Mobility–diffusivity relationship for heavily doped organic semiconductors

The relationship between the diffusivity Dn and the mobility μn of chemically doped organic n-type semiconductors exhibiting a disordered band structure is presented. These semiconductors have a Gaussian-type density of states. So, calculations have been performed to elucidate the dependence of Dn/μn on the various parameters of this Gaussian density of states. Y. Roichman and N. Tessler (Appl. Phys. Lett. 80:1948, 2002), and subsequently Peng et al. (Appl. Phys. A 86:225, 2007), conducted numerical simulations to study this diffusivity–mobility relationship in organic semiconductors. However, almost all other previous studies of the diffusivity–mobility relationship for inorganic semiconductors are based on Fermi–Dirac integrals. An analytical formulation has therefore been developed for the diffusivity/mobility relationship for organic semiconductors based on Fermi–Dirac integrals. The Dn/μn relationship is general enough to be applicable to both non-degenerate and degenerate organic semiconductors. It may be an important tool to study electrical transport in these semiconductors.