  Graphene p-n junctions offer a potentially powerful approach towards
controlling electron trajectories via collimation and focusing in ballistic
solid-state devices. The ability of p-n junctions to control electron
trajectories depends crucially on the doping profile and roughness of the
junction. Here, we use four-probe scanning tunneling microscopy and
spectroscopy (STM/STS) to characterize two state-of-the-art graphene p-n
junction geometries at the atomic scale, one with CMOS polySi gates and another
with naturally cleaved graphite gates. Using spectroscopic imaging, we
characterize the local doping profile across and along the p-n junctions. We
find that realistic junctions exhibit non-ideality both in their geometry as
well as in the doping profile across the junction. We show that the geometry of
the junction can be improved by using the cleaved edge of van der Waals metals
such as graphite to define the junction. We quantify the geometric roughness
and doping profiles of junctions experimentally and use these parameters in
Nonequilibrium Green's Function based simulations of focusing and collimation
in these realistic junctions. We find that for realizing Veselago focusing, it
is crucial to minimize lateral interface roughness which only natural graphite
gates achieve, and to reduce junction width, in which both devices under
investigation underperform. We also find that carrier collimation is currently
limited by the non-linearity of the doping profile across the junction. Our
work provides benchmarks of the current graphene p-n junction quality and
provides guidance for future improvements.
