Abstract
Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbon nanotube and carbon fiber field emitters is discussed.
Highlights
INTRODUCTIONHigh brightness field emission sources in an array (either conical Spindt-like or long wirelike as in carbon fibers and nanotubes) may provide electron beams that meet the needs of accelerators, high power microwave and x-ray sources, and vacuum electronic devices
High brightness field emission sources in an array may provide electron beams that meet the needs of accelerators, high power microwave and x-ray sources, and vacuum electronic devices
We describe the development of a multidimensional image charge approximation useful for a general thermal-field emission equation used in space charge studies8 based on an analytical model using a prolate spheroidal geometry
Summary
High brightness field emission sources in an array (either conical Spindt-like or long wirelike as in carbon fibers and nanotubes) may provide electron beams that meet the needs of accelerators, high power microwave and x-ray sources, and vacuum electronic devices. With very high current per emitter, emitted charge complicates the simulation of space charge affected field emission, in beam optics codes.. Ppreffiffisffiuffiffiffimffiffiffiption of 4QF, where a planar image charge modification, Q 1⁄4 q2=16pe0 1⁄4 0:36 eV nm and. F 1⁄4 qE: in the image charge formula, the electric field E always appears with the electron charge Àq. The convention here is to use F qE with units of (eV/nm). F will be referred to by its colloquial usage of “field” insofar as F in (eV/nm) is numerically equal to E in (GV/m).
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