Modeling field emitter arrays using nonlinear line charge distribution

摘要

Modeling high aspect ratio field emitter arrays is a computational challenge due to the enormity of the resources involved. The line charge model (LCM) provides an alternate semi-analytical tool that has been used to model both infinite as well as finite sized arrays. It is shown that the linearly varying charge density used in the LCM generically mimics ellipsoidal emitters rather than a Cylindrical-Post-with-an-Ellipsoidal-Tip (CPET) that is typical of nanowires. Furthermore, generalizing the charge density beyond the linear regime allows for modeling shapes that are closer to a CPET. Emitters with a fixed base radius and a fixed apex radius are studied with a view to understanding the effect of nonlinearity on the tip enhancement factor and the emitter current in each case. Furthermore, an infinite square array of the CPET emitters is studied using the nonlinear line charge model, each having a height h = 1500 μm and a base radius b = 1.5 μm. It is found that for moderate external field strengths (0.3 - 0.4 V/μm), the array current density falls sharply for lattice spacings smaller than 4/3 h. Beyond this value, the maximal array current density can be observed over a range of lattice spacings and falls gradually thereafter.