Modeling the effects of electron irradiation on graphene drums using the local activation model

We study the effects of electron irradiation on suspended graphene monolayers and graphene supported on SiO₂ substrates in the range 5.0 × 10¹⁵–4.3 × 10¹⁷ electrons/cm². The suspended graphene monolayers are exfoliated over SiO₂ substrates containing micrometer-sized holes, with graphene completely covering the hole, and are referred to as graphene drums. The irradiation was performed using a scanning electron microscope at 20–25 keV electron energy. We observe a two-stage behavior for the I_D/I_G, I_D′/I_G, and I_D/I_D′ ratios as a function of the average distance between defects, L_D, where I_D, I_G, and I_D′ are the intensities of the Raman D, G, and D′ peaks, respectively. Good fits to the dependence of the ratios on L_D are obtained using the local activation model equation. The fits are used to characterize the defects at high defect densities. We also carried out annealing studies of samples irradiated to the first stage and used an Arrhenius plot to measure activation energies for defect healing, E_a. We measured E_a = 0.90 eV for the graphene drums, consistent with the hydroxyl groups; for supported graphene, we measured E_a = 0.36 eV, consistent with hydrogen adsorbates. We also studied the surface of the drums using atomic force microscopy and found no observable holes after irradiation and annealing. Our results show that the local activation model is useful in characterizing the defects in graphene drums.