Effect of nonuniform work function on space-charge-limited current

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Abstract
The effect of a nonuniformly emitting cathode on a space-charge-limited diode is analyzed. The first part of the analysis is a calculation of the extent to which inhomogeneities in the space charge are reduced by the motion of electrons in directions parallel to the cathode surface. It was found that, in typical cases, outside of a small layer adjacent to the cathode, the space-charge density is virtually constant on surfaces parallel to the cathode. Because of this the total diode current was found to be given by Child’s law even when the cathode has patches whose emission is saturated.