Influence of image force potential on the shot noise properties of field emitters

A quantum-mechanical wave impedance approach is used to calculate the shot noise power spectrum of the emission current from planar metallic cathodes starting with the Landauer-Buttiker formalism. 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 below the Schottky result 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 regimes (Fowler-Nordheim approximation). 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. The approach can be readily extended to include space-charge effects in the vacuum gap.