We propose and analyze the concept of the vertical hot-electron terahertz (THz) graphene-layer detectors (GLDs) based on the double-GL and multiple-GL structures with the barrier layers made of materials with a moderate conduction band off-set (such as tungsten disulfide and related materials). The operation of these detectors is enabled by the thermionic emissions from the GLs enhanced by the electrons heated by incoming THz radiation. The electron heating is primarily associated with the intraband absorption (the Drude absorption). We calculate the responsivity and detectivity as functions of the photon energy, GL doping, and the applied voltage for the GL detectors (GLDs) with different number of GLs. The detectors based on the cascade multiple-GL structures can exhibit a substantial photoelectric gain resulting in the elevated responsivity and detectivity. The advantages of the THz detectors under consideration are associated with their high sensitivity to the normal incident radiation and efficient operation at room temperature at the low end of the THz frequency range. Such GLDs with a metal grating, supporting the excitation of plasma oscillations in the GL-structures by the incident THz radiation, can exhibit a strong resonant response at the frequencies of several THz (in the range, where the operation of the conventional detectors based on A$_3$B$_5$ materials, in particular THz quantum-well detectors, is hindered due to a strong optical phonon radiation absorption in such materials).
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