The electric field at hole injecting metal/organic interfaces as a cause for manifestation of exponential bias-dependent mobility

• The Mott–Gurney–Murgatroyed current–voltage model is investigated.
• Electric field at the hole injecting metal/organic contact affects the current.
• Singularity of a hole charge density at the contact is removed.
• Hole mobility depends on the interfacial electric field at the contact.
• The empirical exponential bias dependent mobility of holes is redundant.

It is shown that the well-known empirical exponential bias-dependent mobility is an approximation function of the relevant term emerging in the Mott–Gurney space charge limited current model when the constant non-zero electric field at the hole injecting metal/organic interface Eint is taken into account. The term in question is the product of the bias-independent (but organic layer thickness-dependent) effective mobility coefficient and the algebraic function, f(λ), of the argument λ = Eint/Ea, where Ea is the externally applied electric field. On account of the non-zero interfacial field, Eint, the singularity of the spatial dependence of the hole current density, p(x), is removed. The resulting hole drift current density, j, is tested as a function of Ea against a number of published room temperature hole current j–Ea data sets, all characterized by good ohmic contact at the hole injecting interface. It is shown that the calculated current density provides a very good fit to the measurements within a high range of Ea intervals. Low values of Ea, are investigated analytically under the assumption of hole drift-diffusion. The extremely large internal electric fields at the anode/organic junction indicate drift-diffusion to be an improbable process for the structures investigated. However, a description of hole transport throughout the whole interval of experimental Ea values may be obtained at low values of Ea by an extended Mark–Helfrich drift model with traps occupying the exponentially distributed energy levels, followed by the extended Mott–Gurney model description within the remaining part of the Ea interval. In both models the same (bias-independent) effective mobility coefficient is incorporated into the calculations. The results present evidence that within the framework of the extended Mott–Gurney expression the properly derived term should replace the empirical exponential bias-dependent mobility, making it redundant in the interpretation of j–V data.