Scaling analysis of field-enhanced bandtail hopping transport in amorphous carbon nitride

Hopping transport within a bandtail distribution of localized electronic states has been investigated in amorphous carbon nitride (a-C1-xNx: H, x = 0.23) as a function of temperature T and electric field F. The conductivity sigma follows Mott's law in the ohmic regime, i.e. ln (sigma(ohmic)) varies linearly with T-1/4, while at higher field, a scaling law, ln (sigma/sigma(ohmic)) = phi[F-S/T] with S = 0.67 (+/- 0.05), is found. Data are fully consistent with a field-enhanced bandtail hopping (FBTH) model in which the effective temperature concept describes the non-equilibrium occupation probability of tail states. A "filling rate" method, considering forward non-activated hopping transitions, is developed to analyze the high field regime of FBTH. For an exponential distribution with disorder energy E-o, increasing F shifts the transport energy E-DL towards shallower tail states, with a density of states N(E-DL) similar to (F)(3) (E-o)(-4). In this model, FBTH is parametrized using ln sigma(T, F) vs T-1/4 plots, which provide field-dependent apparent values of prefactor (ln sigma(oo)) and slope (T-o(1/4)). As F increases, both parameters strongly decrease. This behavior (observed in a-C1-xNx:H, x=0.23, for F > 5 x 10(4) V cm(-1)) is a signature of band tail hopping transport. Our FBTH model predicts a minimum value sigma(oo)(min) of sigma(oo)(F), which is indeed observed in a-C1-x N-x:H (x=0.23) for T < 70 K (sigma(oo)(min) approximate to 10(-6) S cm(-1) at F-min approximate to 3 x 10(5) V cm(-1)). Near F-min, kT(eff)*=(1/kT(eff)-1/E-o)(-1) is parametrized by kT*(eff)similar to F-q. The value of q that best reproduces the experimental results, q = 0.7 +/- 0.1, is consistent with the scaling exponent S = 0.67 and with the density of states parameters deduced from the Ohmic regime. Hence, this "filling rate" method applied to FBTH transport appears to be very useful to analyze the apparent prefactor sigma(oo)(F) and to derive the effective temperature T-eff(T, F) which governs bandtail states occupation and FBTH conductivity. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.