We present analytical physics-based compact models for the Schottky barriers at the interfaces between the organic semiconductor and the source and drain contacts in organic thin-film transistors (TFTs) fabricated in the coplanar and the staggered device architecture, and we illustrate the effect of these Schottky barriers on the current-voltage characteristics of the TFTs. The model for the source barrier explicitly takes into account the field-dependent barrier lowering due to image charges. Potential solutions have been derived by applying the Schwarz-Christoffel transformation, leading to expressions for the electric field at the source barrier and for the contact resistance at the source contact. With regard to the drain barrier, a generic compact-modeling scheme based on the current-voltage characteristics of a barrier-less TFT is introduced that can be applied to any compact dc model. Finally, both models are incorporated into an existing charge-based compact dc model and verified against the results of measurements performed on coplanar and staggered organic TFTs with channel lengths ranging from 0.5 μm to 10.5 μm.