The Optical Bandgap of Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ (\textit{n}=1$\sim $5, 10) Ruddlesden-Popper Phases

The Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ Ruddlesden-Popper homologous series is of particular interest because its n=$\infty $ member SrTiO$_{3}$ exhibits such a wide range of properties including high dielectric constant, tunable dielectric constant, and superconductivity. In this study we explore the optical bandgaps of the Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ ($n$=1$\sim $5, 10) Ruddlesden-Popper phases. This is the first time that a phase-pure $n$=10 Ruddlesden-Popper phase has ever been made. Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ ($n$=1$\sim $5, 10) thin films were grown on (001) LSAT substrates by reactive molecular-beam epitaxy. (001) LSAT substrates provide good lattice match ($<$ 1{\%} mismatch) to the entire Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ series. For the $n$=10 sample, we also deposited it on (001) SrTiO$_{3}$ substrates. SrTiO$_{3}$ substrates provides nearly strain-free growth for the $n$=10 phase. The optical properties of the thin films were studied using \textit{ex situ} spectroscopic ellipsometry. We measured the indirect bandgap of the Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ ($n$=1$\sim $5, 10) Ruddlesden-Popper phases on LSAT and their values decrease monotonically from 3.48 eV ($n$=1) to 3.14 eV ($n=\infty )$ with increasing $n$. The bandgaps of the Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ ($n$=1$\sim $5, 10) Ruddlesden-Popper phases fall between the high bandgap SrO ($n$=0) and SrTiO$_{3}$ ($n=\infty )$ end members of the series.