Phonon scattering limited mobility in the representative cubic perovskite semiconductors ${\mathrm{SrGeO}}_{3}$, ${\mathrm{BaSnO}}_{3}$, and ${\mathrm{SrTiO}}_{3}$

Phonon scattering limited mobility in the representative cubic perovskite semiconductors ${SrGeO}_{3}$ , ${BaSnO}_{3}$ , and ${SrTiO}_{3}$

Christian A. Niedermeier, Yu Kumagai, Keisuke Ide, Takayoshi Katase, Fumiyasu Oba, Hideo Hosono, and Toshio Kamiya

Phys. Rev. B 101, 125206 – Published 24 March 2020

Abstract

Cubic perovskite oxides are emerging high-mobility transparent conducting oxides (TCOs), but Ge-based TCOs had not been known until the discovery of metastable cubic ${SrGeO}_{3}$ . $0.5 \times 0.4 \times 0.2 − m m^{3}$ large single crystals of the cubic ${SrGeO}_{3}$ perovskite were successfully synthesized employing the high-pressure flux method. The phonon spectrum is determined from the IR optical reflectance and Raman-scattering analysis to evaluate the electron transport governed by optical phonon scattering. A calculated room-temperature mobility on the order of $3.9 \times 10^{2} c m^{2} V^{- 1} s^{- 1}$ is obtained, identifying cubic ${SrGeO}_{3}$ as one of the most promising TCOs. Employing classical phonon theory and a combined experimental-theoretical approach, a comprehensive analysis of the intrinsic electron mobility in the cubic perovskite semiconductors ${SrGeO}_{3}$ , ${BaSnO}_{3}$ , and ${SrTiO}_{3}$ is provided based on the magnitude of polarization and eigenfrequency of optically active phonons.

Received 26 December 2019
Accepted 28 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.125206

Physics Subject Headings (PhySH)

Classical transport Dielectric properties Electrical conductivity Electronic structure Optical phonons Phonons

Perovskites Semiconductor compounds Single crystal materials

Crystal growth Density functional calculations Fourier transform infrared spectroscopy Infrared techniques Raman spectroscopy Reflectivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christian A. Niedermeier ^1,*, Yu Kumagai¹, Keisuke Ide¹, Takayoshi Katase¹, Fumiyasu Oba^1,2, Hideo Hosono^1,2, and Toshio Kamiya^1,2

¹Laboratory for Materials and Structures, Tokyo Institute of Technology, Yokohama 226–8503, Japan
²Materials Research Center for Element Strategy, Tokyo Institute of Technology, Yokohama 226–8503, Japan

^*Corresponding author: c-niedermeier@mces.titech.ac.jp

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Vol. 101, Iss. 12 — 15 March 2020

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Figure 1
(a) The cubic perovskite ${SrGeO}_{3}$ crystal structure. (b) Optical micrograph of a cubic ${SrGeO}_{3}$ single crystal. (c) The 100 out-of-plane HR-XRD pattern of a cubic ${SrGeO}_{3}$ single crystal with the intensity plotted on a logarithmic scale. (d) PBE0-calculated band structure along high-symmetry directions in the first Brillouin zone indicates 2.7-eV indirect and 3.4-eV direct band gaps and a large CB dispersion. (e) Reflection ellipsometry spectrum for the evaluation of (f) the absorption coeffient data $α^{1 / 2}$ and $α^{2}$ indicate optical band gaps in agreement with the specular reflectance $R$ edge and the calculated values.
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Figure 2
(a) IR reflectance spectrum of a mirror-polished cubic ${SrGeO}_{3}$ polycrystalline pellet. (b) Raman-scattering spectrum of a cubic perovskite ${SrGeO}_{3}$ single crystal. The first-order Raman peaks at 493 and $742 c m^{- 1}$ provide the ${LO}_{2}$ and ${LO}_{3}$ phonon frequencies in the dispersion model, as given by the maxima of the loss function $- Im (ɛ^{- 1})$ .
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Figure 3
(a) Real part of $ɛ_{1}$ of the dielectric function of cubic ${SrGeO}_{3}$ , ${BaSnO}_{3}$ , and ${SrTiO}_{3}$ . The LO phonon frequencies correspond to the zeros of $ɛ_{1}$ . (b) The maxima of the imaginary part $ɛ_{2}$ of the dielectric function and the loss function $- Im$ ( $ɛ^{- 1}$ ) correspond to the frequency of TO and LO phonon modes, respectively. The peak heigths of the TO and LO phonons indicate the magnitude of polarization, but it must be considered that the peak broadening due to damping ( $γ_{μ} > 0$ ) is taken into account.
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Figure 4
Calculated phonon band structures of cubic ${SrGeO}_{3}$ , ${BaSnO}_{3}$ , and ${SrTiO}_{3}$ obtained by density-functional perturbation theory. The three IR-active TO modes at the Γ point of the first Brillouin zone (empty circles) are schematically illustrated based on the calculated ion displacement vectors. The inactive eigenmodes are indicated with a cross. The LO eigenfrequencies at the Γ point are indicated by the horizontal lines.
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Figure 5
Relaxation time of carrier scattering $τ_{ν}$ at $T = 298$ K by LO phonons as a function of the phonon energy $ℏ ω_{l_{ν}}$ and oscillator strength $ɛ_{l_{ν}}$ for cubic (a) ${SrGeO}_{3}$ , (b) ${BaSnO}_{3}$ , and (c) ${SrTiO}_{3}$ , according to Eqs. (5) and (6). The smallest relaxation time among the three LO phonon modes, which is the most crucial for the intrinsic electron mobility, is indicated by the dashed line. The LO peak heights of the loss function $- Im$ ( $ɛ^{- 1}$ ) indicate the magnitude of polarization, but it must be considered that the peak broadening due to damping ( $γ_{μ} > 0$ ) is taken into account.
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Figure 6
IR reflectance spectrum of a mirror-polished, 2 at.% La-doped cubic ${SrGeO}_{3}$ ( ${La}_{0.02} {Sr}_{0.98} {GeO}_{3}$ ) polycrystalline pellet.
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Physical Review B

covering condensed matter and materials physics

Phonon scattering limited mobility in the representative cubic perovskite semiconductors ${SrGeO}_{3}$ , ${BaSnO}_{3}$ , and ${SrTiO}_{3}$

Christian A. Niedermeier, Yu Kumagai, Keisuke Ide, Takayoshi Katase, Fumiyasu Oba, Hideo Hosono, and Toshio Kamiya

Phys. Rev. B 101, 125206 – Published 24 March 2020

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Physical Review B

covering condensed matter and materials physics

Phonon scattering limited mobility in the representative cubic perovskite semiconductors SrGeO3, BaSnO3, and SrTiO3

Christian A. Niedermeier, Yu Kumagai, Keisuke Ide, Takayoshi Katase, Fumiyasu Oba, Hideo Hosono, and Toshio Kamiya

Phys. Rev. B 101, 125206 – Published 24 March 2020

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Phonon scattering limited mobility in the representative cubic perovskite semiconductors ${SrGeO}_{3}$ , ${BaSnO}_{3}$ , and ${SrTiO}_{3}$