An Introduction to Gas Discharges by A. M. Howatson (Auth.)

By A. M. Howatson (Auth.)

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In the absence of an electric field, there is an equilibrium in which the rate of production of charged particles is just balanced by the rate of recombination. If now a small voltage is applied to the electrodes, producing a field strength E of about 1 V/cm or less, current flows by the movement of the already existing ions and electrons. If the current is small enough, it will scarcely upset the equilibrium and its value is therefore proportional only to the speed at which the ions and electrons can move to the electrodes; since the mobilities are nearly constant under these conditions, the current density j is proportional to E.

This is the Schottky effect; it can be calculated by classical methods in terms of the force on an electron. At room temperatures the total emission is still low for ordinary field strengths. If, however, the electric field is in the order of 106 volts/cm an electron current flows which is appreciably greater than the calculated thermionic value. The reason for this can be properly explained only in terms of quantum mechanics, but in essence the field serves to pull electrons through the potential barrier represented by the work function, however small their thermal energy.

By inserting in eqn. e, it can be shown that mobility is affected in a precisely analogous way to diffusion. H ~ DJße and which is inversely proportional to B2. 2). In practice, drift across the field is often found to vary as \jB rather than \/B2, an effect known as Böhm diffusion which can be explained in terms of small-scale instabilities. The diffusion of positive ions is affected in the same way as that of electrons; but we should note that for concentration gradients in the same direction Hall diffusion occurs in opposite directions, while Hall drift in a field E occurs in the same direction for the two species.

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