Band-gap engineering of rutile-structured SnO2−GeO2−SiO2 alloy system

Rutile-structured germanium oxide $(\mathrm{r}\text{\ensuremath{-}}{\mathrm{GeO}}_{2})$, an ultrawide band-gap (UWBG) semiconductor, is a promising candidate for future high-power electronics because of its excellent properties, including ambipolar dopability, high carrier mobilities, and a higher thermal conductivity than $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. In this paper, focusing on a wide variety of its applications, we propose an UWBG alloy system based on $\mathrm{r}\text{\ensuremath{-}}{\mathrm{GeO}}_{2}$ and other rutile-structured oxides $({\mathrm{SnO}}_{2}\text{\ensuremath{-}}{\mathrm{GeO}}_{2}\text{\ensuremath{-}}{\mathrm{SiO}}_{2})$ and clarify the electronic structure and electrical properties based on experiments and the first-principles calculations. Experimentally, (001)-oriented $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ alloy thin films with an entire range of Ge compositions $(x)$ were grown by a mist chemical vapor deposition technique. Structural characterizations show that the fabricated $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ alloy films with $x\ensuremath{\le}0.96$ and the well-crystallized part of the film with $x=1.00$ have uniform chemical compositions and the same epitaxial relations with $\mathrm{r}\text{\ensuremath{-}}{\mathrm{TiO}}_{2}$ (001) substrates. Transmission electron microscopy observations reveal that there are few dislocations in $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{0.66}{\mathrm{Sn}}_{0.34}{\mathrm{O}}_{2}$ because of relatively small in-plane lattice mismatch. In contrast, many dislocations are observed near the film/substrate interface in $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{0.96}{\mathrm{Sn}}_{0.04}{\mathrm{O}}_{2}$. Lattice constants of the alloys both along the $a$ and $c$ axes decrease with increase in Ge compositions. Their band gaps were determined by spectroscopic ellipsometry analysis, indicating that the band gaps increase as Ge compositions increase $(3.81\ensuremath{-}4.44\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$ with a bowing parameter of 1.2 eV. The values of lattice constants and the trend of band-gap transitions obtained by calculations are in good agreement with those of experimentally obtained each other. Then we presented the calculated natural band alignments of $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ and $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ alloys, suggesting the possibility of $p$-type doping in $\mathrm{r}\text{\ensuremath{-}}{\mathrm{GeO}}_{2}$ and Ge-rich $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ and availability of $\mathrm{r}\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$ and Si-rich $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ as a blocking layer of other rutile-structured devices. Finally, electrical measurements demonstrated $n$-type conductivities in $\mathrm{r}\text{\ensuremath{-}}{\mathrm{Ge}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ $(x\ensuremath{\le}0.57)$.