Modeling the transition from ohmic to space charge limited current in organic semiconductors

This paper presents a model for charge transport in organic and polymeric diodes that provides a physical explanation of the transition from ohmic to space-charge limited current (SCLC) regimes. The proposed model is based on two established models: a unified model for the injection and transport of charge in organic diodes, including a proper boundary condition for the free charge density at the metal–organic interface; and a temperature and electric-field dependent mobility model. The model reproduces published experimental current–voltage characteristics (for different temperatures and device lengths). The modeling results highlight the importance of the boundary condition at the interface that is used to explain different trends and their transitions in the current–voltage characteristics: linear, quadratic and a higher than quadratic trend at high electric fields. The model uses a finite charge at the interface to eliminate any dependence of the parameters of the mobility model with the length of the organic layer. Importantly, this result differs from others that consider an infinite charge at the interface, and make use of a length-dependent mobility, or other more complex models that incorporate a dependence with the free charge density in order to avoid such a dependence with the device length.