A quantitative analysis of the voltage-current relationships of fixed charge membranes and the associated property of "punch-through"

Abstract

A theoretical analysis of the voltage-current relationship is carried out in a membrane consisting of two fixed charge regions, of opposite sign, in contact. This is achieved by applying the diffusion equations to this system in conjunction with the Poisson-Boltzmann equation. The latter has been successfully applied by Mauro to determine the profiles of the electrostatic potential in his treatment of the capacitative property of such a system. It is shown that the system displays the property of rectification and is very similar in many respects to a solid state P-N junction diode. It is also shown that for the case of reverse bias, an electrical breakdown phenomena can occur. This is referred to as the "punch-through" effect. "Punch-through" was observed in experiments on the electrical characteristics of the membranes of Chara australis and Nitella sp. The experimental results are discussed in relation to the theoretical analysis.