The role of electronic friction of low-energy recoils in atomic collision cascades

The role of electronic friction of low-energy recoils in atomic collision cascades A. Duvenbeck 1 and O. Weingart 2 and V. Buss 2 and A. Wucher 1 1 Department of Physics, University of Duisburg-Essen, D-47048 Duisburg, Germany 2 Department of Theoretical Chemistry, University of Duisburg-Essen, D-47048 Duisburg, Germany Abstract We investigate the influence of low-energy recoils with respect to the electronic excitation of solids generated in atomic collision cascades. It is found that the electronic friction experienced by recoil atoms moving with kinetic energies below 10 ev contributes substantially to the total excitation energy dissipated into electronic degrees of freedom. The collision dynamics, on the other hand, remain virtually unchanged if the friction loss of these particles is switched on or off. This is illustrated by looking at the yield, emission sites and energies of sputtered surface atoms. 1 Introduction The bombardment of a solid metal surface with kev-ions initiates a complex sequence of atomic collisions in a near-surface region. The temporal and spatial evolution of this atomic collision cascade may not only lead to the ejection of particles from the surface ( sputtering ) [1,2], but also to electronic excitation which manifests, for instance, in the phenomenon of ion-induced kinetic electron emission [3]. Due to the strongly localized nature of the collision dynamics generating the excitation, a model description of this phenomenon needs to describe the collision dynamics along with the transport of the excitation energy. We have recently developed a model [4 6] that allows for the space- and time resolved calculation of electronic excitation energy densities in an atomic collision cascade. The model treats electronic friction as well as electron promotion as source terms of excitation energy that is carried away from the original spot of excitation according to a nonlinear diffusion equation. While the frictional source term is treated within the Lindhard model [7] Preprint submitted to Elsevier 26 October 2006

of electronic stopping, electron promotion energies are described using abinitio calculated correlation diagrams [8 10] in combination with a stochastic Landau-Zener treatment [11] of the resonant electron transition from a promoted quasi-molecular orbital into a free conduction band state. So far, this model has been applied to the chemically inert self-bombardment scenario involving the impact of a 5-keV Ag atom onto an Ag(111) surface [4,11,5,6]. The simultaneous calculation of particle kinetics and electronic excitations - the latter being evaluated in terms of an excitation energy density profile E( r, t) - has revealed that the majority of the kinetic energy originally imparted to the system may be dissipated into electronic degrees of freedom rather than in collision dynamics [5]. At first glance, this value appears surprising, since it is well known that the energy loss is dominated by nuclear rather than electronic stopping in the energy range explored here. Moreover, the validity of the Lindhard stopping power for slow secondary recoil atoms with kinetic energies below 10 ev has been questioned [12], although recent ab-initio time-dependent DFT calculations indicate its applicability in this regime as well [13]. In view of this discussion, it appears to be highly desirable to assess the relative role of low-energy recoils in the kinetic excitation process. This paper aims at a more detailed investigation of the contribution of lowenergy recoils to the excitation energy generated by electronic friction. An interesting question arising in this context is in how far the electronic stopping of slow secondary recoils in the cascade alters the microscopic particle kinetics particularly in view of sputtering of atoms. These questions are addressed by expanding our previous studies on kinetic excitation during self-sputtering of silver under impact of kev Ag projectiles. In order to elucidate the role of lowenergy recoils, we include a kinetic energy threshold for the onset of electronic friction, thereby switching off this energy loss mechanism for all particles in the system which are moving slower. The influence of such a threshold on the energy partition as well as on the sputtering dynamics are explored for one selected impact event. 2 Model The simulation model employed in this work has been described in detail earlier [4,11,6]. Briefly, we use a classical molecular dynamics (MD) code [14 16] to follow the temporal dynamics of all particles of the system, which are assumed to interact via a parametrized many body potential (MD/MC-CEM [17]) fit to the properties of solid silver. The employed model single crystallite with dimensions 42x42x42 Å 3 contains N = 4500 atoms arranged in 18 layers, its non relaxed surface being oriented in the (111)-direction. The electronic energy loss experienced by all moving particles is treated as a 2

2500 2000 energy (ev) 1500 1000 only electronic friction restricted to atoms with E kin > 10 ev 500 only electronic friction el. friction (with el. promotion) el. promotion 0 0 100 200 300 400 500 600 700 time (fs) Fig. 1. Volume-integrated excitation energy generated by electronic friction and electron promotion (solid lines), electronic friction exclusively (dotted line) and electronic friction restricted to particles with kinetic energies above 10 ev (dashed line). source of electronic excition energy transferred to the electronic sub-system, which is treated as a quasi-free electron gas. Two different excitation mechanisms are considered, namely electronic friction (experienced by all particles in motion) and electron promotion in close binary collisions. The excitation energy generated by electronic friction of a particle i at position r i (t) with kinetic energy E (i) k ( r,t) within a time interval dt is directly evaluated from the molecular dynamics as [4] N de 1 ( r,t) = A Ek( r i i,t) δ( r i r)dt (1) i=1 and assumed to be instantaneously and locally transferred to the electronic subsystem. The constant A depends on the projectile as well as the electron density and is evaluated as 2.9 10 12 1/s (see Ref. [4]) for an Ag atom moving in silver. Collisional excitation is treated in terms of a curve crossing mechanism based on the Fano-Lichten electron promotion model [8]. In short, we assume that during a close binary encounter quasi-molecular orbitals (MO) are transiently formed and shifted in energy as a function of interatomic distance r. These correlation diagrams are determined from ab-initio calculations and reveal a strong upward shift of the atomic 4d-orbital with decreasing r. If such a violent collision is embedded into the electron gas representing the solid silver, the promoted MO intersects the Fermi energy at a critical interatomic distance of r c = 1.5 Å. For r < r c, resonant electronic transitions may occur from the promoted orbital into unoccupied conduction band states. The transition 3

probability as a function of internuclear distance and its dependence on the continuum-orbital coupling has been recently discussed in Ref. [11]. The energy difference between the promoted MO at a certain interatomic distance and the Fermi level then constitutes the excitation energy of the hot electron injected into the conduction band. For the purpose of the present paper this energy is assumed to be transferred to the electronic sub-system as an additional source term besides the electronic friction. In order to establish an upper estimate of the influence of electron promotion, we employ the largest possible excitation energy by assuming the transition to occur at the distance r min of closest approach. The transport of electronic energy away from the original point of excitation is described by a nonlinear diffusion equation E( r, t) t (D (T l ( r,t),t e ( r,t), Λ( r,t)) E( r,t)) = N A Ek( r i i,t) δ( r i (t) r(t)) + i=1 + κ E MO (r min )(κ)(t)) E F t δ(t t (κ) min) δ( r r (κ) min), (2) the right of which representing the two source terms as explained above. In Eq.(2) E MO (r) denotes the parametrization of the diabatic energy curve of the quasi-molecular orbital. At each time step, the summation index κ in the collisional excitation source term loops over all violent binary encounters with a minimum interatomic distance r min < 1.5Å as identified from the MD simulation. Equation (2) is numerically solved up to a total simulated time of 750 fs employing a Neumann boundary condition at the surface and pseudoinfinite boundary conditions parallel to the surface and in bulk direction. For details of the rather complex numerical treatment of boundary conditions see our previous publication Ref. [6]. 3 Results In line with previous publications, the model described in section 2 has been applied to the impact of a 5-keV silver atom onto an Ag(111) surface under normal incidence. The particular impact point was chosen such as to produce a rather large event with many sputtered atoms. Inspection of the resulting particle dynamics reveals that this leads to the development of a collisional spike where many particles are simultaneously in motion. It should be noted that this scenario does not necessarily represent the average event produced unter these bombarding conditions. Figure 1 shows the volume-integrated total energy transferred to the electronic system as a function of time after the projectile impact. Considering 4

y (Å) 50 45 40 35 30 25 20 15 10 5 0-5 with friction of low-energy recoils Y=19 9.1 5.9 25.1 0.5 13.7 0.5 0.6 0.3 0.1 22.2 1.2 136.5 4.2 5.6 0.7 4.1 42.9 0 5 10 15 20 25 30 35 40 45 (a) x (Å) y (Å) 50 45 40 35 30 25 20 15 10 5 0-5 without friction of low-energy recoils Y = 20 12.8 42.9 22.2 5.9 4.1 1.3 4.5 0.4 26.7 5.6 14.2 4.2 1.8 136.4 5.8 4.7 0 5 10 15 20 25 30 35 40 45 50 (b) x (Å) Fig. 2. Emission sites of particles sputtered from the topmost crystal layer and their kinetic energy (ev) at the time of emission with frictional energy losses of low-energy recoils turned on and off. electron promotion and non-restricted electronic friction as excitation energy sources, we observe that after 750 fs about 60 % of the kinetic energy initially introduced into the system have been transferred into the electronic subsystem. At 750 fs about 930 ev of the total excitation energy are generated by collisional excitation compared to 2200 ev originating from electronic friction. Repeating the calculation, but excluding the electron promotion mechanism we obtain the dotted curve in Fig. 1. In this case, we find a total amount of 2350 ev of excitation energy generated by electronic friction, which is about 150 ev higher than the frictional contribution in the calculation employing both excitation mechanisms. This finding is obviously due to the fact that the additional excitation energy generated by electron promotion is lost from the dynamics, thus leading to a reduced overall friction loss. In order to assess the role of low-energy recoils we have also repeated the calculation by switching off the electronic friction mechanism for all particles moving with kinetic energies lower than 10 ev. The resulting energy transfer is plotted as a dashed line in Fig. 1. It is seen that under these conditions the total amount of energy dissipated by electronic friction is substantially reduced. Inspection of the temporal evolution reveals that a substantial part of the total kinetic excitation energy is mediated via a large number of slow, low-energy recoils during the late stages of the cascade. Note that this is a clear signature of the spike character of the event simulated here, indicating that this finding cannot necessarily be generalized to linear collision cascades as well. In view of their large influence on electronic excitation, it is of interest to investigate the role of frictional energy losses experienced by low-energy recoils with respect to the collision dynamics itself. In particular, we are interested 5

to find out whether the number or characteristics of sputtered particles are influenced by turning the electronic friction of low-energy recoils off and on. In order to visualize the results, Figure 2 shows a comparison of the lateral surface sites from which atoms have been sputtered in both calculations, i.e. (a) with frictional losses of low-energy recoils and (b) without that contribution. The axes are calibrated with the origin at the upper left corner of our simulation volume, and the impact point is therefore located at x=y=20 Å. In addition, each emission site is labeled with the kinetic energy of emission of the corresponding sputtered atom. First, we note that the total number Y of sputtered atoms remains virtually unchanged (19 and 20 in cases (a) and (b), respectively). Comparing the emission site distribution, one finds 13 of the total emitted atoms to be ejected from the same surface spots with virtually the same kinetic energy. In two cases, atoms are ejected from the same spot but with different kinetic energies. In two other cases, two or three atoms with low kinetic energy are emitted instead of one with higher energy. Only two instances are found where no corresponding emission is observed between (a) and (b). These observations substantiate that the frictional energy loss of low-energyrecoils does not significantly modify the trajectory as one might have supposed to in view of the chaotic nature of many-body collision dynamics. 4 Conclusion The important message of this paper is that low-energy recoils may play a dominant role in the kinetic excitation of solids by impact of energetic particles. More specifically, we find that electronic friction experienced by these particles accounts for about 50 % of the total energy transferred to the electronic sub-system. In this context the finding of Ref. [13] appears to be very important, since it indicates that the Lindhard energy loss mechanism may be operational for these low-energy particles, as well. In spite of their significance with respect to electronic excitation we find that the frictional energy loss experienced by low-energy recoils does not substantially influence the collision dynamics itself. Acknowledgment We acknowledge financial support from the Deutsche Forschungsgemeinschaft in the frame of the Sonderforschungsbereich 616 entitled Energy Dissipation at Surfaces. Furthermore, we would like to thank B.J. Garrison for providing us with the basis of the molecular dynamics code and H. Urbassek, M. Schleberger and J. Bloemen for discussion. 6

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