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

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! Figure out how to say why empirical is less than ideal… Indicate that track sizes on the order system sizes of interest for <1keV events…. highly scaled techs are now on the scale of systems that can be directly simulated… (e.g. devices with active regions with size scales 10s nm) (fix) That low events can generate disordered regions on this size scale… for large device sizes, volume averaged properties are sufficient, while for highly scaled devices require single event level understandings…. for hihgly scaled devices, statistical understanding is insufficient… *Not integrated approach, rather approach for highly scaled studies… PKA Secondary Terminal Subclusters

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

Identifying Terminal Subclusters PKA Secondary Terminal Subclusters 500 eV displacement 15 eV displacement Write that XYZ is (100,010,001) in Si…

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

Identifying Terminal Subclusters Fraction of initial momentum along displacement direction remaining 500 eV Fraction of initial momentum Fix discussion of agreement with empirical <>1keV understanding <=100 eV Time

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

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

Experimental Melt Tracks A.F.M.J. Carvalho, et al., APL 90 073116 (2007) “A MURI collaborator”, don’t forget to put in citation…. FIG. 1. Top view of an AFM topographical measurement tapping mode of 0.63 MeV 208Pb32+ ion tracks in Si crystals with an 11.8 nm SiO2 layer irradiated at grazing incidence under 1° at 51010 ions/cm2. Ions have traversed from bottom to top white arrow. The number of tracks is in agreement with the expected average ion impact areal density of 9 per m2. The brightest regions correspond to the highest topographical areas and the darkest zones represent the lowest topographical edges. The outline around a track corresponds to the reference mark for the topographic height profile along the track. The white arrow refers to the ion beam direction. AFM image of recrystalized Si along glancing Pb ion tracks at the Si/SiO2 interface. White arrow shows incident ion direction

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 Fix bullets. Highly scaled stuff, not just QM issues…