High-resolution simulation of field emission

Abstract

High-resolution simulations of field emission electron sources have been made using the electron optics program EGN2. Electron emission distributions are made using the Fowler-Nordheim equation. Mesh resolution in the range of 1-5 {angstrom} is required to adequately model surface details that can result in emission currents in the range found experimentally. A typical problem starts with mechanical details with dimensions of about 1{mu}. To achieve high resolution a new boundary is defined by the tip, a nearby equipotential line, and a pair of field lines. The field lines (one of which is normally the axis of symmetry) define Neumann boundaries. This new boundary is then used by the boundary preprocessor POLYGON to create an enlarged version of the problem, typically by a factor of ten. This process can be repeated until adequate resolution is obtained to simulate surface details, such as microprotusion, that could sufficiently enhance the surface electric fields and cause field emission. When simulating experimental conditions under which emission of several microamperes per tip were observed, it was found that both a locally reduced work function and a surface protrusion were needed to duplicate the experimental results. If only a local region of reduced work function is used,more » the area involved and the extent of the reduction both need to be very large to reproduce the emission. If only a surface protrusion is used, it is possible to get the observed emission current with a reasonable protrusion of length a few times radius, but then the resulting beam spreads over a very large solid angle due to the strong local radial electric fields. 8 refs., 14 figs., 1 tab.« less