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Single crystal lanthanum strontium aluminum tantalum oxide, (LaAlO3)0.29(SrTa1/2Al1/2O3)0.71 or (La0.29Sr0.71)(Al0.65Ta0.36)O3 (LSAT), is a substrate for the epitaxial growth of oxide thin films. Optical properties in the form of the complex dielectric function (ε = ε1 + iε2) and index of refraction (N = n + ik) of LSAT from 0.033 to 5.887 eV are determined from spectroscopic ellipsometry measurements. The indirect band gap and lowest direct gap energies are identified at 4.72 and 5.70 eV, respectively. Eight infrared active phonon modes are identified in the 283 to 1127 cm−1 spectral range and ascribed to chemical bonding.
© 2016 Optical Society of America
1. Introduction
Lanthanum strontium aluminum tantalum oxide, (LaAlO3)0.29(SrTa1/2Al1/2O3)0.71 or (La0.29Sr0.71)(Al0.65Ta0.36)O3 (LSAT), has a cubic crystalline structure, a lattice constant of 3.868 Å, and belongs to space group [1]. LSAT proves to be a good single crystal substrate for epitaxy of a range of materials, including strain-enabled ferroelectric films of SrTiO3 [2], multiferroics such as PbVO3 [3], Ruddlesden-Popper phases such as the insulator Srn + 1TinO3n + 1 [4] or the superconductor Sr2RuO4 [5], YBa2Cu3O7 superconductors [6], and even for GaN [7] and AlN [8]. LSAT is somewhat transparent in the visible range [9,10] and is often used in studies in which some degree of transparency is important. Additionally, infrared phonon mode absorption features of epitaxial films grown on LSAT have also been studied [11]. In order to understand the properties of films on LSAT substrates, the optical response of LSAT from the infrared to ultraviolet range must first be determined. Therefore, we have extracted the complex dielectric function (ε = ε1 + iε2) and the complex index of refraction (N = n + ik) from 0.033 to 5.887 eV, determined the band gap energy, and identified infrared transverse optical (TO) phonon modes for single-crystal LSAT at room temperature using spectroscopic ellipsometry.
2. Experimental details
A commercial (CrysTec GmbH, Berlin, Germany) single side polished LSAT single crystal has been characterized by spectroscopic ellipsometry from which spectra in ε and N are extracted. A rotating compensator multichannel ellipsometer (J. A. Woollam Co., M-2000) [12,13] is used to measure the spectral range from 0.742 to 5.887 eV (1671 to 211 nm) over 300 optical cycles to collect 695 spectral points. The sample has also been measured over the spectral range from 0.033 to 0.742 eV (38 to 1.7 μm) using a Fourier transform infrared (FTIR) ellipsometer (J. A. Woollam Co., FTIR-VASE) also based upon rotating compensator principles [13] with data collected over 50 optical cycles at 4 cm−1 spectral resolution. In both cases, the sample is measured at room temperature at a single angle of incidence of 70° as it is cubic and optically isotropic. Depolarization spectra also collected range from less than 1.5% below the band gap into the near infrared and increases to 2.5% prior to significant absorption due to vibrational modes. These low values indicate that the unpolished side of the LSAT single crystal is sufficiently scattering over the transparent range of the sample.
A divided spectral range analysis [14,15] is applied over the near infrared to the near ultraviolet range, 0.742 to 5.887 eV, to determine the surface layer thickness on semi-infinite bulk LSAT. A Sellmeier oscillator [16] and a constant additive term to ε1 is used to represent ε for semi-infinite LSAT in the 0.742 to 4.681 eV spectral range since strong absorption features are not present. An oscillator assuming critical points with parabolic bands [17] is used to represent ε from 5.322 to 5.887 eV where above band gap electronic transitions are expected. The data collected between these two ranges, 4.681 to 5.322 eV, is near the absorption onset or band edge, and no assumption is made about the shape of ε2 in this weakly absorbing region. Spectra in ε for the surface layer is represented using a Bruggeman effective medium approximation [18] consisting of 0.5 bulk LSAT and 0.5 void volume fractions. This surface layer may consist of effects from both surface protrusions and contaminants, which are not separately accounted for here. An unweighted error function, σ, is used in all least squares regression analyses [19] to deduce the common surface layer thickness of the LSAT sample and parameters describing ε over each respective range.
3. Results and discussion
The surface layer of the polished side of the LSAT single crystal is determined to be 14.93 ± 0.07 Å thick from the divided spectral range analysis, consistent with Ref [4]. After obtaining and fixing this value, numerical inversion [20] is performed over the full 0.742 to 5.887 eV range to obtain ε. Figure 1(a) compares the experimental ellipsometric spectra [sin(2Ψ)sin(Δ), sin(2Ψ)cos(Δ), and cos(2Ψ)] with the fit generated using the parametric models in the divided spectral range analysis. The resultant ε obtained by numerical inversion and parametric ε for LSAT over each spectral range are also shown in Fig. 1(b). There is good agreement between inverted spectra in ε and the respective parametric models applied in the non-absorbing (0.742 to 4.681 eV) and above gap (5.322 to 5.887 eV) spectral ranges. The inverted spectra in ε is continuous across the full measured spectral range, including the region from 4.681 to 5.322 eV ignored in the parametric divided spectral range fit.
Fig. 1 (a) Experimental ellipsometric spectra (open circles) and model fit (solid lines) of (LaAlO3)0.29(SrTa1/2Al1/2O3)0.71 or (La0.29Sr0.71)(Al0.65Ta0.36)O3 (LSAT) single crystal from 0.742 to 5.887 eV. (b) Complex dielectric function (ε = ε1 + iε2) spectra for LSAT from 0.742 to 5.887 eV obtained by numerical inversion (open circles) and parametric fits (solid lines) in the non-absorbing and heavily absorbing spectral ranges.
The absorption coefficient, α, is determined using ε deduced from numerical inversion in order to extract the band gap. α1/2 and α2 are plotted as functions of photon energy as shown in Fig. 2. The slopes of each graph are then extrapolated, and the zero intercepts of α1/2 and α2 are found to determine the indirect and direct gaps, respectively [21]. By averaging the two zero intercepts of α1/2 related to phonon contributions, the indirect band gap is 4.72 ± 0.01 eV. The α2 zero intercept yielded a direct band gap of 5.70 ± 0.01 eV. It should be noted that the error reported is that from the mathematical fit. The spectral resolution in the ultraviolet for this instrument is approximately 0.03 eV, so the absolute value of the error should only be considered accurate to within an upper limit of 0.1 eV. A measurement with finer spectral resolution, such as with a monochromator based ellipsometer, would yield improved accuracy. The upper photon energy limit measured by Gibbons and Trolier-McKinstry [9] is only slightly greater than the indirect gap value identified here and ε1 obtained below the gap is similar to both [9, 10].
Fig. 2 Indirect (a) and direct (b) band gaps of LSAT found using the absorption coefficient (α). The indirect band gap is found by extrapolating the two slopes of α1/2 and averaging the zero intercepts. The direct band gap is found by linear extrapolation of α2 to the zero intercept. Error bars listed are from the linear fits.
The surface layer thickness is then fixed for the analysis of the 0.033 to 0.742 eV range infrared measurement and numerical inversion used to obtain ε as shown in Fig. 3. Spectra in ε over this range is parameterized using a factorized model [22–27] to identify positions of the TO and longitudinal optical (LO) phonon modes in the Lowndes formalism. The factorized model parameterization is:
where ωTO and ωLO are the TO and LO resonance frequencies, γTO and γLO are the associated broadening, and ε∞* is an amplitude term. A Sellmeier oscillator is also included in the parameterization of ε. Parameters describing features in ε along with possible interpretations of the chemical origins of each feature are listed in Table 1. As only the strongest TO modes are included in the parametric model with other weaker modes absent (see inset of Fig. 3), the LO mode frequencies here are simply fitting parameters without additional physical meaning.Fig. 3 Spectra in ε for LSAT obtained by numerical inversion (open circles) and factorized model parameterization (solid lines) from 0.033 to 0.15 eV. Inset uses a log energy scale to highlight lower amplitude features in inverted ε2 and additional peaks are marked with arrows.
Table 1. Parameters describing the transverse optical (TO) and longitudinal optical (LO) infrared phonon modes identified for LSAT using the factorized model (σ = 1.67 x 10−2, ε* = 0.654 ± 0.001, Sellmeier parameters are A = 0.00077 ± 0.00025 eV2 and E0 fixed at 0. Parameters ωTO and ωLO are the TO and LO resonance frequencies; γTO and γLO are the corresponding broadenings.
The TO mode at 283 cm−1 could correspond to tantalum-oxygen (Ta-O) bonds [28]. The resonance feature at 661 cm−1 may be due to Ta-O bonding, along with lanthanum-oxygen (La-O) and aluminum-oxygen (Al-O) bonds [29–33]. The TO mode present at 396 cm−1 can also be ascribed to Al-O and La-O bonding, and that at 437 cm−1 attributed to Al-O [28,32,33]. McDevitt and Baun [28], Sheibley and Fowler [32], and Nyquist and Kagel [33] all report vibrational modes representing Al2O3. Since this specific bonding configuration is not present in the LSAT structure, peaks found at these energies in LSAT may represent particular Al-O bonds. Additionally, Andrews et. al. [29] mentions an Al-O aggregate around 645 cm−1. Strontium-oxygen bonding has been found to be weakly represented in terms of infrared phonon mode absorption [28]. Due to the chemical complexity of LSAT, it is also likely that overlapping features contribute to some of the broader background effects as seen in Fig. 3, the TO peak positions agree well with those seen from infrared reflectance measurements of LSAT by Nuzhnyy et. al. [11]. Due to the complexity of the LSAT unit cell, to the best of our knowledge detailed calculations of its phonon modes have not yet been reported.
The log-scale inset in Fig. 3 displays that there are at least four additional low amplitude absorption features within the infrared range. The frequencies of these features are 563, 783, 856, and 1127 cm−1. The peaks at 563 and 856 cm−1 may correspond to Al-O and La-O bonding [29,30,32,33], while the peak at 783 cm−1 appears to be a somewhat small shoulder of the TO mode at 661 cm−1. The peak at 1127 cm−1 could correspond to Al-O bonding [29].
4. Summary and conclusions
Figure 4 summarizes spectra in ε and N for LSAT over the infrared to ultraviolet range from 0.033 to 5.887 eV (211 nm to 38 μm). Spectra in ε1 in Figs. 1(a) and 4 agree with those reported by Gibbons and Trolier-McKinstry [9] and Hu et. al. [10]. The indirect band gap for LSAT has been identified as 4.72 eV. TO infrared phonon modes possibly due to various chemical bonding in the LSAT structure have been observed at 283, 396, 437, and 661 cm−1 with additional low amplitude features identified at 563, 783, 856, and 1127 cm−1.
Fig. 4 Spectra in (a) ε from 0.033 to 5.887 eV and (b) complex index of refraction, N = n + ik, from 211 nm to 38 μm for LSAT spanning the infrared (solid circles) to near infrared – ultraviolet (open circles) range.
Funding
University of Toledo start-up funds; Ohio Department of Development (ODOD) Ohio Research Scholar Program (Northwest Ohio Innovators in Thin Film Photovoltaics, Grant No. TECH 09-025); Office of Naval Research (ONR) (N00014-11-1-0665); National Science Foundation (NSF) (DMR-1420620).
Acknowledgments
The authors would like to thank Prof. Roman Engel-Herbert at the Pennsylvania State University for supplying the LSAT sample supported by his ONR grant. Prof. Darrell Schlom acknowledges support by the Center for Nanoscale Science, with funding from the NSF MRSEC program (DMR-1420620).
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