Optical properties of ferroelectric films Hf$_x$Zr$_y$O$_2$ and La : Hf$_x$Zr$_y$O$_2$ according to ellipsometry data

Recently ferroelectric properties have been found in hafnia-based nanosized films. Such films are of the utmost interest for development of a universal memory, which combines the advantages of random access memory and flash memory. The paper studies optical properties of hafnia-zirconium oxide films Hf$_x$Zr$_y$O$_2$ and lanthanum-alloyed hafnia-zirconium oxide films La : Hf$_x$Zr$_y$O$_2$. Fluctuations of thickness in Hf$_x$Zr$_y$O$_2$ do not exceed 3.5%, fluctuations of thickness in La : Hf$_x$Zr$_y$O$_2$ films – 3.2%. Optical properties are analyzed based on effective-medium theory. According to effective-medium theory data, Hf$_x$Zr$_y$O$_2$ films contain 46% HfO$_2$, 54% ZrO$_2$, La : Hf$_x$Zr$_y$O$_2$ films contain 47.5% HfO$_2$, 52.4% ZrO$_2$, 2.5% La$_2$O$_3$.