF B accumulates holes in the HOMO band (d).

electrode approaches zero and the FET channel gets ”pinched off” at the drain electrode. Further increasing the magnitude of VDS does not increase IDS, which is why this is called thesaturation regime, where

I_DS^sat= W

2LµCi(VGS−VT h)². (2.3) The linear and saturation regimes can be seen in Figure 2.8, which shows the output and transfer characteristics of an organic FET.

Important properties for characterizing transistors includeVT h, the FET mobility, or the on/off ratio, which is stated as an order of magnitude (e.g., 10⁷ as in Figure 2.8b) and is simply calculated by dividing IDS in the on

2.3. Organic field-effect transistors 21

0 10 20 30

0 1 2 3 4

IDS (µA)

V_DS (V)

sub-

V

Th+V

DS /2 IDS (A)

VOn

0 10 20 30 40 50

10^-13 10^-11 10^-9 10^-7 10^-5

0 1 2 3 4 5 6

IDS (µA)

a

b

GS = 25 V

20 V

15 V 5 V; 0 V 10 V

VDS = 5 V 4 V 3 V 2 V 1 V

V_DS (V)

Figure 2.8: Output (a) and transfer (b) characteristics (trace and retrace) of a bottom- gate/bottom-contact n-channel organic FET fabricated by laminating a single crystal of PDIF-CN2onto a Si/SiO2/Cytop substrate with pre-patterned gold electrodes. The output characteristics (a) show howIDS increases linearly forVDS < VGS−VT h, becomes non- linear aroundVDS ≈VGS−V_{T h}and saturates forVDS > VGS−V_{T h}. From the transfer characteristics (b), various properties of the FET can be extracted: the threshold voltage VT his extracted by linear extrapolation ofIDSvs. VGS(right axis) to zero, while the linear FET mobilityµF ET is proportional to dIDS/dVGS. By plotting log(IDS) vs. VGS (left axis) one can read out the onset voltageVOn≈ −0.5 V, below which the transistor is in the off state. The on/off ratio in this FET (taken asIDS(VGS = 30V)/IDS(VGS = -1 V) for VDS = 5 V is on the order of 10⁷.

state by that in the off state (at voltages which are typically mentioned). VT h

is extracted by linearly extrapolatingIDS vs. VGS to zero (and subtracting VDS/2). Since the FET mobility depends on the magnitude of the in-plane electric field|E|~ =V_DS/Lasµ∝exp(√

E) [59,60], it makes sense to compare the values of µ of different semiconductors for smallV_DS (i.e., in the linear regime). A common way to calculateµis from the transfer characteristics, by taking the derivative ofI_DS with respect to V_GS:

µ_{F ET} = L W

1 VDS·Ci

dI_DS dVGS

. (2.4)

If the contact resistanceR_C of the FET is small compared to the channel resistanceR_ch,µ_{F ET} is equal to the charge carrier mobility on the surface of the semiconductor. If, however, R_C is comparable to (or larger than) R_ch, FET mobility is limited by charge injection and the carrier mobility in the channel can be determined in a four-terminal configuration, where two voltage probes are introduced in between the source and drain electrodes on one side

of the FET channel. VDS and L in equation 2.4 are then substituted by the potential dropV_xxacross and the distanceL⁰ between the voltage probes.

2.3.2 Electron versus hole channel devices

In principle, organic semiconductors should be ambipolar – i.e., conduct elec- trons and holes depending on the applied gate bias – as suggested by Figure 2.7. In practice, however, organic FETs tend to be unipolar, with the majority working asp-channel devices. On the one hand, this is due to the energy differ- ence between the work function of the metal contacts (commonly Au, Φ_Au∼ 5 eV) and the HOMO/LUMO levels of the organic semiconductors, which in most cases is much smaller for the HOMO level than for the LUMO level. This facilitates injection of holes from the contacts into the organic semiconductor, while electron injection is suppressed. On the other hand, the shallow energy of the LUMO levels makes electrons susceptible to trapping by hydroxyl (-OH) groups present at the interface with the gate dielectric (e.g., SiO2) [13] or by ambient oxidants (such as O2or H2O). Since the HOMO energy levels of most organic semiconductors are deeper than the energy level of these trap states, holes are much less affected by hydroxyl groups or ambient oxidants.

The energy level mismatch can be improved by using low work function metals such as Ca (Φ_Ca ∼ 3 eV). However, such metals oxidize in air and therefore the devices can only operate in vacuum or need to be encapsulated.

The issue of hydroxyl groups on the surface of the gate dielectric can be im- proved by surface passivation with self-assembled monolayers [13]; however, a better solution is to use different gate dielectrics, e.g. polymers, where no hydroxyl groups are present. Since both problems are related to the shallow LUMO energy level, a common approach is to lower the energy levels of the organic semiconductors. This can be achieved by adding electron-withdrawing substituents (such as cyano groups) to the π-conjugated part of the semicon- ductors or by fluorination [14,61]. As a rule of thumb, the LUMO level should lie deeper than∼4 eV [28] in order to prevent trapping of electrons upon ex- posure to ambient atmosphere.

As the focus until the mid-2000s had been on hole transporting devices, there are still more high-performance p-type than n-type semiconductors.

However, after identifying processes which trap electrons and suppress n- channel operation [13], a lot of effort has been put into identifying high- mobility electron transporting semiconductors [14, 28, 62]. Nowadays, there are several novel n-type (and ambipolar) molecules and polymers, which are air-stable and exhibit high FET mobility values≥1 cm²/Vs [62,63], compa- rable to the best p-channel organic FETs.