# Alternating Bias Assisted Annealing of Amorphous Oxide Tunnel Junctions

D. P. Pappas<EMAIL_ADDRESS>Rigetti Computing, 775 Heinz Avenue,
Berkeley, CA 94710, USA  M. Field  Rigetti Computing, 775 Heinz Avenue,
Berkeley, CA 94710, USA  C. Kopas  Rigetti Computing, 775 Heinz Avenue,
Berkeley, CA 94710, USA  J. A. Howard  Rigetti Computing, 775 Heinz Avenue,
Berkeley, CA 94710, USA  X. Wang  Rigetti Computing, 775 Heinz Avenue,
Berkeley, CA 94710, USA  E. Lachman  Rigetti Computing, 775 Heinz Avenue,
Berkeley, CA 94710, USA  Lin Zhou  Ames National Laboratory, Ames, IA 50011,
USA  Department of Materials Science and Engineering, Iowa State University,
Ames, IA 50011, USA  Jinsu Oh  Ames National Laboratory, Ames, IA 50011, USA
Department of Materials Science and Engineering, Iowa State University, Ames,
IA 50011, USA  K. Yadavalli  Rigetti Computing, 775 Heinz Avenue, Berkeley, CA
94710, USA  E. A. Sete  Rigetti Computing, 775 Heinz Avenue, Berkeley, CA
94710, USA  A. Bestwick  Rigetti Computing, 775 Heinz Avenue, Berkeley, CA
94710, USA  M.J. Kramer  Ames National Laboratory, Ames, IA 50011, USA
Department of Materials Science and Engineering, Iowa State University, Ames,
IA 50011, USA  J. Y. Mutus  Rigetti Computing, 775 Heinz Avenue, Berkeley, CA
94710, USA

###### Abstract

We demonstrate a transformational technique for controllably tuning the
electrical properties of fabricated thermally oxidized amorphous aluminum-
oxide tunnel junctions. Using conventional test equipment to apply an
alternating bias to a heated tunnel barrier, giant increases in the room
temperature resistance, greater than 70%, can be achieved. The rate of
resistance change is shown to be strongly temperature-dependent, and is
independent of junction size in the sub-micron regime. In order to measure
their tunneling properties at mK temperatures, we characterized transmon qubit
junctions treated with this alternating-bias assisted annealing (ABAA)
technique. The measured frequencies follow the Ambegaokar-Baratoff relation
between the shifted resistance and critical current. Further, these studies
show a reduction of junction-contributed loss on the order of $\approx 2\times
10^{-6}$, along with a significant reduction in resonant- and off-resonant-two
level system defects when compared to untreated samples. Imaging with high-
resolution TEM shows that the barrier is still predominantly amorphous with a
more uniform distribution of aluminum coordination across the barrier relative
to untreated junctions. This new approach is expected to be widely applicable
to a broad range of devices that rely on amorphous aluminum oxide, as well as
the many other metal-insulator-metal structures used in modern electronics.

Cabrera-Mott oxidation, annealing, amorphous material, tunnel junction quantum
computing, superconducting qubits, transmon, SQUID

††preprint: AIP/123-QED

##  I Introduction

The preparation of amorphous thin film materials is surprisingly simple and
devices based on them are ubiquitous in electronics, but their morphology is
surprisingly complex and challenging to control. Among other similar
materials, amorphous aluminum oxide tunnel (a-AlOx) junctions stand out due to
their importance in both cryogenic and room temperature devices. Applications
range from those that utilize the Josephson effect Josephson (1962), such as
SQUID magnetometers Clarke (2004), superconducting qubits Devoret (1997);
Nakamura  _et al._ (1999), amplifiers Castellanos-Beltran  _et al._ (2009);
Macklin  _et al._ (2015), RSFQ logic Likharev and Semenov (1991), to room
temperature magnetic tunnel junctions and memory elements Zhu and Park (2006);
Rippard  _et al._ (2002); O’Dwyer (2004).

Figure 1: (a) Oxide growth on aluminum according to the Cabrera-Mott mechanism
Cabrera and Mott (1949); Zhang  _et al._ (2022a). The primary assumption is
that electrons can freely ionize adsorbed oxygen. This leads to a relatively
low voltage, $V_{\mathrm{Mott}}\sim 1\mathrm{V}$, that creates a strong
electric field in the thin oxide. Aluminum cations and oxygen anions at the
surfaces and in the barrier feel opposite forces due to this field and
exchange places, mediated by vacancy motion. (b) Method of mixing the
Al/AlOx/Al trilayer by applying alternating voltages, on the order of
magnitude of $V_{\mathrm{Mott}}$ but less than the dielectric breakdown
voltage O’Dwyer (2004), between the two plates. This applies alternating and
opposing forces on the two species.

Due to the cryogenic application of these oxide barriers for Josephson
junctions, we can probe not only their resistance but also the prevalence of
defects and loss using superconducting qubits. This is especially relevant to
the field of quantum information since a-AlOx is a key ingredient in transmon
qubits Koch  _et al._ (2007), the invention of which has fueled much of the
rapid development of superconducting applications research over the past
decade. The junction properties are crucial in the overall properties and
performance of the qubit. Most importantly, the critical current, $I_{c}$ of
the barrier sets the Josephson energy of the device,
$E_{J}=I_{c}\Phi_{0}/2\pi$, where $\Phi_{0}$ is the flux quantum, which
determines the parameters such as the frequency, anharmonicity, and charge
noise sensitivity. Specifically, $I_{c}$ can be predicted by the
Ambegaokar–Baratoff formula, i.e. $I_{C}=\pi\Delta/2eR_{n}$ van Duzer (1999),
where, the variables $R_{n}$ and $\Delta$ are the resistance of the junction
(in its normal state) and the superconducting gap of the electrodes.

Unfortunately, while it is essential that $I_{c}$, and hence $R_{n}$, is well
defined, a large spread of $R_{n}$ in nominally identical junctions is
typically observed, on the order of 5-10% at the wafer level Muthusubramanian
_et al._ (2023). This is due to both intrinsic properties and extrinsic
effects. Intrinsic issues include the exponential dependence of the tunneling
on the thickness Zeng  _et al._ (2016); grain structure; and interface
roughness. Extrinsic effects arise from the effects of lithography
uncertainties Bilmes  _et al._ (2021), processing, electrostatic sensitivity,
and circuit design.

Figure 2: Schematic diagram of the bias schemes used to anneal tunnel
junctions. (a) A block diagram of the apparatus. In all cases, the voltage
source has the positive terminal connected to the top electrode and the
negative terminal connected to the bottom electrode sitting on the substrate.
(b) A circuit diagram. (c) Bias pulses at $\mathrm{V_{A}}$ are applied for 1
second. In this paper $\mathrm{V_{A}}$ = 0.9 V. Between the bias pulses a low
measurement pulse of $\mathrm{V_{M}}$ = 10 mV is used to measure the low bias
resistance of the junction. (d) Data for voltage-assisted annealing using
alternating bias assisted anneal (ABAA) at $80\degree\mathrm{C}$ vs. unipolar
(positive and negative w.r.t. the top electrode) voltage pulses. The maximum
voltage amplitude $V_{A}=\pm 0.9\mathrm{V}$ with a 1-second pulse length. The
area of the junction under test is $1.55~{}\mu\mathrm{m}\times
0.24~{}\mu\mathrm{m}=0.37~{}(\mu\mathrm{m})^{2}$. The inset is a zoom in on
the start of the ABAA process and shows the cyclic change in junction
resistance with a repeated sequence of small and large resistance changes when
applying alternating bias bipolar pulses.

Moreover, the amorphous nature of the oxide layer results in the inclusion of
defects that can cause two-level systems (TLS’s) near the qubit frequency that
typically reduce coherence, or the defects can result in two-level fluctuators
(TLF’s) at very low frequencies that push the qubit frequency around Martinis
_et al._ (2005); Schlör  _et al._ (2019).

The default method of making junctions, also used in this work, employs
thermal oxidation of an aluminum surface described by the Cabrera-Mott model
which shows the initial oxidation is driven by an intrinsic electric field
Zhang  _et al._ (2022a); Cabrera and Mott (1949). This process is convenient
and powerful because it is conformal and self-limiting in thickness. In the
thin-barrier limit the formation of the oxide barrier is governed by drift-
dominated atomic diffusion Zhang  _et al._ (2022a); Xu  _et al._ (2012) of the
charged constituent elements, Al3+ and O2-, in opposite directions, as
illustrated in Fig. 1 (a). This diffusion is driven by the strong $E$-field
$\sim$ 1 GV/m generated by the adsorbed ionic ad-layer. In these, and other
metal-insulator-metal oxides, the relevant parameter is referred to as the
Mott voltage, $V$Mott$\approx$ 0.5-1 V for aluminum oxide Cai  _et al._
(2012).

There have been many efforts to improve the properties of the a-AlOx material,
focused primarily on understanding and optimizing the junction formation and
post-processing, i.e. pressure, time, Mallison (1995), interface preparation,
etches, simulations, etc., see Ref. Kim  _et al._ (2020); Cyster  _et al._
(2021) and citations therein. These efforts have met with limited success, and
it is typically assumed that the properties of the junctions, as formed, are
relatively frozen-in and difficult to adjust. For example, annealing the
junctions to high temperatures can slightly change the resistance, globally
heating many junctions has limited efficacy due to nanoscopic morphology
differences of nominally identical junctions at the domain and atomic level.
Since the resistance tends to increase on continued annealing, novel
approaches to sequentially targeting the junctions have been useful in
mitigating these spreads by targeting a slightly lower resistance than desired
and then heating the individual junctions locally to bring them into tolerance
Hertzberg  _et al._ (2021); Zhang  _et al._ (2022b); Kim  _et al._ (2022).
However, these procedures involve the addition of optical elements to the test
and measurement apparatus and appear to be limited to adjustments of the
resistances up to about 10-12%, i.e. on the order of the junction spread. This
limits the number of junction arrays that can be successfully adjusted, based
on the initial distribution of the junctions.

On the other hand, it has been shown that oxidation can be enhanced by an
external voltageKonkin and Adler (2008), for example, that generated by e-beam
bombardment at the surface Ebinger and Yates (1998). When comparing with other
physical material systems, e.g. magnetic Zhang (2001) and piezo-
electricYamamoto  _et al._ (2014), where annealing while applying an
alternating field polarity can have significant positive effects, this
approach has not yet been investigated in connection to a-AlOx tunnel
junctions and is illustrated in Fig 1(b).

##  II Experimental setup and results on junctions

In this work, we have investigated this approach in a protocol that we refer
to as alternating bias-assisted anneal (ABAA). The ABAA technique entails
applying an alternating polarity voltage pulse train to the junctions during a
global, low-temperature anneal. ABAA can be implemented using a conventional
probe station with a low-temperature heating stage, as illustrated in Fig. 2.
Using this technique, it can be expected that the Al3+ cations and O2- anions
in the barrier will be driven in opposite directions at each pulse. By
alternating the bias voltage the ions can be driven out of local, metastable
sites into a lower energy configuration. In general, the guidelines used for
the voltage profiles were that it should be on the order of $V$Mott and less
than the breakdown voltage, $V_{B}\sim 1.5$ V O’Dwyer (2004); Cai  _et al._
(2012). When considering the time duration of the pulse, we note that by
staying well below $V_{B}$ the junction properties were observed to evolve
relatively slowly, on the order of 100’s of seconds, similar to the known
oxidation rates of these surfaces. Finally, a relatively low temperature is
desired to not expose junctions to a higher temperature than the highest
temperature they are exposed to during the fabrication process.

The equipment and pulse sequences used for the tuning consist of a standard
source-measure unit (SMU) and a probe station with a heated platen,
illustrated in Fig. 2(a,b). The SMU was programmed to provide a train of
1-second-long anneal-assist pulses after the wafer was brought to the target
temperature. The pulse amplitudes were set in the range of 0.8 - 1.1 V. The
resistance of the junctions was measured after each pulse with an additional
pulse at low voltage. As shown in Fig. 2(d), when unipolar pulse trains were
applied to the junctions a relatively small change in the resistance was
observed. Changes of about 2% and 6%, respectively, were registered for
negative-only and positive-only voltages after about 200 pulses. However, when
alternating-polarity-bias (AB) pulses were used, as illustrated in Fig. 2(c),
resistance changes of more than 70% were recorded as shown in Fig. 2(d). In
addition, we note two new features of the ABAA process that we address later
in this paper: first, that a cyclic response was typically observed for the AB
pulse trains, as illustrated in the Fig. 2(d) inset; and second, a systematic
jump in the resistance curve typically occurs during the process.

Figure 3: Junction resistance change as a function of the number of AB pulses
for four nominally identical junctions from the same wafer at different
substrate temperatures. In addition to the relatively smooth increase in
junction resistance as the AB pulses are applied, resistance jumps are
observed for each device, sometimes appearing as a random telegraphic
switching of resistance that settles at the higher resistance value.

Further studies including the temperature dependence of this effect are shown
in Fig. 3. We find the rate increases significantly as the temperature is
increased from 25 up to 80$\degree$C. The increase is on the order of
2$\times$ every 10$\degree$C, consistent with that expected from an Arrhenius
law. On the other hand, the size dependence (not shown) is flat over more than
an order of magnitude, indicating that the mechanism is not due to the
perimeter or other side effects. This points to local effects such as
reordering and increased coordination of the atoms in the barrier, leading to
changes in the effective barrier height as atoms reach a more stable
configuration or interfacial modifications such as smoothing or thickening of
the barrier. Furthermore, since the data was taken at constant voltage, we
infer that it is not a current-driven diffusion effect. This has more
practical implications from the perspective of SQUID-based devices, such as
sensors and tunable qubits, because these devices are typically made using two
parallel circuits with junctions that may or may not be the same size.
Finally, we note that the resistance jumps are also evident in the 25, 40, and
60$\degree$C data.

Figure 4: Summary of qubit characterizations. (a) A spectrum of a tunable
qubit that has been treated with ABAA. (b) Measured junction resistance shift
(red dots) resulting from the ABAA trimming of junctions. (c) The blue dots
show the predicted frequency change from untreated values using the
Ambegaokar-Baratoff relation while the orange stars show the measured
frequency change.

##  III Effect of ABAA on transmon qubits

We probe the effect of ABAA on the tunneling properties of the barrier by
characterizing transmon qubits taken from the same wafer with and without
ABAA. We measure a variety of properties associated with the junctions:
whether $I_{C}$ follows the behavior expected by the Ambegaokar-Baratoff
relationship, the impact of the barrier on qubit loss, and the presence of
strongly coupled TLS’s. We measured both tunable and fixed-frequency qubits
Manenti  _et al._ (2021). For this test, we select 5 equivalent chips. Two
chips containing 16 qubits each were treated with ABAA. Of these, 24 qubits
had AB voltage pulses applied (3 qubits failed to a short circuit, 8 tunable
qubits lost tunability), while 8 qubits on the same chip were not subjected to
AB voltage pulsing, and one of these was not measurable. These devices were
characterized contemporaneously with another reference set of one chip heated
to 80$\degree$C for 1 hour to mimic ABAA processing (16 qubits, one of which
was not measurable), and two chips were not post-processed with annealing (32
qubits, 2 were not measurable).

The Ambegaokar-Baratoff parameter set for this ensemble was first determined
using the untreated devices. Then the measured frequencies of the treated
qubits were calculated for various resistance-trimming amounts. For the non-
tunable qubits, this is straightforward, while for the tunable qubits, it is
necessary to find the maximum frequency, i.e. zero flux-bias, point. This
process is illustrated in Fig 4(a), showing the spectrum of a tunable qubit.
The spectrum not only allows one to find the maximum frequency, but it also
probes for the existence of any strongly coupled TLS in this frequency range.
In fact, for this qubit and all of the other tunable devices in the ABAA
ensemble, for a total tunability range of $5.4$ GHz in 9 tunable qubits, we
found no evidence of strongly coupled TLSs. Measurements on reference qubits
that did not receive any additional processing, and those that were heated to
$80\degree$C but not ABAA processed have $0.7$ TLS/GHz and $0.6$ TLS/GHz,
respectively. Furthermore, the low-frequency stability of one of the devices
was monitored over many hours and there was no evidence of coupling to TLFs
Schlör  _et al._ (2019).

Figure 5: Summary of qubit lifetimes. (a): Qubit relaxation time, (b): Qubit
Ramsey decoherence time, and (c) Qubit dephasing time for three populations of
qubits: unprocessed, annealed to 80 $\degree$C, and tuned using ABAA with
$V_{A}$= 1 V, 1 s and T = $80\degree$C. The number of measured qubits in the
Unprocessed data set is $n_{\rm qubit}=30$, the $80\degree$C anneal only set
has $n_{\rm qubit}=22$, and the ABAA tuned set has $n_{\rm qubit}=21$.

In Figure 5 we show coherence metrics for all qubits measured in the study.
Here, each data point corresponds to the median of many measurements on one
particular qubit. We observe that the ABAA processed devices have a higher
median $T_{1}$ than both the unprocessed and the devices that were only heated
to $80\degree$C, although the $T_{2}^{*}$ and $T_{\phi}$ values between sample
sets are not distinguishable within the spread of the values, as shown in
Table 1.

Table 1: Qubit coherence for ABAA treated, 80 $\degree\mathrm{C}$ annealed and unprocessed qubits. The error bars are $1\sigma$ standard deviations. Qubit Coherence |  $T_{1}$ ($\mu$s) |  $T_{2}^{*}$ ($\mu$s) |  $T_{\phi}$ ($\mu$s)
---|---|---|---
ABAA treated | $28.4\pm 8.7$ | $34.1\pm 10.6$ | $62.5\pm 23.1$
80 $\degree$C annealed | $20.9\pm 4.6$ | $29.0\pm 12.7$ | $37.9\pm 39.9$
Unprocessed | $19.5\pm 5.0$ | $22.7\pm 12.3$ | $41.4\pm 45.1$

When analyzing processes that may reduce loss in qubits, it is useful to
compare these metrics in the form of a frequency-normalized loss tangent
($1/(T_{1}\times(f_{01})$); the ABAA tuned sample set has median loss tangent
of $8.8\times 10^{-6}$, while both the $80\degree$C annealed and unprocessed
sets have median loss tangents of $1.0\times 10^{-5}$ and $1.1\times 10^{-5}$,
respectively. We found that the coherence was typically improved after the
ABAA process, indicating that the resistance trimming may have reduced the
median loss tangent in the junction by about $2\times 10^{-6}$. Furthermore,
the effects of the resistance trimming on the qubit frequencies are shown in
Fig. 4(b), where we see that the increase of the resistance results in a
reduced measured frequency, shown in Fig. 4(c) as orange stars. The expected
frequencies (blue circles), compare well with the measured values. We also
find the Ambegaokar-Baratoff relationship is consistent between junctions with
ABAA applied vs. unprocessed with values of $(1.32\pm 0.084)$ pH/$\Omega$ and
$(1.27\pm 0.109)$ pH/$\Omega$ respectively.

Figure 6: Electron microscopy analysis on ABAA-treated junction. (a) a low-
magnification cross-sectional TEM image of the junction. (b) a HAADF-STEM
image and (c) a corresponding STEM-EDS elemental distribution map. (d) High-
resolution TEM image of Al/a-AlOx/Al interfaces. (e) HAADF-STEM image of
Al/a-AlOx/Al interfaces. (f) ELNES of Al23 edge of the ABAA-treated sample
taken from the yellow arrow indicated region in (e), and (g) ELNES of Al23
edge of the untreated AlOx barrier from reference Oh  _et al._ (2024)

Finally, TEM imaging was employed to investigate morphological changes in the
junctions due to the ABAA process. Secondary electron images for the JJ
surface were acquired using a scanning electron microscope (SEM) (Helios,
Thermo Fisher Scientific Ltd.) at 2 kV. Transmission electron microscope (TEM)
samples were prepared by a focused ion beam instrument with a gas injection
system (Helios, Thermo Fisher Scientific Ltd.). The TEM samples were thinned
to electron beam transparency by a Ga+ ion beam from 30 to 2 kV. The TEM
samples were investigated by an aberration-corrected TEM (Titan Cube, Thermo
Fisher Scientific Ltd.) at 200 kV. A high-angle annular dark-field (HAADF)
detector was used for dark-field imaging in scanning TEM (STEM) mode with a
convergent semi-angle and a collection semi-angle of 18 mrad and 74-200 mrad,
respectively. Energy-dispersive X-ray spectroscopy (EDS) and electron energy-
loss spectroscopy (EELS) studies were carried out with probe currents of 250
nA and 50 nA, respectively. Dual EELS was performed to acquire all-electron
energy-loss (ELL) spectra. The plural scattering effect of all the raw ELL
spectra was removed via Fourier-ratio deconvolution.

TEM imaging and EELS analysis of the ABAA-treated sample indicate that the
increase in junction resistivity may be attributed to a more uniform barrier
structure with reduced point defect density. An initial survey of the barrier
thickness across each device showed no apparent difference in thickness
between processed and unprocessed junctions, and the barrier remains amorphous
after processing. A low-mag cross-sectional TEM/STEM image and corresponding
EDS elemental distribution map are shown in Fig. 6(a-c). An amorphous a-AlOx
barrier is observed in the ABAA-treated sample (Fig. 6(d)). HAADF-STEM image
shows a barrier thickness of approximately 2 nm (Fig. 6(e)).

While the ABAA technique does not appear to change the amorphous nature of the
barrier from visual inspection, the chemical analysis tells a different story.
We see a much more homogeneous chemistry in the ABAA-treated a-AlOx than in
untreated junctions. Our previous research showed that the distance between
two main peaks labeled as A and B in Fig. 6(f-g), close to approximately 77.5
eV and 80 eV of the Al L23 energy-loss near edge structure (ELNES)
respectively, can be used to analyze the coordination number of Al Oh  _et
al._ (2024); Bouchet and Colliex (2003); Fritz  _et al._ (2018, 2019); Kimoto
_et al._ (2003); Weigel  _et al._ (2008). Specifically, the Al L3 edges (peak
A) tends to shift to higher energy as Al coordination numbers increase. For
untreated junctions, a spatial variation in coordination number across the
a-AlOx barrier from the untreated junction (Fig. 6(g)) Oh  _et al._ (2024) is
demonstrated and considered as a potential decoherence source. In contrast,
the ABAA-treated junction shows a uniform distribution of Al coordination
number through the barrier, as the peak positions of A and B remain unchanged
across the a-AlOx layer, as shown in Fig. 6(f). This may originate from the
migration/recombination of charged point defects induced by the alternating
bias field Li  _et al._ (2023) giving rise to a more chemically homogeneous
barrier layer. This effect may increase the effective barrier height of the
tunnel junction leading to the observed increase in resistance.

##  IV Conclusion

We find that an alternating bias is effective in assisting the thermal
annealing of a diatomic amorphous material, similar to adding restarts in
simulated annealing solver to avoid local minima Alfonzetti  _et al._ (2006).
This allows for significant modifications of the junction resistance, in
excess of +70$\%$, with apparent reductions in loss and defects. The behavior
of the resistance during the ABAA process showed cyclic small and large
changes in resistance as the positive- and negative-bias voltages were applied
and the junction resistance increased, and typically a single discontinuity in
resistance was observed if sufficient number of pulses were applied. These
results along with the temperature-dependent studies and imaging point to an
assisted annealing mechanism, for example, improved local ordering and/or the
a-AlOx being driven into a lower-energy glassy stateHashimoto  _et al._
(2022); Debenedetti and Stillinger (2001) in the potential energy landscape,
as is indicated by the observed reduction in loss and TLS. In order to confirm
these hypotheses, more studies such as high-resolution imaging and molecular
dynamics that include density-functional theory are required. Regardless of
the mechanism, we expect that a controlled alternating bias-assisted junction
annealing approach will pave the way for building large-scale superconducting
quantum processors by improving qubit frequency targeting, coherence, and
stability. Other applications where targeting tunnel junction resistance is
important may benefit by allowing for more homogeneous junction chains and
ensembles for devices ranging from amplifiers to voltage standards, sensors,
and data storage.

###### Acknowledgements.

The structural and chemical characterization and analysis is based upon work
supported by the U.S. Department of Energy, Office of Science, National
Quantum Information Science Research Centers, Superconducting Quantum
Materials and Systems Center (SQMS) under contract number DE-AC02-07CH11359.
We acknowledge the support of Anna Grassellino and Akshay Murthy. All
resistance measurements were conducted on FormFactor automated probe stations
with the help of Anwar Aslam, Connor Smith, and Brandon Boiko. We thank Hilal
Cansizoglu and the Rigetti fab team members for junction process development
and samples, as well as Rory Cochrane for cryogenic measurements of transmon
devices at mK temperatures. We thank Greg Stiehl for his critical eye in
preparation of this manuscript.

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