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 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!
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

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 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
Write that XYZ is (100,010,001) in Si…

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

6. 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

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 100 fs
Red (hot) atoms: KE > 0.22 eV Black atoms: displaced > 0.2 Å
Note: 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 (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 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

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