The apparent inter-electrode capacitance of a planar diode

Various experiments have suggested that the effective capacitance of a diode is probably dependent on the magnitude of the anode current: this effect, however, is not disclosed by the classic analyses of Benham and of Llewellyn. This paper shows that an analysis which ignores the emission velocity of electrons is not competent to describe the capacitance effects in a diode. A steady-state solution is found for a planar diode in which the emission velocity is not ignored. Also it is calculated that the mean-square velocity of electrons crossing the potential barrier is the same as the mean-square velocity of emission from the cathode. By considering the inertia effect of the electrons in conjunction with the displacement current at the barrier, an expression is derived for the phase angle of an electrode system. This expression shows that the phase angle is markedly dependent on the anode current. It is therefore thought that the analysis describes the basic mechanism of certain capacitance effects which have been observed in triodes. An Appendix contains the steady-state solution of the temperature-saturated planar diode, and curves are given which show the force at the cathode and at the anode as a function of the anode current, expressed as a fraction of the space-charge limited current; also a curve which shows the transit time as a function of the anode current