Anisotropic electron mobility studies on Cl2-NDI single crystals and the role of static and dynamic lattice deformations upon temperature variation

Abstract

The anisotropic electron transport in the (001) plane of sublimation-grown Cl$_{2}$-NDI (naphthalene diimide) single crystals is analysed over a temperature range between 175 K and 300 K. Upon cooling from room temperature to 175 K the electron mobility along the direction of preferred transport monotonously increases from 1.5 cm$^{2}$/Vs to 2.8 cm$^{2}$/Vs according to a distinct temperature relation of $~T^{-1.3}$. At first glance, these characteristics allude to a coherent, i.e. band-like charge carrier transport predominantly governed by inelastic scattering with accoustic phonons. However, as we will demonstrate, the experimental mobility data can be consistently described within the framework of incoherent, hopping-type transport modeled by Levich-Jortner rates, explicitly accounting for the inner and outer relaxation energies related to thermally induced lattice effects and enhanced electron-phonon interaction at elevated temperatures. Complementary band-structure calculations yielding temperature dependent effective mass tensors deviate stronger from experimentally observed spatially anisotropic transport behavior. Thus, these results hint at the fact that by the particular interplay of the transport energies the mobility of a given organic semiconducting material might appear to be band-like in a certain temperature regime even though the underlying charge carrier transport can be of incoherent, hopping-type nature. Building on this description, we further explore the role of the intermolecular electronic coupling and develop a procedure to distinguish between its dependence on static and dynamic lattice deformation upon temperature variation.