Charge Injection in Organic Light Emitting Diodes Governed by Interfacial States Juan Bisquert, Germà Garcia-Belmonte, José M. Montero Departament de Ciències Experimentals, Universitat Jaume I, 12071 Castelló, Spain. Henk J. Bolink Institut de Ciència Molecular, Universitat de València, Poligon La Coma s/n, 46980, Paterna, València, Spain ABSTRACT Charge injection in organic light emitting diodes (OLEDs) is studied by impedance spectroscopy on a solution processable polymer based OLED (PLED) using different metallic cathodes. A negative capacitance is observed in organic light-emitting diodes (OLEDs) at low frequencies which can be explained using a detailed kinetic model based on sequential injection through surface states at the metal/organic interface. In this paper the methodology used to derive this model and its application to experimental data is presented. Keywords: Impedance; negative capacitance; OLED.
1. INTRODUCTION Organic light emitting diodes (OLEDs) are becoming increasingly successful as new display technology.[1],[2] However, even though OLED displays have reached commercialization, there is a continuing need for the improvement of the efficiency and stability. One of the important features of an OLED device is the charge injection from the metallic electrodes to the organic semiconductor layer. This feature plays an important role in the optimization of the device efficiency as it has a large influence on the electron/hole balance in the device and hence on the exciton population. It is therefore important to reduce barrier heights for the carrier injection at the interface to realize low drive voltages, which can lead to high efficiencies. The injection of electrons has been extensively studied using a large variety of electron transport materials and metallic contacts, with and without interfacial layers.[3-6] These studies have led to the assumption that interfacial states play an important role in the injection of charge.[7] One phenomena frequently observed when analyzing the characteristics of OLEDs using impedance spectroscopy is a negative capacitance. In this paper we discuss this negative capacitance [8-15] starting from the known properties of the organic/metal interface and emphasizing the common characteristics of very different systems showing negative capacitance. We argue that the negative capacitance is a normal characteristic of an injection process that occurs by sequential hopping provided that the system is far from thermodynamic equilibrium and a kinetic limitation to the increasing occupation of the intermediate state is operative. A simple but detailed kinetic model for carrier injection at the organic/metal interface will be formulated to describe the experimental observations. The accordance of the model predictions with the experimentally observed phenomena when using different OLED configuration is a strong indication that the charge injection in OLED is governed by the interfacial states formed at the metal molecular interface. The paper is constituted as follows, in section 2, first a brief overview is presented of the ac impedance and its difference to the experimentally observed capacitance profiles in OLEDs. Secondly, the analogy of a frequency and voltage dependence capacitance to other different types of devices is mentioned and used to derive a model for the occurrence in OLEDs. In section 3 the kinetic model is presented followed by a number of different simulations (section 4).
Proceedings SPIE Int. Soc. Opt. Eng. 6192, 619210 (2006). Correspondence:
[email protected]
2. GENERAL STRUCTURE OF A NEGATIVE CAPACITANCE DUE TO OCCUPATION OF INTERMEDIATE LEVEL The ac impedance is given by the fraction of modulated voltage/current, Z (ω ) = ∆V (ω ) / ∆I (ω ) , where ω is the angular frequency of the perturbation. The real part of the capacitance is defined from the impedance as ⎧ 1 ⎫ C (ω ) = Re⎨ ⎬ ⎩ iωZ (ω ) ⎭
(1)
The general structure of the capacitance in a two-contact electronic device is[16] C (ω ) = C 0 + ∆C (ω )
(2)
The term C 0 is due to an instantaneous charging in response to a voltage step, associated to the displacement current. This is the geometric capacitance and it is the only one present when the charge resides only in the contacts. When the charge is spread into the device, there exists also an excess of capacitance ∆C (ω ) due to the dynamic processes that govern the recovery of charge towards the contacts.[16, 17] The frequency dependence of the excess capacitance is related to the rapidity of response of such processes, but in general a finite ∆C (ω ) persists up to very low frequencies, much lower than inverse transit times τ t −1 . We focus our attention in this low frequency range. In space-charge-limited currents with a single carrier, an excess capacitance is found which is constant, negative, and lower in magnitude than C 0 . For example if the current is driven by drift transport and the drift velocity is proportional to the electric field then ∆C = −3C 0 / 4 .[18] For other dependencies of drift-velocity, different values of excess capacitance are found.[19] However in all these cases ∆C < C 0 and ∆C (ω 1 the impedance is “capacitive”, with a negative phase angle of impedance and the impedance plot in the first quadrant of the Z ′ versus − Z ′′ polar co-ordinates. When p / z < 1 , the sign of the second component in Eq. (17) changes and the impedance displays the inductive loop, i.e. the low frequency impedance plot in the fourth quadrant of the Z ′ versus − Z ′′ polar plot. Here the low frequency capacitance is negative and the inductive behaviour increases proportionally to the difference between p and z. The dynamic regimes with positive and negative capacitance identified by ac impedance can be understood from the behaviour of the electron exchange between the different states in the model. At low voltages the carrier interchange occurs mainly between metal and interface states. Carriers hop from metal to interface states, but practically all of them hop back to the metal, consequently metal and interface remain at equilibrium ( E F1 ≈ E F 2 ). When E F1 increases the intermediate states get increasingly occupied. The crossover to negative capacitive behaviour (at p = z ) corresponds to the maximum of occupancy of intermediate states. At this point r23 starts to be higher than r21 , i.e. carriers in the intermediate states flow equally to the bulk as well as back to the metal. Obviously the voltage at which this situation takes place should be lower when E2 sets close to the LUMO level. As voltage increases, back currents become negligible with respect to forward currents and r12 approximates r23 , i.e. carriers flow fluently from metal to bulk through the intermediate states so that the intermediate state occupation decreases with increasing forward bias. The induction finishes at the point where the intermediate states are emptied out.
4 MODEL SIMULATIONS In order to explore the effect of the kinetic parameters on the occupancy and the low-frequency limit of the excess capacitance, we have performed a series of simulations keeping the energy level of the intermediate state in equilibrium E 20 = 0.175 eV, the interfacial state density N I = 4×1016 m-2, and the bulk total electron density N B = 1026 m-3 fixed.
The occupancy of the interfacial state results from evaluating the relative position of the energy level E 2 with respect to the quasi Fermi level [Eq. (4)]. The low-frequency capacitance (excess capacitance) can be calculated by regarding the low-frequency limit of the impedance response [Eq. (17) and (1)]. We have assumed for simplicity that the energy level of the intermediate state shifts linearly with the applied potential as E 2 = E 20 + γ 1 ( E F1 − E F 0 ) , where γ 1 (with 0 < γ 1 ≤ 1 ) is a constant parameter that determines whether the energy E 2 accompanies E F1 ( γ 1 ≈ 1 ) or remains closed to E3 ( γ 1 ≈ 0 ). In the same way, the zero and pole of the admittance function are evaluated [Eq. (18) and (19))]. In Fig. 3 the effect of varying the asymmetry factor α 2 in the range between 0.1 and 0.8 is depicted. High α 2 values increase the probability of hopping to the bulk with respect to hopping back to the metal, and consequently inductive behaviour (negative values of the capacitance) sets in at lower potential. It can be observed by comparing Fig. 3a and 3b that the occurrence of the inductive behavior correlates with the intermediate state occupation. For low α 2 values, the induction is not present and the intermediate state reaches full occupancy. The broad potential range covered by the positive capacitance peak in this last case is due to the shift of the surface energy level with the potential at the high γ 1 ≈ 1 value used, and not to a gaussian DOS, which is not included in this simple model.
Fig. 3. Simulations resulting from varying the asymmetry factor α 2 .
Fig. 4. Simulations resulting from varying the asymmetry factor α 1 .
Fig. 5. Simulations resulting from varying kinetic constant k12 .
By examining Fig. 4 one realizes that the effect of the asymmetry factor α 1 is less pronounced. This parameter has an influence on the slope of the J-V characteristic in the range of high potentials. The effect of the kinetic constants k12 and k 23 can be appreciated in Fig. 5 and fig. 6, respectively. It is evident that k12 sets the value reached by the current in the range of high voltages. A close analysis of the evolution of the rates [Eq. (5-8)] with the applied potential shows that the slope change in the J-V curve happens when r23 >> r12 . This entails that the occupancy of the intermediate state falls near zero at potentials marking the onset of net electron injection. This potential marking the onset of the inductive
behaviour shifts towards lower values for slower injection kinetics, as expected. This is also the effect of k 23 (Fig. 6) without the change in the high-voltage current range.
Fig. 6. Simulations resulting from varying kinetic constant k 23 .
Fig.7. Simulations resulting from varying the energy of the LUMO level E3 .
The net effect of the energy of the LUMO level E3 (Fig. 7) is similar to that observed for the kinetic constant k 23 . The onset of the inductive behavior occurs at lower potentials for low work function metals. It should be pointed out that in case of full occupancy the excess capacitance evolution with the applied voltage (CV characteristics) exhibit a Gaussian behavior. This curve scales with the density of intermediate states and reaches values
for half occupancy approximately equal to 0.3 µF cm-2 for N I = 4× 1012 cm -2 , as observed by using Au contacts in the cathode (Fig. 1). This last observation would suggest that even without net electron injection, the filling of intermediate states at the cathode induces positive excess capacitance observable by impedance spectroscopy.
5 CONCLUSION Charging of interfacial states at the cathode of an organic diode with restricted electron injection reveals a large positive excess capacitance which can be fit to a gaussian DOS. When electron injection from these states to the bulk polymer is possible, a negative capacitance is obtained at forward bias caused by depopulation of the interfacial states. Model calculations shows that the decrease of occupancy is associated with a less fast increase of the dc injection current. The negative capacitance observed is therefore an indication that charge injection in OLEDs occurs via interfacial states. This has important implications for the understanding of charge injection in OLEDs and its optimization.
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