Electronic Excitation in Atomic Collision Cascades

Electronic Excitation in Atomic Collision Cascades Barbara Garrison Zdenek Sroubek Filip Sroubek C. Staudt COSIRES 2004, Helsinki AndreasWucher AndreasDuvenbeck

kinetic excitation • atomic motion in collision cascade • electronic excitation in inelastic collisions • electron emission,charge state of sputtered particles space and time dependent electron temperature ?

excitation model (1) • energy transfer • kinetic energy electronic excitation • electronic stopping power (Lindhard): total energy fed into electronic system : Sroubek & Falcone 1988

electronic friction ? • ab-initio simulation of H adsorption on Al(111) (E. Pehlke et al., unpublished) Lindhard formula works well for low energies

excitation model (2) • diffusive transport • diffusion coefficientmay vary inspaceandtime • „instant“ thermalization • electronic heat capacity depends on Te !

instant thermalization ? • ab-initio simulation of H adsorption on Al(111) (E. Pehlke et al., unpublished) geometry electronic states Fermi-like electron energy distribution at all times !

diffusion coefficient • fundamental relation : • electron mean free path : • relaxation time : • lattice disorder : Fermi velocity electron temperature interatomic distance lattice temperature

numerics solution of diffusion equation by • Green's function • explicit finite differences crystallographic order (rk,ti)

boundary conditions Green's function finite differences z z x x y y 42 Å

MD Simulation 5 keV Ag Ag(111) 4500 atoms trajectory 952 trajectory 207 Ytot = 48 Ytot = 16

lattice temperature • N atoms in cell calculated TL even at Te = 0 ! averaged over entire surface limitation of D

constant diffusivity Green's function finite differences • differences at small times (< 100 fs) • same temperature variation at larger times

electron temperature dependence • Te - dependence small for t > 100 fs D= const (TL = 104 K) Te variable, TL= const

full temperature dependence TL constant, Te variable TL variable, Te variable TL dependence strong ! Te < 1000 K for t > 100 fs

atomic disorder time dependence of crystallographic order (traj. 207) pair correlation function order parameter N atoms in cell

order dependence linear variation of D between 20 and 0.5 cm2/s within 300 fs Green's function finite differences lattice disorder extremely important !

e-ph coupling two-temperature model : surface energy density surface temperature negligible back-flow of energy from electrons to lattice !

Summary & Outlook • MD simulation • source of electronic excitation • diffusive treatment of excitation transport • include space and time variation of diffusivity by • temperature dependence • lattice disorder • MD simulation • calculate Eel and Te as function of • position • time of emission t • Calculate excitation and ionization probability individually for every sputtered atom of sputtered atoms

r Diffusion Coefficient • peak value vs. time (normalized) • time dependent diffusion coefficient : D

excitation probability excitation probability  electronic energy density r (A) Excited atoms emitted later in cascade

r Time Dependence

r Electron Temperature

electron temperature

Energy Spectrum • excitation probability time dependent • small for t < 300 fs • large for t > 300 fs First (crude) estimate : • simulation of energy spectrum • no account of excitation • count all atoms for ground state • count only atoms emitted after 300 fs for excited state simulation experiment

Summary & Outlook • MD simulation • calculate Eel and Te as function of • position • time of emission t • Qualitative explanation of • order of magnitude • velocity dependence of excitation probability (Ag* , Cu*) • Calculate excitation and ionization probability individually for every sputtered atom • Quantitative correlation between order parameter and electron mean free path of sputtered atoms

Electron Energy Distribution • 3 x 3 x 3 Å cell grid • numerical solution of diffusion equation • variable diffusion coefficient D • Te dependence • TL dependence • lattice disorder  electron energy density at the surface

Excitation Co atoms sputtered from Cobalt population partition ground state excited state V. Philipsen, Doctorate thesis 2001

Excitation Ni atoms sputtered from polycrystalline Nickel by 5-keV Ar+ ions velocity distribution excited state ground state V. Philipsen, Doctorate thesis 2001

Electronic Excitation in Atomic Collision Cascades