Transport Properties of the ${\mathrm{La}\mathrm{In}\mathrm{O}}_3/{\mathrm{Ba}\mathrm{Sn}\mathrm{O}}_3$ 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-Schrödinger 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.

Figure 1

Experiments to measure the 2D carrier density (n_2D) of the $\mathrm{LIO}$/$\mathrm{BLSO}$ interface (a) $\mathrm{LIO}$/$\mathrm{BLSO}$ schematic structure with buffer and contact layers. (b) n_2D of the interface at each $\mathrm{LIO}$ thickness in red dots, with the 0.2% doped channel on $\mathrm{Mg}\mathrm{O}$ substrates. The pink dots are for comparison with data of the 0.3% doped channels on STO substrates from Ref. [23].

Figure 2

Thermopower measurement. (a) Experimental setup. The 2DEG sample is placed between the gap of two Peltier devices (one is cooler, the other one is hotter), which is used to generate a temperature difference (ΔT). The ΔT is measured using two tiny K-type thermocouples placed at the edge of the electrodes. The thermoelectromotive force (ΔV) is measured using a digital multimeter. (b) Thermoelectromotive force as a function of temperature difference at the $\mathrm{LIO}/\mathrm{BSO}$ (undoped) interface that shows thermopower of −73 µV K⁻¹.

Figure 3

Results of PS calculations to define the unknown polarization value and deep-donor density in $\mathrm{LIO}$ at the $\mathrm{LIO}$/$\mathrm{BLSO}$ interface. (a) Interface-polarization values on the $\mathrm{LIO}$ side that fits the experimental results. (b) Carrier densities of the quantum well calculated using the interface polarization in (a) are drawn by the green solid lines that explains the experimental result of the blue dots. Increased and decreased carrier densities of thin green lines from the green solid line are calculated using the polarization values that are increased and decreased 20% from the thick solid green line of (a). Carrier densities using constant polarizations in the entire $\mathrm{LIO}$ film are shown as dashed lines, which cannot explain the experimental data. (c) Carrier densities of the quantum well in the cases of $\mathrm{LIO}$ deep-donor densities of 5 × 10¹⁹ cm⁻³, 1.3 × 10²⁰ cm⁻³, and 2 × 10²⁰ cm⁻³ using the interface polarization of the solid green line in (a). The blue dots are experimental results. (d) Changes in minimum conduction-band bending at each deep-donor density of $\mathrm{LIO}$ at $\mathrm{LIO}$ 10 nm. The quantum well is enlarged in the inset.

Figure 4

Influence of the deep-acceptor density and $\mathrm{La}$-dopant density of $\mathrm{BSO}$ on the $\mathrm{LIO}$/undoped $\mathrm{BSO}$ and the $\mathrm{LIO}$/$\mathrm{BLSO}$ interface calculated with the PS equation. (a) n_2D of the quantum well with a deep-acceptor density of 1 × 10¹⁷ cm⁻³, 1 × 10¹⁸ cm⁻³, 1 × 10¹⁹ cm⁻³, 4 × 10¹⁹ cm⁻³, and 6 × 10¹⁹ cm⁻³ as a function of the $\mathrm{LIO}$ thickness. (b) Changes in conduction-band bending at each deep-acceptor density in $\mathrm{BSO}$ with $\mathrm{LIO}$ 10 nm. (c) n_2D of the quantum well with $\mathrm{La}$-donor density from 0 to 5.72 × 10¹⁹ cm⁻³ (0.4% BSLO) as a function of the $\mathrm{LIO}$ thickness. (d) Changes in conduction-band bending at each $\mathrm{La}$-donor density in $\mathrm{BSO}$ at $\mathrm{LIO}$ 10 nm.

Figure 5

Influence of the deep-acceptor activation energy of $\mathrm{BSO}$ and deep-donor activation energy of $\mathrm{LIO}$ on the $\mathrm{LIO}$-undoped $\mathrm{BSO}$ interface calculated with the PS equation. (a) Changes in conduction-band bending at different deep-acceptor activation energy of $\mathrm{BSO}$, 0.5, 1.0, and 1.55 eV at $\mathrm{LIO}$ 10 nm. (b) Polarization adjustments with other deep-acceptor activation energies of $\mathrm{BSO}$. (c) $\mathrm{BSO}$ deep-acceptor density adjustments with other deep-acceptor activation energies of $\mathrm{BSO}$. (d) Changes in conduction-band bending at different deep-donor activation energy of $\mathrm{LIO}$, 1.5, 2.0, and 2.5 eV at $\mathrm{LIO}$ 10 nm. (e) Polarization adjustments with other deep-donor activation energies of $\mathrm{LIO}$. (f) $\mathrm{LIO}$ deep-donor density adjustments with other deep-donor activation energies of $\mathrm{LIO}$.

Figure 6

Influence of the effective masses of $\mathrm{BSO}$ and $\mathrm{LIO}$ on the $\mathrm{LIO}$-$\mathrm{BLSO}$ interface. (a) n_2D of the quantum well with $\mathrm{BSO}$ effective masses of 0.2, 0.42, and 7 m_e as a function of the $\mathrm{LIO}$ thickness. (b) Changes in conduction-band bending at each effective mass of $\mathrm{BSO}$ at $\mathrm{LIO}$ 10 nm. (c) n_2D of the quantum well with $\mathrm{LIO}$ effective masses of 0.2, 0.46, and 7 m_e as a function of the $\mathrm{LIO}$ thickness. (d) Changes in conduction-band bending at each effective mass of $\mathrm{LIO}$ at $\mathrm{LIO}$ 10 nm.

Figure 7

Influence of the dielectric constant of $\mathrm{BSO}$ and $\mathrm{LIO}$ on the $\mathrm{LIO}$-$\mathrm{BLSO}$. (a) n_2D of the quantum well with $\mathrm{BSO}$ dielectric constants of 10, 20, 50, and 100 as a function of the $\mathrm{LIO}$ thickness. (b) Changes in conduction-band bending at each dielectric constant of $\mathrm{BSO}$ at $\mathrm{LIO}$ 10 nm. (c) n_2D of the quantum well with $\mathrm{LIO}$ dielectric constants of 25, 38, and 50 as a function of the $\mathrm{LIO}$ thickness. (d) Changes in conduction-band bending at each dielectric constant of $\mathrm{LIO}$ at $\mathrm{LIO}$ 10 nm.

Figure 8

Influence of the conduction-band offset between $\mathrm{BSO}$ and $\mathrm{LIO}$ on the $\mathrm{LIO}$-$\mathrm{BLSO}$ interface. (a) n_2D of the quantum well with conduction-band offsets of 1.0, 1.6, and 2.4 eV as a function of the $\mathrm{LIO}$ thickness. (b) Changes in conduction-band bending at each conduction-band offset at $\mathrm{LIO}$ 10 nm.

Figure 9

Influence of reduced deep-acceptor density of $\mathrm{BSO}$ on the $\mathrm{LIO}$-undoped $\mathrm{BSO}$ interface calculated with the PS equation at a temperature of 4 K. (a) Conduction-band bending of the interface with 1 × 10¹⁸ cm⁻³, 1 × 10¹⁹ cm⁻³, and 4 × 10¹⁹ cm⁻³ deep-acceptor density. (b) Enlarged views of the conduction band near the interface with sub-band energies of the 2D quantum wells at each of the deep-acceptor densities of $\mathrm{BSO}$.

Figure 10

PS simulation of $(\mathrm{Al}\mathrm{Ga})\mathrm{As}/\mathrm{Ga}\mathrm{As}$ 2DEG. (a) Structure and parameters for calculation. (b) Calculation result of conduction-band energy for the Fermi level of 0 eV. (c) An enlarged view of (b) near the interface of $(\mathrm{Al}\mathrm{Ga})\mathrm{As}$ and $\mathrm{Ga}\mathrm{As}$ with a sub-band energy of the red line.

Figure 11

PS simulation of $(\mathrm{Al}\mathrm{Ga})\mathrm{N}/\mathrm{Ga}\mathrm{N}$ 2DEG. (a) Structure and parameters including the direction of the polarizations for calculation. (b) Calculation result of conduction-band energy for the Fermi level of 0 eV. (c) An enlarged view of (b) near the interface of $(\mathrm{Al}\mathrm{Ga})\mathrm{N}$ and $\mathrm{Ga}\mathrm{N}$ with a sub-band energy of the red line.

Figure 12

PS simulation of $(\mathrm{Mg}\mathrm{Zn})\mathrm{O}/\mathrm{Zn}\mathrm{O}$ 2DEG. (a) Structure and parameters including the direction of the polarizations for calculation. (b) Calculation result of conduction-band energy for the Fermi level of 0 eV. (c) An enlarged view of (b) near the interface of $(\mathrm{Mg}\mathrm{Zn})\mathrm{O}$ and $\mathrm{Zn}\mathrm{O}$ with a sub-band energy of the red line.