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Effect of temperature on the sputtering yield of copper
Surface Science 0 North-Holland
55 (1976) 573-588 Publishing Company
EFFECT OF TEMPERATURE
ON THE SPUTTERING
YIELD OF COPPER f
H.M. WINDAWI * Department Received
of Physics, University of Delaware, Newark, Delaware I971 1, USA
19 August
1975; manuscript
received
in final form 23 January
1976
The effect of temperature on the sputtering yield of copper for low energy argon ion bombardment is investigated. Experimentally, a phase sensitive technique utilizing the spectroscopic emission of sputtered particles is discussed. Analytically, the Langberg model for the sputtering yield is expanded to include the effect of temperature. Atoms of the bombarded surface attain a steady state distribution in the number of their bonds. Changes in either the temperature or the bombardment parameters result in changes in the distribution leading to variations in the sputtering yield. (111) and (110) single crystal and polycrystalline copper surfaces are investigated. Reasonable agreement is obtained between experimental and analytic yield values. The (111) surface shows the largest decrease in yield with an increase in temperature.
1. Introduction The effect of temperature on the sputtering yield was investigated by many authors. The discrepancy in the published data makes it worthwhile to consider the effect of temperature on the factors that influence the sputtering yield. An increase in temperature leads to an increase in the vibrations of atoms about their lattice sites. If one considers a collision sequence to be moving along a closepacked direction, the increased amplitude of the vibrating atom causes an increase in the magnitude of the focussing parameter [l] so that the focussing range is shortened. The transfer of momentum along this direction becomes less efficient. This implies that energy is dissipated in the lattice before a sequence can reach the surface, and hence the sputtering yield is decreased as the temperature is increased. Calculations by Sanders and Fluit [2] showed that the dependence of the total sputtering yield on the focussed collision range was weaker than a direct proportionality. A similar conclusion was reached by Nelson et al. [3]. Damage produced by the bombardment may be decreased by increasing the tem‘rS upported in part by the National Science Foundation. * Present address: Department of Chemical Engineering, Delaware 19711, USA.
University
of Delaware.
Newark,
574
H.M Windawi/Effect of temperature
on sputtering yield
of capper
perature. This can affect the collision by minimizing the defocussing of the collision chains (caused by defects) and increase the efficiency in the transfer of momentum to the surface, On the basis of this argument, the sputtering yield may increase with an increase in temperature. However, interstitiais and vacancies were found to be mobile even at low temperatures [4] so that the defects were annealed out rather quickly [5]. This effect can, therefore, be discounted, particularly for the case of copper, Harrison et al. [Gf, from computer simulation of the sputtering process, Stuart et al ~ [Tf , from the energy spectra of sputtered atoms, and Lehmann and Sigmund [g], from analytical considerations, concluded that sputtering is a surface correlated effect. More recently [9], it was concluded that the focusson contribution to the total sputtering yield accounts for less than 30%. At low energies the fraction can be smaller, since the penetration depth is small [8] and the energy is dissipated before it is focussed backwards. An increase in temperature may lead to a decrease in the transparency of the surface to the incoming ion. Atoms below the surface layer become more exposed to the bombarding ion due to the increased vibration of the atoms. This transparency picture was explained in terms of dechanneling [lo] increase with temperature leading to an increase in the sputtering yield. This effect is, however, more relevant to medium and high energy sputtering, whereas our interest lies in the low energy range. Temperature increase may cause a decrease in effective binding energy of surface atoms [ 1 l] due to the increase in their vibrational amplitude. Surface atoms need to receive a proportionately smaller amount of energy in a collision to be ejected from the surface. This effect is small, however, as the increase in amplitude is not enough to make the effect appreciabIe. Under low energy bombardment at normal incidence, a monolayer may be sputtered away from the surface each second. Thermal activation of migration of surface atoms leads to surface rearrangement. For such a condition activation events are orders of magnitude more frequent than sputtering events [5]. The bombarded surface changes its structural characteristics between two bombarding events due to thermal activation [ 12j. The surface? however, may be considered to be in a steady state condition when sputtered at a given temperature, beam current density and energy. On this premis, we have investigated the effect of temperature on the sputtering yield and the experimental and analytical results are presented.
Sputtering of the samples was carried out with Ar” ions drawn from a magnetically confined dc plasma by biasing the target negatively with respect to the plasma potential [ 131. The sputtering yield was determined by weight loss and spectroscopic measurements. Weight loss measurements were made for one-hour intervals. The
H.M. WindawilEifect of temperature
on sputteting yield of copper
515
length of the sputtering time was chosen so that constant plasma conditions were maintained during the measurements. In the spectroscopic technique, the characteristic emission of the sputtered particles was monitored and analyzed as a function of other parameters. In this technique a fraction of the sputtered atoms, about 10-4-10-3 became excited as they passed through the plasma. The particle excitation resulted from impact by electrons from the electron beam that sustained the plasma. Characteristic emission of the atoms resulted from their radiative de-excitation. Light extracted from the sputtering chamber was mechanically chopped and focussed onto the entrance slit of a 0.5 m scanning monochromator (- 1 A resolution). The signal was processed by a photomultiplier, a lock-in amplifier and a chart recorder (fig. 1). The strongest emission lines of Cu are those of wavelengths 3248 and 3274 A [ 141. These lines were strongly absorbed by the bell-jar and were at about the limit of response of the detector. An order of magnitude weaker lines that lie in the visible range were chosen. In particular, the lines 4023,4063 and 5 106 A were monitored. Since argon was the arcing gas, argon lines were numerous [ 141. Identification of the lines was sometimes difficult. The presence of the copper lines, however, made it possible to identify the argon lines. The presence of argon lines had two advantages. One was to monitor plasma instabilities and the other was to normalize the copper lines with respect to them. Normalization was necessary as changes in the plasma gave rise to variations in the copper signal that were not dependent on the sputtering yield.
CHOPPER MONOCHROMATOR
POLE
MAGNET
PHOTOMULTIPLIER
+ TO VACUUM
PUMPS
I SIGNAL
1. Schematics of the set-upused for monitoring the spectroscopic emission of sputtered particles. Fig.
RM. Windawi/Effect of temperature
516
on sputtering yield of copper
The intensity of an emission line was taken to be proportional to the number of sputtered atoms passing through the plasma. Analysis of the variation in the intensity of a particular line as a function of time, ion energy and target temperature allowed for the determination of relative sputtering yield values as a function of those parameters. Absolute values could not be determined since the excitation crosssections were not known. The relative values were normalized, however, to those obtained from weight loss measurements. Measurements of the sputtering yield variation with temperature were made when the target reached a constant temperature during its sputtering. For these measurements, the target was preheated for about an hour for outgassing purposes.
3. Reklts Fig. 2 shows a monochromator
scan of a section of the emission spectrum ob-
I
4060
4070 WAMLENGTH
4060
I
4050
(A”)
Fig. 2. Part of an emission spectrum showing the relative intensities of copper and argon lines. The copper line resulted from atoms sputtered from a (1OO)Cu surface by 250eV Ar+.
H.M. WindawijEffect of temperature
on sputtering yield of copper
577
I e
Q
50
I
I
100
150
I 200
I
250
I
30 IO
TARGET POTENTIAL (‘4
Fig. 3. Variation of the sputterer yield and target current with the applied potential. The reiative yield values were obtained from the int&ities of the 0.1 I 5106 A line.
served. Fig. 3 shows the dependence of the ionic current density on the potential applied to the target. The figure also shows the dependence of the sputtering yield on the applied potential. The sputtering yield was caiculated by dividing the intensity of a copper emission line (5 106 A) by the ionic current to the target and normalizing the values at 300V. The shape of the yield curve is similar to those obtained by Stuart and Wehner [ 151. Fig. 4 shows the yield versus applied potential curves for three emission lines of copper. The relative intensities of the lines were normalized at 300 V. The figure substantiates the assumption that the sputtering yield may be taken to be proportional to the intensity of an emission line. The time dependence of the sputtering yield was studied by monitoring the intensity of a copper line with sputtering time. Fig. 5 shows the changes that resulted from sputtering a Cu polycrystal. It can be seen that the yield had almost doubled as the sputtering time was increased from zero to twenty minutes. After about twenty
578
H.M. Windawi/Effect of temperature on sputtering yield of copper
B
0
e 1.0 -
8
0
0
I
I
1
I
1
200
100 TARGET
POTENTIAL
I 300
(VI
Fig. 4. Vocation of the sputtering yield with the applied potential. The yield values were obtained from the intensities of the three copper lines; 5 1068 (circles), 40638 (squares), and 4023 p1 (triangles). Yield was normalized to weight loss value at 300 eV.
minutes, the yield was seen to remain constant. Such changes were not observed for Cu monocrystals, namely the (111) and (100) surfaces. For those monocrystals, the yield was seen to reach the high values within one to two minutes. Fig. 6 shows the variation of yield with temperature for a Cu polycrystal. The spectroscopic data (triangles) are shown normalized to data obtained from weight loss measurements at the high temperatures studied. It can be seen that the yield decreased as the temperature was increased. Fig. 7 shows the temperature effect that resulted from the sputtering of a (100) Cu crystal. Each data point was an average of three measurements, each of which was normalized with respect to Ar. The lines involved were Cu 4063 and Ar 4053 8. The yield was seen to decrease by about 14% when the temperature was increased from about 500 to 800 K. Some of the polycrystals that were sputtered gave rise to spot patterns that deviated from the expected cosine distribution [ 161. Fig. 8 shows a pattern obtained
H.M. Windawi/Effect
of temperature
on sputtering yield of copper
519
I
/”
/
/
d
1
I
IO
20
SPUTTERING Fig. 5. Development
of the sputtering
30 TIME
yield of polycrystalline
(min.) copper
with sputtering
time.
from a polycrystal superimposed on that obtained from a (111) single crystal. The polycrystalline pattern was of a ring structure where the rings were formed at angles that corresponded to those of the spots obtained from the (111) crystal. The polycrystal that gave rise to the pattern of fig. 8 was the same one that showed a decrease in the sputtering yield with an increase in temperature. The significance of such a correlation will be discussed later.
4. Discussion 4.1. Swface cleanliness Initial values of the sputtering yield (as determined by weight loss) at about room temperature were low compared to those at higher temperatures. This suggested that surface impurities must be sputtered away before the bombarding beam could encounter surface atoms. The change in the yield as a function of the sputtering time was exhibited in fig. 5. This effect was found to be associated with the sputtering of
580
H.M. WindawijEffect of temperature
on sputten’ng yield of copper
iI
1.4
I.2
I.C
I
I
I
I
600
650
700
750
TEMPERATURE
ioK)
Fig. 6. Effect of tem~rature on the sputtering yield of a p~l~cr~sta~ine copper sampie; (o) weight loss, (5) spectroscopic measurements.
500
600 TEMPERATURE
700
800
(OK1
Fig. 7. Effect of temperature on the sputtering yield of (100) Cu surface.
H.M. Windawi/Effect of temperature
on sputtering yield o,f copper
581
,_.--
n
directions
0
G12>
directions
8. Ejection patterns resulted from 300 eV Ar+ sputtering of a copper poiycrystai (rings) and an (111) copper surface (hatched). The patterns are shown fitted to spots obtained from stereographic projection of the copper lattice on a (111) plane.
Fig.
polycrystals but not with single crystals. This can be explained by the preferential contamination of grain boundaries 1171. Sputtering from the grain boundaries does not take place until the impurities are sputtered away. The implication of this is that weight loss measurements are not reliable. The discrepancy in the published data supports this conclusion. Yield values of 1.O [ 181, 1.3 [ 121, and 1.55 [ 191 were reported for Cu polycrystals sputtered with 300eV Ar+ ions. During sputtering, the surface can be maintained dynamically clean if the rate of removal of surface atoms is made faster than the rate of contamination. Background pressure of about 10e6 torr and current densities of about 8 mA/cm2 (experimental conditions) are adequate to maintain the surface dynamically clean [S] . 4.2. Surface condi tiun Sputtering of a surface results in the formation of surface vacancies and interstitials. The latter are considered to annihilate a substantial fraction of the vacancies so that dynamic surface vacancy concentration is too small to significantly influence the general ejection behavior [5]. This is supported by the fact that preferential ejection patterns obtained from the sputtering of monocrystals do not disappear in a wide range of temperatures, indicating that the ordering of the surface is retained under ionic bombardment [20]. During its bombardment, the surface is not planar since atoms are ejected continuously from it. The surface layer is generally three-dimensional, and its characteristics are determined by the equilibrium distribution of occupied lattice sites. The equilibrium distribution is governed by the distributior~ of ejected surface atoms and
by the thermal activationof tlwmal mig~a~on. For a part&&r surface condition, surface atoms attain a dist~b~~tiou in the number of their bonds, The number of bonds range from a maximum (with binding energy of -4.6eV ]12.21]) to a minimum (with bindiag energy of -25 eY ]l2] >. The surface c~nd~t~o~ is thus expected to ~~~ue~~e the s~ut~e~~~g yield since an atom must overborne its b~~d~~g In order for it to be ejected from the surface.
Thermal activation for the migration of surface atoms of copper on a copper surface has an average activation energy of about 0.5 eV [S, 12, ZZ]. This ~orr~~~nds to about I O6 jumps each second for a surface atom at 350 R. In a sputtesirig experiment, such as discussed here, this means that a surface atom makes about IO5 jumps befom it is sputtered. Thus, a surface atom will have ample time for migm tion to an ~~~~ge~~~~~~most favorable site before the next atom in the neighborhood is sputtered. The migration of an atom from one site to another is equivalent to the ~~a~~Q~ of a vacancy in a reverse order. Similar to itnneahng processes, a steady-state s~u~te~~g condition can be set up where the number of atoms attached to the surface by i bonds is constant in time. i.e,:
One may denote the number of bonds of a surface atom as N and let A$ and N-I, be, res~~t~v~~y, the rnax~un~ and minimum numbers of surface bonds. These atoms have sputtering thresholds denoted by E, and &, respectively. The sputtefing threshold energies are, to a first ~~~rox~rnatio1~~ ~roportio~ai to the number of bonds of surface atoms [23]. Since it is reason;zbte to assume that the activation energ for surface ~~atiol~~ Eu, is determines by the potential an atom must experience, and since the latter is determ~ed by the b~~d~~ of the atom, the activation energy of ovation of a surface atom connected by A$ bonds may be assumed to be proport~~~~ to its sputtering threshold, i-e_, @!I?+where y is a constant. The activation rate for i-bond atoms to become full surface atoms (since a full surface provides the energetically most favorable sites) is, using first order kmetics, @WII by 1241
Due to ir~~d~at~on, coliisions give rise to replacements on the surface as well as rearrangements due to the ejection of the atoms from the surface, The displacement process gives rise to a ~~~~~~ti~ rate of atmx af cextain bonding. The ~rodu~t~ou rate of surface atoms attached by i bonds is given by [25f
H.M. Windawi/Effect
of temperature
on sputtering yield of copper
583
where A is a constant, I and E are the bombarding ion current and energy, respectively. Bi(Nii) is given by the fraction of j-bonded atoms that become i-bonded and by the fraction of i-bonded atoms that becomej-bonded. Bi(Nii) is then given by
Bi(Nij) = C Cifi Nj-fi
Ni
i
(1
)
where fi is the displaced fraction ofj-bond atoms and Ci is the fraction of those displaced atoms producing atoms with i bonds. Assuming random distribution in the production of surface atoms, i.e.
fi=f
and
the steady-state Ni
V
Ci=C,
condition
exp(-.Si/kT)
= AIEcJB-
AIEeNi
(2)
is obtained for non-full surface atoms where N = ZNj and e is a constant. The thermal activation of full surface atoms does not produce new arrangements so that, for full surface atoms, the steady-state condition is given by 0 = iz
Nivexp(-fli/kT)
The probability
+ AIEcjil-AIEeN,
of an atom having a particular
.
(3)
number of bonds, Pi, is given by
Pi = NiIN. From the above steady-state
conditions,
Pi = D/ [ 1 + G exp(-@JkT)] fori=b,b+l,..., pa = D + D
(4)
a-1,and
a~1 G exP(GE.1EilkT) i=b
1 + G exp(-fl;/kT)
’
(9
where G = v/AIEe , and D is a constant characteristic of the surface. Eqs. (4) and (5) can be simplified by ignoring second and higher orders of G exp(-@JkT). The resulting probabilities then become Pi = D[ 1 -G exp(-_&i/kT)]
Pa =D[l-Gexp(-M’alkT)l
,
(da)
+Di$
Gexp(-CrEJkT).
(sa)
H.M. WindawijEffectof temperature on sputteting yield of copper
584
The probabilities can be determined from sputtering yield measurements
if the value of G is known. G may be determined as will be shown below.
4.4. Sputtering yield Dependence of the sputtering yield on temperature is analyzed by incorporating the temperature dependent probabilities obtained above in the temperature-independent equations of Langberg [23]. A discussion of the modeled sputtering process is illustrative. Collisions within a solid are generally collective phenomena. This is particularly true for low energy collisions of less than 10 eV [26,27] energy bombardment. For higher energies, however, interactions may be approximated by a series of consecutive binary collisions, where in each collision the energy and momentum are conserved. The colhsion is completed before the two colliding atoms begin to interact with other atoms. For sputtering near thresholds, a two-collision process was proposed by Langberg [23]. A surface atom requires at least two collisions before it can be sputtered by an ion incident normal to the surface. After the first collision, a maximum potential energy stored in the second collision is found. This is optimized in order that a threshold energy for the sputtering of a surface atom can be determined. Using the Morse potential as the ~teratomic potential, the sputtering threshold energy is then determined as a function of the number of bonds of the surface atom and of lattice parameters of the target. The sputtering yield is determined from the sputtering of atoms with bonds ranging from minimum to maximum. For an ion of energy E, the sputtering yield is given by Eh Y= b’
s Eb
Pi (E-Ei) dEi ,
when b’ is a constant. Inserting the probability equations (4a) and (5a) in the yield equation, the sputtering yield is obtained as a function of ion energy and temperature (for a given ion current) and is given by Y = @i?,-&)[&fr
-gGF
ii
_
(E, +&)I
E-c(E-Ea)-Eb
E-c(E-E,)-E,
where B is a constant
and
-F
-
I
5
1
eXp(-~b~kT)
exp(+E0/k7’)
,
(6)
H.M. WindawilEffect of temperature
585
on sputtering yield of copper
c = (Ea-Ea_l)I(Ea-Eb). The first term in (6) is the temperature independent yield found by Langberg [23] while the second term gives the effect of temperature as a perturbation to the first term. As the temperature is increased, the magnitude of the second term is increased so that the yield is decreased. Eq. (6) was fitted to the experimental data for the (100) surface as shown in fig. 7. The dashed curve was for p = 7.6 X 10e3, which corresponded to an average activation energy of 0.5 eV. B was found to be 2.148 X lop4 eV-* and G was equal to 1.575 X 102. The continuous curve was fitted for p = 1 X 1,0e3. This corresponded to an activation energy of 0.066 eV, which is too low. Fig. 6 shows the fitting to the experimental data for a polycrystal assuming that the surface was dominated by crystallites of (111) orientation. Again, the fitting was for 0.5 eV activation energy. Fig. 9 shows the yield variations with temperature for the three surfaces, (1 lo), (loo), and (111) of copper. B was taken to be such that the yield for the three surfaces was the same at temperatures close to 0 K. This was so, since the average threshold energy is the same for the three surfaces, assuming that the binding energies were the same and that any order is destroyed by the bombardment. It can be seen that while the (111) surface provides the sharpest decrease in the yield as the temperature is increased, the (110) surface provides practically no decrease in its yield with temperature. It should be remembered that when the solid becomes a liq-
1.6 c
1.0
I
I
I
I
500
600
700
600
TEMPERATURE
Fig. 9. Variations of the sputtering yield with temperature per surfaces obtained from eq. (6).
(OK)
for the (1 lo), (loo),
and (111) cop
586
HM. WindawilEffect of temperature
on sputtering yield of copper
uid the surface layer becomes a full plane, so that the binding energy is maximum for all the atoms. However, at temperatures close to the melting point, evaporation dominates 1281. Decrease in the sputtering yield with temperature was observed by Carlston et al. [ 1 l] for (111) Cu surfaces bombarded with 2 to 10 keV Ar+ ions. Similar variations were observed by Elich et al. [IO]. Although our model of the sputtering yield is limited to low energy sputtering, the bonding concept would seem to apply equally to high and low energies. High energy bombardment results in collision cascades which, when intersecting the surface, give rise to sputte~ng. The average energy of the sputtered atoms does not increase significantly with an increase in bombarding energy [29]. Since a sputtered atom has to overcome the binding energy of the surface before it is sputtered, the effect of the binding energy is still significant, even at high energies. It should be emphasized that for the high energy discussed, random (non-channeled) ions bombard the surface. Decrease in the sputtering yjeld with an increase in temperature was also observed by Snouse and Bader [30] for a copper polycrystal sputtered with 3 keV Nl ions. For comparison, the situation was considered to be equivalent to 1.5 keV N+ irradiation and the yield was divided by two. The variation of the yield with temperature was fitted, using the above model for an activation energy of 0.5 eV. This further indicates that the model may be applicable to medium energy sputtering. It should be noted that the approximation made by ignoring second and higher IS reasonable as the factor is small compared to 1. orders of C exp(--@i/kT) 4.5. Polycrystallirie ejection patterns A poIycrystal~ne surface is considered to be madeup of various grain orientations which sputter at different rates when irradiated with an energetic ion beam. The ejection of particles is expected to be along random directions as if the surface were amorphous. A near cosine pattern [ 161 was expected to be obtained when polycrystalline copper targets were sputtered. Some targets, however, produced patterns made of circular rings centered at the point directly above the target surface. This indicated that some preferential ejection was taking place. The fitting of those rings to the (110) spots obtained from a sputtered (111)Cu surface (fig. 8) suggested that the polycrystalline surface was dominated by crystallites with (111) orientations. Further evidence in favor of the above conclusion was the observed decrease in the sputtering yield of those polycrystals with temperature. Fitting the yield variation of the (111) surface with temperature to the yield data obtained from a polycrystalline copper (fig. 6) was reasonable. Domination of polycrystalline surfaces by a certain orientation was also observed by Colligon et al. [31].
H.M. WindawilEffect of temperature
on sputtering yield of copper
587
5. Summary The effect of temperature on the sputtering yield of copper was investigated. Analytically, a model was developed, and results were fitted to data obtained from a spectroscopic technique. The model employed the concept of atomic binding on the bombarded surface. Atoms attained distributions in the number of their bonds, and those distributions depended on the temperature of the target and the bombarding beam current and energy. Variation of either the temperature or the bombarding beam parameters resulted in variations in the sputtering yield. Some preferential ejection of the particles sputtered from polycrystalline copper targets was found. It was argued that these surfaces were dominated by crystallites of (111) rather than random orientations. Verification of this was found by observation of the decrease in yield with temperature that was characteristic of the (111) surface.
Acknowledgements The author wishes to thank Dr. C.B. Cooper for the advice and helpful discussions during the course of work. Discussions with Dr. R.B. Murray were greatly appreciated.
References [l] [2] [ 31 [4] [5] [6] [7] ]8] [9] [lo] [ll] [12] [13] [ 141 [15]
[ 161 [17]
[ 181
R.H. Silsbee, J. Appl. Phys. 28 (1957) 1246. J.B. Sanders and J.M. Fluit, Physica 30 (1964) 129. R.S. Nelson, M.W. Thompson and H. Montgomery, Phil. Mag. 7 (1962) 1385. G.D. Magnuson, W. Palmer and J.S. Koehler, Phys. Rev. 109 (1958) 1990. R.S. Nelson, The Observation of Atomic Collisions in Crystalline Solids (North-Holland, Amsterdam, 1968) p. 215. D.E. Harrison, J.P. Johnson and N.S. Levy, Appl. Phys. Letters 8 (1966) 33. R.V. Stuart, C.K. Wehner and G.S. Anderson, J. Appl. Phys. 40 (1969) 803. C. Lehmann and P. Sigmund, Phys. Status Solidi 16 (1966) 507. R. Behrisch, Proc. Intern. Conf. on Ion-Surface Interaction, Sputtering and Related Phenomena, Garching, 1972. J.J. Elich, H.E. Roosendaal and D. Onderdelinden, Radiation Effects 10 (1971) 175. C.E. Carlston, G.D. Magnuson, A. Comeaux and P. Mahadevan, Phys. Rev. 138 (1965) 759. C.H. Weijsenfeld, Ph.D. Thesis, Univ. of Utrecht (1965) p. 85. H.M. Windawi and C.B. Cooper, Phys. Letters 43A (1973) 491. MIT Wavelength Tables (MIT Press, Cambridge, 1969). R.V. Stuart and G.K. Wehner, J. Appl. Phys. 33 (1962) 2345; Phys. Rev. Letters 4 (1960) 409. G.K. Wehner and D. Rosenberg, J. Appl. Phys. 31 (1960) 177. G.K. Wehner, Phys. Rev. 102 (1956) 690. A. Guntherschulze and K. Mayer, 2. Physik 62 (1930) 607.
588 [ 191 [20] (211 [22] [23] [24] [25] [26] [ 271 [28] [29] [30] [31]
H.M. WindawilEffect of temperature
on sputtering yieM of copper
N. Laegreid and G.K. Wehner, J. Appl. Phys. 32 (1961) 365. C.J. Ogilvie and A.A. Thomson, J. Phys. Chem. Solids 17 (1961) 203; 10 (1959) 222. D.P. Jackson. Radiation Effects 18 (1973) 185. E. Menzel, Z. Physik 132 (1952) 508. E. Langberg, Phys. Rev. 111 (1958) 91; Ph.D. Thesis, Princeton Univ. (1956) (unpublished). M.W. Thompson, Defects and Radiation Damage in Metals (Cambridge Univ. Press, 1969) ch 1. G.S. Anderson. 5. Appl. Phys. 38 (1967) 1607. M.W. Thompson, Phil. Mag. 18 (1968) 377. J.N. Smith, Surface Sci. 34 (1973) 613. R.S. Nelson, Phil. Mag. 11 (1965) 291. R.V. Stuart and G.K. Wehner, J. Appl. Phys. 35 (1964) 1819. T.W. Snouse and M. Bader, in: Trans. Second Intern. Vacuum Congr. (Pergamon, New York, 1962) Vol. 1. p. 271. .J.S. Colligon, C.M. Hicks and A.P. Neokleous, Radiation Effects 18 (1973) 119.
55 (1976) 573-588 Publishing Company
EFFECT OF TEMPERATURE
ON THE SPUTTERING
YIELD OF COPPER f
H.M. WINDAWI * Department Received
of Physics, University of Delaware, Newark, Delaware I971 1, USA
19 August
1975; manuscript
received
in final form 23 January
1976
The effect of temperature on the sputtering yield of copper for low energy argon ion bombardment is investigated. Experimentally, a phase sensitive technique utilizing the spectroscopic emission of sputtered particles is discussed. Analytically, the Langberg model for the sputtering yield is expanded to include the effect of temperature. Atoms of the bombarded surface attain a steady state distribution in the number of their bonds. Changes in either the temperature or the bombardment parameters result in changes in the distribution leading to variations in the sputtering yield. (111) and (110) single crystal and polycrystalline copper surfaces are investigated. Reasonable agreement is obtained between experimental and analytic yield values. The (111) surface shows the largest decrease in yield with an increase in temperature.
1. Introduction The effect of temperature on the sputtering yield was investigated by many authors. The discrepancy in the published data makes it worthwhile to consider the effect of temperature on the factors that influence the sputtering yield. An increase in temperature leads to an increase in the vibrations of atoms about their lattice sites. If one considers a collision sequence to be moving along a closepacked direction, the increased amplitude of the vibrating atom causes an increase in the magnitude of the focussing parameter [l] so that the focussing range is shortened. The transfer of momentum along this direction becomes less efficient. This implies that energy is dissipated in the lattice before a sequence can reach the surface, and hence the sputtering yield is decreased as the temperature is increased. Calculations by Sanders and Fluit [2] showed that the dependence of the total sputtering yield on the focussed collision range was weaker than a direct proportionality. A similar conclusion was reached by Nelson et al. [3]. Damage produced by the bombardment may be decreased by increasing the tem‘rS upported in part by the National Science Foundation. * Present address: Department of Chemical Engineering, Delaware 19711, USA.
University
of Delaware.
Newark,
574
H.M Windawi/Effect of temperature
on sputtering yield
of capper
perature. This can affect the collision by minimizing the defocussing of the collision chains (caused by defects) and increase the efficiency in the transfer of momentum to the surface, On the basis of this argument, the sputtering yield may increase with an increase in temperature. However, interstitiais and vacancies were found to be mobile even at low temperatures [4] so that the defects were annealed out rather quickly [5]. This effect can, therefore, be discounted, particularly for the case of copper, Harrison et al. [Gf, from computer simulation of the sputtering process, Stuart et al ~ [Tf , from the energy spectra of sputtered atoms, and Lehmann and Sigmund [g], from analytical considerations, concluded that sputtering is a surface correlated effect. More recently [9], it was concluded that the focusson contribution to the total sputtering yield accounts for less than 30%. At low energies the fraction can be smaller, since the penetration depth is small [8] and the energy is dissipated before it is focussed backwards. An increase in temperature may lead to a decrease in the transparency of the surface to the incoming ion. Atoms below the surface layer become more exposed to the bombarding ion due to the increased vibration of the atoms. This transparency picture was explained in terms of dechanneling [lo] increase with temperature leading to an increase in the sputtering yield. This effect is, however, more relevant to medium and high energy sputtering, whereas our interest lies in the low energy range. Temperature increase may cause a decrease in effective binding energy of surface atoms [ 1 l] due to the increase in their vibrational amplitude. Surface atoms need to receive a proportionately smaller amount of energy in a collision to be ejected from the surface. This effect is small, however, as the increase in amplitude is not enough to make the effect appreciabIe. Under low energy bombardment at normal incidence, a monolayer may be sputtered away from the surface each second. Thermal activation of migration of surface atoms leads to surface rearrangement. For such a condition activation events are orders of magnitude more frequent than sputtering events [5]. The bombarded surface changes its structural characteristics between two bombarding events due to thermal activation [ 12j. The surface? however, may be considered to be in a steady state condition when sputtered at a given temperature, beam current density and energy. On this premis, we have investigated the effect of temperature on the sputtering yield and the experimental and analytical results are presented.
Sputtering of the samples was carried out with Ar” ions drawn from a magnetically confined dc plasma by biasing the target negatively with respect to the plasma potential [ 131. The sputtering yield was determined by weight loss and spectroscopic measurements. Weight loss measurements were made for one-hour intervals. The
H.M. WindawilEifect of temperature
on sputteting yield of copper
515
length of the sputtering time was chosen so that constant plasma conditions were maintained during the measurements. In the spectroscopic technique, the characteristic emission of the sputtered particles was monitored and analyzed as a function of other parameters. In this technique a fraction of the sputtered atoms, about 10-4-10-3 became excited as they passed through the plasma. The particle excitation resulted from impact by electrons from the electron beam that sustained the plasma. Characteristic emission of the atoms resulted from their radiative de-excitation. Light extracted from the sputtering chamber was mechanically chopped and focussed onto the entrance slit of a 0.5 m scanning monochromator (- 1 A resolution). The signal was processed by a photomultiplier, a lock-in amplifier and a chart recorder (fig. 1). The strongest emission lines of Cu are those of wavelengths 3248 and 3274 A [ 141. These lines were strongly absorbed by the bell-jar and were at about the limit of response of the detector. An order of magnitude weaker lines that lie in the visible range were chosen. In particular, the lines 4023,4063 and 5 106 A were monitored. Since argon was the arcing gas, argon lines were numerous [ 141. Identification of the lines was sometimes difficult. The presence of the copper lines, however, made it possible to identify the argon lines. The presence of argon lines had two advantages. One was to monitor plasma instabilities and the other was to normalize the copper lines with respect to them. Normalization was necessary as changes in the plasma gave rise to variations in the copper signal that were not dependent on the sputtering yield.
CHOPPER MONOCHROMATOR
POLE
MAGNET
PHOTOMULTIPLIER
+ TO VACUUM
PUMPS
I SIGNAL
1. Schematics of the set-upused for monitoring the spectroscopic emission of sputtered particles. Fig.
RM. Windawi/Effect of temperature
516
on sputtering yield of copper
The intensity of an emission line was taken to be proportional to the number of sputtered atoms passing through the plasma. Analysis of the variation in the intensity of a particular line as a function of time, ion energy and target temperature allowed for the determination of relative sputtering yield values as a function of those parameters. Absolute values could not be determined since the excitation crosssections were not known. The relative values were normalized, however, to those obtained from weight loss measurements. Measurements of the sputtering yield variation with temperature were made when the target reached a constant temperature during its sputtering. For these measurements, the target was preheated for about an hour for outgassing purposes.
3. Reklts Fig. 2 shows a monochromator
scan of a section of the emission spectrum ob-
I
4060
4070 WAMLENGTH
4060
I
4050
(A”)
Fig. 2. Part of an emission spectrum showing the relative intensities of copper and argon lines. The copper line resulted from atoms sputtered from a (1OO)Cu surface by 250eV Ar+.
H.M. WindawijEffect of temperature
on sputtering yield of copper
577
I e
Q
50
I
I
100
150
I 200
I
250
I
30 IO
TARGET POTENTIAL (‘4
Fig. 3. Variation of the sputterer yield and target current with the applied potential. The reiative yield values were obtained from the int&ities of the 0.1 I 5106 A line.
served. Fig. 3 shows the dependence of the ionic current density on the potential applied to the target. The figure also shows the dependence of the sputtering yield on the applied potential. The sputtering yield was caiculated by dividing the intensity of a copper emission line (5 106 A) by the ionic current to the target and normalizing the values at 300V. The shape of the yield curve is similar to those obtained by Stuart and Wehner [ 151. Fig. 4 shows the yield versus applied potential curves for three emission lines of copper. The relative intensities of the lines were normalized at 300 V. The figure substantiates the assumption that the sputtering yield may be taken to be proportional to the intensity of an emission line. The time dependence of the sputtering yield was studied by monitoring the intensity of a copper line with sputtering time. Fig. 5 shows the changes that resulted from sputtering a Cu polycrystal. It can be seen that the yield had almost doubled as the sputtering time was increased from zero to twenty minutes. After about twenty
578
H.M. Windawi/Effect of temperature on sputtering yield of copper
B
0
e 1.0 -
8
0
0
I
I
1
I
1
200
100 TARGET
POTENTIAL
I 300
(VI
Fig. 4. Vocation of the sputtering yield with the applied potential. The yield values were obtained from the intensities of the three copper lines; 5 1068 (circles), 40638 (squares), and 4023 p1 (triangles). Yield was normalized to weight loss value at 300 eV.
minutes, the yield was seen to remain constant. Such changes were not observed for Cu monocrystals, namely the (111) and (100) surfaces. For those monocrystals, the yield was seen to reach the high values within one to two minutes. Fig. 6 shows the variation of yield with temperature for a Cu polycrystal. The spectroscopic data (triangles) are shown normalized to data obtained from weight loss measurements at the high temperatures studied. It can be seen that the yield decreased as the temperature was increased. Fig. 7 shows the temperature effect that resulted from the sputtering of a (100) Cu crystal. Each data point was an average of three measurements, each of which was normalized with respect to Ar. The lines involved were Cu 4063 and Ar 4053 8. The yield was seen to decrease by about 14% when the temperature was increased from about 500 to 800 K. Some of the polycrystals that were sputtered gave rise to spot patterns that deviated from the expected cosine distribution [ 161. Fig. 8 shows a pattern obtained
H.M. Windawi/Effect
of temperature
on sputtering yield of copper
519
I
/”
/
/
d
1
I
IO
20
SPUTTERING Fig. 5. Development
of the sputtering
30 TIME
yield of polycrystalline
(min.) copper
with sputtering
time.
from a polycrystal superimposed on that obtained from a (111) single crystal. The polycrystalline pattern was of a ring structure where the rings were formed at angles that corresponded to those of the spots obtained from the (111) crystal. The polycrystal that gave rise to the pattern of fig. 8 was the same one that showed a decrease in the sputtering yield with an increase in temperature. The significance of such a correlation will be discussed later.
4. Discussion 4.1. Swface cleanliness Initial values of the sputtering yield (as determined by weight loss) at about room temperature were low compared to those at higher temperatures. This suggested that surface impurities must be sputtered away before the bombarding beam could encounter surface atoms. The change in the yield as a function of the sputtering time was exhibited in fig. 5. This effect was found to be associated with the sputtering of
580
H.M. WindawijEffect of temperature
on sputten’ng yield of copper
iI
1.4
I.2
I.C
I
I
I
I
600
650
700
750
TEMPERATURE
ioK)
Fig. 6. Effect of tem~rature on the sputtering yield of a p~l~cr~sta~ine copper sampie; (o) weight loss, (5) spectroscopic measurements.
500
600 TEMPERATURE
700
800
(OK1
Fig. 7. Effect of temperature on the sputtering yield of (100) Cu surface.
H.M. Windawi/Effect of temperature
on sputtering yield o,f copper
581
,_.--
n
directions
0
G12>
directions
8. Ejection patterns resulted from 300 eV Ar+ sputtering of a copper poiycrystai (rings) and an (111) copper surface (hatched). The patterns are shown fitted to spots obtained from stereographic projection of the copper lattice on a (111) plane.
Fig.
polycrystals but not with single crystals. This can be explained by the preferential contamination of grain boundaries 1171. Sputtering from the grain boundaries does not take place until the impurities are sputtered away. The implication of this is that weight loss measurements are not reliable. The discrepancy in the published data supports this conclusion. Yield values of 1.O [ 181, 1.3 [ 121, and 1.55 [ 191 were reported for Cu polycrystals sputtered with 300eV Ar+ ions. During sputtering, the surface can be maintained dynamically clean if the rate of removal of surface atoms is made faster than the rate of contamination. Background pressure of about 10e6 torr and current densities of about 8 mA/cm2 (experimental conditions) are adequate to maintain the surface dynamically clean [S] . 4.2. Surface condi tiun Sputtering of a surface results in the formation of surface vacancies and interstitials. The latter are considered to annihilate a substantial fraction of the vacancies so that dynamic surface vacancy concentration is too small to significantly influence the general ejection behavior [5]. This is supported by the fact that preferential ejection patterns obtained from the sputtering of monocrystals do not disappear in a wide range of temperatures, indicating that the ordering of the surface is retained under ionic bombardment [20]. During its bombardment, the surface is not planar since atoms are ejected continuously from it. The surface layer is generally three-dimensional, and its characteristics are determined by the equilibrium distribution of occupied lattice sites. The equilibrium distribution is governed by the distributior~ of ejected surface atoms and
by the thermal activationof tlwmal mig~a~on. For a part&&r surface condition, surface atoms attain a dist~b~~tiou in the number of their bonds, The number of bonds range from a maximum (with binding energy of -4.6eV ]12.21]) to a minimum (with bindiag energy of -25 eY ]l2] >. The surface c~nd~t~o~ is thus expected to ~~~ue~~e the s~ut~e~~~g yield since an atom must overborne its b~~d~~g In order for it to be ejected from the surface.
Thermal activation for the migration of surface atoms of copper on a copper surface has an average activation energy of about 0.5 eV [S, 12, ZZ]. This ~orr~~~nds to about I O6 jumps each second for a surface atom at 350 R. In a sputtesirig experiment, such as discussed here, this means that a surface atom makes about IO5 jumps befom it is sputtered. Thus, a surface atom will have ample time for migm tion to an ~~~~ge~~~~~~most favorable site before the next atom in the neighborhood is sputtered. The migration of an atom from one site to another is equivalent to the ~~a~~Q~ of a vacancy in a reverse order. Similar to itnneahng processes, a steady-state s~u~te~~g condition can be set up where the number of atoms attached to the surface by i bonds is constant in time. i.e,:
One may denote the number of bonds of a surface atom as N and let A$ and N-I, be, res~~t~v~~y, the rnax~un~ and minimum numbers of surface bonds. These atoms have sputtering thresholds denoted by E, and &, respectively. The sputtefing threshold energies are, to a first ~~~rox~rnatio1~~ ~roportio~ai to the number of bonds of surface atoms [23]. Since it is reason;zbte to assume that the activation energ for surface ~~atiol~~ Eu, is determines by the potential an atom must experience, and since the latter is determ~ed by the b~~d~~ of the atom, the activation energy of ovation of a surface atom connected by A$ bonds may be assumed to be proport~~~~ to its sputtering threshold, i-e_, @!I?+where y is a constant. The activation rate for i-bond atoms to become full surface atoms (since a full surface provides the energetically most favorable sites) is, using first order kmetics, @WII by 1241
Due to ir~~d~at~on, coliisions give rise to replacements on the surface as well as rearrangements due to the ejection of the atoms from the surface, The displacement process gives rise to a ~~~~~~ti~ rate of atmx af cextain bonding. The ~rodu~t~ou rate of surface atoms attached by i bonds is given by [25f
H.M. Windawi/Effect
of temperature
on sputtering yield of copper
583
where A is a constant, I and E are the bombarding ion current and energy, respectively. Bi(Nii) is given by the fraction of j-bonded atoms that become i-bonded and by the fraction of i-bonded atoms that becomej-bonded. Bi(Nii) is then given by
Bi(Nij) = C Cifi Nj-fi
Ni
i
(1
)
where fi is the displaced fraction ofj-bond atoms and Ci is the fraction of those displaced atoms producing atoms with i bonds. Assuming random distribution in the production of surface atoms, i.e.
fi=f
and
the steady-state Ni
V
Ci=C,
condition
exp(-.Si/kT)
= AIEcJB-
AIEeNi
(2)
is obtained for non-full surface atoms where N = ZNj and e is a constant. The thermal activation of full surface atoms does not produce new arrangements so that, for full surface atoms, the steady-state condition is given by 0 = iz
Nivexp(-fli/kT)
The probability
+ AIEcjil-AIEeN,
of an atom having a particular
.
(3)
number of bonds, Pi, is given by
Pi = NiIN. From the above steady-state
conditions,
Pi = D/ [ 1 + G exp(-@JkT)] fori=b,b+l,..., pa = D + D
(4)
a-1,and
a~1 G exP(GE.1EilkT) i=b
1 + G exp(-fl;/kT)
’
(9
where G = v/AIEe , and D is a constant characteristic of the surface. Eqs. (4) and (5) can be simplified by ignoring second and higher orders of G exp(-@JkT). The resulting probabilities then become Pi = D[ 1 -G exp(-_&i/kT)]
Pa =D[l-Gexp(-M’alkT)l
,
(da)
+Di$
Gexp(-CrEJkT).
(sa)
H.M. WindawijEffectof temperature on sputteting yield of copper
584
The probabilities can be determined from sputtering yield measurements
if the value of G is known. G may be determined as will be shown below.
4.4. Sputtering yield Dependence of the sputtering yield on temperature is analyzed by incorporating the temperature dependent probabilities obtained above in the temperature-independent equations of Langberg [23]. A discussion of the modeled sputtering process is illustrative. Collisions within a solid are generally collective phenomena. This is particularly true for low energy collisions of less than 10 eV [26,27] energy bombardment. For higher energies, however, interactions may be approximated by a series of consecutive binary collisions, where in each collision the energy and momentum are conserved. The colhsion is completed before the two colliding atoms begin to interact with other atoms. For sputtering near thresholds, a two-collision process was proposed by Langberg [23]. A surface atom requires at least two collisions before it can be sputtered by an ion incident normal to the surface. After the first collision, a maximum potential energy stored in the second collision is found. This is optimized in order that a threshold energy for the sputtering of a surface atom can be determined. Using the Morse potential as the ~teratomic potential, the sputtering threshold energy is then determined as a function of the number of bonds of the surface atom and of lattice parameters of the target. The sputtering yield is determined from the sputtering of atoms with bonds ranging from minimum to maximum. For an ion of energy E, the sputtering yield is given by Eh Y= b’
s Eb
Pi (E-Ei) dEi ,
when b’ is a constant. Inserting the probability equations (4a) and (5a) in the yield equation, the sputtering yield is obtained as a function of ion energy and temperature (for a given ion current) and is given by Y = @i?,-&)[&fr
-gGF
ii
_
(E, +&)I
E-c(E-Ea)-Eb
E-c(E-E,)-E,
where B is a constant
and
-F
-
I
5
1
eXp(-~b~kT)
exp(+E0/k7’)
,
(6)
H.M. WindawilEffect of temperature
585
on sputtering yield of copper
c = (Ea-Ea_l)I(Ea-Eb). The first term in (6) is the temperature independent yield found by Langberg [23] while the second term gives the effect of temperature as a perturbation to the first term. As the temperature is increased, the magnitude of the second term is increased so that the yield is decreased. Eq. (6) was fitted to the experimental data for the (100) surface as shown in fig. 7. The dashed curve was for p = 7.6 X 10e3, which corresponded to an average activation energy of 0.5 eV. B was found to be 2.148 X lop4 eV-* and G was equal to 1.575 X 102. The continuous curve was fitted for p = 1 X 1,0e3. This corresponded to an activation energy of 0.066 eV, which is too low. Fig. 6 shows the fitting to the experimental data for a polycrystal assuming that the surface was dominated by crystallites of (111) orientation. Again, the fitting was for 0.5 eV activation energy. Fig. 9 shows the yield variations with temperature for the three surfaces, (1 lo), (loo), and (111) of copper. B was taken to be such that the yield for the three surfaces was the same at temperatures close to 0 K. This was so, since the average threshold energy is the same for the three surfaces, assuming that the binding energies were the same and that any order is destroyed by the bombardment. It can be seen that while the (111) surface provides the sharpest decrease in the yield as the temperature is increased, the (110) surface provides practically no decrease in its yield with temperature. It should be remembered that when the solid becomes a liq-
1.6 c
1.0
I
I
I
I
500
600
700
600
TEMPERATURE
Fig. 9. Variations of the sputtering yield with temperature per surfaces obtained from eq. (6).
(OK)
for the (1 lo), (loo),
and (111) cop
586
HM. WindawilEffect of temperature
on sputtering yield of copper
uid the surface layer becomes a full plane, so that the binding energy is maximum for all the atoms. However, at temperatures close to the melting point, evaporation dominates 1281. Decrease in the sputtering yield with temperature was observed by Carlston et al. [ 1 l] for (111) Cu surfaces bombarded with 2 to 10 keV Ar+ ions. Similar variations were observed by Elich et al. [IO]. Although our model of the sputtering yield is limited to low energy sputtering, the bonding concept would seem to apply equally to high and low energies. High energy bombardment results in collision cascades which, when intersecting the surface, give rise to sputte~ng. The average energy of the sputtered atoms does not increase significantly with an increase in bombarding energy [29]. Since a sputtered atom has to overcome the binding energy of the surface before it is sputtered, the effect of the binding energy is still significant, even at high energies. It should be emphasized that for the high energy discussed, random (non-channeled) ions bombard the surface. Decrease in the sputtering yjeld with an increase in temperature was also observed by Snouse and Bader [30] for a copper polycrystal sputtered with 3 keV Nl ions. For comparison, the situation was considered to be equivalent to 1.5 keV N+ irradiation and the yield was divided by two. The variation of the yield with temperature was fitted, using the above model for an activation energy of 0.5 eV. This further indicates that the model may be applicable to medium energy sputtering. It should be noted that the approximation made by ignoring second and higher IS reasonable as the factor is small compared to 1. orders of C exp(--@i/kT) 4.5. Polycrystallirie ejection patterns A poIycrystal~ne surface is considered to be madeup of various grain orientations which sputter at different rates when irradiated with an energetic ion beam. The ejection of particles is expected to be along random directions as if the surface were amorphous. A near cosine pattern [ 161 was expected to be obtained when polycrystalline copper targets were sputtered. Some targets, however, produced patterns made of circular rings centered at the point directly above the target surface. This indicated that some preferential ejection was taking place. The fitting of those rings to the (110) spots obtained from a sputtered (111)Cu surface (fig. 8) suggested that the polycrystalline surface was dominated by crystallites with (111) orientations. Further evidence in favor of the above conclusion was the observed decrease in the sputtering yield of those polycrystals with temperature. Fitting the yield variation of the (111) surface with temperature to the yield data obtained from a polycrystalline copper (fig. 6) was reasonable. Domination of polycrystalline surfaces by a certain orientation was also observed by Colligon et al. [31].
H.M. WindawilEffect of temperature
on sputtering yield of copper
587
5. Summary The effect of temperature on the sputtering yield of copper was investigated. Analytically, a model was developed, and results were fitted to data obtained from a spectroscopic technique. The model employed the concept of atomic binding on the bombarded surface. Atoms attained distributions in the number of their bonds, and those distributions depended on the temperature of the target and the bombarding beam current and energy. Variation of either the temperature or the bombarding beam parameters resulted in variations in the sputtering yield. Some preferential ejection of the particles sputtered from polycrystalline copper targets was found. It was argued that these surfaces were dominated by crystallites of (111) rather than random orientations. Verification of this was found by observation of the decrease in yield with temperature that was characteristic of the (111) surface.
Acknowledgements The author wishes to thank Dr. C.B. Cooper for the advice and helpful discussions during the course of work. Discussions with Dr. R.B. Murray were greatly appreciated.
References [l] [2] [ 31 [4] [5] [6] [7] ]8] [9] [lo] [ll] [12] [13] [ 141 [15]
[ 161 [17]
[ 181
R.H. Silsbee, J. Appl. Phys. 28 (1957) 1246. J.B. Sanders and J.M. Fluit, Physica 30 (1964) 129. R.S. Nelson, M.W. Thompson and H. Montgomery, Phil. Mag. 7 (1962) 1385. G.D. Magnuson, W. Palmer and J.S. Koehler, Phys. Rev. 109 (1958) 1990. R.S. Nelson, The Observation of Atomic Collisions in Crystalline Solids (North-Holland, Amsterdam, 1968) p. 215. D.E. Harrison, J.P. Johnson and N.S. Levy, Appl. Phys. Letters 8 (1966) 33. R.V. Stuart, C.K. Wehner and G.S. Anderson, J. Appl. Phys. 40 (1969) 803. C. Lehmann and P. Sigmund, Phys. Status Solidi 16 (1966) 507. R. Behrisch, Proc. Intern. Conf. on Ion-Surface Interaction, Sputtering and Related Phenomena, Garching, 1972. J.J. Elich, H.E. Roosendaal and D. Onderdelinden, Radiation Effects 10 (1971) 175. C.E. Carlston, G.D. Magnuson, A. Comeaux and P. Mahadevan, Phys. Rev. 138 (1965) 759. C.H. Weijsenfeld, Ph.D. Thesis, Univ. of Utrecht (1965) p. 85. H.M. Windawi and C.B. Cooper, Phys. Letters 43A (1973) 491. MIT Wavelength Tables (MIT Press, Cambridge, 1969). R.V. Stuart and G.K. Wehner, J. Appl. Phys. 33 (1962) 2345; Phys. Rev. Letters 4 (1960) 409. G.K. Wehner and D. Rosenberg, J. Appl. Phys. 31 (1960) 177. G.K. Wehner, Phys. Rev. 102 (1956) 690. A. Guntherschulze and K. Mayer, 2. Physik 62 (1930) 607.
588 [ 191 [20] (211 [22] [23] [24] [25] [26] [ 271 [28] [29] [30] [31]
H.M. WindawilEffect of temperature
on sputtering yieM of copper
N. Laegreid and G.K. Wehner, J. Appl. Phys. 32 (1961) 365. C.J. Ogilvie and A.A. Thomson, J. Phys. Chem. Solids 17 (1961) 203; 10 (1959) 222. D.P. Jackson. Radiation Effects 18 (1973) 185. E. Menzel, Z. Physik 132 (1952) 508. E. Langberg, Phys. Rev. 111 (1958) 91; Ph.D. Thesis, Princeton Univ. (1956) (unpublished). M.W. Thompson, Defects and Radiation Damage in Metals (Cambridge Univ. Press, 1969) ch 1. G.S. Anderson. 5. Appl. Phys. 38 (1967) 1607. M.W. Thompson, Phil. Mag. 18 (1968) 377. J.N. Smith, Surface Sci. 34 (1973) 613. R.S. Nelson, Phil. Mag. 11 (1965) 291. R.V. Stuart and G.K. Wehner, J. Appl. Phys. 35 (1964) 1819. T.W. Snouse and M. Bader, in: Trans. Second Intern. Vacuum Congr. (Pergamon, New York, 1962) Vol. 1. p. 271. .J.S. Colligon, C.M. Hicks and A.P. Neokleous, Radiation Effects 18 (1973) 119.