Semi-analytical modeling of large area field emitters having non-identical pins

Abstract

The Line Charge Model (LCM) is an excellent analytical tool to model vertically aligned nano-tips in large area field emitters (LAFE). The linear line charge model is exact for isolated hemi-ellipsoidal nano-tips placed in a uniform external electric field. It has recently been used to model a LAFE with randomly placed identical emitters. The results are accurate when the mean spacing c is moderate to large compared to the emitter height h. In a closely packed LAFE (c⪅0.75h), the LCM underpredicts the apex enhancement factor. We introduce a heuristic correction in the LCM result that yields a better accuracy in predicting the apex enhancement factor over a wider range of mean spacing. The corrected LCM model is then used to simulate emitter shapes having a distribution in the height of emitters and apex radius of curvature Ra. A hybrid approach is adopted for non-ellipsoidal shapes where the line charge density is nonlinear and, hence, harder to implement. Predictions for the apex enhancement factor and the net emission current are found to be reasonably accurate for a LAFE with a wide variation in h and Ra values.