Unravelling the oxygen influence in cubic bixbyite In$_2$O$_3$ on Raman active phonon modes by isotope studies

TL;DR

This study investigates Raman-active phonons in cubic bixbyite In$_2$O$_3$ by integrating DFPT calculations with oxygen isotope substitution ($^{16}$O vs $^{18}$O) and Raman spectroscopy on both bulk and epitaxial films. DFPT reveals that nearly all Raman modes involve coupled In–O vibrations, with $E_{g}^{(4)}$ as a pure oxygen mode, and shows two plateaus in relative isotopic shifts tied to oxygen’s vibrational contribution. Experimentally, ToF-SIMS and XRD confirm high-purity isotope incorporation and crystal quality, while Raman measurements across isotopes demonstrate a monotonic, linear decrease in mode frequencies with increasing $^{18}$O content, in excellent agreement with theory. The findings provide a robust framework for using Raman spectroscopy to probe oxygen-related lattice dynamics and growth dynamics in In$_2$O$_3$, including potential sensing of oxygen vacancies via carefully chosen modes. Overall, the work delivers quantitative, site-resolved insight into lattice vibrations and establishes a practical pathway for isotope-engineered oxide materials physics.

Abstract

In this study, we performed comprehensive investigations on the Raman active phonon modes in cubic bixbyite In$_2$O$_3$, an important oxide based, wide-bandgap semiconductor. Fundamental insights into the lattice dynamics are revealed, by determining the atomistic contribution to all modes and their frequencies by density functional perturbation theory calculations. Those simulations were performed for different compositions of $^{16}$O and $^{18}$O isotope ratios, including their pure states. An increasing red-shift of the mode frequencies with increasing $^{18}$O content for all modes, due to the increased atomic mass, is revealed. For the seven lowest energy modes, this relative shift is below 1%, whereas for the remaining 15 higher energetic modes a shift of about 5.5% was identified. All modes have energy contributions of both indium and oxygen lattice sites, except for one, which corresponds to a pure oxygen vibrational state. Applying Raman spectroscopy, those results could be verified experimentally with excellent agreement. Investigated samples consisted of a bulk single crystal with $^{16}$O isotopes and a MBE grown thin film as the $^{18}$O sample. Time-of-flight secondary ion mass spectrometry confirms the purity of the oxygen isotope in the sample. These isotopologue studies allow for a direct experimental access to fundamental material properties in cubic In$_2$O$_3$ by means of Raman spectroscopy. For example, we speculate, that the presence of oxygen vacancies in In$_2$O$_3$ would result in a shift of modes that are dominated by O-vibrations, e. g., $E_{g}^{(4)}$ or $A_{g}^{(4)}$, towards lower frequencies.

Figures (6)

• Figure 1: Unit cell of cubic bixbyite In$_{2}$O$_{3}$, having space group $Ia\bar{3}$ (206). It comprises of 48 oxygen and 32 indium atoms, a lattice parameters of $a = b = c = 10.117$ Å and $\alpha = \beta = \gamma = 90$°. The image was created using VESTA.momma2011
• Figure 2: Theoretical predictions for the relative energy contributions of indium (black) or oxygen, distinguished by isotope variants $^{16}$O (red) and $^{18}$O (purple), to the Raman-active lattice vibrations are presented. The analysed modes exhibit are modes with (a)$A_{g}$, (b)$E_{g}$ and (c)$F_{g}$ symmetry. The relative energy contribution of each element is represented by the height of the corresponding coloured column. All modes consist of vibrations involving both elements present in the crystal, with the exception of mode $E_{g}^{(4)}$, which is purely oxygen-driven.
• Figure 3: Raman spectra of the $^{16}$O In$_{2}$O$_{3}$ sample, acquired at room temperature, 2.62 eV excitation photon energy and for two different polarization states, $z(xx)\bar{z}$ and $z(xy)\bar{z}$ following the Porto notation. As the $A_{g}$ modes intensity is highly dependent on the polarization state of the scattered Raman photon, this dependence can be applied for an unambiguous mode identification.
• Figure 4: Room temperature Raman spectra, acquired with an excitation photon energy of 3.81 eV, of the investigated cubic bixbyite In$_{2}$O$_{3}$ samples with natural, predominantly $^{16}$O and 96.5% enriched $^{18}$O oxygen abundance, depicted in black and purple, respectively. The two spectra have an artificial offset, for a clearer optical distinguishably. Except for the $F_{g}^{(12)}$ and $F_{g}^{(13)}$ ones (light grey), all Raman active phonon modes could be identified for both spectra. A clear red-shift for the modes stemming from the heavier oxygen isotope is apparent for frequencies above 300 cm$^{-1}$.
• Figure 5: Visualization of the Raman active phonon mode frequencies as a function of the $^{18}$O isotope content. $A_{g}$ modes are symbolized by rectangles, $E_{g}$ modes by circles and $F_{g}$ modes by squares. Compared are experimentally (red) determined wavenumbers with theoretically calculated (purple) values. The theoretical results underestimate the phonon mode wavenumbers slightly compared to the experimental results. However, both methods reveal the behaviour of a decrease in mode energy with rising $^{18}$O content for modes above 300 cm$^{-1}$ contrasting the almost constant behaviour below that threshold.