Modeling the Transient Space-Charge-Limited Current Response of Organic Semiconductor Diodes Using the Master Equation Approach

Application of the master equation approach to the space-charge-limited transient situation is considered. The transient responses of thin organic films are simulated by solving the master equation of transport coupled with the Poisson equation. Hopping of the charge carriers between sites is described by the Miller-Abrahams formula. Sites with the Gaussian energetic distribution are localized on a Cartesian lattice. The solutions are calculated using the fully coupled Newton-Raphson method. The details of implementation permitting efficient stationary and transient simulation of unipolar transport are given. This approach gives much better agreement to the experimentally observed space-charge-limited current transient responses than the widely used drift-diffusion model. It is shown that the time position of the transient peak is affected by the contact barrier height. In the case of thin strongly disordered samples, the best observability of the peak is predicted for the intermediate values of the contact barrier.