  Charge transport properties in organic semiconductors are determined by two
kinds of microscopic disorders, namely energetic disorder related to the
distribution of localized states and the spatial disorder related to the
morphological features of the material. From a semi-classical picture, the
charge transport properties are crucially determined by both the carrier
mobility and the electrostatic field distribution in the material. Although the
effect of disorders on carrier mobility has been widely studied, how
electrostatic field distribution is distorted by the presence of disorders and
its effect on charge transport remain unanswered. In this paper, we present a
modified space-charge-limited current (SCLC) model for spatially disordered
organic semiconductors based on the fractional-dimensional electrostatic
framework. We show that the thickness dependence of SCLC is related to the
spatial disorder in organic semiconductors. For trap-free transport, the SCLC
exhibits a modified thickness scaling of $J\propto L^{-3\alpha}$, where the
fractional-dimension parameter $\alpha$ accounts for the spatial disorder in
organic semiconductors. The trap-limited and field-dependent mobility are also
shown to obey an $\alpha$-dependent thickness scaling. The modified SCLC model
shows a good agreement with several experiments on spatially disordered organic
semiconductors. By applying this model to the experimental data, the standard
charge transport parameters can be deduced with better accuracy than by using
existing models.
