Broad-band ellipsometry study of the anisotropic dielectric response of YAlO3

TL;DR

Broad-band THz–UV ellipsometry quantifies the anisotropic dielectric response of orthorhombic YAlO3 by measuring six high-symmetry orientations on wedged crystals and fitting the results with a diagonal dielectric tensor using the Berreman four-parameter model. The study resolves all 25 infrared-active phonons, characterizing LO–TO splittings, Reststrahlen behavior, and a potential negative refraction regime near the anisotropic LO frequencies, while also mapping the temperature dependence of phonon positions from 10 to 330 K. The work provides a comprehensive, experimentally validated dielectric function $\varepsilon(\omega)$ along the $a$, $b$, and $c$ axes up to 6.5 eV, with both FIR phonon physics and MIR–UV dispersion captured, enabling accurate optical modeling of thin films on YAlO3 substrates. These results offer essential substrate data for strain-engineered oxide heterostructures and inform future spectroscopic studies of complex oxides grown on YAP substrates.

Abstract

We present a broad band (THz to UV) ellipsometry study of the anisotropic dielectric response of the orthorhombic perovskite YAlO3. The ellipsometric measurements have been performed on YAlO3 crystals with three different surface cuts and for six high symmetry configurations of the crystal axes with respect to the plane of incidence of the photons. The obtained data are presented in terms of the Mueller Matrix elements N, C, and S and their features are analyzed and discussed with respect to the anisotropy of the dielectric response tensor. In particular, in the infrared range we have identified all 25 infrared active phonon modes that have been predicted from theoretical studies. We also discuss a negative refraction effect that naturally occurs in the vicinity of an anisotropic longitudinal-optical phonon. Moreover, we have determined the temperature dependence of the phonon parameters between 10 and 330 K. The dielectric response above the phonon range, from about 0.1 to 6.5 eV, is shown to be featureless and characteristic of an insulator with a large band gap above 6.5 eV and is well described by anisotropic Cauchy model.

Figures (6)

• Figure 1: a) Sketch of the distorted perovskite structure of YAlO$_\text{3}$ with the unit cell indicated by the red lines and the atomic position adapted from Suda2003. b) Sketch of a YAlO$_\text{3}$ crystal (light blue) with a wedge angle, $\alpha$, that is mounted with silver paint (gray) on a copper sample holder (orange). Also shown is the coordinate system of the ellipsometer with the plane of incidence of the photon beam defined by the $x$- and $z$-axes and the incident and reflected beam at the angle $\varphi$ with respect to the surface normal. The beam reflected from the backside is deviated by the angle $\delta$. The side of the sample is covered by aluminum tape (violet) to further reduce scattered and unwanted light. c) Wedge angle along the plane of incidence that is required for a deviation of $\delta = 5°$ (red lines) or for a total internal reflection (black lines) calculated as a function of the refractive index and the incidence angle $\varphi$ ranging from 60° (thick lines) to 80° (indicated by the arrows). d) Same as (c) but with the crystal rotated by 90°, i.e. with the wedge perpendicular to the plane of incidence. Horizontal dashed lines mark a wedge angle of 2.3°.
• Figure 2: a) Far-infrared ellipsometry spectra of the Mueller matrix elements $N$, $C$, $S$ of YAlO$_\text{3}$ at 300K with angle of incidence $\varphi = 75°$ measured on $b$-cut (green points) and $c$-cut (blue points) surfaces with the $a$-axis parallel to the plane of incidence. Sketches of the measurement configurations are shown in the inset of the middle panel. Also shown are the best fits with the anisotropic model (blue and green lines) and, for comparison and as guides to the eye, the spectra for a fictive sample with an isotropic response that have been calculated with the parameters of $\varepsilon_a$ (gray lines). Marked by arrows on the bottom panel are the positions of $\omega_\text{TO}$ (black arrows) and $\omega_\text{LO}$ (gray arrows) of $\varepsilon_a$. Dashed vertical lines highlight some of the pronounced anisotropy features in the vicinity of $\omega_\text{LO}$ in the $b$-axis response (green dashed line) and the $c$-axis response (blue dashed line). Solid pin symbols show positions of strong $\omega_\text{TO}$ in the $b$-axis response (green pin) and the $c$-axis response (blue pin). b) Calculated geometric $z$-component of the refracted wavevector for p-polarized light, Re{$\kappa_p$} (thick lines) and Im{$\kappa_p$} (thin lines), with the colors matching the configuration of the experiment. c) Calculated absolute values of the Fresnel coefficients $|r_p|$ (thick lines) and $|r_s|$ (thin lines). d) Calculated argument of the complex Fresnel coefficients $\arg(r_p) = \Delta_p$ (thick lines) and $\arg(r_s) = \Delta_s$ (thin lines).
• Figure 3: a) Far-infrared response along the $b$-axis of YAlO$_\text{3}$ at 300K with $\varphi = 75°$ measured on $a$-cut (red points) and $c$-cut (blue points) surfaces (see the sketches in the inset of the middle panel) and expressed in terms of the Mueller matrix elements $N$, $C$, $S$. Also shown are the best fits with the anisotropic model (red and blue lines) as well as the simulated response of a fictive isotropic sample with the $\varepsilon_b$ parameters as obtained from the anisotropic model (gray lines), as a guide to the eye. Arrows on the bottom panel mark the positions of $\omega_\text{TO}$ (black arrows) and $\omega_\text{LO}$ (gray arrows) of $\varepsilon_b$. Dashed vertical lines highlight some of the pronounced anisotropy features in the vicinity of $\omega_\text{LO}$ in the $a$-axis response (red dashed line) and the $c$-axis response (blue dashed line). Solid pin symbols show positions of strong $\omega_\text{TO}$ in the $a$-axis response (red pin) and the $c$-axis response (blue pin). b) Calculated geometric $z$-component of the refracted wavevector for $p$-polarized light, Re{$\kappa_p$} (thick lines) and Im{$\kappa_p$} (thin lines), with colors matching the configuration of the experiment. c) Calculated absolute values of the Fresnel coefficients $|r_p|$ (thick lines) and $|r_s|$ (thin lines). d) Calculated argument of the complex Fresnel coefficients $\arg(r_p) = \Delta_p$ (thick lines) and $\arg(r_s) = \Delta_s$ (thin lines).
• Figure 4: a) Far-infrared response along the c-axis of YAlO$_\text{3}$ at 300K with $\varphi = 75°$ as measured on $a$-cut (red points) and $b$-cut (green points) surfaces and shown by the Mueller matrix elements $N$, $C$, $S$. Also displayed are the best fits with the anisotropic model (red and green lines) and the response of a fictive isotropic sample simulated with the $\varepsilon_c$ parameters (gray lines), as a guide to the eye. The inset (e) of the middle panel shows a comparison of the model of the real part of dielectric functions $\varepsilon_a$, $\varepsilon_b$, and $\varepsilon_c$. Arrows on the bottom panel mark the positions of $\omega_\text{TO}$ (black arrows) and $\omega_\text{LO}$ (gray arrows) of $\varepsilon_c$. Dashed vertical lines highlight some of the pronounced anisotropy features in the vicinity of $\omega_\text{LO}$ in the $a$-axis response (red dashed line) and the $b$-axis response (green dashed line). Solid pin symbols show positions of strong $\omega_\text{TO}$ in the $a$-axis response (red pin) and the $b$-axis response (green pin). b) Calculated geometric $z$-component of the refracted wavevector for $p$-polarized light, Re{$\kappa_p$} (thick lines) and Im{$\kappa_p$} (thin lines), with colors matching the configuration of the experiment. c) Calculated absolute values of the Fresnel coefficients $|r_p|$ (thick lines) and $|r_s|$ (thin lines). d) Calculated argument of the complex Fresnel coefficients $\arg(r_p) = \Delta_p$ (thick lines) and $\arg(r_s) = \Delta_s$ (thin lines).
• Figure 5: Diagonal elements of the dielectric tensor along the three main crystal axes of orthorhombic YAlO$_\text{3}$. The spectra represent the best fit with an anisotropic model to the ellipsometry data taken at room temperature for six different configurations with respect to the surface cut and the mutual orientation of the crystal axes. Panels a), b), and c) show the far-infrared spectra of $\varepsilon_a$, $\varepsilon_b$ and $\varepsilon_c$, respectively. Thin lines represent the real part of the dielectric function, $\varepsilon_1$, thicker lines the imaginary part, $\varepsilon_2$. The positions of the weak phonons are marked with the pin symbols. Panels d), e), and f) show the extension of the model in the MIR/NIR/VIS/UV ranges on a logarithmic energy scale. Lines represent an anisotropic Cauchy model. Symbols show the result of an anisotropic point-by-point fit.