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Efforts to improve organic field-effect transistors (OFETs) have so far concentrated mainly on their field-effect mobility, but another important parameter is the on–off ratio, i.e., the ratio of the saturation current at maximum absolute gate voltage (Vg) to that at zero Vg. It is shown how an understanding of the so-called “ohmic” current, which reduces this ratio, will perhaps lead to improved performances now it has been recognized that this current is connected with mobile dopants.