Temperature dependence of dispersive hopping transport and diffusion in disordered solids

The time- and temperature-dependent drift mobility μ_d for dispersive transients in disordered solids is $\text{μ}{}_{\mathrm{d}}\text{(T,t) =}\text{L}\text{Et}{}_{\mathrm{T}}$ in terms of distance L, field E and transit time t_T. Since current I ∝ tsu?(1?α) for t <_Tand 0<α<1 by Scher-Montroll theory for hopping among localized states, it follows that $\text{μ}{}_{\mathrm{d}}\text{(T) = αμ}{}_{\mathrm{d}}\text{(T,t)]}{}^{\mathrm{\alpha }}\text{(}\text{L}\text{Eτ}\text{)}{}^{\mathrm{1?\alpha }}$ where τ≈ 10^?13s is estimated. Further $\text{μ}{}_{\mathrm{d}}\text{(T) ∝ exp (}\text{?Δ}{}_0\text{KT}\text{)}$ and the activation energy Δ₀ is time independent. On this basis Δ for the carbazole polymers is ca. zero, that for a-Se is ca. 0.05 eV, and that for a-As₂Se₃ is 0.35 eV rather than 0.5, 0.3 and 0.6 eV respectively on a phenomenological basis for μ_d(T,t). Trap-controlled hopping transport may be excluded. Time-resolved optical studies of excess carrier recombination supplement mobility measurements in a-Si:H and a-As₂Se₃ as well as other systems. Combined results suggest a dielectric response mechanism in which the time-dependent hopping frequency of localized carriers ν ∝ t^α?1 arises from distortion of the medium at localization sites. This is satisfied by Δ(T,t) = Δ₀+(1?α)KTT ln(t/τ) where τ is the mean initial localization time of the carrier, 10^?13?10^?12s, Δio is the height of the barrier at T, and 0<α<l. Consequently ν = ν₀(t/τ)^α?1 exp(frsol|?Δ₀/KT) which applies also to bimolecular recombination.