An organic-heterojunction diode current equation including random site trap density

The current-voltage characteristics of an organic heterojunction (HJ), where random site trap density at the donor-acceptor (D-A) interface is included, is numerically investigated based on the polaron-pair (PP) model (Phys. Rev. B. 82, 155305 (2010)). To derive the analytic equation, the electric field \(F_{I}\) at the D-A interface, which is included in the field parameter b, is first approximated to estimate the polaron-pair dissociation rate, \( k_{ppd}\). It is then assumed that the quasi-Fermi level \( E_{Fp/n}\) at the donor/acceptor lies in the trap energy level (\( E_{trap}\)) at random sites without a direct dependence on applied bias (\( V_{a}\)), but on a HOMO/LUMO with \( V_{a}\) dependence. As a result, the low diode current (DC) at forward bias is attributed to the \( E_{trap}\), which is lower than the LUMO at acceptors, and is higher than the HOMO at donors. This implies that the pattern of DC is at forward biases depending upon the position of \( E_{trap}\).