We study the operation of infrared photodetectors based on van der Waals heterostructures with the multiple graphene layers (GLs) and n-type emitter and collector contacts. The operation of such GL infrared photodetectors (GLIPs) is associated with the photoassisted escape of electrons from the GLs into the continuum states in the conduction band of the barrier layers due to the interband photon absorption, the propagation of these electrons and the electrons injected from the emitter across the heterostructure and their collection by the collector contact. The space charge of the holes trapped in the GLs provides a relatively strong injection and large photoelectric gain. We calculate the GLIP responsivity and dark current detectivity as functions of the energy of incident infrared photons and the structural parameters. It is shown that both the periodic selective doping of the inter-GL barrier layers and the GL doping lead to a pronounced variation of the GLIP spectral characteristics, particularly near the interband absorption threshold, while the doping of GLs solely results in a substantial increase in the GLIP detectivity. The doping engineering opens wide opportunities for the optimization of GLIPs for operation in different parts of radiation spectrum from near infrared to terahertz.
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