Oxygen ordering in untwinned ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ films driven by electrothermal stress

We experimentally investigate the displacement of oxygen vacancies at high current densities in highly untwinned ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ films grown on top of MgO substrates. Transport bridges oriented along the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ crystallographic directions [100] ($a$ axis), [010] ($b$ axis), and [110] $({45}^{\circ }$ from principal axes) reveal that the onset of vacancy migration is mainly determined by the local temperature (or equivalently by the dissipated power) rather than the associated activation energy. Exceeding this threshold value, a clear directional migration proceeds as evidenced by optical microscopy. Concomitant electrotransport measurements show that an intermediate phase, characterized by a decrease in resistivity, precedes long-range migration of vacancies. We numerically demonstrate that this intermediate phase consists of a homogenization of the oxygen distribution along the transport bridge, a phenomenon strongly dependent on the activation energy and the initial degree of disorder. These findings provide some important clues to determine the level of order/disorder in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ films based on electric transport measurements.

Figure 1

Low magnification and high magnification false-colored scanning electron microscopy images of transport bridges along the crystallographic directions $a$ (left), ${45}^{\circ }$ from $a$ (top central panel), and $b$ (rightmost panel). The lower row shows the associated resistivity vs temperature curves obtained at zero applied magnetic field. The inset in the lower central panel shows the ratio ${\rho }_a/{\rho }_b$ as a function of temperature in the normal state.

Figure 2

(a) Evolution of the sample resistivity as a function of the applied pulsed current density for bridges oriented along three crystallographic axes. The power dissipated in the bridges at the onset of the resistivity decrease ($▽$) and increase ($△$), is indicated with black arrows. The inset shows the measurement protocol using pump-probe current pulses and intercalated optical microscopy snapshots. (b) Schematic of the anisotropic $\rho \left(\theta \right)$ following an elliptic angular dependence (upper panel). The lower panel shows the experimentally determined onset of the sample resistivity decrease ($▽$) and the increase ($△$). The gray shadow covers a zone limited by the fittings to Eq. (4) for the extreme (minimum and maximum) power $p_0$ inferred from the experimental data points.

Figure 3

Bright-field optical microscopy images for the bridges oriented along $a, {45}^{\circ }$, and $b$ crystallographic directions after (EM1) mild electromigration with $\sim$ 3% increase in resistance, (EM2) severe electromigration with $\sim$ 30% increase in resistance, and (anti-EM) reversing the current polarity, so-called antielectromigration. All the images were acquired on the same sample in chronological order EM1, EM2, and finally anti-EM under ambient conditions. The black arrows indicate the current direction.

Figure 4

(a) Numerical simulation of the sample resistance for $\rho$ varying from 185 to 365 $\mu \mathrm{\Omega }\mathrm{cm}$ in steps of 20 $\mu \mathrm{\Omega }\mathrm{cm}$. The following parameters have been used for these simulations: $E_a=0.55\mathrm{eV}, \alpha =5\times {10}^{-3}{\mathrm{K}}^{-1}, x_0=0.9, \delta x_0=5\%, x_{min}=0.5$, and $x_{max}=0.95$. (b) Electromigration current determined using a criterion of a 1% increase on resistance as a function of the resistivity extracted from the numerical simulation (blue) and the experiments (orange). The inset shows the power density (left ordinate) and maximum temperature (right ordinate) at the onset of electromigration for samples of different resistivities.

Figure 5

(a) Zoom in showing the numerically calculated initial change in resistance with the current (blue line) of one of the curves in Fig. 4 together with the evolution of the residual function $r$ (orange line). (b) Evolution of the local resistance minima as a function of the degree of oxygen concentration disorder $\delta x_0$. (c) Evolution of the local resistance minima as a function of the activation energy $E_a$.

Figure 6

Numerical simulations reproducing the oxygen vacancy distribution of Fig. 3 using the anisotropic model of Sec. 2b with $E_{a_a}=0.55, E_{a_b}=0.5\mathrm{eV}$.