Electronic Stopping Power in Gold: The Role ofdElectrons and theH/HeAnomaly

Abstract

The electronic stopping power of H and He moving through gold is obtained to high accuracy using time-evolving density-functional theory, thereby bringing usual first-principles accuracies into this kind of strongly coupled, continuum non-adiabatic processes in condensed matter. The two key unexplained features of what observed experimentally have been reproduced and understood: (i) The non-linear behaviour of stopping power versus velocity is a gradual crossover as excitations tail into the d-electron spectrum; and (ii) the low-velocity H/He anomaly (the relative stopping powers are contrary to established theory) is explained by the substantial involvement of the d electrons in the screening of the projectile even at the lowest velocities where the energy loss is generated by s-like electron-hole pair formation only.Non-adiabatic processes are at the heart of aspects of science and technology as important as radiation damage of materials in the nuclear and space industries, and radiotherapy in medicine. Yet, in spite of a long history, the quantitative understanding of non-adiabatic processes in condensed matter and our ability to perform predictive theoretical simulations of processes coupling many adiabatic energy surfaces is very much behind what accomplished for adiabatic situations, for which first-principles calculations provide predictions of varied properties within a few percent accuracy. Substantial progress has been made for weakly non-adiabatic problems such as the chemistry of vibrationally excited molecules landing on metal surfaces [1], but not in the stronger coupling regime of radiation damage. Recently, the electronic stopping power for swift ions in gold has been carefully characterized by experiments [2-4], showing flagrant discrepancies with the established paradigm for such problems [5,6], and only qualitative agreement with time-dependent tight-binding studies [7], and with detailed studies for protons based on first principles [8], leaving very fundamental questions unanswered in spite of the apparent simplicity of the system. Most notably the H/He anomaly: the present understanding predicts a stopping power for H higher than for He at low velocities [6], which strongly contradicts the recent experiments [4].A particle moving through a solid material interacts with it and loses its kinetic energy to both the nuclei and the electrons inside it. At projectile velocities between 0.1 and 1 atomic units (a.u. henceforth) both the nuclear and the electronic contributions to the stopping power (energy lost by the projectile per unit length) are sizeable [7]. Based on the jellium model (homogeneous electron gas) the electronic stopping power, S e , is predicted to be S e ∝ v for a slow projectile traversing a metallic medium [9,10]. Such behaviour has been observed experimentally in many sp-bonded metals [11,12], and the jellium model has allowed deep understanding of the dynamic screening of the projectile and its relation to stopping [13]. Even the jellium prediction of an oscillation of the ...

Stopping power beyond the adiabatic approximation

“…The arguments above, while not answering why our results differ by up to a factor of four with SRIM data, strongly suggest that low velocity stopping data is, in general, not accurately known and even more, they suggest that TD-DFT may help reduce these uncertainties, as it did in the case of light projectiles 24, 27, 28 .…”

Electronic Stopping of Slow Protons in Oxides: Scaling Properties

“…Time-dependent density-functional theory (TD-DFT) calculations of Se of protons in Au confirmed this interpretation [13]. For large band gap insulators, electronic stopping was found to vanish below a threshold velocity vth -e.g., for LiF (band gap Eg,LiF  13.6 eV) at velocities lower than vth  0.1 a.u.…”

Accurate atomistic first-principles calculations of electronic stopping

“…Only recently, the possibility of quantitatively describing the interaction of projectile atoms with the electronic and ionic system of the host material entirely within first-principles calculations has come within reach. [30][31][32][33][34][35][36][37] These recent advances for realistic materials rely on non-perturbative time-dependent density functional theory (TDDFT), 26 and its implementation in efficient electronic-structure codes. 38,39 At this point, however, there are still many open questions regarding, not only the physics of electronic stopping (e.g.…”