Thermomechanical analysis of failure of metal field emitters

Abstract

An analysis of the thermomechanics of metal (chiefly molybdenum) field emitters under normal operating conditions is given. The focus is on various ‘‘intrinsic’’ phenomena and the possibilities of triggering catastrophic breakdown. The heating is found to be predominantly Nottingham in origin (as opposed to ohmic) and is not appreciable unless the currents are well beyond the normal operating regime, e.g., as might occur under arcing conditions. As a result, the increases in temperature in operating tips are generally minimal unless the heat sinking to the substrate is weak, e.g., in ultrasharp tips, in tips on long, narrow posts, and/or in tips with severely degraded thermal conductivity. Apart from these exceptions, the small temperature excursions mean that no thermal runaway, melting, thermal desorption, or other direct thermal effects occur. Thermal stresses are of course also minimal; however, Maxwell stresses can be large under normal operating conditions, approaching the yield strength under high bias conditions.