Flyura Djurabekova, HIP, University of Helsinki 5

Electrical Breakdown in multiscale modeling approach

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 plasmaMethod:Arc MD

~fewfs

~fewns

~ sec/ hours

~10s ns

~ sec/ min

~100s ns

PLASMA

ONSET

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…

28

64 atoms simulation cell in external electrical field

Avaz Ruzibaev

64 or 64+1 Cu atoms simulated(100) lattice

30

Adsorbed atoms

Avaz Ruzibaev

29

Adatoms arrangements

Avaz Ruzibaev

35

Output energies

Cu100 64 atWithout EF

Cu100 64 withEF 0,1 v/A'

Cu100 65 atWithout EF

Cu100 65 withEF 0,1 v/A'

Cu100 65 withEF -0,1 v/A'

E total -76686,1 -76686,25 -77883,398 -77883,682 -77883,430

E fermi -2,4425 -2,375 -2,330 -2,383 -2,285

E surface 2,287 2,278 2,4747 2,4321 2,4698

∆ E fermi -0,0675 0,053 -0,045

=-0.1125 eV

Avaz Ruzibaev

Stefan Parviainen, University of Helsinki 13

Simulating heating: Solve heat equation

dT/dx = 0

~1-5 nm, ρbulk,σbulk

T = 300 K

ρFSE,σFSE

constant temperature

no heat escapes

Stefan Parviainen, University of Helsinki 10

Simulating heating: Find emission points

Stefan Parviainen, University of Helsinki 14

Previous results: Realistic temperature development

Stefan Parviainen, University of Helsinki 16

Previous results: Rayleigh instability(in some cases)

Large piece can break off?(not observed yet)

Stefan Parviainen, University of Helsinki 18

New results: Evaporation

Why?

Stefan Parviainen, University of Helsinki 21

Modeling the surface using KMC

Find out how the surface morphology changes due to the

external electric field during “long” time periods

Seconds instead of picoseconds

Do adatoms “climb up” the tip causing it to grow?

Use existing solid-on-solid KMC code

Modify to account for external field

Calculate transition probabilities using Molecular Dynamics

- This will take some time

Some limitations

- e.g. no overhangs

- Not possible to simulate sharp tips