Reduction of charge offset drift using plasma oxidized aluminum in SETs

Aluminum oxide (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AlO}}_x$$\end{document}AlOx)-based single-electron transistors (SETs) fabricated in ultra-high vacuum (UHV) chambers using in situ plasma oxidation show excellent stabilities over more than a week, enabling applications as tunnel barriers, capacitor dielectrics or gate insulators in close proximity to qubit devices. Historically, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AlO}}_x$$\end{document}AlOx-based SETs exhibit time instabilities due to charge defect rearrangements and defects in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AlO}}_x$$\end{document}AlOx often dominate the loss mechanisms in superconducting quantum computation. To characterize the charge offset stability of our \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AlO}}_x$$\end{document}AlOx-based devices, we fabricate SETs with sub-1 e charge sensitivity and utilize charge offset drift measurements (measuring voltage shifts in the SET control curve). The charge offset drift (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {Q_0}$$\end{document}ΔQ0) measured from the plasma oxidized \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AlO}}_x$$\end{document}AlOx SETs in this work is remarkably reduced (best \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {Q_0}=0.13 \, \hbox {e} \, \pm \, 0.01 \, \hbox {e}$$\end{document}ΔQ0=0.13e±0.01e over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx 7.6$$\end{document}≈7.6 days and no observation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {Q_0}$$\end{document}ΔQ0 exceeding \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\, \hbox {e}$$\end{document}1e), compared to the results of conventionally fabricated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AlO}}_x$$\end{document}AlOx tunnel barriers in previous studies (best \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {Q_0}=0.43 \, \hbox {e} \, \pm \, 0.007 \, \hbox {e}$$\end{document}ΔQ0=0.43e±0.007e over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx 9$$\end{document}≈9 days and most \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {Q_0}\ge 1\, \hbox {e}$$\end{document}ΔQ0≥1e within one day). We attribute this improvement primarily to using plasma oxidation, which forms the tunnel barrier with fewer two-level system (TLS) defects, and secondarily to fabricating the devices entirely within a UHV system.


I.
Long-term charge offset drift measured on W119-C3 We measured long-term charge offset drift on two plasma oxidized Al/AlOx/Al SETs at the same time. In addition to the one shown in the main text (W119-C1), the results from the other SET (W119-C3) are shown in Fig. S1. From the CBO shown in Fig. S1 (a), we can see that this device exhibits larger oscillation period (ΔVg = 17.9 mV ± 0.5 mV) but narrower peak width (FWHM = 6.3 mV ± 0.3 mV for a typical peak at base temperature) compared to the device shown in the main text (ΔVg = 16.26 mV ± 0.04 mV and FWHM = 10.7 mV ± 0.7 mV for a typical peak at base temperature). This results in a smaller linewidth/period ratio, which suggests lower noise/temperature than W119-C1. Again, the nonzero current offset (negative in this case) observed in the CBO is attributed to an imperfect zero on the current preamplifier. Two different preamplifiers were used on each device and had different current offsets. The long-term repetitive CBO in Fig. S1 (b) and the charge offset (Q0) data in Fig. S1 (c) display faster linear drift of (21 ± 1) x 10 3 e/d in this device and an abrupt phase shift at t ≈ 5.6 d. This Al/AlOx/Al SET is also very stable, e.g., charge offset drift ΔQ0 = (0.30 ± 0.014) e over ≈ 7.6 days, compared to previous thermally oxidized Al/AlOx/Al SETs [Ref. 14,[18][19]29 in the main text].
Finally, Fig. S1(d) is the experimental CBO vs. temperature data with a model curve at 0.75 K on this device showing the oscillations dying down with rising temperature and vanishing at T > 1.6 K, which verifies the Coulomb blockade of SET. As discussed in the main text, we estimate the charging energy of this device to be EC/kB = 5.6 K.
(c) (d) . This device exhibits larger oscillation period (ΔV g = 18.3 mV ± 0.3 mV) but narrower peak width (FWHM = 6.3 mV ± 0.3 mV from a typical peak at base temperature) compared to the device shown in the main text (ΔV g = 16.26 mV ± 0.04 mV and FWHM = 10.7 mV ± 0.7 mV from a typical peak at base temperature). (b) Long-term repeating CBO taken over one week as a function of time. Red and green stripes represent peak and valley of CBO, respectively. (c) Extracted charge offset, Q 0 , as a function of time using Guassian method.
This device displays a linear drift of (21 ± 1) x 10 -3 e/d and an abrupt phase shift at t ≈ 5.6 d. ΔQ 0 = (0.30 ± 0.014) e over ≈ 7.6 days. (d) Measured CBO vs. temperature; the CBO oscillations die down with rising temperature and vanish at T > 1.6 K. The blue solid line represents the model CBO curve at 0.74 K.

II.
Charge offset drift measured on Al/AlOx/Al SET devices of an "inline" geometry We also fabricated devices with different geometries. Fig. S2(a) shows the SEM image of two SET islands parallel to each other. The two SETs are reflections of each other with an "in-line" arrangement. Shown in Fig. S2(b) and (c)  from this geometry, this device exhibits a smaller oscillation period (ΔVg = 9.8 mV ± 0.5 mV) as expected. Total charge offset drift, ΔQ0 = (0.68 ± 0.038) e over ≈ 3.9 days with multi-hour breaks. We can see that the oscillation phase and current level fluctuate between measurement intervals, but are stable within an interval. In the middle period of the measurements, there is a 180° phase shift from the beginning, but the phase stays stable for more than two days regardless of the interruptions.

III.
Charge offset drift measured on plasma oxidized SETs made using Co/AlOx/Co We also implemented plasma oxidized AlOx tunnel barriers into Co/AlOx/Co devices. Fig. S3(a) and ( 14, 18-19, 29 in the main text].