Hopping conduction and localized states in p-Si wires formed by focused ion beam implantations

Localized states in p-Si wires formed in n-Si(100) substrates by selective ion implantation using a focused Ga+ ion beam have been investigated. The electrical conductance has the temperature dependence of one-dimensional (1D) variable-range-hopping conduction in the temperature range below 50 K, sigma = sigma(0) exp[-(T-0/T)(1/2)]. The magnetoresistance R(H) of p-Si wires at 4.2 K shows the negative and positive magnetoresistances at weak and strong magnetic fields, which have the relation that R(H)/R-0 proportional to exp(-beta H) and R(H)/R-0 proportional to exp(alpha H-2), respectively, where R-0 is the resistance without the magnetic field H. These characteristics can be explained by the 1D hopping conduction mechanism under the magnetic field. By expanding a three-dimensional model, we derive an equation of positive magnetoresistance in 1D hopping conduction. From the temperature dependence of conductance and positive magnetoresistance, the localization length, hopping distance, and density of localized states are estimated to be about 2 nm, 8-9 nm and about 10(9) cm(-1) eV(-1), respectively. This result indicates that the carrier transport is confined with the region of a few tens of nanometers. (C) 1998 American Vacuum Society.