Theoretical models for electron conduction in polymer systems—I. Macroscopic calculations of d.c. transient conductivity after pulse irradiation

Abstract

The simulation of the transient d.c. conductivity in a quasi one-dimensional system of charges produced by a pulse of ionizing radiation in a solid sample has been performed. The simulation is based on the macroscopic conductivity equations and can provide physical insight into d.c. conductivity measurements, particularly for the case of transient currents in samples with internal space charge.

We consider the system of mobile (negative) and immobile (positive) charges produced by a pulse of ionizing radiation in the sample under a fixed external voltage V₀. The presence of space charge results in an electric field which is a function of both the spatial and the time variable: E(z, t). Given the space charge density, the electric field can be calculated from the Poisson equation. However, for an arbitrary space charge distribution, the corresponding equations can only be solved numerically.

The two non-trivial cases for which approximate analytical solutions can be provided are:

• 1.

  (i) The density of the current carriers n(z, t) is negligible in comparison with the density of immobile space charge N(z). A general analytical solution has been found for this case using Green's functions. The solutions for two cases, viz. the homogeneous distribution of space charge N(z) = N, and the non-homogeneous exponential distribution N(z) = A exp(-Bz), have been separately discussed.

• 2.

  (ii) The space charge created in the pulse without any space charge present prior to the irradiation.