Band gap and mobility of epitaxial perovskite ${\mathrm{BaSn}}_{1-x}{\mathrm{Hf}}_x{\mathrm{O}}_3$ thin films

A wide band-gap perovskite oxide $\mathrm{BaSn}{\mathrm{O}}_3$ is attracting much attention due to its high electron mobility and oxygen stability. On the other hand, $\mathrm{BaHf}{\mathrm{O}}_3$ was recently reported to be an effective high-$k$ gate oxide. Here, we investigate the band gap and mobility of solid solutions of $\mathrm{BaS}{\mathrm{n}}_{1-x}\mathrm{H}{\mathrm{f}}_x{\mathrm{O}}_3$ ($x=0-1$) (BSHO) as a basis to build advanced perovskite oxide heterostructures. All the films were epitaxially grown on MgO substrates using pulsed laser deposition. Density functional theory calculations confirmed that Hf substitution does not create midgap states while increasing the band gap. From x-ray diffraction and optical transmittance measurements, the lattice constants and the band-gap values are significantly modified by Hf substitution. We also measured the transport properties of $n$-type La-doped BSHO films $\left[\left(\mathrm{Ba},\mathrm{La}\right)\left(\mathrm{Sn},\mathrm{Hf}\right){\mathrm{O}}_3\right]$, investigating the feasibility of modulation doping in the $\mathrm{BaSn}{\mathrm{O}}_3/\mathrm{BSHO}$ heterostructures. The Hall measurement data revealed that, as the Hf content increases, the activation rate of the La dopant decreases and the scattering rate of the electrons sharply increases. These properties of BSHO films may be useful for applications in various heterostructures based on the $\mathrm{BaSn}{\mathrm{O}}_3$ system.

Figure 1

Band structure (top) and total/atom resolved partial density of states (PDOS) (bottom) near the Fermi energy for $\mathrm{BaS}{\mathrm{n}}_{1-x}\mathrm{H}{\mathrm{f}}_x{\mathrm{O}}_3$ ($x=0$, 0.25, 0.5, 0.75, 1) as obtained from DFT calculations with GGA-PBEsol exchange correlation functional. The $2\times 2\times 2$ supercell is used for $\mathrm{BaS}{\mathrm{n}}_{1-x}\mathrm{H}{\mathrm{f}}_x{\mathrm{O}}_3$ ($x=0.25$, 0.5, 0.75). The effective masses of the conduction band are $0.2m_0, 0.28m_0, 0.36m_0, 0.41m_0$, and $0.62m_0$, respectively. The TDOS of $\mathrm{BaS}{\mathrm{n}}_{1-x}\mathrm{H}{\mathrm{f}}_x{\mathrm{O}}_3$ ($x=0.25$, 0.5, 0.75) is scaled down to 1/8 in each graph to show each orbital character effectively. The inset is the enlarged PDOS plot for Hf orbitals.

Figure 2

X-ray diffraction patterns of BSHO films grown on a [001] MgO substrate. (a) $\theta -2\theta$ scans of $\mathrm{BaS}{\mathrm{n}}_{1-x}\mathrm{H}{\mathrm{f}}_x{\mathrm{O}}_3$ ($x=0$, 0.2, 0.4, 0.6, 0.8, 1) and its rocking curves of $\mathrm{BaS}{\mathrm{n}}_{1-x}\mathrm{H}{\mathrm{f}}_x{\mathrm{O}}_3$ ($x=0$, 0.2, 0.4, 0.6) around (002) peaks. (b) Reciprocal space map around the (103) Bragg reflection of each BSO and BHO film and the (204) reflection of the MgO substrate. (c) The lattice constant from $\theta -2\theta$ scans and the calculation based on GGA-PBEsol as a function of the Hf content.

Figure 3

Optical transmission spectra of BSHO films grown on a [001] MgO substrate. (a) Optical transmittance of $\mathrm{BaS}{\mathrm{n}}_{1-x}\mathrm{H}{\mathrm{f}}_x{\mathrm{O}}_3$ ($x=0$, 0.2, 0.4, 0.6, 0.8, 1) films. (b) ${\left(\alpha h\nu \right)}^2$ vs $h\nu$ plot and ${\left(\alpha h\nu \right)}^{1/2}$ vs $h\nu$ plot. The band-gap energy is extrapolated from the linear line. (c) Direct and indirect band-gap energy as varying the Hf content from the optical transmission spectra and the calculations based on GGA-PBEsol.

Figure 4

Transport properties of 50-nm BLSHO films with a 60-nm BHO buffer layer grown on a [001] MgO substrate. (a) The carrier concentration as a function of the Hf content in each La doping rate. The dotted lines are fully activated carrier densities in each La doping rate. (b) The Fermi level apart from CBM as a function of the Hf content. (c) The change of mobility as a function of the Hf content in each La doping rate. (d) The mobility as a function of the carrier concentration for each Hf content. La doping rates are denoted at each point. The $\gamma$ value of the dotted line in $\mu \propto n^{\gamma }$ is $-0.29, -0.81, -0.53$, and $-0.12$, respectively, for Hf $0\%, 8\%, 21\%$, and $27\%$ substitution. The open red circles are data of BLSO films (50 nm) with a BSO buffer (150 nm) on a MgO substrate from Ref. [7].