Novel structures, in which an A1GaAs/GaAs modulation doped structure is overgrown on an underlying Be-implanted p-type region, are successfully fabricated using a system in which focused-ion-beam (FLB) implantation and molecular-beam epitaxy chambers are connected through a high vacuum tunnel. The two-dimensional electron; gas (2DEG) at the heterointerface is well controlled by a voltage applied to the Be-FIB written backgate. Though Be out diffusion into the overgrown layer is observed, the sharp front of the out diffusion enables us to fabricate devices with a small separation between the 2DEG and p-type backgate. The three-dimensional hole gas (3DHG) formed by the Be-FIB implantation is used not only as a backgate but also for measuring the interaction between 2DEG and 3DHG.