Field Electron Emission Images Far Away from a Semi-Infinitely Long Emitter: A Multiscale Simulation
© 2018 American Chemical Society. Ab initio calculations reveal that in cold field electron emission from nanostructures, the electron state of top priority not necessarily the occupied state with largest forward kinetic energy but depends on the applied field. We show that single-walled carbon nanotube emission at low fields is dominated by the states with highest forward kinetic energy. On the other hand, high field emission is dominated by states that extend deeply into the potential barrier. We find that the distribution of the local density of states is an important factor for emission, in addition to the forward kinetic energy. We have calculated the wave functions of such states for semi-infinitely long single-walled carbon nanotubes by combining time-dependent density functional theory (TDDFT) with a reactant- product decoupling method. The emission image on a distant screen is found by matching the analytical solution of the wave function calculated with TDDFT on a plane which is a few nanometers away from the apex of the nanostructure. We separate the various angular momentum states of the emitters on the basis of their forward velocity, thus identifying their respective contribution to the image pattern.
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