Defects in inorganic photorefractive materials and their investigations

4 B. Briat et al.
band edge, E X must be expended in order to excite a valence band electron
to the defect X 0 ,transformingitintoX − .
Especially in oxide crystals, the charge carriers tend to couple strongly to
the lattice. Since optical excitations take place under Franck-Condon conditions,
i. e. with the ’lattice kept fixed’ [5, 6], in the case of strong coupling,
thermal levels must be distinguished from optical ones (for an example see
Fig. 2): The final state reached by the optical transition ends in the optical
level, lying higher than the vibrational ground state, the thermal level; for
an example, see section 5. In oxide crystals energy differences between both
types of levels up to about 2.3 eV [7] have been found!
optical
1.6 eV
4+
Rh
3+
4+
3+ thermal
0.95 eV
Fig. 2. Discrimination between optical
and thermal levels, exemplified for
Rh 4+/3+ in BaTiO 3 (see Section 5).
The elastic lattice energies, corresponding
to the electronic groundstate
(upper edge of valence band)
and to the electron excited to the defect,
are shown as depending on a
configuration coordinate Q [6]. Double
arrow: transition to optical level,
vertical in Q-space. Wavy arrow: vibrational
transition to thermal level.
Such charge transfer transitions (e.g. from a valence band oxygen ion to
a defect) or intervalence transitions (from a defect to a conduction band ion)
usually are rather strong, because the electron moves through a considerable
distance, corresponding to a large transition moment [5]. The range of the
transfer is limited by the covalent mixture between the states of the initial
and final ions; this is strongest between those nearest to each other. On the
other hand, internal transitions of crystal field type occur e.g. among the d-
states of one transition metal ion. For ions at crystal sites having inversion
symmetry, such excitations thus are parity forbidden [5]. They become easily
observable in situations without inversion symmetry, e. g. at the tetrahedral
sites of sillenite crystals. Such transitions can also be stronger, if the excited
state is resonant with the conduction band. As a general rule it can still be
stated that the photorefractive effect is triggered most decisively by charge
transfer or intervalence transitions, both because they are strong and because
they lead to defect photoionization.
A further important consequence of lattice coupling is the formation of
polarons. This term is related to the equivalence of corresponding lattice sites
in crystals (Fig. 3). The tunnelling of a charge carrier between these sites competes
with the lattice distortion, tending to break the equivalence by spon-