Charge-dipole energy in imperfect molecular crystals: Application to carbazole in anthracene

Abstract

The charge–dipole energy in a perfect crystal of polar molecules is shown to be zero in the absence of bulk polarization. Rigorous algebraic expressions are derived for the change in charge–dipole energy in an imperfect crystal, taking into account the effective dipole moments induced in the crystal, including the change in polarizability caused by the defect. The results consist of two terms, one from the permanent dipole change at the defect, and the other from the induced dipole change, which arises from the polarizability change at the defect responding to the permanent dipole field in the crystal. Numerical calculations for the charge–dipole energy change and the polarization energy change at molecules near a substitutional carbazole impurity in an otherwise perfect anthracene crystal show that the charge–dipole energy dominates, producing trapping and scattering regions in a distorted dipolar arrangement. The calculated trap depths reach 60 meV, but for electrons are compatible with the published interpretation of mobilities in carbazole-doped anthracene in terms of a trap of depth 34 meV but an apparent concentration 15 times the carbazole concentration, consistent with X trapping at anthracene. Traps as deep as 0.25 eV could be produced by more highly polar substituent molecules.