Charge-Transport Regime of Crystalline Organic Semiconductors: Diffusion Limited by Thermal Off-Diagonal Electronic Disorder

We propose that the electron transport in crystalline organic semiconductors at room temperature (RT) is neither polaronic nor a combination of thermally activated hopping and polaronic transport, as previously thought. Thermal molecular motions cause large fluctuations in the intermolecular transfer integrals that, in turn, localize the charge carrier. This effect destroys the translational symmetry of the electronic Hamiltonian and makes the band description inadequate for RT organic crystals. We used a one-dimensional semiclassical model to compute the (temperature dependent) charge carrier mobility in the presence of thermal fluctuations of the electronic Hamiltonian. This transport mechanism explains several contrasting experimental observations pointing sometimes to a delocalized “bandlike” transport and sometimes to the existence of strongly localized charge carriers.

Figure 1

(Upper panel) Scheme of the model used to describe the charge transport in organic semiconductors. (Lower panel) Example of time evolution of the probability density in the considered model ($K=14500\mathrm{amu}{\mathrm{ps}}^{-2}$, $\tau =300{\mathrm{cm}}^{-1}$, $\alpha =995{\mathrm{cm}}^{-1}/\AA$, $m=250\mathrm{amu}$, $T=150\mathrm{K}$). The profile of the density is represented for each snapshot every 0.15 ps starting from $t=0$ (only 100 sites are shown).

Figure 2

Plot of the temperature averaged squared displacement [in units of $L^2$, Eq. (7)] versus time, using the parameters in the caption of Fig. 1 and the oscillator mass $m$ as indicated on the plot in amu.

Figure 3

Temperature dependence of the mobility for the model system. For both panels $K=14500\mathrm{amu}{\mathrm{ps}}^{-2}$ and $m=250\mathrm{amu}$. (Upper panel) $\tau =300{\mathrm{cm}}^{-1}$ and $\alpha$ varies as indicated in ${\mathrm{cm}}^{-1}/\AA$. (Lower panel) $\alpha =995{\mathrm{cm}}^{-1}/\AA$ and $\tau$ varies as indicated in ${\mathrm{cm}}^{-1}$. For the system size considered here (600 sites) only mobilities below $60{\mathrm{cm}}^{-1}$ are guaranteed to be unaffected by the boundary conditions (for higher mobilities the carrier could interact with its image for some trajectories).