Self focusing of field emitted electrons at an ellipsoidal tip

In models of field emission the needle is usually terminated by a hemispherical cap. Here we choose to terminate it with a hemiellipsoidal cap and use a three-dimensional Wentzel–Kramers–Brillouin method for the computations. This has two important consequences: as the ellipsoid becomes more elongated, (a) the effective emission area is decreased and (b) the quantum mechanically computed electron paths converge toward the needle axis. Both mechanisms produce a self-focusing of the field emitted electrons.