A closed-form DC model for long-channel thin-film transistors with gate voltage-dependent mobility characteristics

A model is derived for the drain current (under DC steady-state operating conditions) of a long-channel thin-film transistor (TFT) with gate voltage-dependent channel mobility. A closed-form expression is obtained for cases in which the average mobility (μavg) can be reasonably approximated by an nth-order polynomial curve fit; a more generalized expression allows the substitution of an arbitrary parameterized equation for μavg, yielding a closed-form expression in cases where the form of the selected mobility expression is such that the requisite integration can be carried out analytically. The model is employed to replicate measured drain current versus drain voltage (ID-VDS) curves for exemplary zinc oxide and zinc tin oxide channel TFTs with highly non-ideal (i.e., gate voltage-dependent) mobility characteristics; in each case, excellent correlation to measured ID-VDS data is obtained, thus validating the proposed model. This model comprises a valuable tool in the preliminary development of novel TFTs for which standard device models are not, in general, appropriate.