Electronic Localization and Bandtail Hopping Charge Transport

Abstract

Our previous modeling of hopping in localized bandtails has improved the description of electrical transport in amorphous carbon films and elemental amorphous semiconductors. This model is further developed to understand the role of the wavefunction localization radius γ -1 and density of states (DOS) distribution N(E) on the T dependence of the conductivity and the thermopower in disordered solids. Using values of the localization parameter LP = N(E F ) γ -3 in the range from 10 -4 to 1 eV -1 , our simulations show that: (i) The assumption of extremely low LP values made in previous works is often irrelevant for comparison with experiments. (ii) For low temperatures or large LP values, a linear relation holds between the dominant transport energy (E t - E F ) and temperature (with a stronger dependence as LP decreases) while a logarithmic dependence is obtained in the high-T range for small LP values. (iii) In the weak localization condition, a T-independent thermopower S(T) is predicted with an absolute value of eS/k (LP) -1/3 . (iv) The relationship σT 1/2 = σ 00 exp (-(T 0 /T) 1/4 holds, as expected for 3D hopping, over a wide temperature range (50-500 K); using the LP value as a parameter, the positive linear correlation between In (σ 00 ) and T 1/4 0 is a signature of an exponential localized bandtail distribution, clearly incompatible with Mott's hypothesis for 'Variable Range Hopping' in an energy-independent DOS distribution near the Fermi level.