THEORIES OF SPUTTERING
Although sputtering was discovered by Grove in 1852 and extensively investigated over the next half-century or so very little theoretical work was attempted. The earlier models were based upon thermal evaporation type processes (Blechschmidt and von Hippel, 1928) and those ideas persisted for some time (Townes, 1944). Momentum transfer processes were also considered (Compton and Langmuir, 1930), but these too were unable to account for the large amount of often
conflicting data. In fact the theoretical development of the subject
was hampered by the lack of consistency in the experimental results due largely to ignorance of the vacuum and surface requirements.
A survey of the significant theories up to the mid 1950’s has been produced by Wehner (1955), while Kaminsky (1964) and later
Carter and Colligon (1968) have treated more recent work. The books
of Nelson (1968) and Thompson (1969) contain additional material. A
brief review of even more recent ideas has been given by MacDonald (1970).
Within the bombarding energy range of interest, from a few electron volts to some thousands of electron volts, the theoretical treatment of collisions in solids is simplified substantially by two
fortuitous circumstances. Classical physics concepts and techniques
are satisfactory, without the complexity of a quantum mechanical approach, and for most interactions only binary collisions need to be
the reasons for these assumptions are given. Thompson (I960) also states the conditions which must be met for classical calculations to be justified. He also delineates the range of validity of some of the
commonly used interatomic potentials. A more rigorous description of the inter-relationship between classical scattering theory and the quantum approach is contained in chapter 1 of Geltman's book (Geltman, 1969). The applicability of classical methods to regular crystal
arrays in which fast particles can be channelled has been considered by Chadderton (1968).
Many different models for sputtering have been proposed, most of which account satisfactorily for some of the observations. For example, one of the early momentum transfer theories due to Keywell (1955) in which an analogy is drawn between neutrons slowing down in a moderator and loss of energy of a particle in the collision
cascade, and after suitable choice of values for the displacement and sputtering threshold energies, leads to yield calculations which are in good agreement with experimental results for 0 to 25 keV argon ions on copper.
Similarly theories in which the mean free path of the incident particles is used to determine the number of primary knock- ons and where the yield is assumed to depend upon the number of displaced particles have given good estimates of the yield (Goldman and Simon, 1958; Kinchin and Pease, 1955; Gr^nlund and Moore, 1960).
The various "transparency" theories which account for the variation in yield as a function of the direction of incidence upon single crystals have been mentioned in chapter 1, as have the
successful attempts by Onderdelinden (1968) to relate similar empirical data to channelling processes.
The processes of simple and assisted focusing, which were introduced to account for the form of the ejection patterns from
single crystal targets have also been discussed briefly earlier.
A more recent theory for the sputtering of amorphous
materials, due to Sigmund (1969) leads to excellent predictions of the sputtering yield over a i^ide range of conditions and with a minimum of assumptions (viz, the ion-target and target-target
collision cross-sections, and the atomic binding energies). The
method used random slowing down in an infinite medium rather than a
binary collision model. It was anticipated (Sigmund, 1969) that the
theory could be extended to cover energy distributions and ejection
characteristics not only of amorphous targets but single crystals as well.
Two theories are available which do predict the form of
the energy distribution of the sputter products. Thompson (1968)
considered the problem from the point of view of collision cascades
in a random solid. Veksler (1970) on the other hand treated a
polycrystalline target as though it were an ensemble of randomly arranged single crystals each one of which undergoes sputtering only through focused collisions.
Thompson has extended his theory to include single crystal sputtering and has succeeded in the case of copper and gold targets in getting good agreement between the theoretical and empirical energy spectra.
However, as stated earlier, the generation of ejection spots from crystals in directions for which focusing action seemed improbable, and from very low energy incident ions, such that any focusing chain length would be very small, caused speculation whether some other processes might not be responsible for the preferential ejection. One such theory, due to Lehmann and Sigmund (1966) has attracted
wide interest and acceptance. An investigation of some aspects of the
theory by means of a computer simulation of the collision sequence has cast some doubts on the importance of the process (Nelson and von Jan, 1968).
It is proposed to consider the theories of Lehmann and Sigmund, and Thompson in some detail because of their relevance to the experimental work performed.
Current theories of ion emission are also considered,
although the position is far less satisfactory than for the neutrals. In fact it appears that to date no really comprehensive theory of ionisation processes associated with sputtering is available.