  We analyze dynamic properties of vertical graphene-base hot-electron
transistors (GB-HETs) and consider their operation as detectors of terahertz
(THz) radiation using the developed device model. The GB-HET model accounts for
the tunneling electron injection from the emitter, electron propagation across
the barrier layers with the partial capture into the GB, and the
self-consistent oscillations of the electric potential and the hole density in
the GB (plasma oscillations), as well as the quantum capacitance and the
electron transit-time effects. Using the proposed device model, we calculate
the responsivity of GB-HETs operating as THz detectors as a function of the
signal frequency, applied bias voltages, and the structural parameters. The
inclusion of the plasmonic effect leads to the possibility of the HET-GBT
operation at the frequencies significantly exceeding those limited by the
characteristic RC-time. It is found that the responsivity of GB-HETs with a
sufficiently perfect GB exhibits sharp resonant maxima in the THz range of
frequencies associated with the excitation of plasma oscillations. The
positions of these maxima are controlled by the applied bias voltages. The
GB-HETs can compete with and even surpass other plasmonic THz detectors.
