The negative mobility: An outcome of the electric field at the hole-injecting metal/organic semiconductor interface that varies as a linear function of the applied bias

The published (room temperature) negative hole mobility, i.e. diminishing hole mobility with an increasing electric field, Ea, of three different organic semiconductors are analyzed in terms of the processes at the hole injecting interface. The charge mobility is described by the product of the effective mobility, μeff, and the algebraic function of the argument defined by the ratio of the electric field at the charge injecting metal/organic interface, Eint, to the externally applied electric field, Ea. It is shown that the negative hole mobility is directly related to the electric field at the hole injecting metal/organic interface, Eint, determined to be a linear function of Ea while the effective mobility, μeff, remains (almost) Ea independent. In particular, for the well-defined P3HT 12 (poly(3-hexylthiophene)) sample in films of (relatively) greater crystallinity a considerably augmented but still negative hole mobility as determined by the current-voltage method has been reported recently. Based upon the above formulation of the charge mobility, it is shown that principally it is the effective mobility, μeff, which is affected by the changing degree of the sample crystallinity while its bias dependence still remains governed by the linear dependence of Eint on Ea that is a characteristic feature of the negative mobility. For the P3HT enhanced crystallinity film the range and the magnitude of the interfacial electric field are changed in a way that the ensuing hole density decrease as a function of Ea then signifies an increased transparency for hole transport within such an organic bulk. It appears that the enhanced crystallization favors conditions for augmentation of the effective hole mobility in conjunction with efficiently increased hole injection at the interface. Consequently, it is the effect occurring at the charge injecting metal/organic junction, described by the algebraic function of the argument Eint/Ea that decisively modulates the Ea dependence of the experimental negative charge mobility. Supported by the presented results this work may then provide a physically viable alternative to otherwise phenomenological descriptions of the negative mobility as described in the literature.