Mobilities of Electrons and Holes in Organic Molecular Solids. Comparison of Band and Hopping Models

Abstract

A comparison is made of the applicability of two limiting models for describing the mobility of excess charges in molecular organic solids. Anthracene is the principal solid examined, but similar calculations are also given for naphthalene. A critical re-evaluation is made of the transfer integrals (which have been calculated from molecular orbital wavefunctions), and an approximate method is given by which one may include the effects of electronic polarization. These transfer integrals are then used to discuss mobilities (1) in terms of simple band theory, in which a delocalized, tight-binding representation is used and (2) in terms of a simple hopping theory, in which a one-site representation is used. The two models are tested for consistency with experiment and for internal, theoretical consistency. It is concluded that as a first approximation, the hopping model is superior to the band model, and gives a quantitatively accurate picture of the physical mechanism underlying charge mobility in molecular organic solids.