The role of the density of states on the hole mobility of disordered organic semiconductors

It was recently demonstrated that the hopping mobility in disordered organic semiconductors depends both on the charge carrier concentration and on the density of states but their relative influence is still an open question. The mobility is almost constant below a certain concentration and increases at large concentration where the density of states is conventionally assumed exponential. Hence the experimental hole mobility in polymer FETs is at least one order of magnitude larger than the hole mobility in LEDs based on the same materials. In order to investigate this issue, the mobility of disordered organic semiconductors is calculated by numerically solving the variable range hopping (VRH) equations in a wide range of carrier concentrations ranging from low concentrations, typical of hole-only diodes, to high concentrations, typical of field effect transistors. The exact mobility is numerically calculated for various density of states (DOS) and it is compared with the experimental data in order to investigate the dependence of the hole mobility on the DOS. Our calculations show that the strong dependence of the hole mobility on the charge carrier density is strictly correlated to the shape of the DOS and that a single gaussian, in general does not explain the mobility behavior in the whole range of concentrations; depending on the material, it could be accurately approximated by a single gaussian, an exponential, or by a combination of both functions.