organic/organic interfaces
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 maandag 19 januari 2009 om 10.00 uur
door
Anna Stefania MOLINARI
Master of Science in Physics,
Universit´a degli studi di Genova, Genova, Itali¨e geboren te Genova, Itali¨e.
Toegevoegd promotor: Prof. dr. A. F. Morpurgo Samenstelling promotiecommissie:
Rector Magnificus voorzitter
Prof. dr. ir. H.W.M.Salemink Technische Universiteit Delft, promotor Prof. dr. A. F. Morpurgo University of Geneva, toegevoegd promotor Prof. dr. T. Takenobu Tohoku University, Sendai
Prof. dr. L. de Cola Universiteit Munster
Prof. dr. R. Coehoorn Eindhoven University of Technology Prof. dr. L. D. A. Siebbeles Technische Universiteit Delft
Prof. dr. S.G. Lemay Technische Universiteit Delft
Prof. dr. Y.V. Nazarov Technische Universiteit Delft, reservelid
Cover design: A.S. Molinari
Front: Optical microscope picture of rubrene single-crystal field-effect transistors. The rubrene crystal has been manually aligned on the prefabricated transistors with different channel length.The area shown in the picture is approximately 1.5× 1 mm2
.
Back: Optical microscope picture of TTF (orange) and TCNQ (yellow) crystals. The crystals shown are 13 mm long, 100-500 µm wide and with a thickness of 50100 µm.
Printed by: Gildeprint, Enschede, The Netherlands Copyright c 2008 by A.S. Molinari
Casimir PhD Series, Delft-Leiden 2008-09 ISBN : 90-8593-046-4
ma per seguir virtute e canoscenza.”
(“...Call to mind from whence ye sprang: Ye were not formd to live the life of brutes, But virtue to pursue and knowledge high.”)
Dante Alighieri, Divine Comedy, Hell XXVI, 116-120
1 Introduction 1
1.1 Organic electronics . . . 2
1.2 Conduction in organic materials . . . 4
1.3 Thesis outline . . . 6
References . . . 7
2 Organic molecular materials 9 2.1 Introduction . . . 10
2.2 Electronic properties of molecular solids . . . 10
2.2.1 Organic molecules . . . 10
2.2.2 Organic crystals . . . 12
2.2.3 Electronics properties of organic crystals . . . 14
2.3 Transport mechanisms and regimes in organic semiconductors . . 16
2.4 Transport at the surface of organic molecular crystal . . . 18
2.4.1 Organic Field-effect transistors . . . 18
2.4.2 Organic charge transfer compounds and interfaces . . . 22
2.5 Transport mechanism across metal/organic interfaces . . . 23
2.5.1 Schottky theory . . . 24
2.5.2 Transport over a barrier: Thermionic emission theory . . . 27
References . . . 29
3 Reproducible low contact resistance in Rubrene single-crystal field-effect transistors with nickel source and drain electrodes 31 3.1 Introduction . . . 32 3.2 Scaling experiment . . . 32 3.3 Contact Resistance . . . 34 3.4 Conclusions . . . 36 References . . . 38 v
4 Bias-dependent contact resistance in rubrene single-crystal
field-effect transistors 39
4.1 Introduction . . . 40
4.2 Different metal contact electrodes . . . 40
4.3 Reproducibility and bias-dependence of the differential conductance 44 4.4 Discussion and conclusions . . . 44
References . . . 46
5 Quantitative analysis of electronic transport through weakly cou-pled metal/organic interfaces 49 5.1 Introduction . . . 50
5.2 Oxidized Copper contacts . . . 50
5.3 Temperature dependence of the differential conductance . . . 51
5.4 Generalized Schottky model . . . 52
5.5 Conclusions . . . 56
References . . . 56
6 Ambipolar Cu- and Fe-phthalocyanine single-crystal field-effect transistors 59 6.1 Introduction . . . 60
6.2 Cu- and Fe-Pc’s . . . 60
6.3 Experimental results . . . 62
6.4 Conclusions . . . 65
References . . . 66
7 High electron mobility in organic single-crystal transistors 69 7.1 Introduction . . . 70
7.2 n-type FETs . . . 70
7.3 Experimental results . . . 72
7.4 Conclusions . . . 78
References . . . 78
8 Metallic conduction at organic charge-transfer interfaces 81 8.1 Introduction . . . 82
8.2 TTF and TCNQ single crystals growth and characterization . . . 83
8.3 Charge transfer interfaces . . . 85
8.4 Experimental results . . . 87
8.4.1 Temperature dependence and metallic conductivity . . . . 89
8.5 Analysis of the interfacial properties . . . 91
References . . . 93 Appendix A: Crystal growth and sample preparation 97 Appendix B: Scaling experiments on pentacene FETs 101
Summary 105
Samenvatting 109
Curriculum Vitae 113
List of publications 115
Introduction
1.1
Organic electronics
Polymers, widely known as plastics, play an important role in modern society. They are used in larger quantities than any other class of materials and can be found not only in packaging but also in constituents components for televisions, computers, instruments, tools, and in countless other items. Plastics are organic materials as wood or paper, and consist of long chain of atoms bonded together. The common modern meaning of the word plastic is “synthetic product made from oil derivatives” (introduced in 1909 by Leo Baekeland the father of Beke-lite, the first synthetic plastic), but the word “plastic” has a more ancient origin, as it derives from the Greek plastikos, which means “able to be molded, pertain-ing to moldpertain-ing” [1]. The interest in plastics lies exactly in their possibility to be “molded” in a very broad sense, that is, molded not only in shape, but also in chemical and physical properties. Indeed, the mechanical, optical and con-ducting properties of organic materials can be tuned by changing their chemical constituents.
Originally, most polymers were known to have insulating properties. This was the case until electrical conduction in organic polymers was reported for the first time. In 1963 Weiss et al. [2] reported high-conductivity in iodine-“doped” oxidized polypyrrole, and in 1977 Shirakawa et al. proved that by adding impu-rities (dopants) like halogens, the electrical conduction of polyacetylene increases several order of magnitude [3]. In recognition for this fundamental breakthrough Alan Heeger, Alan MacDiarmid and Hideki Shirakawa received the Nobel Prize for chemistry in 2000 [4]. The possibility of doping polymers to induce conduction raised not only interest for new studies on organic materials, but it also started a new field of research: Organic Electronics. As Alan Heeger mentioned in his No-bel lecture (December 2000) “The new generation of conductive polymers could offer the electrical and optical properties of metals or semiconductors combined with the mechanical properties and processing advantages of polymers”.
Electronics based on organic compounds have attracted strong attention in the past 30 years because organic materials are lighter, more flexible, and less expensive than inorganic conductors. This does not mean that they are expected to replace silicon. In fact organic materials aim at applications complementary to those based on silicon, where ease of fabrication, mechanical flexibility, low-cost and/or large-area applicability are key issues. Many organic materials are currently being developed and used for applications such as flexible displays [5], electronic paper, field-effect transistors [6] organic solar cells [7], and organic light emitting devices [8]. Even if electroluminescence and photoconductivity in organic compounds was known since the fifties, only the increase in their
quality allowed the improvement of device efficiency, as it is needed for possible applications. Conductive polymers are also expected to play an important role in the emerging science of molecular computers for their applications in electrical components as FETs.
Figure 1.1: Examples of organic devices used for commercial applications as flexible displays, organic displays, organic solar cells.
Organic materials used in devices also offer the possibility of combining, and tune independently, different physical properties. A recent example is offered by studies on non-volatile memories based on conductive and ferroelectric polymers, which reported the possibility of modifying separately conductivity and ferro-electricity, to offer a non-destructive read-out of the device, which is not possible with inorganic ferroelectrics [9]. In addition to that, carbon-based compounds can be used in the form of ink, and printed on plastic, or paper, or possibly tex-tiles. In such a way it is feasible to print active devices through the simple use of “electronic ink”. This new technology, named Printed Electronics, is developing new applications, as flexible display and smart labels (RFID), using of low-cost technology.
Not only polymers are studied and used as the core material for electronic components, but also small conjugated molecules, in the form of thin films or sin-gle crystals. Whereas conjugated polymers are processable from solution, small molecules can usually be deposited more easily by sublimation or evaporation. If solution processable materials are suitable for large area devices and mass
pro-duction, low molecular weight materials grown by vapor sublimation in the form of single crystals can offer high degree of structural ordering. This should result in better device performance. In addition, it also allows the study of the intrinsic electronic properties of the materials. The intrinsic properties of organic materi-als are different from those of inorganic solids due to their particular electronic structure, which is why organic solids are not only interesting for technology, but also for fundamental scientific research. Indeed molecular materials offer the possibility of studying new physical phenomena not observed in any other class of materials.
One of the key application of organic semiconducting materials in electronics is the field effect transistor, which is a main subject of this thesis. Currently, the transistor performance for devices based on organic materials is sufficiently high to compete with devices produced by technology based on inorganic materials: the mobility compares well to that of amorphous silicon and high performance (low threshold voltage and high on/off ratio current) has been reached. In ad-dition, the devices control and reproducibility have been strongly improved over the last years; this could lead to lower costs for fabrication of organic devices. Another important aspect is the possibility of device downscaling, for which or-ganic materials are however not yet as reliable as inoror-ganics. This is because the effect of the resistance of the contact is not negligible when the device channel reaches length of a few microns. Solving this kind of issues requires dedicated and focused research efforts.
1.2
Conduction in organic materials
The study of the intrinsic mobility, charge transport and injection in organic com-pounds is essential in the quest of reaching the ultimate electrical performance of organic devices. However, despite the numerous electronic applications, the underlying physics of charge transport in organic materials is not yet well under-stood, since the nature of bonding in organic semiconductors is fundamentally different from that in inorganic materials. This difference results in reduced hard-ness and lower melting point for organic materials, and it also changes the optical and transport properties. Hence the same properties that make organic materials interesting for technological application cause also difficulties in understanding the transport phenomena.
Since the identification of appropriate and sufficiently simple microscopic the-oretical models is rather difficult, the study of conduction in organic materials has so far been mainly confined to phenomenological approaches. The chemical
structure of organic materials makes the charge carriers interact strongly with the crystal lattice. Furthermore, in field effect transistors, the role of the electrical contacts and of the gate dielectric add complexity to the study of the intrinsic electronic properties of the material. In order to understand charge injection and transport in organic materials, it is fundamental to realize devices whose behavior is therefore not affected by extrinsic effect such as chemical impurities or structural defects.
The investigation of the intrinsic transport properties of organic semiconduc-tors is a central theme of this thesis. The quantity which mainly determines the transport properties of these materials is the carrier mobility. The first studies of the intrinsic mobility in organics have been performed on bulk pure crystals [10], by means of time-of-flight (TOF) experiments. Mobility values as high as 400 cm2
/Vs at low temperature were found for the best crystals. An alternative technique, used to probe the charge transport at the surface of a semiconductor, and not in the bulk, is based on field-effect transistors (FETs). In this case, the conduction of the semiconductor is modulated electrostatically with a gate elec-trode, enabling the study of intrinsic charge transport at larger carrier density compared to the one accessed in TOF measurements.
Regarding the organic compounds used in FETs, the most studied class is rep-resented by aromatic hydrocarbons. Aromatic hydrocarbons consists of molecules whose structure incorporates planar sets of six carbon atoms connected by alter-nating single and double bonds, the benzene ring. When more benzene rings are fused together in a linear chain, for instance, they form the family of the poly-acenes. Single crystals of molecules from this family, like pentacene and rubrene (and also other classes of molecules), show very high mobility as compared to other acenes studied in a FETs configuration in the form of thin films. Note that, organic thin-film transistors (OTFTs), even if widely used in device appli-cation [11], are not ideally suited for the study of intrinsic electronic properties of organic conductors. This is because of the insufficient purity and imperfec-tions in the films that affect the device characteristics and performance. Single crystals, on the contrary, are characterized by high structural order and no de-fect (as grain boundaries), which makes the resulting devices less sensitive to the semiconductor morphology. With single crystals, therefore, the investigation of intrinsic properties of the materials is possible.
Together with organic semiconductors based on a single constituent molecule (such as the polyacenes), another important class of organic material studied is represented by the charge transfer complexes or Donor-Acceptor crystals. They consist of two organic molecules co-crystallized together, in which charge is trans-ferred from one to the other. An example is provided by TTF(Tetrathiofulvalene):
TCNQ(7,7,8,8-Tetracyanoquinodimethane) the first organic metal based on a charge transfer salt. These charge transfer complexes have been studied since the seventies for the rich variety of physical phenomena that they host in fact they can exhibit different electrical behavior depending on the specific constituent molecules, and behave as semiconductors, metals and also superconductors.
Despite the fact that organics materials have been studied extensively in the past, the phenomena taking place at interfaces between organics and metals, or between two organic materials are far from being understood from a microscopic point of view. The purpose of this thesis is contribute to the understanding of transport in these systems.
1.3
Thesis outline
This thesis is structured as follows. Chapter 2 contains general aspects on the organic materials relevant for this thesis, describes the properties of molecular crystals and provides an overview of theoretical concepts that will be important in later chapters.
A critical aspect for the possible downscaling of organic electronic devices is the effect of the contact resistance on the device performance, Chapter 3 focuses on the study of the scaling behavior of rubrene single-crystal field effect transis-tors. The total resistance in FETs is determined by two factors: the resistance of channel (depending on the distance between the source and drain contact) and the contact resistance independent on the channel length. If the contact resistance is high compared to the channel resistance, the device performance is affected. It is therefore important to find contact materials giving the lowest possible contact resistance. In Chapter 3 we report how oxidized nickel contacts show the lowest contact resistance ever reported for organic transistors.
Chapter 4 presents a comparative study of the bias dependence of the contact resistance for different metal electrodes. All the measurements are performed on transistors with short channel length so that the resistance of the channel is negligible compared to that of the contact. From the comparison of the spread in resistance and the bias dependence we found important differences between the different metals. Nickel contacts not only show the best contact resistance but also the lowest spread. Other materials as copper and cobalt show larger spread in the values of the contact resistance, but an excellent reproducibility for the bias dependence of the contact resistance. Finally, noble metals such as gold and platinum give strong irreproducibility in both the absolute value and the bias dependence of the contact resistance.
The contact resistance-dominated FETs, described in Chapter 3 and 4, are characterized by non-linearity at low bias and gate independence, resulting in a peak in the differential conductance around zero volt bias. This peculiar I-V characteristics are due to the formation of a Schottky barrier at the interface between the metal and the semiconductor. Chapter 5 reports the quantitative study of charge injection at metal/organic interface. We show that the gener-alized Schottky theory known for inorganics represent a good description of our observations, at least in the case of oxidized copper contacts.
Organic semiconductors show both p- or n-channel or ambipolar conduction depending on their chemical characteristic. Chapter 6 and Chapter 7 are fo-cused on n-type semiconductors. Chapter 6 we report the study of Cu and Fe Phethalocianine single-crystal FET and show that they exhibit ambipolar trans-port. Chapter 7, instead, reports the measurements of a new molecular compound based on a perylene derivative, showing a very high electron mobility.
After the studies on metal/organic interfaces and charge transport in organic single crystal we present in Chapter 8 a study on the interface between two different crystals. Separated crystals of TTF and TCNQ are grown and assembled together. Even if the conductance of the individual materials is negligibly low, their interface show high conductivity and metallic behavior. We discuss how the phenomenon originates from charge transfer taking places between the two crystals.
References
[1] http://www.etymonline.com/
[2] R. McNeill, R. Siudak, J.H. Wardlaw, and D.E. Weiss Aust. J. Chem. 16, 1056 (1963).
[3] C.K. Chiang, C.R. Fincher Jr., Y.W. Park, A.J. Heeger, H. Shirakawa, E.J. Louis, S.C. Gau, and A.G. MacDiarmid, Phys. Rev. Lett. 39, 1098 (1977). [4] Earlier results were reported by Weiss and coworkers in 1963, and in 1973
has been presented the highly-conductive organic charge transfer complexes, a class of organic compounds showing metallic behavior (TTF-TCNQ) and superconductivity
[5] www.polymervision.com
[6] B. Crone, A. Dodabalapur, Y.Y. Lin, R.W. Filas, Z. Bao, A. LaDuca, R. Sarpeshkar, H.E. Katz, and W. Li Nature 403, 521 (2000); C.D. Dimi-trakopoulos, S. Purushothaman, J. Kymissis, A. Callegari, and J.M. Shaw
Science 283, 822 (1999).
[7] J.J.M. Halls, C.A. Walsh, N.C. Greenham, E.A. Marseglia, R.H. Friend, S.C. Moratti, and A.B. Holmes, Nature 376, 498 (1995); G. Yu, J. Gao, J. C. hummelen, F. Wudl, and A.J. Heeger Science 270, 1789 (1995).
[8] R.H. Friend, R.W. Gymer, A.B. Holmes, J.H. Burroughes, R.N. Marks, C. Taliani, D.D.C. Bradley, D.A. Dos Santos, J.L. Br´edas, M. L¨ogdlund, and W.R. Salaneck, Nature 397, 121 (1999); M.A. Baldo, D.F. O’Brien, Y. You, A. Shoustikov, S. Sibley, M.E. Thompson, and S.R. Forrest, Nature 395, 151 (1998).
[9] K. Asadi, D.M. de Leeuw, B. de Boer, and W.M. Blom Nature Materials 7, 547 (2008).
[10] N. Karl, K.-H. Kraft, J. Marktanner, M. M¨unch, F. Stehle, and H.-M. Uhde, J. VAc. Sci. Technol. A 17, 2318 (1999).
[11] G.H. Gelinck, T.C.T. Geuns, and D.M. de Leeuw Appl. Phys. Lett. 77, 1487 (2000); C.D. Dimitrakopoulos, and P.R.L. Malefant Adv. Mater. 14, 99 (2002).
Organic molecular materials
2.1
Introduction
At present, we are witnessing the development of a new branch of solid-state science, organic-solid-state physics, based on organic compounds. In the past “organic matter” was considered to be related to living organisms [1], and to be responsible for generating the so-called “vital-force”. According to the modern meaning an organic molecule is a molecule containing mainly carbon atoms, in combination with other atoms (typically hydrogen, nitrogen, or sulfur). Organic molecules forming a molecular crystal are bonded together to form solids via Van der Waals forces, whereas for inorganics the bonds are usually of covalent or ionic nature. This difference make the properties of organic materials differ considerably from those of inorganic materials. For example, because of the weak interaction between the organic molecules in the crystal, charge carriers are more sensitive to interactions with the crystal lattice and, in a transistor device, to the presence of a dielectric.
In this thesis we focus on the transport in organic materials, in particular organic single-crystals, and on the injection processes which occur at the interface with a dielectric or a metal. For this study theoretical concepts known to hold for inorganics are taken into account, and compared to what is known, at this time, about charge transport in organics.
In this Chapter we present an overview of the structure and electronic proper-ties of organic molecules and organic molecular crystals (Section 2.2). In Section 2.3 we will discuss the transport mechanism for organic semiconductors analyzing different regimes depending on their structure and their composition. In Section 2.4. we present the basic concepts related to transport in a transistor channel. The final section is devoted to discuss transport mechanisms across metal/organic interfaces.
2.2
Electronic properties of molecular solids
2.2.1
Organic molecules
Organic molecules consist of carbon atoms in combination with other atoms as hydrogen, nitrogen, and oxygen. Countless amount of different organic molecules and organic compounds exist, with very different chemical and physical proper-ties. The huge amount of possible compounds originates from the possibility of the carbon atom to form stable, strong covalent bonds with four different atoms, and, in this way, to form very long structures of interconnecting C-C bonds. When an organic molecule is characterized by the presence of alternating single
and double carbon-carbon bonds it is referred to as conjugated molecule. This thesis is mainly focused on the study of single crystals of conjugated organic molecules. C C C C C C H H H H H H sp orbitals2 p orbital gq bond gp bond a) b)
Figure 2.1: (a) σ bonds : localized bonds held by sp2hybrid orbitals in planar
arrange-ments. (b) π bonds : delocalized bonds spread evenly over six p-orbitals perpendicular to the σ-plane
Since the electronic properties of organic semiconductors are directly linked to the electronic structure of the individual constituent molecule, we will discuss the electronic states of single molecules in some detail. The electronic configuration of an isolated carbon atom consists of two electrons occupying the 1s orbital, two the 2s orbital and two the 2p orbitals. The orbital 1s is very low in energy and it is not participating in the formation of chemical bonds. When carbon atoms bond together in a molecule a mixing of their 2s and 2p orbitals occurs, leading to sp hybridization. For conjugated molecules, the sp2
hybridization in which 3 identical orbitals in plane are formed, together with one pz orbital perpendicular
to the plane are particularly important. The overlap of sp orbitals belonging to two different atoms results in a σ bond, while the overlap of the pz orbitals results
in the π bonds (as shown in Fig. 2.1).
In simple heterocyclic conjugated molecules, such as the benzene ring, inter-changing the position of the single and double bonds in the chain does not affect the electronic structure. The new configuration obtained in this way represents a different and equivalent resonance structure of the molecule. The electronic struc-ture of an actual benzene is determined by a linear combination of all the possible resonance structures. As a consequence of this linear combination, the π bonds spread out over the entire molecule (while the σ bonds are strongly localized between two carbon atoms). The electrons present in the π bonds of conjugated
systems are responsible for most of the chemical and physical properties of the molecules.
For our studies, the most relevant electronic levels of the molecules are the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molec-ular Orbital (LUMO). When the molecules are put together in a crystal, the HOMO and LUMO levels of one molecule hybridize with those of the neigh-bouring ones, leading to the formation of bands (the HOMO and LUMO bands, that correspond to the valence and conduction band respectively in inorganics semiconductors). The difference of the energies of the HOMO and the LUMO corresponds to the band gap. Since the σ bonds are deeper in energy, the HOMO and LUMO are determined by the π bonds. This make the study of π systems of particular interest to understand the conduction processes in organic molecules and in organic molecular crystals (OMCs).
2.2.2
Organic crystals
As mentioned above, the energy gap between the HOMO and the LUMO in the individual molecules determines the band gap of the organic crystal, that for most commonly used molecules, is typically in the range of 1-4 eV [2]. The wide bandgap, together with the HOMO levels that are generally fully occupied (resulting in completely filled valence band and empty conduction band), make pure large-gap organic crystals formed by a singular molecular species electrical insulators (or large gap semiconductors). In this thesis we will mainly focus on their semiconducting properties.
In this work, OMCs based on a number of different molecules have been stud-ied. Some of them belong to very well known families, namely, the Polyacenes, the Perylene derivatives and the Phthalocyanines (as shown in Fig.2.2). Each family, and each molecule, present different characteristics. In what follows we will briefly introduce some relevant details of the families of compounds that we have used, giving an overview of their electronic characteristic and possible applications.
Rubrene belongs to the family of the polyacenes and represent a derivative of tetracene. In crystal form it has a triclinic crystal structure as tetracene, meaning that the unit cell has three unequal dimension and three unequal angles. Within each molecular layer the molecules are packed in a herringbone structure. Because of the presence of side phenyl groups, the orientation of the molecules in the crystal differs from that of tetracene. This results in a larger overlap of the molecular orbitals between adjacent molecules, leading to an improved mobility of the charge carriers in the crystal. This difference also shows how
N N N N N N N N M S S S S C N C N C N C N O O O O N N F F F F F F F F F F F F F F a) b) c) d) e)
Figure 2.2: Structures of the organic conjugated molecules presented in this thesis (a) Rubrene : a derivative of tetracene with phenyl-rings substituting four hydrogen atoms. (b) Metal-phthalocyanine : and heterocyclic molecule containing a metal atom in the center. (c) TTF (tetrathiofulvalene) : containing, besides C and H, also sulfur atoms. (d) TCNQ (7,7,8,8-tetracyanoquinodimethane) : characterized by cyano groups. (e) PDIF-CN2 : molecules from the family of the cyanated parylenes (PDIR-CN2).
the shape of the molecule influences the molecular arrangement in the organic crystal, since it determines its Van der Waals interaction surface (the surface of the union of the spherical atomic surfaces defined by the van der Waals forces) and different molecules (or molecule with different substituted group) with different Van der Waals surface interactions lead to different crystal structure. Studies on rubrene single crystal FETs reported the highest room temperature charge carrier mobility ever measured for organic materials [3]. For this reason rubrene has become one (together with pentacene) of the of the most studied organic semiconductors for transistor devices.
The Phthalocyanines are derivatives of the porphyrines. They form a planar macrocycle with large π electronic system, and they also pack in an herringbone structure. Metal-phthalocyanines (MePc) have a metal atom in the center of the ligand, which determines the electronic properties of the entire molecule. MePcs possess remarkable thermal and chemical stability and can have different structural features.
Perylene represents a conjugated, aromatic hydrocarbon, consisting of two naphtalene molecule and a benzene ring connected by a carbon-carbon bond. In perylene, as well as in Phthalocynines-[4] and pentacene [5]- derivatives, the energy levels can be tuned by substitution with electron-withdrawing groups (flu-oroalkyl substituent and cyano groups). The presence of those groups can lower the energy of the LUMO [6], resulting in better electron conduction. The perylene molecule is the core structure of the family of the PDIs (N,N-dialkyl substituted perylenetetracaboxydiimide derivatives) which have been intensively investigated [7], and the core-cyanated PDI derivatives (e.g. PDIF-CN2) are excellent electron conductors [8].
Other organic molecules presented in this work are Tetrathiofulvalene (TTF) and 7,7,8,8-Tetracyanoquinodimethane (TCNQ). TTF (molecular formula C6H4S4)
is a donor molecule belonging to the heterocyclic organosulfurus compounds. TTF is related to the hydrocarbon fulvalene, (C5H4)2, by replacement of four
CH groups with sulfur atoms. Bulk TTF has unremarkable electrical properties, however the TTF molecule and its derivatives raised strong interest or the pos-sibility of forming salts derived from TTF+
[9]. TCNQ is an acceptor molecule which can be easily reduced to form the radical TCNQ•− if placed in contact with
an electron donor [10]. Single crystals of TCNQ have been used as semiconduc-tors in FETs (reporting one of the highest mobility for n-channel semiconducsemiconduc-tors - ∼ 2 cm2/Vs - [11]) to study conduction properties in the materials.
In this thesis, these and other molecules have been grown by vapor sublimation to form single crystals according to the procedure discussed in the Appendix A, and single crystals of TTF and TCNQ have been, also, assembled as a combined system to study - for the first time - organic charge transfer interfaces (See Section 2.4.2).
2.2.3
Electronics properties of organic crystals
Organic molecules can bond together to form organic molecular crystals. The structure and properties of the constituent molecules are quite directly related to those of the OMCs, since the aromatic molecules are characterized by strong in-tramolecular covalent bonds while intermolecular interaction depends on (weak) Van der Waals forces. This weak intermolecular interaction forces produce only slight changes in the electronic structure of the individual molecules when they are in the environment of the crystal. In a crystal, therefore, the maximum electron density concentrates mainly around carbon atoms and covalent intramolecular C-C and C-C-H bonds, dropping to practically zero value in the intermolecular space. In other words the molecules in an OMC maintain their “identity” [12].
The weak bonding of the molecules cause the organic system to be particularly sensitive to the room temperature molecular motions. Organic molecular crys-tals are sensitive to vibrational and stochastic rotational or translational modes. Between the vibrational modes we can consider separately the intramolecular vi-brations (molecular vivi-brations) and the external vivi-brations (lattice vivi-brations) determined by the molecules oscillating around their equilibrium positions (i.e., phonons). The dynamics associated to the vibrations play a very important role in determining the motion charge carriers in molecular materials, since the vi-bration can result in large changes of the hopping integrals between adjacent molecules [13].
The weak interaction between constituent molecules in a molecular crystal is responsible for the characteristic mechanical and elastic properties of organic molecular crystals, such as flexibility, low melting and sublimation temperatures, and low mechanical strength. It also causes their electronic properties to be considerably different from those of covalently bonded solids. One of the most important difference in organic crystals, compared to inorganics, is the band structure. Continuous bands are formed when free atoms bond together and the “mixing” of their orbitals broadens their discrete energy levels in energy bands (resulting in the formation of the valence and conduction bands). In crystalline materials the stronger is the interaction between close atoms the larger is the energy band. For organics compounds the bands are formed by the combination of the molecular orbitals of the molecules; so the valence band results in the combination of the HOMO levels of the molecules and the conduction band come from the LUMO levels. However, as we have mentioned, the overlap of the molecular orbitals between neighboring molecules is poor. This results in narrow bandwidth (for the HOMO and LUMO levels) for organic materials compared to that of inorganics (∼ 0.5 eV versus ∼ 10 eV for inorganics) [14, 2].
The narrow bandwidth affects enormously the electrical transport in organic crystals, since the charge carriers are not completely delocalized as happens in inorganic solids (due to the much wider bandwidth). Carriers interact with the local crystal environment inducing polarization effect in the crystal. Due to this effect, carriers move in organic crystal carrying a polarization cloud. This results in a deformation of the lattice and induce vibrational modes (different from those characteristic of the crystal) in the closest atoms, which affects the speed of the carriers resulting in low mobilities [15].
2.3
Transport mechanisms and regimes in
or-ganic semiconductors
The difference in band structure for organic materials compared to inorganics, already mentioned, affects the transport mechanisms in OMCs. In “simple” in-organic materials such as silicon a simple band model is applicable, to describe (free) electrons which do not interact with the environment. This model appears to be too simplified for OMCs, since it is not taking into account neither the large vibrations of the molecules nor the coulombic interaction between different electrons, which have a large effect as we stated above.
As a charge carrier is moving in an OMC it interacts with the local envi-ronment, possibly leading to the formation of a polaron. This system formed by the charge and the lattice distortion causes local polarization of the charge carriers, while the energy associated to the transfer integral (J) within neigh-boring molecules determines the tendency for carriers to delocalize. If J is few electronvolts in energy (as it happens for metals) carriers are delocalized and can be described by Bloch waves. However, in organic crystals J ∼100 meV, much smaller than in metals. So, in short, transport in OMCs occurs as competition between two processes: the delocalization of the carriers (eventually leading to the formation of Bloch waves), and the localization of the wave packet as results of interaction with the local surrounding.
A simple picture of the causes involved can be done considering the energy changes occurring to a charge carrier in an OMC. The related energy terms are: δEw representing the charge wave-like motions, the polarization energy δEpol (a
coulomb force) due to the dielectric, and the reorganization energy δEb property
of the individual molecule and related to the deformation of the molecule when charged. If we simply add the energy contributions, it is possible to analyze the nature of charge carriers in organic crystals [15].
δE = δEw+ δEpol + δEb (2.1)
To localize a charge a certain energy is required (due to the fact that the lowest energy level of a confined particle is finite) so that δEw is positive in sign. On
the other hand, the polarization of the lattice is accompanied by gain in energy, in the form of polarization energy and a localized charge on a molecular site may form a molecular ion or a polaron resulting in a gain of reorganization energy. Hence, the terms δEpol and δEb have a negative sign.
If the energy balance reported in Eq. 2.1 is positive the charge carrier is delocalized. Otherwise (δE < 0) the charge carrier will be energetically more
favorable in a localized state and the representation of charge carriers in form of Bloch wave is no longer valid. The carriers should, instead, being considered as moving by hopping from a localization site to another.
Experimentally a possible way to discriminate between the two regimes is studying the temperature dependence of the charge carriers mobility, since the two different regimes have different response as function of temperature. Decreas-ing the temperature causes, in delocalized systems, a decrease in the scatterDecreas-ing probability, and as a consequence the mobility of carriers is expected to increase. In systems where states are localized, either due to intrinsic self-polarization ef-fects or to the presence of deef-fects and disorder, the conduction via hopping is thermally activated and the mobility decreases decreasing temperature.
In practice, the transport regime of carriers in OMCs is in the crossover region between band-type and incoherent hopping. The phonon modes cause distortions in the crystal lattice, leading to a local reorganization of the molecules. The time necessary for the molecules to rearrange is long compared to the characteristic time of the charge moving in the crystal. Therefore the carriers sense a disordered lattice while they are moving, resulting in a so-called dynamical localization [16]. With decreasing the temperature the molecules vibrate less, so the lattice results less distorted and transport is easier. The mobility of the carriers increases as in band transport even if the regime is different. It is the simultaneous combination of all these effects which makes a full understanding of carrier dynamics in OMCs a particularly challenging problem.
The experimental situation is also complex. Experiments on organic single crystal transistors often reported charge carriers mobility decreasing with temper-ature [17]. This tempertemper-ature dependence of the mobility (different, for instance, from what has been observed in TOF measurements) can be attributed to differ-ent effects. Some of these effects are of intrinsic nature, such as the formation of polarons with the gate dielectric [18, 19]. However, often extrinsic effects related to the presence of defects or grain boundaries in the semiconductors [20], or traps at the interface with the dielectric play a major role. Only recently, studies on Hall effect on rubrene single crystal field effect transistors [21] enabled the mea-surement of intrinsic trap-free mobility, helping to clarify the relation between intrinsic mobility and mobility measured in a FET configuration.
2.4
Transport at the surface of organic
molecular crystal
To measure electronic transport in organic crystals is necessary to introduce charge carriers, because high-purity OMC are undoped, large gap semiconduc-tor, in which virtually no free charge is naturally present. Two possible ways to introduce charge are discussed in this section : electrostatic doping by using field-effect transistor (FETs), and charge transfer interfaces. The latter is a new way of inducing carriers at the interface of two different OMCs, which has been first developed in this thesis.
2.4.1
Organic Field-effect transistors
An organic field-effect transistor (OFET) is a Metal-Oxide-Semiconductor Field-Effect transistor (MOSFET) that relies on an undoped organic material as semi-conductor. The study of FETs has been extensively developed with inorganic semiconductors for their application in integrated circuits. However, due to the strong difference in the electronic properties of organic and inorganic materials, it is a priori not obvious that the theory developed for inorganic MOSFETs can be directly applied to understand the behavior of OFETs. In this regard, it is important to underly how the normal theory is applicable for devices working in the inversion regime, whereas in OFETs the devices always work in accumulation. Nevertheless, since the structure and the functioning of OFETs is comparable to that one of MOSFETs the theory known for inorganic materials can be considered as a reasonable starting point in the analysis of organic transistors.
An OFET can be considered as a parallel plate capacitor. The capacitor plates are represented by the metal (gate) electrode and the semiconductor (sep-arated by an insulator layer),where the charge is accumulated. The source and drain contacts are used to probe the conduction of the semiconductor and their separation determines the length of the conduction channel, as shown in Fig. 2.3 Applying a voltage between the gate and the source induces an electric field across the gate dielectric. Due to this field charge carriers are attracted to the surface of the semiconductor, forming the conduction channel at the interface between the semiconductor and the insulator. In this way, the conductivity is controlled by the gate voltage, which determines the density of charge carriers present in the channel. Once the conduction channel is formed, the applied bias between source and drain electron creates a potential difference that causes the charge carriers to flow in the channel. The sign of the applied gate voltage and of the bias voltage determine the kind of carriers induced at the surface
semiconductor A VD VG gate gate dielectric source drain channel
Figure 2.3: Schematic drawing and electronic circuitry of a FET.
of the semiconductor. Positive charges (holes, p+
) are attracted at the surface under negative applied gate voltage, while a positive gate voltage induces negative charges (electrons, n−). It is therefore expected that Ambipolar transport is an
intrinsic characteristic of OMCs, meaning that pure undoped organic materials should allow both holes and electrons transport. However the study of high electron mobility OFETs is considerably more complex in real devices, because, in practice, electrons are more easily trapped at the surface of the semiconductor due to the presence of a variety of defects.
To form the conducting channel it is normally necessary to apply a finite gate voltage, known as the threshold voltage. The magnitude of the threshold voltage depends on several factors as the quality of the source and drain contacts and the amount of traps at the interface semiconductor/gate dielectric.
The applied gate voltage determines how much the bands of the semiconduc-tor shift at the interface with the dielectric. With no gate voltage applied, there is no charge induced in the semiconductor. For p-type semiconductor, once a negative gate voltage is applied the energy bands of the semiconductor will shift upwards and positive charge carriers are induced at the surface of the semiconduc-tor. With a positive gate voltage the bands of the semiconductor shift downwards resulting in depletion of the positive carriers at the interface (see Fig. 2.4). This happens when the valence band is located below the Fermi level of the metal. Eventually, if the magnitude of the (positive) gate voltage is increased, accumu-lation of electrons can be achieved (when the conduction band in the organic semiconductor is shifted below the Fermi level in the contacts). In the behavior of FETs it is possible to discriminate two different operational regimes depending on the absolute value of the source-drain bias. When the absolute value of the source-drain bias is smaller then the difference between the gate voltage and the threshold voltage the FET operate in the so-called Linear regime. The expression for the current then reads :
Ef Ec Ev M I S (a) +++++ + + (b) Ec Ev Ef (c) Ec Ev Ef M M I I S S
Figure 2.4: Band bending diagrams of a Metal-Insulator-Semiconductor (p-type) de-vice (a) Flat bands condition, no gate voltage. (b) Accumulation for negative gate voltage. (c) Depletion for positive gate voltage.
ID =
W
LµCi(VG−VT h)VD. (2.2) Here W and L are the channel width and length, respectively, µ is the carrier mobility and Ci is the capacitance of the gate dielectric per unit area.
The FET operation in the Saturation regime occurs when the source-drain bias is equal or larger than the difference between the gate and the threshold
voltage (VD > VG−VT h). In this case we have: ID = W 2LµCi(VG−VT h) 2 (2.3) In both equations 2.3 and 2.2 the mobility of the carriers appears, so that the analysis of transport measurements in FETs allows to extract the value of µ. Specifically, the mobility can be extracted from the linear regime according to the formula: µ = L W 1 Ci 1 VD δID δVG (2.4)
The mobility is an important parameter, because it measures how easily charge carriers can move. This is why µ is one of the crucial parameters used to determine the quality of an organic semiconductors or device.
Note that the mobility measured using FETs is not always the intrinsic mobil-ity of the carrier in the organic semiconductor for different reason. Factors that can affect the mobility measured in a FET are such as the formation of polarons and the presence of traps in the organic material or at interface. In particular, even the most purified molecular crystal contain residues of chemical impurities, or structural defects, which can act as traps for the charge carriers and make the electronic characteristic deviate from the behavior expected for ideal crys-tals. The relatively low mobility, usually measured on TFTs (10−2 cm2/Vs [22])
is largely due to the presence of grain boundaries in the semiconductor acting as trap site for the charge carriers. This is why it is important to work with organic single crystals, since they are usually characterized by higher structural quality and chemical purity as compared to thin films. In addition, since the conduction in FETs happens at the interface between the semiconductor and the gate dielectric, other trapping sites can originate from the presence of specific chemical groups present at the surface of many commonly used gate dielectrics [6]. Well-known example is provided by hydroxyl groups that are known for the high electron affinity, and can easily trap electrons [23]. This is one of the reason why electron conduction in organic is more difficult to achieve as compared to hole conduction.
Another important factor that affects the measurement of the mobility in a FET configuration is the contact resistance. The contact resistance arises from the injection of charge carriers at the metal/organic interface. For inorganic de-vices the possibility to dope the semiconductor makes the effect of the contact resistance unimportant. In a OFET, instead, the total resistance of the device,
RT(L), is determined by two contributions: the resistance RCh(L) of the
chan-nel, due to the presence of the organic semiconductor, and the resistance of the contacts RC. With the downscaling of the devices the contribution of the contact
resistance is expected to play a major role (details in Chapter 3). To under-stand the effect of the contact resistance on single-crystal FETs, in this thesis we have studied short-channel devices where the channel resistance is negligible compare to that of the contacts. The processes responsible for charge injection at metal/semiconductor contacts will be discussed in Section 2.5.
2.4.2
Organic charge transfer compounds and interfaces
Another possibility to induce charge at the surface of organic materials is by charge transfer. Organic charge transfer salts represent a class of materials consisting of organic donor/acceptor crystallized together to form semiconduc-tors (T T F+Cl−[24]), metals (T T F − T CNQ [25]) and even superconductors
(TMTSF2X with X=PF6, ClO4, [26, 27]). In these material a fraction δ of an
elementary charge, with 0 ≤ δ ≤ 1 is transferred from one to another molecular species inside the crystal (δ = 1 means complete charge transfer). The formation of these systems require π-electrons molecules that are able to accept or donate their electron, depending on their electronaffinity or their ionization potential.
The charge transfer salt TTF-TCNQ is the best known material of this class, as it was the first organic conductor to be discovered [25], at room temperature the charge transfer from the donor (TTF) to the acceptor (TCNQ) is δ = 0.59. The material is built from separate columnar stacks of TTF and TCNQ, and it is characterized by strong ionic bonds [28]. As it happens for strong ionic transfer complex the high conductivity is along the stacking axis; perpendicular to this axis the conductivity is several orders of magnitude lower. This compound shows high conductivity at room temperature ∼ 400 ± 100 (Ωcm)−1 that increases,
with lowering temperature (i.e. metallic-like behaviour), to a maximum of 1.5 104 (Ωcm)−1 at T = 54K.
TTF-TCNQ salt, so as the (T MT SF )2X organic superconductor, represent
the class of one-dimensional (1D) charge-transfer conducting compounds under-going a Peierls instability at low temperature which prevents the stabilization of conduction and superconductivity. Peierls transition is a lattice distortion oc-curring at the transition temperature TP, which produces an insulating state for
T<TP. The lattice distortion is accompanied by a spatial periodic modulation
of the density of the conduction electrons, a charge-density wave. The occur-rence of a Peierls transition in TTF-TCNQ indicates that in this material the conductivity is dominated by the strong anisotropy of the structure of charge
transfer compound. In fact, in TTF-TCNQ two Peierls transitions take place, independently for both the TTF and the TCNQ molecular stacks at T = 54K and T = 38K.
Over the past three decades, charge transfer compounds have been extensively studied for the interesting properties they have shown in the bulk. Until now, however, the possibility of charge-transfer induced conductivity at the surface of organic materials has not been considered. This possibility is of particular interest because the electronic properties at the interface between two materials (heterointerfaces) can be substantially different from those of the constituent components. For inorganic materials, for instance, it has been very recently observed that electrical conduction [29], and even superconductivity [30], can take place at the interface between two insulating oxides.
In this thesis we have tried to understand if charge transfer happens only in the bulk where two different materials are mixed to form one compound, or if it is possible to transfer charge between few layers of two different crystals. Our results suggest how the study of charge transfer interfaces could represent a new way of inducing and transfer charge between organic materials, eventually opening the possibility of finding new effects at the interface of two OMCs.
2.5
Transport mechanism across metal/organic
interfaces
Once a semiconductor is put in contact with a metal, an energy barrier for charge carriers is formed at the interface, as first discussed in details by W. Schottky [31]. The work of Schottky set the basis for the development of the theory which explains the transport across metal/semiconductor interfaces in inorganic mate-rials. Unfortunately, no theory has yet been established to model the injection process at metal/organic interfaces, and it is unclear whether the theory devel-oped for inorganic semiconductor is also applicable to organics. The difficulties encountered in the formulation of a consistent theory for organic materials are in part originating from on the experimental irreproducibility of OTFTs devices. The huge spread in contact resistance and its bias dependence, in fact, has not allowed so far a systematic study of charge injection into organic semiconductors. In this thesis we will show that in high quality metal/organic semiconductor contacts, as they can be realized in organic single crystal transistors, sufficient experimental reproducibility can be achieved. This has allowed us to check exper-imentally the validity of the existing theory for transport across a metal/organic interface. As we will show in Chapter 5, the theory developed for inorganic
semiconductors holds quantitatively also for organic semiconductors.
2.5.1
Schottky theory
When a semiconductor is placed in contact with a metal, a band bending occurs to align the Fermi level of the material with that one of the metal. This requires charge flowing from the semiconductor into the metal as shown in Fig 2.5. The diffusion will continue until the electric field produced by the electrostatic inter-action between the stored charge at the metal surface generates a drift current equal and opposite to the diffusion ones.
(a)
(b)
Efs Ec Ev M S Efm qΦm qΦs M S Efm Efs Ev Ec qΦB0 qVBI qχ Eg qχFigure 2.5: Band bending diagrams of a Metal-Semiconductor (p-type) (a) metal and Semiconductor not in contact. (b) In contact at the thermal equilibrium.
As shown in Fig. 2.5, which focuses on the valence band of the semiconductor, the band bending causes the formation of a barrier that holes have to overcome to be injected in the material. This barrier, ΦB0, is called Schottky barrier and,
in the simplest case, it is determined by the values of the work function in the metal and in the semiconductor. ΦB0 is given by:
ΦB0 =
Eg−q(Φm−χ)
q (2.5)
where Eg is the energy band gap of the semiconductor, Φm the work function of
the metal contact, χ the electron affinity and q the elementary charge.
Once the metal and the semiconductor are placed in contact and the Schottky barrier is formed, injection of charge from the metal into semiconductor results in a lowering of the potential barrier due to a phenomenon known as Schottky effect. When a charge carrier is injected in the semiconductor at a distance x from the metal/semiconductor interface an image-charge is induced at the surface of the metal. The resulting electric field in the semiconductor is the same as the
field generated by an image-carrier of opposite charge at a distance −x from the metal/semiconductor interface. The force due to this image charge, Fi, produces
the lowering of the Schottky barrier and it is given by:
Fi(x) = qEi(x) =
q2
16πǫ0ǫsx2
(2.6)
where Ei is the generated electric field and ǫs is the dielectric constant of the
semiconductor.
The image-force determines a new electrostatic profile of the barrier. Now, in close proximity of the metal/semiconductor interface, where the image force is generated, the electric field can be considered equal to Emax, which is the electric
field at the surface of the semiconductor. This value will be particularly important since it determines the barrier lowering as function of the applied bias and the charge density of carriers. It is possible to obtain the value of the generated electric field by solving the Poisson’s equation (which relate the potential inside the semiconductor and the charge density) inside the semiconductor [32] :
Emax =
r 2qNAVBI
ǫ0−ǫs
(2.7)
where NA is the charge density of the carriers, ǫs the dielectric constant of the
semiconductor and VBI the built-in potential (determined by Φs−Φm).
The image potential Φi, obtained by integration of the image force, and the
potential generated by the electric field responsible of the drift of holes in the semiconductor (as expressed in Eq. 2.7), determine the total potential experienced by the holes :
Φ = Φi−xEmax =
−q 16πǫ0ǫsx
−xEmax (2.8)
The maximum of this potential is the potential barrier that charge carriers have to overcome to be injected into the semiconductor. It is easy to show that this maximum is lower than ΦB0 by an amount :
q∆ΦB = q
r qEmax
4πǫ0ǫs
(2.9)
When an external voltage is applied between the metal and the p-type semi-conductor the bands of the semisemi-conductor will bend downwards or upwards, de-pending on the polarity of the voltage. In the condition of forward bias (nega-tive voltage considering a p-type semiconductor) the built-in potential decreases by the amount VF (Vi = VBI −VF) - because the negative bias increased the
Fermi level of the metal, therefore, the band bending of the semiconductor de-creases. For positive applied voltage, reverse bias, the built-in potential increases (Vi = VBI+ VR). The applied voltage affects the lowering of the barrier since it
modifies the value of Emax, that now can be written as:
Emax=
r 2qNAVi
ǫ0ǫs
(2.10) The resulting energy barrier can be obtained by substituting Eq. 2.10 in Eq. 2.9:
qΦB = qΦB0 −q∆ΦB = qΦB0−q q3 NAVi 8π2ǫ3 0ǫ3s 1/4 (2.11) where ΦB0 is the height of the barrier not considering the Schottky effect, while
∆ΦB represents the barrier lowering (depending also on the applied bias).
Effects due to surface states
We have considered the basic aspect of the band diagram for metal/semiconductor contacts. Experimentally, however, the measurement of the barrier height often deviates from the ideal case that we have discussed, and the reported values for organic semiconductor vary depending on the sample preparation. This effect is attributed to the presence of surface states in the semiconductor band gap and to the presence of an interfacial layer between the two materials. For inorganic semiconductors surface states are caused by the unsaturated (dangling) covalent bonds at the surface of the semiconductor. They are caused by the sharp tran-sition from a solid material to a surface, and result in the presence of electron energy levels inside the energy bandgap. Organic single crystals, however, are van der Waals bonded and no dangling bonds are present at their surface. Never-theless also in this case, surface states can still be present, as they can be induced by the hybridization of molecular states due to the coupling of the molecule at the surface and the metal contact. In the case we are going to discuss in detail in Chapter 5, the formation of a natural oxide layer on the contact determines the strength of this coupling: the oxide acts as a tunnel barrier and a thicker layer results in a smaller coupling.
In the presence of surface states under reverse applied bias (i.e. the condition at which the barrier lowering can be seen experimentally) the general expression for the barrier height given by Eq. 2.11 has to be modified in:
qΦB = qΦB0 −q∆ΦB−qαEmax (2.12)
which according to Eq. 2.11 can be written as: qΦB = qΦB0 −q q3N AVi 8π2ǫ3 0ǫ3s 1/4 −qα 2qNAVi ǫ0ǫs 1/2 (2.13)
The quantity αEmax represents the barrier lowering due to the presence of a
dipolar charge layer associated to the presence of surface states. The value of α is determined by:
α = δǫ0ǫs ǫ0 + q2δDS
(2.14) where δ is the thickness of the interfacial layer determined by the penetration of the metal electronic wave function into the semiconductor, and DS is the density
of the surface states.
As we will discuss in Chapter 5 the inclusion of this term is essential to reproduce the experimental data. From the data and the analysis the value of DS can be extracted.
2.5.2
Transport over a barrier:
Thermionic emission theory
After having described the Schottky effect and the lowering of the barrier un-der reverse applied bias, we now discuss how charge current will flow from the semiconductor into the metal under forward bias condition. The main mecha-nism of charge injection are determined by the transport over the barrier due to thermionic emission or diffusion and tunnel through the barrier [32].
If the barrier height is larger than kT and thermal equilibrium is established without being affected by a net current flowing, thermionic emission is the domi-nant transport mechanism for pure, low doped semiconductors. To calculate the net current flowing through the barrier in this case, we consider separately the current density flowing from the semiconductor to the metal, Jsm, and from the
metal to the semiconductor, Jms. The current Jsm is determined by the
concen-tration of all the carriers with energy sufficient to overcome the potential barrier and it is represented by the formula:
Jsm(V ) = AT2e−qΦB0/kTeqV /kT (2.15)
where A is the Richardson constant defined as: A = 4qπmk
2
h3 (2.16)
In the case of reverse bias Jms does not depend on V, since it only depends
on the barrier height. When V=0 the current density Jms flowing from the metal
to the semiconductor is equal to −Jsm. Therefore setting V = 0 in Eq. 2.15 we
obtain:
The total current density becomes: Jsm+ Jms = AT2e−qΦB0/kTeqV /kT + AT2e−qΦB0/kT (2.18) = AT2 e−qΦB0/kT eqV /kT −1 = J S eqV /kT −1
Summarizing, the expressions for the current under reverse and forward (VR
and VF respectively) bias read :
IR = I0T2e− qΦB kT 1 − e−qVRnkT (2.19) with ΦB = Φ0− q3N A 8π2ǫ3 0ǫ 3 S (VBI + VR) 1 4 −α 2qNA ǫ0ǫS (VBI+ VR) 1 2 (2.20) and : IF = I0T2e− qΦB kT e−qVFnkT −1 (2.21) with ΦB = Φ0− q3N A 8π2ǫ3 0ǫ3S (VBI −VF) 1 4 (2.22) These expressions will be used in our study of short-channel devices (Chapter 5) where the system metal contact/organic semiconductor/ metal contact (MSM) can be modeled as two oppositely biased Schottky diodes connected in series. It will be shown that thermionic emission theory is then suitable to represent the mechanism of charge transport across metal/organic interfaces when the two effects of the barrier lowering due to the applied bias and the presence of a dipole due to surface states are considered.
More in general, the injections mechanisms responsible for the flow of current are : a) transport of charge carriers over the potential barrier - due to thermionic emission or diffusion - and b) quantum mechanical tunneling of charge carriers through the barrier. The diffusion theory includes the effect of the electron collisions in the depletion region and the change in local field depending on the diffusion coefficient [31]. Therefore the prefactor of the total current density does not depend on the Richardons constant nor on the temperature but on the diffusion coefficient and the carrier density (results are shown in Chapter 5). When the width of the potential barrier is small (few nanometers) or the semiconductor is heavily doped is possible to have tunneling through the barrier. Mathematically, the presence of tunneling modifies Eq. 2.18 for the thermionic emission theory and can be expressed by:
J = JS eqV /nkT −1
where n is an ideality factor. Bigger is the value of n, stronger is the tunnel effect and more the current density differs from the one measured by simple thermionic effect.
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Reproducible low contact resistance in
Rubrene single-crystal field-effect
transistors with nickel source and drain
electrodes
We have investigated the contact resistance of rubrene single-crystal field-effect transistors (FETs) with nickel electrodes by performing scaling experiments on devices with channel length ranging from 200 nm up to 300 µm. We find that the contact resistance can be as low as 100 Ωcm with narrowly spread fluctua-tions. For comparison, we have also performed scaling experiments on similar gold-contacted devices, and found that the reproducibility of FETs with nickel electrodes is largely superior. These results indicate that nickel is a very promis-ing electrode material for the reproducible fabrication of low resistance contacts in organic FETs.
This Chapter has been published as I. N. Hulea, S. Russo, A. Molinari and A. F. Morpurgo, Appl. Phys. Lett. 88, 113512 (2006)
3.1
Introduction
The possibility to downscale organic field-effect transistors (FETs) is currently hindered by the high contact resistance present at the interface between the metal electrodes and the organic semiconductor [1]. One of the main experimental prob-lems in the study and optimization of the contact resistance originates from the observed irreproducibility. In spite of the large effort put in the investigation of contact effects [1, 2, 3, 4, 5, 6], the reason for both the high values and the irreproducibility of the contact resistance are not currently understood. Many different phenomena are likely to play an important role, including the presence of grain boundaries at the metal/organic interfaces, the interface fabrication pro-cess (e.g., metal diffusion into the organic semiconductors and extrinsic damage introduced during the device assembly process), fluctuations in the work func-tion of the metal electrodes, etc. Currently, the problem seems to be particularly severe for oligomer-based devices. Whereas for FETs based on a number of dif-ferent polymers it has been found that the contact resistance scales linearly with the carrier mobility [7], for transistors based on oligomers a very broad range of contact resistance values have been measured on identically prepared devices, and no systematic behavior has been observed [6].
To address the issue of contact resistance in oligomer transistors, we have re-cently started the investigation of organic single-crystal FETs with different metal contacts. Single-crystal devices are particularly advantageous for this purpose be-cause their electrical characteristics exhibit an excellent level of reproducibility from sample to sample [8]. This is crucial for a reliable comparison of FETs with different channel length, i.e. to perform scaling experiments from which the value of the contact resistance can be extracted.
3.2
Scaling experiment
In this Chapter we focus on rubrene single-crystal FETs with nickel electrodes. Nickel was chosen because, although it oxidizes in air, its native oxide is conduc-tive and has a work-function of 5.0 eV [9], ideally suited to inject carriers into the highest occupied molecular orbital of many molecular semiconductors. By per-forming a conventional scaling analysis [6, 10, 7] of the electrical characteristics of these devices we extract the value of the contact resistance. We find values of RC
as low as 100 Ωcm, i.e. 50 times smaller than in the best oligomer FET reported to date [6]. The spread in values in the contact resistance measured on transistors fabricated on the same crystal is small (less than a factor of 2); devices fabricated on different crystals exhibit a somewhat large spread, ranging from 100 Ωcm to
1.5 kΩcm (and typically between 200 Ωcm and 1 kΩcm), but still considerably smaller than what has been observed so far in oligomer FETs. For comparison, we have also investigated a number of single-crystal FETs contacted with gold electrodes, the material commonly used for the fabrication of contacts in organic transistors, and found a considerably lower reproducibility level. This indicates that nickel is a very promising material for the fabrication of contacts for organic transistors, even though the surface of the electrodes oxidizes. We note that nickel is also advantageous as compared to gold because it is more mechanically robust, which should minimize the possibility of (electro)migration into organic materials during device operation, and cheaper.
The device layout (see Fig.3.1) is such that FETs with different channel lengths are fabricated on the same single crystal. Many different samples were studied with channel length ranging from 200 nm to 300 µm. Prior to the crystal adhesion, an oxygen plasma treatment is performed to remove residues of resists possibly still present on the SiO2surface. Although the exposure of the electrodes
to oxygen plasma contributes to the oxidation of the nickel surface, it does not preclude the realization of reproducible, low-resistance electrodes.
Figure 3.1: Typical transistor characteristics measured on a rubrene single-crystal FET with Ni source-drain electrodes (width W = 210 µm; length L= 700 µm). The inset shows a top view of one of the devices used in our investigation (for this device the crystal width W is 35 µm).
