DISORDER EFFECTS ON SMALL-POLARON FORMATION AND HOPPING

Abstract

It was noted some time ago that many properties of amorphous semiconductors could be explained if the charge carriers self-trapped to form small polarons. Self trapping occurs when an electronic carrier lingers at a site long enough to permit surrounding atoms to displace in response to the presence of the carrier. The electronic carrier then becomes severely localized within a potential well produced by the atomic displacements. This self-trapped carrier cannot move unless the atoms alter their positions. The localized carrier together with the atomic displacement pattern that confines it is termed a small polaron. The adjective small denotes the severe localization of the electronic state. The energy of a small polaron in a covalent solid is lower than that of a static electron by E{sub b} {triple_bond} F{sup 2}/2k, where F is the force between the carrier and atoms adjacent to it, and k is the material`s stiffness constant. As a result of its severe localization, a small polaron generally moves by phonon-assisted hopping. Small-polarons will only form in covalent crystals whose electronic halfbandwidths are sufficiently narrow, E{sub b} > W. The absence of small polaronic carriers in most covalent crystals presumably indicates that E{sub b} < W inmore » these instances. However, evidence of small polarons is commonly found in disordered materials despite the estimates of E{sub b} and W not being significantly different from those of crystals. It is found that only modest energetic disorder is required to induce small-polaron formation. Here the author succinctly describes essential elements of this work. Second, the author addresses the role of disorder on the adiabatic hopping motion of small polarons.« less