The drift-diffusion interpretation of the electron current within the organic semiconductor characterized by the bulk single energy trap level

Abstract

The closed solution for the internal electric field and the total charge density derived in the drift-diffusion approximation for the model of a single layer organic semiconductor structure characterized by the bulk shallow single trap-charge energy level is presented. The solutions for two examples of electric field boundary conditions are tested on room temperature current density-voltage data of the electron conducting aluminum/tris(8-hydroxyquinoline aluminum/calcium structure [W. Brütting et al., Synth. Met. 122, 99 (2001)] for which jexp∝Va3.4, within the interval of bias 0.4 V≤Va≤7. In each case investigated the apparent electron mobility determined at given bias is distributed within a given, finite interval of values. The bias dependence of the logarithm of their lower limit, i.e., their minimum values, is found to be in each case, to a good approximation, proportional to the square root of the applied electric field. On account of the bias dependence as incorporated in the minimum value of the apparent electron mobility the spatial distribution of the organic bulk electric field as well as the total charge density turn out to be bias independent. The first case investigated is based on the boundary condition of zero electric field at the electron injection interface. It is shown that for minimum valued apparent mobilities, the strong but finite accumulation of electrons close to the anode is obtained, which characterize the inverted space charge limited current (SCLC) effect. The second example refers to the internal electric field allowing for self-adjustment of its boundary values. The total electron charge density is than found typically to be of U shape, which may, depending on the parameters, peak at both or at either Alq3 boundary. It is this example in which the proper SCLC effect is consequently predicted. In each of the above two cases, the calculations predict the minimum values of the electron apparent mobility, which substantially exceed the corresponding published measurements. For this reason the effect of the drift term alone is additionally investigated. On the basis of the published empirical electron mobilities and the diffusion term revoked, it is shown that the steady state electron current density within the Al/Alq3 (97 nm)/Ca single layer organic structure may well be pictured within the drift-only interpretation of the charge carriers within the Alq3 organic characterized by the single (shallow) trap energy level. In order to arrive at this result, it is necessary that the nonzero electric field, calculated to exist at the electron injecting Alq3/Ca boundary, is to be appropriately accounted for in the computation.