Mechanism of surface-tension reduction by electric-field application: Shape changes in single-crystal field emitters under thermal-field treatment

The shape change of the < 100 >-oriented tungsten single-crystal field emitter tip under thermal-field (TF) treatment was systematically studied with increasing remolding field (i.e., reversely polarized field opposite to field-emission polarity) at a constant temperature. The initially hemispherical emitter tip builds up to polyhedral shapes with increasing remolding voltage. These shapes are formed by certain low-index crystal planes. On further increase of the voltage, an overremolding state is reached in which the emitter takes a rugged surface structure. A thermodynamic model is proposed to explain the buildup mechanism utilizing the reduction of the surface tension under the influence of a strong electric field. The theory assumes the emitter-extractor system to comprise an electric capacitor and includes the electrostatic-field energy stored around the emitter into the system under consideration. It is shown that the electrostatic-field energy term in the Gibbs free energy could be interpreted as an effective reduction of the surface tension. The initially moderate anisotropy of the intrinsic surface tension is increasingly enhanced by the electrostatic-field energy through the reduction mechanism. The facets on the emitter surface consequently develop in accordance with the Wulff construction of the equilibrium crystal shape (ECS). By application of an electric field, the surface free-energy anisotropy can be made large enough to induce complete faceting of the crystal even at an elevated temperature where the crystal shape can immediately follow the ECS.