Critical temperature in feedback-controlled electromigration of gold nanostructures

Abstract

This paper presents several experiments demonstrating the need for a more nuanced picture of electromigration (EM) than that of a fixed critical junction temperature at which EM onset occurs. Our data suggests that even for a fixed cross-sectional geometry the critical junction temperature for EM, Tc, varies with environmental temperature, thermal resistance of adjacent regions, and even the direction of the current flow in asymmetric structures. We have performed feedback-controlled EM on nanowires at environmental temperatures between 75 and 260 K and fit the EM onset points with a constant junction power model. We find that average fit critical power is monotonically increasing with decreasing temperature, but is decidedly nonlinear at lower temperatures. We extract and compare the corresponding Tc values using several different thermal models which utilize measured values of nanowire thermal conductivity for our devices: these models all agree on a moderately increasing Tc with decreasing environmental temperature. This is tentatively explained by enhanced current-driven annealing on the voltage ramp prior to EM onset which decreases structural scattering, thereby increasing the critical temperature at which wind-force-driven hopping events will achieve a critical atomic flux. We also obtain fit critical power for a series of bowtie structures of identical constriction but varying adjacent thermal resistance (Rth), and estimate that Tc in the constriction varies with Rth for higher resistance structures. Critical power measurements on a second series of asymmetric bowties further suggests that Tc also depends on the alignment of the electron flow with the temperature gradient at the constriction.