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Scaling analysis of field‐enhanced bandtail hopping transport in amorphous carbon nitride
Author(s) -
Godet C.,
Kleider J. P.,
Gudovskikh A. S.
Publication year - 2007
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200642043
Subject(s) - condensed matter physics , ohmic contact , scaling , physics , amorphous solid , field (mathematics) , density of states , distribution function , materials science , thermodynamics , crystallography , chemistry , quantum mechanics , mathematics , geometry , electrode , pure mathematics
Hopping transport within a bandtail distribution of localized electronic states has been investigated in amorphous carbon nitride (a‐C 1– x N x :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 ( σ ohmic ) varies linearly with T –1/4 , while at higher field, a scaling law, ln ( σ / σ ohmic ) = φ [ 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 0 , increasing F shifts the transport energy E DL towards shallower tail states, with a density of states N ( E DL ) ∼ ( F ) 3 ( E 0 ) –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 σ 00 ) and slope ( T 0 1/4 ). As F increases, both parameters strongly decrease. This behavior (observed in a‐C 1– x N x :H, x = 0.23, for F > 5 × 10 4 V cm –1 ) is a signature of band tail hopping transport. Our FBTH model predicts a minimum value $ \sigma^{00}_{\rm min} $ of σ 00 ( F ), which is indeed observed in a‐C 1– x N x :H ( x = 0.23) for T < 70 K ( $ kT^*_{\rm eff} $ ≈ 10 –6 S cm –1 at F min ≈ 3 × 10 5 V cm –1 ). Near F min , kT * eff = (1/ kT eff – 1/ E 0 ) –1 is parametrized by kT * eff ∼ 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 σ 00 ( F ) and to derive the effective temperature T eff ( T , F ) which governs bandtail states occupation and FBTH conductivity. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)