Improved capabilities of the TurboGAP code for radiation induced cascade simulations: an illustration with silicon

TL;DR

Radiation-damage simulations require accurate energy dissipation and large-scale atomistic modeling, which are challenging with conventional MD. The authors extend TurboGAP with three modules: a two-model electronic energy-loss framework (EPH within TTMD and friction-based FES), adaptive timestep control, and atom-group border cooling, enabling cascades in silicon up to $10^6$ atoms and PKA energies up to $10$ keV. Using a retrained Si GAP with turboSOAP descriptors and a ZBL repulsive term, they compare EPH and FES predictions, showing that EPH yields continuous energy transfer and larger defect clusters, with mixing values in good agreement with experiments, whereas FES is cutoff-dependent. The work demonstrates that combining GAP MLIPs with realistic electronic dissipation at scale yields accurate, efficient predictions of defect evolution, clustering, and ion-beam mixing in semiconductors, paving the way for large-scale radiation-damage studies.

Abstract

TurboGAP is a software package designed for efficient molecular dynamics simulations using Gaussian Approximation Potential (GAP) machine-learning interatomic potentials (MLIP). In this work, we enhance the capabilities of TurboGAP for radiation damage simulations by implementing a two-temperature molecular dynamics model, based on electron density-dependent coupling of electronic and atomic subsystems. Additionally, we implement adaptive calculation of the timestep and grouping of atoms for cell-border cooling. Our implementation incorporates electronic stopping power either through a traditional friction-based model or a more realistic first-principles-derived model. By combining the computational efficiency of TurboGAP with the accuracy of GAP MLIP, we perform cascade simulations in silicon with primary knock-on atom (PKA) energies up to 10 keV. Our simulations scale to systems containing up to 1 million atoms. We study the generation and clustering of radiation-induced defects. We also calculate ion-beam mixing and compare our results with the experimental data, discussing how the GAP-MLIP along with the inclusion of a realistic electronic stopping model improves the prediction of experimental mixing values.

Figures (9)

• Figure 1: The performance of the trained GAP MLIP, stiffened with the ZBL repulsive potential, in predicting the Si-Si dimer interaction in the given range of distance. The "non-stiff" curve shows the prediction of the potential in the absence of the repulsive potential. The prediction of the forces is presented in Supplementary Fig.1. The details of DFT-dimer calculations is also presented in Supplementary material.
• Figure 2: Comparison of the evolution of observables in 100 eV PKA cascade simulation with LAMMPS and implemented modules in TurboGAP. The results show the average over 10 random trajectories simulated with each code.
• Figure 3: Comparison of the full EPH model simulations (inclusion of random and friction forces) using LAMMPS and TurboGAP codes. The electronic system is the same size as the atomic system which is 16.29 Å on all three sides. The equilibration takes place at an intermediate temperature depending on the electronic heat capacity. Values of $C_e$ and $\kappa_e$ used are $3.5\times10^{-6} \; \mathrm{eV/K/\AA^3}$ and $0.1248 \; \mathrm{eV/K/\AA/ps}$, respectively.
• Figure 4: An illustration of equilibrating a system of 216 Si atoms with a sufficiently large electronic heat bath kept at 1400 K using the full EPH model as implemented in the TurboGAP code. With the constant ES coupling parameter the atomic system attains the equilibrium at 1400 K at about 15 ps. The evolution of the total energy of the atomic subsystem and the cumulative energy transfer from the electronic heat bath to the atoms show the conservation of energy in the combined atom-electron system.
• Figure 5: Time evolution of the (a) number of interstitials; (b) cumulative energy transferred to the electronic system, and (c) temperature in the atomic subsystem due to 2.0 keV Si self-ion cascades. The shaded area on each graph represents the standard error of the mean values in the plot.