We report a photo and field (PF)-induced doping of a graphene-heterostructure field-effect transistor (graphene HFET) using a double-layered gate insulator consisting of narrow-bandgap insulator (NGI) and wide-bandgap insulator (WGI). The PF-induced doping in the graphene HFETs with variable NGIs (hafnium oxide, silicon nitride, and hexagonal boron nitride) are investigated, and consequently we reveal that this rewritable/erasable doping behavior is not limited to specific insulating materials, but unexceptionally accomplished when a step-like vertical band diagram, that is graphene/NGI/WGI, is fulfilled in the device. We clearly verify that this doping is originated from PF-induced charge transfer between graphene and defects at the NGI/WGI interface, and then the polarized charges at the NGI/WGI interface pretend to be "remote dopants", shifting Dirac voltage of the device. The remote dopant is highly stable in the dark due to the presence of the adjacent insulators providing enormous energy barriers, but can be efficiently tuned by the modulation of the gate bias and incident photon energy. Because the PF-induced doping mechanism is not limited by specific materials that is still hard to be synthesized as a large scale, the graphene HFET memory devices can be patterned with a large scale using practical fabrication processes, appealing to industrial applications.