Boundary Conditions at Infinity for a Single Blocking Electrode

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Abstract
A mathematical appraisal is made of the boundary conditions at infinity for certain space-charge problems such as the single blocking electrode. Fulfillment of the boundary condition that the potential approach a limiting value at infinity resides in an appropriately devised theorem. The validity of approximate Poisson-type differential equations can be ascertained by invoking the Jacobian. Two separate situations are considered: (1) carriers of either sign mobile, (2) positive charges fixed. The latter corresponds to a problem (first) considered by MacDonald. A new formulation for the latter proves illuminating and an asymptotic solution is deduced for the spatial variation of the potential which reflects the essential exponential nature of its behavior.

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