Current-induced switching in atomic-scale structures
Theoretical Condensed Matter Physics
Final Report Abstract
3 Summary The red-lights indicate the state of completion of the work packages and indicate in which publications the results are explained in detail. WP1 (Scheer): Low-temperature electromigration measurements on atomic contacts made from bulk superconductors (Al, Pb and Nb) as a function of temperature (below and above the critical temperature) and magnetic field (related to objectives O1 and O2). Completed [Rin20,Web18a,Kam15,Jör16,Web18b, 4-6]. Most successful was the work with Pb. We encountered difficulties with the reproducibility of the sample fabrication of Nb and therefore concentrated on the superconductors Pb and Al. No influence of the superconductivity onto the switching behavior was detected, presumably because the threshold currents exceed the critical currents by far and WP2 (Scheer): Low-temperature measurements with normal metals (Au, Cu, Ag) as a function of temperature (O1 and O2). Completed [Rin20,Web18b,Hai20,Her21], but concentrated on Au and Cu, because we came aware of ongoing research activities with Ag in the Halbritter group (BME Budapest), who developed a sample fabrication method for Ag break junctions which turned out to be very involved [20]. So far, no systematic study on Ag atomic contacts at low temperature has been reported. WP3 (Scheer): Room temperature measurements with Au contacts (O2 and O3). Attempted, but not completed, because of difficulties in the data interpretation. Reversible switching is possible both at ambient conditions and in high vacuum with similar properties as at low temperature. However, as control experiments in between the switching cycles we recorded breaking traces and conductance histograms which revealed a very fast contamination of the electrodes. We concluded that ultra-high vacuum conditions would be required to reveal the properties of atomic switches, even of the very inert metal Au properly. We therefore concentrated on the low-temperature measurements. Furthermore, room temperature reversible switching in Au [9] and Ag [21] was meanwhile reported by other authors, although not studied exhaustively. WP4 (Scheer): Optimization of low-temperature and room-temperature setups towards high stability and high speed (O3). Not fully completed, since we concentrated on the low-temperature setup, as explained above. We worked on protocols to increase the probability to form bistable and multivalued switches for Cu [Hai20] and Au [Her21]. WP5 (Nielaba, Pauly): Determination of local energy barriers and forces for mechanical stretching at low and high temperatures and for various metals (Au, Cu, Ag, Al, Pb, Nb) (O1). The investigation of the stretching process in simulations rarely showed a clear barrier. The potential energy surface could be constructed in MD and DFT for Au, Cu, Pb and Al. Nb is considerably more expensive to simulate in DFT than the other metals, so considering limited calculation resources it was put off. Ag was skipped because the experiments on Ag were also skipped. A direct connection to applied forces could not be made in the simulation setup. WP6 (Pauly, Nielaba): Computation of electromigration forces on individual atoms in atomic wires with few particles (e.g. 10 Au particles) using DFT methods, and study of structural evolutions. Development and application of the computational procedure (O1). Completed [Rin19,Rin22] Final report NI 259/14-1 | PA 1744/4-1 | SCHE 505/12-1 Page 11 of 13 WP7: (Pauly, Nielaba): Computation of electromigration forces on individual atoms in atomic wires with a larger number of particles, combining MD and tight-binding methods, and study of structural evolutions. Development and application of the computational procedure (O1). Completed [Ring 19,Rin20,Rin22]. Forces are not as useful as anticipated, as explained before. Therefore WP5-7 were executed differently as initially described in the proposal. The initially proposed approach using potential energy investigations and dynamics simulations proved to be not viable, since the current-induced forces are non-conservative, and the time scales of the current-induced forces and the atomic switching cannot be bridged in normal molecular dynamics simulations. Instead we developed and applied a scheme investigating specifically the vibration modes coupling strongest to the nonequilibrium. Those came with two relevant properties: One were threshold voltages to instability, which are in the same ranges as experimental switching voltages. The other were the modes themselves, which were used to investigate the configuration phase space and can be used to switching a contact in simulation. Summarizing: Developed a new scheme to explain switching in metallic contacts [Rin20] and create switches in simulation [Rin22]. WP8 (Nielaba, Pauly): Study of the bistable switching situation and determination of atomic structures exhibiting this behavior for various metals, temperatures, geometries (O2). Completed [Rin19,Rin22]. We found that metals are suitable candidates for bistable switches, their glass-like surface structure easily allows for the prerequisite phase space structure. The effect of temperature on the bistable switches is below the “effective temperature” of the nonequilibrium electrons (not a temperature – no thermodynamic limit, no equipartition theorem, inherent direction through the modes coupling strongest to the nonequilibrium). It was not possible to identify geometries especially suited to bistable switching from the simulation side, different geometries (e.g., crystal direction) had no influence on the threshold voltages or the contact phase space above those expected from natural variance. WP9 (Scheer, Pauly, Nielaba): Comparison of theoretical and experimental results, including continuous discussions (O1-O3). Completed [Web18b,Ring19,Ring20]. We studied voltage-induced conductance changes of Pb, Au, Al, and Cu atomic contacts. The experiments were performed in vacuum at low temperature using mechanically controllable break junctions. We determined switching histograms, i.e., distribution functions of switching voltages and switching currents, as a function of the conductance. We observed a clear material dependence: Au revealed the highest and almost conductance-independent switching voltage, while Al has the lowest with a pronounced dependence on the conductance. The theoretical study used density functional theory and a generalized Langevin equation considering the pumping of particular phonon modes. We identified a runaway voltage as the threshold at which the pumping destabilizes the atomic arrangement. We found qualitative agreement between the average switching voltage and the runaway voltage regarding the material and conductance dependence and contact-to-contact variation of the average characteristic voltages, suggesting that the phonon pumping is a relevant mechanism driving the rearrangements in the experimental contacts.
Publications
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Current-Induced Switching in Superconducting Break Junctions. Doctoral Thesis, University of Konstanz (2018)
D. Weber
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Superconducting properties of lithographic lead break junctions. Nanotechnology 29, 045703 (2018)
D. Weber, E. Scheer
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Simulating electromigration in atomic contacts. Doctoral Thesis, University of Konstanz (2019)
M. Ring
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Voltage-Induced Rearrangements in Atomic-Size Contacts. Nano Letters 20, 5773 (2020)
M. Ring, D. Weber, P. Haiber, F. Pauly, P. Nielaba, E. Scheer
