Electron resonance-tunneling, negative differential resistance and positive packet formation in polyethylene

Most existing models for the transport of charge through polyethylene, although acknowledging local trapping states arising from physical and chemical disorder, have been based on an underlying energy band continuum of electron and hole states as for a crystalline semiconductor. As a consequence they do not account for a number of factors which are being increasingly acknowledged as important for charge transport in molecular polymer solids generally. On a mesoscopic scale, polyethylene has a complex structure and charge transport through the solid will involve inter- as well as intra-molecular passages. In the following hole transport, which is likely to be very different from electron transport, is considered. Holes are constrained by the bonding structure of the hydrocarbon chains and by any conformational changes involved. In traversing a field-line path between electrodes they will be forced to make inter-molecular transfers through the amorphous phases which will largely determine their transport characteristics. The quantum mechanical electron resonance tunneling features of these transfers, influenced by Boltzmann distributions of the valence states involved, produces a velocity-field relationship having a negative differential resistance (NDR) characteristic and thus to the prediction of positive charge packet propagation at high fields in agreement with experiment. The universal importance of long-range tunneling in a broad spectrum of electronics from nanometric organic molecular electronic devices to redox energy transduction through proteins is emphasized.