Coulomb gap and variable-range hopping in self-organized carbon networks

Carbon networks fabricated by means of a self-organized process, which is i n the focus of our interest, represent disordered porous systems. The degre e of disorder and, accordingly, the values of their electric conductivity e xtending from insulator to metal behavior change via heat treatment under v acuum conditions at process temperatures in the range from 600 to 1000 degr eesC. Upon varying the ambient temperature from 4.2 to 295 K, four transpor t mechanisms can be observed. For carbon nets whose conductivity is far bey ond the metal-insulator transition (MIT), the specific resistivity rho depe nds on the temperature T as rho (T)proportional toT(-b) exp([T-0/T ](1/p)). In the low-temperature range, a Coulomb gap in the density of states locat ed near the Fermi energy level occurs, which means that the characteristic value of the exponent is p=2. At high temperatures, the pre-exponential par t rho (T)proportional toT(-b) dominates. In the intermediate temperature ra nge, we disclose Mott's hopping law with p=3. However, the specific resisti vity of the carbon networks subject close to the MIT follows the power law rho (T)proportional toT(-b) with 0 less than or similar tob less than or si milar to3 at low temperatures. In the high-temperature range, the specific resistivity is characterized by rho (T)proportional to exp(-[T/T-1](c-1)), where the values for c vary from 1.3 to 1.5. The above four charge transpor t mechanisms can be explained by the tails in the density of localized stat es pulled out of the conduction and valence band, as a consequence of disor der and, particularly, by some overlap between these tails. (C) 2001 Americ an Institute of Physics.