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--> 5 Electron Collision Processes Introduction In modeling and simulation of plasma processing applications, quantitative data are needed on the many reactions involving neutral species and positive and negative ions under practical industrial conditions, especially for those substances that are used directly in plasma deposition and etching. For each chemistry to be considered, ideally, electron collision processes involving all possible reactants, products, and intermediates must be investigated. Cross sections or probabilities for the various reaction channels (ionization, excitation, dissociation, attachment, and recombination) will depend on plasma conditions of temperature and on the energy state of the target species. In this chapter, the general availability of electron-impact cross section data is discussed for each reaction channel. Potential sources of new data, both experimental and theoretical, are described. A set of typical plasma processing substances serve as examples in the discussion of electron-collision cross section availability. These include deposition compounds SiH4 and SiO2; etching gases C1, Br, C12, HCl, F2, HBr, BCl3, and CF4, and decomposition and etching products SiClx and SiBrx. Ionization Atoms For constituent atoms present in plasma etching and deposition (F, C1, Br, C, N, S, H, O), ionization cross sections have been measured to within ±20%.1 The situation is similar, if not better, for rare gases used as buffers and dilutants. Single ionization cross sections for all rare gases are known to better than ±8%, for instance. Little ionization data is available for atoms in excited or metastable states,with the exception of laser-excited alkali atoms and metastable rare gases, H, N, and O. Molecules For plasmas with complex molecules present in the feed gas, detailed understanding requires identification of the specific ions formed by electron collisions. Thus, cross sections are needed for production of parent molecular ions and dissociative ionization products. These are distinct from total ionization cross sections (the sum for all channels), which are measured in some cases but do not provide adequate information on the specific ionic species produced. Channel-specific ionization cross sections are available for a variety of plasma processing compounds, including SiH4, CF4, SF6, CCl2F2, and O2, as well as the common purge gas N2. Total ionization cross sections have been reported for C12 and F2. Changes in these cross sections may occur when the target molecules are vibrationally or electronically excited. Experimental techniques are not well developed to study these effects quantitatively. Experimental and theoretical results for the ionization of vibrationally excited molecules show qualitatively a shift of the ionization threshold to lower energies and a significant enhancement of the cross section in the lower energy region near threshold,2 two effects that can drastically affect the ionization balance in a low-temperature plasma. Many dissociative-ionization cross section measurements made prior to 1990 are suspect because many experiments did not properly account for the fact that fragment ions can be produced with excess kinetic energies that are far greater than thermal energies. Ion losses and other discrimination effects involving energetic fragment ions have seriously compromised many dissociative ionization cross section measurements prior to 1990. For the complex molecules used in plasma processing there are only a few
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--> examples of reliable data for dissociative ionization, such as CH4, SiH4, CF4, and SF6; generally the data are lacking. As noted in Chapter 3, "Radiative Processes and Diagnostics," this lack of data for dissociative ionization, especially near threshold, can significantly limit the ability to quantitatively interpret mass spectrometric measurements. This is the case because a common tactic for measurement of radical concentrations with mass spectrometry is to reduce the electron impact energy to near threshold. Generally, this approach allows discrimination between a signal from a parent molecule ionizing dissociatively and the radical of interest. However, if the parent molecule is vibrationally excited (for example), its dissociative ionization cross section may increase near threshold (see discussion above). This results in a significant drop in confidence in the technique, and may invalidate it completely. Very recently, there have been efforts to measure ionization and dissociative ionization cross sections for complex metal-organic and silicon-organic molecules used in deposition plasmas.3 When considering ion formation by dissociation in discharges, polar dissociation must also be taken into account. Although this is usually a minor process for positive-ion formation, it can make a significant contribution to negative-ion formation. Radicals are a class of highly reactive molecular species that are frequent products in plasma processing. Electron-impact ionization cross sections have been measured to ±20% for SiFx and CFx (x = 1-3), NF2, NF, and SO. These studies apply to ground state targets only. Only a few research groups are actively studying electron-impact ionization, and in even fewer cases have the research programs focused on substances pertinent to plasma processing. Theoretical Methods and Advances For molecules and radicals, the state of the art has until recently consisted of empirical and semiempirical methods and simplistic additivity rules. Recently there have been several new developments: (1) two modified additivity rules that attempt to account for molecular bonding; (2) the Deutsch-Mark formalism, which combines a Gryzinsky-type energy dependence with quantum mechanically calculated molecular structure information (also applicable to atoms); and (3) a new binary-encounter dipole theory. Neutral Dissociation In cases where electron-impact dissociation produces electronically excited fragments that decay radiatively, studies use the optical excitation function technique. Emissions have been measured over a wide spectral range. Several molecules relevant to plasma processing have been studied, providing dissociation cross sections for CF4, SF6, NF3, BCl3,4 and several freons and halogenated methane compounds. Using traditional beam techniques to measure cross sections for electron-impact dissociation of molecules into neutral products is extremely difficult, especially when the dissociation fragments are in the ground state or do not radiate. This difficulty is caused by the lack of sensitive methods for detecting neutral fragments. One beam technique that has been used successfully for measurement of dissociation cross sections involves fast neutral beams formed by charge transfer in conjunction with coincident product detection techniques. In these configurations there can be significant uncertainty in the excited state distribution of the neutral target molecules formed in the charge-transfer process. This method has been applied to the relatively simple molecules N2, O2, CO, and, most relevant to plasma processing, C12. The technique can be extended to other simple molecules that are dominated by two-fragment break-up channels. A serious limitation will arise when the method is applied to more complex polyatomic molecules for which many break-up channels with different numbers of fragments compete. This is at present the only suitable method for studying the dissociation of free radicals into neutral ground-state fragments. Another beam technique is the so-called two-electron-beam technique, in which the first electron beam is used to dissociate the target molecules and a second electron beam "downstream" is used to probe the
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--> dissociation fragments. In the most recent variant of this technique, Sugai and collaborators5 measured absolute and relative dissociation cross sections for various molecules relevant to plasma technology (SiH4, CF4, CH4) using threshold ionization mass spectrometry. With this technique, absolute cross sections can be obtained only for those radical species whose ionization cross sections are known in the near-threshold region. Another method, the ''chemical getter'' method, which traps the dissociation products, has been used to determine the total dissociation cross sections for CF4 and CH4. This technique has very limited applicability to other targets. A method with high potential for detection of neutral dissociation fragments in the ground state is laser-induced fluorescence. This method has not, so far, been applied to molecules of interest to plasma processing. Although many fragments can be detected by this method, a limitation is that tunable lasers are available over a limited wavelength range (roughly 250 to 800 nm) that does not include absorption wavelengths of some prominent dissociation fragments in processing plasmas. The dissociation cross section has been calculated theoretically for a few molecules of interest to plasma processing, most notably Cl2 and NF3, for which the calculated cross section agrees reasonably well with experimental data.6 This calculation is based on the application of the complex Kohn variation method, which, in principle, could be used to calculate cross sections for other targets. Calculations have also been performed for BCl3 and SiC2 (V. McKoy, California Institute of Technology, private communication, 1995). Electron-Impact Excitation For atoms, an extensive database of electron-impact excitation cross sections exists. However, due to their corrosive and reactive nature, some atoms relevant to plasma processing (e.g. F, C1, Br) have not been studied. In principle, there is no reason that these atoms could not be studied. Vibrational excitation data are available for many molecules, but only a few that are used in plasma processing, again due to the corrosive nature of many plasma processing molecules. Exceptions are CF4, SF6, and some freons. There is also a shortage of measured data for electronic excitation (particularly to stable states) of complex molecules. Theoretical methods for calculating the electronic excitation of molecules are maturing and, when properly benchmarked by measurements, can provide cross sections with adequate accuracy. Attachment Cross sections for dissociative attachment range from values (for electronegative gases) that are several orders of magnitude larger than cross sections for positive ion formation, to values (for SiF4 and CF4) that are several orders of magnitude smaller than cross sections for positive ion formation. Even when the dissociative attachment cross sections are small, these processes are important for full characterization of the plasma. The negative ions formed may influence the free-electron density and may also participate in nucleation of parasitic dust. Although there have been few measurements, recent exceptions used Fourier transform mass spectrometry techniques and beam techniques to determine dissociative attachment cross sections for SiF4 and CF47 and SiH4.8 Some experimental effort has been devoted to the study of attachment to vibrationally excited molecules.9 There exist virtually no data on electron attachment to radicals, although such species are produced in large numbers in plasmas. Only a few research groups are engaged in these types of measurements. Momentum Transfer, Swarm, and Discharge Measurements For purposes of modeling electrical discharges in gases, it may not be possible or even necessary to use complete, detailed information about the dynamics of electron-molecule collision processes that produce dissociation. It may be sufficient to consider only total or averaged "effective" cross sections that apply to
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--> a particular discharge condition specified, for example, by electric field to gas density ratio (E/N) or local temperature. Relatively reliable total electron collision cross sections can often be derived from analysis of dam from drift-tube or simple discharge experiments. The approach used requires that there be a reasonably well understood self-consistent model for the transport of electrons that can account for observations of such parameters as the electron drift velocity, ionization growth, the longitudinal and transverse diffusion coefficients, the relative intensity of observable atomic or molecular emissions, and so on. The model must be capable of predicting the kinetic energy distribution of the electrons, e.g., from numerical solution of the Boltzmann transport equation or from a Monte Carlo simulation, and must also be consistent with independently determined cross sections (such as ionization cross sections) that are known to be reliable. This method is most often used to derive momentum transfer cross sections, and inelastic cross sections for low threshold processes such as rotation and vibration. There are numerous compendia of momentum transfer cross sections derived in this fashion.10 This approach has also been used successfully to generate fairly complete collision cross section data sets for several atomic and molecular species. However, except for a few cases such as SF6, it has generally been difficult to distinguish dissociation processes from other types of molecular excitation processes. With the advent of more sophisticated diagnostics such as two-photon laser-induced fluorescence, it is possible to measure the densities of neutral dissociation fragments, from which dissociation rates can possibly be extracted. Information about reactive fragment densities can also sometimes be determined indirectly from examining the products of subsequent neutral chemistry in which these species are involved, e.g., fast reactions of H with NO2 to form NO and of F with H20 to form HF. General Comments Of the major system constituents selected as examples, consider SiH4. Silane has been the object of intense study, especially during the last 5 years.11 Fundamental studies have provided cross sections for dissociative ionization, neutral attachment, and dissociative attachment. Cross sections are not available for excited-state targets. Carbon tetrafluoride can be described as a success story, in that it has been the subject of intense study and pertinent data are well known.12 Accurate cross sections have been measured for dissociative ionization (the parent ion CF4+ is unstable). A report of recent measurements on neutral dissociation has been published recently.13 Cross section measurements have been reported for parent ionization of the radicals CFx (x = 1-3) and dissociative ionization of CF3. Measurements have also been made for dissociative attachment (negative ion formation). The picture is less complete for the other species in the example set. For the atoms of interest, ionization and excitation cross sections are known. For C12 and F2, only total ionization and excitation cross sections are known. Vibrational excitation and momentum transfer cross sections have been calculated. No data were found on dissociative ionization or neutral dissociation. For Br2, no data have been reported for. For HCl, cross section sets have been derived from swarm data. Dissociative attachment cross sections have been measured. For HF, vibrational excitation cross sections have been measured and dissociative attachment cross sections derived. No additional data are available, and no complete data set has been proposed. No data were found for HBr and only limited data exist for BCl3.14 By applying existing techniques, one could in principle obtain full data sets for many compounds. The existing database is most complete for those processes that are least relevant for the modeling and diagnostics of processing plasmas, whereas there is a serious lack of reliable experimental data for the most important processes (dissociation into neutral ground-state fragments, data for free radicals, data for vibrationally excited molecules and radicals, and data for excited target species).
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--> It is entirely feasible to construct an electronic database including sources of data for compounds used in plasma processing and files of the corresponding numerical data. Maintained as an ongoing effort and distributed using modem technologies, such a database would improve the efficiency of efforts to model and simulate plasma reactors. Findings Data for electron-neutral collisions are sketchy at best for most species of interest in plasma processing, although some species, such as SiH4 and CF4, have received considerable attention. However, little information is available for dissociation products or for species in excited states. Recent progress in computational methods based on quantum scattering offers the possibility that the costly and time-consuming experiments may be augmented or even replaced by large-scale computation. References 1. T.R. Hayes, R.D. Wetzel, and R.S. Freund, Phys. Rev. A 35:578 (1987); R.S. Freund, R.C. Wetzel, R.J. Shul, and T.R. Hayes, Phys. Rev. A 41:3575 (1990). 2. V. Tarnovsky, A. Levin, H. Deutsch, and K. Becker, J. Phys. B 29:135-49 (1996); R. Celiberto and T.N. Rescigno, Phys. Rev. A 47:1939 (1993). 3. R. Basher, M. Schmidt, and H. Deutsch, Contrib. Plasma Phys. 35:375-94 (1995); S. McGinnis, K. Riehl, and P.D. Haaland, Chem. Phys. Lett. 232:99 (1995); R. Basner, R. Foest, M. Schmidt, F. Sigeneger, P. Kurunczi, K. Becker, and H. Deutsch, Int. J. Mass Spectrom. Ion Processes 153(1):65 (1996). 4. A. Blanks, A.E. Tabor, and K. Becker, J. Chem. Phys. 86:4871 (1987). P.G. Gilbert, R.B. Siegel, and K. Becker, Phys. Rev. A 41:5594 (1990). 5. T. Nakano, H. Toyoda, and H. Sugai, Jpn. J. Appl. Phys. 30:2908 (1991); T. Nakano, H. Toyoda, and H. Sugai, Jpn. J. Appl. Phys. 30:2912 (1991); M. Ito, M. Goto, H. Toyoda, and H. Sugai, Contrib. Plasma Phys. 35:405 (1995); H. Sugai, H. Toyoda, T. Nakano, and M. Goto, Contrib. Plasma Phys. 35:415 (1995). 6. T.N. Rescigno, Phys. Rev. A 50:1382 (1994); T.N. Rescigno, Phys. Rev. A 51:329 (1995). 7. I. Iga, M.V.V.S. Rao, S.K. Srivastava, and J.C. Nogueira, Z. Phys. D 24:111 (1992). 8. P. Haaland, J. Chem. Phys. 93:4066 (1990). 9. L.G. Christophorou, in Nonequilibrium Processes in Partially Ionized Gases, ed. M. Capitelli and J.N. Bardsley (Plenum Press, New York, 1990). 10. See, for example, E. Beaty, J. Dutton, and L.C. Pitchford, A Bibliography of Electron Swarm Data, JILA Information Center Report No. 20 (December 1979). 11. R. Nagpal and A. Garscadden, "Low-Energy Collision Cross Sections for SiH4," J. Applied Phys. 75:703 (1994). 12. R.A. Bonham, "Electron Impact Cross Section Data for CF4," Jpn. J. Applied Phys. 1 33:4157 (1994). 13. H. Sugai, H. Toyoda, T. Nakano, and M. Goto, Contrib. Plasma Phys. 35:415 (1995). 14. R. Nagpal and A. Garscadden, "Electron Collision Cross Section of Boron Trichloride," Applied Phys. Lett. 64(13):1626 (1994).
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