  Gate instability/hysteresis in modulation-doped p-type AlGaAs/GaAs
heterostructures impedes the development of nanoscale hole devices, which are
of interest for topics from quantum computing to novel spin physics. We present
an extended study conducted using custom-grown, matched modulation-doped n-type
and p-type heterostructures, with/without insulated gates, aimed at
understanding the origin of the hysteresis. We show the hysteresis is not due
to the inherent `leakiness' of gates on p-type heterostructures, as commonly
believed. Instead, hysteresis arises from a combination of GaAs surface-state
trapping and charge migration in the doping layer. Our results provide insights
into the physics of Si acceptors in AlGaAs/GaAs heterostructures, including
widely-debated acceptor complexes such as Si-X. We propose methods for
mitigating the gate hysteresis, including poisoning the modulation-doping layer
with deep-trapping centers (e.g., by co-doping with transition metal species),
and replacing the Schottky gates with degenerately-doped semiconductor gates to
screen the conducting channel from GaAs surface-states.
