Accurate and Efficient Interatomic Potentials for Dislocations in InP

This paper introduces highly accurate and efficient Atomic Cluster Expansion (ACE) and MACE machine learning potentials trained on new DFT data, which significantly outperform existing models in predicting dislocation properties in Indium Phosphide (InP) while offering superior computational speed.

The Gist

Imagine a crystal of Indium Phosphide (InP) as a giant, perfectly organized dance floor where thousands of dancers (atoms) hold hands in a specific pattern. This dance floor is the heart of many high-tech devices, like the lasers in fiber-optic internet cables.

However, sometimes the dance floor gets damaged. A "dislocation" is like a glitch in the choreography—a line where the dancers are out of step. If these glitches move or multiply, the device breaks. To fix this, scientists need to understand exactly how these glitches move.

The Problem: The "Gold Standard" is Too Slow

To study these glitches, scientists usually use a super-accurate simulation method called Density Functional Theory (DFT). Think of DFT as a high-definition, slow-motion camera that captures every single dancer's movement with perfect physics. It's incredibly accurate, but it's also painfully slow. Trying to simulate a whole dance floor with DFT is like trying to film a whole stadium of people in slow motion; it would take a computer years to finish a single second of video.

We need a way to watch the whole dance floor move quickly without losing the physics.

The Solution: The "Smart Surrogates"

The authors of this paper built two new "surrogate" models (AI tools) called ACE and MACE.

• The Analogy: If DFT is the slow-motion camera, these new models are like a highly skilled sports commentator. The commentator hasn't filmed every single frame, but they have studied the rules of the game so thoroughly that they can predict exactly what will happen next, instantly.

To train these commentators, the authors didn't just guess. They fed them a massive "textbook" of data generated by the slow-motion camera (DFT). This textbook included:

1. Perfect dancers: The normal crystal structure.
2. Missing dancers: Holes in the floor (vacancies).
3. Extra dancers: People squeezed in where they don't belong (interstitials).
4. The glitch itself: The actual dislocation lines where the dance goes wrong.

The Results: Fast and Accurate

The team tested their new models against the old "textbooks" (previous models) and the "slow-motion camera" (DFT). Here is what they found:

• The Old Models (Vashishta & SNAP): These were like students who memorized the dance steps but forgot the physics. When asked to predict how a glitch moves, they were often wildly wrong (off by 40-50%). They might predict the dancers would trip over each other when they wouldn't.
• The Foundation Models (MP0 & MPA): These are like general knowledge AI. They know a lot about many different dances (materials), but they aren't experts on this specific dance. They were okay, but still made noticeable errors (around 18% off).
• The New Models (ACE & MACE): These are the champion dancers.
  • Accuracy: They predicted the energy of the glitches with less than 4% error. They are almost as good as the slow-motion camera.
  • Speed: This is the magic part. The new models are five times faster than the foundation models and millions of times faster than the slow-motion camera.

Why This Matters

Before this, scientists could only study tiny, broken pieces of the dance floor because the computer couldn't handle the math for a big one.

With these new models, scientists can now simulate millions of atoms moving in real-time. They can watch how a glitch travels across the entire dance floor, how it interacts with missing dancers, and how it eventually causes the device to fail.

In short: The authors built a "fast-forward" button for material science. They created a tool that is fast enough to run big simulations but smart enough to be accurate, allowing us to design better, longer-lasting electronic devices by understanding exactly how they break.

Technical Summary

1. Problem Statement

Indium Phosphide (InP) is a critical III-V semiconductor used in optoelectronic devices. The failure and degradation of these devices are often driven by dislocations (line defects). Understanding dislocation mobility, particularly mechanisms like climb and glide, is essential for improving device reliability.

However, modeling these phenomena presents a significant computational challenge:

• Density Functional Theory (DFT) is accurate but computationally expensive, limiting simulations to small systems (often requiring complex boundary conditions like dipoles or QM/MM coupling to mitigate finite-size effects).
• Existing Interatomic Potentials (IAPs) for InP (e.g., Vashishta, SNAP) or general-purpose foundation models (e.g., MACE-MP0, MACE-MPA) often lack the necessary accuracy to reproduce DFT-level results for complex defect structures, particularly regarding dislocation core energies and stacking faults.

The goal is to develop Machine Learning Interatomic Potentials (MLIPs) that act as accurate, scalable surrogates for DFT, enabling large-scale simulations of dislocation systems in InP without the need for complex boundary conditions.

2. Methodology

Dataset Construction

The authors constructed a specialized dataset of DFT calculations using the RSCAN functional (a regularized SCAN functional) within CASTEP. The dataset was designed to cover atomic environments relevant to dislocations:

• Bulk Properties: Strained zincblende structures in the linear elastic regime.
• Point Defects: Vacancies, antisites, and interstitials (tetrahedral, octahedral, dumbbell) to model defect-dislocation interactions (climb mechanisms).
• Stacking Faults: Coverage of (001), (011), and (111) planes, with a specific focus on the (111) intrinsic stacking fault (ISF) vital for dissociated dislocations.
• Dislocation Cores: Dislocation quadrupole structures (periodic cells containing two opposite Burgers vectors) for $60^\circ$, screw, $30^\circ$, and $90^\circ$ partial dislocations. This allows direct DFT study of dislocations without free surfaces.
• Sampling: Structures were generated via Molecular Dynamics (Langevin dynamics up to 500 K), random perturbations of atomic positions/cells, and the Non-Diagonal Supercell (NDSC) method to capture long-range strain in smaller cells.

Model Training

Two specific MLIP architectures were trained on this dataset:

1. Atomic Cluster Expansion (ACE): A linear model based on the ACE descriptor.
   • Parameters: 6 Å cutoff, correlation order 3 (up to 4-body), total degree 18.
   • Solver: Bayesian Linear Regression (BLR) with a smoothness prior.
2. MACE (Higher-order Equivariant Message Passing Neural Network):
   • Parameters: 90% training / 10% validation split. "64x0e + 64x1o" features (64 scalar + 64 vector messages).
   • Training: 150 epochs with Stochastic Weight Averaging (SWA) enabled from epoch 80 to improve generalization.
   • Loss Weights: Tuned to prioritize energy and force accuracy.

3. Key Contributions

• Specialized Dataset: Creation of a comprehensive InP dataset specifically targeting dislocation physics, including quadrupole structures and various point defects, generated with high-accuracy RSCAN DFT.
• High-Accuracy Surrogates: Development of bespoke ACE and MACE models that significantly outperform existing literature potentials and foundation models for InP-specific tasks.
• Efficiency vs. Accuracy Trade-off: Demonstration that the bespoke MACE model achieves DFT-level accuracy while being ~5x faster to evaluate than the larger foundation models (MP0/MPA).
• Validation Framework: A rigorous benchmark suite covering bulk properties, phonon spectra, point defect formation/migration, stacking faults, and dislocation quadrupole relaxation.

4. Key Results

Accuracy Comparison

The new models were benchmarked against RSCAN DFT and compared to Vashishta, SNAP, MP0, and MPA models.

• Partial Dislocation Formation Energies:
  • ACE & MACE: Errors $\le$ 4%.
  • MACE-MPA (Foundation): Error $\approx$ 18%.
  • Vashishta/SNAP: Errors 42–50%.
• Point Defect Formation Energies: ACE and MACE reproduced DFT values within a few percent. Vashishta and SNAP showed massive errors (e.g., >100% error for some antisites).
• Stacking Faults: ACE and MACE reproduced the DFT energy curves almost exactly. Other models underestimated peak energies or showed incorrect curve shapes.
• Dislocation Quadrupoles:
  • ACE and MACE relaxed quadrupole structures with fractional coordinate RMSEs of 0.44–0.53 ($\times 10^{-2}$) and 0.37–0.52 ($\times 10^{-2}$) respectively, closely matching DFT.
  • Vashishta and SNAP produced unstable or collapsed structures (e.g., SNAP failed to converge the $90^\circ$ quadrupole).
• Migration Barriers: ACE, MACE, and MPA correctly captured the shape and scale of migration barriers for point defects and partial dislocation glide events.

Performance and Efficiency

• Speed: The bespoke MACE model is ~5 times faster than the MP0 and MPA foundation models due to a smaller architecture.
• Throughput: On a single GPU, the bespoke MACE model can perform 1.56 million MD steps/day (for 216 atoms), compared to 0.23 for MP0 and 0.24 for MPA.
• RMSE: The new models achieved binding energy RMSEs of 1.36 meV/atom (ACE) and 2.84 meV/atom (MACE), significantly lower than foundation models (155+ meV/atom).

5. Significance

• Enabling Large-Scale Simulations: These models allow researchers to simulate dislocation systems with $>10^6$ atoms, a scale previously inaccessible to DFT and too inaccurate for existing potentials.
• Foundation Model Validation: While the MPA foundation model showed the best accuracy among general models, the results highlight that fine-tuning foundation models on specific, high-quality datasets (like the one created here) is a viable path to achieving DFT-level accuracy for specific materials.
• Device Reliability: By providing accurate tools to study dislocation mobility and climb, this work directly supports the design of more reliable InP-based optoelectronic devices.
• Open Science: The dataset, scripts, and trained models are made available via GitHub and Zenodo, facilitating further research in semiconductor defect physics.

In conclusion, the paper demonstrates that bespoke MLIPs trained on targeted, high-fidelity datasets offer a superior balance of accuracy and computational efficiency compared to both classical potentials and un-tuned foundation models for studying complex defect phenomena in semiconductors.