Practical considerations in the modeling of field emitter arrays with line charge distributions

Abstract

Predictive models of field emission remain elusive, in part, due to the sensitivity of this process to emitter surface details at length scales ranging from macroscopic to atomic. Moving towards more fully predictive models requires that we develop techniques to disentangle contributions of features on the largest length scales, which can be easily measured and controlled, from contributions on smaller length scales, which are generally difficult to measure or control. Here, specific challenges are addressed, with an emphasis on comparisons between a Line Charge Model (LCM) and experimental measurements of ungated carbon fiber field emitter arrays. The LCM with appropriate corrections is used to understand the macroscale contributions to field enhancement and emission current for physical emitters, with contributions from the microscale structure isolated using suitable approximations. We will show that excellent agreement can be obtained between the LCM and experiments when the net contributions of the microscale structure are substantially similar across the emitters being used, and when appropriate corrections are introduced to account for the structure on the macroscale which is not already included in the LCM.

Wigner wave packets: Transmission, reflection, and tunneling

“…Open boundary conditions [48,76,110], however, require additional considerations that make the time evolution simulations difficult, and therefore, numerical means are advantageous. For an abrupt potential like V d (x), however, ripples appear in f (x, k, t) for large values of k, particularly near regions where V (x) undergoes abrupt changes in magnitude or slope, that cannot be ignored (e.g., Figures (2) and (5) of Ref. [61]), and which undermine finite difference methods applied to Eq.…”

“…Processes associated with the field emission of electrons operate on disparate length scales that span many orders of magnitude [1][2][3]. Tunneling is exquisitely sensitive to the barrier shape [4][5][6], which in turn depends on microscale surface curvature [7][8][9][10][11][12], emitter shape [13][14][15], surface roughness [16][17][18][19][20][21][22] and nearest neighbor (shielding) effects in arrays [23][24][25].…”

Discrepancies and universality in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters

“…Cold field electron emission (CFE) by a conducting surface, when a strong electrostatic field is applied, is a phenomenon that has led to scientific and technological developments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Recently, great attention has been given by field emission community to the research of the electrostatics behind single or small cluster of emitters [17][18][19][20][21][22][23][24][25][26][27], aiming to understand the emitter's interaction that leads to charge-transfer and neighbor-field effects [22]. Particularly, an important Field Emission (FE) characterization parameter is the apex-field enhancement factor (FEF) [4].…”

Unexpected validity of Schottky's conjecture for two-stage field emitters: A response via Schwarz–Christoffel transformation

“…Following the aforementioned motivations, some recent works [12,13,[18][19][20] have studied the validity of Schot- * edgarufba@gmail.com † thiagoaa@ufba.br ‡ caio@ufba.br tky's conjecture (SC) [21]. This conjecture states that the FEF of a two-stage field emitter is the product of the FEFs of each of the two stages.…”