In this paper we present experimental and simulation results of the transient response of amorphous silicon (a-Si) thin film transistors (TFTs) over many orders of magnitude in time after the application of a voltage pulse to the gate. In general three regimes are observed by plotting drain current versus the logarithm of time. At times longer than the carrier transit time and extending up to 1 - 100 msecs, the current rapidly decreases due to trap filling, after which it then slowly decays up until defects are created in the silicon channel when it then finally decays more rapidly again. Our simulation results are in good agreement with the data for the short time trap filling regime, as a function of both gate bias and stress condition. Measurements at elevated temperatures show that the middle slow decay regime is caused by charge injection into interface states or the gate dielectric. Finally we also demonstrate that this slow decay regime does not occur in nin diodes, confirming that it is not caused by defect generation in the a-Si, and is instead related to the presence of the dielectric in a TFT.