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As was true in the sputtering process, energetic ions undergoing implantation can interact with a lattice in two ways: (1) at low energies, ions interact with the lattice as a collective whole; or (2) at higher energies, ions can interact by sequential binary collisions with individual atoms of the lattice. It has been the collective experience of individuals in the field of solid state physics that the second, binary collisional model is the most productive theoretically, and the most accurate when compared with experiments.
Binary collisions of ions with atoms in a solid can be of two types:
Figure 14.20. Ion implantation of the surface of a crystalline material. Implanted ions are
shown as full circles.
clouds of the incident and target atoms. Electrons of either atom can be excited or stripped, causing further ionization. These interactions give rise to electronic stopping.
(2) Nuclear collisions, in which the collisions are dominated by the atomic mass of the ions and target atoms, which is concentrated in their nuclei. Such interactions give rise to nuclear stopping, which can result in sudden changes in direction, and even displacements of target atoms from lattice sites. This terminology is unfortunate since, in the field of solid state physics, ‘nuclear collisions’ do not involve nuclear forces or interactions, the meaning normally understood in fusion research and nuclear physics. In almost all cases, an implanted ion will undergo a large number of collisions before it comes to rest in the lattice.
Interactions of energetic ions with a lattice can be further characterized by two physics regimes: (1) interactions describable by classical mechanics; and (2) interactions requiring a quantum-mechanical description. As will be illustrated later, most industrial applications of sputtering or ion implantation are in the classical physics regime.
The analytical theory of nuclear stopping depends on the distance of closest
approach, b, given by the point at which an incident ion of energy Ei eV gives up its maximum kinetic energy to the potential energy of the target atom. In a head-on collision, the initial kinetic energy will be equal to this potential energy,
E1= eE1 =
Z1Z2e2
4πε0b
where a0 is the Bohr radius, the classical radius of ground-state electrons in hydrogen, given by a0= h2 4π2e2m p = 5.2918 × 10 −11m (14.44) or a0= 0.5918 ˚A. (14.45)
When b < a, the incident ion undergoes Rutherford scattering (a Coulomb
collision) with an electrostatic potential V ∼ 1
r. (14.46)
When b> a, the interaction is screened by the electron clouds, and the repulsive part of the interaction potential is approximated by
V ∼ 1
rn (14.47)
where n is an integer greater than unity. To determine whether the interaction is electronic or nuclear, the penetration parameter,ξ, is defined as
ξ ≡ b
a. (14.48)
Ifξ < 1, the collision is nuclear or Coulomb-like. If ξ ≥ 1, the collision is
electronic.
To determine whether the collision is classical or quantum mechanical, the distance of closest approach, b, is compared to the De Broglie wavelength of the incident ion,
λ = h
2πmrv1
Table 14.4. Slowing down parameters for a 300 keV nitrogen ion implanted in silicon.
Energy E (eV) χ logχ ξ logξ 300 000 141 2.15 0.0273 −1.56 30 000 446 2.65 0.273 −0.564 3 000 1 411 3.15 2.73 0.436 300 4 462 3.65 27.3 1.436 30 14 111 4.15 273 2.436 14 20 655 4.32 585 2.77
where mris the reduced mass,
mr=
M1M2
(M1+ M2)
kg (14.50)
andv1is the velocity of the incident ion,
v1=
2e E1
M1
m/s. (14.51)
The distance of closest approach, b, and the De Broglie wavelength are used to define the quantum scale parameter,χ,
χ ≡ b
λ. (14.52)
When χ ≤ 1, b ≤ λ and a quantum-mechanical treatment is required. If
a ≤ λ (equivalent to ξ ≤ χ) a quantum-mechanical treatment of the electronic
interactions is also required. The division of the ξ–χ space into classical and quantum-mechanical regions is indicated in figure 14.21. For classical
interactions, bothχ > 1.0 and χ > ξ must be satisfied simultaneously. For the nuclear (or Coulomb-like) stopping regime,ξ ≤ 1.0, as indicated in figure 14.21.
For the electronic stopping regime,ξ > 1.0, also indicated in figure 14.21. The utility of figure 14.21 is that as an ion slows down in a solid, the relation
χ ∝ ξ1/2 (14.53)
represents the slowing down of an ion’s velocity. This relation is a straight line of slope 12which terminates at the upper right-hand corner with the Frenkel-pair
energy, the energy required to remove a single atom from deep within the lattice.
This energy is 14 eV in silicon.
The trajectory of a 300 keV N+ ion slowing down to 14 eV in silicon is plotted in figure 14.21 on theχ–ξ plane, and the individual points are listed in table 14.4. The nitrogen ion begins in the classical nuclear stopping regime at an
Figure 14.21. The quantum scale parameter ξ plotted as a function of the screening
parameterχ.
energy of 300 keV. It moves to the upper right-hand corner through the classical regime along a straight line with a slope of 12, and terminates in the electronic stopping regime. In this case, as with most ion implantations of industrial interest, the interactions remain in a regime described by classical physics during the entire slowing-down process.
REFERENCES
Bohdansky J, Roth J and Bay H L 1980 An analytical formula and important parameters for low-energy ion sputtering J. Appl. Phys. 51 2861–5
Langley R A, Bohdansky J, Eckstein W, Mioduszewski W P, Roth J, Taglauer E, Thomas E W, Verbeek H and Wilson K L 1984 Data Compendium for Plasma–Surface
Interactions (Vienna: IAEA) ISBN 92-0-139084-X
Molchanov V A and Tel’kovskii V G 1961 Variation of the cathode sputtering coefficient as a function of the angle of incidence of ions on a target Sov. Phys.–Dokl. 6 137–8 Perry T S 1993 Coming clean IEEE Spectrum 30 20–6
Rakowski W 1989 Plasma modification of wool under industrial conditions Melliand
Textilberichte 70 780–5
Roth J, Eckstein W, Gauthier E and Laszlo J 1991 Sputtering of low-Z materials J. Nucl.
Thomas E W (ed) 1985 Atomic data for controlled fusion research volume III: particle interactions with surfaces ORNL Report 6088/V3
Wiffen F W 1984 Materials requirements and potential solutions for fusion reactors Proc.
IEEE Minicourse on Fusion Experimental/Reactor Systems (17 May, St Louis, MO)
unpublished
Winters H F 1980 Elementary Processes at Solid Surfaces Immersed in Low Pressure
Plasmas (Topics in Current Chemistry 94, Plasma Chemistry III) ed S Veprek and
London in the early years of the 19th century. This work included the electrical arc, developed by Sir Humphry Davy (1778–1829), and the low-pressure glow discharge, developed by Michael Faraday (1791–1867). Two hundred years of plasma-related research and development has left a rich legacy of plasma sources and their variants, a selection of which are discussed in Volume 1 of this book. The many current applications of these sources have been discussed by the US National Research Council (National Academy 1991). Other sources of information on plasma sources and their applications include Boenig (1988), Lieberman and Lichtenberg (1994), Smith (1995), and Lieberman et al (1996).
Not all of the plasma sources discussed in the technical literature have proven practicable or economic for industrial applications. For example, sources requiring high magnetic fields (above approximately 50 mT) over a large volume are at a disadvantage for industrial use because of the decreased reliability and increased capital and operating costs associated with electromagnets. Sources that operate under vacuum are at a disadvantage with respect to those that operate at 1 atm because of the increased capital costs and the requirement for batch processing of workpieces associated with vacuum systems.
In the microelectronic industry, plasma sources that operate under vacuum, at low pressures with long ion mean free paths are preferred to higher pressure sources in order to enhance directional etching. Beyond these technical factors, some plasma sources have not been accepted because of unfavorable patent or licensing issues. Only a relatively small number of plasma sources have achieved, or are likely to achieve, widespread industrial acceptance. In this chapter, we emphasize these ‘standard’ plasma sources, now used in large numbers, as well as selected additional sources that show promise for future development.
The development of atmospheric pressure plasma sources to replace plasma 37
processing in vacuum systems is a current trend in industrial plasma engineering. This trend is likely to continue in the early decades of the 21st century until every possible plasma-processing application involving glow discharges and arcs/torches is conducted at 1 atm, or until it is clear that operation in a vacuum is unavoidable. Thermal plasma processing with arcs or plasma torches, corona treatment, and surface treatment with dielectric barrier discharges has been conducted at 1 atm since their industrial introduction. However, conversion of the industrial plasma-processing applications of vacuum glow discharges to operation at 1 atm has barely begun, and may involve plasma sources discussed in this chapter.
15.1
CHARACTERISTICS OF INDUSTRIAL PLASMA
SOURCES
The plasma sources used in industry are described by their manufacturers and users in terms of a small set of characteristics that define their regime of operation. These source characteristics include the plasma type, the nature of its power supply, the operating pressure, and the mode of interaction of the source with a workpiece. Significant differences in these plasma source characteristics can, nonetheless, generate plasmas for which the active species concentrations, electron number densities, electron kinetic temperatures, sheath potential drops, etc, are very similar, while the technical means of generating the plasma are quite different.
In industrial plasma sources, the active-species concentrations and electron- number densities tend to be proportional to the input plasma power density. If the input power density and other plasma parameters are the same in different plasma sources, the usual result is the same plasma-processing effect on the workpiece, achieved by different means.