We propose and evaluate the vertical cascade terahertz and infrared photodetectors based on multiple-graphene-layer (GL) structures with thin tunnel barrier layers (made of tungsten disulfide or related materials). The photodetector operation is associated with the cascaded radiative electron transitions from the valence band in GLs to the conduction band in the neighboring GLs (interband- and inter-GL transitions). We calculate the spectral dependences of the responsivity and detectivity for the vertical cascade interband GL- photodetectors (I-GLPDs) with different number of GLs and doping levels at different bias voltages in a wide temperature range. We show the possibility of an effective manipulation of the spectral characteristics by the applied voltage. The spectral characteristics depend also on the GL doping level that opens up the prospects of using I-GLPDs in the multi-color systems. The advantages of I-GLPDs under consideration are associated with their sensitivity to the normal incident radiation, weak temperature dependence of the dark current as well as high speed of operation. The comparison of the proposed I-GLDs with the quantum-well intersubband photodectors demonstrates the superiority of the former, including a better detectivity at room temperature and a higher speed. The vertical cascade I-GLDs can also surpass the lateral p-i-n GLDs in speed.
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