SIMPLE TRANSIENT SOLUTIONS FOR PHOTOCONDUCTION AND THE SPACE-CHARGE FIELD IN A PHOTOREFRACTIVE MATERIAL WITH SHALLOW TRAPS

We have found simple analytical solutions for the coupled differential equations that are commonly used to describe unipolar photoconduction in a homogeneous material with shallow traps. Our solutions cover tra nsient photoconduction in the dark after an initial low-intensity puls e of light creates some spatial pattern of photoexcited carriers. We a ssume that there is no conduction in equilibrium in the dark. Our solu tions introduce two parameters to describe the shallow traps: a mean t ime between trapping events in the conduction band and a mean time spe nt in a shallow trap. When used to analyze extensive experimental data on a particular sensitive crystal of n-type cubic Bi12SiO20, our solu tions predict an observed, but unexpected, dependence of carrier grati ng decays (in the dark) on applied electric field. The solutions also correlate transient photoconductivity results with grating-decay behav ior both in the dark and under uniform illumination, giving a mean tim e between shallow traps in the conduction band of 26+/-3 ns, and a mea n time of 800+/-300 ns spent in a shallow trap. A value mu(c), = 5+/-3 cm2/(V s) is inferred for the electron mobility in the conduction ban d between trapping events. Also, the electron diffusion length inferre d from our solutions matches that observed previously by light-induced grating decays.