The Dependence of Raman I_D/I_D' Ratio on Average Distance Between Defects, L_D in Electron-Irradiated Graphene

We report on the dependence of the Raman D to D' peak intensity ratio, I_D/I_D', on the average distance between defects, L_D, in graphene that is electron irradiated at dosages from 4.96 x 10¹⁵ to 4.26 x 10¹⁷ electrons/cm². The samples consist of graphene drums in which exfoliated graphene completely covers micron-sized holes etched into SiO₂ substrates, and graphene supported on solid SiO₂ substrates. The drums were fabricated in air and likely contain air in them during irradiation. I_D/I_D' is observed to vary from 6.3 to 9.0 with L_D. We use the two-stage model equation for defect formation assuming only one type of defect to model I_D/I_D' versus L_D and find excellent agreement with theory. Using thermal annealing, we measure the activation energies for defect healing in graphene drums and supported graphene irradiated to the first stage to be 0.91 and 0.36 eV, respectively, consistent with sp³-type defects. We also measure the full-width-at-half-maximum and the Raman peak positions at varying electron dosages and annealing temperatures.