  Graphene is an attractive material for broadband photodetection but suffers
from weak light absorption. Coating graphene with quantum dots can
significantly enhance light absorption and create extraordinarily high photo
gain. This high gain is often explained by the classical gain theory which is
unfortunately an implicit function and may even be questionable. In this work,
we managed to derive explicit gain equations for hybrid graphene-quantum-dot
photodetectors. Due to the work function mismatch, lead sulfide (PbS) quantum
dots coated on graphene will form a surface depletion region near the interface
of quantum dots and graphene. Light illumination narrows down the surface
depletion region, creating a photovoltage that gates the graphene. As a result,
high photo gain in graphene is observed. The explicit gain equations are
derived from the theoretical gate transfer characteristics of graphene and the
correlation of the photovoltage with the light illumination intensity. The
derived explicit gain equations fit well with the experimental data, from which
physical parameters are extracted.
