Origin of morphotropic phase boundary in thin-film Hf0.5Zr0.5O2 on the TiN electrode

Abstract

Our study aims to clarify the morphotropic phase boundary observed in Zr-doped hafnia systems. We utilize density-functional-theory calculations to examine various structural phases of (Hf,Zr)O2 thin films on TiN electrodes. We account for Zr composition, film thickness, and temperature to model the free energy of (Hf,Zr)O2 on TiN electrodes. Our assessment of the thermodynamic stability of each structural phase in terms of surface and interface energies under the substrate strain allows us to determine that the substrate strain and temperature significantly reduce the energy differences between different phases. Our findings lead to the energy reversal between tetragonal and orthorhombic phases when the film thickness increases. Based on our results, we propose that the formation of a high-temperature tetragonal phase, arising from the rapid thermal or annealing processes, is crucial to the appearance of the morphotropic phase boundary in Hf0.5Zr0.5O2. Understanding the origin of the morphotropic phase boundary can have significant implications for device applications.