The photorefractive effect in a suitable electro-optic The term ‘defect’ can be used with two different meanmaterial is usually triggered by the photoionisation of ings; first it may stand for a certain chemical entity which defects . Under illumination with an inhomogeneous interrupts the periodicity of a crystal lattice, and second, for light pattern the freed charge carriers are moving in either one of the charge states such a perturbation can acquire.
the valence or in the conduction band from the brighter In the latter case we shall talk of ‘defect charge state’, if regions towards the darker ones, transported by various necessary.
possible driving mechanisms. A charge pattern results; it The procedure which we developed to quantitatively is accompanied by the corresponding space charge field, assess the role of defects in charge transfer processes, espewhich is transformed into a refractive index pattern by the cially in photorefractive crystals, will be exemplified in the electro-optic effect. Fig. 1 demonstrates the three elementary models under which the occurring charge transfer processes can be subsumed . In the 1-center model, the defects representing source and drain of the charge carriers are indentical. In the two other models, 2-centre and 3-valence model, the carriers end at levels different from the initial ones. In the latter situations, photochromism is usually observed, since each of the defect charges absorbs light in different ways. It should be noted that such absorption changes occur also under homogeneous illumination. For a quantitative prediction to the photorefractive performance of a material it is necessary to know the concentrations of the defects in the various possible charge states and their spatial distributions present under defined illumination conditions.
These quantities can be obtained, if a set of parameters is known describing the kinetics of the light-induced charge transfers between the relevant defects. In a later section these parameters will be introduced.
The essential role of defects in the photorefractive effect is obvious. Because of this reason the structure and properties of defects in several inorganic photorefractive crystals have been investigated intensively during the last decade, mainly by EPR studies (BaTiO3, LiNbO3, Sr1-xBax NbO6, KNbO3, Ba1-xCax TiO3, Bi12MO20 (M = Ti, Ge, Si), etc.) [3–5].
At this point it is advantageous to demonstrate a way how the charge transfer processes connected with the defects can be elucidated from the information available about them.
If a method can be outlined how this knowledge leads to insight into the charge transfer processes connected with the Figure 1. The three basic models for charge transfer processes defects, an important step towards an understanding of the between defect gap levels. The lower two lead to light-induced optical properties of the materials has been achieved. optical absorption under homogeneous illumination.
1368 O.F. Schirmer, C. Veber, M. Meyer Figure 2. Setup for combined EPR/optical absorption investigations of light-induced signal changes. The specimen, centred in the EPR cavity between two half-cylindrical quartz rods, is first illuminated by intense monochromatic pump light for typically 60 s; the resulting signal changes are then simultaneously probed by EPR and weak, 1-3 eV, 20 ms pulsed white probe light. The transmitted light, guided by prisms at the quartz rods, is dispersed and registered with a multichannel detector.
following by the system BaTiO3 doped with Rh. This host defect concentrations, deduced from the EPR intensities, lattice has high electrooptic coefficients; therefore only a few to the absorption strengths, also the optical cross-sections transferred charges can already head to measurable index of the absorption bands are obtained. From here on, all changes, and thus the material offers high photorefractive further studies can be based on optical measurements alone.
sensitivity. Doping with Rh increases the infrared response Usually these can be performed at room temperature, where of the system [6–10]. EPR investigations generally fail, but where photorefractive devices are expected to operate. The changes of the optical absorption bands under illumination with pump light allows 1. Method to draw conclusions about the charge transfer processes taking place at these pump energies. Also the defect concenIf applicable, EPR is the most suitable method to obtain trations present under the various experimental illumination information on the chemical, geometrical, electronic and conditions can be deduced. Further parameters describing energetic structure of defects. However, in many cases the charge transfer processes are deduced from the temdefects are EPR-silent. Since these can likewise be involved poral evolution of the defect concentrations occurring after in the charge transfer processes, one has to look for ways switching the lihgt on or off.
to get information on them also. The method which we introduced is able to achieve this and will eventually allow 2. Qualitative identification of the charge to get the quantitative information needed to predict the defect-induced photorefratice properties. In this section transfer processes the procedure is outlined briefly. The first step is to establish the optical absorption bands as fingerprints of The experimental data mentioned in the following is taken the defects on the basis of the available EPR information. from the investigation of a BaTiO3 : Rh crystal grown from As will be shown, this can be done not only for EPR- a BaTiO3 melt unintentionally containing rhodium. The active, but also for EPR-silent defects. By comparing the simultaneous observation of light-induced EPR- and optical Физика твердого тела, 2002, том 44, вып. Parameters of light-induced charge transfer processes in photorefractive crystals Figure 3. b — optical absorption changes of BaTiO3 : Rh after illumination with 17 different pump energies. a — same information plotted in a pseudo-3D plot. Abscissa: probe light energy. Ordinate: pump light energy. Grey shading: absorption changes, as calibrated by bar on top. Assignment to the various charge states of Rh and Fe is indicated by the dashed lines. The thick vertical line is addressed in Fig. 4. An analysis of the plot into its component bands is shown in panel c (state after 1.9 eV pumping). The variation of the plot under different pumping energies is analysed at the right by the appropriate level schemes.
Физика твердого тела, 2002, том 44, вып. 1370 O.F. Schirmer, C. Veber, M. Meyer absorption changes is performed with a setup described earlier  allowing optical absorption measurements within an EPR cavity in a rather flexible way. A scheme is presented in Fig. 2. Absorption changes, resulting when the pump light energy is increased stepwise, starting from low energies, can be shown in the conventional way, as given in Fig. 3, b. More insight into the phenomena taking place is derived if the same infromation is plotted in a pseudo 3D plot exhibited above that, Fig. 3, a.
While abscissa and ordinate mark the probe- and pumplight energies, respectively, the grey shading indicates the absorption changes, their calibration given by the bar at the top. In the experiment, the pump energy is raised successively by the steps marked with the short horizontal thin lines along the ordinate. The indicated diagonal, defined by identical probe- and pump-light energies Eprobe = Epump, is an important guideline allowing to organize the features in the plot. The absorption minima or, alternatively, the lightinduced transparencies lying on the diagonal have to be attributed to primary processes. Here, a given pump energy Figure 4. Comparison of light-induced changes of the Rh4+ EPRphotoionises a defect and the corresponding absorption, signal and the optical absorption along the vertical line in Fig. 3.
caused by this charge transfer, decreases. Such primary A close correlation between both signals is seen. The optical processes are marked by double arrows in Fig. 1. Secondary absorption band at 1.9 eV can thus be attributed to the indicated transfer of valence electrons to Rh4+, shown in two equivalent processes are those triggered by the primary ones; they are ways in the lower panel.
lying outside the diagonal in Fig. 3, a; among them are those given by single arrows in Fig. 1.
Along the vertical line in Fig. 3, a, crossing the minimum at Eprobe = Epump = 1.9 eV, the correlation with the EPR by their optical fingerprints by this consistent interpretation spectra of Rh4+  was studied. The intensities of the procedure.
corresponding EPR and absorption signals are given in From Fig. 3 it is furthermore seen that not all absorption Fig. 4. A close correlation is seen, supporting the assignment changes can be attributed to Rh charge states. The presence to Rh4+ being converted to Rh3+ by photoexcitation of a of unintended Fe background impurities must also be valence band electron, see lower part of Fig. 4. There also considered. This if based on previous work on this element the corresponding process in real space is shown. In this and in BaTiO3 . There, it was shown that Fe4+ is converted comparable investigations it should be kept in mind that the to Fe3+ near 2.6 eV. Fe5+ is recharged to Fe4+ near 2.3 eV.
most intense absorption processes, such as charge transfer The charge transfer absorption of Fe3+ to Fe2+ is peaked at transitions, dominate the weaker ones, such as crystal field energies higher than 3.5 eV , lying above the band edge excitations. The latter can thus be neglected.
of BaTiO3, about 3.2 eV, and thus lies outside of the graph The conversion of Rh4+ creates Rh3+ and a hole in the in Fig. 3. The assignment of the features in Fig. 3 includes valence band. Since an optical absorption band near 3.0 eV the Fe4+ and Fe5+ absorptions. It should be noted that rises in parallel to the decrease of the Rh4+ absorption Fig. 3 contains difference shectra; therefore the extrema in near 1.9 eV, it is likely that the band near 3.0 eV has to this plot can occur at energies slightly different from those be attributed to Rh3+. The hole in the valence band is of the component bands.
not stable. Rather, it will be captured at a suitable trap.
If the pump energy is changed, other charge transAs Rh is the main impurity in the material, it is likely fer transitions will be activated as primary processes.
that the hole is caught at another Rh4+, forming Rh5+.
Accordingly, the difference spectra will be composed of The corresponding band, also rising essentially parallel to varying combinations of the component bands. The graphs the decrease of Rh4+, is seen to lie near 1.7 eV. This at the right side of Fig. 3 illustrate this. As an example the assignment of the Rh absorption bands is also supported consequences of the illumination at 2.4 eV are discussed:
by the fact that the higher valence, Rh5+, has a lower Here a primary process involving the low-energy outskirts absorption energy that Rh3+. It takes less energy to excite of the Fe4+ absorption, subtracted from the Rh3+ band near a valence electron to a highly charged cation defect than to 3.0 eV, is dominant. Pumping with 2.4 eV thus reduces a lower charged one. The described primary charge transfer the concentration of Fe4+, present in the crystal from the process and its secondary consequences comply with the beginning or created from Fe3+ by hole capture during 3-valence model, Fig. 1. One should note that also the EPR the previous illumination with lower pump energies; the silent charge states Rh3+ and Rh5+ have become accessible valence band holes are captured by Rh3+, forming Rh4+.
Физика твердого тела, 2002, том 44, вып. Parameters of light-induced charge transfer processes in photorefractive crystals Also a diagram is given, qualitatively explaining the charge transfer processes triggered by 2.9 eV pump light. Here the fundamental absorptions starts, creating holes which are eventually increasing the concentrations of the higher valences of Rh and Fe. In assessing the right side of Fig. 3 is must be considered that — because of the Franck–Condon principle — optical and thermal levels have to be distinguished: primary transfers excite valence electrons to optical levels, whereas recombination to the valence band starts from thermal levels.
3. Quantitative analysis Assuming that all absorption bands represented by the features in Fig. 5 are caused by the five components Rh5+, Rh4+, Rh3+, Fe5+ and Fe4+, and for simplicity assuming gaussian band shapes, the plot (Fig. 3) can be analysed Figure 5. 3-valence model together with the set of differential equations governing the recharging of the Rh levels following into the Rhi+ bands shown in Figs. 3, c and 6. Since thermally (wavy arrows) and optically (double arrows) induced the optical absorption of a defect ‘i’ is connected to its transfer processes. For simplicity optical and thermal levels have density Ni by i(E) = Ni · Si(E), the energy dependence not been distinguished.
of the absorption cross-sections, Si(E), is given by that of the component absorption bands in Fig. 6. It the respective defect concentrations Ni are known, the cross-sections can be derived quantitatively.
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