Optical phonon modes, static and high frequency dielectric constants, and effective electron mass parameter in cubic In$_2$O$_3$

TL;DR

This study comprehensively characterizes optical phonon modes, dielectric constants, and electron effective mass in cubic In$_2$O$_3$ using spectroscopic ellipsometry, first-principles calculations, and Hall effect measurements, providing new insights into its fundamental properties.

Contribution

It provides the first complete experimental and theoretical determination of all optical phonon modes, dielectric constants, and effective electron mass in cubic In$_2$O$_3$, with high accuracy and consistency.

Findings

All optical phonon modes are identified and characterized.

The static dielectric constant is determined as 10.55±0.07.

The effective electron mass is measured as 0.208±0.006 m_e.

Abstract

A complete set of all optical phonon modes predicted by symmetry for bixbyite structure indium oxide is reported here from a combination of far-infrared and infrared spectroscopic ellipsometry, as well as first principle calculations. Dielectric function spectra measured on high quality, marginally electrically conductive melt grown single bulk crystals are obtained on a wavelength-by-wavelength (a.k.a. point-by-point) basis and by numerical reduction of a subtle free charge carrier Drude model contribution. A four-parameter semi-quantum model is applied to determine all sixteen pairs of infrared-active transverse and longitudinal optical phonon modes, including the high-frequency dielectric constant, $\varepsilon_{\infty}=4.05\pm 0.05$. The Lyddane-Sachs-Teller relation then gives access to the static dielectric constant, $\varepsilon_{\mathrm{DC}}=10.55\pm 0.07$. All experimental results are in excellent agreement with our density functional theory calculations and with previously reported values, where existent. We also perform optical Hall effect measurements and determine for the unintentionally doped $n$-type sample a free electron density of $n=(2.81 \pm 0.01)\times 10^{17}$~cm$^{-3}$, mobility of $\mu=(112 \pm 3)$~cm$^{2}$/(Vs), and an effective mass parameter of $(0.208\pm0.006)m_e$. Density and mobility parameters compare very well with results of electrical Hall effect measurements. Our effective mass parameter, which is measured independently of any other experimental technique, represents the bottom curvature of the $\Gamma$ point in In$_2$O$_3$ in agreement with previous extrapolations. We use terahertz spectroscopic ellipsometry to measure the quasi-static response of In$_2$O$_3$, and our model validates the static dielectric constant obtained from the Lyddane-Sachs-Teller relation.