The influence of inter-oligomer separation distance on observed hopping mobilities in terthiophene-doped polycarbonate

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Abstract
Carrier mobilities for α-terthienyl (α-3T) have been directly determined by dispersing the oligomer in an inert polycarbonate matrix. Over the temperature and concentration ranges studied, hole mobilities (μ h) are found to increase with applied electric field (F) according to In(μ h)α F 1/2. The results may be successfully analysed using a recently developed theory of hopping within a Gaussian distribution of localized states of energetic width [sgrave]. A comparison of [sgrave] values deduced from the thermal variation of zero-field mobilities ([sgrave]T ), and those calculated from time-of-flight lineshapes ([sgrave] LS), indicates that [sgrave]LS< [sgrave]T , and it is consequently necessary to invoke a self-localization energy E p ≈ 0.45eV for the oxidized oligomer state. Concentration studies subsequently suggest that for dilute doping, where the average inter-oligomer separation distance ρ exceeds 11 Å, polaron hopping is non-adiabatic and controlled by wavefunction overlap for which a localization radius ρ 0 = 3.3 Å is deduced. In the concentrated regime (ρ < 11 Å), phase separation occurs and is accompanied by a sharp transition to adiabatic behaviour for which [μ h(T = α)]/ρ 2 = 1.1 × 1013 V−1 s−1. Detailed investigation of the adiabatic region is precluded however by the emergence of deep trapping states which reduce the effective polaron drift-length. It is argued that these states, as opposed to the short radical lifetime of the oligomer, account for the inability to observe a field-enhanced current in pure α-3T. The calculated field-effect mobility of 3 × 10−9 cm2 V−1 s−1for pure α-3T is found to be in substantial agreement with the extrapolated value of 1 × 10−8cm2V−1 inferred from published field-effect mobilities in longer chain oligothiophenes.