Using Machine Learning Potentials to describe collision cascades phenomena in Germanium
Abstract
Understanding how radiation in extreme environments, such as space or nuclear facilities, affects semiconductor behavior is crucial for advanced microelectronics technologies in these domains. Among semiconductors, germanium plays a pivotal role due to its unique electronic properties, but despite its importance, the response of germanium to radiation-induced damages remains an active area of research with unanswered questions. Part of the damages due to the penetration of an incident particle are due to non-ionizing effects such as collision cascades. By colliding with the atoms of the semiconductor's crystalline network the incident particle creates defects such as vacancies, interstitial atoms and clusters of defects known as Displacement Damage (DD). In the case of crystalline semiconductor, such DD can lead to modification of the band structure responsible for unexpected and undesired behaviors.
To describe at the atomic scale the collision cascade and its induced damages, Molecular Dynamic (MD) is often used. Given the high energies of incident particle, which can reach hundreds of keV, large cells containing millions of atoms are needed to carry out the MD calculations. Such number of atoms restrains the use of ab initio methods, and interatomic potentials seem to be a good compromise to reproduce displacement cascades. However, while being fast enough to be used for these large calculations, such potentials exhibit important flaws for the simulation of collision cascades. As they are usually fitted on equilibrium properties they fail to reproduce correctly the non-equilibrium processes that are happening during a collision cascades where atoms' diffusion, local melting and extremely short distances are expected to happen. Machine Learning Interatomic Potential (MLIP) have appeared as a promising alternative to empirical interatomic potential providing near ab-initio accuracy at a fraction of the computational cost. This enables the calculation of key properties such as defect formation energies and migration barriers with high precision. Despite this, simulating millions of atoms over long time scales remains challenging. To address this we propose to use the MiLaDy package 1 , which integrates hybrid descriptors combining fast and cheap descriptors with slow and accurate ones allowing the user to tune the computational cost of the MLIP. A key factor in the success of a MLIP lies in the quality of the training database. In this matter Germanium is particularly challenging using Density Functional Theory as Generalized Gradient Approximation (GGA) functionals such as PBE 2 fail to correctly describe its band gap, and more computational expensive functional, such as range-separated hybrid HSE06 3 are needed to describe Ge's electronic structures, making it impractical to create a germanium database. In this work, we will be using a recently developed functional (PBE + α) 4 able to correctly describe Ge properties at the cost of GGAs. To date, despite Germanium importance in semiconductor technologies, relatively few studies have focused on developing a MLIP for this material, and, to the best of our knowledge, no research has yet applied this method to the study of collision cascades. This work aims to develop a MLIP for germanium based on a new GGA functional, which will enable the study of radiation-induced collision cascades at an ab initio level. The validity of the newly developed MLIP is tested against results obtained with interatomic potentials coupled with advanced corrections accounting for electronic effects 5,6
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