(Invited) Atomistic Study of 4H-SiC Using Ab Initio and Machine Learning Techniques
Authors: Stella Robert , Leroch Sabine , Hössinger Andreas , Waldhör Dominic , Filipovic Lado 
Published: December 2024

Alternatives to silicon for electronic devices for operation at high-power, high temperature, and in rough environments, are highly sought after. In particular, semiconductors with a wide bandgap and high breakdown field when compared to silicon, are desired. In particular, SiC and GaN have shown promise for these applications and are essential for green energy development due to their low power dissipation when operating at high biases. However, the doping of these materials, performed using a sequence of ion implantation followed by high temperature annealing, is much more difficult compared to silicon. The ion implantation, performed using energized ions, can generate amorphous clusters which inhibit the activation of dopants. High temperature annealing is used to improve the activation rate, but incomplete activation is still frequent and greatly depends on the implantation conditions, meaning the ion energies and dose.
Aluminium is mainly used for p-type doping of SiC, but overcoming its incomplete activation and understanding the physical reason behind it is still a significant challenge. To obtain an insight into the formation and subsequent annealing of defects, as well as the resulting activation of Al in SiC, atomistic simulations were conducted. 4H-SiC was used for the studies, as it is highly relevant from a technological perspective. Density functional theory (DFT) was used to examine the exact behavior of point defects and their migrations during high-temperature annealing. In further studies, this can also be used to analyze the electronic structure of specific amorphous clusters and their influence on the activation of acceptors. For larger time and size scales, DFT reaches its computation limit. Instead, molecular dynamics (MD) based on interatomic force fields (FFs) can be used. However, analytical interatomic potentials (IAPs) which are used by classical MD are not able to capture all of the relevant properties, ranging from melted phases, formation of amorphous structures, diffusion of point defects, and mechanical stress build-up. Since SiC is a binary system, the potential should be able to differentiate between the different diffusion mechanisms for silicon and carbon defects as well as the influence of different polytypes. For that purpose machine learning (ML) was merged with DFT to describe that mechanism with improved accuracy. ML-IAPs are trained to reproduce the potential energy of the system, the force on each atom, and the stress on the supercell obtained from DFT simulations. Even though more accuracy can be expected from such FFs, the number of atoms is limited by the computational effort which is higher compared to traditional FFs. Nevertheless, such ML potentials enable the simulation of larger timescales and systems compared to conventional DFT at an improved accuracy over traditional FFs.
ML-IAPs can be classified into neural networks (NN), kernel methods, and linear fitting methods. The trained potentials mostly accounted for silicon point defects. They are compared to a conventional analytical potential to assess their speed, while their accuracy is compared to ab initio data. The moment tensor potential (MTP) is a linear fitting potential, which resulted in a slowdown between one and two orders of magnitude, depending on the chosen form of the potential, compared to an analytic Brenner-type potential. In the figure below, the radial distribution function (RDF) is plotted for amorphous structures, created by an MTP of level 16, an ab initio MD, and a Brenner-type FF. Those structures were created by a melting quench simulation. While the silicon-to-silicon distances are very similar for all three potentials, the Brenner-type potential tends to overestimate the distance of the nearest neighbors for carbon atoms. The MTP yields quantitatively correct results for all three bonding types. Nevertheless, MTP was unable to describe point defects and their diffusion due to the rather high training error of 28 meV per atom. All point defect configurations resulted in a similar formation energy which is in contradiction with the DFT results.
The Gaussian approximation potential (GAP) is a type of kernel method which is around three orders of magnitude slower than the analytical Brenner-type potential, strongly depending on the chosen cut-offs for the different descriptors. Overall, the GAP resulted in a training error of 24 meV per atom, while the training error for the different point defect configurations was rather small at 0.5 meV per atom. Carbon point defects were not included in the training yet and therefore are not described accurately. In contrast to the MTP, the GAP described different silicon point defect configurations very accurately and is, therefore, able to simulate the diffusion of those defects with DFT-level accuracy and on MD timescales.

Figure 1