Charge transport in disordered organic field-effect transistors - PDF document

Contents ix 8 Dopant density determination in disordered organic field-effect transistors 83 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 8.2 Motivation and Realization . . . . . . . . . . . . . . . . . . . . . . . . . 84 8.3 Interpretation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 86 8.3.1 Determination of the dopant density . . . . . . . . . . . . . . . . 86 8.3.2 Determination of the bulk mobility . . . . . . . . . . . . . . . . . 89 8.4 Results for PTV and P3HT . . . . . . . . . . . . . . . . . . . . . . . . . 89 8.5 Shift of the switch-on voltage . . . . . . . . . . . . . . . . . . . . . . . . 91 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 9 Solution-processed ambipolar organic field-effect transistors 97 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 9.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 9.3 Ambipolar transistor operation . . . . . . . . . . . . . . . . . . . . . . . 101 9.4 CMOS-like inverter operation . . . . . . . . . . . . . . . . . . . . . . . 105 9.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 10 Ambipolar field-effect transistors based on a single organic semiconductor 109 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 10.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 10.3 The PIF ambipolar transistor and inverter . . . . . . . . . . . . . . . . . 111 10.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Summary 119 Samenvatting 123 List of Publications 127 Patent Application 128 Curriculum Vitae 129 Dankwoord 131

Chapter 1 General Introduction 1.1 Historical perspective Solid-state electronics was founded by the invention of the bipolar transistor by Bardeen, Brattain and Shockley 1 in 1947. Germanium, the original semiconducting material to fabricate diodes and transistors was soon replaced by single-crystalline silicon. The next major development in the field of solid-state electronics was the invention of the first integrated circuit 2 in 1960, which catapulted us into the information age. Today, the number of devices manufactured on a chip has grown to over several hundreds of million and the feature sizes have shrunk to submicron resolution. Our information, condensed into bits and bytes, travels across the globe, processed by grains of sand, as silicon technology has dominated integrated device manufacturing and will do so for the foreseeable future. Plastics, or organic materials, are strong, lightweight, adaptable, and they can be produced at low temperatures, giving them an economic and technological edge over competing materials, such as wood or ceramics, for the fabrication of packaging materials, furniture, domestic appliances, etc. In the 1960s the development of photo-conductive organic materials for xerographic applications [4] emerged. However it was the discovery of the first highly conducting polymer, chemically doped polyacetylene 3 in 1977, that demonstrated that polymers could be used as electrically active materials as well. This discovery resulted in a huge research effort on conjugated organic materials. Combining the interesting properties of polymers with opto-electronic functional- ity, has demonstrated that organic materials, in their own right, can be the ”core” of a wide range of new opto-electronic devices, such as polymeric light-emitting diodes, polymeric solar cells, and organic integrated circuits. The polymers used in these applications are soluble in organic solvents and can therefore be processed from solution, using techniques such as spin coating, film casting or even inkjet printing. These techniques for film deposition allow large areas to be coated, which is important for the realization of large- 1 The invention of the transistor won them the Nobel prize in physics in 1956 [1,2] 2 which was awarded the Nobel prize in physics in 2000 to Alferov, Kroemer and Kilby [3] 3 This discovery won McDiarmid, Shirakawa and Heeger the Nobel prize in chemistry in 2000 [5–7]

2 General Introduction Figure 1.1: The top left-hand photo shows a 64 by 64 polymer-dispersed liquid-crystal display driven by 4096 polymer TFTs, with solution- processed PTV as the semiconductor. An image containing 256 grey levels is shown, while the display is refreshed at 50 Hz. The top right-hand photo shows a fully processed 150-mm wafer foil containing all-polymer transistors and integrated circuits. The bottom photo shows a monochrome polymer LED segment display, which is used as battery charge state indicator on a Philips shaver. This is the first Polymer LED product that was launched on the consumer market in June 2002. Photos: Philips Research

1.2 Charge transport in polymeric semiconductors 3 area displays as well as for high-volume production of integrated circuits [11]. Also, the mechanical toughness of polymers and the flexibility of polymeric thin films allow their use in flexible displays and flexible electronics (see Fig.1.1). Furthermore, polymers are usually associated with low-processing costs, allowing them to be used in disposable products. The properties of polymers can be tuned by adding functionalizing sidegroups, or by building in elements such as sulfur or nitrogen. A lot of effort is being put in the synthesis of new materials, with improved performance and novel properties. These ad- vantages make them interesting candidates for low-cost, flexible industrial applications. Understanding the optical and electronic properties of these materials on a microscopic level has turned out to be an intriguing challenge that merges the fields of physics and chemistry. For the operation and performance of all these devices the charge transport through the polymer layer is the dominant factor. It is therefore crucial to gain insight into their charge transport mechanisms. In the following section the most widely used descriptions of charge transport in disordered organic semiconductors are presented. Emphasis is put on the presence of disorder. In the context of charge transport, the scope of this thesis is in the physical description of field-effect transistors based on disordered organic semiconductors. 1.2 Charge transport in polymeric semiconductors Conjugated polymers are intrinsically semiconducting materials. They lack intrinsic mobile charge, but are able to transport charge generated by light, injected by electrodes, or provided by chemical dopants. The main constituent of conjugated polymers is the carbon atom. It is the nature of the bonds between the carbon atoms that gives the conjugated polymer its interesting physical and chemical properties. To understand the basics of these molecular bonds it is instructive to understand the shape of the electronic orbitals 4 of the atoms participating in the molecular bond [8]. Carbon, in the ground state, has four electrons in the outer electronic level. The orbitals of these electrons may mix, under creation of four chemical bonds, to form four equivalent degenerate orbitals referred to as sp 3 hybrid orbitals in a tetrahedral orienta- tion around the carbon atom, If only three chemical bonds are formed, they have three coplanar sp 2 hybridized orbitals which are at an angle of 120 o with each other. These bonds are called σ -bonds, and are associated with a highly localized electron density in the plane of the molecule. The one remaining free electron per carbon atom resides in the p z orbital, perpendicular to the plane of the sp 2 hybridization. The p z orbitals on neigh- boring atoms overlap to form so-called π -bonds [9, 10]. A schematic representation of this hybridization is given for the simplest conjugated polymer, polyacetylene, in Fig.1.2. Molecules with σ and π -bonds are schematically represented by single and double alternating chemical bonds between the carbon atoms, and are called conjugated molecules. The π -bonds establish a delocalized electron density above and below the plane of the 4 An atomic orbital is derived using the mathematical tools of quantum mechanics, and is a representation of the three-dimensional volume ( i.e. the region in space) in which the probability of finding an electron is highest.

4 General Introduction � � � � � � � � � � � � �� π �� π �� π �� σ �� σ �� σ �� Figure 1.2: (a) The moleculare structure of polyacetylene, for clarity, hydrogen atoms are not shown. The alternating double and single bonds indicate that the polymer is conjugated. (b) Schematic representation of the electronic bonds in polyacetylene. The p z -orbitals overlap to form π -bonds. molecule. These delocalized π -electrons are largely responsible for the opto-electronic behavior of conjugated polymers. There are large differences between the three-dimensional crystal lattice of most inorganic semiconductors and the amorphous structure of conjugated polymers. Inorganic semiconductor crystalline lattices, such as silicon and germanium, are characterized by long range order and strongly coupled atoms. For silicon and germanium this results in the formation of long-range delocalized energy bands separated by a forbidden energy gap [12]. Charge carriers added to the semiconductor can move in these energy bands with a relatively large mean free path. The limiting factor for this band transport is scat- tering of the carriers at thermal lattice vibrations, i.e. phonons [10, 12]. This is depicted schematically in Fig.1.3a. As the number of lattice vibrations decreases with decreasing temperature, the mobility of the charge carriers increases with decreasing temperature. In conjugated polymers the polymer chains are weakly bound by van der Waals forces 5 . These polymers typically have narrow energy bands, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which can easily be disrupted by disorder. Although electric charge is delocalized along the π - conjugated segments of the polymer backbone, the length of such perfectly conjugated segments is typically limited to length scales of around 5 nm, separated by chemical defects, such as a nonconjugated sp 3 -hybridized carbon atom on the polymer backbone, or by structural defects, such as chain kinks or twists out of coplanarity. Due to the disorder the semiconductor can not be regarded simply as having two delocalized energy bands separated by an energy gap. Instead, the charge transporting sites, which are the segments of the main chain polymer, are subject to a Gaussian distribution of energies (see Fig.1.4b), implying that all states are localized [13]. The shape of the density of states (DOS) is suggested to be Gaussian, because of the observed Gaussian shape of the optical spectra [13]. 5 We note that the carbon atoms in a polymer chain are strongly coupled.

1.2 Charge transport in polymeric semiconductors 5 �� Figure 1.3: Charge transport mechanisms in solids. (a) Band transport. In a perfect crystal, depicted as the straight line, a free carrier is delocalized. There are always lattice vibrations that disrupt the crystal symmetry. Carriers are scattered at these phonons, which limit the charge carrier mobility. The mobility for band transport increases with decreasing temperature. (b) Hopping transport. If the carrier is localized due to defects, disorder or selflocalization, e.g. in the case of polarons, the lattice vibrations are essential for a carrier to move from one site to another. For hopping transport the mobility increases with increasing temperature. The figure is adapted from ref. [10]

6 General Introduction �� Figure 1.4: (a) Schematic view of polymer chains broken up in conjugated segments, which are represented as charge transport sites, between which the charge carriers hop. (b) A representation is given of the smeared out density of states, which is often approximated by a Gaussian distribution for the HOMO and LUMO levels. The specific shape of the DOS is rarely investigated, as it is difficult to determine experimentally. Via chemical doping the DOS itself is often altered by the presence of the dopant counter ions, and via the field-effect no unique DOS can be determined. The shape of the DOS, which is a manifestation of the disorder of the system, is however important for the description of charge transport. Charge carriers move from localized site to localized site, on chain as well as between chains in order to percolate through a thin-film device (see Fig.1.4a) [10,13]. It can be concluded that the charge transport and semiconducting properties of polymeric semiconductors are sensitive to the morphology of the polymer chains and the local structural order within the film. Structural and energetic disorder in conjugated polymer systems are therefore of importance in the description of charge transport. 1.2.1 Hopping transport Due to the disorder and the localization of charge, the motion of the charge carriers in organic semiconductors is typically described by hopping transport, which is a phonon- assisted tunneling mechanism from site to site [14, 15]. This hopping transport takes place around the Fermi level 6 . Many of the hopping models are based on the single- phonon jump rate description as proposed by Miller and Abrahams [16]. In this model 6 The Fermi level is defined as the highest energy level occupied by charge at a temperature of 0 K. At finite temperatures, some levels above the Fermi level are filled and some levels below are empty. The distribution of filled energy levels around the Fermi level is given by the Fermi-Dirac distribution function [12]. The position of the Fermi level is determined by the charge neutrality condition of the system.

1.2 Charge transport in polymeric semiconductors 7 the hopping rate between an occupied site i and an adjacent unoccupied site j , which are separated in energy by E i − E j and in distance by R ij , is described by: � � � − E i − E j exp E i > E j , � � ν ij = ν 0 exp − 2 γ R ij k B T (1.1) 1 E i < E j , where γ − 1 quantifies the wavefunction overlap between the sites, ν 0 is a prefactor, and k B is Boltzmanns constant. The Miller-Abrahams model addresses hopping rates at low temperatures between shallow three-dimensional impurity states, assuming that the electron- lattice coupling is weak. When the Miller-Abrahams model is applied to polymeric semiconductors, it is assumed that the conjugated segments of the polymers play the role of nearly isolated impurity states, and that Eq.1.1 is still valid at high temperatures [16]. Depending on the structural and energetic disorder of the system it can be energet- ically favorable to hop over a longer distance with a low activation energy (energy difference between sites), than over a shorter distance with a higher activation energy. This extension to the Miller-Abrahams model is called variable range hopping [17]. Monroe developed a model describing hopping transport around the Fermi level in an exponential density of states [18]. He found that this hopping description is analytically very similar to a model in which charge carriers are thermally activated to a transport level. For the description of the temperature and gate voltage dependencies of organic field-effect transistors Vissenberg and Matters [19] developed a percolation model based on variable range hopping in an exponential density of states, which will be used throughout this thesis. 1.2.2 Multiple trapping and release model For polycrystalline organic semiconductor layers the temperature dependent transport data is often interpreted in terms of a multiple trapping and release model [20]. In this model the organic semiconductor film consists of crystallites which are separated from each other by amorphous grain boundaries. In the crystallites the charge carriers can move in delocalized bands, whereas in the grain boundaries they become trapped in localized states. The trapping and release of carriers at these localized states results in a thermally activated behavior of the field-effect mobility, which depends on the gate voltage. The description of trapped, i.e. localized, charges which can be thermally activated to a transport level, in this case the band, is very similar to hopping in an exponential density of states [18,19] as stated in the previous section. As the grain boundaries in a polycrystalline system determine the DC charge transport and typically an exponential trap distribution is used to model the experimental data, no clear distinction can be made between hopping transport and multiple trapping and release, on the basis of the temperature dependence of the mobility. One should be able to separate a trap-limited mobility from a hopping mobility if the Hall mobility in a Hall effect experiment could be determined, since in a magnetic field, there will be no Lorentz force on trapped charges [21]. Unfortunately, due to the low charge carrier mobilities, the Hall effect is very difficult to measure experimentally.

8 General Introduction �D� �E� & � + �� 6 6 Q Q 379 3�+7 �F� �G� 2 2 Q Q 2 2 2& � & �� 339 2& �� & �� 339 �I� �H� 3HQWDFHQH �J� 2 Q 2 3,) 3&%0 Figure 1.5: Molecular structures of the conjugated materials studied in this thesis: (a) poly(2,5-thienylene vinylene) (PTV), (b) poly(3-hexyl thiophene) (P3HT), (c) poly([2-methoxy- 5-(3’,7’-dimethylocyloxy)]-p-phenylene vinylene) (OC 1 C 10 - PPV), (d) poly([2,5-(3’,7’-dimethylocyloxy)]-p-phenylene vinylene) (OC 10 C 10 -PPV), (e) pentacene, (f) poly(3,9-di-tert- butylindeno[1,2-b] fluorene) (PIF), (g) [6,6]-phenyl C61-butyric acid methyl ester (PCBM).

1.3 Scope of this work 9 1.2.3 Polarons Next to the disorder-induced localization of charge, the strong electron-phonon coupling in organic materials results in localization of charge. An excess charge carrier on a conjugated polymer chain can minimize its energy by a local lattice deformation. This quasipar- ticle consisting of charge and a lattice deformation, or phonon cloud, is called a polaron. As polarons represent a local distortion of the lattice, the associated energy levels must split off from the HOMO level and the LUMO level. These energy levels, which reside in the energy gap, have often been observed in optical absorption experiments on charged conjugated polymer films [22–24]. In polaronic charge transport, not only the charge moves under an applied electric field but the lattice deformation moves with it. Typically, for hopping transport of polarons, a description in terms of Miller-Abrahams hopping [16] is insufficient, as multiphonon hopping rates need to be considered [25,26]. 1.3 Scope of this work In this thesis we study charge transport in organic semiconductors. We do this by focusing on the physical characterization of disordered organic field-effect transistors. It will be made clear that the disorder in the polymer films is crucial for the interpretation of the data. The field-effect transistor geometry allows variation of the charge carrier density in the semiconductor, without the presence of counter ions. Therefore, the transistor allows a rather clean study of the charge transport in organic semiconductors as a function of the charge carrier density and temperature. In the following section the operation of the silicon metal-oxide-semiconductor field-effect transistor (MOSFET) is described. In the experiments we find that the organic transistors are in several respects not comparable to silicon MOSFETs. Therefore, in this thesis we redefine and reevaluate basic transistor parameters, such as the threshold voltage, the field-effect mobility, the contact resistance and the dopant density. Subsequently, we study the charge transport as a function of charge density and temperature, giving insight into the charge transport mechanisms. And finally, we investigate the stability of the polymer layer and discuss why typically only unipolar transistor behavior is observed experimentally. The conjugated organic materials used throughout this thesis are given in Fig.1.5. 1.3.1 The field-effect transistor The MOSFET can basically be considered as a parallel plate capacitor, where one conducting electrode, the gate electrode, is electrically insulated, via an insulating oxide layer, from the semiconductor layer (see Fig.1.6). Two electrodes, the source and the drain, are contacted to the semiconductor layer. By applying a gate voltage, V g , with respect to the source electrode, charge carriers can electrostatically be accumulated or depleted in the semiconductor at the semiconductor-insulator interface. Due to this field-effect the charge carrier density in the semiconductor can be varied. Therefore, the resistivity of the semiconductor, and hence the current through the semiconductor (upon application of a source-drain field), can be varied over orders of magnitude [27]. Since the MOSFET can

10 General Introduction � �� Figure 1.6: Schematic of a thin-film field-effect transistor. �� J �� )% � J �� )% � J �� )% � J �� )% � J �� )% � J �� )% � J �� )% � J �� )% � J �� )% � � � � � � � � � � � � � � � � �� J �� J �� J � ) � ) � ) �� J �� J �� J �� 0HWDO��,QVXODWRU��6HPLFRQGXFWRU 0HWDO��,QVXODWRU��6HPLFRQGXFWRU Figure 1.7: Energy level band diagram of an ideal metal-insulator- semiconductor diode structure with a p-type semiconductor: (a) flat-band condition, (b) accumulation, (c) depletion. be switched between a conducting and a non-conducting state, it is widely used as the basic building block of binary logic. The band-bending diagrams of a p-type transistor in the different operating regimes are schematically given in Fig.1.7. In equilibrium the Fermi levels of the materials align, by charge carriers which move to or from the semiconductor-insulator interface. When a bias is applied which is equal to the difference between the Fermi levels of the gate metal and the semiconductor, no band bending will occur in the semiconductor at the semiconductor-insulator interface, i.e. the energy bands in the semiconductor will be flat (see Fig.1.7a). This biasing condition is defined as the flat-band voltage. If the Fermi level of the metal and semiconductor are similar this flat-band voltage will be 0. For a p-type semiconductor, the application of a negative gate voltage will induce charges at the semiconductor-insulator interface (these charges are supplied by the source and drain contacts). In effect the Fermi level of the gate metal is varied with a value of qV g , where q is the elementary charge, causing band bending in the semiconductor layer as is schematically represented in Fig.1.7b. For a positive applied V g the energy bands in the p-type semiconductor are bent downwards, and the mobile positive charge carriers are depleted from the semiconductor-insulator interface. In this case the transistor is biased

1.4 Outline of this thesis 11 in the depletion mode (see Fig.1.7c). 1.4 Outline of this thesis In Chapter 2 the switch-on voltage and the field-effect mobility in disordered organic field-effect transistors are introduced. It is argued that the use of classical MOSFET theory for the description of these transistors is not a priori justified. In fact a scruti- nizing look at the data of FETs based on three different organic semiconductors reveals that MOSFET theory neglects basic properties of these materials, particularly disorder, and should therefore not be used. Alternative characterization parameters are introduced which will be used throughout the remainder of this thesis. In the third section of chapter 2 the hole transport in light-emitting diodes and field- effect transistors is compared. The experimental hole mobilities extracted from both types of devices, based on a single polymeric semiconductor, can easily differ by three orders of magnitude. This apparent discrepancy in the charge transport description is resolved by demonstrating that the hole mobility depends strongly on the charge carrier density in disordered organic semiconducting polymers. In Chapter 3 the temperature dependence of the field-effect mobility is investigated in two solution-processed disordered organic field-effect transistors (PTV and pentacene). We find thermally activated behavior, with an activation energy that depends on the induced charge density in the transistor. Upon extrapolation of the data to infinite temperature we find an empirical relation, termed the Meyer-Neldel rule, which states that the mobility prefactor increases exponentially with the activation energy. From this analysis a characteristic temperature is extracted that does not vary much between different materials. The possible implications of this observation in terms of charge transport are given. As a follow-up to the previous chapter the field dependence of the in-plane conductivity is investigated in PTV and P3HT in Chapter 4 . Using an empirical relation for this field-dependence we find an isokinetic temperature that is comparable to the values obtained from the Meyer-Neldel experiments of Chapter 3. Implications of these findings are addressed. In Chapter 5 , we investigate the scaling behavior of FETs. It is demonstrated that downsizing of the transistor channel does not automatically result in an improve- ment of integrated circuit performance. This is due to parasitic resistances at the metal- semiconductor contact. We find an empirical relation between the charge-carrier mobility in the polymeric semiconductor and the parasitic resistance. In Chapter 6 we investigate the dopant density in polymeric semiconductors in the classical way by means of impedance spectroscopy of metal-insulator-semiconductor diodes. The diodes, based on poly(3-hexyl thiophene), are measured and analyzed as a

12 General Introduction function of bias voltage, measurement frequency and temperature. We find that simple Mott-Schottky analysis can only be applied here if the relaxation time of the semiconducting polymer is taken into account. The long relaxation times are a direct result of the disorder in the semiconducting polymer layer. In Chapter 7 we investigate the instability of P3HT under oxygen exposure and illumination. P3HT forms a charge-transfer complex with molecular oxygen, which results in an acceptor density increase with time. This acceptor density change with time, is investigated by means of photoimpedance measurements as a function of wavelength. The measurements show that the acceptor creation efficiency peaks upon excitation of the molecular oxygen-polythiophene contact charge transfer complex. An alternative method for the determination and monitoring of the dopant density is given in Chapter 8 , where the dopant density is extracted directly from the transfer characteristics of transistors based on PTV and P3HT. It is demonstrated that, due to the fact that in disordered semiconductors the charge carrier mobility depends on the charge density, the bulk current can be separated from the field-effect current in the total current density. It is found that the morphology of the polymer film is crucial for the stability of transistors that are prone to oxygen doping effects. In the first 5 chapters we have looked at unipolar p-type organic field-effect transistors. In Chapter 9 we use a blend of hole-conducting OC 1 C 10 -PPV and electron- conducting PCBM to construct a solution-processed ambipolar organic field-effect transistor. The characteristics of this kind of transistor are measured and analyzed and CMOS- like inverter operation is demonstrated, paving the way for solution-processable CMOS- like logic circuitry. As was demonstrated in the previous chapter a suitable choice of electrode and semiconductor can result in ambipolar FETs. In Chapter 10 we show that even a single solution-processed organic semiconductor can be used in ambipolar transistors, demonstrating that in principle an intrinsic organic semiconductor can transport both polarities of charge. Important parameters for experimental observation of this ambipolar behavior are extrinsic effects such as workfunction mismatch and material purity.

References [1] http://www.nobel.se/physics/laureates/1956/press.html [2] W. Shockley, Bell Syst. Techn. J. 28 , 435 (1949). [3] http://www.nobel.se/physics/laureates/2000/press.html [4] D.M. Pai and B.E. Spingett, Rev. Mod. Phys. 65 , 163 (1993). [5] http://www.nobel.se/chemistry/laureates/2000/press.html [6] C.K. Chiang, C.R. Fincher, Y.W. Park, A.J. Heeger, H. Shirakawa, E.J. Louis, S.C. Gan, A.G. MacDiarmid, Phys. Rev. Lett. 39 , 1098 (1977). [7] C.K. Chiang, M.A. Druy, S.C. Gau, A.J. Heeger, E.J. Louis, A.G. McDiarmid, Y.W. Park and H. Shirakawa, J. Am. Chem. Soc. 100 , 1013 (1977). [8] P.W. Atkins, Physical Chemistry , Oxford University Press (1986). [9] R.E. Peierls, Quantum theory of solids , Oxford University Press, London (1955). [10] M. Pope and C.E. Swenberg, Electronic Processes in Organic Crystals and Poly- mers , Oxford University Press (1999). [11] A.R. Brown, C.P. Jarrett, D.M. de Leeuw and M. Matters, Synth. Met. 88 , 37 (1997). [12] C. Kittel, Introduction to solid state physics , 6th edition (John Wiley & Sons, Inc 1986). [13] H. B¨ assler, Phys. Stat. Sol. B 175 , 15 (1993). [14] E.M. Conwell, Phys. Rev. 103 , 51 (1956). [15] N.F. Mott, Canadian J. Phys. 34 , 1356 (1956). [16] A. Miller and E. Abrahams, Phys. Rev. 120 , 745 (1960). [17] N.F. Mott and E.A. Davies, Electronic processes in non-crystalline materials , 2 nd Edition, Oxford University Press, London (1979). [18] D. Monroe, Phys. Rev. Lett. 54 , 146 (1985).

14 References [19] M.C.J.M. Vissenberg and M. Matters, Phys. Rev. B 57 , 12964 (1998). [20] G. Horowitz, R. Hajlaoui and P. Delannoy, J. Phys. III 5 , 355 (1995). [21] D. Emin, private communication, D. Emin, Phys. Today 35 , 34 (1982). [22] K.E. Ziemelis, A.T. Hussain, D.D.C. Bradley and R.H. Friend, Phys. Rev. Lett. 66 , 2231 (1991). [23] P.A. Lane, X. Wei and Z.V. Vardeny, Phys. Rev. Lett. 77 , 1544 (1996). [24] R. ¨ Osterbacka, C.P. An, X.M. Jiang and Z.V. Vardeny, Science 287 , 839 (2000). [25] T. Holstein, Ann. Phys. 8 , 325 (1959). [26] D. Emin, Adv. Phys. 24 , 305 (1975). [27] S.M. Sze, Physics of semiconductor devices , 2 nd edition, John Wiley & Sons, (New York, 1981).

Chapter 2 The switch-on voltage and the field-effect mobility in disordered organic field-effect transistors Abstract In this chapter we critically evaluate two characterization parameters of disordered organic field-effect transistors. • The switch-on voltage is defined as the flat-band voltage, and is used as characterization parameter. The transfer characteristics of the solution processed organic semiconductors pentacene, poly(2,5-thienylene vinylene) and poly(3-hexyl thiophene) are modeled as a function of temperature and gate voltage with a hopping model in an exponential density of states. The data can be described with reasonable values for the switch-on voltage, which is independent of temperature. This result also demonstrates that the large threshold voltage shifts as a function of temperature reported in the literature constitute a fit-parameter without a clear physical basis. • The experimentally determined field-effect mobility is compared to the local charge carrier mobility, which takes into account the charge density distribution in the transistor. It is demonstrated that the experimentally determined field-effect mobility is a reasonable estimate for the local mobility of the charge carriers at the interface. In the last section of this chapter the transistor description is compared to the models used for polymeric light-emitting diodes and it is demonstrated that the two device descriptions can be unified, when the large differences in charge densities in the two device geometries are taken into account.

16 The switch-on voltage and the field-effect mobility 2.1 The switch-on voltage 2.1.1 Introduction The charge transport in organic field-effect transistors (FETs) has been a subject of research for several years. It has become clear that disorder severely influences the charge transport in these transistors [1, 2]. Studies on the effect of molecular order ultimately resulted in the observation of band transport in high quality organic single crystals [3]. The electrical transport in these crystals is well described by monocrystalline inorganic semiconductor physics [3,4]. However, devices envisaged for low-cost integrated circuit technology are typically deposited from solution [5, 6], resulting in amorphous or polycrystalline films. In these solution-processed organic transistors the disorder in the films dominates the charge transport, due to the localization of the charge carriers. The disorder is observed experimentally through the thermally activated field-effect mobility and its gate voltage dependency [7,8]. These observations have thus far been modeled using multiple trapping and release [9], variable range hopping [8] and grain boundary charging [10]. A further common feature of disordered organic field-effect transistors is the temperature dependence of the threshold voltage, V th [10]. In this paragraph, the temperature dependence of V th in disordered organic field- effect transistors is addressed. It is argued that V th , as used in literature for the description of organic transistor operation, is a fit parameter with no clear physical basis. Instead, a switch-on voltage, V so , is defined for the transistor at flat-band. We model the experimental data obtained on solution-processed pentacene, poly(2,5-thienylene vinylene) (PTV) and poly(3-hexyl thiophene) (P3HT), with a disorder model of variable-range hopping (VRH) in an exponential density of states [8]. The modeling shows that good agreement with experiment can be obtained with reasonable values for the switch-on voltage, which is independent of temperature. Furthermore, it is found that the shift of the Fermi-level with temperature has no influence on V so . 2.1.2 Experimental In the experiments we used heavily doped Si wafers as the gate electrode, with a 200 nm thick layer of thermally oxidized SiO 2 as the gate-insulating layer. Using conventional lithography, gold source and drain contacts are defined with an interdigitated geometry. The SiO 2 layer is treated with the primer hexamethyldisilazane (HMDS) to make the surface hydrophobic. The samples are measured under high vacuum (10 − 7 mbar) in an Oxford optistat CF-V flow cryostat, using a Hewlett-Packard 4156A semiconductor parameter analyzer. The films of PTV are truly amorphous whereas the pentacene films are polycrystalline. The P3HT films can be considered nanocrystalline, as ordered regions of this regioregular polymer alternate with disordered regions [1]. We do not observe any hysteresis in the current-voltage characteristics and the curves are stable with time (in vacuum). The field-effect mobilities in the devices have been estimated from the transconductance [7] at a gate voltage, V g = − 19 V at room temperature and are given in Table 2.1. For the P3HT transistor described here the processing conditions were not optimized to give the high mobilities reported in literature [1].

2.1 The switch-on voltage 17 Table 2.1: Values obtained by using Eq.2.6 to model the transfer characteristics of solution-processed pentacene, PTV and P3HT. T DOS represents the width of the exponential density of states, σ 0 is the conductivity prefactor, α − 1 the effective overlap parameter, V so the switch- on voltage, and µ RT the field-effect mobility at V g = − 19 V and room temperature. σ 0 [10 6 S / m] α − 1 [ ˚ µ RT [ cm 2 / Vs ] T DOS [K] A] V so [V] 2 × 10 − 3 PTV 382 5 . 6 1 . 5 1 2 × 10 − 2 pentacene 385 3 . 5 3 . 1 1 6 × 10 − 4 P3HT 425 1 . 6 1 . 6 2 . 5 2.1.3 The classical threshold voltage The difficulty of defining a threshold voltage in disordered organic transistors was already pointed out by Horowitz et al. [11]. The threshold voltage in inorganic field-effect transistors is defined as the onset of strong inversion [4]. However, most organic transistors only operate in accumulation and no channel current in the inversion regime is observed. Nevertheless, classical metal-oxide-semiconductor field-effect (MOSFET) theory is often used to extract a V th from the transfer characteristics of organic transistors in accumulation. The square root of the saturation current is then plotted against the gate voltage, V g . This curve is fitted linearly and the intercept on the V g -axis is defined as the V th of the transistor. For disordered transistors this method neglects the experimentally observed dependence of the field-effect mobility on the gate voltage [7,12]. In an attempt to take this into account in the parameter extraction several groups have used an empirical relation to fit the field-effect mobility [10,13], � γ , � µ = K V g − V th (2.1) where K , γ and V th are fit parameters. Fitting of current-voltage characteristics of the transistors, using either this empirical relation or the square root technique, has resulted in a temperature dependent V th [10, 14]. The shift of V th with temperature is as large as 15 V in the temperature range of 300 K to 50 K [10]. However, for transistors based on the same materials in the crystalline phase, for which MOSFET theory is valid, the shift of V th with temperature is at most ≃ 0.5 V [4]. This observation raises the question: why, for a disordered system, the shift of V th with temperature is so much larger than in its crystalline counterpart. To answer this question, we first have to realize that, in both types of analysis mentioned, the extracted V th is a fit parameter. This fit parameter has no direct relation with the original definition of the threshold voltage in MOSFET theory. Also, depending on the range of V g over which the data is fitted in disordered transistors, the value of the extracted V th will be different. Therefore, we argue that V th as defined in MOSFET theory has no physical relevance in the description of the operation of disordered organic transistors. Despite these issues, some suggestions have been given

18 The switch-on voltage and the field-effect mobility in literature to explain the large temperature dependence of the apparent V th , such as a widening of the bandgap [14], and displacement [10] of the Fermi level with decreasing temperature. 2.1.4 Definition of the switch-on voltage Instead of V th as characterization parameter, we will use the gate voltage at which there is no band-bending in the semiconductor, i . e . the flat-band condition (see Fig.1.7a). We call this the switch-on voltage, V so , of the transistor. Below V so the variation of the channel current with the gate voltage is zero, while the channel current increases with V g above V so . For an unintentionally doped semiconductor layer, V so is then only determined by fixed charges in the insulator layer or at the semiconductor/insulator interface. In that case V g becomes V g − V so . Without these fixed charges V so should in principle be zero [4]. 2.1.5 Modeling and discussion Here we will model the experimental DC transfer characteristics obtained on three different disordered organic field-effect transistors to estimate the temperature dependence of V so . Because we are looking at disordered systems, we use the variable range hopping model proposed by Vissenberg and Matters [8]. The charge transport in this model is governed by hopping, i.e. thermally activated tunneling of carriers between localized states around the Fermi level, E F . The carrier may either hop over a small distance with a high activation energy or over a long distance with a low activation energy. In the disordered semiconducting polymer the density of states (DOS) is described by a Gaussian distribution [16]. For a system with both a negligible doping level compared to the gate-induced charge and at low gate-induced carrier densities the Fermi level is in the tail states of the Gaussian, which is approximated by an exponential DOS [8](see also section 2.3): � � N t E g ( E ) = exp (2.2) k B T DOS k B T DOS where N t is the number of states per unit volume, k B is Boltzmann’s constant, and T DOS is a parameter that indicates the width of the exponential distribution. The energy distribution of the charge carriers is given by the Fermi-Dirac distribution. If a fraction, δ ∈ [0 , 1], of the localized states is occupied by charge carriers, such that the density of carriers is δ N t , then the position of the Fermi-level is fixed by the condition [8]: � E F � π T δ = exp � . (2.3) � k B T DOS T T DOS sin π T DOS Using a percolation model of variable range hopping, an expression for the conductivity as a function of the charge carrier occupation δ and the temperature T is derived [8]: TDOS � � δ N t ( T DOS / T ) 4 sin   T T π T DOS σ (δ, T ) = σ 0 (2.4)   ( 2 α) 3 B c

2.1 The switch-on voltage 19 where σ 0 is a prefactor of the conductivity, B c is a critical number for the onset of percolation, which is ≃ 2.8 for three-dimensional amorphous systems [17], and α − 1 is an effective overlap parameter between localized states. To calculate the field-effect current we have to take into account that in a field-effect transistor the charge density is not uniform. Using the gradual channel approximation ( | V g | ≫ | V ds | , where V ds is the source-drain voltage), we neglect the potential drop from source to drain electrode. To take into account that the charge-density decreases from the semiconductor-insulator interface to the bulk, we integrate over the accumulation channel: t � I ds = WV ds dx σ [ δ( x ), T ] , (2.5) L 0 where L , W , and t are the length, width and thickness of the channel, respectively. From Eqs. 2.4 and 2.5 we obtain the following expression for the field-effect current: � � � 2 k B T DOS WV ds ǫ semi ǫ 0 σ 0 T I ds = 2 T DOS − T Lq ǫ semi ǫ 0 TDOS � 4   � � � T T DOS T sin π T T DOS ×   ( 2 α) 3 B c   �� 2 TDOS �� ǫ semi ǫ 0 − 1 � � � T C i V g − V so × (2.6) 2 k B T DOS ǫ semi ǫ 0 where q is the elementary charge, ǫ 0 is the permittivity of vacuum, ǫ semi the relative dielectric constant of the semiconductor, and C i is the insulator capacitance per unit area. Eq.2.6 is used to model the transfer characteristics of solution processed PTV, pentacene, and P3HT as a function of V g and T . The four parameters σ 0 , α − 1 , T DOS , and V so were used to model all the curves, with a value of B c =2.8. After this initial fit, each curve was individually modeled with only V so as variable parameter, with the other parameters fixed. From this modeling, no temperature dependence of V so was observed. The results of the modeling are shown in Figs.2.1, 2.2, and 2.3. The fit parameters are given in Table 2.1. Good agreement is obtained for all three semiconductors. The single constant V so for all temperatures accounts for any fixed charge in the oxide and/or at the semiconductor- insulator interface. Also, the low values obtained for V so are realistic numbers. Because the measurement resolution in the low current regime is limited to 1-10 pA, the onset of the experimental curves in Figs.2.1, 2.2, and 2.3, seems to be shifting to more negative gate voltages with decreasing temperature. This is due to current decrease as a function of temperature, as a result of the thermally activated field-effect mobility (see Chapter 3) [18]. This effect does not translate in a temperature dependence of V so . Analysis of the data with the square root technique yields an apparent threshold voltage shift with temperature of 15 V for the PTV. Eq. 2.1 gives similar results. The values obtained for the prefactor of the conductivity σ 0 seem to be too high with respect to theoretical con- siderations [15]. The conductivity prefactor is discussed further in Chapters 3 and 4.

20 The switch-on voltage and the field-effect mobility � �� Figure 2.1: I ds versus V g of a PTV thin-film field-effect transistor for several temperatures. The solid lines are modeled using Eq.2.6. W=2 cm, L=10 µ m, V ds = − 2 V . The inset shows the structure formula of PTV. � �� Figure 2.2: I ds versus V g of a pentacene thin-film field-effect transistor for several temperatures. The solid lines are modeled using Eq.2.6. W=2 cm, L=10 µ m, V ds = − 2 V. The inset shows the structure formula of pentacene.

2.1 The switch-on voltage 21 � �� Figure 2.3: I ds versus V g of a P3HT thin-film field-effect transistor for several temperatures. The solid lines are modeled using Eq.2.6. W=2.5 mm, L=10 µ m, V ds = − 2 V . The inset shows the structure formula of P3HT. � �� . � � � � �� ) � �� ) � �� Figure 2.4: Fermi-level displacement as a function of temperature, calculated using Eq.2.3 and the parameters of Table 2.1

22 The switch-on voltage and the field-effect mobility We note that, the Fermi level shifting with decreasing temperature [10] has no effect on V so . The Fermi level shift, which results from the Fermi-Dirac distribution of the charge carriers in the exponential density of states, is calculated from Eq.2.3 and is found to be ≃ 0.04 eV over a temperature range of 200 K (see Fig.2.4). This displacement does not result in a shift of V so with temperature. 2.1.6 Conclusion It was argued that the threshold voltage extracted from the transfer characteristics of disordered organic transistors, using MOSFET theory or Eq.2.1, is only a fit parameter if the strong inversion regime is not observed in the transfer characteristics. The use of this parameter in the physical description of organic field-effect transistors is therefore incor- rect. Instead, we have defined a switch-on voltage for unintentionally doped disordered organic field-effect transistors as the gate voltage that has to be applied to reach the flat- band condition. Using a disorder model of hopping in an exponential density of states, the experimental data of solution-processed PTV, pentacene and P3HT could be described with reasonable values for the switch-on voltage, which is temperature independent. The use of V so as characterization parameter of disordered organic field-effect transistors is not limited to the model described here, but is generally applicable. 2.2 The field-effect mobility 2.2.1 Introduction As mentioned in the previous section the transport properties in disordered organic semiconductors are dominated by localized states. For polymeric light-emitting diodes an important consideration for device modelling is the non-uniform charge distribution in the device. As stated above, the charge distribution in a FET is also non-uniform, it decreases from the semiconductor/insulator (S/I) interface to the bulk, and it depends on the applied V g . Therefore, it is not trivial to assign one field-effect mobility to all carriers in the accumulation channel of a disordered organic field-effect transistor. Here, we calculate the variation of the charge carrier mobility through the thickness of the accumulation channel. It is found that only a small error is made by assuming that all carriers are moving at the semiconductor-insulator interface with the same mobility, at a given V g . In polymeric field-effect transistors (FETs) charge carriers are induced by a gate electrode across an insulating layer. By applying a negative voltage at the gate electrode the top of the valence band bends upward closer to the Fermi level (see Fig.1.7b). This band bending gives rise to a positive accumulation layer into the semiconductor next to the interface. Applying a voltage V ds between the source and the drain contact gives rise to a current in the channel. In literature, typically this current in the linear regime of the FET is described by: V ds I ds = WC i V g µ FE L , (2.7) with C i V g the total amount of accumulated charge carriers, V ds / L the electric field in the channel, and µ FE the field-effect mobility. It is important to note that the use of the total

2.2 The field-effect mobility 23 amount of induced charge C i V g in Eq.2.7 is only valid when all charge carriers have the same mobility. In that case, the field-effect mobility is calculated from [7]: � L ∂ I ds � (2.8) µ FE = . � WC i V ds ∂ V g � V ds → 0 To check the validity of this equation for disordered organic FETs, we calculate the charge distribution in the device from Poisson’s equation. Then we use the hopping model described in the previous section to calculate a local mobility, and compare the results with the values obtained from Eq.2.8 for both P3HT and PTV field-effect transistors. 2.2.2 Calculation of the charge distribution Again, an unintentionally doped system is considered. In the gradual channel approximation the distribution of charge carriers has to be described only in the direction perpendicular to the S/I interface ( x , see Fig.1.6). The distribution of the electric field, F x , in the accumulation layer perpendicular to the S/I interface is given by [12]: � V � 1 / 2 � � � �� 2 � V ′ �� dV ′ � � � F x = q δ N t , (2.9) � � ǫ 0 ǫ semi � � 0 where V ′ is the local potential, which varies from zero far away in the semiconductor bulk to V in the accumulation channel. The potential distribution as a function of the distance from the S/I interface, x , follows from the relation: � V 0 dV ′ (2.10) x = F x ( V ′ ) V where V 0 is the surface potential of the S/I interface. From the variation of the gate- induced potential V ( x ) as a function of distance x the density of holes δ N t ( x ) can be calculated. The induced charge per unit area Q ind is related to the gate voltage as follows: V g = Q ind + V so = ǫ 0 ǫ semi F x ( 0 ) + V so , (2.11) C i C i where F x ( 0 ) = F x ( V = V 0 ) is the electric field at the S/I interface. By increasing the gate voltage the surface potential increases resulting in an increase of charge carrier density. Assuming V so =0, δ N t ( x ) is calculated for an undoped semiconductor with C i =15.5 nF/cm 2 and ǫ semi =3. In Fig.2.5 the concentration of charge carriers as a function of distance x is shown for gate voltages of V g = − 19 V and V g = − 10 V . At V g = − 19 V the charge carrier density decreases from 3.5 · 10 19 cm − 3 at the S/I interface ( x = 0) to 3 · 10 16 cm − 3 at a distance of 10 nm from the S/I interface. For V g = − 10 V the total induced charge is about half that of V g = − 19 V . This calculation is performed using classical electrostatics, and we have neglected quantum effects close to the semiconductor- insulator interface. It should be noted that the calculated charge distribution is not specific for organic semiconductors but is generally applicable to field-effect devices of undoped semiconductors in the linear operating regime, since it only depends on C i and ǫ semi .

24 The switch-on voltage and the field-effect mobility �� J �� J �� W δ � �� Figure 2.5: Numerical calculated distribution of charge carriers in the accumulation channel perpendicular to the S/I interface for V g = − 19 V and V g = − 10 V, calculated for ǫ semi = 3 and C i =15.5 nF/cm 2 . 2.2.3 Modeling the mobility variation In order to take into account the charge carrier dependent mobility we use again the hopping model described in the previous section. From Eq.2.4 an expression for the local mobility is derived: TDOS � � ( T DOS / T ) 4 sin   T T π µ l = σ (δ, T ) = σ 0 T DOS (δ N t ) T DOS / T − 1 (2.12)   ( 2 α) 3 B c q δ N t q Using the parameters from Table 2.1 the local mobility is calculated as a function of distance from the S/I interface and is plotted in Fig.2.6 for V g = − 19 V at room temperature for PTV and P3HT. For PTV the modeled local mobility varies from 2.1 · 10 − 3 cm 2 /Vs at the S/I interface to 8.4 · 10 − 4 cm 2 /Vs at a distance of 5 · 10 − 10 m from the S/I interface. For P3HT the local mobility varies from 6.6 · 10 − 4 cm 2 /Vs at the interface to 1.2 · 10 − 4 cm 2 /Vs at a distance of 5 · 10 − 10 m from the interface. The calculations show that in a polymeric FET even for moderate gate voltages, variations in the local mobility are considerable. Thus, due to the inhomogeneous charge carrier density in a disordered FET the local mobility demonstrates a strong variation in the active channel.

2.2 The field-effect mobility 25 � �� O � � � � � � � �� O � � � � � � � �� Figure 2.6: The local charge carrier mobility as function of position in the accumulation layer for (a) a PTV FET and (b) a P3HT FET at V g = − 19 V . The extracted field-effect mobility as determined from Eq.2.8 is given as the solid symbol in both figures.

26 The switch-on voltage and the field-effect mobility 2.2.4 Discussion of the field-effect mobility For the interpretation of the charge transport in disordered FETs it is crucial to understand how such a mobility distribution compares to the experimentally extracted field-effect mobility, using Eq.2.8. In Fig.2.6 the local mobility (Eq.2.12) and the field-effect mobility (Eq.2.8) are compared. With this modeling we find that the local mobility of the charge carriers at the S/I interface at V g = − 19 V is 15% and 9% larger then the extracted field- effect mobility for PTV (Fig.2.6a) and P3HT (Fig.2.6b), respectively. The reason for this relatively small difference is that (as shown in Figs.2.5 and 2.6) not only a major part of the charge carriers is located close to the interface, but also that these charge carriers have the highest mobility. As a result the field-effect current is mainly determined by the charge carriers at the interface. Consequently, the error due to the approximation used in Eq.2.8, namely that all charge carriers have the same mobility, is relatively small and amounts typically to 10-15%. 2.2.5 Conclusion In disordered organic field-effect transistors the dependence of the mobility with gate voltage is determined by the charge carrier dependence of the local mobility. Taking into account the distribution of the charge carrier density in the active channel perpendicular to the insulator the local mobility has been calculated as a function of position in the accumulation layer. It is demonstrated that for disordered organic FETs, in spite of the strong variations in the local mobility in the active channel, the experimentally determined field-effect mobility (Eq.2.8) is a reasonable estimate for the local mobility of the charge carriers at the semiconductor-insulator interface. 2.3 Unifying the charge transport in polymeric FETs with PLEDs 2.3.1 Introduction The experimental hole mobilities extracted from FETs can differ by three orders of magnitude from the hole mobilities extracted from polymeric light-emitting diodes (PLED), based on the same polymeric semiconductor. We resolve this apparent discrepancy by considering that the hole mobility depends strongly on the charge carrier density in disordered semiconducting polymers. This is demonstrated in this section by a system- atic study of the hole mobility as a function of temperature and applied bias in PLEDs and FETs based on poly(2-methoxy-5-(3’,7’-dimethyloctyloxy)- p -phenylene vinylene) (OC 1 C 10 -PPV) and in PLEDs and FETs based on amorphous poly(3-hexyl thiophene) (P3HT). In contrast to the variable range hopping description in an exponential density of states for FETs described in the previous section, the transport in polymeric light-emitting diodes (PLED) is typically described by hopping in a Gaussian density of states with long- range electronic correlations [16,19–21]. We unify the charge transport description in the two device geometries for both materials by demonstrating that in the energy range of

2.3 Unifying the charge transport in polymeric FETs with PLEDs 27 � � � � � � � � � � � �� Figure 2.7: Temperature dependent current density versus voltage characteristics of a P3HT hole-only diode, with a thickness of 95 nm and active area 10 mm 2 . The solid lines represents the description of the space-charge limited current model, incorporating the field dependence of the mobility (Eq.2.13). The inset shows the molecular structure of P3HT. interest the exponential density of states, which consistently describes the FET measurements at high carrier densities, is a good approximation for the Gaussian density of states, which consistently describes the PLED measurements at low carrier densities. 2.3.2 Experimental results Field-effect transistors were fabricated using P3HT and OC 1 C 10 -PPV as the semiconductor (For experimental details see section 2.1.2) and were modeled with Eq.2.6. The modeled parameters are given in Table 2.2. For P3HT and OC 1 C 10 -PPV we find a field- effect mobility at -19 V of respectively 6 × 10 − 4 cm 2 /Vs and 5 × 10 − 4 cm 2 /Vs. Also PLEDs of P3HT and OC 1 C 10 -PPV were fabricated and the current density, J , versus applied bias, V , is measured as a function of temperature. The J − V characteristics of OC 1 C 10 -PPV PLEDs can accurately be described by space-charge limited currents, with a field- and temperature dependent mobility [19–21]. This mobility is well described by a transport model based on hopping in a correlated Gaussian disordered system [16, 22]: � 3 � � � � 2 �� σ DOS � � 3 σ DOS 2 qaF µ h = µ ∞ exp + 0 . 78 − 2 (2.13) − , 5 k B T k B T σ DOS with µ ∞ the mobility in the limit T → ∞ , σ DOS the width of the Gaussian DOS, a the intersite spacing, and F the applied electric field. The J − V characteristics of a P3HT

28 The switch-on voltage and the field-effect mobility Table 2.2: Values obtained by modeling the transfer characteristics of OC 1 C 10 -PPV and P3HT FETs using Eq.2.6. The P3HT data is taken from Table 2.1. T DOS represents the width of the exponential DOS, σ 0 is the prefactor of the conductivity, α − 1 is the effective overlap parameter between localized states, and V so is the switch- on voltage as defined in section 2.1. Also given are the values obtained using Eq.2.13 to model the J − V characteristics of the hole- only diodes. The OC 1 C 10 -PPV diode data are taken from [19]. σ DOS is the width of the Gaussian DOS and a is an average transport site separation. σ 0 [10 6 S / m] α − 1 [ ˚ T DOS [ K ] A] V so [ V ] σ DOS [eV] a [ nm ] OC 1 C 10 PPV 540 31 1 . 4 0 . 5 0 . 112 1 . 4 P3HT 425 1 . 6 1 . 6 2 . 5 0 . 098 1 . 7 PLED can also accurately be modeled with space-charge limited currents in combination with Eq.2.13, as is demonstrated in Fig.2.7. The modeled parameters from Eq.2.13 are given in Table 2.2. We find at low electric fields hole mobility values for P3HT and OC 1 C 10 -PPV of respectively 3 × 10 − 5 cm 2 /Vs and 5 × 10 − 7 cm 2 /Vs. These values are upto three orders of magnitude lower as compared to the mobility values obtained from the FETs. 2.3.3 The mobility - charge density relation Experimentally, we find for both semiconductors large differences in mobility values when measured in different device geometries. Because we study amorphous polymer films, we argue that anisotropy in the transport parallel or perpendicular to the substrate surface can not be the origin of this mobility difference. Instead, we propose to investigate the mobility versus volume charge density relation for both type of devices, as it is well known that the charge carrier mobility in disordered organic semiconductors depends strongly on the charge carrier density. For the diode, the mobility at low electric fields and at room temperature can directly be obtained from the space-charge limited currents [19, 23]. The lowest charge carrier density, p l , in a diode, where the current is limited by space-charge, is found at the non- injecting contact and is given by [23]: p l = 3 � ǫ 0 ǫ semi V � (2.14) , ql 2 4 where q is the elementary charge, and l is the semiconductor layer thickness. For the FET, the experimental field-effect mobility is determined as a function of gate bias using Eq.2.8 and we calculate the volume charge carrier density, p = δ N t , at the semiconductor/insulator interface as a function of gate voltage, as outlined in section 2.2.

2.3 Unifying the charge transport in polymeric FETs with PLEDs 29 �� '26 �� '26 �� K µ �� Figure 2.8: Charge carrier mobility as a function of the hole density for P3HT and OC 1 C 10 -PPV determined in a hole-only diode (p < 10 17 cm − 3 ) and in a field-effect transistor (p > 10 17 cm − 3 ). The dashed lines are a guide to the eye. The hole mobility versus the volume charge density for P3HT and OC 1 C 10 -PPV are given in Fig.2.8, where the values at low charge density ( p < 10 17 cm − 3 ) are derived from the PLED data and the values at high charge density ( p > 10 17 cm − 3 ) are derived from FET data. From Fig.2.8 we see that the mobility starts to increase rapidly with charge carrier density when the charge density is larger than a certain minimum value. Fig.2.8 shows that when measured at the same high values of volume charge carrier density the field-effect mobility of OC 1 C 10 -PPV is nearly equal to the field-effect mobility of P3HT. Furthermore, the dependence of the field-effect mobility on charge carrier density is stronger for OC 1 C 10 -PPV, which is likely due to the presence of stronger energetic disorder in the OC 1 C 10 -PPV as compared to P3HT, as reflected by the larger value of T DOS for OC 1 C 10 -PPV. The strong energetic disorder explains the low mobility values reported for OC 1 C 10 -PPV based light-emitting diodes [19], which operate at relatively low carrier densities as compared to field-effect transistors. The large differences in mobility values obtained from diodes and FETs, based on a single semiconducting polymer, are direct results of the large difference in charge densities in these devices. 2.3.4 Unification of the LED and FET models To further emphasize this point we compare the modeled parameters obtained from the PLED and the FET current voltage characteristics. In Fig.2.9 the obtained Gaussian density of states for P3HT is plotted as a function of energy, in a semilogarithmic plot. For the total number of states per unit volume, N t , we have used a value of 3 · 10 20 cm − 3 , which

30 The switch-on voltage and the field-effect mobility � �� '26 �� Figure 2.9: The Gaussian DOS (dashed line), as obtained from the hole-only diode analysis and the exponential DOS (solid line), as obtained from the field-effect transistors as a function of energy for P3HT. The exponential DOS is found to be a good approximation of the Gaussian DOS. roughly corresponds to 1 / a 3 ( a =1.5 nm). Additionally, the exponential DOS of P3HT as obtained from the FET characteristics is shown, which is described by the characteristic temperature T DOS . For the charge carrier density range in which the P3HT FET operates, we find that the exponential distribution with T DOS =425 K is a good approximation of the Gaussian DOS with σ DOS =0.098 eV. This same analysis holds for the obtained OC 1 C 10 - PPV data [24]. This demonstrates that the two theoretical descriptions are consistent. The mobility description at high carrier densities, which employs an exponential DOS, is an accurate representation of the mobility description at low carrier densities, which uses a Gaussian DOS. 2.3.5 Conclusion In conclusion, the large mobility differences reported for conjugated polymers used in PLEDs and FETs have been shown to originate from the strong dependence of the mobility on the charge carrier density. The exponential density of states, which consistently describes the field-effect measurements, is shown to be a good approximation of the tail states of the Gaussian density of states used in the description of PLEDs.

References [1] H. Sirringhaus, P.J. Brown, R.H. Friend, M.M. Nielsen, K. Bechgaard, B.M.W. Langeveld-Voss, A.J.H. Spiering, R.A.J. Janssen, E.W. Meijer, P.T. Herwig and D.M. de Leeuw, Nature (London) 401 , 685 (1999). [2] S.F. Nelson, Y.-Y. Lin, D.J. Gundlach and T.N. Jackson, Appl. Phys. Lett. 72 , 1854 (1998). [3] M. Pope and C.E. Swenberg, Electronic Processes in Organic Crystals and Polymers , Oxford University Press (1999). [4] S.M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981) [5] C.J. Drury, C.M.J. Mutsaers, C.M. Hart, M. Matters and D.M. de Leeuw, Appl. Phys. Lett. 73 , 108, (1998). [6] G.H. Gelinck, T.C.T. Geuns and D.M. de Leeuw, Appl. Phys. Lett. 77 , 1487 (2000). [7] A.R. Brown, C.P. Jarrett, D.M. de Leeuw and M. Matters, Synth. Met. 88 , 37 (1997). [8] M.C.J.M. Vissenberg and M. Matters, Phys. Rev. B, 57 , 12964 (1998). [9] G. Horowitz, R. Hajlaoui and P. Delannoy, J. Phys. III, 5 , 355 (1995). [10] G. Horowitz, M.E. Hajlaoui and R. Hajlaoui, J. Appl. Phys. 87 , 4456 (2000). [11] G. Horowitz, R. Hajlaoui, H. Bouchriha, R. Bourguiga and M. Hajlaoui, Adv. Mater. 10 , 923 (1998). [12] M. Shur, M. Hack and J.G. Shaw, J. Appl. Phys. 66 , 3371 (1989). [13] N. Lustig, J. Kanicki, R. Wisnieff and J. Griffith, MRS Symp. Proc. 118 , 267 (1988). [14] B-S. Bae, D-H. Cho, J-H. Lee and C. Lee, MRS Symp. Proc. 149 , 271 (1989). [15] D. Emin, private communication. [16] H. B¨ assler, Phys. Stat. Sol. B 175 , 15 (1993). [17] G.E. Pike and C.H. Seager, Phys. Rev. B 10 , 1421 (1974).

32 References [18] E.J. Meijer, M. Matters, P.T. Herwig, D.M. de Leeuw and T.M. Klapwijk, Appl. Phys. Lett. 76 , 3433 (2000). [19] P.W.M. Blom, M.J.M. de Jong and J.J.M. Vleggaar, Appl. Phys. Lett. 68 , 3308 (1996). [20] P.W.M. Blom, M.J.M. de Jong and M.G. van Munster, Phys. Rev. B 55 , R656 (1997). [21] H. C. F. Martens, P. W. M. Blom and H. F. M. Schoo, Phys. Rev. B 61 , 7489 (2000). [22] S.V. Novikov, D.H. Dunlap, V.M. Kenkre, P.E. Parris and A.V. Vannikov, Phys. Rev. Lett. 81 , 4472 (1998). [23] M.A. Lampert and P. Mark, Current Injection in Solids (Academic, New York, 1970). [24] C. Tanase, E.J. Meijer, P.W.M. Blom and D.M. de Leeuw, submitted.

Chapter 3 The Meyer-Neldel Rule in organic field-effect transistors Abstract We have measured and analyzed the temperature and gate voltage dependencies of the field-effect mobility in organic field-effect transistors. We find that the mobility prefactor increases exponentially with the activation energy in agreement with the Meyer-Neldel rule. This behavior is demonstrated in the mobility data of solution-processed pentacene and poly(2,5-thienylenevinylene) and in mobility data reported in literature. Surprisingly, the characteristic Meyer-Neldel energy for all analyzed materials is close to 40 meV. Possible implications for the charge transport mechanism in these materials are discussed.

34 The Meyer-Neldel rule 3.1 Introduction The temperature and gate voltage dependence of the charge carrier mobility, µ FE , of organic-based field-effect transistors (FET) have been the subject of research for some years now [1–7]. However, the charge transport mechanisms in these organic devices are still not fully understood. Reports vary from thermally activated behavior [2, 3, 5] to temperature independent transport [4]. Moreover, large variations in the experimental data on even nominally the same samples make it difficult to obtain an accurate picture of the transport mechanism [4, 6]. Band-like transport in extended states has been reported in the past for high-purity single crystals [1]. It should be noted that in contrast to this highly orderded system the carrier transport in disordered or partially ordered systems is governed by localized states, which results in a different transport mechanism. The temperature and gate voltage dependencies of µ FE in organic FETs have been described in terms of multiple trapping [3], hopping [7] and Coulomb blockade [5]. A common factor in all these models is the gate voltage dependence of the activation energy, E a . Whenever a property, say X , has a thermally activated behavior, � − E a � X = X 0 exp , (3.1) k B T and E a is a variable, it is empirically found [8] that the prefactor, X 0 , increases exponentially with the activation energy: � E a � X 0 = X 00 exp . (3.2) E MN This relation between the prefactor X 0 and E a is known as the Meyer-Neldel rule (MNR) [8]. Here k B is the Boltzman constant, T the absolute temperature, X 00 is a constant prefactor and E MN is the so-called Meyer-Neldel energy. A combination of Eqs. 3.1 and 3.2 gives the general form: � 1 � �� 1 X = X 00 exp − E a k B T − , (3.3) E MN which implies a single crossing point for different activation energies at an isokinetic temperature determined by the Meyer-Neldel energy: T 0 = E MN / k B . The MNR has been observed in a wide variety of physical, chemical and biological processes [9]. However, the microscopic origin of the MNR and therefore, the physical meaning of E MN , are still a topic of discussion in literature [9]. In this work we demonstrate that the MNR applies to the field-effect mobility data of solution-processed pentacene and poly(2,5-thienylene vinylene) (PTV) FETs, as well as to mobility data reported in literature. We discuss the relation between the transport mechanism in organic FETs and the possible origin of the MNR. 3.2 Experimental In the experiments we used heavily doped Si wafers as the gate electrode, with a 200 nm thick layer of thermally oxidized SiO 2 as the gate-insulating layer. Using conventional lithography, gold source and drain contacts were defined with a channel width

3.3 Demonstration of the MNR 35 � �� V � G �� J �� Figure 3.1: I ds vs. V g for pentacene (V ds =-2 V (open squares) and -20 V (filled squares)) and PTV (V ds =-2 V (open circles) and -40 V (filled circles)) at 290 K in vacuum (10 − 7 mbar). V g was swept from +2 to -30 V and back to +2 V. W =2 cm and length L =10 µ m. The SiO 2 layer was treated with the primer hexamethyldisilazane (HMDS) to make the surface hydrophobic. The films of both pentacene and PTV were deposited using a precursor-route process [2,10,11]. The obtained PTV films are truly amorphous [12]. The pentacene films are polycrystalline with a planar spacing of 14.3 ± 0.1 ˚ A [12], which corresponds to the bulk triclinic phase of pentacene [13,14]. The samples were measured under high vacuum (10 − 7 mbar) in an Oxford optistat CF-V flow cryostat, using a Hewlett-Packard 4156A semiconductor parameter analyzer. The source-drain current, I ds , is plotted as a function of gate voltage, V g , in Fig. 3.1 for both the pentacene and PTV transistors at 290 K. We do not observe any hysteresis in the measurements and the curves are stable in time (in vacuum). 3.3 Demonstration of the MNR The temperature dependence of µ FE is evaluated in the linear regime [2] of the I ds − V ds characteristics (at a low source-drain voltage V ds = − 2 V ). The applied gate field in this regime is much larger than the in-plane drift field, which results in an approximately uniform density of charge carriers in the active channel. We calculate µ FE [2,3] from L ∂ I ds µ FE = , (3.4) WC i V ds ∂ V g where C i is the capacitance of the insulator per unit area. In Fig. 3.2 we plot µ FE vs. T − 1 [15] for pentacene.

36 The Meyer-Neldel rule � � �� D � �� J �� ( �� ) �� J �� J �� J �� J �� J �� Figure 3.2: Temperature dependence of the field-effect mobility of pentacene. The inset shows the dependence of the activation energy on the gate voltage. � �� D � �� J �� J �� ( �� J �� ) �� J �� J �� J �� J �� Figure 3.3: Temperature dependence of the field-effect mobility of PTV. The inset shows the dependence of the activation energy on the gate voltage.

3.4 Implications for the charge transport 37 � � �� D �� Figure 3.4: extrapolated prefactor, µ 0 , as a function of E a for pentacene(filled squares) and PTV(open circles). We can fit the data [22] in Figs. 3.2 and 3.3 with � − E a � µ FE = µ 0 exp (3.5) k B T and upon extrapolation to high T we clearly find a common crossing point of the curves. Plotting the prefactor, µ 0 , logarithmically as a function of E a for both pentacene and PTV (see Fig. 3.4), results in a straight line. This demonstrates that the experimental results are in agreement with the MNR. From Fig. 3.4 we find E MN ≈ 38 meV and E MN ≈ 42 meV for pentacene and PTV respectively. When this analysis is also used on the gate voltage dependent mobility data reported in literature, we find that the MNR also holds for the mobility data on dihexyl-sexithiophene measured by Horowitz et al. [3] ( E MN ≈ 43 meV) and for the previous studies of pentacene ( E MN ≈ 34 meV) and PTV ( E MN ≈ 35 meV) [2]. Furthermore, for C 60 FETs it was found that E MN ≈ 36 meV [23,24]. Surprisingly, for all these materials the value of E MN is close to 40 meV. 3.4 Implications for the charge transport Now we will discuss the relation between the transport mechanism and the origin of the MNR. In inorganic amorphous semiconductors the MNR has been attributed to a displacement of the Fermi level in an exponential density of states (DOS) [16, 17, 25, 26]. A consequence of this interpretation is, that in order to calculate a physically reasonable value for the prefactor (of conductivity or mobility) one has to assume physically unrea- sonable values for the attempt frequency for hopping, which can vary between 10 3 and

38 The Meyer-Neldel rule 10 28 s − 1 [27–31]. Furthermore, Yelon et al. [29, 30] have argued that the MNR can not be solely due to an exponential DOS, as the MNR is much more generally applicable. They attribute the difficulty of interpreting the prefactor values in the DOS model to the assumption that the excitation process involves only one phonon [32,33]. If the activation energy is large compared to the typical phonon energies available, multiple excitations are required for a hopping event to occur. They show that a multiphonon process can explain the MNR and that the large spread in values of the prefactor can be accounted for with reasonable values for the attempt frequencies [29,30]. In organic FETs, the interpretation of the MNR in terms of a Fermi level shift would be consistent with the hopping [7] and multiple trapping models [3]. In that case E MN is equal to the width of the DOS [27] (the T DOS parameter from Chapter 2) and no physical meaning is attributed to the prefactor µ 0 . We argue that the ubiquitous value of E MN is more likely due to a characteristic transport mechanism in organic materials rather than to one general DOS. Whether the interpretation given by Yelon et al . [29, 30, 34] is applicable to our results on organic FETs hinges on the question whether it is justified to describe the hopping of a charge carrier from one conjugated segment (or molecule) to the next, as a multiphonon process. We note, that if the charge carrier is a localized polaron [35,36], Emin argued that the transport should be a multiphonon process, even if the phonon energies are comparable to E a [37,38]. This interpretation would imply that the observed MNR is a direct consequence of the polaronic nature of the charge carriers. 3.5 Conclusions In summary, we have shown the validity of the MNR in organic-based FETs. The ubiquitous value of E MN ≈ 40 meV is an indication of a common origin of the MNR in organic FETs. We have argued that the MNR is directly linked to the charge transport mechanism and possibly even to polaronic carriers.

References [1] M. Pope and C. E. Swenberg, “Electronic processes in organic crystals”, Oxford Uni- versity Press, New York, (1982). [2] A. R. Brown, C. P. Jarrett, D. M. de Leeuw and M. Matters, Synth. Metals 88 , 37 (1997). [3] G. Horowitz, R. Hajlaoui and P. Delannoy, J. Phys III France 5 , 355 (1995). [4] S. F. Nelson, Y.-Y. Lin, D. J. Gundlach and T. N. Jackson, Appl. Phys. Lett. 72 , 1854 (1998). [5] W. A. Schoonveld, J. Wildeman, D. Fichou, P. A. Bobbert, B. J. van Wees and T. M. Klapwijk, to be published in Nature. [6] L. Torsi, A. Dodabalapur, L. J. Rothberg, A. W. P. Fung and H. E. Katz, Phys. Rev. B 57 , 2271 (1998). [7] M. C. J. M. Vissenberg and M. Matters, Phys. Rev. B 57 , 12964 (1998). [8] W. Meyer and H. Neldel, Z. Tech. Phys. 18 , 588 (1937). [9] For examples see references in [29,30] [10] A. R. Brown, A. Pomp, D. M. de Leeuw, D. B. M. Klaassen, E. E. Havinga, P. T. Herwig, K. M¨ ullen, J. Appl. Phys. 79 , 2136 (1996). [11] P. T. Herwig and K. M¨ ullen, Adv. Mater. 11 , 480 (1999). [12] A. R. Schlatmann, E. J. Meijer and D. M. de Leeuw, unpublished X-ray diffraction results. [13] R. B. Campbell and J. M. Robertson, Acta Cryst. 14 , 705 (1961). [14] I. P. M. Bouchoms, W. A. Schoonveld, J. Vrijmoeth and T. M. Klapwijk, Synth. Met. 104 , 177 (1999). [15] We note that the MNR in inorganic FETs is sometimes evaluated by analyzing the sheet conductance of the channel [16,17]. However, the extraction of E MN , using the sheet conductance, may be inaccurate due to a decrease of the effective accumulation channel thickness with increasing V g [18, 19]. We therefore look at µ FE instead, as suggested by Fortunato and co-workers [20,21].

40 References [16] R. Schumacher, P. Thomas, K. Weber and W. Fuhs, Sol. State. Comm. 62 , 15 (1987). [17] R. Schumacher, P. Thomas, K. Weber, W. Fuhs, F. Djamdji, P. G. Le Comber and R. E. I. Schropp, Phil. Mag. B 58 , 389 (1988). [18] M. Yamaguchi and H. Fritsche, J. Appl. Phys. 56 , 2303 (1984). [19] A. P. Gn¨ adinger and H. E. Talley, Proc. IEEE, 916 (1970). [20] G. Fortunato, L. Mariucci and C. Reita in “Amorphous and Microcrystalline Semi- conductor Devices” Volume 2 , 355, Editor: J. Kanicki, Artech House, Norwood (1992). [21] G. Fortunato, D. B. Meakin, P. Migliorato and P. G. Le Comber, Phil. Mag. B, 57 , 573 (1988). [22] We note that the mobility curves of the PTV show a deviation from simple Arrhenius behavior at low temperatures. This behavior has thus far been modelled with a specific distribution of traps [3] and hopping in an exponential density of states [7]. [23] J. Paloheimo and H. Isotalo, Synth. Met. 55 , 3185 (1993). [24] J. C. Wang and Y. F. Chen, Appl. Phys. Let. 73 , 948 (1998). [25] H. Overhof, J. Non-Cryst. Sol. 97/98 , 539 (1987). [26] M. Ortuno and M. Pollak, Phil. Mag. B 47 , L93 (1983). [27] P. Irsigler, D. Wagner and D.J. Dunstan, J. Phys. C 16 , 6605 (1983). [28] B. Movaghar, J. Phys. Coll. C4 , 73 (1981). [29] A. Yelon and B. Movaghar, Phys. Rev. Lett. 65 , 618 (1990). [30] A. Yelon, B. Movaghar and H. M. Branz, Phys. Rev. B 46 , 12244 (1992). [31] A. M. Szpilka and P. Vis˘ cor, Phil. Mag. B 45 , 485 (1982). [32] A. Miller and E. Abrahams, Phys. Rev. 120 , 745 (1960). [33] N. F. Mott and E. A. Davis “Electronic Processes in Non-Crystalline Materials”, second edition, Clarendon Press Oxford (1979). [34] H. M. Branz, A. Yelon and B. Movaghar, MRS Symp. Proc. 336 , 159 (1994). [35] T. Holstein, Ann. Phys. 8 , 325 (1959). [36] A. J. Heeger, S. Kivelson, J. R. Schrieffer and W.-P. Su, Rev. Mod. Phys. 60 , 781 (1988). [37] D. Emin, Phys. Rev. Lett. 32 , 303 (1974). [38] D. Emin, Adv. Phys. 24 , 305 (1975).

Chapter 4 The isokinetic temperature in disordered organic semiconductors Abstract We have investigated the field dependence of the in-plane conductivity in poly(2,5-thienylene vinylene) and poly(3-hexyl thiophene) thin films. The conductivity is found to have a square root dependence on the lateral electric field. The values for the characteristic temperature, obtained from the empirical field-dependent mobility relation are very similar to the values found for the isokinetic temperature in Meyer-Neldel experiments on poly(2,5- thienylene vinylene) and poly(3-hexyl thiophene) field-effect transistors. The possible relation between the field-dependent mobility and the Meyer-Neldel rule is discussed in the context of charge transport in disordered organic semiconductors.

42 The isokinetic temperature 4.1 Introduction Due to possible industrial applications, opto-electronic devices based on disordered organic semiconducting layers are receiving much attention [1–4]. The disorder in the organic films dominates the charge transport. Typically, low mobilities with a thermally activated behavior are observed. Transport is mostly described by hopping. Several interesting physical features are associated with transport through disordered materials, such as the Meyer-Neldel rule (MNR) [5], which we demonstrated in the previous chapter. This rule states that the prefactor of the thermally activated mobility increases exponentially with the activation energy. For a number of materials we found the characteristic isokinetic temperature associated with the MNR to be in the range of 440-510 K [6]. At high electric fields in disordered systems the mobility becomes field dependent, which can be described by the empirical relation [7,8]: � − � √ � µ = µ 0 exp k B T + γ F (4.1) with, � 1 1 � (4.2) γ = B k B T − , k B T 0 where k B is Boltzmann’s constant, T the absolute temperature, F the applied electric field and � the low field activation energy. The field dependence as given in Eq.4.1 is observed in a wide range of disordered materials, with typical values for the parameters of � =0.5 eV, T 0 ∼ 500-600 K and B =3 · 10 − 5 eV(m/V) 1 / 2 [9–11]. It has been suggested that the Meyer-Neldel rule and the field dependent mobility are related effects [11,12]. To investigate this hypothesis we have studied both effects in two organic semiconductors, poly(2,5-thienylene vinylene) (PTV), and poly(3-hexyl thiophene) (P3HT). 4.2 Results The in-plane conductivity, σ , was measured using interdigitated gold contacts on glass and the MNR using regular MISFET structures, as described in Chapter 2. X-ray experiments on the PTV films did not yield reflections [6], indicating that the PTV films are amorphous. The P3HT films are nanocrystalline. In Figs.4.1 and 4.2 σ is plotted as a function of F 1 / 2 for various temperatures. We do not observe space-charge limited currents in the range of electric fields shown in Figs.4.1 and 4.2. At low fields ohmic behavior is observed in Fig.4.2. Figs.4.3 and 4.2 show the temperature dependence of σ for different electric fields. The data are well described by Eq.4.1 [13] and the values of � , B , and T 0 fitted for both PTV and P3HT are given in Table.4.1. The obtained values are in agreement with data published for other materials [9–11]. Fig.3.3 shows the field-effect mobility for a PTV transistor as a function of T − 1 for different gate voltages. The same is plotted for P3HT in Fig.4.5. The curves are fitted to Arrhenius behavior with a gate voltage dependent prefactor and activation energy, as was outlined in the previous chapter.

4.2 Results 43 � �� 6 Q �� Figure 4.1: In-plane conductivity of PTV as a function of F 1 / 2 for various temperatures. L=2 µ m, W=2 cm. The lines are fits to Eq.4.1. The inset shows the structure formula of PTV. � �� & � + �� 6 �� Q �� Figure 4.2: Measured in-plane conductivity of P3HT as a function of F 1 / 2 for various temperatures. L=5 µ m, W= 50cm. The lines are fits to Eq.4.1. The inset shows the structure formula of P3HT.

44 The isokinetic temperature � �� Figure 4.3: In-plane conductivity of PTV as a function of T − 1 for various electric fields. The lines are Arrhenius fits. The intersection of the fitted curves at high temperatures demonstrates the MNR [5,6] with a characteristic isokinetic temperature of 4.9 · 10 2 K for PTV and 4.6 · 10 2 K for P3HT. Interestingly, the characteristic temperature of the MNR in PTV and P3HT is close to these values. This indicates that the origin of the T 0 in the field dependence (Figs.4.3 and Fig.4.4) could be the same as the isokinetic temperature observed in the Meyer-Neldel rule (Fig.3.3 and Fig.4.5) [11,12]. Table 4.1: Values obtained by fitting the field dependence of the conductivity σ with Eq.4.1 for PTV and P3HT. � is the low field activation energy, B is the field dependent coefficient as given in Eq. 4.2, T 0 ,σ is the isokinetic temperature determined from the field-dependence data of Figs.4.3 and 4.4, and T 0 , FE is the isokinetic temperature determined from the field-effect experiments of Figs.3.3 and 4.5. B [eV ( m / V ) 1 / 2 ] � [eV] T 0 ,σ [K] T 0 , FE [K] 2 . 3 · 10 − 5 5 . 2 · 10 2 4 . 9 · 10 2 PTV 0 . 46 4 . 7 · 10 − 5 5 . 3 · 10 2 4 . 6 . · 10 2 P3HT 0 . 40

4.2 Results 45 � �� Figure 4.4: In-plane conductivity of P3HT as a function of T − 1 for various electric fields. The lines are Arrhenius fits. � �� @ �� 9 H > �� D ( �� 9 J �>9@ �� ( �� ) � �� Figure 4.5: Field effect mobility of a P3HT transistor as a function of T − 1 for different gate voltages. The lines are Arrhenius fits.The inset shows the activation energy as a function of the gate voltage.

46 The isokinetic temperature 4.3 Discussion of the isokinetic temperature An investigation into a possible relation between the isokinetic temperature observed in the Meyer-Neldel experiments (see the previous chapter) and in the field-dependence of the mobility, requires a careful examination of the empirical relations from which they originate, Eq.3.3 and Eq.4.1, and the underlying physical mechanisms. 4.3.1 The field-dependent mobility Although Eq.4.1 gives a good description of the mobility as a function of temperature and electric field, it still lacks theoretical justification. Other approaches to understand the √ ln (µ) ∼ F relation have been proposed. B¨ assler argued that the observed field dependence of the mobility is related to the intrinsic charge transport in disordered materials [14]. The disorder model developed by B¨ assler and coworkers [14, 15] is based on a Gaussian distribution of localized states, and considers that hopping between sites is subject to both energetic and spatial disorder. Monte Carlo simulations of hopping transport in a Gaussian distribution of localized states has suggested that the field dependence of the mobility is a natural consequence of the presence of disorder [14]. There is general agreement that the field-dependency observed at fields as low as 1 MV/m is related to the presence of correlations in site-energies in the disordered material, and can be described by [16]: � 3 � � � �� σ DOS � � 2 � 3 σ DOS qaF 2 µ = µ ∞ exp − + 0 . 78 − 2 , (4.3) 5 k B T k B T σ DOS with µ ∞ the mobility in the limit T → ∞ , σ DOS the width of the Gaussian DOS, and a the intersite spacing. Various physical mechanisms for the origin of these correlations in the Gaussian model have been suggested. Yu et al. considered molecular geometry fluctuations such as phenylene-ring torsion out of the plane of the molecule, which will influence the steric energy of neighbouring molecules, and results in long-range energy correlations between molecular sites [17]. Rakhmanova and Conwell considered structural disorder, where the morphology of the polymer is crucial, and the long-range correlations between sites arise due to local variations in order. Sites in ordered regions are suggested to have lower site energies than those in amorphous regions [18], which again will result in long-range energy correlations. Similar modeling based on the argument of structural disorder was given by Vissenberg [19]. In principle any model of Gaussian disorder that incorporates long-range energy correlations between sites will give rise to a √ F dependence of ln (µ) . In addition to the different physical interpretations of the field-dependent mobility, the Gaussian disorder model and the empirical relation of Eq.4.1 also predict that the temperature dependence of the mobility should be distinct from each other. The zero field mobility is expected to vary as µ = µ 0 exp ( − �/ k B T ) from Eq.4.1, whereas it should follow a much stronger variation as µ = µ 0 exp ( − [2 σ DOS /( 3 k B T ) ] 2 ) from Eq.4.3. An evaluation of the µ F = 0 as a function of temperature should therefore allow the applica- bility of the two models to be tested. Unfortunately, in polymer systems typically only a

4.4 Conclusions 47 small temperature range can be scanned experimentally, and therefore a clear distinction between ln (µ) ∼ T − 1 and ln (µ) ∼ T − 2 cannot be made. 4.3.2 The Meyer-Neldel rule As stated in the previous chapter, the Meyer-Neldel rule is also an empirical relation, the physical justification of which is still heavily under debate. The discussion of the origin of the MNR has focussed on multi-phonon hopping rates. Entropy change associated with these hopping rates would lead to the MNR [20,21](see the previous chapter). 4.3.3 Comparison of the MNR with the field-dependent mobility It is instructive to compare the two physical pictures that emerge from the discussion around the isokinetic temperature. In the first picture, it is the environment in which the charge carriers move that is important: a manifold of localized states in a Gaussian energy distribution with long- range correlations [16]. The nature of the charge carriers themselves, or the specifics of the charge transfer from one localized state to the next, is taken as simple as possible. Mostly Miller-Abrahams hopping rates [22] are considered, a single-phonon assisted transfer process, for holes and electrons. In the second picture, the nature of the carriers and the charge transfer description is of importance and the long-range environment is not: polaronic carriers, quasi particles that consist of charge accompanied by a lattice deformation, that require multiple phonons from their surroundings to move from a localized site to the next [21,23]. This requires a much more complex mathematical treatment of the site to site hopping process. 4.4 Conclusions The fact that polarons are the charge carrying species in these polymeric systems and that disorder is tantamount for the description of charge transport, would suggest that a combination of the two interpretations arising from the discussion of the isokinetic temperature would give a more complete description of charge transport. This then results in a charge transport picture of polaronic charge carriers, that move with a multi-phonon transfer rate between localized states, which have a Gaussian energy distribution and long- range energy correlations.

References [1] C.J. Drury, C.M.J. Mutsaers, C.M. Hart, M. Matters and D.M. de Leeuw, Appl. Phys. Lett. 73 , 108 (1998). [2] A.R. Brown, C.P. Jarrett, D.M. de Leeuw and M. Matters, Synth. Met. 88 , 37 (1998). [3] H. Sirringhaus, P.J. Brown, R.H. Friend, M. Nielsen, K. Bechgaard, B. Langeveld- Voss, A. Spiering, R.A.J. Janssen, E.W. Meijer, P.T. Herwig and D.M. de Leeuw, Nature 401 , 685 (1999). [4] Z. Bao, A. Dodabalapur and A.J. Lovinger, Appl. Phys. Lett. 69 , 4108 (1998). [5] W. Meyer and H. Neldel, Z. Techn. Phys. (Leipzig), 18 , 588 (1937). [6] E.J. Meijer, M. Matters, P.T. Herwig, D.M. de Leeuw and T.M. Klapwijk, Appl. Phys. Lett. 76 , 3433 (2000). [7] D.M. Pai, J. Chem. Phys. 52 , 2285 (1970). [8] W.D. Gill, J. Appl. Phys. 43 , 5033 (1972). [9] P.W.M. Blom and M.C.J.M. Vissenberg, Mater. Scie and Engin. R27 , 53 (2000) and references therein. [10] P.W.M. Blom, M.J.M. de Jong and M.G. van Munster, Phys. Rev. B 55 , R656 (1997). [11] D.B.A. Rep, B.-H. Huisman, E.J. Meijer, P. Prins and T.M. Klapwijk, Mat. Res. Soc. Symp. Proc. 660 (2001). [12] A. Peled and L. Schein, Phys. Scripta 44 , 304 (1991). [13] We assume that the field and temperature dependence of σ are due to the mobility and not the charge density. [14] H. B¨ assler, Phys. Stat. Sol. B 175 , 15 (1993). [15] M. Abkowitz, H. B¨ assler and M. Stolka, Phil. Mag. B 63 , 201 (1991). [16] S.V. Novikov, D.H. Dunlap, V. Kenkre, P. Parris and A. Vannikov, Phys. Rev. Lett. 81 , 4472 (1998).

50 References [17] Z.G. Yu, D.L. Smith, A. Saxena, R.L. Martin and A.R. Bishop, Phys. Rev. Lett. 84 , 721 (2000). [18] S. V. Rakhmanova and E.M. Conwell, Appl. Phys. Lett. 76 , 3822 (2000). [19] P.W.M. Blom and M.C.J.M. Vissenberg, Mater. Scie. Eng. R27 , 53 (2000). [20] A. Yelon and B. Movaghar, Phys. Rev. Lett. 65 , 618 (1990). [21] D. Emin, Phys. Rev. B 61 , 14543 (2000). [22] A. Miller and E. Abrahams, Phys. Rev. 120 , 745 (1960). [23] T. Holstein, Ann. Phys. 8 , 325 (1959).

Chapter 5 Scaling behavior and parasitic series resistance in disordered organic field-effect transistors Abstract The scaling behavior of the transfer characteristics of solution-processed disordered organic field-effect transistors with channel length is investigated. This is done for a variety of organic semiconductors in combination with gold injecting electrodes. From the channel length dependence of the transistor resistance in the conducting ON-state we determine the field-effect mobility and the parasitic series resistance. The extracted parasitic resistance, typically in the M � -range, depends on the applied gate voltage, and we find experimentally that the parasitic resistance decreases with increasing field-effect mobility.

52 Scaling behavior and parasitic series resistance 5.1 Introduction The interest in organic field-effect transistors has grown rapidly due to envisaged applications such as integrated circuits [1] and active-matrix displays [2]. Research has mainly been focused on improving the field-effect mobility, µ FE [3–7], which is known to depend on material purity and processing conditions. For transistors based on solution- processed organic semiconductors µ FE typically ranges between 10 − 4 and 10 − 1 cm 2 /Vs. The switching speed of organic integrated circuits can be estimated from the performance of the individual transistors and is roughly proportional to ∼ µ FE / L 2 [8], where L is the channel length of the transistor. To reach higher switching speeds, the search for higher mobility materials is therefore important, but it is also of great interest to downsize the transistor geometries. In this work the scaling behavior of the transfer characteristics with transistor channel length is investigated for a variety of solution-processable organic field-effect transistors. 5.2 Experimental In the experiments we use heavily doped Si wafers as the gate electrode, with a 200-nm- thick layer of thermally oxidized SiO 2 as the gate-insulating layer. Using conventional lithography, gold source and drain contacts of 100 nm thick are defined with channel widths ranging from 1 mm to 1 cm and channel lengths between 0.75 and 40 µ m. The structures typically have an underetch of 0.5 µ m, which we neglect in the following analysis. A 10 nm layer of titanium acts as an adhesion layer for the gold on the SiO 2 . The SiO 2 layer is treated with the primer hexamethyldisilazane to make the surface hydrophobic. No special care is taken to clean the gold surface prior to deposition of the semiconductor. Poly(2,5-thienylene vinylene) (PTV) films as semiconductor layer are deposited using a precursor-route process [8]. We systematically varied the processing conditions for the conversion from precursor to PTV and we determined the average de- gree of conversion using the method described by Fuchigami et al. [9]. This enabled us to systematically study PTV transistors at various degrees of conversion ranging from 60% to 100%, and consequently over a range of field-effect mobilities, between 10 − 4 and 10 − 3 cm 2 /Vs. Poly(3-hexyl thiophene) (P3HT) is spincoated from a 1 wt% chloroform solution [7]. Films of poly([2-methoxy-5-(3’,7’-dimethyloctyloxy)]- p -phenylene vinylene) (OC 1 C 10 -PPV) and poly([2,5-di-(3’,7’-dimethyloctyloxy)]- p -phenylene vinylene) (OC 10 C 10 -PPV), are spun from a 0.5 wt% toluene solution. Pentacene thin films are deposited using a precursor-route process [4, 8]. The measurements are performed on freshly prepared samples in order to minimize external doping and degradation effects [10]. The PTV, OC 1 C 10 -PPV, OC 10 C 10 -PPV and pentacene samples are measured in air, whereas the P3HT samples are measured in vacuum and dark after a thermal dedope procedure [11]. The electrical characteristics are recorded using an HP4155B semiconductor parameter analyzer.

5.3 Scaling behavior 53 5.3 Scaling behavior Typical source drain current, I ds , versus gate voltage, V g , characteristics for solu-tion- processed PTV and P3HT are shown in Fig.5.1, for different channel lengths, where the channel width, W , is kept constant. The position of the switch-on voltage, V so (see Chap- ter 2) [12], which determines the onset of the field-effect and is defined as the flat-band condition of the transistor, does not vary much between the transistors with different channel length. At low source-drain voltage, V ds = − 2 V , where the in plane electric field is much smaller than the applied gate field (gradual channel approximation) [8], the field- effect mobility is evaluated using: L ∂ I ds � � (5.1) µ FE V g = , WC i V ds ∂ V g where C i is the capacitance of the insulating layer per unit area. The field-effect mobilities for both PTV and P3HT are found to depend on the channel length of the transistor, which can be seen from the insets of Fig.5.1. This means that the extracted µ FE is a device parameter rather than a material parameter of the organic semiconductor. By comparing the output characteristics multiplied by the channel length, i.e. at constant source-drain field, for short- and long channel transistors we clearly see an effective current decrease for shorter channel lengths, which is demonstrated for P3HT in Fig.5.2. Furthermore, at low drain voltages the output characteristics of the long transistor show ohmic behavior [13], whereas for the short channel transistors, at low drain voltages, superlinear output characteristics are observed. Because µ FE is decreasing with reduced L , the reduction of the channel length will not result in the expected increase of the switching speed in circuits. From amorphous silicon thin-film transistors it is well known that the presence of source and drain parasitic resistances, R s and R d respectively, can give rise to an apparent µ FE that decreases with decreasing channel length [14,15]. This is due to the fact that in shorter channels, a relatively larger fraction of the applied source-drain voltage drops over the parasitic resistance, as compared with the long channel transistors. To be able to evaluate the performance of the organic semiconductor, a correction for the parasitic resistance, R p = R s + R d , is required [16,17]. A theoretical approach to this end was presented by Horowitz et al. [18]. Experimentally, it has been demonstrated that the influence of R p can be reduced by modifying the interface between the current injecting contacts and the organic semiconductor [19, 20]. Kelvin probe force microscopy has been employed for experimental evaluation of R p [13]. Here, we investigate the scaling behavior of the transistor current [15,21,22] to estimate R p . 5.4 Parasitic series resistance determination We plot the total device-resistance, R ON = V ds / I ds , as a function of the nominal channel length, L , for different gate voltages in Fig.5.3. In the linear operating regime of the transistor the channel resistance varies linearly with the channel length. The parasitic resistance, R p = R s + R d , at the source and drain contacts is assumed to be independent

54 Scaling behavior and parasitic series resistance � �� / �� µ P �� µ P �� µ P �� µ P �� µ P �� µ P V G �� µ P �� µ P �� µ P �� µ P �� µ )( �FRUUHFWHG�IRU�5 S �� ( ) �� µ �� J �� J �� / �� µ P �� µ P �� µ P �� µ P �� µ P �� µ P V � �� G �� µ P � � �� µ P � � � �� ( µ )( �FRUUHFWHG�IRU�5 S ) �� µ �� J �� J �� Figure 5.1: I ds vs V g at V ds = − 2 V , for different channel lengths for (a) PTV, converted at 80 o C under 150 mbar of HCl partial pressure [8]. The characteristics are measured in air at room temperature, W=1 mm. (b) P3HT, W=1 mm, in vacuum at room temperature after a thermal dedoping treatment [11]. The insets show the corresponding µ FE - values derived from the gatesweeps by using Eq.5.1.

5.4 Parasitic series resistance determination 55 � � �� J �� J �� V G � � � J �� J �� J �� GV �� Figure 5.2: The normalized output characteristics for two P3HT transistors with L=0.75 µ m (closed circles) and L=40 µ m (open squares). Clearly the current in the short transistor is more dominated by the parasitic series resistance as compared to the long transistor. of L . The R ON can then be expressed as [15]: � R ON ( L ) = ∂ V ds � (5.2) = R ch ( L ) + R p . � ∂ I ds � V ds → 0 , V g The experimental data are, in first order, well described by this equation, with R ON depending linearly on L (see Fig.5.3). From the slopes of the plots in Fig.5.3 we find the channel resistance, R ch , the inverse of which, [ � R ON /� L ] − 1 , is the channel conductivity. From the derivative of the channel conductivity, the field-effect mobility, corrected for R p can be obtained: �� − 1 � � R ON ∂ � L � � = µ FE V g WC i (5.3) ∂ V g The resulting corrected mobilities are plotted in the insets of figure 5.1. The corrected � � curve yields a higher overall µ FE V g . From the insets of Fig.5.1b it is clear that for the 40 µ m-channel, the influence of R p is small, as µ FE obtained from Eq.5.1 is close to the corrected mobility. We note that any non-linearity of µ FE with V g in our samples cannot a priori be attributed to the presence of an R p [18], but is more probably the result of a specific density of states in the semiconductor at the semiconductor/insulator interface (see Chapter 2). From the analysis with Eq.5.2 we find R p in Fig.5.3 as the intercept

56 Scaling behavior and parasitic series resistance � �9 J ��9 �� 9 J ��9 �9 J ��9 �9 J ��9 �� Ω � �9 J ��9 �� 1 � 2 � �� µ �� 9 J ��9 �� 9 J ��9 �9 J ��9 �9 J ��9 �� Ω � �9 J ��9 �� 1 � 2 � �� µ �� Figure 5.3: Total device resistance R ON , calculated with Eq.5.2 from the data in Fig.5.1, as a function of the mask channel length for various gate voltages, for (a) PTV, (b) P3HT.

5.4 Parasitic series resistance determination 57 � � �� 379��PEDU�+&O FRQYHUVLRQ�GHJUHH�YDULHG EHWZHHQ��DQG�� 379��PEDU�+&O FRQYHUVLRQ�GHJUHH�YDULHG EHWZHHQ��DQG�� 379��PEDU�+&O FRQYHUVLRQ�GHJUHH�YDULHG � EHWZHHQ��DQG�� 2& � & �� 339 �2& �� & �� 339 S � � �3�+7 �� 3�+7��IURP�UHI�>��@� �SUHFXUVRU�SHQWDFHQH � �� )( �� Figure 5.4: The parasitic resistance times the channel width as a function of the effective field-effect mobility for a number of polymeric semiconductors and pentacene. of R ON at L = 0. This R p , typically on the order of M � for our devices, is found to decrease with increasing gate voltage, i.e. with increasing carrier density. From the analysis with Eq.5.2 we can find R p in Fig.5.3 as the intercept of R ON at L = 0. This intercept depends on the applied gate voltage, which implies that R p decreases with increasing gate voltage, i.e. with increasing carrier density. We find experimentally that both the field-effect mobility and the parasitic resistance depend on V g . In Fig.5.4 we plot the experimentally determined R p , multiplied with the channel width, and effective µ FE obtained from the scaling analysis of several organic semiconductors. Also data from a P3HT study of Sirringhaus et al. [16] is included. An empirical relation is observed between the charge carrier mobility in the polymeric semiconductor and the parasitic resistance for the polymeric semiconductor in contact with the gold/titanium stack. A possible reason for this empirical observation is that the density of localized states in the polymer is of importance for the charge injection efficiency. The dependence of R p on µ FE is probed experimentally by accumulating charge in the semiconductor, by means of the field-effect, where we change the position of the Fermi level in the density of states. Why this results in a very similar dependence of µ FE on R p for different polymeric semiconductors is unclear at present. In literature it has been demonstrated that injection-limited current into a disordered polymer can be described by thermally assisted hopping from the electrode into the localized states of the polymer, which are broadened due to disorder [23]. As a representation of this effect, the R p for injection into a semiconducting polymer is found to depend on the charge carrier mobility in the polymer [24]. For the molecular semiconductor pentacene the data is more scattered and does not follow the trend observed for the polymeric transistors (see Fig.5.4). We attribute this to the polycrystalline nature of the pentacene films, which

58 Scaling behavior and parasitic series resistance depends on the processing conditions. The origin of the observed parasitic series resistance, or injection-limited current, can be due to a combination of effects. In general, geometrical or morphological contact problems between the semiconductor film and the gold contacts can be of importance, which is indicated by the scattered pentacene data. However, the data for the polymers are much more consistent and suggest that the injection barrier is related to material parameters of electrode and semiconductor layer rather than processing variations. A mismatch between the workfunction of the gold, at 5.1 eV, and the highest occupied molecular orbital (HOMO) level of the semiconductors (for the materials used here: around 5.2 eV) would lead to an injection barrier for holes. The width of this injection barrier can be nar- rowed by accumulating charge in the semiconductor, through the field-effect, by applying a V g [25]. For a small barrier height, in the order of the thermal energy k B T , this will result in an ohmic parasitic resistance, whereas for higher barrier heights a non-ohmic parasitic resistance will be present at the electrode/semiconductor interface. 5.5 Conclusions In conclusion, we have used channel length dependent measurements to experimentally determine the effective field-effect mobility, corrected for parasitic series resistance, in a variety of spin-coated organic field-effect transistors. The understanding and reduction of parasitic series resistances is important for downsizing of the organic transistor geometries, to be able to reach higher switching speeds for integrated circuits. For the investigated transistors we extract a parasitic series resistance which depends on V g . This parasitic resistance is attributed to an injection barrier with a height in the order of a few times k B T , which results in an ohmic parasitic series resistance. Experimentally, we find that the parasitic resistance decreases with increasing charge carrier mobility for the investigated polymeric field-effect transistors.

References [1] G.H. Gelinck, T.C.T. Geuns, D.M. de Leeuw, Appl. Phys. Lett. 77 , 1487 (2000). [2] H.E.A. Huitema, G.H. Gelinck, J.B.P.H. van der Putten, K.E. Kuijk, C.M. Hart, E. Cantatore, P.T. Herwig, A.J.J.M. van Breemen, and D.M. de Leeuw, Nature (London) 414 , 599 (2001) [3] D.J. Gundlach, Y.Y. Lin, T.N. Jackson, S.F. Nelson, and D.G. Schlom, IEEE Elec. Dev. Lett. 18 , 87 (1997). [4] P. T. Herwig and K. M¨ ullen, Adv. Mater. 11 , 480 (1999). [5] H. Sirringhaus, R.J. Wilson, R.H. Friend, M. Inbasekaran, W.Wu, E.P. Woo, M. Grell, and D.D.C. Bradley, Appl. Phys. Lett. 77 , 406 (2000). [6] Z. N. Bao, Y. Feng, A. Dodabalapur, V. R. Raju, and A. J. Lovinger, Chem. Mat. 9 , 1299 (1997). [7] H. Sirringhaus, P.J. Brown, R.H. Friend, M.M. Nielsen, K. Bechgaard, B.M.W. Langeveld-Voss, A.J.H. Spiering, R.A.J. Janssen, E.W. Meijer, P.T. Herwig, and D.M. de Leeuw, Nature (London) 401 , 685 (1999). [8] A. R. Brown, C. P. Jarrett, D. M. de Leeuw, and M. Matters, Synth. Metals 88 , 37 (1997). [9] H. Fuchigami, A. Tsumura, and H. Koezuka, Appl. Phys. Lett. 63 , 1372 (1993). [10] M. Matters, D. M. de Leeuw, P. T. Herwig, and A. R. Brown, Synth. Met. 102 , 998 (1999). [11] D.B.A. Rep, B.-H. Huisman, E.J. Meijer, P. Prins, and T.M. Klapwijk, Mat. Res. Soc. Symp. Proc. 660 JJ7.9. [12] E.J. Meijer, C. Tanase, P.W.M. Blom, E. van Veenendaal, B.-H. Huisman, D.M. de Leeuw, and T.M. Klapwijk, Appl. Phys. Lett. 80 , 3838 (2002). [13] L. B¨ urgi, H. Sirringhaus, and R.H. Friend, Appl. Phys. Lett 80 , 2913 (2002). [14] M. Shur and M. Hack, J. Appl. Phys. 55 , 3831 (1984).

60 References [15] S. Luan and W. Neudeck, J. Appl. Phys. 72 , 766 (1992). [16] H. Sirringhaus, N. Tessler, D.S. Thomas, P.J. Brown, and R.H. Friend, Festk¨ orper- probleme 39 , 101 (1999). [17] L. Torsi, A. Dodabalapur, and H.E. Katz, J. Appl. Phys. 78 , 1088 (1995). [18] G. Horowitz, R. Hajlaoui, D. Fichou and A. El Kassmi, J. Appl. Phys. 6 , 3202 (1999). [19] J. Wang, D.J. Gundlach, C.C. Kuo, and T.N. Jackson, 41st Electr. Mater. Conf. Di- gest, pg 16 (1999). [20] Y.Y. Lin, D.J. Gundlach, and T.N. Jackson, Mat. Res. Soc. Symp. Proc. 413 , 413 (1996). [21] K. Terada and H. Muta, Jap. J. Appl. Phys. 18 , 953 (1979). [22] J.G.J. Chern, P. Chang, R.F. Motta and N. Godinho, IEEE Elect. Dev. Lett. 1 , 170 (1980). [23] T. van Woudenbergh, P.W.M. Blom, M.C.J.M. Vissenberg and J.N. Huiberts, Appl. Phys. Lett. 79 , 1697 (2001). [24] Y. Shen, M.W. Klein, D.B. Jacobs, J.C. Scott and G.G. Malliaras, Phys. Rev. Lett. 86 , 3867 (2001). [25] S.M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).

Chapter 6 Frequency behavior and the Mott-Schottky analysis in poly(3-hexyl thiophene) metal-insulator-semiconductor diodes Abstract Metal-insulator-semiconductordiodes with poly(3-hexyl thiophene) as the semiconductor were characterized with impedance spectroscopy as a function of bias, frequency, and temperature. We show that the standard Mott-Schottky analysis gives unrealistic values for the dopant density in the semiconductor. From modeling of the data, we find that this is caused by the relaxation time of the semiconductor, which increases rapidly with decreasing temperature due to the thermally activated conductivity of the poly(3-hexyl thiophene).

62 Frequency behavior and the Mott-Schottky analysis 6.1 Introduction Low-cost organic integrated circuits are being more and more recognised as a poten- tially interesting industrial application. This has increased the efforts to develop high- performance devices. The development of solution-processable high-mobility polymers [1,2] and of technology for all-polymer integrated circuits [3,4] is promising. However, from the application point of view the lifetime of the devices is an important issue. The limited lifetime of current devices is mainly determined by the increase in conductivity, σ , of the semiconductor upon doping in air and light [4,5]. To study the doping effects in high-mobility polymeric semiconductors we used metal-insulator-semiconductor (MIS) diodes with poly(3-hexyl thiophene) (P3HT) as the semiconductor. We measured the temperature and modulation frequency dependence in these devices. The standard Mott-Schottky analysis to extract the dopant density, N A , yields erroneous results for large frequency and temperature ranges. Analysis of the data will show that this is due to the temperature dependence of the relaxation time of the P3HT. We model the data with a simple equivalent circuit and argue that the temperature dependence of the semiconductor relaxation time is due to thermally activated conductivity of P3HT. 6.2 Experimental The MIS diodes were fabricated on glass, using patterned Indium-Tin-Oxide (ITO) con- � photoresist was spin- tacts as gate electrode. A 300 nm insulating layer of novolak R coated on top of the gate. Over the insulator a 200 nm thick P3HT film was spun from a 1 weight % chloroform solution. Finally, a 10 nm gold layer was evaporated through a shadowmask to form an ohmic contact with the P3HT layer. A cross-section of the device is given in the inset of Fig.6.1. The capacitance, C , of the diode can be changed by depleting or accumulating charge in the semiconductor at the interface with the insulator. The thickness of the insulator layer, d ins , determines the maximum value of C : C ins = ǫ ins ǫ 0 A (6.1) , d ins where ǫ ins is the relative dielectric constant of the insulator, ǫ 0 the permittivity of vacuum and A the area of the device. The minimum value of C is determined by the relative dielectric constants of the insulator, ǫ ins , and the semiconductor, ǫ semi , and the total distance between the conductive layers. When the semiconductor layer is partially depleted, the depletion layer acts as a capacitance in series with the insulator capacitance. We calculate the total diode capacitance from the modulus of the impedance, Z , and its phase angle, � , using: C = − sin �/(ω | Z | ) , with ω =2 π f mod , where f mod is the modulation frequency. The capacitances of the MIS diodes scaled with the area of the devices, ranging from 9 to 36 mm 2 , in the entire biasing regime. The results presented in this work represent typical data measured on more than 10 MIS diodes. All impedance measurements were done with a Schlumberger 1260 Impedance Gain-Phase Analyzer in vacuum ( < 10 − 5 mbar) in an Oxford CV-flowcryostat.

6.3 The Mott-Schottky analysis 63 � � *R OG �� 3�+7 5HVLVW �� *OD VV �� ,72 �� J �� Figure 6.1: Capacitance of the P3HT MIS diode at 137 Hz as a function of V g for different temperatures. The area of this device was 36 mm 2 . 6.3 The Mott-Schottky analysis Typical capacitance vs gate bias, V g , ( C − V g ) curves at different temperatures are given in Fig. 6.1 for f mod =137 Hz. The gate voltage is applied on the ITO contact, with the gold electrode at 0 V. The capacitance is clearly a function of V g , and the semiconductor shows p-type behavior. When the temperature is lowered, we observe that the value of the accumulation capacitance becomes lower, whereas the depletion capacitance remains constant. Using the standard Mott-Schottky analysis [6,7], we extract the dopant density from these curves: 2 ∂ � C − 2 � (6.2) = q ǫ semi ǫ 0 N A A 2 , ∂ V g where q is the elementary charge. The derived dopant densities are plotted as a function of temperature in Fig.6.2 for several values of f mod . At low temperatures the extracted N A drastically rises and seemingly depends on the measurement frequency. We consider this behavior of N A to be physically unrealistic, and it is taken to indicate that the use of Eq.6.2 is not justified for the entire temperature and frequency range. We will show below why this is the case and what the criteria are for extraction of N A . 6.4 Equivalent circuit modelling In Fig. 6.3a we plot the accumulation capacitance, C A , at V g = − 20 V as a function of temperature for several modulation frequencies. Fig. 6.3b gives the corresponding phase,

64 Frequency behavior and the Mott-Schottky analysis �� $ � �� Figure 6.2: N A as a function of temperature for different frequencies, as derived from the curves in Fig.6.1 using Eq.6.2. � A , at V g = − 20 V . Clearly, both C A and � A have a frequency dependence. The maximum slope of C A with temperature coincides with the maximum in � A . We find that the maximum of � A is thermally activated with an activation energy of 0.36 eV, as shown in the inset of Fig.6.3a. We reason that the observed thermally activated behavior is due to the conductivity of the semiconductor layer. A similar argumentation was used by Stallinga et al. in a study of pn junctions based on a poly(phenylene vinylene) derivative [8]. Furthermore, this value compares well with E A = 0 . 36 eV obtained from bulk conductivity experiments on P3HT [9]. The activation energy is usually interpreted as the distance of the Fermi level in the bulk of the semiconductor to a certain transport level higher up in the density of states [9–11]. The assumption of the thermally activated conductivity allows us to model the data in accumulation for different temperatures with a simple equivalent circuit which is given in the inset of Fig.6.4. We describe the semiconductor layer by its geometric capacitance, C s , in parallel with the layer resistance, R s . The geometric insulator capacitance is C ins and we add a contact resistance, R c , for the ITO and the gold top contact. This simple model yields a good fit to the experimental data (see Fig.6.4). The fitted values are given in Table 6.1. The obtained values for C ins and C s correspond to their geometrical values, and the conductivity derived from R s varies from 1.8 · 10 − 10 S/cm at 250 K to 4.3 · 10 − 9 S/cm at 330 K, which are values comparable to results of bulk conductivity experiments [9]. The expression for the phase angle as a function of frequency is derived as: � − � 1 + ω 2 R 2 � � s C s ( C ins + C s ) � A = arctan . (6.3) � ω 2 R c R 2 s C 2 � ω C ins s + ( R c + R s ) From the equivalent circuit analysis we find that R c is small and can be neglected. The

6.4 Equivalent circuit modelling 65 � � �� @ � ] + > � � �� [ D I P � �� @ �� 7�>. � � $ � ��+] ��+] ��+] � ��+] �� +] �� +] ��+] �� +] �� $ � �� Figure 6.3: (a) Capacitance of the P3HT MIS diode at V g = − 20 V as a function of temperature for different frequencies. The inset shows the frequency at which the phase angle, � A , is at its maximum vs re- ciprocal temperature (b) � A of the MIS diode at V g = − 20 V for different frequencies.

66 Frequency behavior and the Mott-Schottky analysis � �� $ � �� PRG �� Figure 6.4: � A (at V g = − 20 V ) vs frequency for different temperatures. The lines are fits to the data, using the equivalent circuit from the inset. The fit results are given in table 6.1. Table 6.1: Values obtained by fitting the frequency dependence of the impedance and its phase angle (see Fig. 6.4) at V g = − 20 V for different temperatures. The equivalent circuit is given in the inset of Fig. 6.4. R c is the contact resistance, C ins the insulator capacitance and R s and C s the semiconductor resistance and capacitance respectively. T [K] R c [ � ] C ins [nF] R s [k � ] C s [nF] 250 72 ± 2 3 . 99 ± 0 . 03 320 ± 10 3 . 54 ± 0 . 04 264 67 ± 2 3 . 91 ± 0 . 03 120 ± 4 3 . 62 ± 0 . 04 294 76 ± 3 3 . 93 ± 0 . 03 24 ± 1 3 . 59 ± 0 . 06 330 71 ± 3 3 . 98 ± 0 . 03 12 . 8 ± 0 . 6 3 . 53 ± 0 . 07

6.5 The relaxation time 67 frequency at which � A reaches its maximum is derived as [8]: ω max = 2 π f max = 1 1 √ C s ( C ins + C s ), (6.4) R s with a maximum value of � A : � − 2 √ C s ( C ins + C s ) � � max = arctan (6.5) . C ins Thus � max , in accumulation, is purely dominated by the geometric capacitance of the device. Using this model, we find � max ∼ − 70, which is close to the experimental value of -72 degrees. For devices with different geometries, � max is well described by Eq.6.5. At low frequencies the fits in Fig.6.4 start to deviate from the experimental data. This is due to leakage currents through the MIS diode and can be accurately modeled with an added leakage resistance parallel to C ins . The leakage resistance is ∼ 100 M � , which means that for f mod > 25 Hz we can neglect its influence on the determination of N A . We note that the inclusion of the thermally activated conductivity in the semiconductor resistance R s combined with a very simple equivalent circuit is sufficient to model both the temperature and frequency behavior of the MIS diode. 6.5 The relaxation time The erroneous results obtained with the Mott-Schottky analysis are in fact due to the relaxation time or RC -time, τ = R s C s , of the P3HT. The relaxation time causes the increase of N A , shown in Fig.6.2. When the condition 1 /ω ≫ τ. (6.6) is no longer satisfied, the charge carriers can not follow the AC voltage anymore. As a result, one measures a smaller capacitance of the MIS diode with increasing frequency, as shown in Fig.6.3a. As R s increases with decreasing temperature, this restricts the frequency region over which Eq.6.6 is fulfilled even further for lower temperatures. This is why we observe an apparent temperature dependent capacitance as shown in Fig.6.1. We use our understanding of the temperature and frequency behavior to apply Eq.6.2 in a frequency range where these effects are negligible. In this case the lower limit was taken 25 Hz, and we took the upper limit in frequency one decade lower than the inverse of τ , for each temperature. For the present device, we extract a dopant density of 5.4 · 10 15 cm − 3 , comparable to the value of 1 · 10 16 obtained on P3HT by Brown et al [12]. 6.6 Conclusions In summary, we have fabricated and analyzed MIS diodes based on P3HT. We find that the Mott-Schottky analysis may not be used for extraction of the dopant density, N A , over the entire range of temperature and frequency. This is due to the relaxation time of the

68 Frequency behavior and the Mott-Schottky analysis P3HT, ranging from τ = 1 · 10 − 3 s at 250 K to τ = 5 · 10 − 5 s at 330 K. The observed thermally activated behavior related to the relaxation time is attributed to the conductivity of the P3HT.

References [1] Z. Bao, A. Dodabalapur, A.J. Lovinger, Appl. Phys. Lett. 69 , 4108 (1996). [2] H. Sirringhaus, P.J. Brown, R.H. Friend, M.M. Nielsen, K. Bechgaard, B.M.W. Langeveld-Voss, A.J.H. Spiering, R.A.J. Janssen, E.W. Meijer, P.T. Herwig and D.M. de Leeuw, Nature 401 , 685 (1999). [3] C.J. Drury, C.M.J. Mutsaers, C.M. Hart, M. Matters and D.M. de Leeuw, Appl. Phys. Lett. 73 , 108 (1998). [4] G.H. Gelinck, T.C.T. Geuns and D.M. de Leeuw, Appl. Phys. Lett. 77 , 1489 (2000). [5] M.S.A. Abdou, F. P. Orfino, Y. Son, S. Holdcroft, J. Am. Chem. Soc. 119 , 4518 (1997). [6] E.H. Nicollian and J.R. Brews, “MOS (Metal Oxide Semiconductor) Physics and Technology”, Wiley, New York (1982). [7] S.M. Sze, “Physics of semiconductor devices”, Wiley, New York (1981). [8] P. Stallinga, H.L. Gomes, H. Rost, A.B. Holmes, M.G. Harrison and R.H. Friend, J. Appl. Phys. 89 , 1713 (2001). [9] D.B.A. Rep, B.-H. Huisman, E.J. Meijer, P. Prins and T.M. Klapwijk, Mat. Res. Soc Symp. Proc., 660 (2001). [10] A.V. Gelatos and J. Kanicki, Appl. Phys. Lett. 56 , 940 (1990). [11] M.C.J.M. Vissenberg and M. Matters, Phys. Rev. B 57 , 12964 (1998). [12] P.J.Brown, Charge Modulation Spectroscopy of Poly(3-alkylthiophene) , PhD thesis, Cambridge (2000).

Chapter 7 Photoimpedance spectroscopy of poly(3-hexyl thiophene) metal-insulator-semiconductor diodes Abstract Capacitance-voltage characteristics of metal-insulator-semiconductordiodes with poly(3- hexylthiophene) (P3HT) as p-type semiconductor were investigated as function of time, ambient, and illumination. P3HT is rapidly doped upon exposure to both oxygen and light. Changes of the acceptor density profiles with time were determined by using Mott- Schottky analysis of the capacitance-voltage characteristics. The profiles were determined to be constant over the P3HT film thickness. Wavelength dependent photoimpedance measurements show that the acceptor creation efficiency peaks upon excitation of the molecular oxygen-polythiophene contact charge transfer complex at (1.9 ± 0.1) eV.

72 Photoimpedance spectroscopy of P3HT MIS diodes 7.1 Introduction Thin-film field-effect transistors based on p-type organic thiophene-based semiconductors usually are unstable under ambient conditions. The conductivity of the organic semiconductor often increases under exposure of oxygen, light, or a combination thereof [1,2]. As a result, the current modulation, or on-off current ratio, of discrete transistors decreases with time, the gain of logic gates gets less than unity and, consequently, logic circuits stop functioning. As is described in Chapter 8, the acceptor density can be estimated from the pinch-off voltage of discrete ring-type transistors, where the pinch-off voltage is the applied gate voltage at which the depletion region in the semiconductor becomes equal to the thickness of the semiconductor layer [3]. This reported analysis implicitly assumes that the acceptor density is constant over the semiconductor layer thickness. In this work we determine the acceptor profile in the polymeric semiconductor layer, using the Mott-Schottky analysis on measured capacitance-voltage ( C − V g ) characteristics of polymer-based metal-insulator-semiconductor (MIS) diodes. Because we used semitransparent MIS diodes, changes in the impedance could be investigated as a function of time upon exposure to oxygen and/or light. As a typical example we investigated poly(3- hexyl thiophene) (P3HT) MIS diodes. In order to elucidate the doping mechanism, we compared the wavelength dependent changes in the photoimpedance measurements with the absorption spectra of molecular oxygen-polythiophene contact charge transfer com- plexes as reported by Abdou et al. [2]. 7.2 Experimental The MIS diodes are fabricated on glass, using patterned transparent indium-tin-oxide gate � photoresist is spincoated on top of the contacts electrodes. A 300 nm layer of novolak R and subsequently cross-linked upon baking at 150 o C. On top of this insulator a 200 nm thick film of P3HT is spun from a 1 wt% chloroform solution. Finally, a semi-transparant 10 nm gold electrode is evaporated through a shadow mask. The area of the diodes ranges from 9 to 36 mm 2 . A schematic cross-section of the MIS diode is given in the inset of Fig.7.1. After processing, the sample is inserted in an Oxford CF1204 optical flowcryostat, with a vacuum better than 10 − 5 mbar. Impedance measurements are done using a Schlumberger 1260 impedance gain-phase analyzer, with a modulation frequency, f mod of 137 Hz. This frequency is low enough to prevent artifacts in the impedance data due to the low bulk charge carrier mobility of P3HT, as described in the previous chapter [4]. The diode capacitance, C , then follows from the modulus of the impedance, Z , and the phase angle, � , by C = − sin �/( 2 π f mod | Z | ) . For the wavelength dependent photoimpedance measurements the light of an Oriel 66058 tungsten-filament lamp is fed into a Jobin Yvon H25 PLE monochromator. The resulting light beam is focused on the sample in the cryostat. The wavelength of the light is varied between 400 nm and 1100 nm. The power profile of the light incident on the MIS diode is measured. The number of incident pho- tons is calculated from the calibrated power profile of the lamp in combination with the monochromator. The absorption spectrum of a thin film of P3HT is measured and taken equal to the absorption of the P3HT layer in the diode. In the analysis we have assumed

7.3 Flat-band shift under oxygen exposure 73 � � � �� LQ�OLJKW� λ ��QP�YDFXXP �� % ) ∆ � �� LQ�GDUN� ��PEDU�2 � � ��PEDU�2 � �� PEDU�2 � �� PEDU�2 � V �� Q L �� J �� Figure 7.1: Normalized C − V g curves of a P3HT MIS diode in vacuum and after 82 minutes exposure to a 230 mbar dry oxygen atmosphere. The arrow indicates the direction of the shift of the curve upon oxygen exposure. The inset on the left shows a schematic cross section of the MIS diode. The inset on the right shows the flat-band voltage shift as a function of time, for different oxygen pressures, as well as a measurement in vacuum where the MIS diode is exposed to light (wavelength of 700 nm). that any dispersion in the absorption of the semi-transparant gold electrode can be disregarded. After exposure to oxygen and/or light in the cryostat, the P3HT MIS diodes are dedoped by annealing the diodes for several hours in vacuum at 150 o C. This process can be repeated, without apparent degradation of the P3HT [5]. Due to this dedoping procedure there are some variations in the dopant density at the beginning of each experiment. 7.3 Flat-band shift under oxygen exposure The capacitance as a function of gate voltage for an undoped P3HT MIS diode in vacuum and dark is presented in Fig.7.1. Accumulating or depleting charge in the p-type P3HT semiconductor changes the capacitance. The maximum capacitance is obtained in accumulation at high negative gate bias and is determined by the thickness of the insulator, d ins , as: C ins = ǫ ins ǫ 0 A , (7.1) d ins where ǫ ins is the relative dielectric constant of the insulator, ǫ 0 is the permittivity of vacuum, and A is the area of the device. At positive gate bias the semiconductor layer is

74 Photoimpedance spectroscopy of P3HT MIS diodes partially depleted. The depletion layer then acts as a capacitance in series with the insulator capacitance. The minimum capacitance is obtained when the whole film is depleted and is determined by the dielectric constants of the insulator and the semiconductor, ǫ semi , and by the total distance between the electrodes. The steepness of the C − V g characteristics of an MIS diode, when biased in the gate voltage range where the semiconductor layer is partially depleted, is the result of the ease with which the semiconductor can be depleted and is related to the acceptor density and its profile as a function of the depth inside the film. The C − V g characteristics of Fig.7.1 are measured in the dark and in vacuum. The measurements do not change with time in vacuum and dark. The acceptor density and depth profile therefore do not change; P3HT is stable in vacuum and dark. Subsequently, the diodes are measured in dark upon exposure to dry oxygen. The partial oxygen pressure is varied between 0.8 and 230 mbar. The capacitance-voltage characteristics are recorded every four minutes. The final measurement is included in Fig.7.1. These two measurements can be shifted over the voltage axis on top of each other. Apparently, the dominant effect is a shift of the flat-band voltage, V FB , the applied voltage at which there is no band bending in the semiconductor at the semiconductor/insulator interface. The flat-band voltage shift is indicated in the insert of Fig.7.1. The increase of V FB with time is dependent on partial oxygen pressure. Upon exposure to light in vacuum the MIS diode C − V g characteristics also show a flat-band shift (see the inset of Fig.7.1.), which slowly decreases again when the light is turned off. The flat-band voltage shift is likely due to electrostatic charging of the semiconductor/insulator interface. This interpretation agrees with reported shifts of the transfer characteristics of P3HT field- effect transistors (see Chapter 8) [3]. 7.4 Photoimpedance spectroscopy The constant shape of the measurements shown in Fig.7.1 indicate that on the time scale of the measurements (80 minutes) P3HT is stable, with only a flat-band voltage shift, in vacuum and light, and in oxygen in the dark. P3HT is unstable however upon exposure to both oxygen and light. The shape of the capacitance-voltage measurements then gradually changes. Normalized capacitance-voltage curves in 230 mbar of oxygen during illumination at a wavelength of light, λ of 700 nm are presented in Fig.7.2, which also shows that the flat-band voltage shifts. The flat-band shift is difficult to quantify because the slopes of the C − V g curves change as well. Experimentally we find that the changes in the slopes depend on the wavelength of the illumination (not shown). The slope of the C − V g characteristics depends on the density and the depth profile of the acceptors. For a quantitative interpretation we use the Mott-Schottky analysis [6,7]. The capacitance at a certain gate bias corresponds to the depletion depth, d depl , in the semiconductor layer by: � � 1 1 � � d depl V g � − ǫ 0 ǫ semi A (7.2) C � V g C ins Eq.7.2 holds when the contribution to the capacitance of interface states and minority carriers can be disregarded [6]. The acceptor density, N A , at a certain depletion depth can

7.4 Photoimpedance spectroscopy 75 � �� V �� Q L �� λ �� J �� Figure 7.2: Normalized C − V g curves as a function of time in 230 mbar oxygen under illumination of light with a wavelength of 700 nm. now be determined using the Mott-Schottky relation: 2 ∂ � C − 2 � = q ǫ semi ǫ 0 N A A 2 , (7.3) ∂ V g where q is the elementary charge. Combination of Eqs.7.2 and 7.3 yields the acceptor density as a function of depletion depth in the semiconductor layer. We note that the acceptor density profile follows from the shape of the C − V g characteristics only. It does not depend on the value of V g . Hence, in this analysis flat-band voltage shifts have no influence on the profile. This profiling technique probes the holes associated with the acceptors, rather than the acceptors themselves [8]. The evaluated profile of the hole concentration follows the acceptor profile unless the acceptor profile varies spatially over distances less than the Debije length. This is the distance where the electric field emanating from an electric charge falls off by a factor of 1/e: � ǫ semi ǫ 0 k B T L D = , (7.4) q 2 N A where k B is Boltzmann’s constant and T is the absolute temperature. Under flat-band conditions the number of ionized acceptors is equal to the number of mobile holes. The application of a gate bias results in an additional charge in the semiconductor layer. This causes a rearrangement of the mobile holes, which shield the bulk of the semiconductor from the induced charge. The shielding distance, or band-bending region is on the order of the Debije length. Experimentally, this means that the Debije length limitation prevents accurate profiling closer than 3 L D from the interface of the semiconductor with

76 Photoimpedance spectroscopy of P3HT MIS diodes � �� λ �� $ � �� GHSO �� Figure 7.3: Acceptor density profile extracted from the C − V g data of Fig.7.2, using Eqs.7.2 and 7.3, for an undoped P3HT MIS diode in vacuum and dark (filled squares) and after 60 minutes of exposure to 230 mbar dry oxygen and illumination with λ =700 nm (filled circles). the insulator [6, 8]. A typical acceptor density of about 10 16 cm − 3 results in a Debije length of about 20 nm at room temperature. The acceptor profile information can then reliably be determined starting from a depletion depth of about 60 nm from the semiconductor/insulator interface. Acceptor densities in the dark and after illumination at a wavelength of 700 nm in 230 mbar O 2 are presented in Fig.7.3 as a function of depletion depth. In the dark N A is constant over the P3HT film thickness and amounts to about 3 · 10 15 cm − 3 . Upon illumination N A increases, but in first order is constant over the layer thickness. There is only a slight increase in acceptor density at the top contact. Similar profiles were obtained for illuminations at other wavelengths. The profiles with time can now be calculated from the temporal C − V g characteristics of Fig.7.2. We take the values of N A at a depletion depth of 100 nm and plot them in Fig.7.4 as a function of time on a double logarithmic scale. The acceptor density roughly follows a power law dependence under light exposure of 700 nm and O 2 exposure of 230 mbar with an exponent of about 0.3. We note that typically, the conductivity of a variety of oligo- and polythiophenes increases with time as t α with α between 0.2 and 0.5, under ambient conditions [9]. This suggests that the increase of the conductivity on the timescale of the measurements is dominated by an increase in acceptor density. A clue for the doping mechanism can be obtained from the wavelength dependent photoimpedance measurements, which are given in Fig.7.5. In these photoimpedance experiments the MIS diode is exposed for two minutes to light of a certain wavelength in 230 mbar O 2 . Then the C − V g characteristics were recorded in the dark, with the oxygen

7.4 Photoimpedance spectroscopy 77 � �� GHSO �� $ � �� Figure 7.4: Acceptor density at 100 nm depletion depth in the semiconductor layer as a function of oxygen exposure and/or illumination � �� V �� Q L �� λ �� λ �� λ �� λ �� λ �� λ �� J �� Figure 7.5: Normalized C − V g curves as a function of the wavelength incident on the sample in 230 mbar oxygen. The curves were recorded in the dark after 2 minutes of light exposure at each wavelength.

78 Photoimpedance spectroscopy of P3HT MIS diodes �� λ �� Figure 7.6: Relative acceptor density creation efficiency as a function of the incident illumination, for P3HT in 230 mbar O 2 at room temperature. The absorption spectrum of P3HT is given for comparison. pressure constant at 230 mbar O 2 . This procedure was repeated at several wavelengths of light going from λ =1000 nm to λ =600 nm, in a consecutive measurement. Due to the low absorption in the P3HT layer from λ =1000 nm up to λ =700 nm, we assume that the light is uniformly absorbed in the film. For shorter wavelengths the absorption profile of the P3HT film will not be homogeneous anymore, but will result in a depth profile of absorption. We neglect this absorption profile in the measurements up to 600 nm. The acceptor density is determined from Fig.7.5 at a depletion depth of 100 nm as a function of the photon energy. The derivative yields the change in acceptor density with photon energy, where we have assumed that absolute value of N A at the beginning of each measurement has no influence on the increase of N A . This number is corrected for the power profile of the light, by dividing with the incident photon flux. The relative acceptor creation efficiency as a function of photon energy is then obtained by dividing with the absorbance, and is plotted in Fig.7.6. This efficiency, or cross section, indicates the ease with which acceptors are formed in P3HT under illumination in an oxygen atmosphere. The efficiency peaks at (1.9 ± 0.1) eV. This value corresponds roughly to the reported absorption of the contact charge transfer complex between molecular oxygen and polythiophene at 1.97 eV [2]. 7.5 Conclusions In summary, we have investigated the instability of P3HT using semitransparent MIS diodes. We have measured and analyzed the capacitance-voltage characteristics of these

7.5 Conclusions 79 MIS diodes as function of time, ambient and illumination. On the time scale of the measurements in vacuum and light, and in oxygen in the dark, the P3HT MIS diodes only show a flat-band voltage shift. However, upon exposure of the P3HT to both oxygen and light, the capacitance-voltage data show a clear increase of the acceptor density, as is demonstrated using Mott-Schottky analysis. The acceptor density profile is in first approximation constant over the semiconductor film thickness. The wavelength dependent photoimpedance measurements show that the acceptor creation efficiency peaks upon excitation of the molecular oxygen-polythiophene contact charge transfer complex.

References [1] G.H. Gelinck, T.C.T. Geuns and D.M. de Leeuw, Appl. Phys. Lett. 77 , 1489 (2000). [2] M.S.A. Abdou, F. P. Orfino, Y. Son and S. Holdcroft, J. Am. Chem. Soc. 119 , 4518 (1997). [3] E.J. Meijer, C. Detcheverry, P.J. Baesjou, E. van Veenendaal, D.M. de Leeuw and T.M. Klapwijk, J. Appl. Phys. 93 , 4831 (2003). [4] E.J. Meijer, A.V.G. Mangnus, C.M. Hart, D.M. de Leeuw, T.M. Klapwijk, Appl. Phys. Lett. 78 , 3902 (2001). [5] D.B.A. Rep, B.-H. Huisman, E.J. Meijer, P. Prins and T.M. Klapwijk, Mat. Res. Soc. Symp. Proc., 660 , JJ7.9.1 (2001). [6] E.H. Nicollian and J.R. Brews, “MOS (Metal Oxide Semiconductor) Physics and Technology” , Wiley, New York (1982). [7] S.M. Sze, “Physics of semiconductor devices” , Wiley, New York (1981). [8] D.K. Schroder, “Semiconductor Material and Device Characterization” , Wiley (1990). [9] L. Luer, H.-J. Egelhaaf and D. Oelkrug, Optical Materials 9 , 454 (1998).

Chapter 8 Dopant density determination in disordered organic field-effect transistors Abstract We demonstrate that, by using a concentric device geometry, the dopant density and the bulk charge carrier mobility can simultaneously be estimated from the transfer characteristics of a single disordered organic transistor. The technique has been applied to determine the relation between the mobility and the charge density in solution-processed poly(2,5-thienylene vinylene) and poly(3-hexyl thiophene) thin-film field-effect transistors. The observation that doping due to air exposure takes place already in the dark, demonstrates that photo induced oxygen doping is not the complete picture.

84 Dopant density determination in organic transistors 8.1 Introduction For the development of polymeric integrated circuits the stability of the characteristics of the organic semiconductor layer is an important issue. One of the limiting mechanisms is an increase in p-type doping due to a charge-transfer reaction with ambient molecular oxygen (see chapter 7) [1]. An increase of doping leads to an increase of the conductivity of the bulk semiconductor, which reduces the current modulation, or on-off ratio, of the transistor [2,3]. Here we will demonstrate that, by using a ring-type transistor geometry, we can directly estimate the dopant density and the bulk mobility from the transfer characteristics of a single disordered organic field-effect transistor (FET). This allows monitoring of the dopant density change in time. The disentanglement of the dopant density and bulk mobility in the bulk conductivity will be crucial to understand and counteract the instabilities observed in polymeric transistors. As an example we discuss the dopant density increase under the influence of oxygen exposure in poly(2,5-thienylene vinylene) (PTV) and poly(3-hexyl thiophene) (P3HT) field-effect transistors. 8.2 Motivation and Realization The field-effect behavior of disordered organic FETs has been described in terms of hopping of charge carriers in an exponential density of localized states by Vissenberg et al . [4]. The relative position of the Fermi level, E F , in the density of states (DOS), which determines the charge carrier mobility [4,5], is then dominated by the gate induced charge carriers, C i V g , where C i is the insulator capacitance per unit area. Similar con- cepts have been used to understand the superlinear increase of the bulk conductivity with doping [6,7], where the relative position of E F is dominated by the dopant density, N A . Disordered organic FETs typically operate in accumulation mode. This means that there is no depletion layer, which is present in inversion layer devices [8], that isolates the conducting channel from the semiconductor bulk. As a consequence, a low conductivity in the bulk layer is required for a large on-off current ratio [5], defined as the ratio of currents at V g = 0 V and -20 V. When the bulk conductivity is not negligible, we ex- pect a clearly observable crossover from field-effect dominated current to bulk dominated current in the transfer characteristics of a doped accumulation mode disordered organic transistor [9]. Conventional devices with an unshielded drain electrode suffer from parasitic currents outside the transistor area [10, 11], which may obscure the crossover from field- effect dominated current to bulk dominated current. These parasitic currents arise due to the unpatterned semiconductor layer. This can be circumvented by using a ring-type transistor geometry, where the source electrode forms a closed ring around the transistor channel, with the drain electrode, at which the current is monitored, in the center (see inset of Fig.8.1). In the experiments we used heavily doped Si wafers as common gate electrode, with a 200-nm-thick layer of thermally oxidized SiO 2 as the gate-insulating layer. The SiO 2 was treated with hexamethyldisilazane to make the surface hydrophobic. With conventional lithography gold source and drain electrodes were defined, with a channel length,

8.2 Motivation and Realization 85 � �� YDFXXP �� VHF�LQ��PEDU�DLU ��PLQ�LQ��PEDU�DLU �� PLQ�LQ��PEDU�DLU �� PLQ�LQ��PEDU�DLU �� V �� G � �� J �� Figure 8.1: PTV FET transfer characteristics as a function of time in 10 mbar air, in dark, L = 10 µ m , W = 2 . 5 mm. Clearly visible is the crossover from a bulk depletion transistor to an accumulation transistor. The inset shows a topview of the source-drain geometry of the ring-type transistors. L , varying between 10 and 20 µ m, and channel widths, W , of 1 mm and 2.5 mm. As a last step a 200 nm thick semiconductor layer is spincoated over the contacts. The semiconductors used, are poly(2,5-thienylene vinylene), which is applied as precursor from a 0.5 wt% chloroform solution and subsequently formed in-situ by conversion at 150 o C in vacuum [12], and poly(3-hexyl thiophene) which was spun from a 1 wt% chloroform solution. All transfer characteristics in this study were measured in the linear operating regime of the transistor, at source-drain voltage, V ds = − 2 V , at room temperature, in the dark. Fig.8.1 shows the transfer characteristics of a PTV thin-film field-effect transistor, with a ring-geometry. The initial curve is measured in vacuum after a thermal dedoping procedure [13]. After this measurement 10 mbar of air is let into the chamber. The time at which the valve is opened to admit the air is denoted as t = 0. Subsequently, the evolution of the transfer characteristics in air is monitored as a function of time. The initial curve shows a characteristic p-type semiconducting behavior. At negative gate voltages, V g , holes are accumulated in the semiconductor at the semiconductor- insulator interface. These accumulated charges move under the influence of the lateral source to drain field, resulting in the source-drain current, I ds . At positive V g the holes are depleted from the semiconductor layer and no mobile charges are left to carry the current. Upon prolonged exposure to air, in dark, we observe two changes in the transfer characteristics. Firstly, in the depletion regime of the transistor (at positive gate voltages) an additional current appears, which increases with oxygen-exposure and time. This feature

86 Dopant density determination in organic transistors can also be found in transfer characteristics of conventional device geometries, published by other groups [14–16]. Secondly, the onset of the field-effect, i.e . the switch-on voltage, V so , which was defined in Chapter 2 as the gate voltage at which the transistor is at the flat-band condition [17], is shifted slightly to more positive gate voltages with respect to the initial curve. 8.3 Interpretation and Analysis The features reported in Fig.8.1 are readily understood when the transistors are considered as accumulation mode FETs. When the conductivity of the bulk layer increases, an additional current will flow in the bulk that is not modulated by the field-effect (schematically depicted in Fig.8.2a). The magnitude of this bulk current compared to the channel current determines whether the gate electrode can still switch the FET between the on and the off state, at V g = 0 V and -20 V. An increase of the dopant density in the semiconductor, results in an effective bulk depletion transistor (similar to a junction field-effect transistor) in parallel to the accumulation field-effect transistor. If this kind of FET is driven far enough into depletion, eventually the entire film will be depleted of mobile charge and no more current will flow. The voltage at which this happens is called the pinch-off voltage, V pinch (see Fig.8.2c). We argue that the occurrence of the clearly observable crossover from field-effect behavior to bulk behavior in Fig.8.1 is due to the fact that in disordered semiconducting polymers the mobility depends on the charge density. In a system where the mobility is constant and the same for both field-effect and the bulk, this crossover is not observed [18]. 8.3.1 Determination of the dopant density From V pinch , we can directly determine the dopant density, N A , provided that we correct for the experimentally observed shift of V so , as described in Section 8.5 below. The initial curve, obtained after the thermal dedoping procedure and measured in vacuum, is taken as reference measurement, and its V so is estimated at a current level of 1 pA. We can now determine V pinch , which we also extract at a current level of 1 pA, with respect to V so from the initial transfer characteristics. In the following analysis we assume that the dopant density in the initial curves is negligible. The error introduced in the analysis by determining V pinch at 1 pA is small as the current drop typically is steep at that current level. For a small source-drain field we assume that the depletion of the semiconductor takes place uniformly over the entire channel length (see Fig.8.2b) and that the dopants are uniformly distributed throughout the semiconductor layer 1 . The depletion layer width in a doped semiconductor is given by [8]:  �  1 + 2 C 2 � � W depl = ǫ 0 ǫ semi V g − V so i  , − 1 (8.1)  C i q N A ǫ 0 ǫ semi 1 Dopant uniformity was investigated in chapter 7

8.3 Interpretation and Analysis 87 �D� VHPLFRQGXFWRU � � LQVXODWRU JDWH �E� � � �F� � � Figure 8.2: Schematic of an accumulation-modeFET, showing a p-doped semiconductor: + indicates a positive charge in the semiconductor ⊖ indicates a negatively charged counterion. (a) The transistor in accumulation, the current is composed of the field-effect current and the bulk current, resulting from the dopant density. (b) Develop- ment of a depletion region when a positive gate bias is applied. The extent of the depletion region is indicated by the dotted line. Here the current only flows in the undepleted bulk. (c) The film is fully depleted, no more current flows beyond pinch-off.

88 Dopant density determination in organic transistors �� $ � �� Figure 8.3: dopant density, extracted using Eq.8.4, vs time for several air pressures, in dark. where ǫ 0 is the permittivity of vacuum, ǫ semi the relative dielectric constant of the semiconductor, q the elementary charge and A the active transistor area (length times the width). By using the insulator capacitance per unit area, C i = ǫ 0 ǫ ins (8.2) , d ins and the semiconductor layer capacitance, C semi = ǫ 0 ǫ semi A , (8.3) d semi we can recalculate Eq.8.1 for the pinchoff condition, V g − V so = V pinch , at which the depletion layer width is equal to the semiconductor layer thickness, d semi , to: 2 V pinch ǫ 0 (8.4) N A = � , � d 2 ǫ semi + 2 d semi d ins q semi ǫ ins where d ins is the film thickness of the insulator layer, and ǫ ins is the relative dielectric constant of the insulator. The dopant density, derived using Eq.8.4, as a function of time at different air pressures, is plotted in Fig.8.3. We observe that the initial increase of N A upon exposure to oxygen is the biggest difference between the measurements at different pressures. In PTV this initial increase occurs within two minutes after exposure, in the dark. For the P3HT this is a much slower process in the dark, as can be seen from Fig.8.3. In most models

8.4 Results for PTV and P3HT 89 the charge-transfer reaction with molecular oxygen, requires exposure to light [1]. The measurements in the dark presented here, demonstrate that further analysis into the doping mechanisms is required, and that the mechanisms differ quantitatively for different materials. 8.3.2 Determination of the bulk mobility At V g = V so there is no band bending at the semiconductor-insulator interface, no accumulation and no depletion (see Fig.1.7a). The measured current at V so must then be flowing in the bulk, through the entire film-thickness. We find that the current values at V so in the doped films typically vary linearly with the applied source-drain voltage, in- dicative of bulk ohmic behavior. From the current flowing at V so we can calculate the bulk charge carrier mobility: � LI ds � µ bulk = (8.5) � N A qWd semi V ds � V g = V so Knowing N A from Eq.8.4, we can determine µ bulk using Eq.8.5. We remark that the shape of the curves in depletion can be described by modeling the curves with � , I ds = WV ds N A q µ bulk � d semi − W depl (8.6) L using the values obtained from Eq.8.4 and Eq.8.5. 8.4 Results for PTV and P3HT As a typical result, the bulk mobilities of PTV and P3HT as a function of the dopant density are given in Fig.8.4. For both materials the dependence of µ bulk on the dopant density is found to be roughly µ ∼ N 2 . 3 A . For comparison the field-effect mobilities, extracted from the linear operating regime of the transistors, using L ∂ I ds (8.7) µ FE = , WC i V ds ∂ V g are also given. The charge accumulated at the semiconductor-insulator interface is calculated using Poisson’s equation, and the charge distribution in the semiconductor is neglected [19]. We find that the dependence of mobility on charge density is not the same for the bulk and the field-effect [20]. The µ bulk − N A relation obtained here was also found in studies at dopant densities of 10 19 -10 20 cm − 3 [2]. These observations suggest that chemical doping of the film not only influences the relative position of the Fermi level in the DOS. In fact, the presence of the dopant counterions will alter the DOS itself, a phenomenon well known from studies on amorphous silicon [21]. The bulk mobility of P3HT is found to be much higher than the bulk mobility of PTV (see Fig.8.4). We argue that this is due to a more ordered film in the case of P3HT [22],

90 Dopant density determination in organic transistors � �� EXON �� ( �� ) � � EXON �� )( �� N O X � � EXON �� E � �� EXON �� EXON �� EXON �� )( �� $ �� LQGXFHG �� Figure 8.4: The bulk charge carrier mobility in PTV and P3HT estimated using Eq.8.5 vs the dopant density for several air pressures, in dark. For comparison also the field-effect mobility as a function of induced charge at the semiconductor-insulator interface of a transistor in vacuum, is given for both materials. which can result in a higher bulk mobility. From studies of PTV deposited using a different precursor-route [2], we initially did not find the bulk features in the dark and air as described above. Only after additional thermal treatment, which did not change the field-effect behavior, the bulk feature appeared. As the polymer did not degenerate due to this thermal treatment, we conclude that a morphology change in the bulk of the polymer results in an increased bulk mobility, and therefore in an added bulk contribution to the current. Morphological differences between the semiconductor bulk and the semiconductor/insulator interface will result in different relative contributions of the bulk current and the field-effect current to the total source-drain current. The bulk current increases with time due to the doping with oxygen. For a system with a low mobility in the bulk in combination with a high field-effect mobility, the influence of this bulk current increase on the total transistor current can be neglected for a longer period of time than in a system with a high bulk mobility. Study of the bulk morphological aspects of disordered organic semiconductors, and their influence on the stability of devices is therefore of importance. We remark that reducing the thickness of the semiconductor layer will also significantly reduce the bulk current, which we observed experimentally by preparing semiconductor layers with a thickness in the order of 10 nm. The results in Fig.8.4 demonstrate the power of our experimental technique, which allows the disentanglement of the dopant density and the bulk mobility in the bulk conductivity.

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