Electrical Breakdown between Metal Electrodes in High Vacuum. I. Theory

Abstract

A theoretical description of electrical breakdown across narrow gaps in high vacuum is presented under conditions for which surface cleanliness, work functions, gap geometry, and cathode surface roughness are well defined. Two basic initiating mechanisms are considered: (1) thermal processes initiated at both the anode and the cathode by the prebreakdown field-emitted electron current, and (2) mechanical processes resulting from yield of one of the electrode surfaces under the action of electrostatic stress produced by the electric field in the gap. In the case of thermal breakdown initiation, there exists a boundary between an anode and a cathode-initiated arc which can be expressed in terms of the factor γ by which the gross field in the gap is enhanced at the tip of microscopic cathode protrusions. Solution of the heat conduction equation is given for the general case of dc or pulsed gap voltages. This leads to a distinction between three ranges of pulse duration, and for each region, a simple analytical expression is given for the boundary value γ0 which separates cathode- and anode-initiated breakdown. Based on the considerations presented here, some practical limitations of several electrode materials are given.