Temperature-dependent dielectric function of bulk SrTiO$_3$: Urbach tail, band edges, and excitonic effects

摘要

We report the temperature-dependent complex dielectric function of pristinebulk SrTiO$_3$ between 4.2 and 300 K within the energy range of 0.6-6.5 eVdetermined by spectroscopic ellipsometry. Fundamental indirect and directband-gap energies have been extracted and are discussed with regard to existingstate-of-the-art theoretical calculations. Furthermore, the dielectric functionaround the fundamental direct gap is analyzed by considering excitonic states.The excitonic effects, including the Coulomb enhancement of the continuum, arecharacterized using an extension of the Elliott's formula considering both thereal and imaginary parts of the dielectric function. The Urbach tail below theindirect edge shows an unconventional temperature-dependent behavior correlatedto the microstructural changes near the structural phase transition around 105K from the low-temperature tetragonal phase to the cubic phase. Thetemperature-dependent characterization reveals that the fundamental indirectedge as well as the Urbach tail are affected conspicuously by the structuralphase transition while the fundamental direct edge is not. Moreover, theindirect edge follows Varshni's rule only in the cubic phase and the directedge exhibits an anomalous linear increase with increasing temperature.