The electric field emanating from the surface of a poled ferroelectric can control the conduction properties of an overlying semiconducting film; this combination of materials can thus serve as a non-destructive readout, non-volatile memory device. Here we will describe a variety of experimental studies of these devices designed to probe the physics of their operation. The experimental systems included sputtered, n-type semiconductor (SC) films of In2O3and ZnO deposited on bulk PLZT ferroelectrics (FE) and thin PZT FE films. Two distinctly different types of device response were measured in this study; in the first, the change in SC film conductance observed in the remanent FE state is in the direction expected from the remanent polarization vector in the ferroelectric. In the second, typically seen in thin film FE devices, the opposite behavior is observed. We find that these two general cases of behavior, including the observed variations of the SC film conductances and carrier mobilities, can be described by a general model which takes into account not only the FE displacement vector, but also charge injected from the semiconductor into the ferroelectric during biasing of the gate.