Effect of Coulomb correlation on charge transport in disordered organic semiconductors

Charge transport in disordered organic semiconductors, which is governed by incoherent hopping between localized molecular states, is frequently studied using a mean-field approach. However, such an approach only considers the time-averaged occupation of sites and neglects the correlation effect resulting from the Coulomb interaction between charge carriers. Here, we study the charge transport in unipolar organic devices using kinetic Monte Carlo simulations and show that the effect of Coulomb correlation is already important when the charge-carrier concentration is above ${10}^{-3}$ per molecular site and the electric field is smaller than ${10}^8$ V/m. The mean-field approach is then no longer valid, and neglecting the effect can result in significant errors in device modeling. This finding is supported by experimental current density-voltage characteristics of ultrathin sandwich-type unipolar poly(3-hexylthiophene) (P3HT) devices, where high carrier concentrations are reached.

Figure 1

Calculated charge-carrier mobility $\mu$ as a function of the electric field $F$, at various charge-carrier concentrations $c$ and disorder strengths $\sigma$, for relative dielectric constant ${\varepsilon }_{\mathrm{r}}=3$ and $T=290$ K. Solid curves: ME results $\left({\mu }_{\mathrm{ME}}\right)$. Symbols: KMC results $\left({\mu }_{\mathrm{KMC}}\right)$. Dashed curves: ${\mu }_{\mathrm{ME}}$ multiplied by the empirical mobility reduction factor given by Eqs. (1, 2, 3).

Figure 2

Calculated charge-carrier mobility $\mu$ as a function of the carrier concentration $c$, at various disorder strengths $\sigma$ (a) or temperature $T$ (b), for $F={10}^7$ V/m and relative dielectric constant ${\varepsilon }_{\mathrm{r}}=3$. Solid curves: ME results $\left({\mu }_{\mathrm{ME}}\right)$. Symbols: KMC results $\left({\mu }_{\mathrm{KMC}}\right)$. Dashed curves: ${\mu }_{\mathrm{ME}}$ multiplied by the empirical mobility reduction factor given by Eqs. (1, 2, 3).

Figure 3

Calculated charge-carrier mobility $\mu$ as a function of the relative dielectric constant ${\varepsilon }_{\mathrm{r}}$ at various carrier concentrations $c$, for $\sigma =0.1$ eV, $F={10}^7$ V/m, and $T=290$ K. Solid curves: ME results $\left({\mu }_{\mathrm{ME}}\right)$. Symbols: KMC results $\left({\mu }_{\mathrm{KMC}}\right)$. Dashed curves: ${\mu }_{\mathrm{ME}}$ multiplied by the empirical mobility reduction factor given by Eqs. (1, 2, 3).

Figure 4

Ratio $J_{\mathrm{KMC}}/J_{\mathrm{ME}}$ of the current densities $J_{\mathrm{KMC}}$ and $J_{\mathrm{ME}}$ as obtained from KMC and ME simulations, respectively, for symmetric unipolar sandwich-type devices at various device thicknesses $L$ and injection barriers $\mathrm{\Phi }$, for $V/L={10}^7$ V/m (a) and $V/L={10}^8$ V/m (b), respectively. The devices contain a single layer of a semiconductor with a Gaussian DOS of width $\sigma =0.1$ eV and with ${\varepsilon }_{\mathrm{r}}=3$, studied at $T=290$ K.

Figure 5

Simulated carrier concentration profiles for symmetric unipolar devices with $\sigma =0.1$ eV at $T=290$ K. (a) 100-nm-thick device with an injection barrier $\mathrm{\Phi }=0.4$ eV, studied at a voltage $V=1$ V. (b) 10-nm-thick device with $\mathrm{\Phi }=0$ eV, at $V=1$ V. Solid curves: ME results. Symbols: KMC results. The displayed carrier concentration is equal to the laterally averaged site occupation probability.

Figure 6

Current density-voltage characteristics for P3HT devices, for various active layer thicknesses and temperatures. The open symbols are the experimental data. Open squares, triangles, and diamonds are characteristics of different samples fabricated under nominally identical conditions. The data given by the open squares are also shown in Fig. 4 of Ref. [44]. Solid curves: ME results. Filled symbols: KMC results.