Edge doping in graphene devices on SiO$_{2}$ substrates

The conductivity of single layer and bilayer graphene ribbons 0.5–4 $\mu$m in width fabricated by oxygen plasma etching is studied experimentally. The dependence of the electron concentration in graphene on the ribbon width is revealed. This effect is explained by the edge doping of graphene due to defects arranged in SiO$_{2}$ near the ribbon edges. The method of the formation of abrupt $p$–$n$ junctions in graphene and structures with a constant electron concentration gradient in the graphene plane with the help of edge doping is proposed.