Amorphous In-Ga-Zn-O thin-film transistors (a-IGZO TFTs) show a high mobility, a small sub-threshold swing, and a low OFF-current, and they are considered to be one of the most promising TFT for new flat-panel displays (FPDs). The high mobility originates from the unique electron transport in a-IGZO. The transport properties are different from those in conventional semiconductor materials like Si, for example, the mobility increases with increase of the electron concentration and/or temperature. Therefore, the new mobility model for a-IGZO is necessary. In addition, as pixel sizes in the FPDs decreases, a channel-length, L, of a-IGZO TFTs becomes shorter. It indicates that it is important to understand the operation of short-channel a-IGZO TFTs.