Ž . Synthetic Metals 111–112 2000 359–361 www.elsevier.comrlocatersynmet Modeling of performance characteristics of OLED Igor Yu. Goliney Institute of Materials Research and Engineering, 3 Research Link, Singapore 119260, Singapore Abstract Ž . This report deals with modeling of performance characteristics of the organic light-emitting diodes OLED in the case of tunneling and thermionic injection into emitting layer. The performance characteristics include voltage dependence of current and quantum efficiency of the device. It is shown that the onset of the radiation of the OLED is determined by the unipolar injection of the charge carriers with lower barrier and the slow decrease of the device efficiency at large applied voltage is due to the electric field dependence of the mobility of charge carriers. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Organic light-emitting diodes; Tunneling; Thermionic injection 1. Injection limited electron current In the case when diffusion and thermal activation of the charge carriers, a single light-emitting layer is described with the following equations: d E 4p e sy n y p 1 Ž . Ž. d x ´ d j n syernp 2 Ž. d x j s j q j 3 Ž. n p j s m nE , j s m pE 4 Ž. n n p p where n is the electron density, p is the hole density, j , n j and j are the electron, hole and total currents, respec- p tively, m and m are the electron and hole mobilities, r is n p the recombination rate in the Langivin form, e is the electron charge, and ´ is the dielectric constant of the organic semiconductor. Electron and hole mobilities depend on electric field wx according to the following formula 1 m s m exp ErE . 5 Ž. ( ž / nŽ p . n 0Ž p 0. n 0 p 0 Ž . This system of equation was solved together with the boundary condition on both contacts. The hole injection contact was suggested to be ohmic, i.e., the density of Ž . E-mail address: i-goliney@imre.org.sg I.Yu. Goliney . holes on the electrode was put to be equal to the thermal equilibrium value. Electron injection on the cathode was supposed to be a sum of the thermionic and tunneling injection in the form 2 < < ( j s AT exp w y eeE r´ rkT 6 Ž. ž / th c where A is the Richardson constant and f is the height c of the potential barrier. Tunneling current was chosen in the form j s A E 2 exp yE rE 7 Ž . Ž. tu tu tu where A and E are be determined from WKB approxi- tu tu wx mation with account for image potential 2 . Efficiency dependence on voltage for such system for the case when tunneling is the major mechanism of injec- tion is shown in Fig. 1. Analysis of the curve shows that at low voltage–current in the system is predominantly due to holes as electric field on the cathode is not sufficient to cause injection of the electrons. Electric field in the system is close to zero at the anode and rises approximately proportionally to the square root of the distance from wx anode 3 with correction for the mobility dependence on the electric field. With increasing voltage, as the field at the anode reaches certain value that allows electron tunneling, device begins to emit light. Analysis of the numerical solution shows that the gradual decrease of the efficiency of the device at larger voltages is due to the increased mobility of the charge carriers in the stronger electric field. 0379-6779r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. Ž . PII: S0379-6779 99 00324-0