Publication No.2



A. Stashans, H. Pinto.
Self-trapped polarons in BaTiO3 and SrTiO3 crystals - 5th Int. Conf.
Comput. Phys., Kanazawa (Japan), 1999, p1-10.

Abstract:
The quantum-chemical methods for crystals are of special importance since can compute 
energy bands of different materials and at microscopic level can resolve fundamental 
problems which is not possible to settle analitically and/or experimentally. One of the 
interesting areas of research in titanates is carrier self-trapping study in the perfect 
lattice. Despite that the polarons are involved in all relevant light-induced charge-
transfer reactions in these materials, to our knowledge no attempts had been done so 
far to study the hole self-trapping possibilities in pure BaTiO3 and SrTiO3 crystals, 
which are of high technological importance due to their wide range of applications. We 
have utilized advanced INDO computational scheme modified for crystal calculations in 
order to carry out these studies.
     Embedded molecular cluster (EMC) consisting of 90 atoms was used for both crystals. 
A hole was inserted into the cluster and the electronic band structure was computed self-
consistently without any a priori assumption of the electronic density distribution. 
Because of the hole presence atomic displacements occur in the system leading to the 
reduction of the total energy of EMC. Thus calculated relaxation energy was found to be 
3.85 eV for the BaTiO3 and 2.90 eV for SrTiO3 crystals, respectively. In order to 
estimate hole localization energy we have used Fowler approximation which gives us the 
localization energy value equal to the "center of gravity" of the oxygen 2p valence 
band. This value was computed considering the Wannier reprezentation of localized states 
and Fourier transform of the valence band energies giving 2.36 eV and 2.85 eV for BaTiO3
and SrTiO3, respectively. The hole self-trapping energy was estimated as a difference 
between the negative relaxation and positive localization energies leading us to the 
conclusions that: (i) a spontaneous polaron self-trapping will occur in the BaTiO3 
lattice with energy gain of 1.49 eV while (ii) this process is practically impossible 
in the SrTiO3 crystal (energy gain is only 0.05 eV). We also discuss the possible spacial 
configurations of self-trapped polarons and lattice distortion due to the Jahn-Teller 
effect.
    The calculated absorption energy, 0.5 eV, in BaTiO3 crystal is supposed to 
correspond to the shallow acceptor energy level found in numerous experiments and located 
around 0.5 eV above the top of the O 2p valence band. So we suggest that self-trapped 
polarons are significantly responsable for non-linear photoconductivity phenomenon in 
the BaTiO3 crystal. These point defects have not been observed experimentally by the 
EPR or ENDOR direct measurements due to the zero nuclear spin on regular O atoms. 
Our suggestion is supported by the fact that these defects obviously do not occur in 
the SrTiO3 crystal where the non-linear photoconductivity also does not exist.



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