No abstract

Temperature-activated charge transport in disordered organic semiconductors at large carrier concentrations, especially relevant in organic field-effect transistors ͑OFETs͒, has been thoroughly considered using a recently developed analytical formalism assuming a Gaussian density-of-states ͑DOS͒ distribution and MillerAbrahams jump rates. We demonstrate that the apparent Meyer-Neldel compensation rule ͑MNR͒ is recovered regarding the temperature dependences of the charge carrier mobility upon varying the carrier concentration but not regarding varying the width of the DOS. We show that establishment of the MNR is a characteristic signature of hopping transport in a random system with variable carrier concentration. The polaron formation was not involved to rationalize this phenomenon. The MNR effect has been studied in a OFET based on C 60 films, a material with negligible electron-phonon coupling, and successfully described by the present model. We show that this phenomenon is entirely due to the evolution of the occupational DOS profile upon increasing carrier concentration and this mechanism is specific to materials with Gaussian-shaped DOS. The suggested model provides compact analytical relations which can be readily used for the evaluation of important material parameters from experimentally accessible data on temperature dependence of the mobility in organic electronic devices. Experimental results on temperature-dependent charge mobility reported before for organic semiconductors by other authors can be well interpreted by using the model presented in this paper. In addition, the presented analytical formalism predicts a transition to a Mott-type charge carrier hopping regime at very low temperatures, which also manifests a MNR effect.

We developed an analytical model to describe hopping transport in organic semiconductors including both energetic disorder and polaronic contributions due to geometric relaxation. The model is based on a Marcus jump rate in terms of the small-polaron concept with a Gaussian energetic disorder, and it is premised upon a generalized effective medium approach yet avoids shortcomings involved in the effective transport energy or percolation concepts. It is superior to our previous treatment [Phys. Rev. B 76, 045210 (2007)] since it is applicable at arbitrary polaron activation energy E a with respect to the energy disorder parameter σ . It can be adapted to describe both charge-carrier mobility and triplet exciton diffusion. The model is compared with results from Monte Carlo simulations. We show (i) that the activation energy of the thermally activated hopping transport can be decoupled into disorder and polaron contributions whose relative weight depend nonlinearly on the σ /E a ratio, and (ii) that the choice of the density of occupied and empty states considered in configurational averaging has a profound effect on the results of calculations of the Marcus hopping transport. The σ /E a ratio governs also the carrier-concentration dependence of the charge-carrier mobility in the large-carrier-concentration transport regime as realized in organic field-effect transistors. The carrier-concentration dependence becomes considerably weaker when the polaron energy increases relative to the disorder energy, indicating the absence of universality. This model bridges a gap between disorder and polaron hopping concepts.