Figure 3

Illustrating the use of a pre-barrier to enhance the transmission of an electron wavepacket through a triangular field emission barrier of height 15 eV. (a) Transmission probability is shown as a function of energy E of an electron incident on a triangular barrier with a slope determined by the electric field F on the vacuum side. The FDTD result compares well with the analytical solution of Forbes and Deane²². We also show the analytical solution derived by Fowler and Nordheim (FN) on the basis of the WKB approximation. The vertical line indicates where the electron energy is equal to the barrier height. The FN solution breaks down for electron energies just below the barrier height. (b) The transmission probability for four energies below the pre-barrier height as a function of the pre-barrier width, showing the constructive and destructive interference. (c) The transmission probability for energies both below and above the pre-barrier height as a function of the pre-barrier width. Enhancement of transmission is only observed in when the incident electron energy is above the barrier height. Here the energy of the incident electron is 10.5 eV.