migration of di- and tri-interstitials in silicon

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