Insights on molecular P implantation for scalable spin-qubit arrays

Technical Summary: Insights on Molecular P Implantation for Scalable Spin-Qubit Arrays

Problem Statement
Solid-state spin-qubits utilizing the spin of phosphorous donors ($^{31}$P) in silicon substrates are a leading candidate for quantum computing. While spin coherence has been significantly improved, a critical challenge remains: the precise and scalable placement of donor atoms within the silicon lattice. For optimal qubit operation, donors must be positioned 7–20 nm beneath the surface. Current ion-beam implantation techniques offer scalability but suffer from placement uncertainty orders of magnitude higher than Scanning Tunneling Microscope (STM) lithography.

To mitigate this, recent proposals suggest using molecular ions (specifically $PF_2$) rather than mono-atomic phosphorous ions. The hypothesis is that molecular ions can generate a high electronic signal for detection while maintaining placement uncertainty comparable to 9 keV mono-atomic P ions. However, existing Binary Collision Approximation (BCA) methods, which assume molecules break apart immediately upon impact, fail to capture many-body effects, the integrity of the molecule during penetration, the precise nature of the electronic signal, and the specific radiation damage profile caused by molecular versus mono-atomic implantation.

Methodology
The authors employed Molecular Dynamics (MD) simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to investigate the differences between mono-atomic and molecular ($PF_2$) ion irradiation of silicon.

• Simulation Setup: Large simulation cells ($43.5 \times 43.5 \times 65.7$ nm$^3$) with crystalline silicon (c-Si) structures were used to track penetration dynamics, including channeling. A smaller cell with a 5 nm amorphous silica ($a$-$SiO_2$) layer was used to simulate the natural oxide layer found on wafers.
• Potentials: Interactions were modeled using the Stillinger-Weber (SW) potential for Si-Si interactions (chosen for computational efficiency and accuracy comparable to machine-learning potentials), the ZBL potential for ion-lattice interactions, and Lennard-Jones potentials for intra-molecular interactions.
• Conditions: Simulations were conducted at 300 K. Molecular ions ($PF_2$) were assigned a total energy of 20.041 keV to ensure the constituent P atom had an energy of 9 keV. An incidence angle of 7 degrees was used to minimize channeling probability, and the presence of the $a$-$SiO_2$ layer was varied to assess its effect on energy loss and molecular integrity.
• Analysis: The study tracked energy loss, electronic stopping power, defect formation (using Wigner-Seitz analysis), and defect clustering. Electronic stopping was modeled to simulate the generation of electron-hole pairs used for detection.

Key Results

1. Molecular Integrity and Energy Loss:
   Contrary to the BCA assumption that molecules break apart immediately upon surface impact, MD simulations revealed that $PF_2$ molecules often remain intact or partially intact (as $PF$ complexes) for several nanometers into the substrate. In pure c-Si, over 40% of cases showed one Fluorine atom detaching before 6 nm depth while the second remained close to Phosphorous. The presence of the $a$-$SiO_2$ layer increases collision frequency, causing earlier dissociation.

   • Energy Spread: P ions lose approximately 1 keV more energy than F ions when passing through the $a$-$SiO_2$ layer.
   • Implantation Profiles: Molecular implantation results in a flatter depth profile with P atoms pushed slightly deeper compared to mono-atomic implantation. This is attributed to the molecule acting as a single, heavier projectile until it dissociates. Notably, molecular implantation produced a stronger "long tail" of channeled ions, likely due to the higher effective energy of P atoms entering the c-Si after traversing the oxide layer.

2. Electronic Signal and Channeling Detection:
   The study analyzed the correlation between the electronic stopping signal (used to detect implantation depth) and the final position of the P atom.

   • Signal Correlation: A weak correlation (Pearson coefficient $r \approx 0.5$) was found between the electronic signal intensity and the final penetration depth of the P atom alone. However, the signal correlates strongly with the average penetration depth of all three molecular components (P + 2F).
   • Channeling Ambiguity: A strong electronic signal does not necessarily indicate that the P atom is channeled, as the signal can be generated by any of the three atoms in the $PF_2$ molecule. Conversely, the authors note that a low signal implies a non-channeling event from any of the particles. Therefore, while a strong signal is ambiguous (potentially arising from a channeled F atom while P is correctly placed, or vice versa), a low signal reliably indicates that no channeling occurred for any constituent.
   • Detection Limit: The authors found that using a signal threshold to discriminate channeling events results in significant uncertainty; roughly half of the events cannot be properly labeled as channeled or non-channeled based solely on signal intensity. However, events with strong signals can be safely discarded to avoid channeling risks, even if this potentially discards correctly implanted P atoms.

3. Radiation Damage and Defect Evolution:

   • Synergistic Damage: Molecular implantation generates a greater number of defects and a wider distribution of defect counts compared to the sum of three independent mono-atomic ions. This indicates a "synergistic damage effect" where overlapping collision cascades from the closely spaced atoms of the molecule create more extensive damage.
   • Clustering: Defects in molecular implantation tend to form larger clusters (some exceeding 500 atoms) centered around the P atom. These large clusters are often vacancy-rich amorphous pockets.
   • Role of Oxide Layer: The $a$-$SiO_2$ layer reduces the entry energy of the atoms, which limits the size of the largest defect clusters, potentially reducing the annealing requirements for lattice recovery.
   • Annealing Implications: The presence of large, vacancy-rich clusters and specific defect pairs (like E-centers) poses a risk to the electrical activation and quantum properties of the qubit. These defects require high-temperature annealing for recovery, but the specific damage profile of molecular ions suggests that standard annealing protocols for mono-atomic ions may need adjustment to suppress detrimental atomic diffusion.

Significance and Claims
The paper claims to provide a comprehensive molecular dynamics-based assessment of molecular $PF_2$ implantation, challenging several assumptions inherent in current BCA-based models and experimental interpretations.

• Refutation of Immediate Dissociation: The study demonstrates that the assumption of immediate molecular breakup at the surface is inaccurate; molecules often penetrate a few nanometers before dissociating, leading to overlapping cascades and synergistic damage.
• Signal Interpretation: The authors caution against the direct association of high electronic signals with P-atom channeling. They argue that in molecular implantation, a high signal may originate from any constituent atom, making it an unreliable sole indicator for the depth or channeling status of the specific P donor. Conversely, a low signal is a reliable indicator of non-channeling for all particles.
• Damage Profile: The research highlights that molecular implantation creates a distinct damage landscape characterized by larger, clustered defects compared to mono-atomic implantation. This necessitates a re-evaluation of post-implantation annealing strategies to ensure the donor is electrically activated without residual strain or defects that could degrade qubit performance.

In summary, while molecular ions offer a pathway for scalable qubit production, the paper concludes that their use introduces complexities in placement detection and damage recovery that must be carefully managed, particularly regarding the interpretation of electronic signals and the optimization of thermal annealing processes.