IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 10, NO. 1, JANUARY/FEBRUARY 2004 37 Monte Carlo Modeling of the Light Transport in Polymer Light-Emitting Devices on Plastic Substrates Shu-jen Lee, Aldo Badano, and Jerzy Kanicki, Senior Member, IEEE Abstract—A Monte Carlo method for modeling the light transport phenomena in organic polymer light-emitting devices (PLEDs) has been reported previously (Badano and Kanicki, 2001). The advantage of this simulation method is its ability to model bulk absorption, thin-film coatings, and uneven or irregular surfaces by tracking the photon polarization in realistic device structures. We have applied this method to analyze the PLEDs spectral outputs and out-coupling efficiencies. We have established that the calculated out-coupling efficiencies are approximately the same for the red and green PLEDs. Using a description of uneven surfaces with Fresnel analysis, we showed that the nonsmooth interfaces (as modeled by the algorithm for uneven surfaces) between light-emitting polymer and hole transporting layer increase the probabilities of out-coupling and wave-guiding of the internally generated light. In this paper, we use this method to calculate the angular distribution of the PLED light-emission. We found that the Monte Carlo simulated PLED light-emission angular distribution shows better agreement with the experimental data than previously used models relying on standard refraction theory at one interface [2]. Index Terms—Monte Carlo simulation, out-coupling efficiency, plastic substrate, polymer light-emitting devices. I. INTRODUCTION I N GENERAL, it is accepted that the external quantum efficiency of the organic polymer light-emitting devices (PLEDs) is limited by several major losses: charge injection at the contacts (anode and cathode), charge transport within the organic materials, electron and hole radiative recombination, photoluminescent efficiency, and light out-coupling efficiency [3]. Using a standard refraction theory, it was estimated that the photon out-coupling efficiency is about 1/5 of the total inter- nally generated photons [2]. Several methods for improving the light out-coupling efficiency have been used to overcome this limitation set by the light escape cone of the substrate. These methods include introduction of textured surfaces or interfaces [4], [5], usage of ordered microlens arrays or microsphere media [6], [7], usage of reflecting surfaces or distributed Bragg Manuscript received June 9, 2003; revised October 20, 2003. This work was supported by the National Institutes of Health (NIH) grant. S. Lee is with the Macromolecular Science and Engineering and the Solid- State Electronics Laboratory, College of Engineering, University of Michigan, Ann Arbor, MI 48109 USA. A. Badano is with the Division of Imaging and Applied Mathematics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Rockville, MD 20857 USA. J. Kanicki is with the Solid-State Electronics Laboratory, Department of Elec- trical Engineering and Computer Science, and the Macromolecular Science and Engineering, University of Michigan, Ann Arbor, MI 48109 USA and also with the Center for Polymers and Organic Solids, University of California, Santa Bar- bara, CA 93106 USA (e-mail: kanicki@eecs.umich.edu). Digital Object Identifier 10.1109/JSTQE.2004.824073 reflectors [8], [9], and usage of a thin silica aerogel layer [10]. Several models have also been proposed for modeling optical transport in organic light-emitting devices, such as the half-space optical model [11], one-dimensional ray-tracing [5], and quantum mechanical microcavity model [12], [13], [26]. We have used a Monte Carlo approach to analyze the PLED light out-coupling efficiency [1]. This method has the flexibility for modeling events such as absorption, wave-guiding, scat- tering, out-coupling, and trapping in the light-emitting devices. The advantage of the Monte Carlo simulation method is that it takes into account the details of device geometry. The Monte Carlo simulation includes the angular and spectral distributions of the emitted photons, the point-spread function, the specular and diffuse reflection coefficients, and a summary of scattering events statistics. In this paper, we describe the results of Monte Carlo simu- lation used to investigate the factors contributing to PLED an- gular light-emission pattern. Also, the effect of the nonsmooth interfaces on the PLED light out-coupling efficiency is simu- lated. The simulation results are compared with the PLED ex- perimental results. II. METHODS A. Optical Modeling In this paper, we used a Monte Carlo method for the simula- tion of light transport processes in PLEDs [1], [14], [24]. This code, originally developed to study light transport in radiation detectors has been improved in the physics description and in its ability to model light-emissive structures typical of flat-panel display devices. The current version of the code, DETECT-II, is being used to investigate light transport problems in detectors [16], cathode-luminescent display devices [17], and thin-film light-emissive devices. The Monte Carlo method makes use of the generation of photons with random direction according to a distribution function describing the nature of the light-emis- sion. In this analysis, the light source within the organic polymer layer is considered isotropic from a single point situated in the center of the device, Fig. 1. We assumed the light source being described by the photoluminescence (PL) spectra of the light- emitting materials [24]. The photon histories are then followed through a sequence of interactions that includes absorption and Fresnel refraction. At the optical boundaries, an analysis is per- formed depending on the surface type and material properties using Fresnel’s equations and considering the polarization of the incoming photon [1]. When the film thickness is comparable with the photon wavelength, we use modified Fresnel coeffi- cients to describe the optically thin-film effect. The reflection 1077-260X/04$20.00 © 2004 IEEE