Mobility-diffusivity relationship for heavily doped organic semiconductors

The relationship between the diffusivity D _n and the mobility μ _n 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 D _n /μ _n 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 D _n /μ _n 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.