Correlated electron-hole mechanism for molecular doping in organic semiconductors

The electronic and optical properties of the paradigmatic F4TCNQ-doped pentacene in the low-doping limit are investigated by a combination of state-of-the-art many-body ab initio methods accounting for environmental screening effects, and a carefully parametrized model Hamiltonian. We demonstrate that while the acceptor level lies very deep in the gap, the inclusion of electron-hole interactions strongly stabilizes dopant-semiconductor charge transfer states and, together with spin statistics and structural relaxation effects, rationalize the possibility for room-temperature dopant ionization. Our findings reconcile available experimental data, shedding light on the partial vs. full charge transfer scenario discussed in the literature, and question the relevance of the standard classification in shallow or deep impurity levels prevailing for inorganic semiconductors.

Figure 1

Representation of the model system for molecular doping here studied with embedded many-body perturbation theory calculations. Molecular structures of (a) pentacene and (b) F4TCNQ and of (c) the complex including the dopant surrounded by its six pentacene neighbors $(1+6$ CPX, QM region, ball-and-stick model). The $1+6$ CPX is embedded in the pentacene crystal (MM region, wide-frame representation).

Figure 2

(a) Energies of diabatic CT states $({\varepsilon }_{i0}^{CT}$ in eV) with electrons localized on the central F4TCNQ (cross) and hole in the HOMO of each pentacene molecule $i$. Intermolecular couplings $(t_{i0}^{CT}$ and $t_{i0,j0}^h$ in meV) are annotated on the respective bonds. (b) Same parameters as in the previous panel but for CT states with the hole in the pentacene $\mathrm{HOMO}-1,{\varepsilon }_{i1}^{CT},t_{i1}^{CT}$, and $t_{i1,j1}^h$.

Figure 3

Electron-hole distance dependence of the exciton binding energy $E_b^{\pm }$ of localized (diabatic) CT states $E_b^{\pm }=P^{\pm }-P^{+}-P^{-}$. $P^{+},P^{-}$, and $P^{\pm }$ are the polarization energies for holes, electrons, and ion pairs computed with the CR model, all extrapolated in the infinite bulk limit. The exciton binding energy approximately follows a screened Coulomb potential $-{\left({\varepsilon }_r{r}_{eh}\right)}^{-1}$ (dashed line for ${\varepsilon }_r=3.5)$.

Figure 4

(a) Isocontour representation of the frontier molecular orbitals corresponding to the (b) $GW$ energy levels computed for the embedded $1+6$ CPX. (c) BSE optical absorption spectrum of the embedded CPX. The striking difference between the HOMO-LUMO gap and the energy of the corresponding $S_1$ transition quantifies the strength of the electron-hole binding energy.

Figure 5

(a) Optical absorption spectrum of F4TCNQ-doped pentacene computed ab initio (BSE) and with the model Hamiltonian 1 for the $1+6$ and $1+N$ complexes at the geometry of the neutral molecules. Gray bars mark bands observed in experiments [4]. Hole (red) and electron (blue) density for the lowest-energy optically allowed excitations from (b) BSE and (c) model calculations. The BSE representation corresponds to the hole-averaged electron-density and electron-average hole-density associated with the electron-hole two-body $\psi ({\mathbf{r}}_e,{\mathbf{r}}_h)$ BSE eigenstates. Transition energies and oscillator strengths $f$ are annotated.

Figure 6

(a) Dopant charge in the ground state (0 K) and at room temperature (300 K) as a function of the DOP-OSC energy mismatch. The temperature-independent green curve refers to a system at relaxed geometry. (b) Sketch of the diabatic potential energy surfaces illustrating the Jahn-Teller instability for a hypothetical $1+2$ system. (c) Optical absorption of a (un)relaxed $1+N$ system. The inset shows the charge distribution of the vibrationally-relaxed ground state with a fully ionized dopant $\left(Q_{\mathrm{DOP}}=-0.99e\right)$. All results from Hamiltonian 1.

Figure 7

Representation of the $1+2$ CPX (QM region, ball-and-stick model) embedded in the pentacene crystals (MM region, wideframe representation) employed in the present validation. The isocontour representation shows the averaged electron-hole density for the lowest Bethe-Salpeter $S_1$ excitation, presenting charge transfer along the same crystallographic direction as for the $1+6$ CPX $S_1$ excitation studied in Sec. 3.