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A modeling of organic field-effect transistors’ (OFETs’) electrical characteristics is presented. This model is based on a one-dimensional (1-D) Poisson’s equation solution that solves the potential profile in the organic semiconducting film. Most importantly, it demonstrates that, due to the common open-surface configuration used in organic transistors, the conduction occurs in the film volume below threshold. This is because the potential at the free surface is not fixed to zero but rather rises also with the gate bias. The tail of carrier concentration at the free surface is therefore significantly modulated by the gate bias, which partially explains the gate-voltage dependent contact resistance. At the same time in the so-called subthreshold region, we observe a clear charge trapping from the difference between C-V and I-V measurements; hence a traps study by numerical simulation is also performed. By combining the analytical modeling and the traps analysis, the questions on the C-V and I-V characteristics are answered. Finally, the combined results obtained with traps fit well the experimental data in both pentacene and bis(triisopropylsilylethynyl)-pentacene OFETs.