⚛️ quantum physics

Analysis of Hydrogen Contamination in Al/AlOx/Al Josephson Junctions

This study combines molecular dynamics simulations with quantum transport calculations to reveal that hydrogen contamination in Al/AlOx/Al Josephson junctions forms specific surface motifs following a beta-binomial distribution, ultimately acting as effective p-type doping that increases transmission and induces a predictable variability in Josephson energy.

Original authors: Yu Zhu, Aldilene Saraiva-Souza, Félix Beaudoin, Hong Guo

Published 2026-03-17

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CC BY 4.0

Original authors: Yu Zhu, Aldilene Saraiva-Souza, Félix Beaudoin, Hong Guo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to build the world's most delicate, high-speed computer. This isn't a laptop with a keyboard; it's a quantum computer, a machine that uses the weird rules of physics to solve problems impossible for normal computers.

The heart of this machine is a tiny switch called a Josephson Junction. Think of this junction as a very specific "sandwich": two slices of aluminum bread with a very thin layer of "jelly" (aluminum oxide) in the middle. This jelly layer is crucial. It's so thin that electrons can quantum-tunnel through it, allowing the switch to work.

However, there's a problem. Just like a sandwich left out in a humid kitchen, this quantum sandwich can get contaminated. Specifically, hydrogen atoms (the simplest, smallest atoms in the universe) sneak in.

This paper is a detective story about how these tiny hydrogen intruders ruin the sandwich, why they do it, and how much they mess up the computer's performance. Here is the breakdown in simple terms:

1. The Problem: The "Humid Kitchen" Effect

When scientists make these quantum switches, they try to keep them in a perfect vacuum. But sometimes, tiny amounts of water vapor (which contains hydrogen) or other gases get in.

The Analogy: Imagine trying to build a perfect glass wall. If even a few specks of dust get stuck in the glass, the wall becomes weak. In quantum computers, these "specks" are hydrogen atoms. They cause two big problems:
1. Variability: No two sandwiches turn out exactly the same. One might work at 5 GHz, another at 5.1 GHz. This makes it hard to tune the computer.
2. Noise: The hydrogen atoms act like tiny, jittery batteries that flip back and forth, creating static noise that kills the quantum information.

2. The Investigation: A Digital Simulation Lab

The researchers couldn't just look at the real junctions with a microscope because the atoms are too small and the process happens too fast. Instead, they built a virtual laboratory using supercomputers.

The Movie (Molecular Dynamics): They created a digital movie of aluminum atoms meeting oxygen and water molecules. They sped up time massively (like a time-lapse video of a flower blooming) to see how the "jelly" layer forms.
The Result: They found that the hydrogen atoms don't just sit randomly. They act like glue, sticking to the surface of the jelly layer, mostly forming little chains like "Aluminum-Oxygen-Hydrogen."
The Lottery: They ran this simulation 400 times. They discovered that the number of hydrogen atoms in each sandwich follows a predictable pattern (a "beta-binomial distribution"). It's like rolling dice: you can't predict exactly how many hydrogen atoms will land in one specific sandwich, but you can predict the average for a whole batch.

3. The Impact: The "P-Type" Doping Effect

Next, they asked: "Okay, we have these hydrogen atoms. What do they actually do to the electricity?"

The Analogy: Think of the tunnel barrier (the jelly) as a hill that electrons have to jump over.
The Discovery: The hydrogen atoms act like shovels that dig a trench in the hill. They lower the barrier slightly and change the electrical landscape.
The "P-Type" Label: In the world of electronics, this is called "p-type doping." It's like adding a specific ingredient to a cake that changes how it rises. In this case, the hydrogen makes it slightly easier for electrons to tunnel through, but it also shifts the "frequency" of the switch.

4. The Conclusion: How Much Does It Matter?

By combining their "dice roll" simulation (how many hydrogens get in) with their "electricity" simulation (how hydrogens change the flow), they calculated the final result.

The Prediction: For a standard quantum junction, the presence of this average amount of hydrogen (about 2.5% of the atoms) means the switch will vibrate at a frequency of 10.92 GHz.
The Uncertainty: However, because the number of hydrogen atoms varies from sandwich to sandwich, there is a "wobble" or uncertainty of ±0.26 GHz.

Why This Matters

This paper is like a mechanic explaining why your car engine sometimes sputters.

Before: Engineers knew hydrogen was bad, but they didn't know exactly how it got in, where it hid, or how much it changed the engine's performance.
Now: They have a map. They know the hydrogen hides near the surface, they know the statistical odds of how many get in, and they know exactly how much it shifts the frequency.

This knowledge helps engineers build better "sandwiches" (quantum chips) with less variability, which is a giant leap toward building reliable, large-scale quantum computers that can actually solve real-world problems.

1. Problem Statement

Hydrogen contamination in Aluminum/Aluminum Oxide/Aluminum (Al/AlOx/Al) Josephson junctions is a critical challenge in the scaling of superconducting quantum computers.

Device Variability: Hydrogen incorporation leads to significant device-to-device variability in critical current ( $I_c$ ) and Josephson energy ( $E_J$ ), complicating the calibration of large-scale qubit arrays.
Coherence Loss: Hydrogen-related defects act as Two-Level Systems (TLS), causing charge noise, or as magnetic defects, causing flux noise. Both mechanisms degrade qubit coherence times.
Knowledge Gap: While experimental data (e.g., SIMS) confirms hydrogen concentrations ranging from 1.1% to 4.1% in tunnel barriers, the statistical distribution of hydrogen atoms, their specific atomic binding motifs, and their precise impact on electronic transport properties remain poorly understood at the atomistic level.

2. Methodology

The authors employed a multi-scale computational approach combining Molecular Dynamics (MD) for structural generation and Quantum Transport calculations for electronic property analysis.

A. Molecular Dynamics (MD) Simulations

Goal: To simulate the growth of the amorphous AlOx barrier in the presence of Oxygen ( $O_2$ ) and Water ( $H_2O$ ) to determine the statistical distribution and location of hydrogen atoms.
Approach:
- System: An Al(111) surface slab (20 layers) exposed to a gas of 750 $O_2$ and 30 $H_2O$ molecules in a vacuum region.
- Potential: Used CHGNet, a charge-informed graph-neural-network machine learning potential, to calculate interatomic forces.
- Acceleration Strategy: To overcome the timescale gap between MD (picoseconds) and experimental oxidation (minutes), the authors used a "high density acceleration" method. By placing a high density of $O_2$ molecules, the oxidation rate was accelerated by orders of magnitude, effectively simulating ~266 ns of oxidation in 3 ps of simulation time.
- Sampling: 400 statistically independent simulations were run starting from different initial gas configurations.

B. Quantum Transport Calculations

Goal: To quantify the impact of hydrogen on the tunneling current and Josephson energy.
Approach:
- Model: Constructed Al/Al $_2$ O $_3$ /Al junction models. The amorphous barrier was approximated by crystalline $\alpha$ -Al $_2$ O $_3$ to reduce computational cost, justified by the exponential dependence of tunneling on barrier height/thickness rather than amorphous disorder.
- Software: Used NanoDCAL, implementing Non-Equilibrium Green's Function (NEGF) combined with Density Functional Theory (DFT).
- Electronic Structure: Employed a GGA+U scheme (with $U=1.0$ eV on Al $p$ -orbitals) to correct the band gap and ensure accurate band alignment between Al and Al $_2$ O $_3$ .
- Scenarios: Compared a pristine junction (JJ) with a junction containing a single hydrogen atom at the interface (JJ-H).

3. Key Results

A. Statistical Distribution of Hydrogen

Distribution Type: The number of hydrogen atoms ( $n$ $n$ ) across the 400 samples follows a beta-binomial distribution, reflecting the self-limiting nature of the oxidation process.
- Fitted parameters: $\alpha = 17.69$ , $\beta = 15.36$ , $M = 40$ .
- Mean hydrogen count: $21.41 \pm 4.62$ atoms per simulation cross-section ( $34.17 \times 34.17$ Å $^2$ ).
Concentration: The resulting average hydrogen concentration is 2.56 ± 0.54 at.%, consistent with experimental observations.

B. Structural Analysis (Binding Motifs)

Location: Most hydrogen atoms reside near the AlOx surface.
Dominant Motifs:
- 91.3% of H atoms bind via hydroxyl (-OH) groups, forming Al-OH (37.0%) or Al-OH-Al (54.3%) motifs.
- 5.4% form Al-H $_2$ O motifs.
- Rare motifs include interstitial sites and Al-H bonds.
Implication: The prevalence of Al-OH-Al motifs suggests hydrogen acts as a bridge or defect within the oxide network.

C. Electronic Transport Impact

Transmission Coefficient: The presence of a single H atom increases the transmission coefficient ( $T(E)$ ) near the Fermi level ( $E_F$ ).
Band Shift: Hydrogen incorporation shifts the electronic structure by approximately 0.8 eV, moving $E_F$ closer to the valence band edge.
Doping Mechanism: This shift indicates that H atoms act as effective p-type dopants. This is verified by a Mulliken charge of +0.44 on the H atom.

D. Device-to-Device Variability

By combining the statistical distribution of H atoms (from MD) with the transmission changes (from DFT), the authors derived the probability distribution for Josephson energy ( $E_J$ ).
Prediction: For a junction with an average H content of 2.56 at.%, the Josephson energy is predicted to be:
$E_J/h = 10.92 \pm 0.26 \text{ GHz}$
The uncertainty ( $\pm 0.26$ GHz) represents the standard deviation arising solely from the statistical fluctuation of hydrogen incorporation.

4. Significance and Contributions

Atomistic Mechanism: The study provides the first comprehensive atomistic picture of how hydrogen incorporates into AlOx barriers, identifying specific binding motifs (Al-OH-Al) and their statistical prevalence.
Quantitative Variability: It establishes a direct link between the stochastic nature of oxidation (beta-binomial distribution of H) and the resulting variability in qubit parameters ( $E_J$ ). This allows for better prediction of yield and calibration overhead in large-scale quantum processors.
Transport Physics: The finding that hydrogen acts as a p-type dopant in AlOx offers a new physical explanation for the variability in critical currents, moving beyond purely geometric explanations (thickness variations).
Methodological Framework: The paper demonstrates a robust workflow combining machine learning potentials (CHGNet) for realistic oxide growth and NEGF-DFT (NanoDCAL) for transport, bridging the gap between fabrication processes and device performance.

5. Conclusion

The research concludes that hydrogen contamination is an intrinsic source of variability in Josephson junctions. The statistical fluctuations in hydrogen content, driven by the self-limiting oxidation process, lead to a predictable spread in Josephson energy. Understanding these mechanisms is essential for mitigating device variability and improving the coherence of superconducting qubits as they scale toward fault-tolerant quantum computing. Future work will focus on calculating the specific TLS loss associated with the identified Al-OH motifs.