Non-adiabatic Electron-ion Dynamics in Ion-irradiated 2D Materials

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1 Non-adiabatic Electron-ion Dynamics in Ion-irradiated 2D Materials Alina Kononov, André Schleife University of Illinois at Urbana-Champaign OCI ACI DE-AC02-06CH11357

2 Focused Beam Techniques Focused Ion Beam (FIB) Scanning Electron Microscopy (SEM) Helium Ion Microscopy (HIM) G. Hlawacek, V. Veligura, et al.: J. Vac. Sci. Technol., (2014)

3 Focused Beam Techniques Focused Ion Beam (FIB) Scanning Electron Microscopy (SEM) Helium Ion Microscopy (HIM) Micro/nano-machining Produces rough, amorphous surface Imaging Requires conducting or coated sample Both imaging and nano-machining All types of samples Ultrahigh resolution Minimal sample damage G. Hlawacek, V. Veligura, et al.: J. Vac. Sci. Technol., (2014)

4 Projectile Impacts Material Ion (H +, He 2+, Xe 25+ ) 25 kev Target Material (Al, C) ~ 1 nm

5 Projectile Traverses Material Stopping Power Entrance-Side Secondary Electrons Exit-Side Secondary Electrons

6 Projectile Exits Material Transferred Electrons Entrance-Side Secondary Electrons Exit-Side Secondary Electrons

7 Open Questions Secondary electron yield H + C Xe n+ C Beam energy (kev) Meckbach, Braunstein, Arista: J. Phys. B., Wilhelm, Gruber, Ritter, et al.: PRL, 2014.

8 Open Questions Secondary electron yield H + C Xe n+ C Beam energy (kev) Meckbach, Braunstein, Arista: J. Phys. B., Wilhelm, Gruber, Ritter, et al.: PRL, Relationships between charge transfer, energy transfer, and secondary electron emission? Dynamic evolution? Dependence on projectile velocity, charge, type; target thickness? first-principles approach

9 Workflow Calculate ground state of target material (DFT) Evolve orbitals over time (TDDFT) Analyze time-dependent electron density

10 Why Blue Waters? Calculate ground state of target material (DFT) Evolve orbitals over time (TDDFT) Analyze time-dependent electron density 100 atoms 1000 electrons 5000 electronic relaxation steps 25,000 node hours 50 GB wavefunctions 3 fs simulated time 0.3 as time step 10k time steps 15k node hours 400 density files 70 MB / density 30 GB data Dependence on: projectile velocity projectile charge impact parameter target thickness 30 simulations 700k node hours 2 TB data

11 Density Functional Theory (DFT) Formulate many-body quantum physics in terms of electron density: Solve eigenvalue problem self-consistently:

12 Time-Dependent Density Functional Theory (TDDFT) Evolve orbitals over time:

13 Time-Dependent Density Functional Theory (TDDFT) Evolve orbitals over time: Plane-wave basis LDA 4th order Runge-Kutta

14 Cray Blue Waters IBM Blue Gene/Q Sequoia Schleife, Draeger, Anisimov, Correa, and Kanai: Comput. Sci. Eng., 2014.

15 Electron Density Analysis: Secondary Electron Yield Challenges: Periodic boundary conditions cause merge Long simulations in large cells accumulate significant integration error

16 Secondary Electrons Integrate electron density outside target

17 Secondary Electrons: Integration Error Integrate electron density outside target Subtract time-dependent integration error Obtained from simulation without projectile

18 Secondary Electrons: Convergence wrt Cell Length all 5 points first 4 points last 4 points Integrate electron density outside target Subtract time-dependent integration error Obtained from simulation without projectile Extrapolate cell-size convergence

19 Secondary Electrons: Convergence wrt Cell Length all 5 points first 4 points last 4 points Integrate electron density outside target Subtract time-dependent integration error Obtained from simulation without projectile Extrapolate cell-size convergence

20 Electron Density Analysis: Projectile Charge Challenges: Distinguish projectile electrons from Target electrons Secondary electrons

21 Inside Target: Charge Partitioning Projectile Electrons DDEC6 charge partitioning method Valid before secondary electron emission Stopping Power (Ha/a 0 ) Derivative of total energy

22 Outside Target: Hydrogen Orbital Analysis P 1s (r)/2 P un. (r)/10 4 Integrate electron density in spherical shells around projectile Fit to linear combination of hydrogen orbitals and uniform density R 2 = 0.92 n 1s = 0.22 n un. = 2.8 x 10-5

23 Outside Target: Hydrogen Orbital Analysis P 1s (r)/2 P 2s (r) P un. (r)/10 4 Integrate electron density in spherical shells around projectile Fit to linear combination of hydrogen orbitals and uniform density R 2 = 0.92 n 1s = 0.22 n un. = 2.8 x 10-5 R 2 = 0.96 n 1s = 0.21 n 2s = n un. = 2.2 x 10-5

24 Outside Target: Superposition of 1s and 2s cell length Apply hydrogen orbital analysis to extract orbital occupations over time ± 0.30 ev n 1s = ± n 2s = ± n tot = ± 0.010

25 Summary and Outlook Accomplished: Overcome finite size effects in calculating secondary electron yield Use long cells Subtract integration error Extrapolate convergent value Accurately determine projectile charge Charge Partitioning Orbital analysis Ongoing Work: Charge distribution within target Dependence of physical quantities on Target material thickness Target material type (Al, C) Projectile type (H +, He 2+, Xe 25+ ) Projectile velocity Projectile trajectory Compare to experiment

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