Dynamic Model Development for the Temperature-Dependent Characterization of CsPbI₂Br Perovskite Thin Films via Spectroscopic Ellipsometry

Spectroscopic ellipsometry (SE) is a widely used characterization technique for estimating the thickness and optical constants of thin films. Less commonly, it is performed as a function of temperature, providing valuable insights into the temperature dependence of a film’s optical and morphological properties. This information can prove useful in various contexts, from enhancing the fundamental understanding around a material’s structure to optimizing a device’s optoelectronic performance. Most studies on temperature-dependent SE adopt a methodology where the sample is allowed to stabilize at consecutive temperature intervals, for each of which a static model is developed. However, this approach is likely to conceal information around real-time mechanisms and effects.<br/><br/>In this work, we propose a new approach for the fitting of temperature-dependent SE results. This approach relies on the use of a continuous heating ramp and the development of a singular dynamic model that can describe in real-time the evolution of a thin film under increasing temperature. Unlike most previous studies, special emphasis is placed on the inclusion of thickness and roughness variations, due to lattice expansion/contraction and grain coalescence. In particular, the increase of the surface roughness, despite being commonly overlooked, can lead to erroneous fitting results due to increased light scattering.<br/><br/>We use this modelling approach to characterize the real time annealing effect on thermally evaporated CsPbI₂Br thin films and quantify various temperature-dependent parameters. This way, we gain insight into the crystallization mechanism of vacuum evaporated inorganic perovskites, which is still under-investigated when compared to the crystallization of solution-processed films. The as-deposited films, which are initially in the orthorhombic perovskite phase, exhibit extremely low roughness, associated with small grain size. As the temperature increases, the transition to the tetragonal phase is marked by a significant shift in bandgap energy. Followingly, the transition to the cubic phase is indicated by a pronounced increase in the film’s roughness, signaling the onset of grain coalescence. Once this process is complete, prolonging the annealing duration does not significantly impact the grain size and morphology. Finally, we extract and interpret various temperature-dependent parameters, like the Urbach energy, the thermo-optic coefficient, and the interband transition energies.<br/><br/>The validity of the presented results is further corroborated through additional ex and in situ characterization measurements, including grazing incident wide angle X-Ray scattering, atomic force microscopy, profilometry, and reflectance/transmittance measurements. This demonstrates that the proposed dynamic modeling of temperature-dependent SE results constitutes a high-throughput, reliable, and versatile characterization approach that can partially replace multiple, even costlier and less accessible, techniques.