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 (α_M) for this array is also derived. Since α_M≪1, it follows that a macroscopic pre-exponential correction factor (λ_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 λ_M may cause great theoretical over-prediction of the value of J_M.