Mass distributions of ions sputtered by cluster impacts on carbon, copper and gold targets

International Journal of Mass Spectrometry and Zon Processes, 94 (1989) 25-39 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

MASS DISTRIBUTIONS IMPACTS ON CARBON,

R.J. BEUHLER

BY CLUSTER TARGETS

and L. FRIEDMAN

Chemistry Department, (First received

OF IONS SPUTTERED COPPER AND GOLD

25

Brookhaven

13 December

National Laboratory,

Upton, NY 11973 (U.S.A.)

1988; in final form 13 April 1989)

ABSTRACT Results of sputtering studies of carbon, copper and gold surfaces with energetic water cluster ions are presented. Secondary ion products were determined using quadrupole mass analysis of ions generated in the cluster impact process. Clusters containing as many as nearly 3000 water molecules with energies up to 240 keV were used as projectiles. Ion yields in cluster sputtering were shown to be a very small fraction of the total sputtered product. Very similar distributions of secondary ions were determined with a wide range of cluster sizes and energies. Relatively large yields of energetic atomic ions and smaller yields of polyatomic ions with much lower kinetic energies are consistent with a sputtering mechanism with minimal cooling by thermal conduction prior to the sputtering process.

INTRODUCTION

Hypervelocity cluster ions can penetrate solid surfaces on impact and generate high energy density collision spikes. The relatively small surfaceto-volume ratios of these collision spikes limit cooling by thermal conduction and facilitate very rapid ejection of sputtered products [1,2]. This is in contrast to sputtering mechanisms from collision spikes which cool very rapidly by thermal conduction. In the latter case only a very small fraction of the projectile energy is utilized in the sputtering process. For example, Almen and Bruce [3] in studies with 45 keV krypton ions on carbon and copper targets found sputtering yields of between two and three carbon atoms/incident ion and about ten copper atoms per incident ion. With cluster impacts sputtering yields are much larger. 300 keV water clusters sputter between 10000 and 50000 carbon atoms from carbon targets [4]. With approximately 7.5 eV required for the sublimation of carbon atoms and a kinetic energy distribution in the sublimed carbon atoms of the order of 10 eV or more, a sputtering yield of 20000-30 000 atoms per cluster impact would account for most of the projectile energy leaving a small 0168-1176/89/$03.50

0 1989 Elsevier Science Publishers

B.V.

26

fraction to be dissipated in thermal conduction. These very large sputtering yields, considered from the standpoint of an energy balance, indicate a sputtering mechanism which generates significant yields of molecular sputtering products. Mass distributions of secondary ions sputtered from carbon, copper and gold targets were determined to obtain some insight into the nature of molecular sputtered products. We recognized that ionic yields represent a small fraction of the total product and that the correlation of ionic and neutral mass distributions is speculative. However, if both neutral and ion products are generated from very high energy density atomic assemblies, a qualitative correlation between the respective mass distributions is reasonable. The questions of interest in this preliminary survey of mass spectra of cluster-impact sputtered products focus on the relative yields of atomic ions at the low mass end of the spectrum and the much larger species that might be found at the high end of the spectrum. Relative yields of atomic particles measure direct ejection processes and decomposition of high energy density polyatomic fragments in flight during the time required for mass analysis. The detection of diatomic and polyatomic ions establishes either evaporation of these species from collision spikes that have been cooled by thermal conduction or their formation from larger energetic species in unimolecular decay processes after ejection from the solid. Thus the mass distribution of polyatomic species could either reflect the extent of conductive cooling of the collision spike prior to particle ejection or support a shock wave model for the sputtering process [2,5,6]. EXPERIMENTAL

Details of the methods used for the generation, mass analysis and acceleration of water cluster ions used in this work have been published [7]. Water cluster ions were prepared by free jet or nozzle expansion of a weakly ionized plasma of water vapor in helium carrier gas. The relatively narrow mass distribution was then subject to mass analysis using a low frequency quadrupole mass analyzer. The product mass analyzed beam was then accelerated with a Cockroft-Walton [7] to energies as high as 300 keV and impacted on target surfaces in the high voltage terminal. Secondary electron yields from the bombarded targets were determined and provided an additional basis for the identification of the projectile ions at the impact surface [8]. Mass analysis of secondary ions was initially attempted using time-of-flight (TOF) techniques. This approach to mass analysis failed to provide results with sufficient resolution to identify masses in the lower molecular weight

27

region of the spectra where the most abundant ion yields were found. This failure was due in part to limitations arising from working in a limited space at voltages in excess of 200 keV in the high voltage terminal and in part to initial angular and kinetic energy distributions of secondary ions and their metastability. The TOF studies established upper limits of the masses of secondary ions produced from the respective targets. Resolved mass spectra were obtained with a quadrupole mass analyzer. Targets were set at a 45” angle to the axis of the primary cluster beam. Secondary ions were collected at an angle of 45 o to the plane of the target surface or 90” with respect to the axis of the primary beam. The quadrupole mass analyzer was constructed from an assembly of l/4 inch rods and operated with Extrel power supplies. Two mass ranges were investigated using supplies operating at 5.1 and 1.5 MHz, respectively. The higher frequency served for the analysis of ions with m/z ratios between 1 and 150 and the lower frequency covered the mass range of approximately 50-1200. Ions were detected with an off-axis channel plate secondary electron multiplier which was floated at 3500 eV to increase sensitivity to higher molecular weight ions. The multiplier was used in a pulse counting mode to facilitate the comparison of integrated mass analyzed ion currents. with primary projectile ion currents measured with a picoammeter attached to the target. Experiments with a Faraday cup set very close to the target, in place of the quadrupole mass analyzer, were used to obtain absolute ion yields with 240 keV primary beams. These measurements of the largest ion yields were used to calibrate the collection efficiency of the quadrupole mass analyzer. The picoammeter signals measuring primary beam intensities had to be corrected for secondary electron emission from the target. This was done using independently obtained secondary electron data [8].

DISCUSSION

OF RESULTS

Relative ion yields A plot of the ratio of the integrated yield of mass analyzed ions to the projectile ion intensity is given in Fig. 1. Faraday cup experiments designed to measure the total secondary ion yields show that roughly 90% of the secondary ion yield is lost in mass analysis when the quadrupole mass analyzer is operated under conditions of minimum resolution and maximum transmission, i.e. the conditions operative for the collection of data presented in Fig. 1. With carbon sputtering ratios estimated at between 10000 and 50000 carbon atoms [9] per water cluster impact at a projectile energy

28

-61v

I0

CLUSTER

1OKV 1OOKV ACCELERATION ENERGY

Fig. 1. Ratios of integrated secondary ion yields produced by impact of water cluster ions on a carbon target to primary ion beam intensities. Secondary ions were mass analyzed with a quadrupole mass analyzer and detected with a channel plate off-axis multiplier operated in a pulse counting mode. The currents derived from the counts s-l were ratioed to primary ion currents measured with a picoammeter and corrected for secondary electron yields from the carbon target. Faraday cup measurements taken with geometry designed to efficiently collect secondary ions established the collection efficiency of secondary ions at approximately 10% for primary beams with 240 keV kinetic energy.

in excess of 200 keV, the ratio of sputtered ions to sputtered neutral product is much less than 1%. The increase in ion yield with increasing ion energy parallels the increase in energy deposited in electronic stopping processes with ion energy. However, the velocity dependence of electronic stopping is not reflected in the data. The much larger clusters containing nearly 3000 water molecules fall on the same curve as the smaller 80 molecule projectiles. Differences in the respective sizes of thermal spikes and rates of cooling are important in determining the probability of ion ejection. The identity of the curves on which the lighter and the heavier projectiles fall may be fortuitous and certainly merit additional study. The results in Fig. 1 are presented to prove the relative small magnitude of ion yields in cluster impact sputtering. Relatively low yields of sputtered ions reflect low ion densities in surfaces of hot collision spikes. Under these circumstances, there is a higher probability

29

of sputtering equal.

ions as larger

molecular

fragments,

if all other

factors

are

Mass spectra Complete mass spectra obtained from cluster impacts on carbon, copper and gold targets are presented in Fig. 2. These spectra were taken under low resolution conditions to minimize observational problems in the detection of

CARRON TARCKT

E(H*O),;&

12

kl

4a

f.?O

a4

166

240

is.2

h-e”

%?a

264

MASS

cui COPPER TARGET E(II*O),+&240 KeV

::

2;

COLD TARGET

H(rr,O);,,at240 KeV

Au;

s 2

AU> Au;

k

Au; do0

400

600

r a00

Au; AUS too0

1200

MASS

Fig. 2. Ion mass distributions of products of 240 keV water cluster impacts on solid targets, carbon, copper and gold. All data were taken with quadrupole resolution settings identical to those used for measurements of ion yield shown in Fig. 1, which were the lowest resolution settings or highest transmission compatible with complete resolution of the masses shown.

30

atomic ions with high kinetic energy and to provide for the maximum efficiency of collection of the highest molecular weight ions. The mass distributions of secondary ions generated by cluster impact are of interest in assessing the potential of energetic clusters as projectiles for the generation of secondary ion mass spectra and for the study of energy transfer in the collective interactions of high velocity cluster atoms with atoms in a solid target. The relative abundances of the energetic C+ ions are somewhat underestimated in the spectrum shown because of the effect of kinetic energy on the collection efficiency of these ions. The results suffice to show that with the targets studied the atomic ions are abundant reaction products. A crude extrapolation or correction of the effect of kinetic energy on collection efficiency of C+ ions supports this conclusion for the carbon spectrum in Fig. 2. There is evidence of more abundant yields of ions containing odd numbers of atoms. This is consistent with theoretical evidence for the greater stability of odd numbered clusters and experimental evidence in studies of clusters produced in supersonic expansions of species generated in laser-induced plasmas [lo]. The higher molecular weight species produced in laser-induced expansions are not observed in the cluster-impact secondary mass spectra. The secondary spectra reported in this paper are not formed from species cooled with a carrier gas. Furthermore, the pressure gradient near the target surface is such that extensive growth of the type possible in jet expansion processes is not possible in our experiments. The mass distributions observed 10e6 or 10e5 s after cluster impact owe their character to unimolecular decay processes which are sensitive to the chemistry of the respective systems studied. Lifetimes of ions ejected from collision spikes can be calculated using the classical Rice-Ramsberger-Kassel (RRK) rate equation [ll].

where n is the number of internal degrees of freedom, E the threshold energy for decomposition, v the frequency factor, and E the excess energy in the polyatomic fragment. With minimum time requirements for mass analysis and detection of 10e6 s and frequency factors for unimolecular decomposition of approximately 1013 s-l, the energy dependent term in the RRK equation must be a fraction with an absolute value smaller than lo-’ to give rate coefficients less than lo6 s-l and ion lifetimes greater than 10e6 s. The RRK equation can be rewritten in the form

where p is the energy density.

p is defined

as the ratio of the excess energy

31

to the number of atoms in the fragment undergoing unimolecular decomposition. For larger fragments, p is approximately equal to E/(n/3). For energy densities as small as twice threshold energies, rate coefficients of the order of 2 X lo’* s-r are calculated for values of n between 12 and 10000. The fact that excess energy scales with the number of atoms in the fragment ejected from a collision spike makes these fragments prone to atomization prior to detection unless the atomic assembly in the solid has been subjected to considerable cooling by conduction. The transient nature of the very high collision spike energy densities plays a critical role in the determination of mass distributions of sputtered products. For larger secondary clusters, with 20 or more atoms, energy densities must be reduced to values less than roughly 20% of threshold energies for decomposition to produce detectable polyatomic fragments. In the case of carbon fragments, energy densities must be less than about 1 eV. Differences between mass distributions from carbon targets and copper or gold targets can be accounted for by the greater stability of the polyatomic fragments of carbon, i.e. higher threshold energies for decomposition. Ackerman and coworkers [12] have shown a correlation between the bond energies of homonuclear diatomic molecules and the heats of sublimation for 40 elements including carbon, copper and gold. It is reasonable to assume that a closer correlation will hold for polyatomic clusters because of the similarity in bonding in solid lattices and in polyatomic clusters of the same element. Dependence

of spectra on projectile

mass

We noted above that unresolved TOF mass spectra were insensitive to projectile mass and energy. This was found generally to apply to mass distributions determined with quadrupole mass analysis. Spectra obtained with projectiles containing 73, 80 and 990 water molecules with 240 keV energy are very similar in spite of the tenfold variation of mass and over threefold variation in velocity (Fig. 3). Only a portion of the low molecular weight spectra is presented to show a representative, detailed portion of the ion mass distribution. The results with higher molecular weight secondary ions were found to be very similar to those presented in Fig. 2. Figure 3 (bottom) contains a partial mass spectrum of carbon ions produced by a projectile beam that was more intense than that generally used in these studies by a factor of 100. The high intensity (lop9 A), irradiation was made in an attempt to determine the origin of the hydrocarbon ion fragments observed in these spectra. The possibility of loading the carbon surface with hydrogen from the cluster projectiles was considered as an alternative to the generation of hydrocarbon peaks from a background of pump oil on the target surface. The ambient pressure in the ion chamber

Ii

2i

48

60

CARBON TARGET Ii(ElO)&ut

240

KeV

CARBON TARGET a(ir,o);, at 240

Key

I

ri

2;

ri

6b

ML Fig. 3. Partial secondary ion mass spectra generated by impact of 240 keV water clusters on a carbon target. The upper two spectra show very similar mass distributions produced by clusters varying in size by a factor of more than ten and in velocity by a factor of roughly three. The upper spectra show considerable amounts of hydrocarbon ions in addition to the atomic carbon and polyatomic carbon fragments. The bottom spectrum was obtained by increasing the primary ion current by roughly two orders of magnitude to 10e9 A. This higher intensity primary beam sputtered at a rate faster than the rates of adsorption of trace hydrocarbon impurities in the vacuum system at ambient pressures of approximately 1 x lop6 torr.

was less than 10e6 torr. The major contributors to this background pressure were assumed to be water, oxygen and nitrogen. The suppression of hydrogen containing ions with increased beam intensity was proof that the hydrocarbon ions were indeed formed from the steady state adsorption of background hydrocarbon molecules. The generation of very similar mass spectra of carbon fragments established the point that the hydrocarbon contaminants were not contributing extensively to the carbon spectra.

33

The insensitivity of mass distributions to projectile size and velocity is taken as evidence for the generation of collision spikes with very similar energy densities by these projectiles. Faster or more energetic projectiles penetrate into deeper layers of the target. They give larger sputtering yields but transfer energy at rates very similar to slower projectiles. This is predicted for isolated two-body energy transfer processes by classical nuclear stopping theory [13]. We shall assume that on impact, cluster atoms lose energy to target atoms at rates calculable from classical nuclear stopping theory [13]. Energy densities were calculated by taking the energy loss per target layer from each projectile atom as if it were transferred to a single target atom. The energy transfer processes in cluster penetrations of targets are much more complicated than interactions of isolated projectile atoms with isolated target atoms but the net effect of the simultaneous interaction of n projectile atoms with n target atoms in a given layer of target can be modeled as the sum of a set of two-body projectile-target atom interactions. No consideration is given to the possibility of several cluster atoms in successive layers of a cluster assembly interacting with the same target atom or to the effect on the stopping power of increased target density resulting from compression of the target by cluster impact. Both of these effects would tend to increase the estimated energy densities from our lower limit estimates. The important features of energy densities determined almost exclusively by nuclear stopping interactions is the magnitude of the energy densities with respect to the magnitudes of binding energies, and the relative insensitivity of energy densities to projectile velocities over a wide range of velocities. Energy densities are estimated to be roughly an order of magnitude larger than heats of sublimation or binding energies of carbon, copper and gold, respectively. A plot of the velocity dependence of the rate of the energy loss of oxygen atoms penetrating carbon targets is presented in Fig. 4. With the thickness of an atomic layer of carbon approximately 2.2 A, maximum rates of energy loss of about 75 eV atom-’ result. A significant reduction in the relative yields of atomic and diatomic carbon atoms is found with 240 keV projectiles containing 2728 water molecules (Fig. 5). With projectile oxygen atom energies less than 100 eV the curve in Fig. 4 predicts much lower rates of energy deposition which would radically alter sputtering rates and mechanisms. In addition, the less energetic oxygen atoms generate much shallower collision spikes with larger surface-to-volume ratios available for thermal conduction. The spectrum at the top of Fig. 5 begins to show oxygen containing ions and smaller relative yields of bare carbon fragment ions. The low velocity ion beam is limited to interaction with the very top layers of the target while higher velocity beams create collision spikes penetrating to depths of ten or more layers. Figure 5 (middle) shows results obtained with the 2728 water cluster ions

34

NUCLEAR STOPPING POWER, OXYGEN ON CARBON

60

I

40

-

I

I

I

I

I

I

I

I

I

2

3

4

5

6

7

0

OXYGEN

9

VELOCITY/107cm/sec

Fig. 4. Energy deposited in stopping of high velocity oxygen atoms calculated using Lindhard theory. The flat line is calculated using an approximation of Nielsen and the more accurate Lindhard curve is based on the Thomas-Fermi approximation for the interaction of isolated atoms in particle penetrations into solids. This plot shows the relative insensitivity of energy densities in collision spikes to projectile velocity over the velocity range of our experiments. The relative constancy of energy densities account for the insensitivity of mass distributions to projectile velocity in these experiments.

with kinetic energy reduced to 100 keV. This spectrum shows evidence for the reflection of protonated water molecule ions not seen with the higher velocity projectiles. Oxygen atoms in these clusters have less than 40 eV kinetic energy, insufficient to penetrate several layers of carbon surface. The failure to observe atomic carbon ions is consistent with the formation of a very shallow collision spike with a very low energy density. Low energy hydronium ions or more highly water-solvated protons would not be expected to participate in endothermic charge transfer processes leading to the production of gaseous carbon ions. The failure to observe oxygen or oxygenated species among secondary ions generated by more energetic clusters raises interesting questions that merit further study. The bottom spectrum in Fig. 5, showing secondary ions produced by the impact of cluster oxygen atoms with less than 30 eV per oxygen atom, begins to show evidence of surface chemical reactions between the hydrocarbon surface contaminants and also the reflection of hydronium ions with no detectable bare carbon atomic or fragment ions. Ion transmission in quadrupole mass analyzers varies with resolution settings which control the ratio of r.f. to d.c. voltages on the quadrupole analyzer rods. Variations of these voltages have the effect of varying the aperture through which ions must pass for mass analysis. Quadrupole mass analyzers are considered to be insensitive to ion kinetic energy provided that

35

CAREON TUGIT

NH2 o&q at

100

rev

Fig. 5. Spectra obtained with lower velocity primary ion beams incapable of deep surface penetrations or deposition of energy densities comparable to those deposited by much smaller projectiles with the same total kinetic energy. These spectra show the transition from the interactions with the bulk of a carbon target, at least ten atomic layers and the top surface layer. Conductive cooling reduces the available energy density in the “shallow collision spike”. The velocity of the 9.1 keV projectile responsible for the bottom spectrum is approximately 1.7 X lo6 cm s-l. With the oxygen atom kinetic energy of approximately 30 eV, nuclear stopping energy loss theory predicts a penetration of only one atomic layer. The probability of the observation of Ha0 + increases with decreasing projectile velocity (see lower spectrum).

ion residence times in the analyzer rod systems are sufficient for several r.f. cycles. This “insensitivity” to kinetic energy is generally observed with electrically accelerated ions with velocity components parallel to the axis of

36

stable ion trajectories. However, if ions are generated with significant radial velocity components, the effect is similar to the variation of d.c. rod voltages to increase resolution or decrease ion transmission. So far we have no information available on the angular distributions of sputtered products, but if atomic carbon is formed with excess kinetic energy with velocity components perpendicular to the axis of ion collection then high resolution quadrupole mass analysis would disfavor collection of the more energetic atomic fragments. Spectra presented in Fig. 6 show the effect of varying the resolution settings on the low molecular weight portion of the secondary ions from carbon targets. Similar results (not shown) were obtained with copper and gold targets. Atomic ions are not efficiently collected in low transmission (high resolution) studies. The higher kinetic energy distri-

CARBON TARGET R(H20&,ai 250 KeV LO" TR4NSUISSION

CARBON TARGET H(rr,O&.t 240 KeV HIM TRANSMISSION

MASS

CARBON TARGET H(rr,O);,ot 240 Kd’ LOT TRANSMISSION

nL

CARBON TARGET H(HpO);~at 240 KOV HICE TRANSMISSION 20 VOLT MTARDATION

60

MASS

Fig. 6. Low molecular weight spectra of secondary ions from carbon targets showing the effect of increased resolution on the transmission of atomic and polyatomic carbon ions. The higher kinetic energy atomic ions are suppressed because of velocity components, perpendicular to the axis of ion collection, large enough to remove these ions from stable trajectories through the analyzer. With lower d.c. rod voltages, lower resolution and higher analyzer transmission, atomic ions are collected much more efficiently. The spectra on the right were taken with much higher analyzer transmission but with 10 and 20 V retarding potentials on the analyzer rods. These conditions sufficed to filter the lower kinetic energy polyatomic fragments from the spectra.

37

butions of atomic species and to a lesser extent diatomic species become apparent when retarding potentials are applied to the quadrupole rod system. Retarding potentials of 20 eV filter most of the polyatomic fragments and permit the transit of a significant fraction of energetic atomic ions. The effects of increased resolution and retarding potentials show that atomic carbon ions are formed with significant axial and radial velocity distributions. The kinetic energy distributions of the higher molecular weight fragments are much lower than those of the atomic and diatomic ions. These results point out the observational problems in the determination of mass distributions of sputtered ions. The spectra presented, unless otherwise noted, were taken under the lowest resolution conditions compatible with the determination of resolved spectra. Some distortions remain but the results are considered to be a reliable representation of mass distributions which may slightly underestimate atomic ion yields. The extent to which ion yields reflect neutral product yields can not be answered without data on the relative rates of evaporation and unimolecular decomposition of the respective species. Kinetic energy distributions of products are also needed to establish the magnitude of the energy densities of their precursors. The relatively high kinetic energies of atomic ions indicate their formation in processes insensitive to energy dependent terms in rate equations. Under these circumstances similar relative yields of neutral atomic products are expected. In addition to other kinetic factors, the probability of the formation of a C, + ion is proportional to n when there are very small concentrations of ions in the collision spike. The distribution of polyatomic products obtained by dividing the respective C,,+ species by n is the distribution of neutral species that would be produced if rate coefficients for the production of C,, and C,,+ were equal. Corrected distributions are presented in Fig. 7. The dominance of atomic yields is more pronounced but there is, at least in the case of carbon, enough polyatomic product, with lower heats of sublimation per atom than atomic carbon, to establish a balance between the projectile energy and the energy required for sputtering 191. CONCLUSION

The results presented above can be summarized as follows: Carbon targets produce ions containing the largest numbers of atoms followed by copper and then gold. In all the spectra there appear to be larger yields of ions containing odd numbers of atoms. In addition, mass distributions have been found to be insensitive to projectile mass and velocity over a wide range of values. This insensitivity has been correlated with energy deposited via nuclear stopping processes and is limited to a range of projectile

38

CAREON~

TARCKT

R(iizO),wct 110

KeY

COPPKR TARGET E(E20);ooat 340 KeV

NUMBER

OF ATOMS

x ,h

IN

FRAGMENT

GOLD TARGKT R(rI,O);,at 240 KS?”

2 2 5

N”hfiER

:F

AT&

;N

FRtlCMEi’T

Fig. 7. Mass distributions of neutral products yields calculated from ion mass distributions using the assumption that the rates of neutral fragment sputtering paralleled the relative rates of ion fragment sputtering. This is tantamount to the assumption that small differences in fragment ionization potentials had little effect on the relative rates of ion desorption from systems with very high energy densities. The basis for obtaining the data in this figure was recognition of the very low density of ionization in the collision spike and the assumption that the probability of finding a C + ion in a molecular fragment increased linearly with the number of atoms in the fragment.

velocities which permit target penetration and nuclear stopping energy transfer. Evidence has been presented for the production of atomic ions with much higher kinetic energies than the polyatomic products. Ion yields have been determined and are very small fractions of the total sputtering yields. The results obtained so far are consistent with the production of a major fraction of the sputtered products from a collision spike that has undergone insufficient conductive cooling to produce stable high molecular weight

39

cluster ion products. The dominance of atomic sputtering products with relatively high kinetic energy taken with much lower kinetic energy polyatomic species supports the conclusion that there is extensive sputtering of polyatomic products followed by gas phase unimolecular decomposition reactions. ACKNOWLEDGEMENTS

This research was carried out at Brookhaven National Laboratory under contract DE-AC02-76CH00016 with the U.S. Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. REFERENCES 1 J. Michl, Int. J. Mass Spectrom. Ion Phys., 53 (1983) 255. 2 I.S. Bitensky and E.S. Parilis, Nucl. Instrum. Methods Phys. Res. B, 21 (1987) 26. 1961 Pergamon 3 0. Almen and G. Bruce, Trans. 8th Natl. Vacuum Symp., Washington, Press Inc., New York, 1961, Vol. 1, p. 245. 4 R.J. Beuhler and L. Friedman, unpublished work. 5 Y. Kitazoe and Y. Yamura, Radiat. Eff. Lett., 50 (1980) 39. 6 J. Sunner, M.G. Ikonomou, and P. Kebarle, J. Mass Spectrom. Ion Processes, 82 (1988) 221. 7 R.J. Beuhler and L. Friedman, J. Chem. Phys., 77 (1982) 2549. 8 R.J. Beuhler and L. Friedman, J. Appl. Phys., 48 (1977) 3928. 9 M.W. Matthew, R.J. Beuhler, M. Ledbetter, and L. Friedman, Nucl. Instrum. Methods Phys. Res. B, 14 (1986) 448. 10 G. Seifert, S. Becker and H.J. Dietsze, Int. J. Mass Spectrom. Ion Processes, 84 (1988) 121. 11 R.E. Weston and H. Schwarz, Chemical Kinetics, Prentice Hall, Englewood Cliffs, NJ, 1972, p. 128. 12 G. Verhaegen, F.F. Stafford, P. Goldfinger and M. Ackerman, Trans. Faraday Sot., 58 (1962) 1926. 13 J. Lindhard, M. Scharff and H.E. Schiott, K. Dan, Vidensk. Selsk. Mat. Fys. Medd., 33 (1963) 14.