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.

Since a few breakthroughs in the fundamental understanding of the effects of swift heavy ions (SHIs) 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 and spans many orders of magnitude in time: from attoseconds in ion-impact ionization depositing an extreme amount of 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 times of the final 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 hybrid 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 the ab initio-based modeling of the evolution of the electronic properties, Monte Carlo simulations of nonequilibrium electronic transport, molecular dynamics modeling of atomic reaction including phase transformations and damage on the surface and in the bulk, kinetic Mote Carlo of atomic defect kinetics, and finite-difference methods of track interaction with chemical solvents describing etching kinetics. We outline the modern methods that couple these approaches into multiscale and combined 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 phenomenon. Important future directions of research and model development are also outlined.

The event-by-event Monte Carlo code, TREKIS, was recently developed to describe excitation of the electron subsystems of solids in the nanometric vicinity of a trajectory of a nonrelativistic swift heavy ion (SHI) decelerated in the electronic stopping regime. The complex dielectric function (CDF) formalism was applied in the used cross sections to account for collective response of a matter to excitation. Using this model we investigate effects of the basic assumptions on the modeled kinetics of the electronic subsystem which ultimately determine parameters of an excited material in an SHI track. In particular, (a) effects of different momentum dependencies of the CDF on scattering of projectiles on the electron subsystem are investigated. The 'effective one-band' approximation for target electrons produces good coincidence of the calculated electron mean free paths with those obtained in experiments in metals. (b) Effects of collective response of a lattice appeared to dominate in randomization of electron motion. We study how sensitive these effects are to the target temperature. We also compare results of applications of different model forms of (quasi-) elastic cross sections in simulations of the ion track kinetics, e.g. those calculated taking into account optical phonons in the CDF form vs. Mott's atomic cross sections. (c) It is demonstrated that the kinetics of valence holes significantly affects redistribution of the excess electronic energy in the vicinity of an SHI trajectory as well as its conversion into lattice excitation in dielectrics and semiconductors. (d) It is also shown that induced transport of photons originated from radiative decay of core holes brings the excess energy faster and farther away from the track core, however, the amount of this energy is relatively small

Response of dielectric crystals: MgO, Al₂O₃ and Y₃Al₅O₁₂ (YAG) to irradiation with 167 MeV Xe ions decelerating in the electronic stopping regime is studied. Comprehensive simulations demonstrated that despite similar ion energy losses and the initial excitation kinetics of the electronic systems and lattices, significant differences occur among final structures of ion tracks in these materials, supported by experiments. No ion tracks appeared in MgO, whereas discontinuous distorted crystalline tracks of ~2 nm in diameter were observed in Al₂O₃ and continuous amorphous tracks were detected in YAG. These track structures in Al₂O₃ and YAG were confirmed by high resolution TEM data. The simulations enabled us to identify recrystallization as the dominant mechanism governing formation of detected tracks in these oxides. We analyzed effects of the viscosity in molten state, lattice structure and difference in the kinetics of metallic and oxygen sublattices at the crystallization surface on damage recovery in tracks.

Structure changes and their formation threshold in swift heavy ion (SHI) tracks in Al ₂ O ₃ are studied using a combined start-to-end numerical model. The hybrid approach consists of the Monte-Carlo code TREKIS, describing kinetics of the electronic subsystem, and classical Molecular Dynamics for lattice atoms. The developed approach is free from a posteriori fitting parameters. Simulations of Xe 167 MeV ion impacts show that relaxation of an excess lattice energy results in formation of a cylindrical discontinuous disordered region of about 2 nm in diameter. Recent transmission electron microscopy observations agree with these results. The threshold of an SHI track formation is estimated to be ~6.1 keV nm ⁻¹ . Calculated x-ray diffraction patterns of irradiated material demonstrate more pronounced damage of the Al atoms sublattice near SHI trajectories. Modeling of Xe ion tracks overlapping demonstrates that the damaged area can be restored to a near virgin state. Estimations give 6.5 nm as the minimal distance between the Xe ion trajectories resulting in recovery of the transformed structure produced by the previous ion.