Determining charge state of graphene vacancy by noncontact atomic force microscopy and first-principles calculations.

Graphene vacancies are engineered for novel functionalities, however, the charge state of these defects, the key parameter that is vital to charge transfer during chemical reactions and carrier scattering, is generally unknown. Here, we carried out atomic resolution imaging of graphene vacancy defects created by Ar plasma using noncontact atomic force microscopy, and made the first determination of their charge state by local contact potential difference measurements. Combined with density functional theory calculations, we show that graphene vacancies are typically positively charged, with size-dependent charge states that are not necessarily integer-valued. These findings provide new insights into carrier scattering by vacancy defects in graphene, as well as its functionalization for chemical sensing and catalysis, and underline the tunability of these functions by controlling the size of vacancy defect.