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Recent analyses of the field enhancement factor (FEF) from multiple emittershave revealed that the depolarization effect is more persistent with respect tothe separation between the emitters than originally assumed. It has been shownthat, at sufficiently large separations, the fractional reduction of the FEFdecays with the inverse cube power of separation, rather than exponentially.The behavior of the fractional reduction of the FEF encompassing both the rangeof technological interest $0<c/h\lesssim5$ ($c$ being the separation and $h$ isthe height of the emitters) and $c\rightarrow\infty$, has not been predicted bythe existing formulas in field emission literature, for post-like emitters ofany shape. In this letter, we use first principles to derive a simpletwo-parameter formula for fractional reduction that can be of interest forexperimentalists to modeling and interpret the FEF from small clusters ofemitters or arrays in small and large separations. For the structures tested,the agreement between numerical and analytical data is $\sim1\%$.

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters