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

Abstract

AbstractHopping transport within a bandtail distribution of localized electronic states has been investigated in amorphous carbon nitride (a‐C1–x Nx :H, x = 0.23) as a function of temperature T and electric field F. The conductivity σ follows Mott's law in the ohmic regime, i.e. ln (σohmic) varies linearly with T–1/4, while at higher field, a scaling law, ln (σ /σohmic) = φ [FS /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 E0, increasing F shifts the transport energy EDL towards shallower tail states, with a density of states N (EDL) ∼ (F)3 (E0)–4. In this model, FBTH is parametrized using ln σ (T, F) vs T–1/4 plots, which provide field‐dependent apparent values of prefactor (ln σ00) and slope (T01/4). As F increases, both parameters strongly decrease. This behavior (observed in a‐C1–x Nx :H, x = 0.23, for F > 5 × 104 V cm–1) is a signature of band tail hopping transport. Our FBTH model predicts a minimum value $ \sigma^{00}_{\rm min} $ of σ00(F), which is indeed observed in a‐C1–x Nx :H (x = 0.23) for T < 70 K ($ kT^*_{\rm eff} $ ≈ 10–6 S cm–1 at Fmin ≈ 3 × 105 V cm–1). Near Fmin, kT *eff = (1/kTeff – 1/E0)–1 is parametrized by kT *eff ∼ Fq. 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 σ00(F) and to derive the effective temperature Teff(T, F) which governs bandtail states occupation and FBTH conductivity. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)