Space charge field effect

As far as photoelectrochemical processes are concerned, the most important physical process is the space-charge field effect on the carrier distribution. As discnssed, the... 

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. 

We note from Eq. (15) that the space-charge field is shifted in space by n/2 with respect to the intensity pattern [Eq. (11)], which corresponds to a distant shift of Ag/4 in the x direction (Fig. 3d). This space-charge field induces an index volume grating via the Pockels effect (Fig. 3e). The refractive index including the fundamental component of refractive index modulation with magnitude of An can be written as... 

When the space-charge field can be constructed, the index modulation can also be built correspondingly. This mechanism can be a linear EO effect or an index modulation via alignment of the NLO chromophore in a low glass transition... 

The presence of a trapping center is very important since Eq. (19) indicates that the steady-state strength of the photoinduced space-charge field depends on the number density of the deep traps. Nevertheless, the nature of the traps in organic PR materials is the least studied of all the elements for the PR effect. The main reason is the lack of structural information of the trapping centers. The amorphous nature of these materials warrants the existence of a variety of trapping centers, such as energy levels localized at impurities or structural defects. However, one can differentiate between deep traps, which are localized... 

The last requirement for a PR effect is the mechanism for index modulation in the response of the space-charge field. Two mechanisms have been found to lead to index change EO response and birefringence. 

The bipolar single-trap model assumes that both electrons and holes share identical trap centers. Since sequential trappings of the electrons and holes by the identical centers mean the neutralization of the electric charge, the effective space-charge field will depend on the relative power (i.e., the mobilities) of electron and hole transports. The expressions for the writing and erasing diffraction efficiency are [100] ... 

Figure 3 Refractive index change associated with the orientational enhancement effect. The arrows represent the direction of the total field Ej which is the sum of the applied and space-charge fields.

Although the dominant means to create a space-charge field within the interference pattern in liquid crystals is given by Eq. (2), it has been shown that there are other mechanisms to create a space-charge field. One is derived from the conductivity anisotropy and is known as the Carr-Helfrich effect [43,49] ... 

The linear electro-optic effect (see Chapter 4) transfers the periodically modulated space-charge field into a refractive index grating ... 

By the HTOF technique, an interference pattern from two ps or ns laser pulses creates a sinusoidal distribution of carriers. Under the influence of an applied field, the carriers separate. As the charge separation proceeds, a space-charge field is created that can be probed with a cw laser through the electrooptic effect. The space-charge field reaches a maximum when the carriers have drifted to a position of anticoincidence with the immobile distribution of carriers of opposite polarity. Further drift causes a decrease of the space-charge field until coincidence is reached again. The diffraction efficiency versus time shows oscillatory behavior. From the time tmax that corresponds to the first maximum, the mobility can be derived from the relationship... 

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),------).

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. 

---