Coulomb forces and doping in organic semiconductors

A heuristic approach to describing excitonic processes, doping, and transport is developed for all organic semiconductors but with an emphasis on crystalline molecular semiconductors. A simple equation is proposed that semiquantitatively defines "excitonic" semiconductors, XSCs, a classification that includes most organic semiconductors and some inorganic materials. The same electrostatic and spatial factors that cause exciton formation upon light absorption in XSCs, as opposed to the formation of free electron-hole pairs, also control the doping process and carrier transport. Doping studies of XSCs are reviewed with an emphasis on the more recent, quantitative investigations. One conclusion is that most added charge carriers in doped XSCs are not free but rather are electrostatically bound to their conjugate dopant counterions. A superlinear increase in conductivity with doping density is thus expected to be, and apparently is, a universal attribute of XSCs. The interactions between the crystal structure, its dielectric properties, and the doping efficiency are probed via two substitutional dopant molecules in two different crystalline host lattices. An analogy is drawn between purposely doped XSCs and adventitiously doped XSCs such as pi-conjugated polymers: in both cases the number of free carriers is a small, and field-dependent, fraction of the total carrier density. The Poole-Frenkel mechanism accounts naturally for the expected interactions between carriers bound in a Coulomb well and an applied electric field. Together with a field-dependent mobility, this mechanism is expected to semiquantitatively describe the conductivity in doped XSCs.