Electron–hole competition in photorefractive materials with shallow traps

We present a steady-state solution of a model of the photorefractive that which includes donor shallow traps and deep traps with electrons and holes as charge carriers. Both electrons and holes are assumed to be photoexcitable from the deep traps. Holes may recombine only to the deep traps, whereas electrons may recombine to the ionized shallow traps or to the deep traps. Electrons trapped in the shallow traps may be re-excited thermally and optically. The grating in the shallow traps is in phase with the illumination pattern at low intensities and is out of phase with it at higher intensities. The intensity at which the switching occurs is determined in terms of material parameters and grating spacing. The phase of the charge grating in the deep traps is not a function of intensity but is only a function of the dominant charge carrier. These charge gratings do not vanish as grating spacing becomes infinitely large, although the sum of them vanishes thereby leading to no space-charge field. We will discuss the consequence of the intensity dependence of the phase of the shallow traps' charge grating on the value of the space-charge field in various regimes.