Changes in the optical absorption induced in the Bi12TiO20:Al crystal by exposition to short- and long-wavelength radiation

The impurity absorption model is used to describe the experimentally observed reversible changes in the optical absorption spectrum induced in the Bi12TiO20:Al crystal by subsequent exposition to short-wavelength radiation with λi, = 532 nm and longer-wavelength radiation with λn changing from 588 to 1064 nm. The model takes into account the photoinduced transitions between two metastable states of a deep defect center leading to the change of its position in the crystal lattice under conditions of strong lattice relaxation.


Introduction
Bi 12 TiO 20 (BTO) crystals belonging to the sillenite family are promising for application in dynamic holography based on counter interaction of light waves in reflective geometry [1 -4]. This is due to high values of the space charge field of reflective holograms formed in the BTO crystals due to considerable concentration of photoactive defect centers inherent in the crystals through which the photoinduced redistribution of the electric charge occurs [5,6]. The special feature of the BTO crystals is the strong photochromic effect also observed at room temperatures; it consists in reversible changes of the optical absorption induced by exposition to visible radiation [7,8]. The main reason for the increase in the optical absorption in the BTO crystals is considered to be the capture of photoexcited charge carriers (electrons) from deep donor centers to less deep traps characterized by the photoionization cross section larger than in the initial state [9 -11]. Such process in which the nonequilibrium charge carriers participate can lead to an increase in the photorefractive sensitivity of the BTO crystals in the near-IR range of the spectrum [12,13]. Another reason for the increased absorption in the BTO crystals that is not associated with electron photoexcitation to the conduction band can be generation of defects for which intracenter transitions occur as a result of exposition to light [11]. In [14] the intracenter character of transitions in the BTO:Al crystal in the wavelength range from 500 to 900 nm characterized by a resonant dependence of the photo-and thermoinduced changes in the light absorption was suggested.
Detailed experimental investigations performed in [15,16] demonstrated that exposition to shortwavelength radiation with the wavelength λ i = 532 nm caused an increase in the optical absorption in the BTO:Al crystal and resulted in the spectrum whose shape in the wavelength range 470-1000 nm was independent of the initial crystal state. The subsequent exposition to a longer-wavelength radiation with λ n changing from 588 to 1064 nm led to the enhanced transmittance of the BTO:Al crystal in the entire examined spectral range. In this case it was established that the enhanced transmittance fixed in the saturation region depended nonmonotonically on the wavelength and reached a maximum at λ n ~ 670 nm. It should be noted that the observed changes in the optical absorption spectra for the BTO:Al crystal during enhanced-diminished transmittance cycles were reversible and well reproduced experimentally.
In the present work, to describe the experimentally observed reversible changes in the optical absorption spectrum induced in the BTO:Al crystal by subsequent exposition to short-and longwavelength radiation, the model is considered that takes into account strong relaxation of the lattice during photoinduced transitions between two metastable states of a deep defect center. The redistribution of center concentrations over the states that differ by the photoabsorption cross sections arising during such transitions leads to changes in the optical absorption additional to changes caused by the photoinduced electron redistribution over the deep donors via the conduction band and by generation and decay of defects for which intracenter transitions occured.

Theoretical model
As is well known [17 -19], localized optically induced changes in the electronic configuration of the deep defect centers of some types in semiconductor and dielectric materials are accompanied by considerable reconstruction of such centers manifested via changes in their positions in the lattice. This effect called the photoinduced lattice relaxation [17] leads to the possibility of photocontrollable change of the properties of crystals comprising such centers and of their application as recording media [18]. The configuration coordinate diagram [17,19] best described the change in the geometry of the defect caused by the change in its electronic state.
Let us consider the deep defect center that can be in two metastable states A and C with the potential energy minima shifted along the configuration coordinate Q (Fig. 1). The parabolas E d1 (Q) and E d2 (Q), described by the well-known relations [20] characterize the energies of the ground (1) and excited (2)   Q corresponding to the quantum energy 12  causing optical transitions from the ground to the excited state 12 2 and to the energy 21  of optical transitions back to the ground state can be obtained from Eqs. (1)-(4) in the following form: Assuming that the energy distributions for the defect center concentrations in the ground state, 11 (1) and (2), we find their dependences on the corresponding configuration coordinates where 10 d N and 20 d N are particle concentrations in the ground state for Q = Q 1 and in the excited metastable state for Q = Q 2 , respectively; k B is the Boltzmann constant, and T is the absolute temperature.
Taking into account Eqs. (7) and (8), the expressions determining the spectral dependence of the absorption coefficient where S d1 and S d1 are the photoabsorption cross sections for the ground state and excited state, respectively. Thus, the optical absorption in the crystal caused by the examined deep defect center is spectrally dependent, and its absorption coefficient ()

Approximation of the spectral dependences of the optical absorption
The spectral dependences of the optical absorption in the BTO:Al crystal observed experimentally in [15] can be approximated by the impurity absorption model that takes into account the contribution of electrons photoexcited from deep donor centers to the conduction band and the intracenter transitions [11] supplemented by the model of the defect center interacting with the lattice that is based on the application of the configuration coordinate diagram considered above. Below we restrict ourselves by an analysis of the approximation of three experimental dependences from [15] shown by open circles in Fig. 2. Dependence 1 in this figure shows the absorption spectrum for the BTO:Al crystal exposed in the initial stage of each experiment to laser radiation with the wavelength λ i =532 nm and the intensity I i = 15.4 mW/cm 2 for 1930 s. This dependence was reproduced well irrespective of the initial state of the BTO:Al sample [15]. Spectral dependences 2 and 3 shown in Fig. 2 illustrate the subsequent exposition of the crystal to continuous laser radiation with the wavelength λ n = 663 nm (I n = 270 mW/cm 2 and the exposure time until saturation t n = 960 s) and λ n = 780 nm (I n = 4 mW/cm 2 and t n = 6420 s), respectively, in the second stage of the experiments leading to the enhanced transmittance of the crystal.
The approximation of the experimental spectral dependences of the optical absorption in the BTO:Al crystal yielded the following values of the model parameters for the absorption coefficient caused by deep defect centers and described by Eqs. (9) and (10) Table 1 for laser radiation with three wavelengths used in experiments by Dyu et al. [15] and for nonmonochromatic radiation of a semiconductor light-emitting diode with the average wavelength λ n = 588 nm. For nonmonochromatic radiation, the experimental technique was analogous to that used in [15]. In the first stage, the BTO:Al sample was irradiated by laser radiation with the wavelength λ i = 532 nm that caused the diminished transmittance of the crystal; the subsequent sample exposition to incoherent radiation with λ n = 588 nm and intensity I n = 0.3 mW/cm 2 in the second stage caused the enhanced transmittance of the crystal with saturation at t n = 2760 s. To approximate satisfactorily the spectral dependences, three intracenter transitions with the Gaussian spectral characteristics and maxima at quantum energies of 1.49, 1.62, and 1.77 eV must be taken into account together with the electron photoexcitation to the conduction band from four donor centers with average ionization energies of 1.08, 1.56, 1.96, and 2.75 eV. The energy parameters of the defect centers that characterized these processes in the BTO:Al crystal were close to those used in [11]. The approximated spectral dependences shown in Fig. 2 by solid curves demonstrate good agreement with the available xperimental data.
An analysis of the model parameters used to approximate the experimental spectral dependences of the optical absorption in the BTO:Al crystal demonstrated the following. The increased optical absorption induced in the BTO:Al crystal by exposition to short-wavelength radiation with the wavelength λ i = 532 nm was due to the increased contribution of the intracenter transitions to the radiation absorption, photoinduced increase in the degree of occupation by electrons of the centers with ionization energies of 1.08 and 1.96 eV, and photoexcitation of deep defect centers and their transition from the ground state to the excited metastable state (see Fig. 1). The subsequent exposition to long-wavelength radiation led to the reduced contribution of intracenter transitions to the absorption during occupation by electrons of the centers with ionization energies of 1.08 and 1.96 eV. In this case, the degree of occupation by electrons of the center with ionization energy of 1.56 eV increased, and the concentration of the deep defect centers in the excited state decreased due to their photoinduced transitions to the ground state.
Thus, the observed nonmonotonic dependence of the enhanced transmittance for the Bi 12 TiO 20 :Al crystal, having the diminished transmittance, on the wavelength λ n of radiation leading to the enhanced transmittance can be caused not only by quantitative changes of contributions to the impurity absorption described in [11], but also by photoinduced transitions of the deep defect center between the ground and excited states, accompanied by strong electron-phonon interaction with distortion of the crystal lattice. For energy of the radiation quantum with λ i = 532 nm corresponding to the vertical transition from the state A ( Fig. 1) with maximum concentration of the centers to the ground state, they are effectively translated to the excited state (АВ transition), leading to the diminished transmittance of the crystal. The enhanced transmittance of the crystal will be maximum for radiation with energy of the quantum at which the CD transition occurs (in the examined case, at the wavelength n  670 nm).

Conclusions
Thus, the reversible changes in the optical absorption spectrum for the BTO:Al crystal observed experimentally in [15] and induced by the subsequent exposition to short-and long-wavelength radiation are well described by the impurity absorption model, considering the photoexcitation of electrons from the deep centers to the conduction band and the intracenter transitions [11], complemented by the model of deep defect centers with two metastable states interacting with the lattice. The photoinduced transitions between these states are accompanied by changes in the configuration coordinates. The observed photoinduced changes in the optical absorption in the BTO:Al crystal can be caused not only by the photoinduced electron redistribution over the deep donors via the conduction band and by generation and decay of defects for which the intracenter transitions occur, but also by redistribution of the deep center concentration between two metastable states with different photoabsorption cross sections.