Comparison of simulations to experiment for a detailed analysis of space-charge-limited transient current measurements in organic semiconductors

Abstract

Space-charge-limited current transients (also referred as time resolved dark injection) is an attractive technique for mobility measurements in low mobility materials, particularly the organic semiconductors. Transients are generally analyzed in terms of the Many-Rakavy theory, which is an approximate analytical solution of the time-dependent drift-diffusion problem after application of a voltage step. In this contribution, we perform full time-dependent drift-diffusion simulation and compare simulated and experimental transients measured on a sample of triaryl-amine based electroactive dendrimer (experimental conditions: $\ensuremath{\mu}\ensuremath{\approx}{10}^{\ensuremath{-}5}$ cm${}^{2}/\text{(Vs)}$, $L=300$ nm, $E<{10}^{5}$ V/cm). We have found that the Many-Rakavy theory is indeed valid for estimating the mobility value, but it fails to predict quantitatively the time-dependent current response. In order to obtain a good agreement in between simulation and experiment, trapping and quasi-ohmic contact models were needed to be taken into account. In the case of the studied electroactive dendrimer, the experimental results were apparently consistent with the constant mobility Many-Rakavy theory, but with this model, a large uncertainty of $20%$ was found for the mobility value. We show that this uncertainty can be significantly reduced to $10%$ if a field-dependent mobility is taken into account in the framework of the extended Gaussian disorder model. Finally, we demonstrate that this fitting procedure between simulated and experimental transient responses also permits to unambiguously provide the values of the contact barrier, the trap concentration, the trap depth in addition to that of the mobility of carriers.