Simulation of charge transport in organic semiconductors: A time-dependent multiscale method based on nonequilibrium Green's functions

In weakly interacting organic semiconductors, static disorder and dynamic disorder often have an important impact on transport properties. Describing charge transport in these systems requires an approach that correctly takes structural and electronic fluctuations into account. Here, we present a multiscale method based on a combination of molecular-dynamics simulations, electronic-structure calculations, and a transport theory that uses time-dependent nonequilibrium Green's functions. We apply the methodology to investigate charge transport in ${\mathrm{C}}_{60}$-containing self-assembled monolayers, which are used in organic field-effect transistors.

Figure 1

(a) Scheme of the SAMFET device containing the ${\mathrm{C}}_{60}$-based SAM, and (b) snapshot of the SAM (top view), consisting of $75{\mathrm{C}}_{10}$-PA and $25{\mathrm{C}}_{60}\text{−}{\mathrm{C}}_{18}$-PA molecules on ${\mathrm{AlO}}_x$.

Figure 2

(a) Time-resolved MO energies of the SAM. Shown are the energies of the HOMO and of unoccupied MOs. The red dashed line represents the Fermi level, $E_F=-5.1$ eV. The grey shaded area is the range of states that are located in the transport window when a bias voltage of 3.5 V is applied. (b)–(d) Examples of MOs from the unoccupied spectrum. (e) Energy level scheme of the device with the levels of the SAM coupled to the continuous spectrum of levels of the electron reservoirs in the electrodes, with temperature $T$ and chemical potentials ${\mu }_{\alpha }=E_F\pm \text{eV}/2$, where $V$ is the applied bias and $\alpha =l,r$.

Figure 3

Current obtained with the TD-NEGF method (a) and the Landauer approach (b) for bias voltages 2.6, 2.8, and 3.0 V. The dashed lines are the absolute currents, while the bold lines refer to the current averaged over a symmetric time span of 200 fs. (c) Time-resolved MO energies ${\epsilon }_1$–${\epsilon }_{10}$, where ${\epsilon }_1$ corresponds to the LUMO of the SAM. (d) $\overline{N}=\text{Tr}{\rho }_S$, representing the number of electrons in the system for 2.6, 2.8, and 3.0 V. The temperature is $T=300$ K.

Figure 4

$I\text{−}V$ characteristic obtained by averaging the TD-NEGF current over the time window 200–400 fs. The bold line depicts the time-averaged net current $I$, while the shaded area represents the fluctuations, given by the standard deviation $\mathrm{\Delta }I$.