The Electric Field in Diodes and the Transit Time of Electrons as Functions of Current

Equations, applicable to all the most simple symmetries, are developed as approximate solutions of the related problems of potential distribution and transit time in diodes as functions of current. For the case of coaxial cylinders, calculations based on these equations have been made. Although these calculations fail to confirm Ivey's suggestion that the ratio of the field at the cathode with any degree of space-charge to that in the absence of space-charge is a universal function of the ratio of the actual current to the space-charge-limited current, they suggest that the function varies slowly as the geometry is changed. Thus small corrections to the function developed for parallel planes suffice to give a solution of high accuracy for any ratio of anode to cathode radius. Functions, applicable to electrons moving between coaxial cylinders, are tabulated to facilitate calculations of off-cathode field, off-anode field, transit time, and the potential distribution for any fraction of the space-charge-limited current.