Local insulator-to-superconductor transition in amorphous InO$_x$ films modulated by e-beam irradiation

Abstract

We present a novel method enabling precise post-fabrication modulation of the electrical resistance in micrometer-scale regions of amorphous indium oxide (a-InO$_x$) films. By subjecting initially insulating films to an electron beam at room temperature, we demonstrate that the exposed region of the films becomes superconducting. The resultant superconducting transition temperature ($T_c$) is adjustable up to 2.8 K by changing the electron dose and accelerating voltage. This technique offers a compelling alternative to traditional a-InO$_x$ annealing methods for both fundamental investigations and practical applications. Moreover, it empowers independent adjustment of electrical properties across initially identical a-InO$_x$ samples on the same substrate, facilitating the creation of superconducting microstructures with precise $T_c$ control at the micrometer scale. Some possible mechanisms for the observed resistance modifications are discussed.

Figures (6)

• Figure 1: (a) A negative PMMA resist mask (yellow) was deposited on highly-doped Si substrates coated with 100 nm of thermally grown SiO$_2$ and (b) patterned using standard EBL. (c) a-InOx thin films (cyan) were then deposited in an oxygen-controlled atmosphere to obtain samples close to the SIT. (d) After lift-off, the pristine samples evolved at room temperature for over a day and were characterized by measuring the $R(T)$ curves down to $\sim1.6$ K. (e) Controlled e-beam exposure to pattern microstructures on the InOx channels resulted in increased conductivity, eventually crossing the SIT.
• Figure 2: (a, b) Geometry of two channels from substrates S2 and S11, and (c, d) their corresponding $R_\square (T)$ curves before (reference) and after the e-beam treatment. Doses are indicated as multiples of the standard dose for PMMA resist, 250 $\upmu$C cm$^{-2}$. A 20 kV e-beam was used to expose samples on substrate S2, finding a progressive evolution with dose, from insulating to superconducting behavior. With a dose of 1000$\times$, the sample became superconducting below 1.9 K. A 2 kV e-beam at higher doses was used to expose samples on S11. All the channels of sample S11 became superconducting after the treatment, with a progressive increase of $T_c$ with dose, from 2.28 K up to 2.84 K, and a diminution of the normal state sheet resistance from 12 k$\Omega$ at 4.2 K (reference sample, not shown) down to less than 1 k$\Omega$ for a dose of 12000$\times$. This anticorrelation of normal state resistivity and $T_c$ is also present in a-InO$_x$ samples made by tuning the O$_2$ pressure during deposition. (e) SEM micrograph of S11, where the left channel had been previously treated (12000$\times$ dose) and the right one was kept pristine until before the capture. No morphological changes could be observed between untreated and treated channels by visual inspection.
• Figure 3: Results of the e-beam treatment with different acceleration voltages. (a) Diagram of the irradiated area, a $1~\upmu$m wide line in the middle of the a-InO$_x$ channel, represented as the shaded area on top of the optical microscope image. (b) $R_\square (T)$ curves measured for substrate S9 before (reference, solid black line) and after the treatment. A clear $T_c$ increase was observed when the acceleration voltage of the electrons was reduced from 20 kV (long-dashed red line, $T_c = 2.0$ K) to 2 kV (short-dashed blue line, $T_c = 2.8$ K). (c) Evolution of $T_c$ with the acceleration voltage EHT for three different samples.
• Figure 4: The spatial resolution of the e-beam treatment was tested using different acceleration voltages and geometries, and with a dose of 6000$\times$, almost sufficient to saturate the $T_c$ value (see Fig. \ref{['Figure2']} (d)). (a, b) $1\;\upmu$m wide lines, embedded in an insulating matrix, and separated by an insulating gap of length $s$, were drawn on substrate S9 at both 2 kV and 20 kV. (c, d) On substrate S6, lines of different width $w$, overlapping $10~\upmu$m longitudinally and separated by a distance $s$ transversally were drawn instead. (e, f) Substrate S11 was finally used to draw $1~\upmu$m wide fully superconducting channels separated by an insulating gap of length $s$. As shown, fully superconducting behavior (i.e., $R=0$) was not observed above 1.6 K for $s\geq2\;\upmu$m, and the gap remained insulating for $s\geq4\;\upmu$m. Nevertheless, the superconducting transition of the exposed part remained visible in all samples, evidencing the characteristic sudden resistance drop at a remarkably repeatable $T_c$ within the same batch [see e.g. the shaded area in (f), with the exception of the 100 nm lines in (d)].
• Figure 5: Simulations of the e-beam electron trajectories at different acceleration voltages: (a) 2 kV; (b) 5 kV; (c) 20 kV. The simulations were done using CASINO CASINO, and assuming 30 nm of In$_2$O$_3$ (red), 100 nm of SiO$_2$ (blue) and 10 $\upmu$m of Si (green).