Thermal and non-thermal equilibrium processes of charge extraction in accumulated charge measurement (ACM)

Abstract

Accumulated charge measurement (ACM) is an experimental technique for studying the charge-injection and extraction processes in a condenser comprising the following: metal electrode 1, insulator (INS), organic semiconductor (OS), and metal electrode 2 (M2). In this method, the change in the accumulated charge (Qacc) is estimated by integrating the displacement current when the applied voltage changes from Voff to Voff + Va. Voff is the constant offset voltage and Va is the alternating voltage that is changed step-by-step; Qacc is expressed as a function Va. From the observed dataset of Qacc and Va, ΔQ and VOS are derived, where ΔQ is the degree of charge injection and VOS is the voltage drop within the OS layer caused by Va. The injection barrier at the OS/M2 interface can be evaluated from the plot of ΔQ as a function of VOS. In this study, two theoretical models for analyzing ACM data are developed using the Poisson–Boltzmann equation. On the one hand, the thermal equilibrium (TE) model reflects the TE process, in which charge evacuation simultaneously occurs at the INS/OS and OS/M2 boundaries. On the other hand, the non-thermal equilibrium (NTE) model assumes a two-step charge evacuation process at the interfaces: charge evacuation at the OS/M2 boundary occurs in the first step, followed by charge evacuation at the INS/OS boundary in the second step. The ACM data for condensers constituting pentacene and H2Pc are well reproduced by the TE and NTE models, respectively. The different behaviors of the two condensers can be attributed to the difference in their diffusion constants.