Modeling of Exciplex Recombination in Organic Bilayer Structures
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Modeling of Exciplex Recombination in Organic Bilayer Structures Feilong Liu,1 P. Paul Ruden,1,2 Ian H. Campbell,2 and Darryl L. Smith1,2 1 University of Minnesota, Minneapolis, MN 55455, U.S.A. 2 Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A. ABSTRACT The effect of exciplex dynamics on the device characteristics of organic semiconductor bilayer structures is explored. Exciplex formation, dissociation, and relaxation to the ground state are incorporated into a physics-based device model. The model is applied to both organic light emitting diodes and photovoltaic cells. In the examples, C60 and tetracene parameters are used for the electron and hole transport layers, respectively. INTRODUCTION Exciplex dynamics are important microscopic processes at interfaces between two different organic materials.1,2 These processes play a key role in organic opto-electronics where bilayer structures are typically employed.3-5 In organic light emitting diodes (OLEDs), exciplex emission has been observed at the interface between the electron transport layer (ETL) and the hole transport layer (HTL).6-8 In organic photovoltaic cells (OPCs), exciplex formation and relaxation to the ground state impact the device efficiency.9-11 In this paper, we explore the exciplex-related processes and their consequences for both OLED and OPC applications. C60 and tetracene form a representative pair of materials for the ETL/HTL bilayer structure. MODEL FORMULATION Before discussing the exciplex dynamics, it is necessary to briefly introduce the microscopic processes in the bulk region. An electron and a hole at the same molecule can form a correlated pair due to their mutual Coulomb attraction, which is called an exciton. The rate of this process is proportional to both the electron density n and the hole density p. As the mobilities in organic semiconductors are low, the rate constant γL is assumed to be of Langevin form: γL = e(µn+ µp)/ε,12 where e is the magnitude of the electron charge, and ε is the dielectric constant. The process is limited by the transport of electrons and holes to the particular molecule where the exciton is formed rather than by the local exciton formation rate. Because of its high binding energy, exciton dissociation in the bulk is extremely rare. At the interface, a similar process can occur with the formation of an exciplex, where the electron resides on one molecule in the electron transport layer and the hole resides on an adjacent molecule in the hole transport layer. The exciplex formation rate can be written in an analogous form: γexpn-ap+a(1-Nexp(2)/N(2)), where γexp is the exciplex formation coefficient , n-a (p+a) are the electron (hole) density in the layer one molecule size, a , from the nominal interface. Nexp(2) is the exciplex (sheet) density, and N(2) is the interface molecular density. Here
we have assumed that each molecule pair at the interface can accommodate only one exciplex, therefore the formation rate is proportional to the fraction of unoccupied molecules, 1-Nexp(2)/N(2). Another
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