Electron collisions

Foltz et al.36 have made systematic measurements of electron collisions with laser excited Na nd Ryderg atoms using an apparatus similar to the one shown in Fig. 13.1 but differing in two respects. First, an electron beam is used instead of an ion beam, and second, a magnetic shield encloses the electron beam and interaction region. 

While electrons in conventional beams have velocities too high to have large cross sections, thermal electrons have large cross sections for state changing collisions with Rydberg atoms, and these collisions have been studied in a systematic fashion. Specifically, metastable He atoms in a stationary afterglow have been excited to specific Rydberg states with a laser.37 38 The populations of 

Pillet, R. Kachru, N.H. Tran, andT.F. Gallagher, Abstracts, ICPEAC 13, eds. J. Eichler, W. Fritsch, I. V. Hertel, N. Stotlerfoht, and U. Wille (North Holland, Amsterdam, 1983). 

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The probability for a particular electron collision process to occur is expressed in tenns of the corresponding electron-impact cross section n which is a function of the energy of the colliding electron. All inelastic electron collision processes have a minimum energy (tlireshold) below which the process cannot occur for reasons of energy conservation. In plasmas, the electrons are not mono-energetic, but have an energy or velocity distribution,/(v). In those cases, it is often convenient to define a rate coefficient /cfor each two-body collision process ... 

Nitrogen molecules, a major constituent of air, are excited by electron collisions and the excitation energy is transferred to the O 2 molecules, or the N2 molecules may be dissociated and O atoms fonned via the reactions... 

The light regions in the discharge result from electron collisions with neutral atoms in the gas and from recombination of electrons and positive ions to give atoms. 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

In general, the substrate temperature will remain unchanged, while pressure, power, and gas flow rates have to be adjusted so that the plasma chemistry is not affected significantly. Grill [117] conceptualizes plasma processing as two consecutive processes the formation of reactive species, and the mass transport of these species to surfaces to be processed. If the dissociation of precursor molecules can be described by a single electron collision process, the electron impact reaction rates depend only on the ratio of electric field to pressure, E/p, because the electron temperature is determined mainly by this ratio. 

In a silane-hydrogen discharge the feedstock gases SiHa and H2 take part in all the processes that occur. A large number of reactions have been proposed (see e.g. Kushner [190]). Nienhuis et al. [191] have performed a sensitivity analysis in their self-consistent fluid model, from which a minimum set of reactions have been extracted for a typical low-pressure RF discharge. Tables II and III list these reactions. They will be used in the plasma models described in subsequent sections. The review articles on silane chemistry by Perrin et al. [192] and on hydrogen by Phelps [193] and Tawara et al. [194] have been used. The electron collision data are compiled in Figure 13 [189]. 

FIG. 13. Cross sections for electron collisions for SiH4-H2 (a) SiH4. (b) Si2H (dotted lines) and H2 (solid lines). Abbreviations are ion, ionization dis. dissociation vib. vibrational excitation att, attachment. See Table II for details and references. (Adapted from G. J. Nienhuis. Ph.D. Thesis. Uni-versiteit Utrecht. Utrecht, the Netherlands. 1998. with permission.)... 

II. 51 Pa for H2, and 0.55 Pa for Si2H6. With these partial pressures, and the data on electron collisions as given in Table II, first the EEDF can be calculated, followed by the calculation of the electron transport coefficients and electron impact rates. From a comparison of a Maxwellian EEDF and the two-term Boltzmann... 

The high-energy electrons generated in the plasma mainly initiate the chemical reactions by reactions with the background gas molecules (see Table 12.1). Direct electron impact reactions with NO are usually not important for NO decomposition, as in real flue gas, as well as in experiments in simulated gas, the concentrations of NO are very low (some hundreds of ppm), and therefore, the probability of electron collisions is also low. 

In the presence of oxygen, NO is mainly oxidized to NOz, by reactions with O atoms and with ozone [33,46,76-78], The rate constant of molecular dissociation of 02 by electron collisions is almost two orders of magnitude higher than the dissociation of N2 in... 

Shimamori and Hatano (1976) describe a Febetron-injected microwave cavity apparatus for measuring electron concentration following pulse irradiation. Its application to thermalization in Ar and CH4 is similar to the method of Warman and Sauer (1975). In a related experiment, Hatano et al. (private communication) measure the electron collision frequency directly. 

Intensities of collisionally excited lines relative to hydrogen lines depend on the ionic abundance and on the balance between excitation by electron collisions and de-excitation by both electron collisions and radiation. The emission rates per unit volume are given respectively by ... 

X-rays High-energy electron collisions o I 0 1 c 1 o X-rays for detecting broken limbs... 

The reagent ions are produced by introducing a large excess of reagent gas (e.g., methane) relative to the analyte into an electron impact (El) ion source. Electron collisions produce CH j and CH3 which further react with methane to form CH5 and C2H3 ... 

In Equation 3, e and m are the impinging electron energy and mass, (e) is the reaction cross section, and / (e) is the electron energy distribution function. Of course, if an accurate expression for fie) and if electron collision cross sections for the various gas phase species present are known, k can be calculated. Unfortunately, such information is generally unavailable for the types of molecules used in plasma etching. 

In the etchant-unsaturate model described by Equation 7-10 41), specific chemical species derived from electron collisions with etchant gases are considered. 

The model of electron scattering in high-mobility systems applied in the simulations is rather simplified. Especially, the assumption that the electron velocity is randomized at each scattering to restore the Maxwell-Boltzmann distribution may be an oversimplification. If the dissipation of energy by electron collisions in a real system is less efficient than that assumed in the simulation, the escape probability is expected to further increase. 

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