Field Enhancement Factor for a Tall Closely-Spaced Array of Identical Conducting Posts, and Implications for Fowler-Nordheim Theory

This paper derives an approximate formula for the field enhancement factor for a tall closely-packed array of identical conducting posts. It confirms a formula derived from the work of Zhbanov et al. [J. Appl. Phys. 110, 114311 (2011)], but displays the principles underlying collective screening more clearly. A formula for the area efficiency of emission (alpha(M)) for this array is also derived. Since alpha(M)<<1, it follows that a macroscopic pre-exponential correction factor (lambda(M)) must be included in the formula for the macroscopic ("LAFE-average") emission current density (J(M)) for a large-area field emitter (LAFE). Omission of lambda(M) may cause great theoretical over-prediction of the value of J(M).