Physical Insight into the Dependence of Mobility on Carrier Doping Density in Organic Semiconductors

Recently, orders-of-magnitude modulation of mobility has been reported for chemical doping by photoinduced charge-transfer reactions; the carrier density and mobility can be controlled over more than 3 orders of magnitude by varying the photoirradiation time. The mobility changes are attributed to the change in accessible hole trap sites caused by varying the carrier density. However, the dependence of the mobility on the doping density has not yet been fully explored theoretically for chemical doping. Here we present theories to study mobility as a function of doping density for chemical doping. We consider the formation of ion-induced trap states expressed by few energy levels or a Gaussian density of states. We also use band-tail states expressed by an exponential density of states to consider the possibility that structural disorder is caused by chemical doping. The aforementioned theoretical results─one for the ion-induced trap states and the other for the band-tail trap states─were compared with experimental results showing a relatively slow increase in mobility with increasing doping density followed by a sharp increase in mobility toward saturation. The S-shaped dependence of mobility on doping density was more consistent with the model with the ion-induced trap states than the model with the band-tail states near the mobile states caused by structural disorder. These theoretical results indicate that the two types of trap states can be differentiated, which can be further examined using spectroscopic methods. The obtained semianalytical expressions can also be used to estimate the density of states as well as the energy difference between the trapped states and detrapped states from the mobility measurements. The proposed theory is further extended to include band-filling effects relevant to interdomain charge transport.