Electric fields ionization rates

At still higher fields carriers can acquke enough energy from motion in an electric field to create electron—hole paks by impact ionization. Eor siUcon the electron ioniza tion rate, which is the number of paks generated per cm of electron travel, depends exponentially on electric field. It is about 2 X 10 cm for a 50 kV/cm field at 300 K. The electric field causes electrons and holes so created to travel in opposite dkections. They may create other electron—hole paks causing positive feedback, which leads to avalanche breakdown at sufficiently high fields. 

The fluid model is a description of the RF discharge in terms of averaged quantities [268, 269]. Balance equations for particle, momentum, and/or energy density are solved consistently with the Poisson equation for the electric field. Fluxes described by drift and diffusion terms may replace the momentum balance. In most cases, for the electrons both the particle density and the energy are incorporated, whereas for the ions only the densities are calculated. If the balance equation for the averaged electron energy is incorporated, the electron transport coefficients and the ionization, attachment, and excitation rates can be handled as functions of the electron temperature instead of the local electric field. 

The rates and selectivities of these processes are frequently enhanced by the presence of plasmas, in which a high electric field in a gas causes ionization of molecules, and the reactions of these ions and the increased transport alters reaction rates. We will not consider these processes in this chapter. 

The acid-base properties, and hence ionic character, of peptides and proteins also can be used to achieve separations. Ion-exchange chromatography, similar to that described for amino acids (Section 25-4C), is an important separation method. Another method based on acid-base character and molecular size depends on differential rates of migration of the ionized forms of a protein in an electric field (electrophoresis). Proteins, like amino acids, have isoelectric points, which are the pH values at which the molecules have no net charge. At all other pH values there will be some degree of net ionic charge. Because different proteins have different ionic properties, they frequently can be separated by electrophoresis in buffered solutions. Another method, which is used for the separation and purification of enzymes, is affinity chromatography, which was described briefly in Section 9-2B. 

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