DISORDER-INDUCED SMALL-POLARON FORMATION

Small-polaron formation is studied for a disordered multidimensional version of Holstein's molecular-crystal model (MCM). The MCM is appropriate for the study of polaronic effects in covalent semiconductors, where the electron-lattice interactions are short ranged. Our considerations focus on the ''adiabatic'' regime since it prevails in most semiconductors. In this domain the near-neighbor electronic-transfer energies are much greater than the characteristic phonon energy. We consider a situation in which the characteristic near-neighbor electronic-transfer energy t0 and the small-polaron binding energy E(b) are such that the stable carriers in a crystal would be quasifree rather than small polarons: zt0 > E(b), where z is the number of nearest neighbors. We then address how disordering of the transfer energies affects small-polaron formation. In particular, disorder is taken to replace t0 with a distribution of electronic-transfer energies. Small electronic-transfer energies about some sites by themselves stabilize small-polaron formations at these sites. Moreover, stabilization of a small polaron at a site is found to foster the stabilization of a small polaron at sites adjacent to it. This effect enhances the effectiveness with which disorder can trigger the collapse of a steady-state carrier from being quasifree to being a small polaron. That is, disorder reduces the strength of the electron-lattice coupling needed to stabilize global small-polaron formation. With the stabilization of small-polaronic carriers, the electronic transport changes from being that of quasifree carriers (that may occasionally be trapped at small-polaronic sites) to small-polaron hopping.