  Creation of sharp lateral p-n junctions in graphene devices, with transition
widths well below the Fermi wavelength of graphene charge carriers, is vital to
study and exploit these electronic systems for electron-optical applications.
The achievement of such junctions is, however, not trivial due to the presence
of a considerable out-of-plane electric field in lateral p-n junctions,
resulting in large widths. Metal-graphene interfaces represent a novel,
promising and easy to implement technique to engineer such sharp lateral p-n
junctions in graphene field-effect devices, in clear contrast to the much wider
(i.e. smooth) junctions achieved via conventional local gating. In this work,
we present a systematic and robust investigation of the electrostatic problem
of metal-induced lateral p-n junctions in gated graphene devices for
electron-optics applications, systems where the width of the created junctions
is not only determined by the metal used but also depends on external factors
such as device geometries, dielectric environment and different operational
parameters such as carrier density and temperature. Our calculations
demonstrate that sharp junctions can be achieved via metal-graphene interfaces
at room temperature in devices surrounded by dielectric media with low relative
permittivity. In addition, we show how specific details such as the separation
distance between metal and graphene and the permittivity of the gap in-between
plays a critical role when defining the p-n junction, not only defining its
width w but also the energy shift of graphene underneath the metal. These
results can be extended to any two-dimensional (2D) electronic system doped by
the presence of metal clusters and thus are relevant for understanding
interfaces between metals and other 2D materials.
