poster

Molecular Dynamics of damage and sputtering induced by swift heavy ions

M. Beuve$&; N. Stolterfoht&; M. Toulemonde§; C. Trautmann$ ; H.M. Urbassek#

§ CIRIL (Centre Interdisciplinaire de Recherche Ion Laser), Caen, France; $ GSI (Gesellschaft für Schwerionenforschung), Darmstadt, Germany;

& HMI (Hahn-Meitner-Institut), Berlin, Germany; # University of Kaiserslautern, Germany









Abstract

N at Analytical Thermal Spike (ATS) Molecular Dynamics (MD) MD and ATS comparison

Due to its complexity, modelling of damage induced in solids

by swift heavy ions was first undertaken using analytical theories

 

based on model concepts such as thermal spike or pressure pulse

N ion e.g.: P. Sigmund & C.Claussen (81); R.E. Johnson & R Evatt (80) Principle

E0

model. About 10 years ago, Molecular Dynamics (MD) simulations  Solving the Newton equation for N

were started in this field [1], reducing the number of approximations Principle

atoms   R0

in the theoretical description. However, the electronic processes, • Local atomic equilibrium + Thermodynamics principle dri p i

which govern the primary ion-solid interaction and also the 

Experiments • Cylindrical symmetry T = T (r,t) dt M i Applied within the same conditions

subsequent energy transfer from the target electrons to the lattice, are

introduced in these simulations in an ad hoc manner. For instance, • Diffusive transport of energy   - Condensed-gas solid : Argon

n dp i   

sputtering predictions are generally obtained considering that a fixed  dE  dE T 1   T    ri 0 1

 V (r ,...., r ,... r )

fraction of the projectile energy loss is deposited inside a cylinder of     1  n for high C (T)  rK(T)  dt

i N - Same initial temperature profile:

fixed radius. Thus, effects related to the radial extension of the  dx  dx t r r   r  (Cylinder or Gaussian profile)

electron cascade (e.g. velocity effect) can not be taken into account. t  0 : T  T0 (r)

Furthermore, for high-energy depositions, the sputtering yield is e.g.: n=1 for condensed Ar Molecular dynamics  Analytical Thermal Spike

predicted to be proportional to the stopping power which is in C(T) specific heat ; K(T) thermal conductivity • Advantages (/Monte Carlo Simulation)

n=2 for condensed O2 1 2

disagreement with experimental data. – Collective effects (Shock wave)  dE  dE  dE  dE

n=4 for LiF • Initial temperature profile = Gaussian     for high     for high

The aim of our MD calculations is to explore the influence of – Adapted to strong perturbations  dx  dx  dx  dx

the time and space dependent energy transfer from the electrons to the  n function of the target – Fixed width

– Anisotropic effects (focusson) [H.M. Urbassek et al. 94]

lattice atoms on observable quantities (e.g., sputtering and track size). – Total energy = Stopping power

For this purpose, we use the electron-phonon coupling mechanism • Sputtering = sublimation process

developed by Toulemonde et al. [2] in the thermal spike model. The

Analytical theories • Disadvantages Analytical Thermal Spike = Incorrect

evolution of the electronic temperature Te(r,t) is described by a • Great number of analytical models Y   dt dS (T) – Computing time is huge!!!

continuum equation that is coupled to the Newton equations of the Explanations

target atoms (MD). We can assess, for example, the influence of the • Large number of approximations t,S  Small samples (N104 to 105 )

projectile velocity and of the electron phonon coupling on the atom • Based on thermodynamics considerations Result • Velocity distribution Non Maxwellian

n  Simple system model (Lennard-Jones)

dynamics.  dE  • Transport of energy Not Only diffusive

e.g.: - Gas Flow   n2

 dx     1    12    6  • Effect of pressure wake

V0 (r1 ,...., ri ,... rN )   VL  J (rij ) with VL  J (r )  4       

1 H. M. Urbassek, H. Kafemann, R. E. Johnson, Phys. Rev. B 49, 786 (1994) - Shock wave or pressure pulse

i j 2

 r   r   • Energy transport to the surface… Tsurf>Tbulk

2 M.Toulemonde, J. M. Costantini, Ch. Dufour, A. Meftah, E. Paumier and - Thermal spike  

F.Studer Nucl. Instr. Meth. B116 (1996)37 [E.M. Bringa et R.E. Johnson 98-99]

 n depends on the models (1, 3/2, 2, 3)







Why does MD give n =1 ? Isotropic random kick Time-dependent energy transfer

Principle

Principle :  Energy is progressively and periodically introduced

Effect of potential?

The energy is transferred to atoms (or during a time  with a period  /N (N from 100 to 1000).

Lennard-Jones n=1 eventually extracted from atoms) by a random  Each transfer of energy is equal to 1 dE

(Lz is the thickness of the target) Lz

isotropic kick processes: N dx

Other potentials n1 

? A kick of energy E0 instantaneously changes

Morse potential [E.M. Bringa et al. 00] the atom momentum according to the equations:

- 1 parameter more to change stiffness

- Obtained n~1.5 but: q / M  v f  v i

 0

N

t

 (1)

2 E0 / M  v 2  vi2

- Potential ~ hard sphere

- Shockwave



 f

 For each energy transfer i, only the atoms that set in the

solid and within the cylinder of axe, the ion trajectory, and of

- Artificial q fixed radius R0 (R0 =2) received an energy E0(i).

1 dEThen

Effect of energy deposition ? E0(i)  L z Nat(i)

vi N dx

Experimental argument Before Kick After (Nat(i) is the number of atoms in the solid setting in the cylinder)

=> Velocity effect

- vi and vf are respectively the velocity before and

Theoretical argument

after the kick, R0  = 0 s t = 20 ps

=> Work of Toulemonde et al.

- M is the atom mass,

- E0 is the energy transferred to the atom and may be

....In this work , we investigated some negative, The energy transfer to the atoms is performed according to

- q is an isotropic momentum. It is randomly tossed the previously described random kick process

effects of the energy deposition up in respect for the set of equations (1).



Observations / Interpretations

Scaling to other materials

• For time scale lower than 10-12 s,

the effect of a

time-dependent energy transfer is irrelevant Lennard Jones potential  Time scaling

Thermal spike model of M at M at

• For a time scale of 10-11s : t  

Toulemonde et al. Effect of energy deposition …  U

• the power exponent is clearly modified.

F. Seitz et J.S.Koehler (23) ; M. Toulemonde et al. (92) e.g.: Cu: tCu= 0.17 tAr

The Idea:

• for y  1 energy diffuses and can no longer  Cu atom dynamics is faster

Principle :  To check the effects of a more realistic  Time effect should appear sooner

produce an efficient sputtering

 Based on two coupled equations: energy deposition beyond the fixed radial profile,

we consider the thermal spike developed by • for y >> 1 less energy is taken away by non Such time scales match, for instance, with F-

T 1   T 

( I ) Ce (Te ) e  rKe (Te ) e   g(Te - Tat )  A(r , t ) linear mechanisms (pressure pulse...). The centre creation in alkali halides.

t r r 

 r  Toulemonde et al.

sputtering is then more efficient

T 1  

( II ) Cat (Tat ) at 

T 

rKat (Tat ) at   g(Te - Tat )

[N. Itoh et K. Tanimura 90]

 = 10 ps t = 20 ps

t r r 

 r  Parameter of the simulation:

• one for the atomic subsystem - Atomic subsystem : Solid argon

- Similar to the ATS model Potential : Lennard-Jones



• one for the electronic subsystem consisting of: - Electron subsystem : Insulator

C(T) = 1 J cm-3 K-1

Observations / Interpretations

- A(r,t), takes into account :

i) Electronic excitations by the incident ion (10-18 s) K(T) = 2 J cm-1 s-1 K-1 Effect of a rather realistic energy deposition:

ii) Transport of the excitations by electronic cascades - Electron phonon-coupling : Very strong • a velocity effect can clearly be observed

(10-18 ~ 10-15 s)

- g = 0 for Tat > Te

- A heat equation dealing with thermal • the power exponent is hugely modified

electrons - g = 2 10 14 W cm-3 K-1 for Tat < Te

• the area concerned by sputtering is quite large. Its radius

Close to the value for SiO2 [Toulemonde et al. 2000]

• g(Te-Tat) represents energy transfers due to reaches a value up to 11 (larger than the Bohr adiabatic

electron-phonon coupling (g is constant) Some details: radius)

- The sample is decomposed in n cylinders Ci of axe, the

Advantages ( / Analytical Thermal spike): • although the atomic temperature stays lower than the

ion trajectory and of radius Ri = iR0 , i [0, n-1]

sublimation temperature (Tsub= 640 K = kB-1.Us=55 meV.kB-1),

- i) Includes electron dynamics instead of a - n-1 domains Di are defined as Di = Ci \ Ci-1. A last one is the yield can reach very large value (e.g.: 150 at/ion)

simple fixed profile of deposited energy. defined as Dn = sample \ Cn-1

• for high dE/dx, the sputtering occurs in a collective way. A

- ii) Propose a process of energy transfer from block of matter suddenly flows out (in less than 20 ps).

electrons to atoms: electron-phonon coupling

A very large value of electron-phonon coupling

- iii) Takes account for phase transformation

(melting, superheating…)  Energy transfer occurs before:

Dn

• any thermal diffusion of the electronic energy

Limits: - At each time step t of the whole simulation (electron y

and atomic dynamics) and for each domain, • any local thermodynamic equilibrium for the atomic

- Assumes local atomic equilibrium subsystem. The notion of specific heat could not be used

- the atomic temperature Tat is evaluated

- Does not take account for any mechanism such here to describe the atomic evolution

- a transfer of energy is performed between both

as shock wave, focus on.... subsystems according to the formulae

Ion H H H H (*) He He He He (*) [E.M. Bringa et R.E. Johnson 98]

Energy [MeV/n] 0.5 0.3 0.2 0.11 6.5 3.25 1.8 0.6

- Considers the target as an infinite medium g(Te - Tat )tVi (Vi volume of Di ) A shock wake takes away energy from the track

dE/dx [eV/Å] 3.78 5.23 6.5 7.47 7.42 11.2 15.5 21.7

- Assumes sputtering as an evaporation process The energy is given to (or taken from) the atoms y 158.5 219 272. 5 313 311 470 650 910

according to the described random kick process.

Note: outside the sample, g is set equal to 0 to solve the electron

Bragg Peak (*) Other observations / Suggestions

dynamics even far away from the ion trajectory

5 The analysis of some movies seems to indicate that:

10

General conclusion (a) • for H(0.11MeV), a significant part of the sputtered atoms

Au (210) would be ejected perpendicularly to the surface

- From this work, we learned that it may not be 4

10 • for He(0.6MeV/n), more atoms seems to be ejected at

diff. sputter yield (F, Li)









realistic to model swift-ion interaction with solids

depositing suddenly a fixed part of the stopping large angles,

power in a cylinder of fixed radius.

- We showed that a more realistic time-dependent

10

3 ? Indeed, in the latter case, a block of matter, which

contains a great number of atoms, undergoes an evolution in

I (150) the vacuum soon after its ejection:

and space-dependent energy deposition may

drastically modify the sputtering yield. - a kind of explosion occurs because the atoms, surrounding

2 it in the solid, are now missing

- In particular, for the first time, non-linear

relations between yield and stopping power were

? 10 Ni (70)

q=0°

45°

- the highly perturbed surface attracts the last ejected atoms

and then deviates them to higher angles

showed with Molecular Dynamic for high

1

stopping power. 10 Both these phenomena would produce a more isotropic

a60-75°

distribution.

- This work opens directions to new extensive

studies. Indeed, the whole process of swift-ion These suggestions, which are qualitatively in agreement

0

interaction with solid (including electronic 10 with measurements performed for LiF target (except for the

excitations, transport, eventual trapping…), has, a -80 -40 0 40 80 sharp peak at 0°), have to be confirmed by angular

priori, to be considered.. H (0.11 MeV) t = 30 ps angle q He (0.6 MeV/n) t = 30 ps distribution calculations.