PDD-1_PF

Technical Description of the Predictive Framework: Perfectly Defected Diamond

The Perfectly Defected Diamond framework is a multiscale, hybrid computational platform designed to systematically predict and optimize the formation and stability of nitrogen–vacancy (NV) centers in diamond. By integrating classical molecular dynamics (MD), density functional theory (DFT), machine learning (ML), and quantum defect performance metrics, the framework establishes a deterministic, data-driven pathway from implantation conditions to qubit-quality evaluation.

Unlike traditional empirical approaches, which rely on iterative ion implantation and annealing experiments, this framework generates a digital twin of the fabrication process, allowing comprehensive exploration of parameter space (ion energy, fluence, angle, annealing conditions, stress environments) and direct linkage to quantum observables (coherence times, charge stability, optical transitions).

1. Molecular Dynamics (MD) Module

At the foundational level, the framework employs classical MD simulations to capture the ultrafast dynamics of ion implantation into diamond.

Force fields:

Tersoff potential models long-range C–C interactions within the diamond lattice.

Ziegler–Biersack–Littmark (ZBL) potential governs short-range, high-energy nuclear collisions between implanted ions and lattice atoms.

Lennard–Jones + Coulombic terms may be included to account for surface passivation or adsorbates.

Processes captured:

Ballistic ion trajectories and stopping profiles.

Primary knock-on atom (PKA) cascades and displacement-per-atom (DPA) statistics.

Vacancy generation, clustering, and lattice disorder.

Stress accumulation and strain relaxation.

Post-implantation annealing is modeled using MD to probe vacancy migration kinetics, nitrogen–vacancy pairing probabilities, and defect stabilization mechanisms at elevated temperatures (800–1200 K).

The MD module thus establishes the structural landscape of implantation damage and defect precursors from first principles of atomic motion.

2. Density Functional Theory (DFT) Module

The structural outputs of MD (candidate NV configurations, vacancy clusters, stress fields) are passed into DFT calculations for quantum-level validation.

Methodology:

Spin-polarized GGA-PBE with optional hybrid functionals (HSE06) for improved gap accuracy.

Plane-wave basis sets with projector-augmented wave (PAW) pseudopotentials.

Supercells representing shallow (<10 nm) and bulk NV environments.

Key quantities computed:

Charge state energetics (NV⁰ vs NV⁻ stability as a function of Fermi level and surface termination).

Zero-phonon line (ZPL) optical transition energies for NV⁻.

Spin triplet state splitting and hyperfine coupling constants.

Defect–defect interaction energies and charge compensation behavior.

This DFT layer provides electronic and quantum mechanical fidelity to the atomistic defect landscapes predicted by MD.

3. Machine Learning (ML) Predictor

Given the vast combinatorial space of implantation parameters, direct MD + DFT sampling is computationally infeasible. To address this, the framework incorporates a supervised ML engine that learns the mapping between process parameters and quantum performance outcomes.

Training data: thousands of MD/DFT simulations labeled with defect yields, charge stability, and coherence metrics.

Features: implantation energy, angle, fluence, annealing profile, stress state, surface chemistry, vacancy distributions, Surface Damage Index (SDI).

Algorithms: ensemble methods (gradient boosting, random forests) and deep feedforward neural networks.

Outputs:

Continuous maps of NV formation probability and depth distributions.

Predicted spin coherence times (T₂) from learned correlations with local defect environments.

Uncertainty quantification for robust extrapolation into untested regimes.

The ML predictor enables rapid evaluation of unexplored fabrication conditions and acts as an optimization engine for inverse design.

4. Implantation Metrics

To ensure realistic simulation-to-experiment translation, the framework incorporates explicit implantation metrics, derived from MD trajectories and validated against experimental benchmarks (e.g., SRIM).

Input controls: ion energy (0.5–20 keV), incident angle (0–10°), dose (single or multi-step), and annealing profile (single-step vs multi-step gradient).

Derived metrics: depth distribution histograms, lateral straggle statistics, surface damage indices (SDI), and vacancy–nitrogen pairing rates.

Composite implantation score (Q-score) that weights NV yield against surface damage penalties.

This ensures a quantitative bridge between simulation outputs and fabrication parameters.

5. Quantum Metrics

The final evaluation layer quantifies quantum performance relevance, translating atomistic structures into qubit functionality.

NV Yield (Y_NV): probability of forming NV centers per implanted ion.

Depth-weighted Yield (Y_NV,depth): penalizing deeper NVs, emphasizing shallow (<10 nm) centers.

Spin coherence time (T₂): estimated via correlations with strain, defect density, and charge compensation environments.

Charge state stability (ΔE_NV0/NV−): determining usable optical and spin-active centers.

Surface Damage Index (SDI): quantifying decoherence sources.

A composite quality function is defined:

Q=f(YNV,YNV,depth,T2,ΔE,SDI)Q = f\left( Y_{\mathrm{NV}}, Y_{\mathrm{NV,depth}}, T_2, \Delta E, SDI \right)Q=f(YNV​,YNV,depth​,T2​,ΔE,SDI)

which ranks fabrication strategies by their predicted quantum utility.

6. System Output

The integrated MD–DFT–ML–Metrics pipeline produces a predictive fabrication map.

Inputs: desired NV depth, minimum coherence requirement, permissible processing constraints.

Outputs: optimized implantation and annealing protocols, predicted NV density, expected coherence performance, and uncertainty bounds.

This map serves as a digital guidebook for experimental NV engineering, replacing trial-and-error with rational, computationally validated design.