In order to establish this quantitative calibration, the EPR signal of Rh4+, for experimental reasons being given by the first derivative of the resonant microwave absorption, is integrated twice. This number, proportional to the amount of spins in the sample, is compared to the corresponding quantity of a known number of spins of a paramagnetic EPR standard. For this purpose small single crystals of CuSO4 · 5H2O of defined weight were used. On this basis the Rh4+ density in the material is determined .
Then, the change of the Rh4+ EPR signal under illumination with 1.9 eV light is compared to the correlated change of the Rh4+ optical absorption hand. Since the decrease of the number of Rh4+ ions can be inferred from the provious EPR calibration, the procedure allows to derive values of the Figure 6. Energy dependence of the optical absorption crossabsorption cross-section of Rh4+, as given in Fig. 6. Their sections of the three Rh charge states involved.
energy dependence is given by the gaussian fit. Assuming as an approximation, that the participation of the Fe charge states in Fig. 3 is only a minor effect, the validity of the 3-valence model can be taken as the basis for the in the Table. One deduces a total Rh concentration, further arguments. Since in this model two Rh4+ ions are RhT = Rh3+ + Rh4+ + Rh5+, of about 40 ppm.
converted to Rh3+ and Rh5+, respectively, the changes of All the parameters governing the charge transfer prothe concentrations under illumination with 1.9 eV, inducing cesses connected with the 3-valence model, as applicable the Rh4+ primary charge transfer process, are:
in first approximation ot BT : Rh, are comprised by the Rh5+ = Rh3+ = -1/2 Rh4+. By comparing the concorresponding system of differential equations  displayed centration changes to those of the corresponding absorption bands in Fig. 3, the absorption cross-section of Rh3+ in Fig. 5. These rate equations describe the kinetics of the Rh charge states; the symbols have the following and Rh5+ are derived. They are also given in Fig. 6.
meanings (‘i’ indicating the Rh charge state species):
With these quantities available, the concentrations of Rhi+ — density of the charge state; I — light intensity;
Rh3+, Rh4+ and Rh5+ present in the crystal before illumination can now be determined. From the total Si — absorption cross-sections; qi — probabilities that absorption of the crystal one finds the values included charge state ‘i’ is ionised after absorption; i — thermal Физика твердого тела, 2002, том 44, вып. 1372 O.F. Schirmer, C. Veber, M. Meyer Figure 7. Rise (I = 0) and decay (I = 0) of the light-induced changes of the Rh5+, Rh4+ and Rh3+ concentrations. The metastable deviation of the steady state changes under I = 0 from the equilibrium, expected to be zero, is small (about 1%) compared to the unchanged background of Rhi+. Therefore, this small deviation is neglected.
ionisation rates; i — capture coefficients; p — hole density values, the parameters listed in the Table were identified in valence band. by fitting the numerical solutions of the rate equations to the data. The analysis of the photorefractive properties of Fig. 7 displays the corresponding changes of the defect the investigated specimen is in progress. Comparison with densities, induced by illumination with 12 mW/cm2 HeNe present results will take place when the necessary data is light and their decay after ending the illumination. It available.
surprises that at room temperature they do not return to the initial state in the latter situation. Apparently this represents a metastable non-equilibrium situation, caused by a slow 4. Discussion back reaction in the dark. The mobility of holes, thermally excited to the edge of the valence band, is more impeded The basis of the presented method is the use of optical by potential fluctuations than the mobility of holes lightabsorption bands as fingerprints of the existing defects, induced during the forward reaction. This argument is established byt means of the available EPR information.
supported by the data taken at 50C. Here the changes relax As shown, also EPR-silent lattice irregularities can often to essentially zero because the hole mobility is increased be labelled and identified on this way. In this manner the at elevated temperatures even in the presence of potential scope of defect studies is extended beyond that accessible fluctuations. Because then also the recombination processes to EPR measurements. The range of detectable defects is are faster, the steady state amplitudes of the changes are more than doubled because now it is possible also to verify smaller than at room temperature.
the presence of the EPR-silent majority of defects. The However, it should be considered that the light-induced method is applicable if the light-induced defect recharging absorption changes shown in Fig. 7 amount not only about leads to a photochromic situation. This is not a serious 1% of the initial Rhi+ concentrations. Neglecting this very limitation, however. If not fulfilled at room temperature, small relative mismatch between zero and the steady state this condition is usually valid at low temperatures where shallow traps tend to be populated by charge carriers after photoexcitation, while being empty at room temperature.
Parameters describing charge transfer processes in BaTiO3 involvFrom defect investigations under such conditions one can ing Rh charge states then extrapolate to the behaviour at room temperature Generally valid Parameters characteristic for the investi- where photorefractive devices are expected to operate.
parameters gated crystal (initial Rh concentrations) There have been previous studies of BaTiO3 : Rh in which the charge transfer parameters responsible for the photoreq4 0.5 Rh4+ 1.0 · 1017 cm-fractive properties of the material have been derived [9,10].
q5 0.5 Rh3+ 4.0 · 1017 cm-The present investigation differs from these studies in two 4 9.3 · 10-2 s-1 Rh5+ 0.5 · 1017 cm-respects. 1) Previously data from photorefractive measure5 1.3 s-1 RhT 5.5 · 1017 cm-3 (= 40 ppm) ments were used to derive — in a rether indirect way — 3 1.4 · 10-12 cm3/s 4 3.9 · 10-11 cm3/s the denstities of the defect charge states involved. Our Si(E) see Fig. 6.
present treatment obtains these densities independently and Физика твердого тела, 2002, том 44, вып. Parameters of light-induced charge transfer processes in photorefractive crystals can thus eventually check whether the photorefractive data are reproduced. 2) Based on the energy dependence of the defect-related optical cross-sections we get the quantitative information on the parameters of the light-induced charge transfer processes for a wide range of light energies. In each of the previous studies the analysis was limited to one light energy only.
Concluding, we have described a method by which the charge transfer processes occurring in doped insulating crystals can be analysed with respect to paths photoexcited charge carriers are taking between the involved defects.
The method allows the quantitative determination of the parameters governing such processes. It is entirely based on the EPR information on the defects. Eventually it can lead to a prediction of the sensitivity of a doped photorefractive material.
References  Photorefractive Effects and Materials / Ed. by P. Gnter, J.-P. Huignard. Topics in Applied Physics 61, Springer (1988).
 K. Buse. Appl. Phys. B64, 273; 391 (1997).
 O.F. Schirmer, H.-J. Reyher, M. Whlecke. In: Insulating Materials for Optoelectronics / Ed. by F. Agull-Lpez. World Scientific (1995).
 O.F. Schirmer, M. Meyer, A. Rdiger, C. Veber, A. Mazur.
Optical Materials, in print.
 O.F. Schirmer. In: Defects and Surface-Induced Effects in Acvanced Perovskites. Kluwer (2000). P. 75.
 G.W. Ross, P. Hribek, R.W. Eason, M.H. Garrett, D. Rytz.
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