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
• gt1 keV Accurate methods exist
• but terminal subclusters are lt1 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 _at_ 100 fs Red atoms KE gt
0.22 eV Black atoms displaced gt 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
lt100 eV
Time
7
Damage Scaling with Energy

• Natoms with KE gt 0.22 eV ? Natoms with ?r gt
  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 _at_ 100
fs
Red (hot) atoms KE gt 0.22 eV Black atoms
displaced gt 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 lt1 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