Electrical field dependence of hopping conduction in self-organized carbon networks

Abstract

The influence of the electrical field on the variable range hopping process of porous carbon networks is examined in the range of validity of the law lnσ(T)∝T-1/2, where σ and T mean electrical conductivity and temperature, respectively. We show that the field dependence of the samples investigated in the vicinity of the metal-insulator transition clearly distinguishes four characteristic regions. At low values of the applied electrical field, we have ohmic conductivity. Upon increasing the electrical field E, the electrical conductivity σ rises, first following the law lnσ(E)∝En, where n changes from 1.4 to 2.6 with increasing distance from the metal-insulator transition on the insulating side. Then, at higher electrical field, the conductivity turns to the relation lnσ(E)∝E1.0. The temperature dependence of the hopping length of the charge carriers, determined within the above field regime, develops as l(T)∝T-0.9. At temperatures where the ohmic behavior in the Coulomb gap occurs and obeys the law lnσ(T)∝T-1/2, the electrical conductivity caused by thermally nonactivated charge carriers at high fields complies with lnσ(E)∝E-1/3. The current density j changes as lnj(E)∝E-1/6. The temperature dependence of the threshold electrical field, which characterizes the transition from the low-field to the high-field range, follows Eth∝T1.5. © 2002 American Institute of Physics.