The existence of a significant electron drift instability (EDI) in the Hall thruster is considered one of the possible causes of the abnormal increase in axial electron mobility near the outlet of the channel. In recent years, extensive simulation studies have been conducted to investigate the characteristics of EDI, but the excitation and growth mechanisms of EDI in both linear and nonlinear stages are unclear. In this work, a one-dimensional PIC model on the azimuthal direction of the thruster near-exit region is established to gain further insights into the mechanism of the EDI in detail, and the effects of different types of propellants on EDI characteristics are discussed. The changes in axial electron transport caused by EDI under different types of propellants and electromagnetic field strengths are also examined. The results indicate that EDI undergoes a short linear growth phase before transitioning to the nonlinear phase and finally reaching saturation through the ion Landau damping. EDI drives a significant ion heating in the azimuthal direction through electron-ion friction before entering the quasi-steady state which increases the axial mobility of the electrons. Applying propellants with lighter atomic weight can effectively suppress the oscillation amplitude of EDI, but increases the linear growth rate of EDI as well as the frequency and phase velocity. The axial electron mobility increased under the EDI by three orders of magnitude compared to the classical mobility, this simulated result obtained are consistent with experimental phenomena. The change in the type of propellant is not sufficient to significantly alter the electron axial mobility. It’s also found that collisions between electrons and neutral gases have a significant impact on electron axial mobility under the influence of EDI, increasing the strength of the electric field and decreasing the strength of the magnetic field both effectively suppress the axial transport of electrons.