Abstract
Drift-diffusion models are widely used to describe the transport and interactions of charge carriers in organic light emitting diode (OLED) devices. Solving these accurately and robustly is important for parameter optimisation and for predicting the effects of device design on the OLED's performance. Such models are generally expressed as systems of ordinary differential equations that are challenging to solve numerically for multiple reasons: the equations are inherently stiff; the discretised model equations are often ill-conditioned; and it can be difficult to impose internal boundary conditions between material layers. Here, we develop a numerical method based on finite element discretisation on a non-uniform mesh. The numerical results show that the solver deals with the stiffness of the problem, but extreme changes in carrier concentration still give rise to numerical difficulties. Later, we discuss approximate (asymptotic) solutions to the OLED model, suggesting the possibility to systematically derive reduced order OLED models.
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