Space-time evolution of electron cascades in diamond

Abstract

Abstract:The impact of a primary electron initiates a cascade of secondary electrons in solids, and these cascades play a significant role in the dynamics of ionization. Here we describe model calculations to follow the spatiotemporal evolution of secondary electron cascades in diamond. The band structure of the insulator has been explicitly incorporated into the calculations as it affects ionizations from the valence band. A Monte-Carlo model was constructed to describe the path of electrons following the impact of a single electron of energy E ∼ 250 eV. This energy is similar to the energy of an Auger electron from carbon. Two limiting cases were considered: the case in which electrons transmit energy to the lattice, and the case where no such energy transfer is permitted. The results show the evolution of the secondary electron cascades in terms of the number of electrons liberated, the spatial distribution of these electrons, and the energy distribution among the electrons as a function of time. The predicted ionization rates (∼ 5-13 electrons in 100 fs) lie within the limits given by experiments and phenomenological models. Calculation of the local electron density and the correspond-1 e-mail:ziaja@tsl.uu.se, szoke1@llnl.gov, spoel@xray.bmc.uu.se, hajdu@xray.bmc.uu.se ing Debye length shows that the latter is systematically larger than the radius of the electron cloud, and it increases exponentially with the radial size of the cascade. This means that the long-range Coulomb field is not shielded within this cloud, and the electron gas generated does not represent a plasma in a single impact cascade triggered by an electron of E ∼ 250 eV energy. This is important as it justifies the independent-electron approximation used in the model. At 1 fs, the (average) spatial distribution of secondary electrons is anisotropic with the electron cloud elongated in the direction of the primary impact. The maximal radius of the cascade is about 50Å at this time. At 10 fs the cascade has a maximal radius of ∼ 70Å, and is already dominated by low energy electrons (> 50%, E < 10 eV). These electrons do not contribute to ionization but exchange energies with the lattice. As the system cools, energy is distributed more equally, and the spatial distribution of the electron cloud becomes isotropic. At 90 fs, the maximal radius is about 150Å. An analysis of the ionization fraction shows that ionization level needed to create an Auger electron plasma in diamond will be reached with a dose of ∼ 2 × 10 5 impact X-ray photons perÅ 2 if these photons arrive before the cascade electrons recombine. The Monte-Carlo model described here could be adopted for the investigation of radiation damage in other insulators and has implications for planned experiments with intense femtosecond X-ray sources.The treatment of electron cascades in this paper is restricted to low energy electrons (E impact = 250 eV) and weakly ionized samples where only a few interatomic bonds are perturbed. We chose diamond as a model compound because of its significan...

Reabsorption of Soft X-Ray Emission at High X-Ray Free-Electron Laser Fluences

“…For a full theoretical description, simulations of the complete Auger cascade, including the time evolution of the core-and valence-excited states, are necessary, including possible multiple excitations. These simulations have been performed for different materials and parameter spaces including water and ice [27][28][29][30], while they mostly concentrated on much lower fluence ranges.…”

“…In each inelastic scattering event, a portion of the electron kinetic energy is transferred to a water molecule, ultimately creating a valence excitation in this molecule. A single primary Auger electron can create tens of valence excitations within a few femtoseconds [26][27][28][29][30]. The detected XE photons result from the radiative decay of the core-ionized molecule [ Fig.…”

Ionization by impact electrons in solids: Electron mean free path fitted over a wide energy range

“…Refs. 29 and 30͒ have been based on mean free paths for impact ionization obtained with optical models. 5,6 Those mean free paths were valid at high impact energies only.…”

Unified model of secondary electron cascades in diamond

“…In contrast, Auger electrons are slow (v ∼ 95Å/fs in carbon), so they remain longer in a sample, and it is likely that they will thermalize there. An analysis of electron cascades initiated by Auger electrons in diamond is described in [2].A detailed description of electron cascades initiated by an electron impact of energy between ∼ 0.5 − 12keV is needed for a better understanding of radiation damage in larger samples as secondary ionization caused by propagating photoelectrons is significant there. Such processes need to be investigated for planned experiments with free-electron-lasers (FEL).…”

“…This approach takes into account the valence and core ionizations of an atom, following the inelastic scattering of a free electron. This approximation works well for energies up to about 10 keV, and in this energy regime core ionization are responsible for not more than about 10 % of the total number of ionizations in solids [14].In this paper elastic scattering is treated in the muffin-tin potential approximation [1,2,5,6]. In previous studies on low-energy electrons (with energies up to, E = 0.4 keV), we used programs from the Barbieri/Van Hove Phase Shift package [15].…”