Small-Shot Effect and Flicker Effect

The Flicker Effect.—J. B. Johnson observed, under certain conditions (oxide coated and tungsten filaments, low frequencies, electron currents high but not high enough for space charge effects), voltage fluctuations across connected resonant circuits which were much larger than the theory of the small-shot effect would lead one to expect. Analyzing Johnson's curves, it is found that this effect increases as the square of the electron current $i_0$ instead of as the first power as in the case of the small-shot effect. This fact supports Johnson's hypothesis that the effect is independent of the small-shot effect and that it should be attributed to fluctuations in the properties of the surface (flickering) resulting in fluctuations in the electron current. The trend with the natural frequency of the connected circuit is likewise different from that observed in the small-shot effect. This can hardly be due to a statistical cause, and one must furthermore assume that there is a time element involved in the elementary process underlying the flicker effect. The elementary atomic process underlying the flicker effect is the appearance of an individual foreign atom or molecule in the surface of the cathode, changing the ability of the surface to emit electrons so long as the foreign atom remains. The influence exerted upon the current by foreign atoms in the surface may be calculated with sufficient approximation from the electrical image theory and Langmuir's doublet theory. The effect is proportional to the current density, and of such magnitude as to indicate that each foreign atom exerts its doublet effect uniformly over the surface. From the assumptions that the elementary atomic processes are independent of one another and that the length of stay of the foreign atoms in the surface conforms to statistical laws, the frequency distribution of the flicker effect is derived and compared with Johnson's experiments, whence it is possible to determine the length of stay of the foreign atom in the surface. The total number of foreign atoms in the surface of an oxide coated filament is computed from Johnson's measurements as being about $\frac{1}{3}$ of all the atoms present in the surface; while the average length of stay is estimated from the curves to be about.001 second. The number of foreign atoms appearing per unit time on the surface is some 200 times as great as the number of atoms of residual gas striking the surface per unit time, from which it is inferred that the essential cause of the flicker effect with oxide cathodes lies in a continual exchange of positions by the components of the oxide. For tungsten filaments the mean length of stay is greater than $\frac{1}{20}$ second; the number of foreign atoms appearing in the surface per unit time is some 20,000 times smaller than with oxide filaments, so that in this case it would be possible to ascribe the flicker effect to residual gas atoms striking the tungsten surface and remaining on it a longer or shorter time. The variation of the flicker effect with the square of the total current follows from the assumption that the current change due to one foreign atom is proportional to the total current. From this assumption also follows the relative independence upon temperature. A value is given for the mean square voltage fluctuation produced by the effect in terms of the impedance of the connected circuit, and formulas are given for circuits of various kinds. Measurements with two circuits, one being resonant and the other a pure resistance should provide a definite check of the calculated length of stay of the foreign atoms.