Crossover from Super- to Subdiffusive Motion and Memory Effects in Crystalline Organic Semiconductors

Abstract

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining exact diagonalization technique, Monte Carlo approaches, and maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super-to subdiffusive motion occurs in the range 150 ≤ T ≤ 200 K, where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model which can successfully explain low frequencies features of the absorption spectra. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.PACS numbers: 72.80. Le, 78.40.Me Small molecule organic semiconductors, crystals of small molecules held together by van der Waals forces, are the focus of an intensive research activity being the material basis for the organic electronics, and in particular for the plastic electronics, a rapidly developing field [1]. Because of the weak van der Waals intermolecular bonding, there is a small overlap between the electronic orbitals of these small molecules leading to narrow electronic bands: the transfer integral t turns out to be about 100 meV [2,3]. At the same time the electronphonon interaction (EPI) plays a crucial role [4] and, now, it is well established that it stems from Peierls's coupling mechanism [5]. EPI exhibits a strong momentum dependence, and, given the pronounced anisotropy of these compounds [6], typically the coupling of the electrons with the lattice vibrations is described by using a one-dimensional tight-binding model involving Einstein phonons with the lattice displacements affecting the electronic hopping integral [2,7] (Su-Schrieffer-Heeger coupling [8]). However the charge transport understanding in organic semiconductors remains limited. Indeed from an experimental point of view ultrapure crystals of pentacene or rubrene exhibit: 1) actived transport at low temperatures[6, 9, 10] (up to ≃ 160 K); 2) a band-like mobility up to room temperature, i.e. the mobility decreases as T −α with α ≃ 2[9, 11]. At the same time, at room temperature, optical absorption spectra are characterized by a broad peak centered around 40 meV [12], reminiscent of disordered systems in the insulating phase. It has been shown that the rapid drop of the mobility below 160 K is due to the crossover to the trap dominated regime (extrinsic disorder). Measurements of the transverse Hall conductivity [9,13] allowed to extract the intrinsic, trapfree mobility that increases always with cooling (shallow traps do not contribute to the Hall voltage since the Lorentz force is zero for these charge carriers). It remains to explain the puzzle regarding the simultaneous presence of the signat...

The Transient Localization Scenario for Charge Transport in Crystalline Organic Materials

“…5, fall very close to the RTA, Ehrenfest and convolution methods presented above (we have rescaled the data of Ref. [102] to the value of the transfer integral J = 143meV for comparison with the other methods). Using the formalism presented in Sec.…”

“…Accordingly, the authors of Ref. [102] fit the numerical data based on the Drude-Lorentz model, which highlights the existence of an electronic bound state with a finite radius.…”

“…[70] (see next Section), Ref. [102] proposes a phenomenological modeling of the optical absorption data. De Filippis et al interpretation of the numerical results is based on the assumption that a large polaron is formed due to the correlation between the carrier and the induced molecular deformation, i.e.…”

“…(1) by De Filippis et al [102] The authors combine diagrammatic [117] and worldline Monte Carlo approaches to evaluate the conductivity on the imaginary time axis. An analitycal continuation scheme is then used to obtain the complex optical conductivity on the real axis [118] with the aid of exact diagonalization of a small cluster.…”

“…(32) allows to infer the time-dependent quantum dynamics of charge carriers from the calculated [92,102] or measured [92] optical absorption in an organic semiconductor. Eq.…”