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In this paper, we propose an analytic model for inverted-staggered organic thin-film transistors, and we use the proposed model to investigate the dependence of contact effect on the voltage bias, the film thickness of the organic semiconductor, and the channel length. In our model, the variable-range-hopping transport is adopted for the conduction in the horizontal direction to the semiconductor-insulator interface, and the space-charge-limited conduction is adopted for the conduction in the vertical direction by considering the molecular orientations. Qualitative agreement is obtained between simulation and measurement in the steady-state characteristics. From simulation study, we notice that the contact resistances vary with the source-gate voltage and with the source-drain voltage, the film thickness requires to be optimized to improve the on-current and the linearity in the linear operating regime, and the overlap length between the gate electrode and the source/drain contact needs to be guaranteed for the short-channel devices because it would not be scaled as much as the channel length.