Photorefractive effect in the presence of shallow trapping sites

To explain a number of anomalous photorefractive effects, we present a complete analytical solution to a band transport model of the photorefractive effect which includes a shallow trapping level in addition to the deep donor and acceptor levels of the conventional models. We assume that a single charge carrier, for example, electrons, is responsible for transport. At room temperature and in the dark, the shallow level is completely empty, while the deep donor level is partially full. Light excites charges from each level to the conduction band. In addition, the electrons in the shallow traps can be thermally excited to the conduction band. The free carriers are assumed to recombine to either level in a time which is short compared to the grating build-up time. We solve for the space charge grating in each level and the space charge field in steady state as a function of light intensity and grating spacing. We also solve for the time development of these gratings in the dark in a certain regime of parameters. The predictions of the model agree well with results of photorefractive dark decay experiments in both Bi12SiO20 and BaTiO3, as well as transient photoconductivity experiments in Bi12SiO20.