Quantum Mechanical Description of Displacement Damage

Quantum Mechanical Description of Displacement

DamageMatthew J. Beck1, Ryan Hatcher1, R.D. Schrimpf2,

D.M. Fleetwood2,1, and S. T. Pantelides1

1Department of Physics and Astronomy2Department of Electrical Engineering and Computer Science

Vanderbilt University, Nashville, TN 37235 USA

MURI ReviewJune 13th, 2007

Support: AFOSR

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

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

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

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

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

Identifying Terminal Subclusters

15 eV displacement

PKA

Secondary

Terminal Subclusters

500 eV displacement

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

Identifying Terminal Subclusters

500 eV

15-100 eVFr

act

ion o

f in

itia

l m

om

en

tum

Fraction of initial momentum along displacement direction

remaining

500 eV

15-100 eV

Time

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

Identifying Terminal Subclusters

500 eV

<=100 eV

Fract

ion o

f in

itia

l m

om

en

tum

Fraction of initial momentum along displacement direction remaining

Time

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

Damage Scaling with Energy• Natoms with KE > 0.22 eV N atoms 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

Note: 0.22 eV T m

SiRed (hot) atoms: KE > 0.22 eV Black atoms:

displaced > 0.2 Å

25 eV displacement: Dynamic

“messiness” @ 100 fs

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

Damage Scaling with Energy

15 eV, 8 atoms

500 eV, 8 secondaries, 64 total atoms?

Melt cylinder along ion track!

Diameter for 500 eV ion: 3 nm

1.5 nm

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

Experimental Melt Tracks

AFM image of recrystalized Si along glancing Pb ion tracks at the Si/SiO2 interface. White

arrow shows incident ion direction

A.F.M.J. Carvalho, et al., APL 90

073116 (2007)

Matthew J. Beck

m.beck@vanderbilt.eduMURI Review, June 2007

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