$\mathrm{Nb}$-Based Nanoscale Superconducting Quantum Interference Devices Tuned by Electroannealing

In this work, we show that targeted and controlled modifications of the Josephson-junction properties of a bridge-type $\mathrm{Nb}$ nanoSQUID can be achieved by an electroannealing process allowing us to tune and tailor the response of a single device. The electroannealing consists in substantial Joule heating produced by large current densities followed by a rapid temperature quench. We report on a highly nontrivial evolution of the material properties when performing subsequent electroannealing steps. As the current density is increased, an initial stage characterized by a modest improvement of the superconducting critical temperature and normal-state conductivity of the bridges, is observed. This is followed by a rapid deterioration of the junction properties, i.e., decrease of critical temperature and conductivity. Strikingly, further electroannealing leads to a noteworthy recovery before irreversible damage is produced. Within the electroannealing regime where this remarkable resurrection of the superconducting properties are observed, the nanoSQUID can be operated in nonhysteretic mode in the whole temperature range and without compromising the critical temperature of the device. The proposed postprocessing is particularly appealing in view of its simplicity and robustness.

Figure 1

SEM image of the pristine $\mathrm{Nb}$ nanoSQUID S1 (a). The scale bar corresponds to 200 nm. (b) The superconducting transition of the device. (c) The current-voltage characteristic at 1.8 K. The arrows indicate the sweep direction of the bias current. In (a), the yellow dotted line indicates the effective area $A_{\mathrm{eff}}$ of the nanoSQUID.

Figure 2

Critical current of the pristine SQUID S1 as a function of the applied magnetic field for four different temperatures. Black lines correspond to the theoretical prediction assuming a linear current-phase relation according to the model described in Ref. [26]. The numbering from $n_v=-3$ to +4 in the panel corresponding to $T=5$ K, indicates the vorticity. The fitting parameters obtained from the simulations are listed in Table 1.

Figure 3

SEM images obtained during the electroannealing process for sample S3. The upper left panel shows the values of the maximum resistance ($R_{\max }$) in red (squares) obtained at a current $I_{\mathrm{EA}}$ and the minimum resistance ($R_{\min }$) in blue (dots) obtained after the current has been reduced to 1 $\mu \mathrm{A}$. (a)–(d) selected SEM images after the device has been submitted to EA.

Figure 4

(a) Selected set of $R(T)$ curves for sample S1 measured with an applied current $I=1\mu \mathrm{A}$ after subsequent electroannealing processes. (b) Evolution of the critical temperature of the weak link $T_c^{\prime }$ and the critical temperature of the arms of the SQUID $T_c$. (c) The normal-state resistance $R_{10\mathrm{K}}$ as a function of the EA number. $I_{\mathrm{EA}}$ is given for some EA steps with the same color code as in (a). Regions I, II, and III are described in the text.

Figure 5

Critical current of the SQUID as a function of the applied magnetic field for three different temperatures after EA14 (sample S1). The parameters of the simulations are listed in Table 2. The numbering from $n_v=-3$ to +3 in the panel corresponding to $T=5$ K, indicates the vorticity.

Figure 6

Maximum value of the critical current $I_c^{\max }$ (a) along with the relative peak-to-peak amplitude oscillation $\mathrm{\Delta }{I}_c/I_c^{\max }$ (b), after each EA step for $T=5$ K (sample S1). EA numbers with no data point correspond to situations with no measurements.

Figure 7

Critical current $I_c$ and retrapping current $I_r$ of sample S4 as a function of temperature for the pristine sample (a), after EA07 (b), EA09 (c), and EA13 (d). The temperature above which the current-voltage characteristics become reversible, $T_h$, is indicated in (a). The blue colored area in the inset of (a) shows that the range where the SQUID can be operated in the dissipative state is increased by EA process at expense of reducing $I_c$. The insets in (b)–(d) show $I_c(B)$ and $I_r(B)$ for the corresponding EA step at 3 K.

Figure 8

Voltage oscillations observed for sample S4 after EA13. The bias currents are 132, 130, 104, and 30 $\mu \mathrm{A}$ for $T=1.8$, 3, 5, and 7 K, respectively.