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Register a new userOptical phonon modes, static and high frequency dielectric constants, and effective electron mass parameter in cubic In$_2$O$_3$
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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, $varepsilon_{infty}=4.05pm 0.05$. The Lyddane-Sachs-Teller relation then gives access to the static dielectric constant, $varepsilon_{mathrm{DC}}=10.55pm 0.07$. 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 $(0.208pm0.006)m_e$. 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.
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I use first principles calculations to investigate the thermal conductivity of $beta$-In$_2$O$_3$ and compare the results with that of $alpha$-Al$_2$O$_3$, $beta$-Ga$_2$O$_3$, and KTaO$_3$. The calculated thermal conductivity of $beta$-In$_2$O$_3$ agrees well with the experimental data obtain recently, which found that the low-temperature thermal conductivity in this material can reach values above 1000 W/mK. I find that the calculated thermal conductivity of $beta$-Ga$_2$O$_3$ is larger than that of $beta$-In$_2$O$_3$ at all temperatures, which implies that $beta$-Ga$_2$O$_3$ should also exhibit high values of thermal conductivity at low temperatures. The thermal conductivity of KTaO$_3$ calculated ignoring the temperature-dependent phonon softening of low-frequency modes give high-temperature values similar that of $beta$-Ga$_2$O$_3$. However, the calculated thermal conductivity of KTaO$_3$ does not increase as steeply as that of the binary compounds at low temperatures, which results in KTaO$_3$ having the lowest low-temperature thermal conductivity despite having acoustic phonon velocities larger than that of $beta$-Ga$_2$O$_3$ and $beta$-In$_2$O$_3$. I attribute this to the fact that the acoustic phonon velocities at low frequencies in KTaO$_3$ is less uniformly distributed because its acoustic phonon branches are more dispersive compared to the binary oxides, which causes enhanced momentum loss even during the normal phonon-phonon scattering processes. I also calculate thermal diffusivity using the theoretically obtained thermal conductivity and heat capacity and find that all four materials exhibit the expected $T^{-1}$ behavior at high temperatures. Additionally, the calculated ratio of the average phonon scattering time to Planckian time is larger than the lower bound of 1 that has been observed empirically in numerous other materials.
We determine the anisotropic dielectric functions of rhombohedral $alpha$-Ga$_2$O$_3$ by far-infrared and infrared generalized spectroscopic ellipsometry and derive all transverse optical and longitudinal optical phonon mode frequencies and broadening parameters. We also determine the high frequency and static dielectric constants. We perform density functional theory computations and determine the phonon dispersion for all branches in the Brillouin zone, and we derive all phonon mode parameters at the Brillouin zone center including Raman-active, infrared-active, and silent modes. Excellent agreement is obtained between our experimental and computation results as well as among all previously reported partial information from experiment and theory. We also compute the same information for $alpha$-Al$_2$O$_3$, the binary parent compound for the emerging alloy of $alpha$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$, and use results from previous investigations [Schubert, Tiwald, and Herzinger, Phys. Rev. B 61, 8187 (2000)] to compare all properties among the two isostructural compounds. From both experimental and theoretical investigations we compute the frequency shifts of all modes between the two compounds. Additionally, we calculate overlap parameters between phonon mode eigenvectors and discuss the possible evolution of all phonon modes into the ternary alloy system and whether modes may form single mode or more complex mode behaviors.
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