The electrical characteristics of fixed charge membranes: solution of the field equations.

A theoretical analysis is made of the electrical characteristics of a membrane containing two fixed charge regions, of opposite sign, in contact. Profiles of ion concentrations, electrostatic potential, space charge density, as well as the voltage-current characteristics were obtained by numerical integration of the field equations on a computer. Comparison with the predictions of an earlier analysis of this system (Coster, 1965) shows that the latter is valid to a good approximation for membranes > 70 A in thickness. In particular the form of the electrical characteristics, including the punch-through effect, have been verified by the computer analysis. The range of useful validity of the earlier analysis, the use of Boltzmann statistics when currents are present, and variation of membrane capacitance with applied potential, are discussed in the light of the results obtained.