Understanding the Double Doping of Organic Semiconductors Via State Energy Renormalization upon Charging

The double ionization of molecular dopants enables the doping efficiency (free charges per dopant molecule) to rise above 100%. However, the current models of doped organic semiconductors based on Fermi-Dirac statistics fail to explain the double ionization of dopants and also the analogous situation of bipolaron formation on a host polymer. Here, we address this shortcoming by considering the renormalization of the state energies upon electron transfer between host and p-dopant. We vary the model parameters-the reorganization energy and evolutions of ionization energies and electron affinities upon charging-and plot the fractions of doubly ionized, singly ionized, and neutral species. The model shows good agreement with experimental measurements of doubly ionized p-dopants and bipolarons on a p-doped polymer. With these insights, we suggest that the state energy renormalization upon charging is the key parameter to be minimized for double ionization of dopants or maximized to avoid formation of bipolarons on the host.