| The electric field enhancement obtained from sharp emitting structures is of great practical and theoretical interest. In this thesis, we use conformal mapping to investigate the field enhancement of several rectilinear and circular geometries, including a single rectangular ridge, a trapezoidal ridge, a semi-circle, and their superposition, i.e., one ridge on top of another. Simplified scaling laws have been derived where possible.;The composite field enhancement factor of the double ridge with a micro-protrusion on top of a macro-protrusion is well approximated by the product of the individual protrusions' field enhancement factors over a wide range of geometric aspect ratios, as conjectured by Schottky. Where the approximation fails, correction terms in the form of a power series are derived.;Accurate expressions for the divergent electric field near the sharp edges are also derived. These divergent electric fields can be used to obtain accurate estimates of the total current emitted across the surface of a rectangular ridge.;The total emitted current is used to calculate an effective field enhancement for the entire emitting surface. Using the effective field enhancement model, the transition to space charge-limited current density is discussed. |
