A mathematical model is developed for traphyphen;modulated, steadyhyphen;state, hopping transport of spacehyphen;chargehyphen;limited carriers, injected into linear lowhyphen;density polyethylene, doped with oxidized lowhyphen;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 bandhyphen;tail or band conduction, i.e., little or no energy barrier to transport within the crystalline regions, and deep traps located at the crystallinehyphen;amorphous matrix boundaries. Two adjustable parameters, the hopping and trap site separations, are used to give good agreement with the experimental currenthyphen;applied field characteristics in the temperature range 50ndash;85thinsp;deg;C for fields less than 4times;105V/cm, and hopping site concentrations of 2times;1019/cm3and 4times;1019/cm3. For the latter concentration, (corresponding to a separation of about 28 Aring;) at temperatures (35ndash;60thinsp;deg;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 (60ndash;85thinsp;deg;C), detrapping contributes to the steadyhyphen;state current. The activation energy in this latter temperature range is 1.17 eV (at 2times;105V/cm). The final current, field, and temperature equation shows that the hopping and trap energies are additive on a semilog plot ofI/Tvs 1/T. Thus, the fieldhyphen;lowered trap depth is 0.87 eV. This result agrees well with a previously determined crystallinehyphen;amorphous trap depth in virgin linear lowhyphen;density polyethylene.
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