Abstract— A theoretical model to interpret appearances of the threshold voltage shift in hydrogenated amorphous‐silicon (a‐Si:H) thin‐film transistors (TFTs) is developed to better understand the instability of a‐Si:H TFTs for the driving transistors in active‐matrix organic light‐emitting‐diode (AMOLED) displays. This model assumes that the defect creation at channel in a‐Si:H is proportional to the carrier concentration, leading to the defect density varying along the channel depending on the bias conditions. The model interprets a threshold‐voltage‐shift dependency on the drain‐stress bias. The model predicts the threshold voltage shift stressed under a given gate bias applying the drain saturation voltage is 66% of that with zero drain bias, and it even goes down to 50–60% of that when stressed by applying twice the drain saturation voltage.