  Graphene nanomeshes (GNMs) are novel materials that recently raised a lot of
interest. They are fabricated by forming a lattice of pores in graphene.
Depending on the pore size and pore lattice constant, GNMs can be either
semimetallic or semiconducting with a gap large enough (0.5 eV) to be
considered for transistor applications. The fabrication process is bound to
produce some structural disorder due to variations in pore sizes. Recent
electronic transport measurements in GNM devices (ACS Appl. Mater. Interfaces
10, 10362, 2018) show a degradation of their bandgap in devices having
pore-size disorder. It is therefore important to understand the effect of such
variability on the electronic properties of semiconducting GNMs. In this work
we use the density functional-based tight binding formalism to calculate the
electronic properties of GNM structures with different pore sizes, pore
densities, and with hydrogen and oxygen pore edge passivations. We find that
structural disorder reduces the electronic gap and the carrier group velocity,
which may interpret recent transport measurements in GNM devices. Furthermore
the trend of the bandgap with structural disorder is not significantly affected
by the change in pore edge passivation. Our results show that even with
structural disorder, GNMs are still attractive from a transistor device
perspective.
