Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
Migration of di- and tri-interstitials in silicon
M. Posselt, D. Zwicker
Forschungszentrum Rossendorf, Institute of Ion Beam Physics, Dresden, Germany
Pacific Northwest National Laboratory, Fundamental Science Directorate, Richland, WA, USA
F. Gao
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
Motivation
- small interstitial clusters play an important role in the evolution of
radiation damage during post-implantation annealing
- formation:
(i) fast relaxation of highly disordered cascade region immediately
after implantation
(ii) clustering of diffusing interstitial-type defects during annealing
state-of-the-art description of the evolution of interstitial clusters:
mono-interstitial is the only mobile interstitial-type defect
but there are also indications that interstitial clusters are mobile
comprehensive MD study on the migration of di- and tri-I
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
Simulation Method(modified) Stillinger-Weber interatomic potential
search for di- and tri-I with the lowest formation energies “scrambled relaxation method” (cf. Rasband et al.)
(a)
simulation of defect migration (cf. Osetsky, Guinan, et al.)(b)start at T = 0 K with the most stable di- or tri-I configuration
supercell is heated up gently to the diffusion temperature
defect migration is followed for 5 – 50 ns
thermal expansion is taken into account, i.e. N, V(T), T system
mean square displacements of all atoms yields the self-diffusion coefficient per defect Ds
defect diffusion coefficient Dd is obtained from following the trajectory of
the center-of-mass of the defect using the Wigner-Seitz-cell analysis
relatively large supercell (1008+2, 2880+3)
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
di-I with the lowest formation energies
Results
(110)
“Z structure in {110}”I2A
Ef = 6.10 eVEb = 1.74eV
DFT: Richie 2004: 6.46 eV
TB: Rasband 1996: 8.0 eV; Hane 2000: 5.85 eV
CP: Gilmer 1995 (SW): 5.70 eV; Marques 2001 (T3): 6.32 eV
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
(1-10)(111)
“triangle in {111} plus additional atom in a parallel plane”I2B
Ef = 6.14 eVEb = 1.70 eV
DFT: Richie 2004: 6.46 eV 12
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
(110)
“W structure in {110}”I2C
Ef = 6.37 eVEb = 1.47 eV
TB: Rasband 1996: 8.0 eV; Hane 2000: 5.85 eV
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
tri-I with the lowest formation energies
[001]
near (1-10)near (110)
“compact structure, tetrahedron”
I3A
Ef = 7.54 eVEb = 4.22 eV
CP: Gilmer 1995 (SW): 7.08 eV; Lenosky 2000 (EDIP): 8.85 eV; Lenosky 2000 (L): 6.03 eV
TB: Bongiorno 2000: 6.69 eV; Lenosky 2000: 7.83
DFT: Kim 2000: 5.8 eV; Chichkine 2002: 6 eV;
Richie 2004: 6.96-7.11 eV; Lopez 2004: 7.27 eV 14
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
di-interstitial migration
T = 800 KT = 1200 K
T = 1600 K
30
Å
trajectories over a period of 4.4 ns
low T – high mobility along <110> axes, change between equivalent directions occurs seldom and requires a long time
high T – frequent change between equivalent <110> directions
temperature dependent migration mechanism
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
migration along <110>: in a {110} plane, as I2A or I2
C
migration distance: 2nd n.n. distance
I2A
<110>
I2C I2
C
I2A or I2
C
I2A
{110}I2
C
snapshots:
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
migration distance: 1.5*2nd n.n. distancemovie 1(~6 ps)
{110}
atoms belonging to
the defect change
continuously
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
transformation from I2A (or I2
C) to I2B: di-I becomes immobile
movie 2(~6 ps)
{111}
change between equivalent <110> directions
1st step:
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
transformation from I2B to I2
A:
di-I migration continues into a <110> direction (in a {110} plane),
new <110> direction of motion
{110}<111>
I2B
rotation out
of the {111} plane
I2A formation in
a {110} plane
2nd step:
5
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
tri-interstitial migration
T = 1600 K
T = 1500 K
T = 1400 K
trajectories over a period of 14.4 ns
complex migration paths
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
I3A
I3A
migration via different intermediate configurations
migration distance: 2nd n.n. distancesnapshots:
7
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
movie 3(~40 ps)
high atomic
mobility
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
diff
usi
vity
(cm
2 s
-1)
1/kT (eV-1)
Em(eV) D0 (cm2 s-1)
0.22 1.8x10-4
0.38 4.1x10-4
0.82 8.2x10-3
0.90 1.0x10-2
1.6 0.39
1.6 0.11
diffusion coefficients
CP: Gilmer 1995 (SW): ~ 0.2 eV
TB: Hane 2000: 1.35 eV; Kim 1999: 0.7 eV; Richie 2004: 0.5 eV, 0.5 eV
DFT (no MD): Eberlein 2001: 0.5 eV, 0.75 eV; Du 2004: 0.5 eV
Institute of Ion Beam Physics and Materials Research
Mitglied der Leibniz-GemeinschaftCOSIRES 2004
Talk O1 / M. Posselt
Conclusions
- di- and tri-I have a relatively high mobility
- di-I migrates faster than the mono-I and the tri-I, tri-I has the smallest
diffusivity
- mobility of di-I (and of mono-I) are higher than the mobility of the
lattice atoms during defect migration, tri-I migration is slower than
the corresponding atomic diffusion
- di-I: migration mechanism depends on temperature
- state-of-the-art description of the evolution of interstitial clusters
should be critically checked