Abstract: We calculate the average time decay constant τ' of the transmission GaAs NEA cathode under different doping gradients; the analysis suggests that the thickness L of the cathode absorption layer and the doping gradient have a dominant influence on τ', and τ' gradually decreases with the increase of L and doping gradient. The two doping methods involved in the simulation, the e-index doping method and the e-index electric-field doping method with absorption layer concentration, were not found to have an impact on τ'. When L~0.2−0.5 µm is small, the photon energy E_hv is significant to τ'. As E_hv further increases, the effects of E_hv on τ' gradually decrease. In the process of L and E_hv changes, there is a dynamic competition relationship between the L and E_hv in terms of the influences to τ'. Analyzed that the essence is the dynamic competition between the surface photoelectron concentration at the initial moment and the distribution of photoelectron concentration in the body, which jointly affects the τ'. The competitive relationship is not a simple superposition of the two parameters, but a complex, alternately dominant relationship. As L increases, E_hv gradually transitions from dominant to secondary, while L transitions from secondary to dominant. Meanwhile, based on τ', the simulation obtained the time response characteristics of the cathode under different doping methods and doping gradients - T_m and FWHM, both of which gradually decrease with the increase of doping gradient, while the e-index electric-field doping method has excellent response characteristics. This simulation result provides the theoretical basis and data support for the application research of transmission GaAs photocathodes in high-speed photography, electronic sources, photomultiplier tubes, and image intensifiers.