Electronic sputtering of solid O 2

Transcription

1 Surface Science 451 (000) Electronic sputtering of solid O E.M. Bringa, R.E. Johnson * Engineering Physics Department, University of Virginia, Charlottesville, VA 903, USA Received 9 July 1999; accepted for publication 8 November 1999 Abstract The bombardment of low temperature condensed gas solids by MeV light ions produces electronic excitations that can decay non-radiatively, transferring kinetic energy to the lattice and causing ejection (sputtering) of atoms. The experimental data for the sputtering yield Y of solid O and N over a range of de/dx are proportional to (de/dx), where de/dx is the energy deposited per unit path length. Parametrizing an analytical thermal spike model with constant track radius gave satisfactory agreement with the data [Johnson et al., Phys. Rev. B 44, (1991) 14]. However, molecular dynamics calculations for solid O indicate that Y is proportional to de/dx at high de/dx for constant track radius and that the energy transport processes differ from those assumed in spike models. Here we propose that the quadratic dependence in the experimental data is due to a track radius that increases with de/dx, opposite to the dependence predicted by the Bohr adiabatic radius. This radius is determined by fast energy transport processes prior to the principal energy release due to lattice motion: e.g. by hole repulsion and diffusion, by cooling electrons, or by excitation transport. Energy transport for a vibrationally excited track was examined, and it was found that sputtering was inefficient for vibrational excitation of solid O. 000 Elsevier Science B.V. All rights reserved. Keywords: Ion solid interactions; Ion solid interactions, scattering, channeling; Molecular dynamics; Oxygen; Single crystal surfaces; Sputtering 1. Introduction lined, a quantitative, first principles model has not been found for molecular condensed-gas solids. The electronic sputtering of low-temperature, Analytic models of sputtering based on the condensed-gas solids has been a topic of interest so-called thermal spike model have been used by for the last 0 years. This process produces an many authors [6 11] to understand and extrapo- atmosphere on Europa, a moon of Jupiter [1], and late the experimental data. For instance, when the it can give insight into the non-radiative decay electronic excitations are produced by an energetic processes occurring in solids [ 5]. Although a ion, a indrically symmetric region is assumed significant body of data has been available and to be energized. This is described by an energy many of the controlling processes have been outand deposition per unit path length in the solid, de/dx, a track width r. The thermal diffusion equation is then used to calculate the temperature * Corresponding author. Fax: as a function of radius and time, T(r, t). The addresses: ebringa@virginia.edu (E.M. Bringa), sputtering yield Y is obtained by calculating the rej@virginia.edu (R.E. Johnson) particle flux using the surface temperature /00/$ - see front matter 000 Elsevier Science B.V. All rights reserved. PII: S ( 00 )

2 E.M. Bringa, R.E. Johnson / Surface Science 451 (000) T (r, t), which is typically set equal to T(r, t). have a diameter of several hundred nanometers. surf When the initial track width is narrow the analytical On the other hand, a swift light ion will create a models predict Y3(dE/dx) [6,7,10]. The track of excitations that will extend only several energy contributing to electronic sputtering, i.e. tens of Å. Earlier, sputtering of small samples of the non-radiative relaxation energy, is some frac- an O -like material were studied in which the well tion of the electronic stopping power, (de/dx) depth was reduced to enhance the vibrational to e [,1]. In some earlier studies (de/dx) has been translational coupling [0 3]. Recently, we eff used to represent this fraction. Here we use de/dx. showed that over a range of excitation densities In Ref. [] the spike model with constant diffu- the sputtering yields for atomic and molecular sivity was normalized to the experimental data and solids had similar dependences on excitation used to describe the dependence of the yield on density [14]. de/dx. However, when the non-radiative energy Simulation details can be found in a number of release in the track of excitations has an energy papers [ 13,14,17 19]. For solid Ar, which has an density e nu, where U is the binding energy for fcc crystalline structure, we consider atoms inter- a material of density n, we have shown using acting through a Lennard Jones (L-J) (6 1) molecular dynamics (MD) simulations that energy potential. Solid O was simulated as the atoms in transport by thermal diffusion fails. Rather, a each molecule interacting with atoms in neighbor pressure pulse carries energy away from the track, molecules via an L-J potential and atoms within while a melt front controls the heat flow near the the molecule interacting with each other via a track [13,14]. We also showed that when a free Morse potential. Parameters were chosen for a c surface is present, T (r, t) is much greater than crystal. The parameters for the Ar and O simulations are given in Refs. [13,14,17,18]. Ar and O bulk surf the bulk temperature, T (r, t) [14,15], unlike the approximation used in most models [16]. Here we have the same binding energy U=0.08 ev, similar study sputtering of low temperature solid O in densities, n=0.06 Å 3 for Ar and n=0.08 Å 3 which the internal degrees of freedom can, in for O, and similar L-J lengths, s=3.405 Å for Ar principle, affect the energy transport and the sputtering yield. l is l=n 1/3. and s=.988 Å for O. The mean lattice spacing Experimental data for sputtering of solid O A indrical region of radius r was excited give Y3(dE/dx) over a limited range of excitation by giving each atom within this volume a kinetic densities as in the thermal spike models [,3]. In energy E in a random direction. The effective exc Refs. [14,17] we found in MD simulations that de/dx is de/dx=n E /d#npr E, where n is l exc exc l the yield exhibits a non-linear dependence on the number of particles per layer within r and d de/dx at low de/dx, having a spike-like character, is the separation between layers. Therefore, the but a linear yield for both atomic and molecular criterion for a narrow spike is E &U. Any time exc solids at high de/dx when a constant track radius delays in the conversion of electronic excitation r was used. Since this is the region applicable to into kinetic energy of the atoms in the lattice are the sputtering of solid O, we compare the energy ignored here. transport in atomic and molecular solids and then The energy required to dissociate an O mole- discuss the O data. cule is E =5.1 ev. When E >E, the current d exc d MD simulations treat atoms from a dissociated molecule on the same footing as atoms that belong. MD simulations to a particular molecule, and recombination is only possible with the atom that belonged to the Recently, vibrational to translational energy same molecule. This is not correct, and modificaconversion following uniform excitation of solid tions are in progress. For O, fast ion bombardment can directly dissociate molecules and O was studied using classical MD calculations [18,19]. This study used an excitation geometry dissociation occurs following electron recombination. like that in laser ablation, where the laser spot can These processes all release kinetic energy.

3 110 E.M. Bringa, R.E. Johnson / Surface Science 451 (000) Simulations that were carried out earlier [4] on vibrational and rotational modes as well as translasmaller samples suggested that the yields were tion. Rotational modes equilibrate with translainsensitive to the manner in which the energy was tional modes, but vibrational modes do not, as put into the system. Here we re-examine that. seen in the radial temperature profiles in Fig. 1 Sputtering yields were calculated for the (001) for r =s and E =0.5 ev/atom (de/dx=3.9 surface, as in Refs. [14,18]. The local kinetic exc ev/å). After 6 ps (dotted lines), T #T #T /4 temperature of the atoms and molecules, T(r, t), tr rot vib inside the track. These profiles are not Gaussian was calculated for indrical shells of mean radius and their evolution does not follow a simple diffur [14,18]. sion equation. If the bumps in the translational temperature profiles (not clearly seen in Fig. 1 owing to the logarithmic scale) due to the pressure 3. Atomic versus molecular solids pulse are neglected, then the data can be roughly fit to a Gaussian with an effective but changing Atomic fcc structures, like crystalline Ar, favor thermal diffusivity k [5,6]. The effective diffusivenergy transport along the nearest neighbor direc- ity is in the range 8 5 Å/ps, close to the thermal tions (a number of figures and movies representing diffusivity for O at 50 K (calculated using data the cases treated in this paper can be found at our from Ref. [7]) and that of liquid O at 60 K, web site k#9 Å/ps (calculated using data from NIST ). Chemistry WebBook [8]). For fcc Ar, de/dx=10 30 ev/å and r = 5s, For solid O T and T are 50% larger at the 5 10% of the energy is taken away from the track tr rot region by focusons during the first picosecond. After that, a supersonic pressure pulse takes away another 0% of the energy. In the track, the molten solid controls heat flow and lasts for several picoseconds. For the molecular solid studied the scenario changes. co has a pair distribution function similar to that for liquid O [0 3], which quenches focusons. The pressure pulse exists, but it is not as pronounced. Snapshots [5] of both atomic and molecular samples show the expanding pressure pulse as well as the central molten region. Only half the energy goes to translational modes for the molecular sample. For the atomic sample, the energy contours at 1 ps have a square shape due to focusons along nearest neighbor directions. For the molecular sample the pressure pulse has a roughly circular shape, indicating an isotropic radial energy transport. Focusons can arise at lower temperatures (below 4 K ) where the a phase is stable, since this phase has an structure similar to the fcc structure. However, this phase gives a yield with the same dependence on de/dx as that for the c phase. More figures and movies describing this process can be Fig. 1. Temperature profiles for O E =0.5 ev and r =s found at our web site exc using random excitation. T, T, and T are shown at three edu/~emb3t/o/o.html. vib tr rot different times. de/dx=3.9 ev/å ps after excitation (solid Temperature profiles in the first tens of pico- line), 1.01 ps after excitation (dashed line), 6.01 ps after excitation (dotted seconds control the sputtering. Energy can go into line).

4 E.M. Bringa, R.E. Johnson / Surface Science 451 (000) surface, but in the atomic case the mismatch ally excited, the sample expands along the track between the bulk and surface temperature is larger. and coupling is very small during the first 100 ps. Outside r, T is roughly the same at the surface By contrast, the principal contributions to sputterand in the bulk. We can define a shell occupation ing typically occur in much shorter times when the vib for our sample n(r, t)=n(r, t)/n(r, 0), where inder is excited by giving the molecules transla- N(r, t) is the number of particles at time t in the tional energy. For E = ev, r =5s=15 Å, shell of mean radius r. When E >U a crater is exc exc de/dx=74.6 ev/å, T is roughly the same as formed. For a sample of 15 layers, n(r) can decrease tr before excitation, at least during the first few 50 80% inside the crater radius and can increase hundred picoseconds. For larger energy deposition, by 0 30% at the crater rim. Outside the rim, n(r) as for E =4 ev, r =5s=15 Å, de/dx= does not differ much from one. Taking only the exc ev/å, there is a little coupling and the transsurface layer, an increase of 50% in occupation is lational temperature increases slightly, but T seen up to r#5s. This lattice expansion was also tr remains below 100 K all the time, even inside the observed for uniform excitation [18,19] and a track, as does the rotational temperature. Unlike large T is maintained due to the reduced cou- vib the random excitation case above, surface temperpling to translational nodes. For uniform excita- atures are only slightly larger than bulk tempertion, the onset of equilibration of the vibrational atures. Of course, vibrational energy must modes occurred when the lattice became highly eventually diffuse out of the track and slowly disordered and fluid-like [19]. Here the lattice is couple to the translational modes, possibly inducdisordered, but only within the track. For the ing very late sputtering. simulations performed, no onset of rapid conver- Fig. shows temperature profiles for E = sion T T was seen. exc vib tr For r <5l and E >U MD simulations show exc that the energy deposited in translational modes is rapidly carried away from the track and, therefore, the hot region does not last long enough to produce a thermal spike. When the energy is deposited as a vibrational excitation it has been shown [18,19] that the gradual coupling to translational modes can take several tens of picoseconds. This may lead to a longer-lasting hot region that behaves closer to a model spike. In Section 4 we also explore this scenario. 4. Vibrational excitations Vibrational excitation of the solid was initiated by giving each atom of the O molecules inside r a kinetic energy E in outward-opposite directions. For uniform vibrational excitation, as in exc laser ablation, and no expansion (constant molecular) density the translational modes coupled with the vibrational modes and the translational temperature eventually increased [18,19]. However, if the solid was allowed to expand rapidly, which was the case when there was a free surface, the vibrational coupling to the lattice was much less efficient. When only a indrical track is vibration- Fig.. Temperature profiles for O E =4± ev and exc r =5s using vibrational excitation, de/dx=149 ev/å ps after excitation (solid line), 1.01 ps after excitation (dashed line), 5.51 ps after excitation (dotted line).

5 11 E.M. Bringa, R.E. Johnson / Surface Science 451 (000) ± ev, i.e. the excitation energy is a rectangular where B is a constant, a is a coefficient for the s distribution in energy, instead of a delta function. reflection of energy from the surface; a =1 for no s For this case, 5% of the particles have energies reflection and a = for total reflection. Using s above the dissociation threshold and energy is k=1.4 Å/ps, similar to the one found from MD, transported away from the center by the dissoci- and a =1.5, we obtain the fit shown in Fig. 3. s ated particles transferring energy to the cold lattice Using a gas-like k [,6] gives a larger yield. Since outside of r. After 10 ps the number of ejected analytic spike models do not give a good quantitative description of the energy transport for molecules is 500, whereas it was one for the excitation of a single vibrational energy of 4 ev, E >U and require an empirical diffusivity, below exc which is below the dissociation limit. In a more we apply the MD results for the yield in order to realistic simulation, the dissociated O would react explain the O data. with the nearest O molecule to form ozone in a In Ref. [17] the sputtering yield of a number of highly vibrational state. In solid N, however, the atomic solids was shown to increase roughly with free atoms do not recombine rapidly and transfer increasing indrical radius for fixed de/dx in the energy to translational modes more effectively. high de/dx regime. Here, we have shown that in excitation of solid O such a scaling also roughly applies. Therefore, the MD yields from a indrical spike in the high de/dx regime can be approximately parametrized using the following formula: 5. Sputtering yield Y#C(r /l )x(l/u)(de/dx), x#1. Experimental data for the yield of O bom- barded with MeV He+ from Ref. [] is presented For co and r =s our MD results give in Fig. 3. The effective stopping power is only a C#0.09. Therefore, if we assume that the effective fraction g of the tabulated stopping power; g= indrical radius for the energy deposition at the 0.4 Ref. []. The data from Ellegaard et al. [3] time when dissociative recombination occurs KeV H+ and H+ is also included, treating increases with de/dx, the experimental data are 3 (de/dx) as additive [3]. In addition, because the understandable in terms of a indrical region e particles have lower velocities we used a higher energized by dissociative recombination, a spike. efficiency, g=0.48 [9]. Both yields are quadratic That is, writing r /l#a(l/u )(de/dx), with A a in de/dx. On the other hand, bombardment with constant, Y#CA(l/U )(de/dx). Using this expres- KeV electrons or megaelectron-volt protons for sion, the MD calculation of yields from a indriwhich de/dx is low gives Y#dE/dx [,1,30]. cally energized region can be used to fit the The average energy necessary to produce one experimental results, giving A=0.06. In this fit ion pair in O is W=3.5 ev. For 0.5 MeV/amu r only has to vary between s and 6s (6 18 Å) He+, de/dx=.6 ev/å, the mean free path for over the relevant range of de/dx. Below we discuss producing an electron hole excitation l is l= the possibility that the effective track radius W/(dE/dx)=1.44 Å. The layer separation is increases with de/dx Å, giving 4.7 excitations per layer. If we take For the MeV He ions, the infratrack, where the radius of the track core to be the Bohr adiabatic primary excitations are created, has a size usually radius r [31], then r =r hn/(w )=1.18s, taken to be the Bohr adiabatic radius, which B B giving a fully excited inder. In Ref. [] the yield decreases with increasing de/dx above the maxi- was normalized to the yield in the linear regime, mum in the stopping power, as pointed out often. so the thermal conductivity k was not needed. The However, the energy density deposited in this yield from Ref. [] calculated at high de/dx using region becomes very large, with neighboring atoms a constant diffusivity and fixed r =.9l, where often multiply ionized. Therefore, rapid migration l=n 1/3, can be written as: of energy from this region must occur before the non-radiative relaxation events energize the lattice. Y=B(a/k)(l/U)(dE/dx), Whereas in atomic condensed-gas solids the radial s

6 E.M. Bringa, R.E. Johnson / Surface Science 451 (000) Fig. 3. Yields for O as a function of de/dx. Experimental data for He+ bombardment [] (solid circles), and H+ and H+ 3 bombardment [3] (solid squares). Fit from MD parametrization, using r /l=0.06(l/u )(de/dx) (solid line), which is the same as the fit from Ref. [] using r /l=.9, k=1.4 Å/ps, and a s =1.5. transport by excitons prior to sputtering is large of Å before they thermalize and their range is [4,9], it has been shown that the transport prior proportional to the energy of the primary ion. to sputtering must be <50 Å in solid N. Rapid Therefore, this radius also decreases with increasing de/dx over the ion velocities of interest. As (<1 ps) transport of excitation energy over distances of the order of a few lattice spacing occurs the range of the electrons decreases and de/dx by charge exchange of multiply charged species increases, the energy density in the track increases with neighbors, by migration of holes and mutual rapidly, and the radius at which the critical energy repulsion of neighboring holes, by the cooling density is attained increases. Using eq. (8) from electron cloud (delta rays), and finally by excitation Ref. [3] to estimate that radius at which the transport. Here, we presume that when the excitation critical energy density is reached, we find it varies density in the track core is very high, transport roughly linearly with de/dx. Using g=0.4 and a occurs until a critical energy density is reached. critical density equal to U gives A=0.0, which is Energy may be transferred to the lattice during close to the value obtained above from the MD this transport process and after the critical energy fit. Therefore, we propose that a small variation density is reached, by non-radiative decay pro- of the track radius can account for the observed cesses (e.g. dissociative recombination [9]). sputtering yield. However, we also realize that a Outside of r, the initial radial excitation density non-linear energy deposition process, like B produce by a fast ion is determined by the delta Coulomb explosion [33 35], could also account electrons. These electrons can travel several tens for the observations. A critical energy density has

7 114 E.M. Bringa, R.E. Johnson / Surface Science 451 (000) also been used to explain electronic sputtering of ionic solids (LiF) [36]. A track radius that changes with energy may also be able to explain [37,38] large sputtering yields in the nuclear regime for cluster self-bombardment of gold [11,39]. thank D. Bahr for useful discussions. Thanks to Susan Chang for making some of the movies and figures at the web site. This work was supported by the National Science Foundation division of Chemistry and Astronomy. 6. Summary and conclusions References As we showed earlier for atomic solids [13,14], the radial energy transport in co cannot be easily [1] R.E. Johnson, Rev. Mol. Phys. 88 (1996) 305. modeled by a diffusion equation. For the O sample [] R.E. Johnson, M. Pospieszalka, W.L. Brown, Phys. Rev. studied there is a molten core and a pressure pulse, B 44 (1991) 14. but focusons do not play a role. Focusons appear [3] O. Ellegaard, J. Schou, B. Stenum, H. Sørensen, P. Børgensen, Surf. Sci. 167 (1986) 474. in the a phase, which is stable below 4 K. Again [4] G. Zimmerer, Nucl. Instrum. Methods B: 91 (1994) 601. we showed that the surface plays a crucial role; [5] D. David, T. Magnera, R. Tian, J. Michl, Rad. Eff. 99 having a temperature higher than the bulk indi- (1986) 47. cates that energy transport towards the surface is [6] P. Sigmund, C. Claussen, J. Appl. Phys. 5 (1981). important [15]. [7] R.E. Johnson, R. Evatt, Rad. Eff. 5 (1980) 187. Vibrational excitations alone cannot explain the [8] O. Ellegard, J. Schou, H. Sørensen, Europhys. Lett. 1 (1990) 459. large sputtering yields observed for solid O, since [9] O. Ellegaard, J. Schou, B. Stenum, H. Sørensen, R. Pedrys, they do not couple significantly to other modes Nucl. Instrum. Methods B: 6 (199) 447. during the first several hundred picoseconds. For [10] M. Jakas, Rad. Eff. Defects Solids 153 (000) 157. the laser-ablation case [18,19], disorder was neces- [11] A. Brunelle, in preparation. sary for the vibrations to couple to translations. [1] K.M. Gibbs, W.L. Brown, R.E. Johnson, Phys. Rev. B 38 (1988) For an amorphous solid, or for a crystal with [13] E.M. Bringa, R.E. Johnson, Nucl. Instrum. Methods B: defects, this coupling may increase. However, 143 (1998) 513. co studied here is already disordered, so only [14] E.M. Bringa, R.E. Johnson, Ł. Dutkiewicz, Nucl. Instrum. small changes are expected. More realistically, Methods B: 15 (1999) 67. dissociations, either formed initially or on recombi- [15] E.M. Bringa, M. Jakas, R.E. Johnson, in preparation. [16] H.M. Urbassek, P. Sigmund, Appl. Phys. A 35 (1984) 19. nation, will transfer large amounts of kinetic [17] E.M. Bringa, R.E. Johnson, M. Jakas, Phys. Rev. B 60 energy to the lattice, leading to sputtering. (1999) We showed that the de/dx regime over which [18] Ł. Dutkiewicz, R.E. Johnson, R. Pędrys, J. Low Temp. the O sputtering yields are quadratic corresponds Phys. 111 (1998) 747. [19] Ł. Dutkiewicz, R.E. Johnson, R. Pędrys, A. Vertes, J. Phys. to a yield linear in de/dx if the track radius if Chem. A (1999) 95. fixed. Therefore, the electronic sputtering yield [0] S. Banerjee, R.E. Johnson, S. Cui, P.T. Cummings, Phys. measurements for solid O can be explained by Rev. B 43 (1991) assuming that the effective track radius increases [1] S. Banerjee, M. Liu, R.E. Johnson, Surf. Sci. 55 (1991) with deposited energy over the relevant range of L504. de/dx, and the size range of r obtained from [] S.T. Cui, R.E. Johnson, Int. J. Quantum Chem. 3 (1989) 575. this analysis is reasonable. [3] R.E. Johnson, M. Liu, J. Chem. Phys. 104 (1996) [4] E.M. Bringa, Nucl. Instrum. Methods B: 153 (1999) 64. [5] D. Fenyö, R.E. Johnson, Phys. Rev. B 46 (199) Acknowledgements [6] H.M. Urbassek, H. Kafemann, R.E. Johnson, Phys. Rev. B 49 (1994) 786. [7] Y.A. Freiman, V.V. Sumarakov, A. Jeżowski, P. Stachow- We want to thank Łukasz Dutkiewicz for allow- iak, J. Mucha, Low. Temp. Phys. (1996) 148. ing us to use and modify the MD program he [8] NIST Chemistry WebBook, wrote for solid O [18,19]. E. Bringa wants to chemistry/.

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