Effect of pulse duration on current-induced selective oxygen migration in high-Tc superconductors

Abstract

High current densities can induce the directional diffusion of atoms in metallic films. In YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO), this electromigration process selectively acts on oxygen atoms lying in the Cu-O chains, permitting to vary the oxygen concentration in a targeted spot of high current density. This approach has proven successful in mapping the phase diagram of the material as a function of carrier concentration or as a way to manufacture memristive devices owing to its reversibility under small bipolar excitations. Thus far, most of the investigations have been limited to pulsed excitation with current/voltage pulses on a millisecond or longer scale, for which thermal effects undeniably influence the process. In the present work, we explore the impact of pulse length $δt$ on the onset current of electromigration, $I_{\text{EM}}$, of YBCO bridges, covering the range from 200 ns to 1 ms. As $δt$ decreases below $\sim 10~μ$s, $I_{\text{EM}}$ exhibits a rapid increase. Analytical and numerical estimates of the local temperature show that as pulses shorten, the temperature decreases, making the electromigration process more athermal. These findings are relevant for the operation of memristors and should be taken into account when describing the effects of thermomagnetic instabilities in thin films.

Figures (6)

• Figure 1: (a) Schematics of the measurement setup. Two different pulse generators are used. One contact of the sample is always connected to the pulse generator's output, whereas the other contact is either connected to ground (with the unipolar pulse generator) or to the bipolar pulse generator, as pictured by the full or dotted lines on the left of the sample, respectively. The pulse generator applies a voltage along the samples and the current thus circulates horizontally. The vertical voltage leads allow for a four-point measurement of the constriction resistance. Panels (b)-(e) show the pulse shape evolution for the unipolar (b,d) and bipolar (c,e) pulse generator output current (b,c) and four-point voltage across the constriction (d,e) as a function of the pulse length. The distortion of the voltage pulse is apparent for the shorter pulses, whereas the current pulses remain less affected. The pulse length is indicated in panels (b) and (c) in µs.
• Figure 2: Consecutive resistance curves for a pulse sweep from long (1ms) to short (244ns) pulses in the same sample. Panel (a) displays the evolution of $R_{\text{pulse}}$. The inset shows the evolution of the resistivity temperature coefficient $\alpha$ after each electromigration cycle, again derived from the data of Semba2001. Panel (b) shows the evolution of $R_{\text{min}}$. The gradual increase of $R_{\text{min}}$ with decreasing pulse length arises because all measurements are performed on the same sample. A slight decrease of $R_{\text{min}}$ is observed before entering the electromigration regime. The right axis converts the resistance change into oxygen content using data from Semba2001. The inset defines the electromigration current $I_{\text{EM}}$ as the value where $R_{\text{min}}$ has increased by 3%. The final resistance reached at a given pulse width becomes the starting resistance for the next sweep. Panel (c) shows the empirical $\beta$ coefficient as a function of the pulse length. The inset displays the same data as $\beta \delta t$ vs $\delta t$.
• Figure 3: Panel (a) and (b): Dependence of the electromigration current on the pulse length for different scanning orders: long-to-short ($\bigtriangledown$) or short-to-long pulses ($\bigtriangleup$)). Panel (a) shows measurements on a single sample during cycling $\delta t$ from short to long pulse lengths and back, whereas panel (b) shows the results for two independent samples. (c) Numerical estimation of the electromigration current as a function of the pulse length. (d) Dependence of the electromigration current on the pulse length, obtained through finite element simulations.
• Figure 4: (a) Estimation of the central constriction temperature using Eq. (\ref{['eqn:sample_thermometer']}) as a function of the pulsed current. Each curve has been colored according to the pulse length, as in Fig. \ref{['fig:EM_curves']}). The inset gives the temperature for a fixed current pulse amplitude (7 mA). It can be seen that longer pulses result in higher temperatures. (b) Comparison of different models to assess the temperature during electromigration for varying pulse lengths. Models: You et al.you_analytic_2006 (Eq. (\ref{['eqn:you']}) with $\alpha = 1$), sample as a thermometer (Eq. (\ref{['eqn:sample_thermometer']})), heat balance model (Eq. (\ref{['eqn:T_EM']})). The vertical line at $\delta t_c = 2$ µs indicates the critical time above which the You et al. model is expected to lose validity.
• Figure 5: (a) Simulation domain: The back side of the substrate (green) is kept at $T_0$, while the top surfaces (substrate and YBCO film) can also exchange heat via convection at the top). (b) Depiction of the mesh used in the finite element simulations. The blue domain is the YBCO film, in which the (i) heat transfer with Joule heating, (ii) electrokinetics and (iii) electromigration is solved. The leftmost side is kept grounded, whereas the right side is subjected to the current pulses. The difference in electric potential between the two central vertical leads is used to compute the four-point resistance. The gray domain is a part of the substrate, in which only heat transfer is solved for.