Shot Effect in Space Charge Limited Currents

The shot effect in space charge limited currents from tungsten and thoriated tungsten has been investigated. The effective fluctuation level is recognized, in general, as the combination of a depression due to pure space charge, and an elevation due to the liberation of electrons by positive ions. The magnitude of the elevation may be such as to carry the fluctuation level far above that for the same current under temperature limitation, or it may simply alter the form of the depression curve. The abnormal fluctuations observed have been analyzed, and their cause traced to inherent mixed emission from the metal surface. The effect of age and heat treatment has been studied for specimens of tungsten. A double grid tube has been used for obtaining a space stream consisting solely of electrons, and the conditions determined under which this stream is governed by the laws of pure chance applying in the simple shot effect theory. With this arrangement space charge measurements of fluctuations can be made over a considerable range with the same degree of precision attainable with temperature limited currents. Considerations involving statistical correlation between instantaneous values of the anode current provide a possible theoretical basis for the space charge depression of shot effect. This treatment yields an expression for the ratio of the mean square value of the fluctuation voltage under given space charge conditions to that under strict temperature limitation of the current: $\frac{{{\overline{V}}_s}^2}{{{\overline{V}}_t}^2}=f\left(\frac{i_0}{i}\right)e^{-\frac{{\omega }^2}{2{\alpha }^2}}$ ${\mathrm{i}}_0$ is the space current, $i$, the saturation current, or total emission associated with a particular emitter temperature, and their ratio characterizes the space charge situation. It has been shown that in the absence of abnormal effects, the depression of the mean square fluctuation voltage which results is independent of the frequency, $\frac{\omega }{2\pi }$, at which it is measured. This conclusion provides information regarding the spread of the correlation function defined in the theoretical section. A relation showing the fluctuation depression proportional to the square of the current depression under space charge is indicated.