Prediction of Charge Mobility in Amorphous Organic Materials through the Application of Hopping Theory

The application of hopping theory to predict charge (hole) mobility in amorphous organic molecular materials is studied in detail. Application is made to amorphous cells of N,N'-diphenyl-N,N'-bis-(3-methylphenylene)-1,1'-diphenyl-4,4'-diamine (TPD), 1,1-bis-(4,4'-diethylaminophenyl)-4,4-diphenyl-1,3,butadinene (DEPB), N4,N4'-di(biphenyl-3-yl)-N4,N4'-diphenylbiphenyl-4,4'-diamine (mBPD), N1,N4-di(naphthalen-1-yl)-N1,N4-diphenylbenzene-1,4-diamine (NNP), and N,N'-bis[9,9-dimethyl-2-fluorenyl]-N,N'-diphenyl-9,9-dimethylfluorene-2,7-diamine (pFFA). Detailed analysis of the computation of each of the parameters in the equations for hopping rate is presented, including studies of their convergence with respect to various numerical approximations. Based on these convergence studies, the most robust methodology is then applied to investigate the dependence of mobility on such parameters as the monomer reorganization energy, the monomer-monomer coupling, and the material density. The results give insight into what will be required to improve the accuracy of predictions of mobility in amorphous organic materials, and what factors should be controlled to develop materials with higher (or lower) charge (hole) mobility.