Due to the inherent property of large contact and parasitic resistances in amorphous InGaZnO (a-IGZO) thin film transistors (TFTs), a metal-semiconductor-metal (MSM) structure is a key element in a-IGZO TFTs. Therefore, voltage drops across resistances and MSM structure should be fully considered in the modeling and characterization of a-IGZO TFTs. A physics-based semiempirical model for the current-voltage characteristics of the MSM structure for the source-channel-drain contact in a-IGZO TFTs is proposed and verified with experimental results. The proposed model for the current in a-IGZO MSM structures includes a thermionic field emission [JTFE∝exp(VR,Schottky/Vo)] and trap-assisted generation (Jgen∝VR,Schottky) in addition to the thermionic emission current (JS: Independent of the bias) under reverse bias. Experimental result suggests that electrical characteristics of the MSM structure depend not only on the Schottky barrier but also on the bulk property of the a-IGZO active layer.