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Migration of di- and tri-interstitials in silicon

Migration of di- and tri-interstitials in silicon. M. Posselt , D. Zwicker. Forschungszentrum Rossendorf, Institute of Ion Beam Physics, Dresden, Germany. F. Gao. Pacific Northwest National Laboratory, Fundamental Science Directorate, Richland, WA, USA.

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Migration of di- and tri-interstitials in silicon

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  1. Migration of di- and tri-interstitials in silicon M. Posselt, D. Zwicker Forschungszentrum Rossendorf, Institute of Ion Beam Physics, Dresden, Germany F. Gao Pacific Northwest National Laboratory, Fundamental Science Directorate, Richland, WA, USA

  2. comprehensive MD study on the migration of di- and tri-I 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

  3. search for di- and tri-I with the lowest formation energies “scrambled relaxation method” (cf. Rasband et al.) (a) (b) simulation of defect migration(cf. Osetsky, Guinan, et al.) 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 Simulation Method (modified)Stillinger-Weber interatomic potential relatively large supercell (1008+2, 2880+3) 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

  4. (110) Results di-I with the lowest formation energies I2A “Z structure in {110}” Ef = 6.10 eV Eb = 1.74eV CP: Gilmer 1995 (SW): 5.70 eV; Marques 2001 (T3): 6.32 eV TB: Rasband 1996: 8.0 eV; Hane 2000: 5.85 eV DFT:Richie 2004: 6.46 eV

  5. (1-10) (111) I2B “triangle in {111} plus additional atom in a parallel plane” Ef = 6.14 eV Eb = 1.70 eV DFT:Richie 2004: 6.46 eV 12

  6. I2C “W structure in {110}” (110) Ef = 6.37 eV Eb = 1.47 eV TB: Rasband 1996: 8.0 eV; Hane 2000: 5.85 eV

  7. [001] near (1-10) near (110) tri-I with the lowest formation energies I3A “compact structure, tetrahedron” Ef = 7.54 eV Eb = 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

  8. 30 Å T = 1200 K T = 800 K T = 1600 K di-interstitial migration trajectories over a period of 4.4 ns temperature dependent migration mechanism 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

  9. <110> I2A I2C I2C {110} I2C I2A I2A or I2C migration along <110>:in a {110} plane, as I2A or I2C snapshots: migration distance: 2nd n.n. distance

  10. migration distance: 1.5*2nd n.n. distance movie 1 (~6 ps) atoms belonging to the defect change continuously {110}

  11. change between equivalent <110> directions 1st step: transformation from I2A (or I2C) to I2B: di-I becomes immobile movie 2 (~6 ps) {111}

  12. {110} <111> rotation out of the {111} plane I2A formation in a {110} plane I2B 2nd step: transformation from I2B to I2A: di-I migration continues into a <110> direction (in a {110} plane), new <110> direction of motion 5

  13. T = 1600 K T = 1500 K T = 1400 K tri-interstitial migration trajectories over a period of 14.4 ns complex migration paths

  14. I3A I3A migration via different intermediate configurations snapshots: migration distance: 2nd n.n. distance 7

  15. movie 3 (~40 ps) high atomic mobility

  16. diffusivity (cm2 s-1) 1/kT (eV-1) diffusion coefficients 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 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

  17. 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 - state-of-the-art description of the evolution of interstitial clusters should be critically checked • 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

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