Electronic Excitation in Atomic Collision Cascades COSIRES 2004, Helsinki C. Staudt Andreas Duvenbeck Zdenek SroubekFilip Sroubek Andreas Wucher Barbara Garrison

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 ?

Outline model results outlook

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

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 ab-initio simulation of H adsorption on Al(111) (E. Pehlke et al., unpublished) Lindhard formula works well for low energies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 coefficient may vary in space and time „instant“ thermalization –electronic heat capacity depends on T e !

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 ab-initio simulation of H adsorption on Al(111) (E. Pehlke et al., unpublished) geometryelectronic states Fermi-like electron energy distribution at all times !

diffusion coefficient fundamental relation : electron mean free path : relaxation time : lattice disorder : Fermi velocity lattice temperatureelectron temperatureinteratomic distance

numerics Green's function explicit finite differences solution of diffusion equation by crystallographic order ( r k,t i )

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

Outline model results outlook

MD Simulation 5 keV Ag Ag(111) trajectory 952 trajectory 207 Y tot = 16 Y tot = atoms

lattice temperature N atoms in cell even at T e = 0 ! averaged over entire surface calculated T L limitation of D

excitation energy density Green's function with constant D

electron temperature Green's function with constant D r

constant diffusivity –differences at small times (< 100 fs) –same temperature variation at larger times Green's functionfinite differences

constant diffusivity –differences at small times (< 100 fs) –same temperature variation at large times Green's functionfinite differences

electron temperature dependence D = const ( T L = 10 4 K) T e variable, T L = const Te - dependence small for t > 100 fs

electron temperature dependence T e - dependence small for t > 100 fs D = const ( T L = 10 4 K) T e variable, T L = const

full temperature dependence T L constant, T e variable T L variable, T e variable T L dependence strong ! T e 100 fs

full temperature dependence T L constant, T e variable T L variable, T e variable T L dependence strong ! T e 100 fs T L dependence strong ! T e 100 fs

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

time and space dependence traj. 207 no lattice disorder electron temperature

order dependence linear variation of D between 20 and 0.5 cm 2 /s within 300 fs Green's functionfinite differences lattice disorder extremely important !

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

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 E el and T e as function of –position –time of emission t Calculate excitation and ionization probability individually for every sputtered atom of sputtered atoms

Diffusive transport Problem temporal development of collision cascade –increase of lattice temperature T L –increase of electron temperature T e reduction of electron mean free path defect creation / melting –amorphization of crystal –only short range order left –mean free path ~ interatomic spacing Time and space dependence of diffusion coefficient D

time and space dependence traj. 207 no lattice disorder electron temperature

time and space dependence traj. 207 no lattice disorder electron temperature

time and space dependence traj. 207 no lattice disorder electron temperature

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

disorder parameter define local cell containing N atoms atom positions { } with FCC lattice :

disorder parameter time dependence of disorder (traj. 207)

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

Time Dependence r

Electron Temperature r

Atomic Disorder radial distribution function time after impact

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 E el and T e 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

excitation model (2) diffusive transport –diffusion coefficient –electron mean free path due to atomic disorder in collision cascade

Electron Energy Distribution 3 x 3 x 3 Å cell grid numerical solution of diffusion equation variable diffusion coefficient D –T e dependence –T L dependence –lattice disorder  electron energy density at the surface

Ionization Oechsner & Sroubek 1983Wucher & Oechsner 1988 secondary ion formation Ta + O 2 Ar + Ta +

Ionization Non adiabatic model Excited substrate –non equilibrium between electrons and lattice –thermal equilibrium among electron gas –electron temperature T e I  solidvacuum EFEF z* EaEa needed : Sroubek et al.1988

Excitation Rh atoms sputtered from Rh(100) surface Winograd et al. 1991

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

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

Excitation De-excitation model –excitation in cascade (?) –de-excitation above surface MD – simulation –excitation in binary collisions if –relaxation with lifetime  i within solid  a above surface E rrcrc Bernardo et al Shapiro et al and later Bathia & Garrison 1994 Wojciechowski & Garrison Bernardo et al Excitation probability r

Metastable Silver Atoms population energy spectra Ag ( 2 S 1/2 ) and Ag* ( 3 D J ) sputtered from silver Berthold & Wucher 1995

Excitation Model atomic motion electronic energy excitation of d – hole localization on sputtered atom resonant electron transfer Needed : 5s 4d I  E* solidvacuum