Energy distribution functions

We have seen various kinds of explanations of why may vary with 6. The subject may, in a sense, be bypassed and an energy distribution function obtained much as in Section XVII-14A. In doing this, Cerefolini and Re [149] used a rate law in which the amount desorbed is linear in the logarithm of time (the Elovich equation). 

Gorse C and Capitelli M 1996 Non-equilibrium vibrational, electronic and dissociation kinetics in molecular plasmas and their coupling with the electron energy distribution function NATO ASI Series C 482 437-49... 

Amadei, A., Apol, M. E. F., Di Nola, A., Berendsen, H. J. C. The quasi-Gaussian entropy theory Free energy calculations based on the potential energy distribution function. J. Chem. Phys. 104 (1996) 1560-1574... 

Figure 13. Electron energy distribution functions of a CH4/H2 plasma as a function of pressure, (a) 50 mTorr. (b) 40 mTorr. (c) 30 mTorr. (d) 20 mTorr. (e) 10 mTorr. Reprinted with permission from [88], K. Okada et al., J. Vac. Sci. TechnoL, A 17, 721 (1999). 1999, American Institute of Physics.

Electron energy distribution function The distribution function of electrons in a plasma. That of a low-pressure radiofrequency plasma generally consists of two Maxwellian distributions, that is, fast and slow electrons. 

For low-pressure plasmas containing mainly inert gases the electrons can be characterized by a Maxwellian electron energy distribution function (EEDF). How-... 

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. 

A second type of gas phase collision is that occurring between the various (heavy) species generated by electron impact reactions, as well as between these species and the unreacted gas-phase molecules (25,2d). Again, dissociation and ionization processes occur, but in addition, recombination and molecular rearrangements are prevalent. Similar rate expressions to that of Equation 2 can be written for these collisions (27). In this case, the concentration of each chemical species, along with the collision cross section, and the species energy distribution function must be known if k is to be calculated. Clearly, much of this information is presently unknown. 

Figure 5. Electron energy distribution functions for various gases and gas mixtures. (Reproduced with permission from Ref 24 J...

That is, the high-pressure limit dissociation rate coefficient of A, k, is independent of the density ([M]) of the system. Under these conditions, [A ] is related to the thermal energy distribution function by... 

Troe s analysis summarized above requires the knowledge of both low- and high-pressure rate constants, in addition to an empirically determined to describe the actual fall-off behavior. We already discussed methods for the estimation of high-pressure rate parameters. The low-pressure rate parameters can be estimated by recognizing the fact that ko represents pure energy transfer limitations, and thus can be determined from rate of collisional energization of A and from the thermal energy distribution function K E, T) ... 

Rotational-vibrational energy distribution function I 10-3 erg-sec Nuclear spin quantum number... 

Accordingly, the catalytic activity in a given catalytic reaction depends on only four factors. Two of them are specific for the system as a whole the activation energy and the reaction order. The latter may be reduced to the heat of adsorption, as b0 is a nearly universal constant. The other two factors are, at least in first approximation, properties of the catalyst its surface area F and its energy distribution function. Future work will have to answer the question of which parameters control, qualitatively and quantitatively, these four factors. 

Fig. 5. Energy distribution functions for electrons ejected from tungsten by 10 eV noble gas ions. Verticale lines on the abscissa indicate the energies E — 2( ). (From Ref )...

The same situation is to be expected for the excited states with the only difference that now the most probable energy states are shifted by the stored excitation energy upwards or downwards depending on whether the excited molecule acts as a donor or as an acceptor 20>. These energy distribution functions for a molecule in the ground state and in the excited state are represented in Fig. 3. They can be described by the following equations ... 

---