Citation for published version (APA): Woudenbergh, T. V. (2005). Charge injection into organic semiconductors s.n.

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1 University of Groningen Charge injection into organic semiconductors Woudenbergh, Teunis van IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2005 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Woudenbergh, T. V. (2005). Charge injection into organic semiconductors s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 Charge Injection Into Organic Semiconductors T. van Woudenbergh

3 Voor mijn ouders, broers en zussen The work described in this thesis was performed at the Materials Science Center in Groningen, and forms part of the research programme of the Dutch Polymer Institute (DPI), Technology Area Functional Polymer Systems, project 275. Printed by Universal Press - Science Publishers / Veenendaal, The Netherlands. Typeset in Times using L A TEX 2ε. Cover design by Froukje van Woudenbergh. Copyright 2005 Teunis van Woudenbergh.

4 Rijksuniversiteit Groningen Charge Injection Into Organic Semiconductors Proefschrift ter verkrijging van het doctoraat in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, dr. F. Zwarts, in het openbaar te verdedigen op vrijdag 20 mei 2005 om uur door Teunis van Woudenbergh geboren op 9 juli 1977 te Breukelen

5 Promotor: Beoordelingscommissie: Prof. dr. ir. P. W. M. Blom Prof. dr. V. I. Arkhipov Prof. dr. R. Coehoorn Prof. dr. ir. B. van Wees ISBN-nummer:

6 Contents Introduction 1 1 Charge injection Interface barriers Interface barrier formation Contact barrier types Experimental definition of contact barrier types in organic semiconductors Band-bending Barrier lowering Classical injection models Charge transport Gaussian disorder model (GDM) Polarons Hopping based injection model Temperature dependence of the injection current Temperature dependence of the charge injection in organic semiconductors Introduction Experimental Absence of interface states Charge injection from an injection limited electrode Application of the hopping injection model Influence of disorder on the temperature dependence of the charge injection Conclusion Hole injection in a polymer light-emitting diode Introduction Incorporation of the hole injection into the device model Experimental Enhanced hole injection in the presence of electrons Electron traps at hole contact A close look at the origin of the enhanced hole injection Temperature dependence of the enhanced hole injection

7 vi Contents Barrier dependence of the enhanced hole injection Conclusions Electron-enhanced hole injection in blue polyfluorene based polymer LEDs Introduction Experimental Polymer synthesis Results Electro-optical characteristics of a PEDOT:PSS/PFO/Ca LED Regime 1: electron dominated J V characteristics Regime 2: switch-on Regime 3: on-state Discussion Conclusions Charge injection across a polymeric heterojunction Introduction Injection model for organic-organic interfaces Experiment Results Injection-limited transport across the polymeric heterojunction Potential drop across the PPV injecting layer Comparison of the experiment with the OOI model Discussion Influence of carrier concentration Drift-diffusion device model Modified OOI model Application of the heterojunction in a PLED Electro-optical characteristics of double layer PLEDs Reduction of the exciton quenching Conclusions List of publications 87 Summary and conclusions 89 Samenvatting en conclusies 95 Dankwoord 101

8 Introduction Electrical conduction is found in materials that have electrons free to move. The most common examples are the metallic elements. At the other hand, materials with tightly bound electrons are electrically insulating. The difference in conduction is really tremendous, spanning a 30 orders of magnitude [1]. The difference between both classes of materials is found in their electronic properties. All materials consist of interacting elements. The elements are the atoms, and the interactions take place by their outer electrons. This "interaction"tells the electrons to all have a different quantum state (for example a different energy), which is a result of a fundamental law called Pauli exclusion principle. As a consequence, the electrons will fill-up states with different energies, and they will form a band. This is schematically depicted in figure 1(a) for electrons in 1 dimension. Normally, the pieces material of interest are large, a lot of electrons are interacting, and the energy band can be considered as a continuum of states. It is observed from figure 1(a) that electrons with a positive as well as a negative velocity are present. This is allowed, because they represent different quantum states. On average, there is an equal amount of electrons flowing in both directions, and the net transport is zero. When an electric field is applied (e.g. such to exert on all electrons a force in the positive direction), all the electrons will change their velocity. Higher energetic quantum states at the right (positive velocity) get occupied, as is depicted in figure 1(b). Because the energy difference between the states is small compared with the thermal energy, the quantum states with higher energy can be easily occupied. But now there is an unbalance between the amounts of electrons having velocities in a positive and a negative direction, and as a result there is net electron transport. The interaction of the electrons in the presence of the ion cores of the material causes forbidden energy regions, so-called band gaps (figure 1(c)). For metals, the energies of the top most free electrons are somewhere in the middle of the band, and free states are available for electrons at virtually no extra energy, as depicted in figure 1(b). As a result, there is electron transport upon application of an electric field. For insulators, the electrons fill up a whole band, as in figure 1(c), and excitation over the band gap is required to disturb the symmetric distribution of electrons moving in all directions. As a result, when the excitation is not possible (for example the thermal energy is small compared with the band gap energy) no electrons will be able to occupy the states above the band gap, the symmetric distribution is not disturbed and there is no electron transport. This is essentially the origin of the large difference in conduction between a metal, like e.g. copper, and an insulator, like SiO 2. Semi-conducting materials have properties of both. At absolute zero temperature they are perfect insulators, while at room temperature their conduction is poor but detectable. This is

9 2 Introduction (a) (b) (c) Energy Band gap velocity occupied state unoccupied state Figure 1: Energy-velocity relation for a free electron gas (1D). Each state(arrow) corresponds with a certain velocity (length of the arrow) of the electron in that state. (a) equal amount of electrons in states with positive c.q. negative velocity. (b) upon an applied electric field all electrons are accelerated in a certain direction (here:positive). The thick arrows represent the states that contribute to a net positive velocity. (c) The creation/existence of a band gap, due to the presence of the ionic atom cores in the material. In this picture, the electronic states are filled-up until the band gap, and consequently this band-diagram represents an insulator or semiconductor, depending on the size of the band gap. caused by a small band gap, that enables the excitation of a substantial amount of electrons over the band gap to contribute to the transport. The electrical conduction can be strongly enhanced by electrical or chemical doping of the semiconductor. In this case the injection of electrons or addition of dopant atoms causes a high electron concentration in the empty band above the band gap. In semiconducting elements like a transistor this specific property of the semiconductor is employed. Another important feature of the semiconductor is the electrical or optical excitation of charge carriers. By injection of charge carriers from metal contacts, excited charge carrier pairs are created that can give light upon recombination. The reverse process occurs when exciting a charge carrier pair by shining light on the semiconductor, that after dissociation leads to charge carrier flow to the metal contacts. These fundamental processes result in well-known everyday applications, the light emitting diodes (LEDs) and solar cells. Conventionally, inorganic compounds like Silicon (Si) and Germanium (Ge) have the electronic properties that make them semiconductors. They have been used thoroughly in all electronic equipment. The superiority of polymers over inorganic compounds is mainly the ease of processability. Around 1930, the view of the polymer as a chemical entity, previously considered as physical aggregate, emerged [2]. The world of synthetic polymers was born, and they found -and findtheir way in the enormous field of applications from low cost dispensable tools like bags to medical high quality elements like protheses and catheters. However, polymers have been considered insulators, due to their specific electronic properties. Until 1977, when it was discovered accidentally that a thousandfold addition of catalyst resulted in a silvery polymer, that became conducting upon doping with iodine [3]. The reason for the semiconducting behaviour in such polymer is the so-called conjugation,

10 3 E C C C C C C LUMO HOMO gap v Figure 2: Scheme of orbitals (top left) involved in the bonding between carbons in a conjugated backbone (bottom left). Picture taken from [4]. Electronic structure of the conjugated backbone, showing two bands with the level just below the gap being the HOMO and the level just above the gap the LUMO. Picture taken from [5]. the alternation of single and double bond. The carbon atoms in the backbone bind to three adjacent atoms, two carbons of the backbone and one side group, e.g. a hydrogen. The fourth electron finds itself in the perpendicular p z orbital, and the mutual overlap of neighbouring p z electrons causes the formation of π-bands, that consist of the delocalized electrons, figure 2. The delocalized π-electrons fill up a whole band, and consequently an conjugated molecule or polymer is an intrinsic semiconductor. The π-bands in the organic semiconductor are normally called Molecular Orbitals. The filled π-band is called the Highest Occupied Molecular Orbital (HOMO), and the empy π- band is called the Lowest Unoccupied Molecular Orbital (LUMO). Some typical examples organic molecules and conjugated polymers (CPs) are given in figure 3. The reader can convince him/herself that this systems are indeed conjugated (alternation of single and double bond along the molecule or the repeat unit of the CP). The Su-Schrieffer-Heeger (SSH) theory describes the electronic structure of conjugated polymers [6]. It takes account of electron-phonon coupling. Furthermore, a postulation is made in the model that the p z orbitals may not be equally spreaded along the chain, but can be slightly paired. This p z -pairing results in the common representation of the p z electrons in alternating single and double bonds (conjugation, see figure 2). It also gives rise to the semiconducting behaviour of (undoped) CP s -they would have been metallic if the p z orbitals would have been equally spreaded. Another model that explains the electronic structure is the Peierls-Hubbard model, that also takes account of electron-electron Coulombic interaction [7, 8]. The model calculations in effect give rise to a whole spectrum of quasi-particles, both charged (net on-chain charge, e.g. by doping or charge injection) and un-charged. The most important un-charged particle is the soliton, which is a local distortion of the conjugation (figure 4). It is essentially a local reversion of the conjugation, and is localized to several chain atoms. It can only exist in polyacetylene, because this molecule has the interesting property that each carbon atom in the chain is coupled to an identical carbon atom in the chain. Therefore it doesn t matter which two neighbours have their p z orbitals paired. This is a so-called degenerate state. At the other hand, in for example PPV, it matters which carbon atoms in the chain pair together, and a soliton cannot exist. The most important charged particle is the polaron. The polaron essentially is also a local distortion of the conjugation, but now initiated by an extra

11 4 Introduction n trans-polyacetylene (PA) n poly(para-phenylene) (PPP) polythiophene (PT) S n R R' Alkyl substituted poly(p-phenylene vinylene) (R-PPV) n n R R' Alkyl substituted polyfluorene (R-PF) Figure 3: Some basic CPs (conjugated polymers), top. At the bottom, two examples are given of commonly used polymers. The side-chains (R,R ) are added for solubility of the polymer, which makes them easy processable. Normally, the side groups are non-conjugated carbon chains (alkyl chains). Pictures taken from [5]. charge carrier (figure 5) [9]. The polaron is the quasiparticle that in the models for CP s causes the charge transport. In contrast to the charge carriers in the inorganic counterparts, like Si and Ge, the polaron in a CP is not a free charge carrier, but is bound to the CP-crystal. However, in the models that consider CPs as crystals, as described here, the polaron is considered to be delocalized (free) to a certain extent, as is illustrated in figure 5. The binding is caused by the relative long residence time of the charge carrier on a chain atom. Therefore, the nuclei have time to relax to new equilibrium positions due to the presence of the charge carrier. This gives rise to the polaron. Due to the relaxation of the nuclei, the polaron has a lower energy than the LUMO [10]. However, these models did overlook disorder effects. There can be a variation in energy (energetic disorder) between two interacting elements, e.g. two chain atoms or two chains. When this variation is of the same order as the coupling energy, the interaction is disrupted, and the wave-functions of the two sites do not overlap [11]. In this case, the charge carrier has to hop creation of soliton antisoliton pair separation phase A domain wall phase B phase A Figure 4: Formation of a soliton. Picture taken from [5].

12 5 A A electron acceptor positive polaron electron acceptora A positive polaron Figure 5: Formation of polaron, in polyacetylene (above) and poly-(p-phenylene) (below), shown for the case of doping with an electron acceptor. Picture taken from [5]. from one site to another. The interaction between the different CP chains (interchain interaction) is due to van der Waals interaction, which is very weak. Therefore, even a small amount of structral or energetic disorder can completely destroy the electronic overlap of neighbouring CP chains. It is therefore likely that interchain interaction is governed by hopping. But also the conjugation of the chain itself can be non-perfect, e.g. due to strong bending of chains (kinks) or local non-conjugation (e.g. photo-oxidation), that also results in dominance of hopping in the intrachain interaction. For hopping, the charge transport is very poor, in agreement with the low mobilities observed for CP s [12,13]. The activation energy of the charge carrier mobility on temperature has a value of 0.4 to 0.6 ev for a whole range of different polymers and molecules. As a result, the observed transport properties point towards an intrinsic transport property for organic semiconductors [12]. This model was furthermore strongly supported by similar transport properties observed in small conducting molecules dispersed in a non-conducting matrix. Both the semiconducting polymers and these dispersed molecules resembled exactly the same functional dependence on field and temperature [13]. As a consequence, one should think of a semiconducting polymer as a non-perfect conjugated system, the polymer chains being folded and kinked like a spaghetti (figure 6). + Figure 6: Schematic representation of a number of PPV-chains. The black parts are the conjugated parts, separated by parts with broken-up conjugation (white spots). The charge carrier has to hop from one site to another.

13 6 Introduction V 2 1 Ca Al Ca or Ba Active layer (CP) PEDOT:PSS ITO Glass substrate ITO 1 hν Figure 7: Left: device layout of a typical polymer light-emitting diode (PLED). Right: working principle of a PLED. Four important processes have been shown (according to the numbers in the picture):(1) Injection (2) Transport (3) Exciton formation (4) Emission. The last two steps together form the recombination process. The broken-up conjugation causes small regions with intact conjugation to act as transport sites in a surrounding of insulating material. The variation in the extension of the conjugation causes a spreading of the energy levels of the LUMO and HOMO, which will be treated in more detail in paragraph A major breakthrough in the field of organic semiconductors was the discovery of lightemission from an electrically adressed polymer [14]. The ease of processing, combined by pure colors make it an ideal candidate for lighting applications. Especially the display world is highly interested in the semiconducting polymers, as they have also other advantages over liquid crystal displays (e.g. high switching speed, wide viewing angle, pure colors) and cathode ray tube (e.g. low energy consumption, flat screen, light weight), and this stimulated the research of conjugated polymers strongly. A typical polymeric light emitting diode (PLED) (figure 7) consists of a transparent bottom contact, normally indium tin oxide (ITO). On top of this bottom contact, a thin semiconducting polymer layer is deposited. Layer thicknesses of this active layer are typically of the order of 100nm, due to the low mobility. This thin layer can easily be shorted, because the bottom layer (glass/ito) is not completely flat, and spikes of ITO can pierce through the active layer and shorts are created. Therefore normally a layer of poly(3,4- ethylene dioxythiophene) doped with poly(styrene sulfonic acid) (PEDOT:PSS) is put on the the ITO before the semiconducting polymer is deposited. It acts as a flattening layer and beside, although PEDOT:PSS is metallic, it has quite a large resistance, and therefore reduces leakage from shorts. An additional advantage of PEDOT:PSS is its constant work-function, whereas the work-function of ITO tends to decrease with time. On top of the semiconducting polymer, Ca or Ba is deposited. A cover layer of Al is commonly deposited consecutively to protect the reactive Ca or Ba against oxygen. Due to the low mobility, the current density in the device is rather low. As a consequence the light output per area (light intensity) is low, and relatively large areas are

14 7 required to get a reasonable light output for lighting applications. This in turn also means that a large area display like a backlight for a LCD or a computer screen can be easily made from CPs, as its light intensity naturally fits the conditions for this type of applications (100 Cd/m 2 ). In our lab, we use "display"areas ranging from 3 3 mm 2 to 1 1 cm 2. The device operation is depicted schematically in figure 7. The ITO or ITO/PEDOT:PSS bottom contact injects holes in (extract electrons from) the HOMO, whereas the Ca or Ba top contact injects electrons from the LUMO. The charge carriers move towards each other, and due to their Coulomb interaction they attract each other in their vicinity, which can result in formation of a bound electron-hole pair (exciton), followed by emission of light. The last two processes are commonly called recombination. The energy of the exciton is emitted as a photon. For a small bandgap polymer ( 2 ev) the emitted photon is observed as red light. A typical example is poly(2-methoxy- 5-(3,7 -dimethyloctyloxy)-p-phenylene vinylene) (OC 1 C 10 -PPV) (see figure 8). For a large bandgap polymer ( 3 ev) the emitted photon is observed as blue light. A typical example is poly(9,9-dioctylfluorene, 2,7-diyl) (PFO) (figure 8). Thus by tuning the electronic properties of the polymer, especially the choice of the backbone, the color of the emitted light can be chosen. Since the discovery of polymeric light emitting diodes (PLEDs), it has directly been recognized [15] that charge injection is an important process with regard to their device performance. The charge injection process may be hindered by the presence of an interface barrier at either the electron or hole contact. Such interface barriers result in an unbalanced charge carrier injection, which gives rise to an excess of one carrier type and consequently in a large decrease of the conversion efficiency. For a small energy barrier the contact can facilitate any required injection rate, and the performance of the device is limited by the properties of the polymer itself (bulk-limited). The metallic contacts that are available from nature, like Calcium (Ca), Barium (Ba), Aluminum (Al), Silver(Ag), and Gold(Au) have a limited range of work-functions, varying from φ M 3 ev for Ca and Ba to φ M 5 ev for Au [16]. Also ITO and PEDOT:PSS have Red LED Blue LED Bulk-limited Injection-limited? O Ca LUMO H3CO n HOMO ITO n Ca ITO + + Figure 8: Relevance of charge injection: two situations are shown, a red (OC 1 C 10 -PPV) and a blue(pfo) light-emitting polymer are shown. Also shown are the HOMO and LUMO of the PPV (Ref. [16]) and PFO (Refs. [17, 18]). The polymers are both sandwiched between an ITO ( 5eV) and a Ca( 3eV) contact, and the processes of charge injection and recombination are shown. The red PLED is bulk limited [19], whereas it is expected that the blue PLED is injection limited by the large hole barrier.

15 8 Introduction a work-function of 5 ev. PEDOT:PSS has the advantage over ITO that it maintains this high work-function, whereas the ITO work-function is slowly reducing with time. Consequently, with the range of available contacts, for small band gap polymers like (OC 1 C 10 -PPV) (see figure 8) the interface energy barrier for both electrons and holes is small, and injection does not limit the device performance [19]. However, a large band gap polymer like the blue light-emitting poly(9,9-dioctylfluorene, 2,7-diyl) (PFO) has a highest occupied molecular orbital (HOMO) of ev (Refs. [17, 18]), and consequently the injection into the HOMO is expected to severely limit the performance (figure 8). The understanding of the charge injection mechanism in organic semiconductors and the consequences for the performance of light-emitting diodes are the motivation for the work presented in this thesis. In order to understand the charge injection first in the next chapter a number of models for charge injection and transport will be presented. In the subsequent chapters the experimental results are written down. The experimental investigation of the injection mechanism is condensed in chapter 2. Chapter 3 deals with the incorporation of an injection-limited contact in a PLED device. It demonstrates the importance of understanding the charge injection for applications. Chapter 4 is devoted to device performance of a blue light emitting diode. Then in chapter 5 the charge transport across a polymer/polymer heterojunction with a large interface energy barrier is investigated. A useful application of such a injection limited polymer/polymer heterojunction is employed at the end of chapter 5.

16 Chapter 1 Charge injection In this chapter we will describe the basic definitions of an interface barrier, and the injection current from a metal contact. For semiconductors with a low mobility, like the CPs, the transport away from the contact is crucial to describe the injection current. Therefore, also the transport in a CP is described. It will turn out that in commonly used CPs like OC 1 C 10 -PPV charge is transported by hopping in an energetically disordered potential landscape. This has profound consequences for the charge injection, and a newly developed model for injection in CPs is introduced at the end of the chapter. 1.1 Interface barriers Interface barrier formation The basic definition of an interface energy barrier is given by the energy offset between the band-edge or molecular orbital in the semiconductor and the Fermi-level of the metal. In figure 1.1 the formation of a metal-semiconductor contact is shown for an intrinsic semiconductor with a defect free interface. The representation of the barrier formation is taken from Ref. [20] and has been modified to apply to an intrinsic semiconductor. In Ref. [20] the interface barrier formation is explained for a doped semiconductor, but the CP s we use for PLEDs are not (only unintenionally) doped. It will be explained in paragraph what the main difference is between the well-known doped semiconductor and the undoped semiconductor that is used here (figures 1.1, 1.2, and 1.3). Before contact (left picture in figure 1.1), the two systems are in their original state. The semiconductor has a conduction band level E C at χ from the vacuum level V L. The Fermi-level E F S is located halfway the band gap. The work-function of the semiconductor φ S is defined as the distance of the semiconductor Fermi-level from the vacuum level, φ S = V L E F S. The energy difference between the valence band level E V and the conduction band energy E C is the band gap energy E g, E V = E C E g. The work-function of the metal amounts to φ M, and equals the distance of the metal Fermi-level E F to the vacuum level, φ M = V L E F. It should be noted that energies are represented in ev throughout this thesis. Therefore, energies are written like electrostatic potentials E = φ, instead of the normal

17 Φ Φ Φ Φ Φ δ 10 Charge injection conversion E = qφ. Now the formation of an interface barrier will be described. We will focus on the energy off-set between the metal Fermi-level and the conduction band level. Upon contact, the Fermi levels of the metal and semiconductor line out (all three next pictures in figure 1.1). When the work-function of the metal is smaller (φ M < φ S ), electrons from the metal will flow into the semiconductor to shift its Fermi-level (accumulation). When the work-function of the metal is larger (φ M > φ S ), electrons will flow from the semiconductor into the metal, lowering the semiconductor Fermi-level (depletion). The latter is the case in figure 1.1. When the metal and semiconductor are contacted, but there is still a gap between both surfaces (e.g. by making contact between the metal and the semiconductor at some other surface), there will be an electric field in this gap due to the exchanged charge. The conduction band E C is always χ below the vacuum level, where χ is the electron affinity. Upon closing the gap δ between the metal and semiconductor, the vacuum level at both sides of the gap lines out, and consequently, E C E F = φ M χ upon intimate contact (right picture). The energy barrier φ b is the energy a charge carrier needs to go from the Fermi-level of the metal, E F into the conduction level of the semiconductor E C, and consequently φ b = E C E F = φ M χ. χvl gap E C S V L V L V L M E F E g E FS E v b - + E C E F E v b - ++ E C E F E v b W E C E F E v Figure 1.1: Formation of an interface energy barrier between a metal contact and a semiconductor (taken from Ref. [20] and modified for the case of an intrinsic semiconductor). The picture shows the formation of a contact barrier for the case of a neat, defect free contact. The energy barrier is given by φ b = φ M χ. It is also observed from figure 1.1 that far from the contact, the semiconductor tries to establish the original state, as it was before contact. The distance required to bend the conduction or valence band towards its original distance from the Fermi-level is called the depletion/accumulation width W. The width of the depletion zone will be treated in more detail in paragraph Contact barrier types In figure 1.2 three fundamentally different contacts are described for an intrinsic semiconductor: (1) when the contact work-function is larger than the semiconductor work-function (φ M > φ S ),

18 Φ Φ Φ Φ Φ 1.1 Interface barriers 11 the electrons are depleted from the semiconductor, as has been described in paragraph Due to the electron-depletion, the contact region cannot supply enough charge carriers to the bulk of the semiconductor, and the contact is called blocking or injection-limited for electrons. At the same time, the contact region contains an excess of holes (figure 1.2a). As a result, the contact region can supply any charge flow demanded by the bulk of the semiconductor, and the contact is called Ohmic or bulk-limited for holes. (2) When φ M = φ S (figure 1.2b), the Fermi-levels of the contact and the semiconductor are already lined out, and no charge redistribution is required upon contact. This is called a neutral contact: both the electron and hole contact have an interfacial concentration of charge equal to their intrinsic free carrier concentration. (3) When the contact work-function is smaller than the semiconductor work-function (φ M < φ S, figure 1.2c), the situation is reversed from (1): the electrons are accumulated in the semiconductor, and the electron contact is Ohmic. The hole contact is now injection limited. V L χvl V L b E C E F M b s E C E F b E C E F E v (1) (2) (3) E v + E v Figure 1.2: Different barrier types for an intrinsic semiconductor. Situation (1), φ M > φ S, corresponds with an injection limited electron contact and an Ohmic hole contact. Situation (2) shows a neutral contact (φ M = φ S ) and situation (3) is the reverse of situation (1), φ M < φ S ; the hole contact is injection limited, the electron contact is Ohmic. The energy barrier φ b, in this pictures shown for electrons is for each situation given by φ b = φ M χ Experimental definition of contact barrier types in organic semiconductors The maximum current in an organic semiconductor is obtained when the excess charge is maximal, that is determined by the electrostatics. This is called space charge limited current (SCLC). For a field-independent mobility, the SCLC is directly given by the Mott-Gurney equation J SCLC = 9 8 εµv 2 L 3 (1.1) For conjugated polymers like OC 1 C 10 -PPV the mobility is field dependent, as is explained in paragraph 1.3.1, and the maximum current J SCLC can be found from a numerical calculation.

19 12 Charge injection The experimental observation of SCLC results in the statement that the contact is Ohmic. In the case of SCLC the voltage and thickness dependence must follow equation 1.1, (or the numerical calculation in case of a field-dependent mobility). When the mobility can be determined independently, the SCLC can be directly calculated without any free parameters. The mobility can be measured from transient techniques, that measure the transit time of charge carriers. When the current measured through the conjugated polymer is smaller than this maximum current it is said that the current is injection-limited. One can define an efficiency factor, η, which represents the ratio of the measured current J from a particular contact, and the maximum current, η = J/J SCLC. For an Ohmic contact, η = 1, and for an injection-limited contact, η < 1. The experimental definition of contact barrier type, Ohmic contact for SCLC and injectionlimited contact for ILC is different from the definitions of the Ohmic, neutral and injectionlimited contacts from the last paragraph (figure 1.2). It is estimated from theoretical calculations that for a contact barrier of φ b 0.3 ev the current is space charge limited at room temperature [21] and consequently the contact is Ohmic (both from the fundamental and the experimental definition). When φ b 0.3 ev, the current that the contact can supply is smaller than SCLC (at room temperature) and the current is limited by injection. As a result, from the experimental definition, the contact is called injection-limited, irrespective of the fundamental definition (figure 1.2), that can be either Ohmic, neutral or injection-limited, depending on φ M φ S. For an injection-limited current (ILC), the amount of injected charge is too small to give a significant bending of the electrostatic potential. Therefore, the electric field in injection-limited devices is constant, and the required voltage V for a value of the ILC scales with the thickness, J ILC = J ( ) V L, that is different from SCLC. For intermediate injection barriers, φb 0.3 ev at room temperature, there is some built-up of charge in the device, but not enough to reach the SCLC. The dependence of current on voltage and thickness will be in between that of SCLC and ILC. In the next paragraph an example is given of the band-bending of an injection limited device to get some feeling for the relative small influence of space charge when considerable injection barriers are present Band-bending The band-diagrams in figure 1.1 and figure 1.2 are sketched for an intrinsic semiconductor. However, metal contacts on n- or p-type semiconductors are more common in applications. For such n- or p-type doped semiconductors, it is known that the depletion width is small compared with the bulk of the semiconductor. The depletion width W in that case depends on the doping concentration, and ranges from 10 nm for heavily doped semiconductors (N D = m 3 ), and 100 nm for moderately doped semiconductors (N D = m 3 ), to > 1µm for lightly doped semiconductors (N D < m 3 ). A difference between the above described n-type semiconductor and the organic semiconductor is that the latter is not (only unintentionally) doped. As a consequence, the band-bending at the contact is not caused by the dopant, but by the carriers that are injected in or extracted from the intrinsic semiconductor, as has been shown in figure 1.1. In contrast with a doped semiconductor, the charge that can be injected in or extracted from an intrinsic semiconductor decreases very rapidly when the distance E C E F or E F E V increases. As a result, the deple-

20 1.1 Interface barriers 13 tion/accumulation charge is neglibly small and the depletion/accumulation width is very large. As a result, in practice, the whole semiconductor is depleted or accumulated (depending on the metal work-functions). This has been explicitly calculated for a sandwich device, consisting of a bottom and top metal contact with arbitrary work-functions, and a CP layer in between. For this calculation, the drift-diffusion equation for electrons is used in thermal equilibrium. In thermal equilibrium, the quasi-fermi level E F n of electrons (and also that of the holes) is constant, and the electron (and hole) current is zero: J n = 0 = qµ n nf + qd n dn dx The electric field F is found from the net charge carrier concentration: (1.2) ε df e dx = p n, (1.3) where the hole concentration p is set to zero (unipolar or electron-only device). The electrostatic potential φ is given by dφ = F. (1.4) dx We focus here on the conduction band and therefore we have chosen the value of the electrostatic potential to equal energy of the conduction band with respect to the Fermi-level of the system: φ = E C E F. For a thickness of the semiconductor larger than the depletion width, L > W, and a unipolar device (hole concentration is neglible), the relation between electrostatic potential and distance (and thus the band-bending) can be found analytically [22]. The boundary conditions are the carrier concentration at the contact, ( n 0 = N C exp φ ) b, (1.5) kt and the zero-field (straight band) at φ = φ S χ: dφ dx = 0. (1.6) φ=φs χ The parameter N C in equation 1.5 is the effective site density, which value depends on the transport site concentration, N sites, and on their distribution in energy (g(e)). Using equations results in the expression for distance as function of potential: ( ) (1/2) [ 2kT ε x = {sin 1 exp en C ( φ φs + χ 2kT )] [ ( sin 1 φb φ S + χ exp 2kT ( φs χ exp 2kT )]} The depletion width W is easily found by using φ = φ S χ in equation 1.7. For a CP like OC 1 C 10 -PPV, φ S χ 1.2 ev, and the depletion width amounts to W 10 m! ). (1.7)

21 14 Charge injection Obviously, device thicknesses are much smaller than this depletion width (L 100 nm). Therefore we have calculated the band bending numerically. The numerical program is based on a so-called shooting algorithm : at the first grid point, the left contact, all parameters are known, except the electric field F [0], which is guessed. The Fermi-level of the system, E F is set to zero. The electrostatic potential is set equal to the conduction band, φ[0] = E C [0] E F, the electron concentration is found by entering the barrier of the left contact, φ b1, in equation 1.5. The electron concentration in the next grid point i is calculated by discretization of equation 1.2. Once the electron concentration in point i is known, one can calculate the electric field and electrostatic potential in point i, by equations 1.3 and 1.4. This is repeated until one arrives at the right contact, and the second boundary condition, the electron concentration at the right contact, is checked (φ b2 is the barrier of the right contact): ( n[i max ] = N C exp φ ) b2. (1.8) kt This is repeated with improved guesses of F [0] until the second boundary condition is fulfilled. In figure 1.3 the calculated band-bending is shown for a CP with a E g = 2 ev band gap and a device thickness of L = 240 nm, at room temperature. Two situations are shown, a device with contact barriers of φ b1 = 0.1 ev and φ b2 = 0.5 ev for the bottom and top metal contact, and a device with contact barriers φ b1 = 0.5 ev and φ b2 = 0.7 ev. In both cases, the metal contacts have a Fermi-level above that of the semiconductor and will inject charges into the semiconductor to shift its Fermi-level, resulting in electron accumulation zones at the contact. The largest effect, the tilting of the band, is caused by the Fermi-alignment between the two metals, which bends the semiconductor potential in between them uniformly. This is (a) 0.5 (b) 0.7 φ (ev) ev E C E C E FS 1 ev 0.5 ev φ (ev) E C E C 0.5 ev 1 ev E FS 0.7 ev x (nm) x (nm) Figure 1.3: Band diagram of metal/organic-semiconductor/metal structure. φ = 0 ev corresponds with the Fermi-level of the system. Two devices are shown: (a) The band offset between metal I and the semiconductor is 0.1 ev, for metal II it is 0.5 ev; (b) The band offset between metal I and the semiconductor is 0.5 ev, for metal II it is 0.7 ev. The solid lines show the numerically calculated band-bending and the dashed lines show the analytically calculated (equation 1.7, Ref. [22]) band-bending for (a) a 0.1 ev barrier and (b) a 0.5 ev barrier.

22 1.1 Interface barriers 15 called the built-in field. It is an important parameter for devices with a different bottom and top contact, and as a rule of a thumb, the built-in voltage V bi = φ M1 φ M2. Furthermore, close to the 0.1 ev contact the band-bending due to excess electrons from the metal is still quite strong. It demonstrates the intention of the semiconductor to re-establish the original situation away from the contact, with E C E F = 1.0 ev. However, this situation is by far not reached, because the device length is too small. The depletion width for this semiconductor amounts to W 1 m (!). The numerical program is compared with the analytic expression for the limit L > W (equation 1.7). It shows that close to the 0.1 ev contact the band-bending in the device, although L << W, is in agreement with the analytic expression, i.e. the band-bending is dominated by the accumulated electrons. Further away from the left contact the band-bending (or better said, band tilt) in the device is stronger than expected from the analytical expression, due to the presence of the built-in field. Figure 1.3b shows the device with two large contact barriers. It is demonstrated that the band-bending in this device is completely dominated by the contacts. This can be interpreted as follows: the charge concentration in the semiconductor is too low to cause any reasonable bandbending. The only charge that is of importance is present at the metal-semiconductor interface, and causes a constant electric field inside the semiconductor (the built-in field). As a result, for such a device space charge effects are negligible and it will be observed from experiment that the device is injection-limited Barrier lowering An electron leaving a metal will induce a positive charge density at the metal surface to screen its electrostatic field. This screening effect can be represented by an image charge of the electron at the same distance in the metal. The force between the electron and the image charge is F = e2 4π(2x) 2 ε = e2 16πεx 2 (1.9) where x is the distance electron-metal interface, and ε is the dielectric permeability of the semiconductor, ε = ε 0 ε r. As a result, apart from the work done by the electron in the electric field, U = ef x, there is an extra amount of work done U(x) = e2 F dx = x 16πεx. The resulting potential energy of the electron (or hole for the case of hole injection) as measured from the metal Fermi-level is (in ev): U(x) e = φ b e xf (1.10) 16πεx The interplay between electrostatic potential xf and image potential causes a maximum electrostatic potential height given by U max ef = φ b φ = φ b (1.11) e 4πε Equation 1.11 shows that at electric field F, the energy barrier a charge carrier feels is lower than the original φ b. This is called the Schottky effect or also image force or barrier lowering [23,24]. In figure 1.4 the two components of the electrostatic potential, the band-tilt by the applied field

23 16 Charge injection and the image force potential, together with their sum (equation 1.10) is shown. Also shown is the lowering of the barrier, φ 0.19 ev. 1.0 Potential energy (ev) 0.5 B B U(x) F = 5 x 10 7 V/m Fermi- Level Metal Semiconductor 15 X (nm) Figure 1.4: Band diagram at a metal/(organic-)semiconductor contact. The energy barrier between the metal and the semiconductor is φ b = 0.95 ev. Zero potential energy corresponds with the Fermi-level of the metal. The straight solid line shows the band-tilt due to the external field (F = V/m), the dashed line shows the image force potential, and the thick solid line shows the sum of the two, which is the actual potential landscape in the semiconductor (equation 1.10). The barrier lowering φ is also depicted, which in this case amounts to φ 0.19 ev. 1.2 Classical injection models The classical injection mechanism used to describe charge injection is thermionic emission, which results in a current density J given by [23] ( J = A T 2 exp (φ ) b φ), (1.12) kt with A the effective Richardson constant, T the temperature and φ b the effective barrier, due to the offset in energy levels at the interface. Equation 1.12 is based on the relation between kinetic energy and velocity of delocalized charge carriers. Furthermore, at sufficient high fields, tunneling from the contact will become important due to strong band bending. It has been pointed out that the thermionic emission model is not applicable to low mobility semiconductors (µ 10 3 m 2 /Vs) [25]. For low mobility semiconductors, backflow will occur due to the large concentration of charge carriers accumulated at the interface. In fact, for low mobility semiconductors the velocity of the charge carriers in the bulk of the semiconductor is smaller than that in the interfacial area [23], which result in a stack of carriers at the interface, as depicted in figure 1.5. The velocity of charge carriers in the bulk of the material is proportional to the

24 1.3 Charge transport 17 (a) Thermionic emission φ B (b) Diffusion limited thermionic emission φ B J φb / kt φb / kt ( ) e J µ T high mobility low mobility e Figure 1.5: Schematic representation of two important classical injection models (a) for high mobility semiconductors, injected charge carriers will easily flow away from the interface, and the injection current is entirely determined by the injection rate, j exp( φ b /kt ) (thermionic emission) (b) for low mobility semiconductors, the injection rate is faster than the current flow into the semiconductor, and consequently the injection current is the product of the number of injected carriers and the mobility in the bulk of the semiconductor, j µ(t ) exp( φ b /kt ) (diffusion-limited thermionic emission). mobility. As a result, the diffusion-limited injection current is predicted to follow [25] ( J = qn V µ(t )F exp (φ ) b φ), (1.13) kt with N V the effective density of states in the semiconductor, and F the applied electric field. The same result has also been obtained in the case of insulators at low or moderate fields, where space-charge effects are unimportant [26]. It should be noted that in both thermionic emission (high mobility) and diffusion limited injection (low mobility), the barrier height φ b plays a dominant role in the injection limited current (ILC). For conjugated polymers like poly(p-phenylene vinylene) (PPV) the hole mobility typically amounts to µ = cm 2 /Vs [13], and the injection process is expected to be completely diffusion limited. In order to explain the ILC in PPV a recombination current due to backflow of charge carriers has been taken into account [27]. This injection model has been extended by considering surface recombination to be a field enhanced process, which is in fact a re-derivation of equation 1.13, using a different approach [28]. Conclusively, for conjugated polymers as PPV it is expected (equation 1.13, Refs. [25,27,28]) that the temperature dependence (T-dependence) of the ILC is proportional to µ(t )exp( φ b /kt ). As a result, it is important to obtain knowledge about the field- and T-dependence of the mobility in PPV. 1.3 Charge transport Gaussian disorder model (GDM) Abundant research has been performed on the mobility parameters of derivatives of PPV, like OC 1 C 10 -PPV and poly(2-methoxy-5-(2 -ethylhexyloxy)-p-phenylene vinylene) (MEH-PPV) which

25 18 Charge injection is a similar polymer with slightly different side groups. For these PPV-derivatives, people have especially focused on the hole mobility [15, 29 31]. For investigation of the hole mobility, devices have been fabricated with an electron blocking top contact. In this case only holes from the bottom contact will be injected, and such a structure is normally named a hole only device (inset of figure 1.6). A measurement of the hole current in OC 1 C 10 -PPV gives a quadratic relation between current and voltage at low biases, indicative of space charge limited current [29]. At higher biases the current starts to increase more rapidly with voltage, implying an increase of the mobility. Varying the temperature, it is found that the mobility is also strongly T-dependent, and as a result, a phenomenological relationship for the hole mobility µ p of PPV is found [31]: µ p (F, T ) = µ 0 (T ) exp(α F ) (1.14) with µ 0 (T ) = µ exp( kt ) (1.15) and α = B( 1 kt 1 kt 0 ) (1.16) with the Boltzmann constant k = ev/k. The current-density for a field-dependent mobility can be calculated numerically taking account of equations 1.2 and 1.3 (neglecting diffusion). In figure 1.6a the current density-voltage (J V ) characteristics of a hole-only of OC 1 C 10 -PPV are shown, together with the calculated characteristics. In figure 1.6b the T- dependence of the zero-field mobility µ 0 is shown. For the calculated µ 0 (T ), an activation energy = 0.48 ev, and a mobility prefactor µ = m 2 /Vs have been found. Anal- (a) 10 3 (b) J (A/m 2 ) ITO PPV Au V (V) T=299 K T=272 K T=246 K T=221 K T=195 K T=168 K µ (m 2 /Vs) /T (1/K) Figure 1.6: (a) Current density-voltage (J V ) characteristics of a hole-only of OC 1 C 10 -PPV (plotted as symbols) together with the calculated current density (solid line). The only variable in the calculation is the mobility, from which the zero field mobility is plotted in figure (b) as a function of reciprocal temperature (1/T ). The solid line is the calculated zero-field mobility from equation 1.15 with an activation energy = 0.5 ev.