Hopping conductivity with distributed energy-barrier heights

Abstract

An alternative expression for the temperature dependence of hopping conductivity is proposed. A conduction model is proposed based on a collection of many independent Arrhenius-type processes. The density in the material considered has a A-shaped distribution as a function of activation energy, for example Gaussian, isosceles, and scalene distributions. The validity of the model has been checked with the electrical-conductivity data of disordered carbon fibers which show a metal-insulator transition. The result is that the conductivity data between 4 and 250 K fit well to the form T [1exp( E/kT-)]', where T is temperature and E activation energy, and is related to the degree of disorder in the system. This form is the simplest form derived from the isosceles distribution; however, a better fit is obtained from the scalene distribution with more complex form. By using the proposed conduction model, the activation energy E is found to decrease systematically as the insulator-metal transition is approached by heat treatment. Also this model can yield the widely observed fractional temperature dependences of hopping conduction: x = 1, 2, -, ', and -' in the conventional form exp -( To/T) .

A novel conductivity mechanism of highly disordered carbon systems based on an investigation of graph zeta function

“…contribute to the conductivity. The mechanism provides the TDEC which is in good agreement with the experimental results of Kuriyama [14] and reproduces the (apparent) metal-insulator transition in [15]. Further in [20,21], it was microscopically assumed that the Wigner surmise comes from the quantum chaos in the small particles because the ACFs consists of small pieces of graphite [8]; each piece of small graphite might be regarded as a quantum box and it is known that its energy eigenvalue is described well by the random matrix theory (RMT) and obeys the Wigner surmise (I.1) [22].…”

“…The electrical and structural properties of the ACFs were studied by Kuriyama and Dresselhaus [14,15] and others [8,9]. Since the ACF consists of small pieces of graphite, the X-ray diffraction and Raman spectra show that the heat-treated process (HTP) of the ACFs modifies the structure and the size of the pieces drastically changes [8,9].…”

Electrical properties of self-assembled carbon networks

“…͑1͔͒ for variable range hopping ͑VRH͒. In the papers, [19][20][21][22][23][24][25] Mott's law ͓Eq. ͑1͔͒ was established for carbon fibers in the temperature range from 4.2 to 100 K with pϭ2.…”

Correlating magnetotransport and diamagnetism ofsp2-bonded carbon networks through the metal-insulator transition

“…However, there is also a history of such effects occurring in networks composed of nano-sized domains of sp 2 -bonded carbon. In particular, metal-insulator transitions have been found to occur in activated carbon fibers, [25][26][27][28] graphene oxide, 6 glassy and amorphous carbon materials, [29][30][31] fluorine-intercalated graphite fibers, 32 and carbon nanotube buckypapers. 33 The transition in many cases is induced by heat treatments which adjust the size of the sp 2 -bonded domains.…”

“…33 The transition in many cases is induced by heat treatments which adjust the size of the sp 2 -bonded domains. [25][26][27][28][29][30][31]33 The effect of these structural modifications on the electronic and magnetic properties of the networks can be quantified through a variety of different experimental techniques. Magnetoresistance and electronic transport characterize how localization lengths behave on either side of the metal-insulator transition.…”