Disorder Imposed Limits\nof Mono- and Bilayer Graphene\nElectronic Modification Using Covalent Chemistry

Abstract

A central question in graphene chemistry is to what extent\nchemical\nmodification can control an electronically accessible band gap in\nmonolayer and bilayer graphene (MLG and BLG). Density functional theory\npredicts gaps in covalently functionalized graphene as high as 2 eV,\nwhile this approach neglects the fact that lattice symmetry breaking\noccurs over only a prescribed radius of nanometer dimension, which\nwe label the S-region. Therefore, high chemical conversion is central\nto observing this band gap in transport. We use an electrochemical\napproach involving phenyl-diazonium salts to systematically probe\nelectronic modification in MLG and BLG with increasing functionalization\nfor the first time, obtaining the highest conversion values to date.\nWe find that both MLG and BLG retain their relatively high conductivity\nafter functionalization even at high conversion, as mobility losses\nare offset by increases in carrier concentration. For MLG, we find\nthat band gap opening as measured during transport is linearly increased\nwith respect to the <i>I</i>_<i>D</i>/<i>I</i>_<i>G</i> ratio but remains\nbelow 0.1 meV in magnitude for SiO₂ supported graphene.\nThe largest transport band gap obtained in a suspended, highly functionalized\n(<i>I</i>_<i>D</i>/<i>I</i>_<i>G</i> = 4.5) graphene is about 1 meV, lower\nthan our theoretical predictions considering the quantum interference\neffect between two neighboring S-regions and attributed to its population\nwith midgap states. On the other hand, heavily functionalized BLG\n(<i>I</i>_<i>D</i>/<i>I</i>_<i>G</i> = 1.8) still retains its signature\ndual-gated band gap opening due to electric-field symmetry breaking.\nWe find a notable asymmetric deflection of the charge neutrality point\n(CNP) under positive bias which increases the apparent on/off current\nratio by 50%, suggesting that synergy between symmetry breaking, disorder,\nand quantum interference may allow the observation of new transistor\nphenomena. These important observations set definitive limits on the\nextent to which chemical modification can control graphene electronically.