The relation between the empirical mobility model parameters used for amorphous thin film transistors and physical device parameters is analyzed, when both localized and free carriers have to be considered to represent the device behavior. A simple procedure is presented to obtain the characteristic temperature and trap concentration of the DOS at the conduction band, using only the linear transfer characteristic at room temperature. An empirical analytical expression that represents analytically the dependence of the surface potential on the gate voltage is presented and validated. Using this expression, the procedure described to calculate the above mentioned parameters is completely analytical. The procedure presented is applied to experimental data of a-IGZO TFTs fabricated with two different technological process.