Numerical study of the electrostatic field gradients present in various planar emitter field emission configurations relevant to experimental research

In this work, a general finite element software has been used to analyze the electrostatic field in various experimental configurations employed for measuring the field emission properties of planar emitters. The configurations studied are: (1) the metallic sphere-anode, (2) the cylindrical probe with spherically rounded tip, (3) the cylindrical probe with flat tip, (4) the flat anode separated from the cathode by insulating round spacers touching both cathode and anode, (5) flat spacers touching both cathode and anode, and (6) flat spacers touching the anode but not touching the cathode. The validity of the ideal capacitor approximation was investigated for the cathode surface electric field for each configuration using typical dimensions for each of them, and obtained the magnitude of the electric field near critical areas that could lead to residual gas ionization, dielectric breakdown and emission of electrons from non-desired cathode areas.