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A surface-potential-based analytic direct-current I -V model for amorphous indium-gallium-zinc-oxide thin-film transistors is proposed by adopting an effective electron density (neff) model for inclusion of both free carriers and localized charges in the channel. The proposed neff is efficient in reducing the error caused by neglecting the localized electron density nloc and allows a closed form of the analytic I-V model. The potential drop across the parasitic resistance RP in the source and drain regions is also fully considered in the model. Finally, we confirmed good agreement of the proposed model with measured IDS-VDS characteristics over a wide range of VGS and VDS.