

BiographyWeifeng Zhou was born in 1988 in Suzhou, China. He studied Electrical Engineering in Shanghai Jiao Tong University, China, where he received his bachelor's degree in 2011. In 2014 he received his dualmaster degrees from Shanghai Jiao Tong University and Georgia Institute of Technology, US. Starting in 2014 he worked as a research assistant at the Institute of Electromagnetic Theory at RWTH Aachen University, Germany, where he received his doctoral degree (Dr.Ing.) in 2020 for his work on numerical simulations of organic lightemitting diodes. In 2021 he joined the Institute for Microelectronics at TU Wien as a postdoctoral researcher and is currently working on modeling of tunneling current in SiC MOS transistors. 
The Study of Organic LightEmitting Diodes through Master Equations
In our work, a selfconsistent numerical model of the master equations for charge carriers and excitons coupled with the Poisson equation was developed for simulating the electrical and luminescent features of organic lightemitting diodes (OLEDs).
In past decades, numerical modeling of OLEDs has been done through driftdiffusion models and Monte Carlo methods. The driftdiffusion model, however, is fundamentally inappropriate for the treatment of disordered organic materials, which possess carrier relaxation effects and filamentary carrier hopping paths. The Monte Carlo method has a rather low CPU efficiency, which makes a series of simulations with different sets of parameters challenging.
The very first master equation model that can perform simulations of smallsignal quantities, current noise, stationary and timeresolved electroluminescence of OLEDs was demonstrated in our work. It has the advantage of being closer to OLED physics than the driftdiffusion model and of higher CPU efficiency at extreme current levels than the Monte Carlo method. Moreover, a full NewtonRaphson approach ensures a quadratically converging system, which can be seen in Fig. 1.
By including charge carrier generation and recombination in the master equation model, carrier transport under bipolar injection in OLEDs can be calculated. The stationary IV characteristics are calculated according to a RamoShockleytype theorem. Based upon stationary results, the smallsignal analysis is carried out under sinusoidal steadystate conditions at arbitrary biases and frequencies (cf. Fig. 2). The power spectral density of the terminal current, which is a measure of the fluctuation in charge carrier numbers, can be obtained by noise analysis based on the Langevin approach. Moreover, by further extending the master equation model to consider exciton effects, stationary IV characteristics and luminous efficacies of phosphorescent OLEDs doped with various emitter profiles were successfully reproduced (Fig. 3). Strategies for improving the device efficiencies can therefore be tested. Furthermore, the timeresolved current and luminescence properties of the phosphorescent OLEDs were also modeled by transient simulations based on the implicit Euler scheme. Results from the transient simulations are found to be consistent with those from the stationary and smallsignal analyses.
Fig. 1: The rootmeansquare of the change in potential as a function of the number of the Gummel loop (circle) and full Newton iteration (plus) in a simulation of a typical OLED.
Fig. 2: Measured (symbols) and simulated (lines) frequencydependent negative smallsignal susceptance at different temperatures of a polymer LED with a Ca cathode.
Fig. 3: Measured (symbols) and simulated (lines) luminous efficacies of a phosphorescent OLED with different doping concentrations and profiles.