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

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.