Figure 2. Simulation results with electric potentials from 10V to 160V.

Radial distance is from the center of the NLGE tip. a, The electric field distribution at the tip shows peak flattening. Voltages correspond to the same colors in all panels b, The conductivity distribution at the tip shows nanoscale confinement of the breakdown. c, The current density at the tip is as high as several mega-amperes/m². d, At the nanoscale tip, Joule heating of the order of mega-watts/cm³ is generated by the high current density. e, Increases in the steady state temperature at the NLGE tip are surprisingly small due to extremely rapid heat dissipation from nanoscale volumes. f, Simulations reveal that even micron scale tips would encounter large temperature rises causing irreversible thermal damage.