  Using atomistic quantum simulation based on a tight binding model, we
investigate the formation of energy gap Eg of graphene nanomesh (GNM) lattices
and the transport characteristics of GNM-based electronic devices (single
potential barrier structure and p-n junction) taking into account the atomic
edge disorder of holes. We find that the sensitivity of Eg to the lattice
symmetry (i.e., the lattice orientation and the hole shape) is significantly
suppressed in the presence of the disorder. In the case of strong disorder, the
dependence of Eg on the neck width is fitted well with the scaling rule
observed in experiments [Liang et al., Nano Lett. 10, 2454 (2010)]. Considering
the transport characteristics of GNM-based structures, we demonstrate that the
use of finite GNM sections in the devices can efficiently improve their
electrical performance (i.e., high ON/OFF current ratio, good current
saturation and negative differential conductance behaviors). Additionally, if
the length of GNM sections is appropriately limited, the detrimental effects of
disorder on transport can be avoided to a large extent. Our study provides a
good explanation of the available experimental data on GNM energy gap and
should be helpful for further investigations of GNM-based devices.
