Local electrostatic effects of surface structure on field emission

We examined the classical electrostatic effects due to geometric surface structures on conductive field emission needles numerically using the finite element method and compared our results to several commonly applied analytic relations. Analysis of the morphology of electrochemically prepared Mo needles by high-resolution transmission electron microscopy was incorporated in the numerical analysis in the form of small surface protrusions and gross needle shape. We found that the error between the electrostatic potential defined by popular analytic equations and both analytic equations derived in prolate spheroidal coordinates and finite element method results was significant for ellipsoidal needles with and without surface protrusions. The morphology of the surface protrusion was found to introduce a significant nonlinear potential barrier near the needle surface. Finally we numerically analyzed a nonsymmetric, nonhomogeneous experimental needle indicating that even larger errors in the electrostatic potential can be expected relative to analytic equations.