Steady-state bulk trap-modulated hopping conduction in doped linear low-density polyethylene

Abstract

A mathematical model is developed for trap-modulated, steady-state, hopping transport of space-charge-limited carriers, injected into linear low-density polyethylene, doped with oxidized low-density polyethylene. Poole field lowering of the trap depth is also included. The hopping sites are carbonyl groups provided by the dopant, lying in the amorphous regions of the sample. We assume band-tail or band conduction, i.e., little or no energy barrier to transport within the crystalline regions, and deep traps located at the crystalline-amorphous matrix boundaries. Two adjustable parameters, the hopping and trap site separations, are used to give good agreement with the experimental current-applied field characteristics in the temperature range 50–85 °C for fields less than 4×105 V/cm, and hopping site concentrations of 2×1019/cm3 and 4×1019/cm3. For the latter concentration, (corresponding to a separation of about 28 Å) at temperatures (35–60 °C) that are too low to thermally detrap injected carriers (that are trapped before reaching the steady state), conduction takes place by hopping in the amorphous regions over an energy barrier of 0.30 eV. At elevated temperatures (60–85 °C), detrapping contributes to the steady-state current. The activation energy in this latter temperature range is 1.17 eV (at 2×105 V/cm). The final current, field, and temperature equation shows that the hopping and trap energies are additive on a semilog plot of I/T vs 1/T. Thus, the field-lowered trap depth is 0.87 eV. This result agrees well with a previously determined crystalline-amorphous trap depth in virgin linear low-density polyethylene.