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

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.