1 keV, while those of Thompson’s group (Thompson, 968; Farmery and Thompson, 968) are for incident energies in the vicinity of 40 keV.
Some of the results of Stuart and Wehner are reproduced here and form figures 2.3a, b, c, d and e and 2.5a and b.
The target material, bombarding ion and its energy, and the direction of observation are shown on each diagram.
Some marked similarities occur in these spectra (and others
not shown here). This would in part be due to the factors common to
each of the experiments.
a. Bombarding energies were all in the 100 to 3000 eV
range, while all of the ones illustrated have energy of 600 eV.
b. The bombarding ions were all incident normal to the
c. Observations were restricted to a few directions of
emission, with the most common angle being 0° (i.e. normal) and 60° to the surface normal.
d. Most of the data are for incident mercury ions, although
measurements were made with rare gas ions.
The common features of the energy spectra can be readily summarised.
The shape of the energy spectrum does not depend strongly on
mass number of the ion from argon through to mercury. In addition it
will be noted that the spectra due to helium and neon ions are similar,
although they differ quite substantially from that of the larger mass
particles. These points are illustrated in figures 2.3a and b where
energy distributions produced by argon, krypton, xenon, mercury,
helium and neon ions are shown. For the heavier ions the peak heights
occur at approximately the same energy (3 to 4.5 eV) and with the peak heights normalised to the same value, the shape of the rise and
fall of the curves show little variation. And again, the position of
the peak height and the shape of the curves are very similar for the two low mass ions.
The changes introduced to the energy spread of the particles for different emission directions but otherwise similar conditions to
a. and b. are shown in c. and d. of figure 2.3. The shift in the
energy corresponding to the maximum value is much lower for normal
exit (0°) than at 60°. Figure 2.3d, which substitutes xenon and
krypton for mercury shows similar changes so that the results of
these three ions at normal emission (like those at 60°), do not differ significantly.
Figure 2.3e, which is for a polycrystalline target can be
compared with the single crystal results measured under similar conditions and shown in figure 2.3c.
Once again the change in the shape of the spectrum due to differing direction of observation are. similar. However the spread in the spectra is not as pronounced for the polycrystalline copper
as the monDcrystalline. This does imply that some crystallographic
dependence is evident.
Tf these curves are replotted on (i) log-log and
(ii) log-linear scales (figure 2.4a and b respectively) it is seen that the high energy region for the mercury (and argon) ion bombardment of both the mono- and poly-crystalline faces measured at 60° to the normal is linear in (i) and hence the emission can be represented by
N(E) a E " 1*6,
while for both targets in the 0° position the spectrum has the form
__ X > - * • O •: X * L d " U S1 ,0) >- O X UJ 2 UJ 0/ tO 2 * 5 "
On the other hand the 1200 eV argon ion bombardment of a polycrystalline gold specimen resulted in a spectrum which does not fit either a power law or exponential relationship.
For other polycrystalline material there occurred a steady increase in the position of the peak height with mass number from aluminium (3.0 eV) through to uranium (12.6 eV) , coupled with a decrease in the rate with which the curve falls with energy so that the corresponding energy at which the emission has fallen to half the peak value are 10 eV and 40 eV respectively.
Two additional sets of curves for copper single crystal targets irradiated with 600 eV mercury ions are reproduced as
figures 2.5 a and b. In these the ions were incident normal to (100)
and (111) faces and the observations made at 35° (<110> direction) and normal to the surface, and at 45° (<110> direction) and normal to the
In both cases the energy corresponding to the peak
emission in the <110> direction exceeds that in the normal direction
and the proportion of high energy particles is also higher. The
two normal direction spectra are barely distinguishable, although they
originate from different crystal faces. The difference between
the two <110> spectra (when compared with figure 2.3c) seems to be due more to the angle of observation than any crystallographic
dependence. The higher energies recorded in the <110> direction
are at variance with the work of Weijsenfeld (1967) who found that ejection in this direction corresponded to the minimum mean energy.
Stuart and Wehner expressed disappointment with their
results in that they did not show any clear evidence of any particular
mechanism such as focusing. Indeed the spectra were so similar that
it appears from them that the processes which lead to ejection are probably largely independent of the crystallography, even though the
differential yield, as shown by the spot patterns varied substantially with direction.
This interpretation may be far from correct. As observed
earlier in this chapter the measurements for copper targets probably did not extend to sufficiently high energies to allow differentiation
between the operating mechanisms. In addition, because measurements
for different crystallographic directions of emission had to be made at different angles, the "random" contribution to the spectrum was
also different. Musket and Smith (1968) have shown that well defined
spots are visible even when 80% of the intensity in the region of
a spot is due to an assumed random cosine distribution of particles. In Stuart and Wehner's results a 20% increased contribution, due to some spot forming mechanism, possibly focusons, would be swamped by the increased yield due to the random beam.
It does not seem possible to meaningfully strip any random component from the observed spectra partly because the magnitude of the
readings in the high energy region is so small. Furthermore the
method of normalisation used (i.e. making the peak height all the same) does not permit the magnitude of the random contribution in a particular direction to be determined from, say, the polycrystalline results.
Ben’yaminovich and Veksler (1964) found that for poly
crystalline nickel and tantalum targets bombarded by mercury ions with energy 400 to 1200 eV, the detected energy spectra could be
N(E) = A exp (-E/Eq) , 10<E<100 eV.
Because they detected ions which were assumed to be produced in the arc by ionisation of the neutrals, they considered the neutral spectrum should be of the form
N(E) = BE^ exp (-E/E ).
This energy dependence of the spectrum is different from the two forms measured by Stuart and Wehner for mono- and poly crystalline copper and for tantalum which also obeys a power law,
N(E) cc E~2 *2 .
As commented earlier sputtered ions are included in the measured particle numbers and at least their contribution to the total
count should not be multiplied by the correction factor for the time
spent in the plasma. The presence of the plasma at the target surface
could so modify the conditions that a much higher than normal component of the sputtered beam is ionised at the surface rather than in
passing through the plasma.
In addition once a particle is ionised its interaction with the plasma will change and its kinetic energy can be subject to some
considerable variation. That is the number density of ions' of a
particular energy may not be simply related to the neutral density of
the same energy. Consequently it is difficult to draw any firm
The results of Politick et al (1968) for sputtered potassium show a velocity spectrum of the form
n(V) ^ v 2 *2 , which corresponds to an energy spectrum, n(E) «= E“ s/2.
The most informative and consistent energy distribution
results are those due to Thompson. In these experiments the incident
particle energy (40 keV) was sufficiently high to ensure reasonable penetration depths with the possibility of the generation of significant
collision cascades. If focused collision sequences occur in solids it
would be reasonable to expect to see evidence of them in the sputter products.
The energy spectra for gold and copper single crystals lend considerable support to the idea that focused collision play a
significant role in preferential sputtering.
Figure 2.6a and 2.6b are taken from Thompson (1968) and
Farmery and Thompson (1968). They represent the energy distribution
of the sputtered particles for the conditions shown, plotted as logarithmic functions. The principal characteristics of all these curves is the approximate dependence
N(E) a E~2 .
The time of flight form of the distributions show appreciable
structures (as distinct from the results quoted earlier). Part of this
is no doubt due to the much higher energy resolution of the apparatus
used in collecting these data. Figures 2.7a and b, (also from the
original papers) show the time spectrum for copper single crystal ejection in the <110> and <100> directions respectively, together
» ® <110>
Energy Spectra - Gold
\ l - • N •« v’. S' * \ «• •\ \ \ • « ‘
V.\• . • *
A10~7 Fig. 2.6a
<110> 1 ■ N(E) <100> Copper Spectra E eV E eV 1000 100 10 1 8 6 p(t) 4 2 1 10 102 103 t ysec random Fig. 2.7a
p ( t ) E e v 1000 100 10 1 r andom <100> 1000 F i g . 2 . 7 b t pisec P ( t ) P ( t ) <110> 1000 <100> 1 0 0 0
bF i g . 2 . 8
with the contributions to the measured total of the random, simple focusing and assisted focusing emission as calculated from the Thompson collision cascade theory.
The equivalent spectra for gold targets forms figure 2.8. Even the polycrystalline spectra for gold show considerable
structure (figure 2.9).
By applying the Thompson theory to these results it was possible to calculate for copper:
a. Focusing energy of 50 ± 10 eV for the <110> direction.
b. Assisted focusing energy of 320 ± 50 eV for the
The corresponding values for gold crystals were 167 ± 25 eV and 500 ± 100 eV respectively.
'fence, while the energy spectra derived from low energy bombardment do not convey much understanding about the collision processes which result in sputtering, the higher energy experiments of Thompson’s group amount to quite substantial evidence in favour of random cascades in conjunction with focused collision sequences.
2.332 Ionised particles
Experimental curves of the energy distributions of sputtered ions are available for a variety of combinations of incident ions and
targets. Results representative of three bombarding energy groups are
those of Adylov et al (1970), (300-2800 eV ions incident on molybdenum); Hennequin (1968), (8 keV argon ions on polycrystalline copper and
aluminium); and Jurela and Perovic (1968)(40 keV argon ions on a range of polycrystalline targets).
Poly. Au 1000 t ysec Fig. 2.9 N(E) Fig. 2.10
Hennequin used a retarding potential method to determine the particle energy, but does not appear to have measured the transmission coefficient of his apparatus at different energies. The measured energy distribution for copper ions can be expressed in the form