Frontiers, challenges, and solutions in modeling of swift heavy ion effects in materials

Since a few breakthroughs in the fundamental understanding of the effects of swift heavy ions (SHI) decelerating in the electronic stopping regime in the matter have been achieved in the last decade, it motivated us to review the state-of-the-art approaches in the modeling of SHI effects. The SHI track kinetics occurs via several well-separated stages: from attoseconds in ion-impact ionization depositing energy in a target, to femtoseconds of electron transport and hole cascades, to picoseconds of lattice excitation and response, to nanoseconds of atomic relaxation, and even longer macroscopic reaction. Each stage requires its own approaches for quantitative description. We discuss that understanding the links between the stages makes it possible to describe the entire track kinetics within a multiscale model without fitting procedures. The review focuses on the underlying physical mechanisms of each process, the dominant effects they produce, and the limitations of the existing approaches as well as various numerical techniques implementing these models. It provides an overview of ab-initio-based modeling of the evolution of the electronic properties; Monte Carlo simulations of nonequilibrium electronic transport; molecular dynamics modeling of atomic reaction on the surface and in the bulk; kinetic Mote Carlo of atomic defect kinetics; finite-difference methods of tracks interaction with chemical solvents describing etching kinetics. We outline the modern methods that couple these approaches into multiscale multidisciplinary models and point to their bottlenecks, strengths, and weaknesses. The analysis is accompanied by examples of important results improving the understanding of track formation in various materials. Summarizing the most recent advances in the field of the track formation process, the review delivers a comprehensive picture and detailed understanding of the phenomena.Comment: to be submitte

Latent tracks of swift Bi ions in Si3N4

Parameters such as track diameter and microstruture of latent tracks in polycrystalline Si3N4 induced by 710 MeV Bi ions were studied using TEM and XRD techniques, and MD simulation. Experimental results are considered in terms of the framework of a 'core-shell' inelastic thermal spike (i-TS) model. The average track radius determined by means of electron microscopy coincides with that deduced from computer modelling and is similar to the track core size predicted by the i-TS model using a boiling criterion. Indirect (XRD) techniques give a larger average latent track radius which is consistent with the integral nature of the signal collected from the probed volume of irradiated material. © 2020 The Author(s). Published by IOP Publishing Ltd

Molecular dynamics simulations of non-equilibrium systems

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Effect of valence holes kinetics on material excitation in tracks of swift heavy ions

A considerable part of the excess energy of the electronic subsystem of a solid penetrated by a swift heavy ion (SHI) is accumulated in valence holes. Spatial redistribution of these holes can affect subsequent relaxation, resulting in ionizations of new electrons by hole impacts as well as energy transfer to the target lattice. A new version of the Monte Carlo code TREKIS is applied to study this effect in $Al_{2}O_{3}$ for SHI tracks. The complex dielectric function (CDF) formalism is used to calculate the cross sections of interaction of involved charged particles (an ion, electrons, holes) with the target giving us ability to take into account collective response of a target to excitations.We compare the radial distributions of the densities and energies of excited electrons and valence holes at different times to those obtained under the assumption of immobile holes used in earlier works. The comparison shows a significant difference between these distributions within the track core, where the majority of slow electrons and valence holes are located at femtosecond timescales after the ion impact. The study demonstrates that the energy deposited by valence holes into the lattice in nanometric tracks is comparable to the energy transferred by excited electrons. Radii of structure transformations in tracks produced by these energy exchange channels are in a good agreement with experiments

Time-resolved electron kinetics in swift heavy ion irradiated solids

The event-by-event Monte Carlo model, TREKIS, was developed to describe the excitation of the electron subsystems of various solids by a penetrating swift heavy ion (SHI), the spatial spreading of generated fast electrons, and secondary electron and hole cascades. Complex dielectric function formalism is used to obtain relevant cross sections. This allows the recognition of fundamental effects resulting from the collective response of the electron subsystem of a target for excitation that is not possible within the binary collision approximation of these cross sections, e.g. the differences in the electronic stopping of an ion and in the electron mean free paths for different structures (phases) of a material. A systematic study performed with this model for different materials (insulators, semiconductors and metals) revealed effects which may be important for an ion track: e.g. the appearance of a second front of excess electronic energy propagation outwards from the track core following the primary front of spreading of generated electrons. We also analyze how the initial ballistic spatial spreading of fast electrons generated in a track turns to the diffusion ~10 fs after ion passage. Detailed time-resolved simulations of electronic subsystem kinetics helped in understanding the reasons behind enhanced silicon resistance to SHI irradiation in contrast to easily produced damage in this material by femtosecond laser pulses. We demonstrate that the fast spreading of excited electrons from the track core on a sub-100 fs timescale prevents the Si lattice from nonthermal melting in a relaxing SHI track

Electron Emission from Silicon and Germanium after Swift Heavy Ion Impact

The presented Monte Carlo model simulates excitation of the electron subsystem of semiconductors by a penetrating swift heavy ion (SHI). The cross sections of interaction of an ion with the electron subsystem of a target are calculated via the complex dielectric function formalism, which accounts for all the collective modes of the electron ensemble of the target. The predicted electron inelastic mean free paths are in a very good agreement with those from the NIST database. The calculated SHI energy losses coincide well with SRIM and CasP codes. The model is used to calculate the spectra of electrons emitted from germanium and silicon targets during SHI irradiation. These spectra agree well with the experimental data

Effect of Atomic Structure on Excitation of the Electronic Subsystem of a Solid by a Swift Heavy Ion

An effect of different phase states of a solid on excitation of its electronic subsystem due to penetration of a swift heavy ion (SHI) is examined on example of silicon dioxide (crystalline quartz vs. amorphous glass). The complex dielectric function formalism describing collective response of the electronic and ionic subsystems of a condensed target to excitation is used to calculate scattering cross sections of a penetrating ion and electrons generated due to target ionizations. A Monte Carlo model based on these cross sections is applied for tracing electron kinetics in the nanometric vicinity of the trajectory of a swift heavy ion. It is demonstrated that differences of the maximal values of the SHI energy losses and the electron inelastic mean free paths calculated for two phase states of SiO2 do not exceed 10–15%, whereas the elastic mean free paths differ more significantly

Monte-Carlo modeling of excitation of the electron subsystem of ZnO and MgO in tracks of swift heavy ions

Monte Carlo code TREKIS is applied to trace kinetics of excitation of the electron subsystem of ZnO and MgO after an impact of a swift heavy ion (SHI). The event-by-event simulations describe excitation of the electron subsystems by a penetrating SHI, spatial spreading of generated electrons and secondary electron cascades. Application of the complex dielectric function (CDF) formalism for calculation of the cross sections of charged particle interaction with a solid target allows to consider collective response of the target to perturbation, which arises from the spatial and temporal correlations in the target electrons ensemble. The method of CDF reconstruction from the experimental optical data is applied. Electron inelastic mean free paths calculated within the CDF formalism are in very good agreement with NIST database. SHI energy losses agree well with those from SRIM and CasP codes. The radial distributions of valence holes, core holes and delocalized electrons as well as their energy densities in SHI tracks are calculated. The analysis of these distributions is presented