Novel diffusion mechanism in the presence of excited electrons?

Ever since Ernest Rutherford performed his famous scattering experiments [1], the interaction of energetic particle radiation with matter has not lost any of its original fascination. On the contrary, it has developed into one of the most common and important probes of microscopic detail: Electron and ion beams unravel atomistic and crystal structure and provide invaluable insight by means of transmission-electron and helium-ion microscopy, respectively. In addition, focused-ion-beam machining manipulates materials and fabricates structures at the micro- and nano-scale, for modern applications including photonic, plasmonic, and microelectromechanical systems. While this tremendous potential triggers broad technological interest in energetic particle radiation across industry, medicine, nuclear energy, and outer-space applications, a deep understanding of radiation-induced damage requires fundamental research.

One of the most intriguing questions around ionizing radiationis the balance of creation and repair of damage. Creation of damage is associated with collision cascades—a series of binary collisions induced by the incoming ion—in which lattice atoms are displaced, forming point defects. Repair of defects is attributed to annealing—a lattice temperature increase following energy deposition into the target material. Both effects are consequences of ionizing radiation; in particular, swift heavy ions are known to either exacerbate or mitigate damage in a material [2]. Developing a better understanding of the underlying mechanisms and, eventually, deliberately switching between both regimes bears great promise for new radiation-hard materials in cutting-edge applications and for operating existing materials more efficiently in extreme environments where they are exposed to radiation.

Our current understanding of processes that emerge in a material upon interaction with fast, charged particles involves multiple time and length scales: Initially, when ionic-lattice response is too slow, high-energy, charged particles predominantly scatter inelastically with the target’s electronic system. The incoming ion transfers energy to the electrons, slows down and, eventually, predominantly scatters elastically with lattice atoms. Details about simulation techniques, experimental approaches, and how the projectile velocity affects the interaction mechanism across length and time scales can be found in Ref. [3]. While damage created during the later stage is well described by collision cascades developing on pico-second or longer time scales [4], understanding the initial, inelastic-scattering stage is more difficult: Electronic excitations occur on sub-femtosecond time scales and subsequent electronic and ionic relaxations extend well into the picosecond range.

Both, ultrafast processes and multi-time scale aspects render the experimental and computational description challenging. Contrary to known mechanisms for defect formation during elastic scattering, there is comparably little study on inelastic, non-equilibrium electron–ion dynamics. Since electronic excitations are commonly ignored for the sake of a simpler description, their impact on formation and evolution of defects is unknown! However, irradiation, especially with swift heavy ions, gives rise to interesting non-equilibrium electron–ion dynamics, since these deposit significant amounts of kinetic energy into electronic excitations. Along with increasing practical use of swift heavy-ion beams, the goal of fabricating small nanostructures and to precisely dope materials, e.g. for quantum-bit applications, requires accurate approximations that correctly take contributions of electronic excitations into account. While the total amount of energy deposited into the target is smaller for light projectiles, e.g. highly energetic protons, they experience significant electronic stopping [5][6][7][8][9], ultimately leading to lattice heating and annealing.

To understand non-equilibrium electron–ion dynamics in solids and to explain whether energetic particle radiation anneals or creates defects, a full quantum-mechanical treatment of nuclei and electrons is ideal. Since this is infeasible even using state-of-the-art supercomputers, current research is devoted to developing accurate and practical first-principles descriptions. To this end, we recently combined several cutting-edge approximations [10]: We model excited electrons using real-time time-dependent density functional theory [11] in Ehrenfest dynamics simulations, going significantly beyond standard first-principles Born–Oppenheimer dynamics. We propagate time-dependent Kohn–Sham equations in real time, which has been demonstrated to accurately predict energy transfer to electrons in diverse materials [5][6][7][8][9], allowing us to precisely simulate creation of non-thermalized hot-electrondistributions. After removing the projectile from the simulation, we continue real-time propagation, to explore ultrafast electron dynamics toward thermalization. Finally, to address the multi-time-scale character, we extract Kohn–Sham occupation numbers and incorporate those as occupation constraint into constrained density functional theory. Using the nudged-elastic band method, we quantify the influence of hot-electron distributions on atomic diffusivity.

After developing this framework, we use it to study a neutral oxygen vacancy in proton-irradiated magnesium oxide [10]. The cover image of this issue of Materials Today illustrates the incredible beauty, both esthetic and scientific, of the fascinating electron–ion dynamics emerging in this system. It visualizes the electron density change for one snapshot of our Ehrenfest dynamics simulation of the proton traveling on a [0?0?1] channel closest to the oxygen vacancy, located near the image center. Blue isosurfaces are indicative of electron-density dynamics near the proton and, while atoms are not shown explicitly, the target material can be derived from red isosurfaces. Stunning 360 degree videos illustrating the full dynamics can be found at Ref. [12] and were rendered using the yt code [13].

Our simulations show a clear impact of excited electrons on oxygen diffusion, allowing us to quantify migration barriers in the presence of thermalized and non-thermalized electrons [10]. The strong reduction of an oxygen migration barrier and the enhancement of diffusion hints at the exciting possibility of a novel, hot-electron mediated diffusion mechanism. Further studies are needed to clarify this, and we show that the occurrence of this mechanism strongly depends on the proton kinetic energy and an oxygen-vacancy mid-gap level.

For many scientists, electronic excitations and electron–ion dynamics are, arguably, among the most captivating topics in contemporary materials research. Understanding fundamental quantum–mechanical interactions and manipulating underlying ultrafast processes has implications far beyond radiation damage. For this, tremendous developments are necessary: Computational cost and need for accuracy render simulations challenging. Highest requirements regarding efficiency and massive parallelism [14] illustrate an inherent demand for advanced multi-scale techniques. Vigorous theoretical, numerical, computer-science efforts and cutting-edge high-performance supercomputers are needed to accomplish accurate simulations. Despite these challenges, extraordinary promise for fundamental insight and immense potential for appealing benefits for society render quantum dynamics studies fascinating. Excitement for working toward this goal motivates and drives our current computational materials research.


Fruitful discussions with Ravi Agarwal, Xavier Andrade, Alfredo Correa, Yosuke Kanai, and Pascal Pochet are gratefully acknowledged. Financial support from the Sandia National Laboratory-UIUC collaboration (SNL grant no. 1736375) and the Government Scholarship to Study Abroad from the Taiwan Ministry of Education is acknowledged. An award of computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.

Further reading

[1] E. Rutherford LXXIX
The scattering of and particles by matter and the structure of the atom
Philos. Mag., 21 (125) (1911), pp. 669-688, 10.1080/14786440508637080

[2] S. Zinkle, L. Snead
Scripta Mater., 143 (2018), pp. 154-160, 10.1016/j.scriptamat.2017.06.041

[3] B. Wirth et al., J. Nucl. Mater. 329-333 (2004) 103 – 111, Proceedings of the 11th International Conference on Fusion Reactor Materials (ICFRM-11). doi: URL

[4] R.S. Averback, T.D. de la Rubia
Solid State Phys. 51 (C) (1997), pp. 281-402, 10.1016/S0081-1947(08)60193-9

[5] A. Schleife, et al.
Comput. Sci. Eng., 16 (5) (2014), pp. 54-60, 10.1109/MCS.E2014.55

[6] A. Schleife, Y. Kanai, A.A. Correa
Phys. Rev. B, 91 (2015), Article 014306, 10.1103/PhysRevB.91.014306

[7] A. Lim, et al.
Phys. Rev. Lett., 116 (2016), 10.1103/PhysRevLett.116.043201

[8] A.A. Correa
Comput. Mater. Sci., 150 (2018), pp. 291-303, 10.1016/j.commatsci.2018.03.064

[9] C.-W. Lee, A. Schleife, Electronic stopping and proton dynamics in InP, GaP, and In0.5Ga0.5P from first principles. URL

[10] C.-W. Lee, A. Schleife, Hot-electron mediated ion diffusion in proton irradiated magnesium oxide. URL

[11] E. Runge, E.K.U. Gross
Phys. Rev. Lett., 52 (12) (1984), pp. 997-1000, 10.1103/PhysRevLett.52.997

[12] C.-W. Lee, A. Schleife, Electronic excitation of proton-irradiated mgo,^ and (2016).

[13]M.J. Turk, B.D. Smith, J.S. Oishi, S. Skory, S.W. Skillman, T. Abel, M.L. Norman
Astrophys. J. Suppl., 192 (1) (2011), p. 1, 10.1088/ 0067-0049/192/1/9

[14] E.W. Draeger, et al.
J. Parallel Distr. Com., 106 (2017), pp. 205-214, 10.1016/j.jpdc.2017.02.005

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DOI: 10.1016/j.mattod.2018.08.004