Calculations are presented of the components of conductance and capacitance of a condenser made of material of continuously varying conductivity. The model is a plane parallel slab with electrodes on the parallel faces, the permittivity being uniform and the conductivity being a function of distance through the slab perpendicular to the faces. Both conductivity and permittivity are taken as independent of frequency. Two different conductivity profiles are considered in detail, one in which the conductivity is a linear function of depth near the surface, and the other in which the resistivity is a similar linear function. Conductivity profiles resembling these might arise from impurity diffusion from the surface, or during crystal growth.
When the ratio of interior to surface conductivity is of the order of ten or less, these models both give impedances which vary with frequency in a manner extremely close to that predicted by a simple Debye model. It may thus happen that experimental curves can be fitted to any of these models equally well, and the number of adjustable constants is the same. The question of which model, if any, is apt must then be decided on other grounds; one set of experimental results is cited to which the layered conductivity model is believed to apply.