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Field emission characteristics from patchwork cathodes: a numerical approach

In this work, to better understand the field emission behaviour from patchwork cathodes, the FE current is calculated, the transmission probability for an electron to cross the barrier between the electron sea of the patchwork cathode and the vacuum is obtained by solving the Schrodinger equation in its integral Lippmann-Schwinger form by means of a Green's function technique. The main point in this numerical approach is the taking into consideration, for the determination of the surface barrier, of the patch-field which is generated by a difference of order 2 eV across nanometric dimension boundaries between the low patch areas and the high surrounding surface. Quantitative relations of the field emission characteristics will be presented and discussed in function of patch geometries and values. In particular, we will highlight the features of the patchwork cathode that can be obtained from experimental field emission current measurements.