Mobility, photorefraction

Figure 3.38. Principle of the photorefractive effect By photoexcitation, charges are generated that have different mobilities, (a) The holographic irradiation intensity proHle. Due to the different diffusion and migration velocity of negative and positive charge carriers, a space-charge modulation is formed, (b) The charge density proHle. The space-charge modulation creates an electric Held that is phase shifted by 7t/2. (c) The electric field profile. The refractive index modulation follows the electric field by electrooptic response, (d) The refractive index profile.

Figure 3.39. Holographic setup for photorefractive molecular glasses. The sample is tilted toward the grating, allowing an applied external field to support the motion of the mobile charges. The phase shift of the refractive index grating can be determined by measuring the transmitted writing beam intensities (two-beam coupling).

The most useful of the known photorefractives are LiNbC>3 and BaTiC>3. Both are ferroelectric materials. Light absorption, presumably by impurities, creates electron/hole pairs within the material which migrate anisotropically in the internal field of the polar crystal, to be trapped eventually with the creation of new, internal space charge fields which alter the local index of refraction of the material via the Pockels effect. If this mechanism is correct (and it appears established for the materials known to date), then only polar, photoconductive materials will be effective photorefractives. However, if more effective materials are to be discovered, a new mechanism will probably have to be discovered in order to increase the speed, now limited by the mobility of carriers in the materials, and sensitivity of the process. 

Figure 1 Phase relationship between the optical interference pattern and the space-charge field. For liquid crystals, this example illustrates mobile anions migrating into the nulls of the interference pattern. The application of an applied electric field Ej is usually required to observe a phase-shifted photorefractive grating.

As shown previously, nematic liquid crystals reorient easily in weak electric fields and their high birefringence provides an efficient electro-optic mechanism that makes them excellent candidates for photorefractive materials. However, charge transport relies on the generation of mobile anions or cations. These mobile charges obey the current density (/) equations given by [82,83]... 

The major advantages of the HTOF technique are that it is not subject to trapping constraints nor the restrictions concerning the absorption depth of conventional photocurrent transient measurements. The principal limitation is that it is limited to photorefractive materials. Malliaras et al. (1995) used the HTOF method to measure mobilities of ternary mixtures of poly(N-vinylcarbazole), 2.4.7-trinitro-9-fluorenone, and 4-(hexyloxy)nitrobenzene. Results obtained by the HTOF method were in good agreement with those obtained by conventional photocurrent transient measurements. 

Recombination of the mobile charges in dark regions is not necessary for the photorefractive effect to be observed, but it is beneficial. If the mobile charges were to be removed completely, or redistributed uniformly with no dependence on the intensity pattern applied, then an immobile pattern of eounterions would still be... 

Figure 4. The photorefractive effect with and without trapping. Top the intensity pattern on the material. Middle O, anion density +, cation density x, ideal distribution of trapping of mobile holes. Bottom comparison of the net charge distribution in the ideal case (no. of cations - no. of anions + no. of trapped holes, x) with the corresponding space charge field in the absence of any trapping or recombination (no. of trapped holes = 0),------).

The initial sensitizer anion presence makes recombination of mobile holes possible in the dark regions. Which are the compensator sites Here, there exist different explanations. One possibility is that some of the electro-optic dye molecules present in photorefractive composites to provide refractive index change may become charged positively. An alternative theory in the case of amorphous materials is that the amorphous disorder leads to defect sites forming local potential minima at which positive charge may be immobilized (Figure 5). 

An important aspect of the photorefractive effect is that the optical response of the material is nonlocal. In Figure 7, the position of the space charge field is displaced to the right of the initial excitation, in the direction of the applied electric field. In the case of a sinusoidal intensity pattern the phase shift between the optical excitation of charges and the electric field their movement produces is a parameter characteristic of a photorefractive material. It depends on the balance between the processes of drift and diffusion of mobile charges and on the number density of sites able to capture the mobile charges. 

More recently the promising range of applications for photorefractive materials has motivated the rapid development of amorphous, organic materials with a strong photorefractive response [5]. Here the chemical composition of the materials may be varied with relative ease and the opportunity to compare materials from different sources should exist. The various processes necessary for photorefraction may be obtained by a single material, or many different molecular species may be mixed in a composite to provide the range of properties needed. These amorphous materials do not have a well-defined mobility for the photogenerated holes that... 

Figure 9. Conventional model of photorefraction in crystals iron impurity forms defect states of variable valence within the forbidden band gap of a lithium niobate crystal. Optical excitation of the divalent state leads to creation of a mobile electron in the conduction band. This is able to move and recombines with a trivalent iron impurity at another location which becomes divalent. The displacement of charge leads to an electric field and the Pockels electro-optic effect leads to local modification of the refractive index.

The field of photorefractivity in organic polymers and glasses has been in existence for less than a decade. The understanding of charge generation in these materials (which are often composites) is not yet mature, and the behavior of some of the more common constituents is understood better. Much of the literature on photo-refraetivity deseribes free earrier generation quantum efficiency measurements only briefly, before a more detailed discussion of other factors such as mobility and electro-optic response. Some of the relevant information pertinent to free carrier generation in these materials is presented here, to be followed by a review of this aspect of the amorphous photorefractives literature. 

Figure 11. Possible relative positions of the energy levels in a typical guest-host photorefractive polymer composite containing PVK, TNF, and an azo-chromophore. A possible sequence of events leading to mobile charge generation is also included.

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