Transport Properties of the LaInO3/BaSnO3 Interface Analyzed by Poisson-Schrödinger Equation

2DEG systems formed in quantum wells of semiconductor heterostructures have been instrumental in advancing science and technology for many decades. Here, we report two unique transport properties of 2DEG formed at the interface of two perovskite oxides ${\mathrm{La}\mathrm{In}\mathrm{O}}_{3}$ ($\mathrm{LIO}$) and ${\mathrm{Ba}\mathrm{Sn}\mathrm{O}}_{3}$ ($\mathrm{BSO}$): the peculiar $\mathrm{LIO}$ thickness dependence of the high two-dimensional (2D) carrier density ($n_{2{\rm{D}}}$) and the very narrow width of the quantum well. We analyze, via Poisson-Schr\"odinger simulation, how the various materials parameters affect the 2D carrier density and its profile when using the ``interface-polarization'' model in which the polarization exists only near the interface. Our simulations show that the known material parameters of $\mathrm{LIO}$ and $\mathrm{BSO}$ are capable of generating a deep and narrow quantum well as suggested by the experimental transport properties and reveal some distinct features of the $\mathrm{LIO}$/$\mathrm{BSO}$ interface from the conventional 2DEGs. Furthermore, they predict how the $\mathrm{LIO}$/$\mathrm{BSO}$ 2DEG will evolve as the defect density decreases.