Critical temperature in feedback-controlled electromigration of gold nanostructures

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, T _c , 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 T _c 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 T _c 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 (R _th ), and estimate that T _c in the constriction varies with R _th for higher resistance structures. Critical power measurements on a second series of asymmetric bowties further suggests that T _c also depends on the alignment of the electron flow with the temperature gradient at the constriction.