  The field-effect-induced modulation of transport properties of 2-dimensional
electron gases residing at the LaAlO$_3$/SrTiO$_3$ and LaGaO$_3$/SrTiO$_3$
interfaces has been investigated in a back-gate configuration. Both samples
with crystalline and with amorphous overlayers have been considered. We show
that the "na\"ive" standard scenario, in which the back electrode and the
2-dimensional electron gas are simply modeled as capacitor plates, dramatically
fails in describing the observed phenomenology. Anomalies appearing after the
first low-temperature application of a positive gate bias, and causing a
non-volatile perturbation of sample properties, are observed in all our
samples. Such anomalies are shown to drive low-carrier density samples to a
persistent insulating state. Recovery of the pristine metallic state can be
either obtained by a long room-temperature field annealing, or,
instantaneously, by a relatively modest dose of visible-range photons.
Illumination causes a sudden collapse of the electron system back to the
metallic ground state, with a resistivity drop exceeding four orders of
magnitude. The data are discussed and interpreted on the base of the analogy
with floating-gate MOSFET devices, which sheds a new light on the effects of
back-gating on oxide-based 2-dimensional electron gases. A more formal
approach, allowing for a semi-quantitative estimate of the relevant surface
carrier densities for different samples and under different back-gate voltages,
is proposed in the Appendix.
