1. CMS HIP Multiscale modelling of electrical breakdown at high electric field Flyura Djurabekova, Aarne Pohjonen, Avaz Ruzibaev and Kai Nordlund Helsinki Institute of Physics and Department of Physics University of Helsinki Finland

2. Flyura Djurabekova, HIP, University of Helsinki 2 Outline  Objectives: RF against DC?  Tools being in use  Multiscale model to approach the problem of electrical breakdown  Dislocations: details  Summary CERN, Geneva Accelerator Laborary, Helsinki

3. Flyura Djurabekova, HIP, University of Helsinki 3 DC vs RF

4. Flyura Djurabekova, HIP, University of Helsinki 4 Tools to get to the business:  In our group we use all main atom-level simulation methods of modern materials modelling  Density functional theory (DFT)  Solving Schrödinger equation to get electronic structure of atomic system  Molecular dynamics (MD)  Simulation of atom motion, classically and by DFT  Kinetic Monte Carlo (KMC)  Simulation of atom or defect migration in time  Simulations of plasma-wall interactions  Simulation of plasma particle interactions with surfaces  Collaborators  We use all of them to tackle the arcing effects!

5. Flyura Djurabekova, HIP, University of Helsinki 5 Multiscale model to simulate electrical breakdown (once more) Stage 1: Charge distribution @ surface Method: DFT with external electric field Stage 4: Plasma evolution, burning of arc Method: Particle-in-Cell (PIC) Stage 5: Surface damage due to the intense ion bombardment from plasma Method: Arc MD ~few fs ~few ns ~ sec/hours ~10s ns ~ sec/min ~100s ns Stage 2: Atomic motion & evaporation + Joule heating (electron dynamics) Method: Hybrid ED&MD model (includes Laplace and heat equation solutions) Stage 3b: Evolution of surface morphology due to the given charge distribution Method: Kinetic Monte Carlo Stage 3a: Onset of tip growth; Dislocation mechanism Method: MD, Molecular Statics…

6. Flyura Djurabekova, HIP, University of Helsinki 6 Plasma onset: extending of classical methods Stage 2: Atomic motion & evaporation + Joule heating (electron dynamics) Method: Hybrid ED&MD model (includes Laplace and heat equation solutions) F. Djurabekova, S. Parviainen, A. Pohjonen and K. Nordlund: “Atomistic modelling of metal surfaces under electric fields: direct coupling of electric fields to a molecular dynamics algorithm”, PRE 83, 026704 (2011)

7. Flyura Djurabekova, HIP, University of Helsinki 7 Some details: Stage 2  Atoms move according Molecular dynamics algorithm, solving Newton equations of motion  But in ED&MD hybrid code for surface atoms as due to the excess or depletion of electron density (atomic charge)  Gauss law is applied to calculate the charges; E is a solution of Laplace equation Thus, the motion of surface atoms is corrected due to the pulling effect of the electric field fiel φ=const (conductive material) ‏ + + + + + + + +

8. Flyura Djurabekova, HIP, University of Helsinki 8 Macroscopic field to… Gauss law states …the atomic level: + +++++++ Two electric forces modify the motion of charged atoms: + Due to the external electric field the surface attains charge External electric field: classical electrodynamic approach

9. Flyura Djurabekova, HIP, University of Helsinki 9 Solution of 3d Laplace equation for the surface with the tip of 20 atomic layers (color represents the charges)

10. Flyura Djurabekova, HIP, University of Helsinki 10 Atom/cluster evaporation from Cu(100) @ 500 K, E 0  1 GV/m Aarne Pohjonen

11. Flyura Djurabekova, HIP, University of Helsinki 11 Evolution of a tip placed on the surface ( Published also as CLIC note) We calculate the effect of high electric fields on the metal surface and consistently introducing this information into Molecular Dynamics simulations of the surface evolution. If temperature of the surface is sufficient, atom evaporation enhanced by the field can supply neutrals to build up the plasma densities above surface. We have also initiated the simulation of image reconstruction for Atom Probe tomography to include a KMC step (Initiation of Kinetic Monte Carlo studies) F. Djurabekova, S. Parviainen, A. Pohjonen and K. Nordlund: “Atomistic modelling of metal surfaces under electric fields: direct coupling of electric fields to a molecular dynamics algorithm”, PRE 83, 026704 (2011)

12. Flyura Djurabekova, HIP, University of Helsinki 12 Dislocation mechanism of tip growth: why voids?  In order to be able to form a stably growing structure, there is a need for a constant and consistent source of constructing pieces.  The randomly distributed dislocations, which are always present in metals are not capable to build surface features due to the absence of repetitiveness.  Any stress concentrator is a possible source of dislocation mechanism.  We study one, which gives sufficiently plausible explanation for the origin of surface feature growth →E→E ++++++++ STRESS  =  0 E 2 /Y

13. Flyura Djurabekova, HIP, University of Helsinki 13 But… We still must explain why the tip growth is possible?  Looking for the plausible explanation of surface roughening and possible mechanisms we found an interesting fact: there is a large field of research on such a mysterious phenomenon as whisker growth.

14. Flyura Djurabekova, HIP, University of Helsinki 14 Recent experiment at CERN (CLIC)  The dislocation motion is strongly bound to the atomic structure of metals. In FCC (face-centered cubic) the dislocation are the most mobile and HCP (hexagonal close-packed) are the hardest for dislocation mobility.

15. Flyura Djurabekova, HIP, University of Helsinki 15 Evolution of the surface held under tensile pressure (caused by electric field?)  If the tensile stress in order of several GPa is applied to the surface with the void, it eventually results in the protrusion on the surface

16. Flyura Djurabekova, HIP, University of Helsinki 16 Dislocation mechanism for mass transport  The protrusion has a clear rhombic shape with the small angle 71 o, which is the angle between two perpendicular to the surface {111} planes.

17. Flyura Djurabekova, HIP, University of Helsinki 17 Stress in the  The strain components  zx and  zy as a function of the z-coordinate of the atom. The atoms are analyzed along the path that starts at the most strained point on void surface and ends to the flat surface of the material, as depicted in fig. 5 for  zx component. The void surface is at the lower end of the z coordinate value (18..24 Å).

18. Flyura Djurabekova, HIP, University of Helsinki 18 New interpretation to the old data:  The concentration of defects in a material is* from standard thermodynamics where H f if the formation enthalpy, E f the formation energy and ΔV the formation volume of the defect. P is the pressure/stress exerted on the material.  Now in the current case due to Gauss law the external electric field exerts a stress on the surface * [Peterson, J. Nucl. Mater. 69 (1978) 3; Ehrhart, Properties and interactions of atomic defects in metals and alloys Landolt-Börnstein, New Series III ch. 2 p. 88-]. → F el ++++++++ STRESS P=  0 E 2

19. Flyura Djurabekova, HIP, University of Helsinki 19 Electric field dependence  Now assuming that the electric breakdown is caused by any defect mechanism, and the crucial step is nucleation of new defects due to the stress from electric field, it is reasonable to assume that breakdown rate BDR  defect concentration c  Moreover, the stress inside the material is of opposite sign to the external pressure. Hence one obtains:  Now grouping terms that are not dependent on the electric field and inserting a fitting prefactor A, this can be rewritten

20. Flyura Djurabekova, HIP, University of Helsinki 20 Electric field dependence  Now to test the relevance of this, we fit the experimental data presented in [Grudiev et al, PRSTAB 12 (2009) 102001] with the model. The result is: Power law fit by Grudiev et al Stress model fit

21. Flyura Djurabekova, HIP, University of Helsinki 21 Estimate of defect radius  The ΔV term depends on the defect type and size, but is for interstitial-like defects of the order of the number of atoms in the defect times the atomic volume .  Our fits gave values of ΔV = 57000 – 124000 .  Now assuming circular prismatic interstitial-like dislocation loops (that can cause tip growth), and that each atom in a loop contributes 1  to the relaxation volume (this is exactly true in the limit of very large dislocations) one can estimate the radius of one loop from πr 2 d = ΔV, where d is the thickness of one atomic layer. Using d ≈ 2 Å and  =3.62 3 /4 for Cu, one obtains a range of loop radii = 32 – 48 nm  This is very reasonable compared to estimates of experimental loop sizes

22. Flyura Djurabekova, HIP, University of Helsinki 22 Electromigration: one of the reason of void formation in metals Void formation in the conductor due to electromigration http://www.usenix.org/events/sec01/full_papers/ gutmann/gutmann_html/ Whisker growth on a conductor due to electromigration

23. Flyura Djurabekova, HIP, University of Helsinki 23 Atomic orbitals as a basis set s p d f Spherical harmonics: Size: Number of atomic orbitals per atom Range: Spatial extension of the orbitals Shape: of the radial part Radial part: z y x

24. Flyura Djurabekova, HIP, University of Helsinki 24 Cu vacuum Planar averaged and macroscopic averaged potential

25. Flyura Djurabekova, HIP, University of Helsinki 25 Electrostatic potential view of the simulated cell Switching on an external field We checked the effect of the size of the vacuum above the cell

26. Flyura Djurabekova, HIP, University of Helsinki 26 Lineup term DeltaV  How to compute DeltaV:  Take the difference between the averaged electrostatic potential and the averaged neutral atom potential.This difference is the profile of the deformation potential DeltaV across the interface.  Plot this last profile, and identify the plateau values at the center of each material (for the case of an interface), or between the center of the vacuum region and the center of the slab (in the case of a surface slab simulation). Neutral Atom Potential Effective potential( ionic + electronic)

27. Flyura Djurabekova, HIP, University of Helsinki 27 Calculation of work function Distribution of electrostatic potential and electronic density as a function of distance from the bottom of the cell vacuum

28. Flyura Djurabekova, HIP, University of Helsinki 28 Band structure term and Work Function Band structure term and Work Function  How to compute Band structure term:  Perform a bulk calculation for each material under the same strain conditions as in the interface or surface. Localize both the top of the valence (TVB) band and the bottom of the conduction band (BCB). The difference between the TVB and BCB of the two  materials is the term referred to as the band structure term.  Our case is surface simulations for the metal. Hence the TVB and BCB coincides and for slab region equal to Fermi energy from bulk simulations. Subtracting from it vacuum energy layer taken from surface simulations we finally find the band structure term DeltaE.  Vacuum layer =1.03 eV Fermi energy for bulk =-1.4 eV

29. Flyura Djurabekova, HIP, University of Helsinki 29

30. Flyura Djurabekova, HIP, University of Helsinki 30 Results of the recent work

31. Flyura Djurabekova, HIP, University of Helsinki 31 Summary  We develop a multiscale model, which comprises the different physical processes (nature and time wise) probable right before, during and after an electrical breakdown event:  The different parts of the general model are started in parallel. We start, continue and develop intense activities to cover all possible aspects.  Most recently our modeling has shown:  The trigger of the sparks is explained by plasma discharge;  Plasma is fed from the tips grown under the high electric field  Tip growth can be explained by the natural relaxation of stresses inside of material by the dislocation’s motions

32. Flyura Djurabekova, HIP, University of Helsinki 32 Dislocation activities: Finalize the publications on theoretical prediction of dislocation activities leading to the formation of surface protrusions in the presence of electric fields. Comparison of Electron densities from quantum and classical model: Calculation of work function by first principles techniques (Density Functional Theory, DFT) in presence of surface defects. Calibration of the DFT results with the classical hybrid ED&MD model continues. Evolution of surface defects in high electric fields: Continue the design and development of Kinetic Monte Carlo model to follow the surface evolution of defects in presence of sufficiently high electric fields. Integrate the image reconstruction for the Atom probe tomography with the experimental measurements form Culham Centre for Fusion Energy. Summary & Future activities

33. Flyura Djurabekova, HIP, University of Helsinki 33