Doping highly ordered organic semiconductors: experimental results and fits to a self-consistent model of excitonic processes, doping, and transport.

An in-depth study of n-type doping in a crystalline perylene diimide organic semiconductor (PPEEB) reveals that electrostatic attractions between the dopant electron and its conjugate dopant cation cause the free carrier density to be much lower than the doping density. Measurements of the dark currents as a function of field, doping density, electrode spacing, and temperature are reported along with preliminary Hall-effect measurements. The activation energy of the current, E(aJ), decreases with increasing field and with increasing dopant density, n(d). It is the measured change in E(aJ) with n(d) that accounts primarily for the variations between PPEEB films; the two adjustable parameters employed to fit the current-voltage data proved to be almost constants, independent of n(d) and temperature. The free electron density and the electron mobility are nonlinearly coupled through their shared dependences on both field and temperature. The data are fit to a modified Poole-Frenkel-like model that is shown to be valid for three important electronic processes in organic (excitonic) semiconductors: excitonic effects, doping, and transport. At room temperature, the electron mobility in PPEEB films is estimated to be 0.3 cm(2)/Vs; the fitted value of the mobility for an ideal PPEEB crystal is 3.4 +/- 2.7 cm(2)/Vs. The modified Poole-Frenkel factor that describes the field dependence of the current is 2 +/- 1 x 10(-4) eV (cm/V)(1/2). The analytical model is surprisingly accurate for a system that would require a coupled set of nonlinear tensor equations to describe it precisely. Being based on general electrostatic considerations, our model can form the requisite foundation for treatments of more complex systems. Some analogies to adventitiously doped materials such as pi-conjugated polymers are proposed.