  Armchair phosphorene nanoribbons (APNRs) are known to be semiconductors with
an indirect bandgap. Here, we propose to introduce new states in the gap of
APNRs by creating a periodic structure of vacancies (antidots). Based on the
tight-binding model, we show that a periodic array of vacancies or nanopores
leads to the formation of an impurity band inside the gap region. We first
present an analytical expression for the dispersion relation of an impurity
band induced by hybridization of bound states associated with each single
vacancy defect. Then, we increase the size of vacancy defects to include a
bunch of atoms and theoretically investigate the effect of nanopores size and
their spacing on electronic band structure, carrier transmission function, and
thermoelectric properties. Our analysis of the power generation rate and
thermoelectric efficiency of these structures reveals that an ANPR can be used
as a superb thermoelectric power generation module.
