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

Abstract

Carbon networks fabricated by means of a self-organized process, which is in the focus of our interest, represent disordered porous systems. The degree of disorder and, accordingly, the values of their electric conductivity extending from insulator to metal behavior change via heat treatment under vacuum conditions at process temperatures in the range from 600 to 1000 °C. Upon varying the ambient temperature from 4.2 to 295 K, four transport mechanisms can be observed. For carbon nets whose conductivity is far beyond the metal–insulator transition (MIT), the specific resistivity ρ depends on the temperature T as ρ(T)∝T−b exp([T0/T ]1/p). In the low-temperature range, a Coulomb gap in the density of states located near the Fermi energy level occurs, which means that the characteristic value of the exponent is p=2. At high temperatures, the pre-exponential part ρ(T)∝T−b dominates. In the intermediate temperature range, we disclose Mott’s hopping law with p=3. However, the specific resistivity of the carbon networks subject close to the MIT follows the power law ρ(T)∝T−b with 0≲b≲3 at low temperatures. In the high-temperature range, the specific resistivity is characterized by ρ(T)∝exp(−[T/T1]c−1), where the values for c vary from 1.3 to 1.5. The above four charge transport mechanisms can be explained by the tails in the density of localized states pulled out of the conduction and valence band, as a consequence of disorder and, particularly, by some overlap between these tails.