Charge Transport by Superexchange in Molecular Host-Guest Systems

Charge transport in disordered organic semiconductors is generally described as a result of incoherent hopping between localized states. In this work, we focus on multicomponent emissive host-guest layers as used in organic light-emitting diodes (OLEDs), and show using multiscale ab initio based modeling that charge transport can be significantly enhanced by the coherent process of molecular superexchange. Superexchange increases the rate of emitter-to-emitter hopping, in particular if the emitter molecules act as relatively deep trap states, and allows for percolation path formation in charge transport at low guest concentrations.

Figure 1

(a) Energy level diagram of a guest ($A$)-host ($B$)-guest ($C$) molecular subsystem, as defined in the main text, indicating the transition state energy $E_T$ and the virtual state energy $E_{\text{virtual}}$, which determine the energy denominator $\mathrm{\Delta }{E}_{\mathrm{ABC}}$ in the expression for the superexchange contribution to the charge transfer from molecule $A$ to $C$ [Eq. (5)]. (b) Calculated hole density of states for the case of 8 mol % $\text{Ir}{(ppy)}_3$ (green, width $\sigma =0.118\mathrm{eV}$) in a TCTA matrix (white, $\sigma =0.136\mathrm{eV}$). The inset illustrates the spatial separation of the $\text{Ir}{(ppy)}_3$ molecules in the matrix. Hole transport between the $\text{Ir}{(ppy)}_3$ molecules is the combined result of direct (dashed arrow) and superexchange (full red arrow) interactions.

Figure 2

Direct (black closed circles) and superexchange (red open circles) transfer integrals between guest molecules and adjacent molecules (guest and host) as a function of their center of mass distance for (a) $\text{Ir}{(\mathrm{MDQ})}_2(acac)$ molecules in an $\alpha$-NPD host and (b) $\text{Ir}{(ppy)}_3$ molecules in a TCTA host, for a guest concentration of 8 mol %.

Figure 3

(a) Guest concentration dependence of the hole mobility of $\alpha \text{−}\mathrm{NPD}:\text{Ir}{(\mathrm{MDQ})}_2(acac)$ and $\mathrm{TCTA}:\text{Ir}{(ppy)}_3$ systems at a hole concentration of $2.0\times {10}^{-4}\mathrm{per}$ molecule and a field of $0.03\mathrm{V}/\mathrm{nm}$, at 275 (red crosses), 300 (black discs), 375 (green squares), and 450 K (blue diamonds). (b) Guest concentration at the mobility minimum, $c_{\min }$, as a function of the temperature. Red circles: $\alpha \text{−}\mathrm{NPD}:\text{Ir}{(\mathrm{MDQ})}_2(acac)$. Green squares: $\mathrm{TCTA}:\text{Ir}{(ppy)}_3$. The lines and curves in (a) and (b) are guides to the eye. Dashed lines: only direct hops. Solid lines: direct and superexchange hops.

Figure 4

(a) Contours of equal ratio between the superexchange hop rate from a trap $A$ to a resonant trap $C$ through a virtual state on host molecule $B$ and the hop rate from a trap $A$ to $B$, as a function of the host-guest transfer integral $H_{hg}$ and the trap depth $\mathrm{\Delta }{E}_{tr}$. The red short-dashed and the green long-dashed horizontal lines at $\mathrm{\Delta }{E}_{tr}=0.3(0.4)\mathrm{eV}$ indicate representative values for the $\alpha \text{−}\mathrm{NPD}:\text{Ir}{(\mathrm{MDQ})}_2(acac)/[\mathrm{TCTA}:\text{Ir}{(ppy)}_3]$ system. The vertical dashed line indicates a representative value for ${\mathrm{H}}_{hg}$. (b) Guest concentration dependence of the probability of guest-guest hopping for equilibrated holes in $\mathrm{TCTA}:\text{Ir}{(ppy)}_3$ at 275 K with a hole concentration of $2.0\times {10}^{-4}$, in a model employing the calculated distribution of the transfer integrals (black discs) and using constant transfer integrals (blue squares). Dashed curves: only direct hops. Full curves: direct and superexchange hops.