A computer simulation program for calculating the energetic Boersch effect in the diode region of the field emission (FE) gun has been developed. The diode system consists of a hyperboloid of revolution as the cathode (FE tip) and a plane electrode as the first anode (extraction anode). The radius of curvature of the FE tip is R_o and the FE tip-to-1st anode distance is d. The simulation has been done for the various combinations of R_o (0.05 approximately 0.4 micrometers ) and d (0.5 approximately 10 mm). The work function of the cathode tip is assumed to be 4.5 eV. The electrons leave the cathode surface at time intervals selected to approximate a Poisson process and also realize a specific emission current using a random number. The positions and velocities of the electrons are successively calculated as a result of the force produced by both the Coulomb interaction and the electric field inside the gun. The resultant energy spread (Delta) E is found to be (Delta) E equals (root)(Delta) E²_o + (Delta) E²_B, where (Delta) E_o is the initial energy width of the emitted electrons and (Delta) E_B is the energy broadening of monochromatically emitted electrons. The simulation also shows that the dependence of (Delta) E_B on R_o, d, and the emission current I_E is given by (Delta) E_B (alpha) I^-0.75_E X R^-0.5_o X d⁰.

Date Published: 3 September 1993
PDF: 5 pages
Proc. SPIE 2014, Charged-Particle Optics, (3 September 1993); doi: 10.1117/12.155689

Published in SPIE Proceedings Vol. 2014:
Charged-Particle Optics
William B. Thompson; Mitsugu Sato; Albert V. Crewe, Editor(s)