- Email: [email protected]
On the origin of the different velocity peaks of particles sputtered from surfaces by laser pulses or charged-particle beams
Applied Surface Science 138–139 Ž1999. 44–51
On the origin of the different velocity peaks of particles sputtered from surfaces by laser pulses or charged-particle beams Antonio Miotello ) , Roger Kelly INFM and Dipartimento di Fisica, UniÕersita` di Trento I-38050 PoÕo, Trento, Italy
Abstract The particles emitted from surfaces irradiated by either laser pulses or charged-particle beams are often analyzed by time-of-flight ŽTOF. spectroscopy. This technique gives, in general, details on the velocity Žthence energy. of the emitted particles, parameters which are of fundamental importance in establishing the mechanisms responsible for the particle emission. However, when experiments are performed in an ambient gas, primary effects may be partially obscured by collisions between the emitted and the ambient particles. Here we will critically analyze certain TOF spectra obtained when particles are sputtered from a surface. To this end we first discuss a variety of velocity laws in connection with the processes which create the different sputtered fluxes. We then compare results which led to two or more velocity peaks, considering in so doing electrons, ions, and laser pulses, as well as the absence or presence of ambient gas. In other words, we try to establish simple criteria to distinguish primary emission mechanisms on the basis of TOF signals. q 1999 Elsevier Science B.V. All rights reserved. PACS: 79.20.Ds; 52.50.Jm; 79.20.H Keywords: Laser-ablation; Ion–surface interaction; Electron–surface interaction
1. Introduction Laser irradiation is widely utilized in three important fields, namely in thin film deposition, in mass spectrometry, and in surface modification. In mass spectrometry, laser ablation of organic material has become an established method for producing molecules and molecular ions in the gas phase. When laser ablation is utilized for mass-spectrometric analysis, it is clearly of fundamental importance to be able to distinguish among the different mecha)
Corresponding author. Tel.: q39-0461-881637; Fax: q390461-881696; E-mail: [email protected]
nisms leading to the velocity distribution of the emitted particles. There is, however, no clear understanding of the entire range of physical processes leading to such velocity distributions. The situation is generally better understood when ions or electrons are utilized to induce sputtering for analytical purposes. In this paper we try to make an attempt to address the problem of the different peaks observed, for example, in time-of-flight ŽTOF. analysis of ejected particles when the peaks are related to the same particle in the same charge state; by contrast, the differences are obvious when the peaks are related to different particles Žatoms or molecules. or to different charge states. To do this, we look at a
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 3 8 5 - 7
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
selected group of experiments performed with electrons, ions, and lasers to induce particle ejection followed by analysis with a TOF apparatus.
2. General aspects of the particle-emission process The velocity distribution function, fsq, of particles emitted thermally from a flat surface at a temperature Ts , when the emission is collisionless, is the ‘half-range’ Maxwellian w1x: fq s Ž Õ x ,Õ y ,Õ z , E I . s
E Ij r2y1
ns
Ž 2p k B Tsrm .
3r2
G Ž jr2 . Ž k B Ts .
jr2
= exp y 2 EI q m Ž Õ x2 q Õ y2 q Õz2 . r2 k B Ts ,
ž
/
Ž 1. Õ x G 0,y ` - Õ y - `,y ` - Õz - `.
Ž 2.
Here fsq has units appropriate to the right-hand side, Õi Ž i s x, y, z . stands for a velocity component, EI is the total internal energy, n s is the number density of the emitted particles near the surface, m is the particle mass, k B is the Boltzmann constant, j is the number of internal degrees of freedom accessible at Ts and for the particular number of collisions occurring, G is the gamma function, and the expression is normalized to n sr2. We use x to refer to the direction normal to the surface. When particles are emitted from a hot surface at number densities which result in collisions, Eq. Ž1. is valid only for the initially emitted particles at x s 0. Beyond x s 0, collisions occur Žmainly for laser irradiation., with the result that negative values of Õ x develop, and the distribution function for Õ x evolves from being proportional to: exp Ž ymÕ x2r2 k B Ts . ,
Õ x G 0,
Ž 3.
to having the form: 2
exp Ž ym Ž Õ x y u KL . r2 k B TKL . ,
y` - Õ x - `.
Ž 4. Here u KL , the center of mass or ‘flow’ velocity, equals the velocity of sound, and T KL was shown to be about 70% of Ts ŽTs , as before, being the surface
45
temperature. or less for a monatomic species. We take as a simple definition of the Knudsen layer ŽKL. the region within a few mean free paths of the target surface in which the change from Eq. Ž3. to Eq. Ž4. occurs as a highly non-equilibrium collision process. The particles which reach the KL boundary, at which point they may or may not enter into free flight, have a distribution function which is a ‘fullrange’ Maxwellian incorporating an explicit centerof-mass or ‘flow’ velocity, u KL , and having a lower temperature, T KL , and a lower gas number density, n KL , than at the surface ŽTs , n s . w2,3x: n KL " f KL Ž Õ x ,Õ y ,Õz , EI . s 3r2 Ž 2p k B TKLrm . EIj r2y1
=
G Ž jr2 . Ž k B TKL .
ž
= exp y
jr2 2
2 EI q m Ž Õ x y u KL . q Õ y2 q Õz2
ž
2 k B TKL
/
/
,
Ž 5. y` - Õ x ,Õ y ,Õz - `.
Ž 6.
On the other hand, the particles which pass beyond the KL boundary and do not enter into free flight are better described by the formalism for an unsteady adiabatic expansion ŽUAE. and therefore have a distribution proportional to: 2
exp Ž ym Ž Õ x y u M . r2 k B TM . , y` - Õ x - `.
Ž 7.
where M s ura ) 1 is the Mach number and a is the sound speed. Note that for a KL, we have M s ura f 1. The picture just presented has emphasized the gas number density, but in reality, both the number density and the length of the emission process are important. In fact, depending on the interplay between the two, one can have situations ranging Ži. from one in which interactions are negligible and Eq. Ž1. can be used, Žii. to one in which only a KL develops but either the supply of vapor then ceases or loss of density becomes important so that a UAE fails to develop ŽEqs. Ž4. and Ž5.., Žiii. to one in which the number density persists and allows a greater or lesser extent of UAE to set in ŽEq. Ž7...
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
46
Finally, to account consistently for the axial and radial velocity distributions of particles ejected in laser ablation, the Maxwell–Boltzmann distribution on a flow velocity was recently modified for a range of flow velocities in the ejected plume w4x. A new expression was derived, essentially from molecular dynamics simulations, to yield: f " Ž Õ x ,Õ y ,Õz ,T ,u max . m s 4p k B Tu max
let the flux of emitted particles in the range Ž Õ x , dÕ x ; " Õ y , dÕ y ; Õz , dÕz . be dÕ x dÕ y dÕz P Õ x f KL . In addition, Õ x s xrt and, since y and z are directions parallel to the target surface and, for example, Õ y is yrt, where t is the flight time, we have dÕ y s d yrt and dÕz s d zrt. Since x is parallel to the target normal and the experiment involves TOF, we have
exp y
mŽ
Õ y2 q Õz2
.
2
2 =exp yb KL Ž w x y u KL t x q y 2 . rt 2 ,
2 k BT
Ž 9.
m
where erf is the usual error function and u max is the maximum value of the flow velocity. ŽThe notation uˆ or uˆ x is also used for u max w5x.. The proposed distribution function has two parameters that are independent of the desorption angle, namely, the temperature of the plume T and the maximum flow velocity u max of the plume propagation. It is unclear to us whether Eqs. Ž7. and Ž8. have forms which are distinct. This problem will be addressed in future work.
where n is 4 for a density-sensitive detector, n is 5 for a flux-sensitive detector, and because of the symmetry of the problem we have taken z s 0. Were conditions for formation of neither a KL nor a UAE fulfilled Ži.e., when the density of emitted particles is lower than ; 1 monolayerr10 ns. then u KL is 0 and 2 T KL s Ts . b KL stands for mr2 k B TKL , m being the particle mass. In the following we analyse separately the two quite different situations, i.e., where there either is not or there is a gas ambient through which the emitted particles propagate. The possibility of collisions between sputtered particles and ambient gas will complicate, as we will see, the main objective of determining the nature of the peaks observed in TOF experiments.
3. The TOF signals
4. TOF of atoms sputtered from alkali halides by electrons
Before going into detail on the TOF peaks which, when appropriately analyzed may give useful information on the primary mechanisms of particle emission from irradiated surfaces, it would be appropriate here to underline briefly that an ion-probe detector ‘ideally’ measures a flux essentially at a point. To extract fluxes at a small-area detector, it is necessary to divide the densities in a one dimensional calculation by time to the fourth power. This means that, when there are two processes, that which is delayed Ži.e., has a greater TOF. is magnified not because of its real magnitude but simply because of a detection problem. Let us make a more specific argument. Let the detector be located a distance x normal to the target and a distance y, z away from the normal, and
In Fig. 1 we report the TOF spectrum of Br atoms leaving a KBr target at 1008C due to bombardment with 540 eV electrons w6x. Here, two peaks, both related to Br atoms, are clearly evident. Most alkali halides irradiated under the same conditions reveal the same features in the TOF spectra: for example, if the target temperature is above 2008C then only one peak appears. This is the peak associated with what are probably thermal particles, i.e., those characterized by a larger TOF Žaverage kinetic energy of the order of 0.03 eV.. The other peak relates to fast particles, i.e., those characterized by a smaller TOF, and which will be called the non-thermal peak. Speaking first of the thermal peak, it can be inferred that this peak is caused by vaporization of Br atoms,
ž ( (
= erf
2 k BT m
yerf
2 k BT
Õx
Ž Õ x y u max .
/
,
Ž 8.
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
47
metal layer has been formed on the surface of the salt. This was observed for AgBr Žthe vapour pressure of the pure metal at 4008C being much less than 10y6 Pd. and for PbI 2 Žvapour pressure of the pure metal at 4008C approximately 10y4 Pd.. 5. TOF of atoms sputtered from alkali halides by an ion beam
Fig. 1. TOF spectrum of Br atoms due to the bombardment with 540 keV electrons of a KBr target at 1008C w6x.
after breaking of K–Br chemical bonds by electron irradiation. The argument is based on the energy distribution of the Br atoms, which is of a Maxwellian type with an average kinetic energy of 0.03 eV. What about the non-thermal peak? To explain this peak, it is appropriate to look at the decay in the bulk of the exciton Žor excitons. created by the electron impact. This decay may promote a focused collision replacement sequence followed by a thermal migration of the H centre, which is essentially related to a halogen atom in an interstitial position and which is able to move in the lattice w7,8x. When the replacement sequence of the migrating H centre reaches the surface, ejection can occur and the energetic feature revealed in the TOF experiments is easily justified through the following argument. The H centre will have an energy of about 2.5 eV w9x. At the surface, this energy can be used to break the bond of a Bry 2 molecular ion and to overcome the surface binding energy. The dissociation energy of the molecular ion is about 1.0 to 1.3 eV w10x. The excess energy may then be released in the form of kinetic energy of the departing halogen atom and will be of the order of 1–2 eV, as observed. Concerning the thermal component of the emitted particles, we should note that if the vapour pressure of the pure metal becomes too low, no metal atoms leave the surface in the experimental time scale. Halogen emission will be stopped completely after a
In Fig. 2 we report the TOF distribution of I atoms sputtered from LiI with a 6 keV Krq beam w11x. Again the spectrum consists of two distinct peaks: the short flight times correspond to an energy of a few eV Ž‘non-thermal’ peak. while the long flight times correspond to thermal energies Ž‘thermal’ peak, with an average kinetic energy of 0.026 eV.. The mass and energy spectra of the sputtered particles thus show clearly that the LiI is sputtered as a result of two distinct processes. The first one Ž non-thermal . is not sensitive to the target temperature and the impinging projectile ŽNeq, Arq, Krq, or Xeq. w11x. The second one Ž thermal . is caused by thermal I atoms and depends very much on the target temperature w11x. The energy distribution spectrum, F Ž E ., related to the non-thermal peak has the form: E F Ž E. A , Ž 10 . 3 Ž E q Eb . which is characteristic of a collision-cascade mechanism governed by a surface binding energy, E b ,
Fig. 2. TOF spectrum of I atoms due to the bombardment with 6 keV Krq ions of a LiI target at room temperature w11x.
48
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
equal to 0.7 eV in the specific example of Fig. 2. In addition, the power law of the observed F Ž E . function indicates that the sputtered atoms, when leaving the surface, experience a planar potential energy barrier characterized by the surface binding energy E b . Concerning the thermal component of the TOF spectrum, note that the ion beam induces a Li–I chemical bond breaking and that subsequent vaporization of the I atoms is due to the high halogen vapor pressure. Non-volatile Li Žthe vapour pressure of the pure metal at 4008C being 0.7 Pd. remains on the surface and can be removed only by the collision-cascade mechanism. Selective sputtering of thermal I atoms due to electronic stopping of incident ions explains also a rapid decrease w11x of the I signal in the case of Heq bombardment. The stopping power of 6 keV Heq in LiI is mainly electronic Žnamely 16 eVrnm, whereas the nuclear stopping power is 4.4 eVrnm. leading to a large enrichment of the non-volatile Li on the surface. The excess of Li atoms can be removed only by a collision cascade process. This mechanism, however, is very inefficient since the nuclear stopping power of Heq is so small.
6. TOF peaks observed in laser-ablation experiments in the presence of an ambient gas 6.1. Discussion of typical experiments At present, it seems that TOF features of the type reported for electron or ion-beam bombardment are not important for laser-induced particle emission from a surface. Two peaks, related to the same particle in the same charge state, are instead seen when laserablation Žat least with ns laser pulses. occurs in the presence of an ambient gas ŽFig. 3.. However, even in this case the results are not fully consistent. Let us examine two different experiments reporting conflicting results. In a recent article, Wood et al. w12x reported new results by laser-irradiating ŽKrF, l s 248 nm, 25 ns FWHM. Si substrates while using background gases of He Žas in the present Fig. 3. and Ar Žas in Figure 1a and 1c of Ref. w12x.. The authors w12x claimed that plume splitting occurs into fast Ž; vacuum speed, approximately as for a gas-dy-
Fig. 3. TOF spectra of Si atoms due to laser irradiation of a Si target ŽKrF laser pulses of 3.0 J cmy2 . in He ambient gas at different pressures w12x. The detection distance was x d s 5 cm. Note that the spectra relate to Si atoms rather than to light.
namical expansion front in vacuum: see Sections 6.2 and 6.3 of Ref. w5x. and background-slowed components. ŽThis problem is also treated in Refs. w5,13x.. Laser irradiation ŽArf, l s 193 nm, 28 ns FWHM. of GeO 2 in different pressures of oxygen was performed by Wolf w14x ŽFigs. 4 and 5.. Time-resolved optical emission spectroscopy was used to analyze the light from the laser-produced plume at several distances above the target surface. The typical TOF profiles serve to clarify the role of the detection distance ŽFig. 4. and the ambient gas ŽFig. 5.. In the profiles of Fig. 4 Žwhere the experiments were performed in vacuum conditions 3 = 10y4 Pa. a splitting of the plume appears which is a function of the distance from the target surface. Considering the fast component Ži.e., that with short TOF. the insensitivity of both the pulse shape and the time-to-peak intensity with distance Ž x s 2 cm and x s 3 cm. suggests that this emission did not originate from material in free flight but from a source of emission which was probably the bright plasma near the surface and which was scattered into the spectrometer. In contrast Žstill considering Fig. 4., the slow component is clearly position-dependent, suggesting that
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
49
effects of the interaction between a pulsed-laser ablation plume and the ambient gas. This model, mainly based on the analogy with an underexpanded jet, predicts oscillatory behaviour of plume expansion and vortex formation at the plume periphery. 6.2. Critique of the model inÕolÕing elastic scattering between a plume and an ambient gas
Fig. 4. TOF spectra of light due to laser irradiation of a GeO 2 target ŽArF laser pulses of 6.5 J cmy2 and 28 ns FWHM.. The analysed optical transition Ždue to GeI. was centered at 269.1 nm, the detection distance was varied w14x, and the ambient gas pressure was always 3=10y4 Pd. There are two components of light, the one with short TOF probably originating at the surface and the one with long TOF originating from the moving Ge atoms.
the light-emitting species ŽGeI. arrived at the observation region with delay times which increased with increasing x. In Fig. 5, Ge TOF profiles are reported for different values of the ambient oxygen pressure at a fixed distance of 1.5 cm from the target surface w14x. The slightly later arrival of the emission peaks with increasing pressure suggests the effects of collisions between the expanding plume front and an impeding force produced by the ambient gas. As with Fig. 4 one recognizes light emission which can be understood as originating at the target surface Žshort TOF. and additional emission from moving Ge atoms. Interestingly, we note that there was no detectable splitting into two components as in Fig. 3, thus leaving the problem of whether the plume should or should not split, when expansion occurs in an ambient gas, an open problem. In addition, it seems that the detection distance is the more important parameter in the sense that the form of the TOF signals depends strongly on this parameter. An explanation of this point may possibly be contained in the modelling proposed in Ref. w15x for the gas-dynamic
The model proposed by Wood et al. w12x to explain plume splitting when expansion occurs in an ambient gas is based on the hydrodynamic equations and on the existence of elastic scattering of the plume particles with the atoms of the background gas. In particular, the plume is broken into orders corresponding to the number of collisions with the background gas. Particles are transferred between the various orders only by collisions and the densities in the individual orders propagate, to give the overall expansion, according to the usual Euler equations. However, a simple examination of the experimental results and of the resulting cross-sections for Si–Ar and Si–He scattering Žthe results for He are as in Fig. 3, while those for Ar are seen in Figure 1a
Fig. 5. TOF spectra of Ge atoms due to laser irradiation of a GeO 2 target ŽArF laser pulses of 6.5 J cmy2 and 28 ns FWHM.. The analysed optical transition was centered at 269.1 nm, the detection distance was fixed at x s1.5 cm, and the pressure of the ambient O 2 pressure was varied w14x. As in Fig. 4, there are two components.
50
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
and 1c of Ref. w12x., allows us to conclude: Ž1. that the theoretical results are numerically inconsistent with some of the experimental results, and Ž2. that the adopted model is too much simplified to treat plume expansion which includes collisions. To elaborate on point Ž1., let us observe that in the case of Ar background gas, when the pressure is 7 Pa the density of Ar atoms, NAr , inside the chamber, is easily calculated to be ; 1.6 = 10 15 atrcm3. Now, the cross-section for the Si–Ar scattering process was assigned numerically, to fit the experimental fluxes, to be s s 5.1 = 10y1 6 cm2 . The mean number of collisions, P, suffered by a given Si particle with the Ar atoms beyond the Knudsen layer and just before the distance x d s 5 cm from the surface, where the Si particle is detected Žboth in the case of He and Ar., is given by the simple relation: P s NAr = s = x d . By including, in the preceding formula, the numerical values Žboth experimental and assigned numerically. P turns out to be ; 4.1. This means that if s were correctly assigned, then essentially all Si atoms would have had several collisions before arriving at x d . By considering now the 8 Pa case, the P value increases by 20% with respect to the 50 mTorr case. With such a small change it is very difficult to understand the big differences in the experimental fluxes of Figure 1a of Ref. w12x. In this respect, the experimental fluxes pertinent to the other gas are also out of trend Žsee the present Fig. 3.. Now, to elaborate on point Ž2., let us remember that the more appropriate theoretical framework to analyse plume expansion by including scattering processes, certainly rests in the use of the Boltzmann equation. However, when appropriate conditions are met w16x, the Euler equations may be used beyond the Knudsen layer. In the Knudsen layer, the emitted particles come to equilibrium with each other through collisional processes ŽEqs. Ž4. and Ž5.. and then the gas Žprovided collisions continue. evolves into a UAE ŽEq. Ž7... Thus, before using the Euler equations instead of the Boltzmann equation, it is necessary to be sure that equilibration has occurred between the particles. This is not the case of the particles being transferred from one order to another in the model of Ref. w12x, the different orders being related to the number of collisions with the ambient gas. Indeed, the particles which are included in some
specific order, after only one collisional event with the background gas, cannot be assumed to be in equilibrium: more than one collisional event is necessary to attain equilibrium w16x and, what is important, is that the collisions must occur between the same particles Ži.e., Si–Si. to realize ideal hydrodynamic conditions. Now, a final point enters when considering the value of the g parameter, i.e., the heat capacity ratio:
gs
jq5 jq3
,
Ž 11 .
where, as before, j is the number of internal degrees of freedom accessible at a given temperature. The g parameter is not apparent in Equations 1 and 2 of Ref. w12x, but indeed it is included in the pressure term p through the relation: p s r a2rg , where a is the sound speed and r is the particle mass density. The g values depend on the state of the particle as well as on the temperature. For example, for a non-ionized Si atom at 4000 K, g is 1.67, while for a singly ionized Si atom, g is 1.56. For excited Si atoms, g may be numerically quite small. The different possible values of g is not a trivial point because, in order to analyse correctly with the hydrodynamic equations the fluxes of particles having different g , it is necessary to implement additional equations to account for the multicomponent flow w17x. The previous discussion on the relevance of g seems here quite important because the detected Si particles w12x, when expanding in vacuum, have a velocity of the order of 2.5 = 10 6 cmrs Žwhich corresponds to a ‘temperature’ of ; 10 6 K. suggesting that electronic excitation processes are involved in the particle emission. Thermal processes, for which the target surface temperature cannot exceed the thermodynamic critical temperature, near which phase-explosion occurs w18x, are apparently not relevant here.
7. Conclusions We have analysed some aspects of the TOF spectra obtained when particles are sputtered from a surface, including examples due to irradiation with
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
electrons ŽFig. 1., ions ŽFig. 2., and laser pulses ŽFigs. 3–5.. TOF, when appropriately analysed, may give fundamental details in establishing the mechanisms responsible for the particle emission. However, when experiments are performed in an ambient gas, primary effects may be partially obscured by collisions between the emitted and the ambient particles. We have critically analyzed certain TOF spectra obtained when particles are sputtered in an ambient gas by showing that conflicting results are reported in the literature. Probably, the different features observed in TOF spectra of the laser-sputtered particles, in an ambient gas, may be connected to the different TOF detection distances from the emitting surface. This is not a trivial point in connection with the model of Ref. w15x, where oscillatory behaviour of the expanding plume and vortex formation are anticipated. In this respect, it would be important to have more extensive experimental TOF spectra collected at different distances from the laser-irradiated surfaces. In addition, we have analysed the models suggested by various authors to explain the behaviour of a plume generated by a laser pulse and propagating in an ambient gas. This suggested that probably the basic physics involved in such a process needs further clarification.
51
References w1x S.I. Anisimov, Sov. Phys. JEPT 27 Ž1968. 182. w2x R. Kelly, R.W. Dreyfus, Surf. Sci. 198 Ž1988. 263. w3x R. Kelly, R.W. Dreyfus, Nucl. Instr. and Meth. B 32 Ž1988. 341. w4x L.V. Zhigilei, B.J. Garrison, Appl. Phys. Lett. 71 Ž1997. 551. w5x R. Kelly, A. Miotello, Nucl. Instr. and Meth. B 122 Ž1997. 374. w6x H. Overeijnder, M. Szymonski, A. Haring, A.E. de Vries, ´ Rad. Eff. 36 Ž1978. 63. w7x N. Itoh, Cryst. Latt. Defects 3 Ž1972. 115. w8x G.J. Dienes, R. Smoluchowski, J. Phys. Chem. Sol. 37 Ž1976. 95. w9x R. Smoluchowski, O.W. Lazareth, R.D. Hatcher, G.J. Dienes, Phys. Rev. Lett. 27 Ž1971. 1288. w10x A.P.M. Baede, D.J. Auerbach, J. Los, Physica 64 Ž1973. 134. w11x M. Szymonski, A.E. de Vries, Rad. Eff. 54 Ž1981. 135. ´ w12x R.F. Wood, K.R. Chen, J.N. Leboeuf, A.A. Puretzky, D.B. Geohegan, Phys. Rev. Lett. 79 Ž1997. 1571. w13x R. Kelly, A. Miotello, A. Mele, A. Giardini Guidoni, J.W. Hastie, P.K. Schenck, H. Okabe, Appl. Surf. Sci. 133 Ž1998. 251. w14x P.J. Wolf, Appl. Phys. A 62 Ž1996. 553. w15x A.V. Bulgakov, N. M Bulgakova, J. Phys. D: Appl. Phys. 31 Ž1998. 693. w16x A. Peterlongo, A. Miotello, R. Kelly, Phys. Rev. E 50 Ž1994. 4716. w17x S. Karni, J. Comp. Phys. 112 Ž1994. 31. w18x A. Miotello, R. Kelly, Appl. Phys. Lett. 67 Ž1995. 3535.
On the origin of the different velocity peaks of particles sputtered from surfaces by laser pulses or charged-particle beams Antonio Miotello ) , Roger Kelly INFM and Dipartimento di Fisica, UniÕersita` di Trento I-38050 PoÕo, Trento, Italy
Abstract The particles emitted from surfaces irradiated by either laser pulses or charged-particle beams are often analyzed by time-of-flight ŽTOF. spectroscopy. This technique gives, in general, details on the velocity Žthence energy. of the emitted particles, parameters which are of fundamental importance in establishing the mechanisms responsible for the particle emission. However, when experiments are performed in an ambient gas, primary effects may be partially obscured by collisions between the emitted and the ambient particles. Here we will critically analyze certain TOF spectra obtained when particles are sputtered from a surface. To this end we first discuss a variety of velocity laws in connection with the processes which create the different sputtered fluxes. We then compare results which led to two or more velocity peaks, considering in so doing electrons, ions, and laser pulses, as well as the absence or presence of ambient gas. In other words, we try to establish simple criteria to distinguish primary emission mechanisms on the basis of TOF signals. q 1999 Elsevier Science B.V. All rights reserved. PACS: 79.20.Ds; 52.50.Jm; 79.20.H Keywords: Laser-ablation; Ion–surface interaction; Electron–surface interaction
1. Introduction Laser irradiation is widely utilized in three important fields, namely in thin film deposition, in mass spectrometry, and in surface modification. In mass spectrometry, laser ablation of organic material has become an established method for producing molecules and molecular ions in the gas phase. When laser ablation is utilized for mass-spectrometric analysis, it is clearly of fundamental importance to be able to distinguish among the different mecha)
Corresponding author. Tel.: q39-0461-881637; Fax: q390461-881696; E-mail: [email protected]
nisms leading to the velocity distribution of the emitted particles. There is, however, no clear understanding of the entire range of physical processes leading to such velocity distributions. The situation is generally better understood when ions or electrons are utilized to induce sputtering for analytical purposes. In this paper we try to make an attempt to address the problem of the different peaks observed, for example, in time-of-flight ŽTOF. analysis of ejected particles when the peaks are related to the same particle in the same charge state; by contrast, the differences are obvious when the peaks are related to different particles Žatoms or molecules. or to different charge states. To do this, we look at a
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 3 8 5 - 7
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
selected group of experiments performed with electrons, ions, and lasers to induce particle ejection followed by analysis with a TOF apparatus.
2. General aspects of the particle-emission process The velocity distribution function, fsq, of particles emitted thermally from a flat surface at a temperature Ts , when the emission is collisionless, is the ‘half-range’ Maxwellian w1x: fq s Ž Õ x ,Õ y ,Õ z , E I . s
E Ij r2y1
ns
Ž 2p k B Tsrm .
3r2
G Ž jr2 . Ž k B Ts .
jr2
= exp y 2 EI q m Ž Õ x2 q Õ y2 q Õz2 . r2 k B Ts ,
ž
/
Ž 1. Õ x G 0,y ` - Õ y - `,y ` - Õz - `.
Ž 2.
Here fsq has units appropriate to the right-hand side, Õi Ž i s x, y, z . stands for a velocity component, EI is the total internal energy, n s is the number density of the emitted particles near the surface, m is the particle mass, k B is the Boltzmann constant, j is the number of internal degrees of freedom accessible at Ts and for the particular number of collisions occurring, G is the gamma function, and the expression is normalized to n sr2. We use x to refer to the direction normal to the surface. When particles are emitted from a hot surface at number densities which result in collisions, Eq. Ž1. is valid only for the initially emitted particles at x s 0. Beyond x s 0, collisions occur Žmainly for laser irradiation., with the result that negative values of Õ x develop, and the distribution function for Õ x evolves from being proportional to: exp Ž ymÕ x2r2 k B Ts . ,
Õ x G 0,
Ž 3.
to having the form: 2
exp Ž ym Ž Õ x y u KL . r2 k B TKL . ,
y` - Õ x - `.
Ž 4. Here u KL , the center of mass or ‘flow’ velocity, equals the velocity of sound, and T KL was shown to be about 70% of Ts ŽTs , as before, being the surface
45
temperature. or less for a monatomic species. We take as a simple definition of the Knudsen layer ŽKL. the region within a few mean free paths of the target surface in which the change from Eq. Ž3. to Eq. Ž4. occurs as a highly non-equilibrium collision process. The particles which reach the KL boundary, at which point they may or may not enter into free flight, have a distribution function which is a ‘fullrange’ Maxwellian incorporating an explicit centerof-mass or ‘flow’ velocity, u KL , and having a lower temperature, T KL , and a lower gas number density, n KL , than at the surface ŽTs , n s . w2,3x: n KL " f KL Ž Õ x ,Õ y ,Õz , EI . s 3r2 Ž 2p k B TKLrm . EIj r2y1
=
G Ž jr2 . Ž k B TKL .
ž
= exp y
jr2 2
2 EI q m Ž Õ x y u KL . q Õ y2 q Õz2
ž
2 k B TKL
/
/
,
Ž 5. y` - Õ x ,Õ y ,Õz - `.
Ž 6.
On the other hand, the particles which pass beyond the KL boundary and do not enter into free flight are better described by the formalism for an unsteady adiabatic expansion ŽUAE. and therefore have a distribution proportional to: 2
exp Ž ym Ž Õ x y u M . r2 k B TM . , y` - Õ x - `.
Ž 7.
where M s ura ) 1 is the Mach number and a is the sound speed. Note that for a KL, we have M s ura f 1. The picture just presented has emphasized the gas number density, but in reality, both the number density and the length of the emission process are important. In fact, depending on the interplay between the two, one can have situations ranging Ži. from one in which interactions are negligible and Eq. Ž1. can be used, Žii. to one in which only a KL develops but either the supply of vapor then ceases or loss of density becomes important so that a UAE fails to develop ŽEqs. Ž4. and Ž5.., Žiii. to one in which the number density persists and allows a greater or lesser extent of UAE to set in ŽEq. Ž7...
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
46
Finally, to account consistently for the axial and radial velocity distributions of particles ejected in laser ablation, the Maxwell–Boltzmann distribution on a flow velocity was recently modified for a range of flow velocities in the ejected plume w4x. A new expression was derived, essentially from molecular dynamics simulations, to yield: f " Ž Õ x ,Õ y ,Õz ,T ,u max . m s 4p k B Tu max
let the flux of emitted particles in the range Ž Õ x , dÕ x ; " Õ y , dÕ y ; Õz , dÕz . be dÕ x dÕ y dÕz P Õ x f KL . In addition, Õ x s xrt and, since y and z are directions parallel to the target surface and, for example, Õ y is yrt, where t is the flight time, we have dÕ y s d yrt and dÕz s d zrt. Since x is parallel to the target normal and the experiment involves TOF, we have
exp y
mŽ
Õ y2 q Õz2
.
2
2 =exp yb KL Ž w x y u KL t x q y 2 . rt 2 ,
2 k BT
Ž 9.
m
where erf is the usual error function and u max is the maximum value of the flow velocity. ŽThe notation uˆ or uˆ x is also used for u max w5x.. The proposed distribution function has two parameters that are independent of the desorption angle, namely, the temperature of the plume T and the maximum flow velocity u max of the plume propagation. It is unclear to us whether Eqs. Ž7. and Ž8. have forms which are distinct. This problem will be addressed in future work.
where n is 4 for a density-sensitive detector, n is 5 for a flux-sensitive detector, and because of the symmetry of the problem we have taken z s 0. Were conditions for formation of neither a KL nor a UAE fulfilled Ži.e., when the density of emitted particles is lower than ; 1 monolayerr10 ns. then u KL is 0 and 2 T KL s Ts . b KL stands for mr2 k B TKL , m being the particle mass. In the following we analyse separately the two quite different situations, i.e., where there either is not or there is a gas ambient through which the emitted particles propagate. The possibility of collisions between sputtered particles and ambient gas will complicate, as we will see, the main objective of determining the nature of the peaks observed in TOF experiments.
3. The TOF signals
4. TOF of atoms sputtered from alkali halides by electrons
Before going into detail on the TOF peaks which, when appropriately analyzed may give useful information on the primary mechanisms of particle emission from irradiated surfaces, it would be appropriate here to underline briefly that an ion-probe detector ‘ideally’ measures a flux essentially at a point. To extract fluxes at a small-area detector, it is necessary to divide the densities in a one dimensional calculation by time to the fourth power. This means that, when there are two processes, that which is delayed Ži.e., has a greater TOF. is magnified not because of its real magnitude but simply because of a detection problem. Let us make a more specific argument. Let the detector be located a distance x normal to the target and a distance y, z away from the normal, and
In Fig. 1 we report the TOF spectrum of Br atoms leaving a KBr target at 1008C due to bombardment with 540 eV electrons w6x. Here, two peaks, both related to Br atoms, are clearly evident. Most alkali halides irradiated under the same conditions reveal the same features in the TOF spectra: for example, if the target temperature is above 2008C then only one peak appears. This is the peak associated with what are probably thermal particles, i.e., those characterized by a larger TOF Žaverage kinetic energy of the order of 0.03 eV.. The other peak relates to fast particles, i.e., those characterized by a smaller TOF, and which will be called the non-thermal peak. Speaking first of the thermal peak, it can be inferred that this peak is caused by vaporization of Br atoms,
ž ( (
= erf
2 k BT m
yerf
2 k BT
Õx
Ž Õ x y u max .
/
,
Ž 8.
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
47
metal layer has been formed on the surface of the salt. This was observed for AgBr Žthe vapour pressure of the pure metal at 4008C being much less than 10y6 Pd. and for PbI 2 Žvapour pressure of the pure metal at 4008C approximately 10y4 Pd.. 5. TOF of atoms sputtered from alkali halides by an ion beam
Fig. 1. TOF spectrum of Br atoms due to the bombardment with 540 keV electrons of a KBr target at 1008C w6x.
after breaking of K–Br chemical bonds by electron irradiation. The argument is based on the energy distribution of the Br atoms, which is of a Maxwellian type with an average kinetic energy of 0.03 eV. What about the non-thermal peak? To explain this peak, it is appropriate to look at the decay in the bulk of the exciton Žor excitons. created by the electron impact. This decay may promote a focused collision replacement sequence followed by a thermal migration of the H centre, which is essentially related to a halogen atom in an interstitial position and which is able to move in the lattice w7,8x. When the replacement sequence of the migrating H centre reaches the surface, ejection can occur and the energetic feature revealed in the TOF experiments is easily justified through the following argument. The H centre will have an energy of about 2.5 eV w9x. At the surface, this energy can be used to break the bond of a Bry 2 molecular ion and to overcome the surface binding energy. The dissociation energy of the molecular ion is about 1.0 to 1.3 eV w10x. The excess energy may then be released in the form of kinetic energy of the departing halogen atom and will be of the order of 1–2 eV, as observed. Concerning the thermal component of the emitted particles, we should note that if the vapour pressure of the pure metal becomes too low, no metal atoms leave the surface in the experimental time scale. Halogen emission will be stopped completely after a
In Fig. 2 we report the TOF distribution of I atoms sputtered from LiI with a 6 keV Krq beam w11x. Again the spectrum consists of two distinct peaks: the short flight times correspond to an energy of a few eV Ž‘non-thermal’ peak. while the long flight times correspond to thermal energies Ž‘thermal’ peak, with an average kinetic energy of 0.026 eV.. The mass and energy spectra of the sputtered particles thus show clearly that the LiI is sputtered as a result of two distinct processes. The first one Ž non-thermal . is not sensitive to the target temperature and the impinging projectile ŽNeq, Arq, Krq, or Xeq. w11x. The second one Ž thermal . is caused by thermal I atoms and depends very much on the target temperature w11x. The energy distribution spectrum, F Ž E ., related to the non-thermal peak has the form: E F Ž E. A , Ž 10 . 3 Ž E q Eb . which is characteristic of a collision-cascade mechanism governed by a surface binding energy, E b ,
Fig. 2. TOF spectrum of I atoms due to the bombardment with 6 keV Krq ions of a LiI target at room temperature w11x.
48
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
equal to 0.7 eV in the specific example of Fig. 2. In addition, the power law of the observed F Ž E . function indicates that the sputtered atoms, when leaving the surface, experience a planar potential energy barrier characterized by the surface binding energy E b . Concerning the thermal component of the TOF spectrum, note that the ion beam induces a Li–I chemical bond breaking and that subsequent vaporization of the I atoms is due to the high halogen vapor pressure. Non-volatile Li Žthe vapour pressure of the pure metal at 4008C being 0.7 Pd. remains on the surface and can be removed only by the collision-cascade mechanism. Selective sputtering of thermal I atoms due to electronic stopping of incident ions explains also a rapid decrease w11x of the I signal in the case of Heq bombardment. The stopping power of 6 keV Heq in LiI is mainly electronic Žnamely 16 eVrnm, whereas the nuclear stopping power is 4.4 eVrnm. leading to a large enrichment of the non-volatile Li on the surface. The excess of Li atoms can be removed only by a collision cascade process. This mechanism, however, is very inefficient since the nuclear stopping power of Heq is so small.
6. TOF peaks observed in laser-ablation experiments in the presence of an ambient gas 6.1. Discussion of typical experiments At present, it seems that TOF features of the type reported for electron or ion-beam bombardment are not important for laser-induced particle emission from a surface. Two peaks, related to the same particle in the same charge state, are instead seen when laserablation Žat least with ns laser pulses. occurs in the presence of an ambient gas ŽFig. 3.. However, even in this case the results are not fully consistent. Let us examine two different experiments reporting conflicting results. In a recent article, Wood et al. w12x reported new results by laser-irradiating ŽKrF, l s 248 nm, 25 ns FWHM. Si substrates while using background gases of He Žas in the present Fig. 3. and Ar Žas in Figure 1a and 1c of Ref. w12x.. The authors w12x claimed that plume splitting occurs into fast Ž; vacuum speed, approximately as for a gas-dy-
Fig. 3. TOF spectra of Si atoms due to laser irradiation of a Si target ŽKrF laser pulses of 3.0 J cmy2 . in He ambient gas at different pressures w12x. The detection distance was x d s 5 cm. Note that the spectra relate to Si atoms rather than to light.
namical expansion front in vacuum: see Sections 6.2 and 6.3 of Ref. w5x. and background-slowed components. ŽThis problem is also treated in Refs. w5,13x.. Laser irradiation ŽArf, l s 193 nm, 28 ns FWHM. of GeO 2 in different pressures of oxygen was performed by Wolf w14x ŽFigs. 4 and 5.. Time-resolved optical emission spectroscopy was used to analyze the light from the laser-produced plume at several distances above the target surface. The typical TOF profiles serve to clarify the role of the detection distance ŽFig. 4. and the ambient gas ŽFig. 5.. In the profiles of Fig. 4 Žwhere the experiments were performed in vacuum conditions 3 = 10y4 Pa. a splitting of the plume appears which is a function of the distance from the target surface. Considering the fast component Ži.e., that with short TOF. the insensitivity of both the pulse shape and the time-to-peak intensity with distance Ž x s 2 cm and x s 3 cm. suggests that this emission did not originate from material in free flight but from a source of emission which was probably the bright plasma near the surface and which was scattered into the spectrometer. In contrast Žstill considering Fig. 4., the slow component is clearly position-dependent, suggesting that
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
49
effects of the interaction between a pulsed-laser ablation plume and the ambient gas. This model, mainly based on the analogy with an underexpanded jet, predicts oscillatory behaviour of plume expansion and vortex formation at the plume periphery. 6.2. Critique of the model inÕolÕing elastic scattering between a plume and an ambient gas
Fig. 4. TOF spectra of light due to laser irradiation of a GeO 2 target ŽArF laser pulses of 6.5 J cmy2 and 28 ns FWHM.. The analysed optical transition Ždue to GeI. was centered at 269.1 nm, the detection distance was varied w14x, and the ambient gas pressure was always 3=10y4 Pd. There are two components of light, the one with short TOF probably originating at the surface and the one with long TOF originating from the moving Ge atoms.
the light-emitting species ŽGeI. arrived at the observation region with delay times which increased with increasing x. In Fig. 5, Ge TOF profiles are reported for different values of the ambient oxygen pressure at a fixed distance of 1.5 cm from the target surface w14x. The slightly later arrival of the emission peaks with increasing pressure suggests the effects of collisions between the expanding plume front and an impeding force produced by the ambient gas. As with Fig. 4 one recognizes light emission which can be understood as originating at the target surface Žshort TOF. and additional emission from moving Ge atoms. Interestingly, we note that there was no detectable splitting into two components as in Fig. 3, thus leaving the problem of whether the plume should or should not split, when expansion occurs in an ambient gas, an open problem. In addition, it seems that the detection distance is the more important parameter in the sense that the form of the TOF signals depends strongly on this parameter. An explanation of this point may possibly be contained in the modelling proposed in Ref. w15x for the gas-dynamic
The model proposed by Wood et al. w12x to explain plume splitting when expansion occurs in an ambient gas is based on the hydrodynamic equations and on the existence of elastic scattering of the plume particles with the atoms of the background gas. In particular, the plume is broken into orders corresponding to the number of collisions with the background gas. Particles are transferred between the various orders only by collisions and the densities in the individual orders propagate, to give the overall expansion, according to the usual Euler equations. However, a simple examination of the experimental results and of the resulting cross-sections for Si–Ar and Si–He scattering Žthe results for He are as in Fig. 3, while those for Ar are seen in Figure 1a
Fig. 5. TOF spectra of Ge atoms due to laser irradiation of a GeO 2 target ŽArF laser pulses of 6.5 J cmy2 and 28 ns FWHM.. The analysed optical transition was centered at 269.1 nm, the detection distance was fixed at x s1.5 cm, and the pressure of the ambient O 2 pressure was varied w14x. As in Fig. 4, there are two components.
50
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
and 1c of Ref. w12x., allows us to conclude: Ž1. that the theoretical results are numerically inconsistent with some of the experimental results, and Ž2. that the adopted model is too much simplified to treat plume expansion which includes collisions. To elaborate on point Ž1., let us observe that in the case of Ar background gas, when the pressure is 7 Pa the density of Ar atoms, NAr , inside the chamber, is easily calculated to be ; 1.6 = 10 15 atrcm3. Now, the cross-section for the Si–Ar scattering process was assigned numerically, to fit the experimental fluxes, to be s s 5.1 = 10y1 6 cm2 . The mean number of collisions, P, suffered by a given Si particle with the Ar atoms beyond the Knudsen layer and just before the distance x d s 5 cm from the surface, where the Si particle is detected Žboth in the case of He and Ar., is given by the simple relation: P s NAr = s = x d . By including, in the preceding formula, the numerical values Žboth experimental and assigned numerically. P turns out to be ; 4.1. This means that if s were correctly assigned, then essentially all Si atoms would have had several collisions before arriving at x d . By considering now the 8 Pa case, the P value increases by 20% with respect to the 50 mTorr case. With such a small change it is very difficult to understand the big differences in the experimental fluxes of Figure 1a of Ref. w12x. In this respect, the experimental fluxes pertinent to the other gas are also out of trend Žsee the present Fig. 3.. Now, to elaborate on point Ž2., let us remember that the more appropriate theoretical framework to analyse plume expansion by including scattering processes, certainly rests in the use of the Boltzmann equation. However, when appropriate conditions are met w16x, the Euler equations may be used beyond the Knudsen layer. In the Knudsen layer, the emitted particles come to equilibrium with each other through collisional processes ŽEqs. Ž4. and Ž5.. and then the gas Žprovided collisions continue. evolves into a UAE ŽEq. Ž7... Thus, before using the Euler equations instead of the Boltzmann equation, it is necessary to be sure that equilibration has occurred between the particles. This is not the case of the particles being transferred from one order to another in the model of Ref. w12x, the different orders being related to the number of collisions with the ambient gas. Indeed, the particles which are included in some
specific order, after only one collisional event with the background gas, cannot be assumed to be in equilibrium: more than one collisional event is necessary to attain equilibrium w16x and, what is important, is that the collisions must occur between the same particles Ži.e., Si–Si. to realize ideal hydrodynamic conditions. Now, a final point enters when considering the value of the g parameter, i.e., the heat capacity ratio:
gs
jq5 jq3
,
Ž 11 .
where, as before, j is the number of internal degrees of freedom accessible at a given temperature. The g parameter is not apparent in Equations 1 and 2 of Ref. w12x, but indeed it is included in the pressure term p through the relation: p s r a2rg , where a is the sound speed and r is the particle mass density. The g values depend on the state of the particle as well as on the temperature. For example, for a non-ionized Si atom at 4000 K, g is 1.67, while for a singly ionized Si atom, g is 1.56. For excited Si atoms, g may be numerically quite small. The different possible values of g is not a trivial point because, in order to analyse correctly with the hydrodynamic equations the fluxes of particles having different g , it is necessary to implement additional equations to account for the multicomponent flow w17x. The previous discussion on the relevance of g seems here quite important because the detected Si particles w12x, when expanding in vacuum, have a velocity of the order of 2.5 = 10 6 cmrs Žwhich corresponds to a ‘temperature’ of ; 10 6 K. suggesting that electronic excitation processes are involved in the particle emission. Thermal processes, for which the target surface temperature cannot exceed the thermodynamic critical temperature, near which phase-explosion occurs w18x, are apparently not relevant here.
7. Conclusions We have analysed some aspects of the TOF spectra obtained when particles are sputtered from a surface, including examples due to irradiation with
A. Miotello, R. Kelly r Applied Surface Science 138–139 (1999) 44–51
electrons ŽFig. 1., ions ŽFig. 2., and laser pulses ŽFigs. 3–5.. TOF, when appropriately analysed, may give fundamental details in establishing the mechanisms responsible for the particle emission. However, when experiments are performed in an ambient gas, primary effects may be partially obscured by collisions between the emitted and the ambient particles. We have critically analyzed certain TOF spectra obtained when particles are sputtered in an ambient gas by showing that conflicting results are reported in the literature. Probably, the different features observed in TOF spectra of the laser-sputtered particles, in an ambient gas, may be connected to the different TOF detection distances from the emitting surface. This is not a trivial point in connection with the model of Ref. w15x, where oscillatory behaviour of the expanding plume and vortex formation are anticipated. In this respect, it would be important to have more extensive experimental TOF spectra collected at different distances from the laser-irradiated surfaces. In addition, we have analysed the models suggested by various authors to explain the behaviour of a plume generated by a laser pulse and propagating in an ambient gas. This suggested that probably the basic physics involved in such a process needs further clarification.
51
References w1x S.I. Anisimov, Sov. Phys. JEPT 27 Ž1968. 182. w2x R. Kelly, R.W. Dreyfus, Surf. Sci. 198 Ž1988. 263. w3x R. Kelly, R.W. Dreyfus, Nucl. Instr. and Meth. B 32 Ž1988. 341. w4x L.V. Zhigilei, B.J. Garrison, Appl. Phys. Lett. 71 Ž1997. 551. w5x R. Kelly, A. Miotello, Nucl. Instr. and Meth. B 122 Ž1997. 374. w6x H. Overeijnder, M. Szymonski, A. Haring, A.E. de Vries, ´ Rad. Eff. 36 Ž1978. 63. w7x N. Itoh, Cryst. Latt. Defects 3 Ž1972. 115. w8x G.J. Dienes, R. Smoluchowski, J. Phys. Chem. Sol. 37 Ž1976. 95. w9x R. Smoluchowski, O.W. Lazareth, R.D. Hatcher, G.J. Dienes, Phys. Rev. Lett. 27 Ž1971. 1288. w10x A.P.M. Baede, D.J. Auerbach, J. Los, Physica 64 Ž1973. 134. w11x M. Szymonski, A.E. de Vries, Rad. Eff. 54 Ž1981. 135. ´ w12x R.F. Wood, K.R. Chen, J.N. Leboeuf, A.A. Puretzky, D.B. Geohegan, Phys. Rev. Lett. 79 Ž1997. 1571. w13x R. Kelly, A. Miotello, A. Mele, A. Giardini Guidoni, J.W. Hastie, P.K. Schenck, H. Okabe, Appl. Surf. Sci. 133 Ž1998. 251. w14x P.J. Wolf, Appl. Phys. A 62 Ž1996. 553. w15x A.V. Bulgakov, N. M Bulgakova, J. Phys. D: Appl. Phys. 31 Ž1998. 693. w16x A. Peterlongo, A. Miotello, R. Kelly, Phys. Rev. E 50 Ž1994. 4716. w17x S. Karni, J. Comp. Phys. 112 Ž1994. 31. w18x A. Miotello, R. Kelly, Appl. Phys. Lett. 67 Ž1995. 3535.