The terahertz current generated by a photoconductive device (PCD) saturates as the power of the input optical pump is increased. This behavior is induced by various screening effects that stem from the interactions between electromagnetic (EM) fields and semiconductor carriers. In this work, these screening effects are numerically analyzed for the first time using a fully-coupled multiphysics approach. Unlike the previously developed simulation frameworks, this approach rigorously models the nonlinear coupling between the EM fields and the carriers and therefore is capable of accounting for the screening effects. It is demonstrated that the results obtained using this multiphysics approach and actual experiments are in excellent agreement. The optical- and radiation-field screening effects are identified in the simulation results and the optical-field screening is found to play a more dominant role in the saturation of the PCD output under high optical pump power levels.