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Towards predictive atomistic simulations of SiC crystal growth

Alexander Reichmann, Zahra Rajabzadeh, Sebastian Hofer, René Hammer, Lorenz Romaner

TL;DR

This work tackles the challenge of simulating SiC crystal growth with realistic time scales, where conventional MD suffers from unrealistically high deposition rates that induce amorphous layers and defects. It introduces and applies the minimum energy atomic deposition (MEAD) method to SiC, incorporating a Gaussian density surface (GDS) based deposition site selection and tfMC/FIRE-like equilibration, guided by the MEAM interatomic potential. The study demonstrates that MEAD can reproduce stable step-flow growth and 4H stabilization on stepped C-terminated 4H SiC surfaces, while flat substrates prefer a mix of 3C/2H polytypes and exhibit more defects; diffusion of deposited atoms and the relationship between step morphology, stacking faults, and dislocations are analyzed. The approach offers a high-fidelity framework for exploring surface phenomena in crystal growth and sets the stage for future investigations incorporating doping, inclusions, or screw-dislocation growth, potentially enhanced by machine-learned interatomic potentials.

Abstract

Simulations of SiC crystal growth using molecular dynamics (MD) have become popular in recent years. They, however, simulate very fast deposition rates, to reduce computational costs. Therefore, they are more akin to surface sputtering, leading to abnormal growth effects, including thick amorphous layers and large defect densities. A recently developed method, called the minimum energy atomic deposition (MEAD), tries to overcome this problem by depositing the atoms directly at the minimum energy positions, increasing the time scale. We apply the MEAD method to simulate SiC crystal growth on stepped C-terminated 4H substrates with 4° and 8° off-cut angle. We explore relevant calculations settings, such as amount of equilibration steps between depositions and influence of simulation cell sizes and bench mark different interatomic potentials. The carefully calibrated methodology is able to replicate the stable step-flow growth, which was so far not possible using conventional MD simulations. Furthermore, the simulated crystals are evaluated in terms of their dislocations, surface roughness and atom mobility. Our methodology paves the way for future high fidelity investigations of surface phenomena in crystal growth.

Towards predictive atomistic simulations of SiC crystal growth

TL;DR

This work tackles the challenge of simulating SiC crystal growth with realistic time scales, where conventional MD suffers from unrealistically high deposition rates that induce amorphous layers and defects. It introduces and applies the minimum energy atomic deposition (MEAD) method to SiC, incorporating a Gaussian density surface (GDS) based deposition site selection and tfMC/FIRE-like equilibration, guided by the MEAM interatomic potential. The study demonstrates that MEAD can reproduce stable step-flow growth and 4H stabilization on stepped C-terminated 4H SiC surfaces, while flat substrates prefer a mix of 3C/2H polytypes and exhibit more defects; diffusion of deposited atoms and the relationship between step morphology, stacking faults, and dislocations are analyzed. The approach offers a high-fidelity framework for exploring surface phenomena in crystal growth and sets the stage for future investigations incorporating doping, inclusions, or screw-dislocation growth, potentially enhanced by machine-learned interatomic potentials.

Abstract

Simulations of SiC crystal growth using molecular dynamics (MD) have become popular in recent years. They, however, simulate very fast deposition rates, to reduce computational costs. Therefore, they are more akin to surface sputtering, leading to abnormal growth effects, including thick amorphous layers and large defect densities. A recently developed method, called the minimum energy atomic deposition (MEAD), tries to overcome this problem by depositing the atoms directly at the minimum energy positions, increasing the time scale. We apply the MEAD method to simulate SiC crystal growth on stepped C-terminated 4H substrates with 4° and 8° off-cut angle. We explore relevant calculations settings, such as amount of equilibration steps between depositions and influence of simulation cell sizes and bench mark different interatomic potentials. The carefully calibrated methodology is able to replicate the stable step-flow growth, which was so far not possible using conventional MD simulations. Furthermore, the simulated crystals are evaluated in terms of their dislocations, surface roughness and atom mobility. Our methodology paves the way for future high fidelity investigations of surface phenomena in crystal growth.
Paper Structure (7 sections, 1 equation, 6 figures)

This paper contains 7 sections, 1 equation, 6 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results and Discussion
  4. Comparison to MD
  5. Conclusion
  6. Acknowledgments
  7. Declaration of competing interest

Figures (6)

  • Figure 1: The MEAD algorithm as we applied it onto the SiC system.
  • Figure 2: The MEAD algorithm applied on the 7$\times$7 stepped (a-c) and flat (d) 4H C-terminated SiC substrate. The amount of tfMC steps in between Si and C depositions was varied between (a) 200, (b) 500 and (c,d) 1000 tfMC steps. The dislocation analysis of the respective final structure is depicted below. The "identify diamond structure" modification of OVITO classifies each atom into one of the following categories with the associated color in brackets: hexagonal diamond (orange), hexagonal diamond 1$^{\text{st}}$ neighbor (bright yellow), hexagonal diamond 2$^{\text{nd}}$ neighbor (lime green), cubic diamond (blue), cubic diamond 1$^{\text{st}}$ neighbor (aquamarine), cubic diamond 2$^{\text{nd}}$ neighbor (bright green) and "other" (white). Here 1$^{\text{st}}$ neighbor indicates that four neighboring atoms are positioned on the lattice, but at least one of its second nearest neighbors is not and 2$^{\text{nd}}$ neighbor indicate that the atom itself is on the lattice, but at least one of its neighbors is either missing or not positioned on a lattice site. The substrate was set to a grey color.
  • Figure 3: The MEAD algorithm applied on a 14$\times$14 stepped substrate using (a) 4000 and (b) 8000 tfMC steps in between depositions. For (a) a larger decay rate of the probability weights was applied, meaning the deposition was forced to be closer to the steps. In (a) a total of 80000 atoms have been deposited while in (b) only 26000 atoms were deposited before the simulations was stopped. The evaluation of their respective surface roughness R$_a$ are depicted in (c) and (d), in a three-dimensional perspective, with the viewpoints inclined towards the [000$\bar{1}$] direction. For the structure (a) a dislocation density analysis is shown in (e) and an analysis of the movement of 14 randomly picked C and Si atoms over the first 15000 MEAD steps is shown in (f). Videos of the step flow growth of both simulations are provided as supplemental materials (in which 1 frame is roughly 200 MEAD steps). They can be viewed under DOI:10.5446/72185 for the simulation using 4000 tfMC steps and DOI:10.5446/72186 for the simulation using 8000 tfMC steps.
  • Figure 4: (a) An analysis of the movement of 14 randomly picked C and Si atoms over the first 15000 MEAD steps. (b) and (c) A statistic of the first 1000 deposited C (b) and Si (c) atoms in terms of their difference in final position compared to their deposition position.
  • Figure 5: Conventional MD crystal growth simulation applied on the 14$\times$14 stepped 4H substrate with. The dislocation analysis is depicted below.
  • ...and 1 more figures