Quantum Mechanical Description of Displacement Damage

1. Quantum Mechanical Description of Displacement Damage Matthew J. Beck1, Ryan Hatcher1, R.D. Schrimpf2, D.M. Fleetwood2,1, and S. T. Pantelides1 1Department of Physics and Astronomy 2Department of Electrical Engineering and Computer Science Vanderbilt University, Nashville, TN 37235 USA MURI Review June 13th, 2007 Support: AFOSR

2. Introduction • NIEL, Kinchin-Pease — threshold displacement energy • Molecular dynamics (MD) — full atomistic dynamics • Limitation: empirical potentials • >1 keV: Accurate methods exist • …but “terminal subclusters” are <1 keV events! PKA Secondary Terminal Subclusters

3. First-principles Molecular Dynamics • State-of-the-art quantum mechanical calculations • Density functional theory, local density approximation • Cell sizes: 216 atoms • Calculation times: 100s of fs Dynamic “messiness” @ 100 fs Red atoms: KE > 0.22 eV Black atoms: displaced > 0.2 Å

4. Identifying Terminal Subclusters PKA Secondary Terminal Subclusters 500 eV displacement 15 eV displacement

5. Identifying Terminal Subclusters Fraction of initial momentum along displacement direction remaining 500 eV 500 eV Fraction of initial momentum 15-100 eV 15-100 eV Time

6. Identifying Terminal Subclusters Fraction of initial momentum along displacement direction remaining 500 eV Fraction of initial momentum <=100 eV Time

7. Damage Scaling with Energy • Natoms with KE > 0.22 eV  Natoms with Δr > 1.17 Å • Even small KE events contribute! • “Hot” atoms predict disordered atoms Damage Scaling: • Density of secondary atoms • independent of direction and energy • Energy of secondary atoms • dependent on initial displacement energy 25 eV displacement: Dynamic “messiness” @ 100 fs Red (hot) atoms: KE > 0.22 eV Black atoms: displaced > 0.2 Å Note: 0.22 eV  TmSi

8. Damage Scaling with Energy  1.5 nm 15 eV, 8 atoms 500 eV,  8 secondaries, 64 total atoms? Melt cylinder along ion track! Diameter for 500 eV ion:  3 nm

9. Experimental Melt Tracks A.F.M.J. Carvalho, et al., APL 90 073116 (2007) AFM image of recrystalized Si along glancing Pb ion tracks at the Si/SiO2 interface. White arrow shows incident ion direction

10. Conclusions • Quantum mechanical calculations are effective tools for probing atomic scale dynamics of <1 keV displacements • Quantitatively identify terminal subclusters • Low energy displacements contribute to dynamical damage formation • Single displacement damage events can disorder volumes of atoms which are significant in highly scaled devices