Fabrication Optimization of Suspended Stencil Mask Lithography for Multi-Terminal Josephson Junctions

TL;DR

This work demonstrates that suspended stencil masks can be reliably used for in situ fabrication of short, multi-terminal Josephson junctions. By systematically varying center width $cw$, arm width $aw$, and the angle of sharpness $\alpha$ across $270$ designs and evaluating them with SEM, the authors map mask yield and minimal dimensions, finding reliable fabrication with $cw$ down to $40\,\mathrm{nm}$ for several configurations. They establish measurement methodologies based on SEM line scans and threshold-based geometry extraction, and discuss data presentation and cross-sample reproducibility. The study provides practical mask-design guidelines and highlights the potential for a PHIDL-based mask library to enable scalable, reliable fabrication of complex, short weak-link networks, while noting deposition-induced strain as an important consideration for future work.

Abstract

Stencil mask lithography is an advanced technique for fully in-situ fabricating Josephson junctions, which is increasingly being used for multi-terminal Josephson junctions. This study provides information on the optimal mask design and mask reliability. For this, 270 mask designs were systematically fabricated and investigated under scanning electron microscope. Reliable statements are made about mask yield, minimal dimensions, and systematic dependencies on the number of superconducting terminals. We find that stencil mask lithography can be used reliably for fabricating multi-terminal Josephson junctions, enabling lateral mask dimensions down to 40$\,$nm on average.

Figures (10)

• Figure 1: a) Visualisation of a suspended stencil mask for a three-terminal junction with normal conducting material (N) deposited underneath. The mask itself is made of three pillars (SiO$_2$) holding up the top Si$_3$N$_4$. b) Deposited Nb on top of the mask. The mask casts a shadow onto the underlying Si substrate. Therefore, the geometry of the mask is directly connected to the resulting device geometry on the substrate. c) Finished three-terminal junction after mask removal and subsequent etching step to separate the superconducting electrodes, revealing the Si substrate.
• Figure 2: Fabricated masks and determination of mask dimensions. a) Scanning electron microscopy image of a fabricated design cell containing three rows for two-, three-, and four-terminal masks, respectively. The arm width was set for each design cell (here $aw = 300\,$nm) and the center width was increased from left (10$\,$nm) to right (100$\,$nm) in 10-nm-steps. Broken (left) and intact (right) stencil masks were easily identifiable under SEM. The red-marked masks were broken and the green-marked masks were intact for this particular design cell. b)-d) In total masks for two-, three-, and four- terminal Josephson junctions were investigated. The images correspond to the masks in a) and their respective frame color equals that of the data, which are presented throughout the study, for the corresponding number of arms. e) Geometry of a three-terminal junction and design parameters used in this study: center width ($cw$), center length ($cl$), arm width ($aw$). Together, they define the angle of sharpness ($\alpha$). f) An exemplary center width measurement of the mask in c) under SEM using a line scan. The position of the line scan is indicated in the SEM image on the right as a white line. In this particular example, the center width was determined to be $cw = 66\,$nm. Information on determining the threshold value (red line) is given in Supplemental Material.
• Figure 3: Number of intact masks $N$ depending on the designed center width $cw$ and designed arm width $aw$ with an accuracy of 25$\,\%$. The more arms a mask has, the smaller its center width can be designed. Above a certain designed $cw$, the number of intact masks is close to 100$\,\%$.
• Figure 4: Geometrical results from the SEM line scans. Each data point is indicated by a marker corresponding to the number of terminals of its mask. The solid lines serve as a guide to the eye and data points are transparent. a) The optimally designed $cw$ depending on the designed $aw$. On average, four-terminal masks can be designed down to 30$\,$nm, three-terminal masks masks down to 40$\,$nm, and two-terminal masks down to 50$\,$nm. b) The smallest realized center width $cw$ vs. designed center width. Two- and three-terminal masks show a linear dependence on $cw$ design whereas the realized $cw$ of the four-terminal masks scatter around a constant value. c) The difference between realized and designed arm width. The dashed red line indicates the case of matching of designed and achieved values of $aw$. All values scatter equally around $-10\,$nm. d) Relation between the realized angle of sharpness $\alpha$ and the realized center width $cw$, assuming an as-designed center length of $cl = 1\,\mu$m.
• Figure S1: Number of intact masks $N$ with two-terminals (a), three-terminals (b), and four-terminals (c). Data shown for each sample individually, with every mask design twice on each sample.