Abstract
Results of optical absorption and electroabsorption (EA) measurements in the vicinity of the interband absorption edge are reported for top-seeded solution-grown crystals of BaTi. In common with other perovskite oxides, the absorption edge in BaTi is found to display Urbach-rule behavior. The exponential absorption tail can be described between 20 and 450 °C by an effective temperature , where K, i.e., . Although no uniquely defined band gap can be extracted from an exponential edge, we propose, on the basis of indirect arguments, that the room-temperature band gaps are 3.38 and 3.27 eV, respectively, for light polarized parallel and perpendicular to the ferroelectric axis. At high temperatures in the cubic phase, the band gap decreases at the rate -4.5× eV/°C. EA measurements in the tetragonal phase show that an applied electric field along the axis shifts the entire Urbach edge rigidly upward in energy by an amount , which is proportional to the square of the total polarization , spontaneous plus field-induced, i.e., . The effect can be described by a temperature-independent band-edge polarization potential having the value eV /. The smaller coefficient could not be measured, because of photoconductivity and carrier-trapping effects. An anomalous increase in the band gap with decreasing temperature within 150°C of the Curie point is attributed to coupling between polarization fluctuations and the band edge. A simple thermodynamic model is shown to describe the temperature dependence of this fluctuation contribution with reasonable accuracy. The results suggest that the correlation volume is at most a weak function of temperature and that does not display critical behavior. This conclusion is consistent with several recent experiments in displacive ferroelectrics. The magnitude of the observed mean square polarization fluctuation contribution to the band-edge position ( meV at ) can be understood using the simple fluctuation theory with the value deduced previously from photoelastic constant measurements. It is also suggested that a mean square polarization fluctuation contribution to the band-edge position is present in the tetragonal phase below approximately 100 °C owing to the proximity of the tetragonal-orthorhombic transition. A fluctuation contribution of about 40 meV is indicated at room temperature.
- Received 13 March 1970
DOI:https://doi.org/10.1103/PhysRevB.2.2679
©1970 American Physical Society