Line shapes in the current-voltage characteristics of single layer metal/organic semiconductor structures as response to the electric field at the charge injecting interface

By incorporating a non-zero electric field at the charge injecting metal/organic interface, Eint, into the Mark-Helfrich model of charge traps exponentially distributed in energy, a general expression for the current density-voltage dependence of single layer metal/organic structures is presented. It is expressed in terms of the solutions of the non-linear algebraic equation relating Eint to the externally applied electric field, Ea. As a result, the finite and continuous spatial distribution of the free and trap charge density at the boundaries and within the organic layer is obtained. Arguments are presented that for an interfacial field directly proportional to the applied electric field, Eint = λ Ea, with λ bounded between 0.1 ≤ λ ≤ 0.99, the λ dependent current density follows an identical bias and organic thickness prediction as the original Mark-Helfrich model, but with a substantially different factor of proportionality. The resulting current density is characterized by a negligible space charge limited current (SCLC) effect. The bias independent Eint at the charge-injecting interface leads to a concave line shape (when viewed through the current axis) in the current-voltage diagram. The intense (but always) finite peak of the free charge density at this interface occurs only for Eint ≪ Ea, thus leading to the strong SCLC effect. These predictions are tested on some published experimental data and good agreement is observed. The combination of an interfacial electric field linearly dependent upon the applied bias up to a given value and constant thereafter results in at least two distinct line slopes in the log j − log Ea plane.