  Porous graphene structures, also termed graphene nanomeshes (GNMs), are
garnering increasing interest due to their potential application to important
technologies such as chemical sensing, ion-filtration, and nanoelectronics.
Semiconducting GNMs designed to have fractional eV band gaps are good
candidates for graphene-based electronics, provided that a mechanism for their
stable and controlled doping is developed. Recent work has shown that
controlled passivation of the edges of subnanometer pores and subsequent doping
by atoms or molecules gives rise to {\it p}- and {\it n}-doped GNM structures.
However, these structures are difficult to fabricate at the nanoscale. Here, we
use first principle calculations to study the effect of the pore size on the
doping physics of GNM structures with larger pores that can potentially host
more than a single dopant. We show that such doping mechanism is effective even
for pores with relatively large radii. We also study the effect of the number
of dopants per pore on doping stability. We find that stable rigid band {\it
n}- and {\it p}-doping emerges in such structures even if the dopants form a
nano-cluster in the pore - rigid band doping is achieved in all {\it n}- and
{\it p}-doping studied. Such doped large-pore GNM structures have potential
applications as field effect transistors, and as transparent conducting
electrodes.
