Molecular collisions

Abstract

Basic concepts of gas-phase collisions were introduced in Chapter 3, where we described only those processes needed to model the simplest noble gas discharges: electron – atom ionization, excitation, and elastic scattering; and ion –atom elastic scattering and resonant charge transfer. In this chapter we introduce other collisional processes that are central to the description of chemically reactive discharges. These include the dissociation of molecules, the generation and destruction of negative ions, and gas-phase chemical reactions. Whereas the cross sections have been measured reasonably well for the noble gases, with measurements in reasonable agreement with theory, this is not the case for collisions in molecular gases. Hundreds of potentially significant collisional reactions must be examined in simple diatomic gas discharges such as oxygen. For feedstocks such as CF 4 /O 2 , SiH 4 /O 2 , etc., the complexity can be overwhelming. Furthermore, even when the significant processes have been identified, most of the cross sections have been neither measured nor calculated. Hence, one must often rely on estimates based on semiempirical or semiclassical methods, or on measurements made on molecules analogous to those of interest. As might be expected, data are most readily available for simple diatomic and polyatomic gases. The energy levels for the electronic states of a single atom were described in Chapter 3. The energy levels of molecules are more complicated for two reasons. First, molecules have additional vibrational and rotational degrees of freedom due to the motions of their nuclei, with corresponding quantized energies E v and E J . Second, the energy E e of each electronic state depends on the instantaneous con-figuration of the nuclei. For a diatomic molecule, E e depends on a single coordinate R, the spacing between the two nuclei. Since the nuclear motions are slow compared to the electronic motions, the electronic state can be determined for any fixed spacing. We can therefore represent each quantized electronic level for a frozen set of nuclear positions as a graph of E e versus R, as shown in Figure 8.1. For a mole-cule to be stable, the ground (minimum energy) electronic state must have a minimum at some value R 1 corresponding to the mean intermolecular separation (curve 1). In this case, energy must be supplied in order to separate the atoms (R ! 1). An excited electronic state can either have a minimum (R 2 for curve 2) or not (curve 3). Note that R 2 and R 1 do not generally coincide. As for atoms, excited states may be short lived (unstable to electric dipole radiation) or may be metastable. Various electronic levels may tend to the same energy in the unbound (R ! 1) limit. R R R