Shot noise power spectrum of planar field emitters

Abstract

A quantum-mechanical wave impedance approach is used to calculate the shot noise power spectrum of the emission current from planar metallic cathodes. The formalism takes into account the effects of the image force potential in front of the cathode. For metals with low work function, the Fano factor which characterizes the reduction of the shot noise power SI below the Schottky result 2 q IA (where q is the magnitude of the charge of the electron and IA is the time average of the anode current) is calculated as a function of the applied external electric field. Simple analytical expressions for the Fano factor are derived for the cathode operated in the thermionic (Richardson) and tunneling (Fowler–Nordheim) regimes. The value of the Fano factor is found to be reduced substantially below the value calculated when the effects of the image charge potential are neglected.