A theoretical study of the properties of a-Si:H thin-film transistors (TFTs) has been performed using uniform and non-uniform distributions of gap states in the a-Si:H layer. The potential profile in the semiconductor is calculated in a straightforward way by solving Poisson's equation numerically. From the band bending the source-drain current ISD(VG) of the TFT is predicted. In addition we calculate the transient discharge current I(t) generated by switching the gate voltage from positive to negative values. In experimental studies such transients are analyzed to obtain an effective density of interface states, Ni(E). We find that N;(E) depends little on the spatial variation of gap states, N(E,x), but sensitively on the energy distribution of N(E,x). It is shown that experimental N;(E) curves and ISD(VG) characteristics from the same sample can be fitted by the same N(E,x) which however cannot be unequivocally determined.