Hopping model for charge transport in amorphous carbon

A numerical hopping model is developed to investigate the temperature depen dence of electrical conductivity in a distribution of localized states. An exponential energy dependence of the density-of-states (DOS) distribution ( N-0/E-0)exp(E/E-0) is assumed, together with a high DOS value (1 x 10(18)-1 x 10(21) cm(-3) eV(-1)) at the Fermi level. The low-field de conductivity is dominated by a subset of the localized states centred at a mean transpor t energy E-t located well above E-F; both E-t and the distribution width (D eltaE much greater than kT) increase with increasing temperature, in the ra nge 50-500 K. It is found that the effective activation energy E-act and ap parent conductivity pre-factor sigma (0) both increase with increasing temp erature. In any given temperature range, E-act decreases with increasing DO S at E-F, while sigma (0) decreases exponentially with increasing E-0. A li near relationship between log(sigmaT(1/2)) and T-1/4 is predicted up to hig h temperatures with a strong positive correlation between the pre-factor si gma (00) and the slope T-0(1/4). This model is applied to electrical transp ort in amorphous carbon and carbon alloys where bonding and antibonding pi orbitals produce highly localized states decoupled from extended sigma stat es. Unlike the classical variable-range hopping at the Fermi level, this mo del describes experimental data using physically acceptable values of N(E-F ), E-0 and the localization radius 1/gamma = 5 Angstrom. Its predictions pr ovide a framework to understand the increased conductivity brought about by 'dopant' atom incorporation.