Bandlike Motion and Mobility Saturation in Organic Molecular Semiconductors

We analyze a model that accounts for the inherently large thermal lattice fluctuations associated with the weak van der Waals intermolecular bonding in crystalline organic semiconductors. In these materials the charge mobility generally exhibits a “metalliclike” power-law behavior, with no sign of thermally activated hopping characteristic of carrier self-localization, despite apparent mean free paths comparable to or lower than the intermolecular spacing. Our results show that such a puzzling transport regime can be understood from the simultaneous presence of band carriers and incoherent states that are dynamically localized by the thermal lattice disorder.

Figure 1

Quantities calculated from the solution of the model Eq. (1), representative for crystalline rubrene at room temperature ($T=0.2t$ with $t=143\mathrm{meV}$ and $\lambda =0.17$ as taken from Ref. 20). (a) spectral function $A(k,\omega )$, showing a well-defined band with a weakly renormalized dispersion; (b) energy-resolved localization length (red [light gray]) and density of states (blue [dark gray]); (c) spatial extent of the electronic wave function; (d) current-current correlation function (red [light gray]), and the same function multiplied by the thermal occupation factor as it appears in Eq. (2) (black dashed line). The blue (dark gray) line is the Boltzmann result for band electrons, $B(\omega )=\sum _k\delta (\omega -{ϵ}_k)v_k^2{\tau }_k$, with ${ϵ}_k$ the band dispersion and ${\tau }_k$ the quasiparticle lifetime. The data are evaluated with ${10}^6$ statistical samples, respectively, on (a),(b) $N=2^{10}$, (c),(d) $2^8$ lattice sites.

Figure 2

Mobility calculated from the Kubo formula in terms of the electron propagators obtained from the numerical simulation. For realistic bandwidth and electron-lattice interaction parameters for organic semiconductors (see Fig. 1), both bandlike conduction and incoherent diffusion contribute to the transport mechanism in the relevant temperature range around room temperature.