Stability and mobility of point defects and point-defect clusters in metals

1. Stability and mobility of point defects and point-defect clusters in metals Nicholas Kioussis W. M. Keck Computational Materials Theory Center California State University Northridge Zhengzheng Chen (CSUN) A. R. Akbarzadeh (CSUN) Nasr Ghoniem (UCLA) Dariush Seif (UCLA) King-Ning Tu (UCLA) Jenn-Ming Yang (UCLA) NSF, DOE

2. Native defects in fcc Cu (111) surface Native defects in bulk bcc Fe Chemistry in fcc Cu (111) surface Effect of strain on formation/migration energies of self interstitials in a-Fe Crucial role of surface in stability and mobility of vacancy clusters in metals Inhibiting Adatom Diffusion through Surface Alloying A. R. Akbarzadeh, Z. Z. Chen, and N. Kioussis, Phys. Rev. B 79, 195404 (2009) Z. Chen, N. Kioussis, K.N. Tu, N. Ghoniem, and J. M. Yang, Phys. Rev. Lett. 105, 015703 (2010) Z. Chen, N. Kioussis, N. Ghoniem, and D. Seif, Phys. Rev. B. 81, 094102 (2010) Effect of surface Sn alloying on the stability and mobilityof a Cu adatom on the Cu-Sn (111) alloy surface Binding and migration of mono-, di- and tri-vacancies in (111) Cu surface

3. I. Ab initio electronic structure calculations • Electron-ion interactions PAW • Exchange correlation functional – PBE • Supercells • Nudged elastic band (NEB) method for the transition-state search to determine the point defect diffusion pathways and migration energies [G. Henkelman and H. J. Jónsson, J. Chem. Phys. 113, 9978 (2000).] II. Mote Carlo calculations Temperature-dependent diffusion of adatoms

4. Formation energy under volumetric deformation at constant volume Formation energy under uniaxial deformation Formation energy of an nv vacancy cluster Binding energy of an nv vacancy cluster (attraction or repulsion of point defects)

5. Effect of strain on formation/migration energies of self interstitial atoms (SIA) in bcc a-Fe Ferritic/martensitic steels are structural materials in fission/fusion applications <111> <110> • Irradiation effects • Embrittlement • Long-term aging of cascades • Formation • Migration • Annihilation SIA <001> • Rare under normal conditions • TEM shows nucleation of SIA clusters in early stage of displacement cascades when irradiation dose above ≈ 1 dpa • SIAs highly mobile and attractive – hence they cluster • Clustered SIAs share same orientation and habit plane, • thus can be described as a prismatic dislocation loops (110) habit plane b = [111]/2

6. Previous calculations of stability and mobility of SIA in un-deformed a Fe C-C. Fu, F. Willaime, and P. Ordejon, Phys. Rev. Lett. 92, 175503 (2004) 4.34 eV 3.64 eV 4.74 eV As the size of the SIA cluster increases there is a transition from <110> to <111> In contrast to other bcc metals the Burgers vector of dislocation loops in a-Fe are observed to be either ½<111> or <100> instead of predominantly ½<111> ??? Mechanism

7. Under irradiation conditions Molecular Dynamics J. Marian, B. Wirth and J. Manuel Perlado, Phys. Rev. Lett. 88, 255507 (2002). Reactions between dislocations with b=1/2<111> 1000 K Snapshots of collision of two loops condensing into a single loop 120 ps [100] junction of 5 SIAs on a (110) plane As the <100> grows and elastic energy density increases the SIA cluster rotates on {100} habit plane In situ TEM experiments J. Arakawa et al, Phys. Rev. Lett. 96, 125506 (2006). ? Strain field of nearby dislocations

8. Isotropic volumetric • Ef decreases with expansion • Ef increases with compression • Release (accumulation) of elastic energy under expansion (compression) Uniaxial e11 (e22) • <111> is insensitive to uniaxial strain direction • Ef decreases with negative strain • Ef insensitive to positive strain Uniaxial e33 Deformation plays an important role on formation energies

9. Angle q between the SIA axis and deformation direction as function of uniaxial strain e33 e33 e33 <11x>|x=2.7 e11 • Under volumetric deformation no rotation of SIA • Under uniaxial deformation <111> → <11x>|x=2.7 <100> reorientation.

10. Migration barriers <11x>|x=2.7 Volumetric compression increases energy barriers for all paths, while expansion decreases them • e33eliminates the energy barrier between <111> and <11x>|x=2.7 • Volumetric expansion (compression) enhances (suppresses) the <111> to <001> rotation

11. Role of surface in stability/mobility of vacancy clusters in Cu (111) surface • Adatoms and advacancies main carriers in mass processes on metal surfaces • Failure under surface electromigration through void growth, evolution and migration driven by surface diffusion, electric field, and mechanical stress Cu (111) surface Binding energy surface Bulk Cu Ef1v = 1.07 eV 2nd layer 3nd layer Ef2v = 2.03 eV Eb2v = 0.11 eV 0.23 eV 0 eV • Coalescence of surface mono-vacancies indicates strong attractive intraplanar surface interaction and weak interplanar interaction • Preferential 2D clustering

12. Migration of surface vacancy clusters Surface monovacancy migration energy barrier 0.62 eV NN surface di-vacancy Migration

13. NN surface tri-vacancy Translation No rotation Rotation & Translation 3-step counterclockwise rotation

14. Inhibiting Adatom Diffusion through Surface Alloying Z. Chen, N. Kioussis, K.N. Tu, N. Ghoniem, and J. Yang, Phys. Rev. Lett. 105, 015703 (2010) • Surface electromigration (EM) involving the diffusion of atoms under the influence of an electric field • Major concern for the reliability of integrated circuits with large current densities which may exhibit significant mass transport, leading to interconnect failure • Copper interconnect: Superior performance and reliability, low electrical resistivity and intrinsically higher EM resistance • Surface alloying with heavy p-block elements (Sn, Pb) - an effective way to improve the EM performance of Cu • Thin Cu3Sn overlayer on Cu surface effectively blocks surface diffusion paths, thus resulting in an EM lifetime improvement of about one order of magnitude ?? Underlying mechanisms that control the kinetics remain unresolved

15. Isolated substitutionalSn atom • ? Preferential site: Solely into the surface layer -- Ef = 0.81 eV • Two substitutional surface Sn atoms • Sn-Sn interaction ? Preferential configuration 4th NN • Oversized Sn (20% larger than Cu) • Sn atoms segregate to and protrude from the surface by 0.6 A°to accommodate size mismatch • Tensile strain in the surrounding region and a Sn-Sn repulsion • Energy landscape for adsorption of a Cu adatom on the Cu-Sn (111) alloy surface which has two 4th-NN Sn atoms • Threefold hollow sites which are NN to Sn are unstable for adsorption due to the protrusion of Sns • Each Sn introduce forbidden areas (FA) within which a Cu adatom is strictly prohibited to adsorb • Sn atoms act as adsorption blocking sites impeding adatom diffusion • Sn atoms bind strongly with in-plane NN Cu atoms but not with NN Cu adatoms

16. Cu Migration paths I and II for a Cu adatom on the Cu-Sn (111) alloy surface with two 4th-NN Sn surface atoms • Increase (60-130 meV) in potential energy for Cu adsorption on 2nd and 3rd NN sites with respect to Sn • Migration barrier between these fcc and hcp sites increases to 84-99 meV • Cu adatom mobility close to Sn substantially reduced Migration paths III for a Cu adatom on the Cu3Sn interface • <110> Cu-Sn-Cu rows with 2nd NN Sn atoms • Increase of connectivity between forbidden areas centered on Sn • Increase of low-mobility areas between Sn atoms • Blocking of fcc to hcp paths available in dilute limit

17. Temperature-dependent Diffusion of a Cu adatom Dilute Sn-pair alloyed surface Cu3Sn/Cu interface Temperature-dependent probability • Diffusion channel between 2 Sn closed at 300K hindering the Cu adatom diffusion • Diffusion path opens with increasing temperature • Blocking propensity more pronounced in the Cu3Sn/Cu interface – improving the surface EM resistance of Cu • Control of adatom diffusion through selective alloying with p-block elements