Large, energetic cluster impacts on surfaces

448

Nuclear

Instruments

and Methods in Physics Research 814 (1986) 448-460 North-Holland,

LARGE, ENERGETIC M.W. MATTHEW,

CLUSTER IMPACTS

R.J. BEUHLEK,

Brookhucv~ MormmlLahorororr.

The competition

f_+mn. New

between sputtering

techniques of transmission electron microscopy. water molecules acccleratcd

used in these \tudie>

I 1973.

or evaporative

cluster ton impact on surfaces can be investigated 150

ON SURFACES *

M. LEDBETTER York

Amsterdam

and L. FRIEDMAN

LSA

cooling and cooling by thermal

b) study of the morphology

conduction

of thermal

of craters or holes produced

Results of a study using protonated

spikes produced

by

in the surfaces using

water molecule clusters containing

as many as

to energies as high as 3OOooO V. impacting on thin carbon surfaces will be presented. The clusters

may be considered

as species which are intermediate

between atomic and small molecule projeclilcs

in processes that can be modeled by rwo-body

stopping power theory. and macromolecular

projectlIes which compress sohd targets and transfer energy by generation of shock waves

and continuum

phenomena.

from observation

Threshold

of energy transfer processes that depart sigmficanrly

Craters or holes as small as 20-30

The morphology the formation

clusler sizes and energies for production

mteractiona

wth

which

transfer energy on impact and penetration

energy losses gwen by

of the lacter type process can he determined

from predictions of stopping pourr

k in diameter were produced in thin carhon films by 50 molecule proronated

water cluster ion>.

of rheze craters and holes and larger ones produced by larger cluster ions provide direct experimental

of rhermal spikes. The technique provtdes promise as a method of permanently

crudely

theory. evidence for

altering surface structure>.

1. Introduction

Energy transfer in collisions of hypervelocity ions with solid surfaces takes place in times of the order of 10 I4 s and can generate extremely high energy densities in a solid target. Atomic or very small molecular ions penetrate the target leaving a track with relatively large surface area which can cool very rapidly by thermal conduction with a relatively minor fraction of the transferred energy dissipated by evaporation or sputtering. Cluster ions deposit energy in volume elements of the target with much smaller surface to volume ratios facilitating more extensive evaporation processes with the possible formation of surface craters or holes in thin target films. The observation of the formation of microscopic craters or holes in ion bombarded surfaces is evidence for either extensive irradiation with intense atomic or molecular ion beams or bombardment with energetic “macroions” capable of producing local high energy densities which last long enough 10 permit slower evaporation processes to compete with conductive cooling. Transfer of energy from projectile to target, in the case of macroion bombardment, has been treated using a hydrodynamic model in contrast to the two-body collision approach used to calculate energy transfer associated with impact and penetration of atomic projectiles. The nearly simultaneous interaction of n pro*

This

research

Laboratory

was carried

under contract

US Department

OUI

at

Brookhaven

DE-AC02-76CHO16

National with the

of Energy.

0168-583X/86/$03.50 :l, Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

jectile-cluster-atoms with a similar number of target atoms will, if the cluster is sufficiently large. produce a shock wave which compresses the target and projectile systems. This transient compression is accompanied by a transient increase in density and temperature with irreversible heating of both target and projectile atoms. This model has been used to analyze data obtained in studies of collisions of simulated micrometeorites [ 1.21. iron clusters, with target surfaces. These iron clusters contained a minimum of 10’ atoms and were accelerated electrostatically to velocities as high as 4 x 1Oh cm/s. Craters were observed after generating energy densities estimated at approximately 10” erg/g. The experimental results were consistent with plastic deformation of the projectile on impact. and the structural states of both projectile and target materials governed by Rankine-Hugoniot theory. In principle with this hydrodynamic model for energy transfer, energy densities achievable on impact are limited only by the specific energies that can be generated in the acceleration of projectile ions. Limits of energy densities are conceivable when projectiles are accelerated to the point at which surfaces are penetrated by projectile atoms and the model of a hydrodynamic interaction of a projectile with an “impenetrable” surface breaks down. The projectile velocities used in the micrometeorite experiments were not considered beyond the range of validity of the hydrodynamic model. With smaller higher velocity cluster projectiles one encounters the question of the boundary between compression and penetration. One may also consider the

M. W. Mutthew et al. / Lcrrge energetrc cluster impacts on surJuces

boundary between discrete and continuum processes in terms of the critical size of cluster required to produce interactions which deviate significantly from atomic energy transfer processes [3]. Projectile velocities in our experiments may be beyond the range of validity of models based on assumptions of impenetrable surfaces. A proper theoretical treatment of the phenomena requires analysis of the dynamics of interaction of many body projectiles with many target atoms over a considerable depth of target penetration. We shall limit our attention in the present study to consideration of energy transfer in cluster impact as a stopping power problem with the objective of determining how well the results can be fitted with a modified stopping power model. The problem of investigation of energy transfer processes in cluster ion bombardment is complicated because depths of penetration may be shallow and the observation of holes in thin films or craters in solid surfaces do not directly measure the depths of projectile penetration. The transfer of energy in target-target atom collisions can reduce or increase crater or hole dimensions depending on competitive rates of conductivity and evaporation. Energy losses by electron emission [4] or radiative processes [6] are not expected to carry much energy away from the target in our experiments. Projectile velocities were, in all cases in this work, below thresholds for extensive electronic excitation in the target. With transient phenomena resulting from impact and penetration having lifetimes less than lo-‘* s, there may be insufficient time for equilibration of energy between electronic and translational or vibrational degrees of freedom in the hot atom assembly generated by impact. The experiments that we have carried out were irradiation of thin carbon targets with mass analyzed beams of water molecule cluster ions. Targets were then examined using transmission electron microscopy to determine densities, sizes and shapes of craters or holes

Table 1 Summary

produced by the collisions. Clusters containing between 20 and 150 water molecules were accelerated to kinetic energies up to 300 keV. With 50 water molecule cluster ions, incident energy densities of about 3 X lOI erg/g were deposited in targets, over 20 times the maximum energy densities achieved in the earlier simulated micrometeorite studies [l].

2. Results The results are summarized in table 1 and presented in figs. 1-6. Figs. la and b show bright and dark field micrographs of holes generated in 65 A thick carbon films by impact of 300 keV water molecule clusters, having 100 water molecules and a single proton. The holes are approximately 70 A in diameter. They appear to be somewhat larger in the dark field micrograph, because the higher contrast in this method of imaging reveals a reduction in carbon film thickness immediately around the hole which is not visible in the bright field micrograph. The density of holes is in good agreement with the value expected from the number of particles estimated hitting the carbon film. The agreement is qualitative because of uncertainties in corrections of absolute integrated current measurements for secondary electron yields. Fig. 2a shows very deep craters in 150 A carbon films produced by 300 keV, 150 water molecule clusters. These craters are as large as 150 A at the impact surface and appear to taper down to diameters of about 100 A. Fig. 2b shows the same target films after being shadowed with gold to improve contrast. There is a higher density of dark gold grains around the inner edge of the conical craters and clear evidence for very tiny gold grains trapped at the base of the crater on an extremely thin layer of carbon. The carbon left in the film at the base of the crater is estimated to be less then 5 atomic layers, probably no more than 3. Stereo views

of results Energy

Projectile

Target

WV) (H@)x&+ (H@),&+ (HzO),,H+ (Ar)&

300 300 200 300

65 150 65 65

(H,O),,H+ (H@)&+ (H,O),,H+

100 175 240

105 A carbon 105 A carbon 105 A carbon

(H,O)&+ (H&V&+ (H&%$+

300 250 250

105 A carbon

300

95 A Pt-C

(H,O),,H

449

+

A A A A

carbon carbon carbon carbon

95 A Pt-C 95 A Pt-C

Crater or hole diameter (A)

Comments

Fig.

70 A 100-150 40 A 50 A _

holes deep craters shallow craters holes

1a.b 2a,b 3a,b,c 4a,b

no visible holes or craters barely detectable craters

5a 5b

A

15-25 ,k craters 15-25 A craters 15-25 A holes 60 A 60 A _

holes with halos holes ringed with PT higher magnification

5c Sd 6a 6b

no visible holes or craters

III. MOLECULAR

ION ETECTION

450

M. W. Matthew

et al. / Large energetic cluster impacts on surfuces

Fig. 1. Bright field (a) and dark field (b) micrographs of the same area of carbon target bombarded by 300 keV water clusters, each containing 100 water molecules. Carbon foil thickness was 65 A, and the approximate hole diameter was 70 A. Scale length is 1000 A.

shown), of the bright field micrographs shown in fig. 2 establish more clearly the conical shapes of these craters. Figs. 3a and c are slightly out-of-focus bright and dark field views of a 65 A carbon film after bombardment with 200 keV clusters containing 100 water molecules. Thus with the same energy per water molecule much smaller and shallower craters are formed than in the case of the 150 molecule projectiles. Fig. 3b is an in-focus bright field micrograph in which craters are barely perceptible if at all. One would expect to be able to see shallower craters with the thinner 65 A carbon film. Note that the magnification in fig. 3 is about twice that in figs. 1 and 2 so that the out-of-focus craters in fig. 3 are smaller than those produced by the 100 water molecule clusters in fig. 1. The craters produced by the 200 keV, 100 molecule clusters are roughly 40 A in diameter, very close to the maximum value of the projectile diameter (if it were plastically deformed into a disc one molecule thick). Fig. 4 shows bright and dark field micrographs of 65 A carbon films bombarded with 300 keV, 100 molecule, singly charged argon clusters. Here again the dark field micrographs show holes that appear to be fuzzy around

Fig. 2. (a) Bright field micrograph of a 150 A thick carbon foil struck by 300 keV water cluster ions containing 150 water molecules. Note the halos around the holes, indicating the possible formation of conical craters, with smallest diameter c approximately 100 A. (b) Bright field of a similar thickness carbon foil which has been shadowed with gold after impact. Note the aggregation of gold around the periphery of the holes.

(not

the edges. The bright field holes are slightly smaller than those produced by the 300 keV, 100 water molecule clusters, approximately 50 A in diameter. The argon results are presented to show that hole or crater formation in these studies is primarily a physical process and not the result of primarily chemical interactions. Further work using argon as a projectile system is in progress and will be presented in a separate report. Fig. 5 contains a set of films, all 105 A in thickness, irradiated with 50 water molecule cluster ions with energies ranging from 100 keV to 300 keV. The purpose of this study was to investigate the effect of incident energy on crater or hole formation. The 100 keV clusters show no evidence of crater or hole formation. An occasional shallow crater infrequently appears in fig. 5b produced by 175 keV, 50 molecule clusters. Increase of kinetic energy to 240 keV produces a fair density of shallow craters that are quite visible. IncrTase of energy to 300 keV produces holes in the 105 A carbon film with halos surrounding the holes. These halos were the first bright field evidence for evaporation of carbon

M. W. Mutthew et al. / Large energetic cluster impacts on surJaces

451

Fig. 4. Bright field (a) and dark field (b) micrographs of the same area of carbon target bombarded by 300 keV argon clusters, each containing 100 argon atoms. Carbon foil thickness was 65 A, and the approximate hole diameter was 50 A. Scale length in (a) is 1000 A.

Fig. 3. 65 A thick carbon foil bombarded by 200 keV, 100 water molecule cluster ions. (a) bright out of focus field: (b) bright field, in focus; (c) dark field, out of focus. Scale is 1000 A.

around the edges of the holes without significant hole enlargement. Hole diameters are estimated to be between 15 and 30 A in diameter, the smallest that we have made in carbon films with water cluster ions. Preliminary evidence indicates the possibility of making somewhat more uniform small holes in carbon films with argon cluster ions. Fig. 6 shows two different magnifications of holes roughly 60 A in diameter produced in 95 A thick films of 50: 50 carbon and .platinum. There is evidence for segregation of rings of platinum around the hole perimeters. These films were used because of their higher

contrast for electron microscopy to study the effect of cluster sizes on the probability of crater or hole formation. Similar results were obtained with 40 molecule water cluster ions but when cluster sizes of 25 water molecules or less were selected as projectiles no evidence of surface alteration or damage could be detected in these platinum-carbon films. An occasional crater or hole could be seen but these events could be attributed to incomplete mass analysis, with the density of observed events reduced by several orders of magnitude compared with irradiations of the same integrated intensity using larger cluster ions.

3. Experimental Target films supported on 300 or 400 mesh copper grids were examined with a Phillips EM 300 transmission electron microscope. The apparatus for generation, mass analysis and acceleration of cluster ions has been described in detail in earlier publications [4,5]. Cluster ions are generated by expansion of a weakly ionized helium-water vapor mixture from a discharge in a high pressure ion source. The expansion takes place through III. MOLECULAR ION FJECTION

452

M. W. Matthew

et al. / Large energetic cluster impacts on surfaces

Fig. 6. Different magnifications of a 95 A thick platinumcarbon target bombarded with 250 keV, 50 water molecule cluster ions. The scale in each case is 1000 A. A~re~ation of platinum

Fig. 5. Four micrographs demanstrating the onset of hole formation in 105 A carbon foil as the energy of 50 uiater molecule cluster ions is increased. Scale length in (a) is 10010A. The cluster energies were: (a) 100 keV: (b) 175 keV; (c) 240 keV; (d) 300 keV. No holes are observed in (a), small crate rs or holes of 15-25 A diameter are observed in (b) and (c), and 15-25 A diameter holes with small halos are observed in (d).

is seen at the periphery

of the holes.

a supersonic nozzle and skimmer into a high vacuum system containing a quadrupole mass analyzer, acceferation lenses and the target microscope grids. Cluster ion growth can be controlled by adjustment of the gas mixture, temperature, composition and/or pressure in the ion source. The supersonic nozzle geometry provides an additional means of control of cluster ion size distributions. Cluster ion growth takes place almost exciusively in the expansive cooling of the protonated water molecule ions in transit from the nozzle, After passage of cluster ions through the skimmer, relatively low velocity cluster ions are mass analyzed using a quadrupole mass spectrometer constructed from 3/S inch diameter rods. The mass range up to mass-tocharge ratios of 1000 was examined with a 1.5 MHz quadrupole power supply. Clusters with mass-to-charge ratios as high as 80000 were analyzed with a low frequency, 292 kHz, power supply, (Extranuclear Research Corp). Resolution in the latter case was limited to about 1 part in 200. Previous experiments on secondary electron yields from cluster ion impact have shown that water cluster ions are made up exclusively of singly charged ions and that transmitted beams include components that are typically within 5% of the nominal

M. W, Matthew et nl. / Large energetic cluster impacts on surfaces

mass. The possibility of the partial destruction of cluster ion beams by grazing lens collisions or gas phase collisions between the mass analyzer and the target must be considered in these experiments. Careful investigation of secondary electron yields on well-characterized copper targets was used to test focus conditions for beam grazing and vacuum conditions for the possibility of significant gas phase collision induced decomposition processes. A 93 cm long acceleration column was located near the exit of the quadrupole mass analyzer and used to accelerate the cluster ions prior to impact on the carbon target films. The targets were situated about 20 cm beyond the end of the acceleration column. Targets and surrounding vacuum system were housed in a large electrical dome held at high voltage. Information on beam intensity was digitized and transmitted to ground potential on fiber optic linkages. It should be noted that the accelerating fiel$ gradients of up to 3 X lo-’ V/A were insufficient to effect decomposition of the relatively weakly bound cluster ions. The average distance between craters or holes in the target films was controlled by varying the total integrated ion current striking the target. A coverage of between 1 and 2 X 10” impacts/cm* was found convenient for microscopy and sufficient to avoid multiple impacts at the same points in the target. Typical cluster ion fluxes were about 5 x lo-” A/cm2 with target irradiation times limited to 2 to 5 min. Target probes were electrically isolated. Net ion currents were estimated after crude corrections for secondary electron emission. Target grids were supported in spring clamp specimen holders designed for the Phillips EM 300 electron microscopy. Target films were formed by electrical resistance heating of carbon in an evaporator maintained at lo-” Torr or better by oil diffusion pumping with an intermediate liquid nitrogen trap. The evaporated carbon was deposited on freshly cleaved mica or on plastic supports. The plastic was cast on glass using a 0.15% solution of celloidin (Pro-celloidin Fluke) in ethyl acetate and transferred to grids in the usual manner. Following carbon coating the plastic was removed by refluxing with ethylacetate. Electron microscopy was performed at 40 to 100 keV accelerating voltage using the Phillips EM 300, equipped with a double tilt stage having a 3.0 mm focal fength objective lens with a 40 pm thin foil aperture. Brightfield imaging was achieved by conventional meads and dark-field by unidirectional tilt. 4. Discussion

The objectives of this study were to investigate energy transfer processes in collisions of accelerated clus-

453

ter ions with solid surfaces. The results presented in the electron micrographs are morphological, giving dimensions and shapes of craters or holes in thin targets. The observed permanent changes in surface structure reflect sizes and shapes of assemblies of target atoms with sufficient energy for evaporation in the very short times before target cooling takes place. Crater or hole dimensions define “energy ranges” in contrast to particle penetration ranges usually considered in stopping power theory. “Energy ranges” measure distances and depths to which targets are heated above critical temperatures for target atom evaporation. The correlation of crater or hole dimensions with target properties then requires a knowledge of the initial energy density deposited by the projectile in the target and competitive rates of energy dissipation by thermal conduction and target atom or fragment evaporation. As noted above the projectiles used in this study are intermediate between atomic species and “macroions” and thus present a special problem in estimates of details of energy transfer processes in ion impact. We shall first consider the problem of energy densities in terms of stopping power and hydrodynamic mechanisms of energy transfer. Values of assumed energy densities will then be used in illustrative calculations designed to show the nature of time dependent temperature distributions produced by different size cluster ions. After demonstration of the qualitative differences between cluster produced thermal spikes and more familiar spikes produced by atomic penetrations, the models developed by Sigmund and coworkers [7a,7b] will be used to account for the morphology of the observed craters or holes by integration of rate equations for target evaporation over the dimensions of the thermal spikes and the time periods during which temperatures are high enough for target evaporation. For the present, with systems of hundreds or thousands of atoms at temperatures ranging up to millions of degrees only qualitative limits can be set on parameters determining rates of evaporation and thermal conduction. But these limiting values serve both to guide experiment and have crude predictive value giving magnitudes of sizes of craters or holes that can be made in particular targets by cluster ion impact. 4.2. Initiai energy densities The question of the initial temperature distribution or energy density is perhaps the most challenging aspect of this study. In the simulated micrometeorite studies referred to above, with iron projectiles moving with velocities of between 5 and 15 x lo5 cm/s, roughly 10 to 40% of the projectile energy was estimated to be converted to internal energy on impact. Energy transfer from the incident particle was shown to be a steeply rising function of particle velocity. Specific internal III. MOLECULAR ION ElECTION

454

M. W. Matthew

et 01. / Large energetic cluster impacts on surfaces

energies well in excess of lOI2 erg/g were deposited in copper and ahuninum targets by iron projectiles moving with velocities of 3 or 4 X lo6 cm/s. With relatively small projectiles, made of tens to hundreds of atoms or small molecules, the minimum cluster size that is appropriate for the use of a continuum model is a substantial question. Similarly if the cluster projectile is assumed to be an assembly of atoms with each atom depositing energy in the target in a set of two body collision processes, the problem of the maximum number of atoms per cluster for which this approach is valid, even as a crude approximation, must be considered. The continuum model predicts transfer of energy to the target proportional to projectile kinetic energy, whereas the nuclear stopping power model provides for heating greater depths of the target to approximately the same temperature with increasing projectile kinetic energy. The smaller craters created by smaller higher velocity projectiles with the same kinetic energy provide evidence for target penetration rather than energy transfer at an “impenetrable surface” and suggest that estimates of energy transfer using a modified stopping power rather than hydrodynamic model might be more appropriate for projectiles moving with velocities close to or in excess of lo7 cm/s. The flow of energy in target-target atom collisions that accounts for crater formation with simulated micrometeorites is clearly an important factor in the formation of craters with diameters significantly larger than maximum diameters of projectiles, demonstrated in sect. 2 above, The energy transport tends to obscure the nature of target-atom energy transfer processes. With 150 molecule cluster ions with 300 keV kinetic energy, crater depths of approximately 60 atomic layers are observed with carbon film targets. If these depths were taken as the projected range of the cluster atoms then one finds on average value of dE/dx of about 30 eV/target layer. Fig. 7 shows a plot of nuclear stopping power energy loss from oxygen atoms colliding with a carbon target as a function of projectile velocity. The line is calculated from the Nielsen model [8] and the curve from Lindhard theory [9] based on the use of Fermi-Thomas atomic potentials for projectile-target interactions. In the velocity range of our experiments both treatments give about 60 eV/carbon layer for oxygen atom energy loss. This is roughly twice the value estimated for d E/dx from the crater depths produced by 1.50 water molecule clusters colliding with the 60 atomic layer carbon films. It is difficult to explain a large decrease in stopping power for cluster ion atoms associated with collective interaction of many projectile and target atoms confined to a relatively small target volume element. A plausible explanation of the estimated crater depth is that at least l/2 of the depth of the crater is formed by evaporation of carbon atoms heated by conduction of

I

60 -

I

I

,

I

I

NUCLEAR STOPPING POWER, OXYGEN ON CARBON

I

I

I

\ OXYGEN VELOCITY/107cmhec

Fig. 7. Nuclear stopping for an oxygen atom on a carbon target with density of 1O23 atoms/cm3. St is the constant vatue of stopping power based on ref. (81, and SN is a velocity dependent stopping power derived with the Thomas-Fermi interatomic potential.

the energy deposited in the top layers of the target. The nearly simultaneous interaction of many target and projectile atoms raises a serious question in the use of a stopping power dE/dx based on a two body interaction model for calculation of rates of energy deposition in cluster atom impact and penetration processes. If one considers 3 or 4 projectile atoms moving through a layer of target atoms, the target atom that is surrounded by projectile atoms will be maintained in a small volume element with a much higher degree of rigidity than if it were involved in a collision with one isolated projectile atom. Target-projectile interactions can in this way have smaller impact parameters and stronger repulsive interactions than for the “isolated two body systems” of an energetic projectile colliding with an atom in the lattice of the target. Thus one might expect enhanced stopping power with cluster ion penetration, and stopping power that is not as insensitive to projectile velocity as with fast atoms depositing most of their energy as nuclear stopping power. With sufficiently large cluster ions moving with sufficiently high velocity, craters are formed that are much larger in diameter than the projectiles used to make them. The magnitude of this crater enlargement can be used to estimate the extent to which crater depth has been increased over the depth of penetration of projectile atoms. The implicit assumption in an attempt to use this type of information to estimate projected ranges of cluster atoms is that there is very little straggling or wide angle collisions in the penetration processes. Flow of energy outward normal to the axis of penetration is assumed to be accompanied by a similar flow of energy down into the target along the axis of penetration. With 100 water molecule clusters with 200 keV we see craters with diameters close to those of cluster “disc” diameters

M. W. Mutthew et crl. / Large energetrc cluster imprrcts on surfclces

and a maximum penetration of about 15 target layers. With 150 molecule clusters with 300 keV KE, we see crater diameter enlargements of about a factor of 3 with maximum crater depths of about 60 target layers. These observations give values of dE/dx of 130 and 100 eV/layer respectively for these 200 and 300 keV projectiles; both values of d E/dx are larger than expected from stopping power theory. The observation of a much deeper target penetration by 2 keV water molecules in 150 molecule projectiles than in 100 molecule projectiles or in 50 molecule projectiles provides additional evidence to show that energy transfer in cluster ion impacts cannot be accurately treated within the framework of existing stopping power theory neglecting collective interactions of target and projectile atoms. In illustrative calculations presented below a value of 200 eV/atomic layer will be arbitrarily chosen for the initial energy densities produced by penetration of energetic water molecules into carbon targets. The value was selected to give initial energy densities that would obviate the necessity of using extreme values of frequency factors in calculations of rates of evaporation or exotic evaporation mechanisms to account for the extent of target material removed from craters during the limited lifetimes of the thermal spikes. 4.3. Thermal

spike formation

We can consider the transient properties of the assembly of hot atoms produced in terms of rates of cooling by thermal conduction. Seitz and Kohler [lo] have developed a model for conductive cooling of thermal spikes generated by fast particle irradiations. They assumed heated volume elements with either spherical or cylindrical symmetry and a constant thermal diffusion rate defined by the ratio of the thermal conductivity, K, to the product of the heat capacity and density. Bulk values of thermodynamic properties were assumed with recognition of the limitations of this assumption for the microscopic systems undergoing unusual transient conditions of temperature and pressure. Seitz and Kohler were concerned with diffusion of displaced atoms in a “ molten” matrix in the solid. Our attention is focussed on the evaporation of atoms or molecular fragments from a similar energetic atom assembly. Both diffusion and evaporation are processes which can be treated by rate equations of the same general form. Urbassek and Sigmund [7b] have recently developed a theoretical framework for treatment of evaporation processes from thermal spikes. Their model takes into consideration cooling of thermal spikes in three dimensions as well as by evaporation and uses a temperature dependent value of the thermal conductivity. In view of the limited number of experiments in our present study and the general lack of knowledge on the

455

detailed nature of large cluster interactions with solid surface we have chosen to use the more approximate treatment of Seitz and Kohler, ignoring corrections for evaporative energy losses and using bulk values of thermal conductivity with no corrections for the temperature dependence of thermal conductivity. Following Seitz and Kohler, the relation of the temperature T, at any distance from the center of impact to the initial temperature, TO, as a function of time after impact can be expressed by the relation T= T,(l

+y)

-ne-,2/,q1

+yj

(1)

where T and TO are the respective temperatures, r is the radial distance from the center of impact and IJ the radius of the projectile, i.e. the radius of the cross section of initially impacted target. n is + for spherically symmetric geometry and 1 for cylindrical geometry. y is defined by the relation 0% with t the time after impact, K the thermal conductivity coefficient and c the heat capacity per unit volume of the target. Results of illustrative calculations of radial temperature distributions at various times after cluster ion impact are presented in figs. 8a, b and c for clusters containing 150, 100 and 25 water molecules, respectively. A value of 0.061 cm2/s was used for the target heat conductivity to heat capacity ratio. The choice of this value of thermal diffusivity is arbitrary and may not realistically reflect the best possible estimate of this value for conduction of heat radially in thermal spikes in amorphous carbon. Lower values would give longerlived thermal spikes. The choice made gives thermal spike geometries that are qualitatively consistent with sizes of craters observed. The high value chosen, compensates for over-simplifications in the model which neglect cooling by evaporation and helps to explain the failure to observe craters with clusters containing 25 water molecules (fig. 8~). As noted above an arbitrary value of approximately 200 eV/carbon layer was assumed for the rate of energy deposition in the target. The projectile clusters were assumed to deform into discs one molecular layer in thickness on contact with the target. The latter assumption gives an upper limit value for the radius of the cylindrical volume element of target initially penetrated by the projectile. With cluster ion velocities in the region of 2 or 3 X 10’ cm/s there may be insufficient time prior to target penetration for complete deformation of more compact cluster ion structures into thin discs, but results on simulated micrometeorite studies have shown with slower projectiles extensive plastic deformation of the projectile. The larger the estimate of the volume initially penetrated by the projectile the lower the initial energy density or temperIII. MOLECULAR ION EJECTION

M. W. Matthew Ed ul. / L.arge energerrc cluster impacts on surfaces

456

ature. The calculated radial temperature distributions in fig. 8 show a curve obtained by setting time equal to zero in the time and distance dependent equation for

I

(cl)

H

+

(~~0)~~~

ON CARBON

IO5 T(OK) 104

IO2 RADIUS

/

I

/

/

/

,

i

,

(b)

ii, T-ii----7

H

+

(H201,,,

CLUSTER

ON CARBON RAOlUS=l7.5

IO5 T(*K, Id

IO2 RADIUS

(cl

6,

H+ i H201,, CLUSTER 2)”

FOR OXYGEN = 97eV/H

T0=9.8~105

RADIUS

ON CARBON RADIUS = 8.7 i

6,

OK

I 8

temperature of the hot spike. This curve has been included to show the calculated “instantaneous” heat loss from the circumference of the area of impact. The radial temperature distribution at t = 0 might have been more accurately described for times of the order of lo- I4 s. Projectile atoms can move distances of the order of 10 or 15 A in these times and heat regions beyond the 21.4 A radius of the projectile disc in the case of the 150 water molecule cluster ion. With the assumed rate of 200 eV/target layer and neglecting contributions from hydrogen atoms in the water molecules, fig. 8a shows that impact of 150 water molecule cluster ions generates temperatures between 400000 and 1000000 K in the projection of the 21 A disc radius of the cluster on the target surface. After a time period of 3 X lo-” s the temperature at 0 a distance of 70 A from the center of the impact region has risen to 30000 K and temperatures inside this radius have a maximum value of 60000 K. With the smaller 100 and 25 molecule cluster ions the same initial peak temperature results from the same energy loss assumption but the respective radial distributions are considerably reduced both initially and short times after impact. Perhaps the most significant result of the calculations of radial temperature distributions is that with the smaller clusters, temperatures in the thermal spike drop more rapidly. For example after lo-” s the maximum temperatures of the respective spikes are 2000~. 100000, and 30000 K, for the 150. 100 and 25 molecule projectiles. The illustrative calculations of thermal spike cross sectional radii have not taken into consideration the energy losses by cooling at the bottom of the volume element penetrated by the projectiles (as noted above a three-dimensional spike model was developed by Urbassek and Sigmund). With the value of 200 eV/layer assumed as dE/dx in the illustrative calculations. penetration depths of ten layers or slightly more than 20 A units are expected for cluster oxygen atoms with 2 or more keV/atom kinetic energy. Under these circumstances one expects only minor changes in the time dependent radial temperature distributions of the thermal spikes in the first few layers of target as a result of energy conduction into the target along the axis of penetration. The contribution of evaporation to the cooling process has also been neglected. This assumption is reasonable only if rates of thermal conduction are larger than rates of target evaporation. The effect of

Fig. 8. The temperature of the thermal spike generated in a carbon target, based on cylindrical geometry, is plotted as a function of radius for different times after the water cluster ion impact. The value of the nuclear stopping power was assumed independent of the cluster size. The three respective water cluster sizes used were (a) 150 waters; (b) 100 waters: (c) 25 waters.

457 these significant omissions in the development of what at best should be considered a zeroth order approximation is to give thermal spike temperatures that are overestimated in very short time periods after ion impact. Higher values of dE/dx would have to be assumed to give the same temperatures if evaporative cooling and cooling at the base of the crater were considered. 4.4.

Target

evaporation

rates

Rates of target evaporation the classical rate equation

can be calculated

using

p0 is the frequency factor for the evaporative rate process, E the activation energy and T the temperature of the assembly of hot atoms in the thermal spike produced by ion impact. Activation energies of approximately 8 eV have been determined in studies of rates of sublimation of carbon atoms or carbon fragments from solid carbon [11,12]. At temperatures of 1~~0 K and higher, rates of carbon evaporation are determined practically by the frequency factor in the rate equation. With temperatures below 30000 K the exponential term in the rate equation has dropped to a value of 0.04 giving rate coefficients more than one order of magnitude lower and pointing to a rapid cutoff in evaporation with lower temperatures. In consideration of rates of diffusion of energetic atoms at similar temperatures in thermal spikes, Seitz and Kohler assumed frequency factors of the order of 1013 or lOI /s. Sigmund et al. [7a,7b] has treated the problem of the rate of evaporation from thermal spikes in terms of an ideal gas confined by a planar surface potential with the frequency factor in the rate equation given by the product of the number density in the target times the velocity N, “‘N,

kT 2?im I-----l

‘12

’

where N, is the number density of target atoms/unit volume and N, is the surface number density of target atoms, with a square root of temperature dependence for the frequency factor. Frequency factors are relatively “temperature insensitive” but are not temperature independent terms in the evaporation rate equation. The interesting feature of the frequency factor in the rate equation proposed by Sigmund and coworkers is that both the number density and the velocity of carbon molecular fragments decreases with increasing number of carbon atoms/fragment. Thus the advantage gained by transporting more than one carbon atom out of a crater by evaporation of carbon polymer fragments is reduced by a predicted lower rate of evaporation of the heavier, slower and less abundant species.

Values of frequency factor for evaporation of carbon atoms derived from the Sigmund ideal gas model are approximately 10” mof/cm2 s for initial ranges of thermal spike temperatures. With a value of roughly 5 X lo-l6 cm’ for the area occupied by a carbon atom in the target surface a frequency factor of roughly 5 X 1013/s for the evaporation of carbon atoms is obtained. With rates of thermal conduction and evaporation determined to a large extent at high temperature by frequency factors in the respective rate equations, the observation of craters in the carbon films establishes a relation between those frequency factors. Evidence for signficant enlargement of craters over projectile cross sectional areas suggests that rates of thermal conduction must be comparable to, or larger than, rates of target evaporation. If this were not the case. very rapid evaporation would cool target surfaces and preclude formation of craters with diameters two or three times that of the maximum projectile diameters. On the other hand, if rates and frequency factors for evaporation were significantiy smaller than those for thermal conduction it might be possible to have target cooling before extensive evaporation took place with formation of craters that were significantly smaller than projectile cross sections. The general approach of Sigmund and Claussen [7a] can be used to calculate crater volumes but one must keep in mind that thermal conductivity of thin films, activation energies for evaporation from thin films, and energy deposition by cluster ions are all relatively poorly defined in these experiments. The determination of the average size of the fragments sputtered by cluster ion impact is essential if one wishes to use the kinetics of the evaporation process as means of estimating the magnitudes of initial energy densities. Activation energies for carbon atom or dimer or trimer molecule evaporation have been determined to be approximately 8 eV [11,12] but these values are for bulk carbon and may not be accurate for thin films preparations. With these limitations clearly in view the amount of material removed from a cluster impact site can be calculated and compared with observed crater dimensions. The cluster impact is presumed to create a thermal spike at some initial time tO. Material evaporates from the hot surface while the spike volume grows and cools by thermal conduction. At some later time the temperature becomes too low for continued evaporation. The cluster impact is assumed not to deform the target surface; the change in surface profile that occurs during the course of evaporation while craters form is neglected in this analysis as is the energy lost in the evaporation process. The time dependence of temperature is given by a thermal spike model like that discussed above. We have used a constant value of thermal conductivity in contrast to the Sigmund-Claussen treatIII. MOLECULAR ION WECTION

M. W. Matthew et al. / Large energetic cluster impacts on sur/aces

458

r--

ment which assumes the thermal conductivity is proportional to the square root of temperature. A cylindrically symmetrical thermal spike will be considered, with a depth several times that of the radius of the projectile. With this geometry heat near the surface flows primarily outward radially from the center of the spike. The temperature can be considered solely as a function of time and a radial coordinate r. No depth coordinate is considered in the calculation of radial temperature distributions. The depth of the spike is calculated from the projectile energy and an assumed value of d E/dx. The initial temperature distributions as a function of r are, for ease of solution, assumed to be Gaussian,

---

’

(H20)100.H+

01300

keV on 65 i CARBON

300

keV

Llrnll

i

T = T, e-r2/02, with the maximum temperature, To, found by normalizing the energy distribution ia the spike. To is proportional to dE/dx in the cylindrical case, and to c-l, where c is the heat capacity of the target. Temperature distributions as a function of time and distance are then calculated using equations of the form of eq. (1). It is convenient here to replace t in eq. (1) with t’ - tO, where t, = 02/u (a = 4K/c), and t’ 2 t,. The temperature of eq. (1) is substituted in the evaporation rate equation which is integrated over time and the target surface area to obtain the number of evaporated atoms. N, =

/0

m277r drlmdr’NSr+,

e-E/kT.

N, is the number density of carbon atoms in the target surface. As each layer evaporates, the layer below is exposed and in turn starts to evaporate; the number density of atoms available for evaporation is always N,, since the surface is assumed to remain undeformed for purposes of calculation of the evaporation flux. The integral over r can be replaced with an integral over T, and the integral over t’ can be evaluated first. The limits of the time integration are between t0 and

1;

(J= T, I/s -(Y [ T

the result is then

N,vor

TO

/o

dTFTe-

E,k?‘[ ${

:i”“_t;],

This expression can be simplified by substituting x and z defined by the relations kT/E and kT,/E. Thus 2Na ----4-=z NS~,,n~4

2 =dx -e / o x3

,

0

50

100 150 dE/dx (eV/$

200

Fig. 9. The volume of carbon target evaporated a function

of stopping

calculations

power

is calculated as

for a cylindrical

were done for a 100 water

molecule

spike. These cluster ion

impacting a 65 A thick carbon foil at 300 keV. 300 keV would

*o

N e=

IO31

_,,X_

Zdx J0 _e-'/X, x

The integrals can be evaluated analytically and the results are presented in figs. 9, 10 and 11. The plot in fig. 9 shows a calculated value of volume excavated by 100 water molecule cluster ions on thin carbon targets as a function of dE/dx for cylindrical

limit the total number of evaporated

carbon atoms to 3.75 x lo4

if 8 V is required to evaporate each carbon atom. and this value closely matches the approximate of the stopping servation

power

consistent

(dashed vertical

experimental with

volume. Values

the experimental

ob-

lines) are higher than the stopping

power value from fig. 7, the solid arrow.

spikes. The value of the volume of craters experimentally observed is indicated by the horizontal line which intersects the cylindrical spike curve at a value of about 60 eV/A. The value is significantly larger than the D approximately 30 eV/A predicted by stopping power theory. The value of the frequency factor v0 used in the calculations was taken at 5 X 10” /s. A larger value of frequency factor would shift the intersections of the observed volumes with the curves in the figure to lower values of d E/dx but we note that the equation for N, contains the ratio of (Y to y0 and hence we have the ratio of frequency factors in thermal conductivity and evaporation to consider. The effect of reducing or increasing the cluster size is to reduce or increase the dimensions of the thermal spike and the time duration of the volume heated above the threshold temperature for evaporation. Thus the kinetic model can be used to account for the failure to produce visible craters with sufficient energy loss via thermal conductivity. For a

IU.W. Matrhew et al. / Large energetrc cluster impacts on surfaces

particular value of dE/dx and the same total energy larger clusters are expected to give larger craters. The basic question that emerges with the application of the kinetic model is whether one can find a credible fit of experimental observations with a constant value of d E/dx, activation energy for evaporation and frequency factors. We have noted above that the range of values of frequency factors for evaporation is limited by thermal conductivity frequency factors and absolute rates of thermal spike cooling. Thus one cannot have as significant a variation on evaporation rates by the parametric use of frequency factors as with activation energies for evaporation or with evaporation mechanisms. Variation of activation energies for evaporation requires the assumption that species evaporated include higher molecular weight carbon fragments which come off the surface with activation energies considerably different from the

(~20)~~~.

tiCat

300

keV

459

C,, C,,‘or C, fragments which have been determined to have activation energies close to 8 eV. The probability of evaporation processes which require less energy per carbon atom is suggested by comparison of the energy requirement for evaporation of atomic carbon from craters produced by the 150 water molecule 300 keV cluster with the available energy in the projectile. The evaporated volume possible at 8 eV/atom activation energy, given a total energy of 300 keV, is indicated by the horizontal arrow in fig. 10. If one completely ignores energy losses by conduction, 300 keV would produce a crater volume roughly i that experimentally observed if all the carbon came out as atoms. The results suggest that the average size carbon fragment contains at least 3 or 4 carbon atoms and probably is somewhat heavier. With 100 water molecule clusters somewhat smaller craters or holes are generated but here again if any energy is partitioned into thermal conduction carbon molecular fragments must dominate the evaporation process.

on l5OiiCARBON

(H20,,,.

H+

01 175

keV

O” I05

% CARBON

_JT;.;/:///

L/L_.LiL.-.--

I

I 300

keV

+GT

I03

L

0

50

I 500

100

200

dE/dxW/A) 50

Fig. 10. The volume of carbon target evaporated is calculated as a function of stopping power value for a cylindrical spike for a 150 water molecule cluster striking a 150 A thick carbon volume target at 300 keV. The approximate experimental evaporated in this experiment is indicated by the cross hatching. which reflects an uncertainty in hole volume of a factor of two. Below the experimental volume is the limiting value based on the evaporation of single carbon atoms. For this experiment to fit these calculations, it appears that the evaporation of small carbon aggregates has taken place. Again the values of stopping power consistent with the observations were greater than the L-S theory value (vertical arrow).

100

150

200

dE/dxW&)

Fig. 11. The volume of carbon target evaporated is calculated as a function of stopping power value for a cylindrical spike for 0 a 50 water molecule cluster ion impacting a 105 A thick carbon foil at 175 keV. The 175 keV would limit the total number of evaporated atoms to 2.2X104 if 8 V is required to evaporate each carbon atom. The experimental volume evaporated is less than this number, and the values of the stopping powers consistent with the experimental observations (dashed vertical lines) are higher than the value of the stopping power from fig. 7, solid arrow. III. MOLECULAR

ION EIECTION

460

M. W. Matthew et d. / Large energetic cluster impacts on surfaces

In view of the uncertainty with respect to evaporation mechanism it is difficult to come to any conclusions about temperatures and values of d E/dx beyond the recognition that lower limits of temperature must be exceeded if activation energies in the region of 8 eV indeed reflect the barrier to carbon evaporation. With this assumed value the results are still not easily accounted for with a unique value of d E/dx for cluster penetration processes. The calculations suggest that clusters of 100 and 150 water molecules deposit energy in the target at a rate considerably larger than that estimated from Lindhard theory. With smaller clusters i.e. 50 water molecules the value of dE/dx required to account for the carbon transported from the crater is smaller and approaches the theoretical value; see fig. 11.

5. Conclusions Evidence for very high energy densities produced by cluster ion impact on carbon surfaces is obtained from the observation of microscopic holes and craters. The process of cratering, extensively investigated in simulated micrometeorite studies, has been examined not only from the point of view of very high energy density associated with the impact process but from correlation of hole or crater size with the maximum size of plastically deformed projectiles. These correlations and evidence of halos around holes in thicker carbon films support the conclusion that thermal conduction of the excitation energy initially deposited in the target film produces thermal spikes capable of evaporation of significant amounts of carbon in the very short times that elapse before the spikes have cooled to below critical temperatures. The rate of initial energy deposition is estimated to be larger than rates estimated from classical stopping power theory. The enhanced stopping power is attributed to collective or coherent energy deposition from the constituent atoms in the projectile. This enhancement is expected for energy transfer mechanisms that approach hydrodynamic interactions of clusters with very shallow surface penetration. Critical cluster masses and cluster energies have been observed for the formation of visible craters and holes by impact of water cluster ions on carbon films. The surface to volume ratio of a cluster “track” in the solid has been noted as an important factor in the time available for competitive evaporation and conductive cooling processes. Thus smaller clusters approach the critical threshold for crater or hole formation when they generate very small diameter cylindrical tracks which cool rapidly. In addition smaller clusters deposit energy with less “nuclear stopping power enhancement” and produce lower initial temperatures further limiting the extent of target molecule evaporation. Considerable space has been devoted in this report

to attempts

to consider results within the framework of stopping power models. The point that the energy deposited by cluster ions in the target is indeed not in electronic or internal degrees of freedom, initially, in target atoms cannot be overemphasized. The effect of this mechanism of energy deposition is to convert major fractions of projectile energy into sputtering or evaporation of target atoms rather than “heating” of the target. Comparison of the fraction of projectile energy that goes into laser sputtering for example [13,14] and with cluster ion sputtering establishes the point. These considerations indicate capabilities and limitations of technological applications of cluster ion impacts for the generation of very high energy densities and for the preparation of very small craters and holes in targets. Enhanced nuclear stopping power suggests the utility of these projectiles as efficient agents for removal of very thin layers of surfaces by ion bombardment and for possible use in the preparations of surface films with unique properties. nuclear

The authors wish to acknowledge useful and stimulating discussions with Dr. Roger Kelly of the Thomas J. Watson Research Center of IBM, Yorktown Heights, New York, USA.

References

[II H. Dietzel, G. Neukum

and P. Rauser, J. Geophysical Res. 77 (1972) 1375. 121 L. Friedman and G. Vineyard, Comments on At. and Molec. Phys. 15 (1984) 251. [31 J. Jortner, Ber. Bunsenges. Phys. Chem. 88 (1984) 188. [41 R.J. Beuhler and L. Friedman, Nucl. Instr. and Meth. 170 (1980) 309. [51 R.J. Beuhler and L. Friedman, J. Chem. Phys. 77 (1980) 2549. 161 R. Kelly, Radiat. Eff. 32 (1977) 91. [71 (a) P. Sigmund and C. Claussen, J. Appl. Phys. 52 (1981) 990. (b) M. Urbassek and P. Sigmund, Appl. Phys. A35 (1984) 19. enriched isotopes and F31 K.O. Nielsen, Electromagnetically mass spectrometry, (Academic Press, New York, 1956) pp. 68-81. [91 J. Lindhard, M. Scharff and H. Schiett, K. Dan. Vidensk Selsk. Mat. Fys. Medd. 33 (1963) no. 14. [lOI F. Seitz and J.S. Kohler, Solid State Physics 12 (1956) 305. [111 W.A. Chupka and M.G. Inghram, J. Chem. Phys. 21 (1953) 1313. [=I R.E. Honig, J. Chem. Phys. 22 (1954) 126. B.E. I131 R. Kelly, J.J. Cuomo, P.A. Leary, J.E. Rothenberg, Braren and C.F. Aliotta, Nucl. Instr. and Meth. B9 (1985) 329. Nucl. Instr. and Meth. [I41 R. Kelly and J.E. Rothenberg, B7,‘8 (1985) 755.