institute of ion beam physics and materials research mitglied der leibniz-gemeinschaft cosires 2004...

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




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




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)




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




(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




(110)

“W structure in {110}”I2C

Ef = 6.37 eVEb = 1.47 eV

TB: Rasband 1996: 8.0 eV; Hane 2000: 5.85 eV




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




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




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:




migration distance: 1.5*2nd n.n. distancemovie 1(~6 ps)

{110}

atoms belonging to

the defect change

continuously




transformation from I2A (or I2

C) to I2B: di-I becomes immobile

movie 2(~6 ps)

{111}

change between equivalent <110> directions

1st step:




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




tri-interstitial migration

T = 1600 K

T = 1500 K

T = 1400 K

trajectories over a period of 14.4 ns

complex migration paths




I3A

I3A

migration via different intermediate configurations

migration distance: 2nd n.n. distancesnapshots:

7




movie 3(~40 ps)

high atomic

mobility




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




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

institute of ion beam physics and materials research mitglied der leibniz-gemeinschaft cosires 2004...

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