Effects of model approximations for electron, hole, and photon transport in swift heavy ion tracks

Abstract

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.Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST «MISiS» (№ K3-2016-035). The results were obtained using computational resources of MCC NRC "Kurchatov Institute"

Fundamental Phenomena and Applications of Swift Heavy Ion Irradiations

“…Assuming the target is in thermodynamic equilibrium, the DSF can be recast in terms of the complex dielectric function (CDF, ε(ω,q)) of the target employing the fluctuation dissipation theorem [250]. The differential cross section of scattering σ in the non-relativistic case is then written as [91]:…”

“…An example of the electron kinetics during a cascade as modeled with the Monte Carlo code TREKIS [69,91] is shown in Figure 1. A typical electron distribution is created via various processes as described above: (i) the first front of the radial distribution is formed by the photon transport, exciting new electrons via photo-absorption, (ii) the second wave front is formed by delta electrons for which the fastest are from a dissipative wave, leaving behind a trace of secondary electrons via impact ionization, and (iii) the third front of electrons is created by plasmon decays which trigger another dissipating wave with typical energies corresponding to the plasmon energy in the solid (typically around 20-30 eV in dielectrics).…”

“…A typical electron distribution is created via various processes as described above: (i) the first front of the radial distribution is formed by the photon transport, exciting new electrons via photo-absorption, (ii) the second wave front is formed by delta electrons for which the fastest are from a dissipative wave, leaving behind a trace of secondary electrons via impact ionization, and (iii) the third front of electrons is created by plasmon decays which trigger another dissipating wave with typical energies corresponding to the plasmon energy in the solid (typically around 20-30 eV in dielectrics). The majority of the slow electrons produced in the close proximity of the projectile are due to Auger-decays of holes and impact ionizations [91]. It should be emphasized that the wave-like behavior of electrons during the cascades (<100 fs) is of non-equilibrium nature, which cannot be described in general with equilibrium thermodynamics [70].…”

“…It should be emphasized that the wave-like behavior of electrons during the cascades (<100 fs) is of non-equilibrium nature, which cannot be described in general with equilibrium thermodynamics [70]. Figure adapted from [91].…”

Latent tracks of swift Bi ions in Si3N4

“…To simulate the formation of Bi ion latent tracks a hybrid scheme was applied [7,8] for the coupled kinetics of the excitation and relaxation of the electronic and the atomic sub-systems of a material irradiated with highenergy heavy ions. First, the asymptotic trajectory Monte Carlo code TREKIS [9,10] is used to determine the initial parameters which are characteristic of an excited state of the ensemble of electrons as well as energy transferred to lattice atoms via electron-lattice coupling in an ion track. The calculated radial distribution of the energy transferred into the lattice is then used as input data for classical molecular dynamics code LAMMPS [11] used to simulate subsequent lattice relaxation and structure transformations appearing near the ion trajectory.…”