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Abstract
The optical constants and dielectric function of (001) LaAlO3 crystal were investigated at low temperatures down to 10 K in the NIR-VUV spectral range (photon energies 0.8-8.8 eV). Reflection variable angle spectroscopic ellipsometry and transmission spectroscopy were applied. Interband transitions were examined using the Tauc plots and the critical-point analysis. At room temperature, the indirect bandgap of 5.6 ± 0.01 eV and the lowest-energy direct transition at 7.2 ± 0.03 eV were detected. On cooling to 10 K, a blueshift of ∼0.2 eV and ∼0.1 eV was observed for the indirect and direct transitions, respectively. In the transparency spectral range, the index of refraction was found to be nearly temperature-independent and vary with photon energy from 2.0 (1 eV) to 2.5 (5.5 eV). It was suggested that the excellent thermal stability of the index of refraction may be related to the revealed thermally stable interband transitions. The results are of importance for modeling and design of modern optical devices.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Lanthanum aluminate (LaAlO3, or LAO here) belongs to a broad class of perovskite oxide wide-bandgap insulators [Supplement 1 section 1]. The high dielectric permittivity and low losses at microwaves enable the best-known applications of LAO in telecommunications [1,2]. Being transparent for the largest fraction of solar spectrum, LAO is promising for solar-blind UV detectors [3–6], which are now in high demand for diverse applications ranging from inter-satellite communications, military, safety, security, to health. Peculiar physical phenomena at the LAO/SrTiO3 interface attract scientific interest and can enable opto-electronic applications [7,8]. More generally, being structurally and chemically compatible with many functional perovskite oxides and other materials [9–12], LAO crystals or single-crystal films ensure growth of numerous high-quality heterostructures that enable development of cutting-edge optical devices. Explicit knowledge of the optical properties of LAO in the wide spectral and temperature ranges is essential for modeling and design of eventually all novel devices. A few previous studies [13–16] reported on these properties in rather limited ranges of conditions. Here, we focus on the low-temperature behavior of LAO in the NIR-VUV spectral range. The optical constants and dielectric functions of a (001)-cut single-crystal LAO were investigated at temperatures from 300 K down to as low as 10 K and at photon energies from 0.8 eV up to as high as 8.8 eV. Comparing to previous low-temperature studies of LAO, the spectral range was expanded to VUV that made it possible to accurately analyze the temperature-dependent behavior of the lowest-energy interband transition (∼7 eV). The unique combination of the expanded spectral and temperature range makes it possible to obtain results delivering new fundamental knowledge on LaAlO3, which is employed in plenty of modern applications. The methodology described in the manuscript may be helpful in studying the optical properties of other wide-band gap materials, both crystals and thin films.
2. Experimental
LAO crystal with dimensions (10 mm x 10 mm x 1 mm) and (001) surface orientation was purchased from MTI Corp. USA. One side of the crystal was polished using a chemical mechanical method [17,18].
Optical investigations were carried out using a reflection spectroscopic ellipsometry technique [Supplement 1 section 2]. Ellipsometric angles (Ψ and Δ) and depolarization of reflected light were acquired on a J.A. Woollam VUV-VASE variable angle spectroscopic ellipsometer within the photon energy range 0.8-8.8 eV with 0.04 eV step. Low-temperature measurements were performed in a unique ultrahigh-vacuum cryostat (10−9-10−10 mbar) with calcium fluoride windows, being an extension to standard VUV-VASE equipment. The cryostat ensures temperatures from 10 to 500 K and excellent temperature stability. Since the windows of the cryostat are centered at 70°, this angle was chosen as the measurements angle of incidence. The crystal was washed in pure isopropanol prior to placing it into the cryostat. Additionally, the sample was annealed for 3 hours at 500 K in vacuum inside the cryostat in order to evaporate possible surface adsorbates [14].
Two types of regimes were used: 1) the whole spectra were collected at different fixed stable temperatures (300, 250, 200, 150, 100, 50, and 10 K); and 2) the angles were measured at different photon energies (3.5, 4.0, and 4.5 eV) on cooling at a rate of 3 K/min.
Afterwards, the rough side of the crystal was polished, and room-temperature transmission spectra at photon energies 1.5-6.5 eV were acquired on a Perkin Elmer Lambda 1050 spectrophotometer as an addition to the ellipsometric measurements.
The optical constants of the LAO crystal were extracted from the spectra of the ellipsometric angles Ψ and Δ using a commercial WVASE32 software package. We used a model consisting of a semi-infinite crystal and a surface roughness layer. The imaginary part of the model crystal complex dielectric function was presented in a multi-oscillator form using Gaussian oscillators [19]:
The fitted parameters of the model with errors are presented in Table 1. MSE (S4) for all temperatures was ∼0.5. Together with the reasonable error values, it indicates that the set of parameters accurately describes the optical constants.
Table 1. Parameters of the ellipsometric model used.
To ensure sufficient accuracy of the absorption coefficient α < 103 cm-1, which may be poorly resolved by ellipsometry, we measured optical transmission Tr [13,25,26]. The absorption coefficient was determined as follows:
where d is the thickness of the sample, R are reflection losses from the sample’s surface.3. Results and discussion
The obtained optical constants of LAO are summarized as a function of photon energy E and temperature in Fig. 2, which gives a general picture of the low-temperature NIR-VUV behavior of LAO. The detailed data are presented in Supplement 1 Figs. S6. For E < 6 eV, the high transparency is evidenced by both the absorption coefficient [Fig. 2(a)] and extinction coefficient [Fig. 2(c)]. The index of refraction is large in this spectral range [Fig. 2(b)], between 2.0 and 2.5. A shift of the absorption edge towards lower energies occurs on cooling [Figs. 2(a,c)]. This shift has a minor effect on the index of refraction in the transparency range. The slope of n(T) curves in Fig. 2(d) is ∼10−5 K-1. Next, the absorption edge and interband transitions are analyzed in detail.
Fig. 2. (a) Absorption coefficient α, (b) index of refraction n, and (c) extinction coefficient k as a function of photon energy at different temperatures of 300 and 10 K. (d) Index of refraction as a function of temperature at different photon energies 3.5, 4 and 4.5 eV. Solid (open) symbols show the data obtained on cooling (at different fixed temperatures).
We obtained a solid consistency between the absorption coefficient extracted from the ellipsometry measurements and that extracted from the transmission measurements [ Fig. 3]. This observation implies that our ellipsometry data ensure good accuracy for the analysis of α ≥ 103 cm-1 and hence, are sufficient for examination of indirect optical bandgaps. For LAO, an indirect bandgap of 5.5-6.1 eV was previously reported [13–15,27]. Here, to investigate the bandgap energy Eg, we employed the Tauc plots (3):
where the exponent m = 1/2 or m = 2 corresponds to either indirect or direct optical transition, respectively [28–31].Fig. 3. Room-temperature absorption coefficient as a function of photon energy. Red and blue curves show the data extracted from the ellipsometry and transmission measurements, correspondingly.
Good linear fits to [(αE)1/2 ∝ E] were obtained for α < 104 cm-1 at all temperatures [ Fig. 4(a) and Supplement 1 Figs. S8(a)], in accord with the indirect bandgap. The bandgap energy Eg, extracted from the fits, is plotted as a function of temperature in Fig. 4(b). The energy Eg weakly grows with decreasing temperature.
The lowest-energy direct interband transition was identified using the Tauc plots for a direct bandgap and the critical-point (CP) analysis. Again, good linear fits to [(αE)2 ∝ E] were obtained for α > 105 cm-1 at all temperatures [ Fig. 5 and Supplement 1 Fig. S8(b)]. The fitted bandgap energy was found to insignificantly increase, by only approximately 0.1 eV, with decreasing temperature from 300 to 10 K [Supplement 1 Table S2].
Fig. 4. (a) Tauc plot for indirect band gap at 300 K. Dotted line shows fit. (b) Energy of the indirect bandgap, Eg, determined from the Tauc plots, as a function of temperature.
In the CP analysis, we considered the dielectric function for an ensemble of two-dimensional CPs [32–35]. The second derivative of the dielectric function is then
Fig. 6. Second derivative of the (a) (c) real and (b) (d) imaginary parts of the dielectric function at 300 and 10 K. Solid curves show fits.
Both the energy of the direct bandgap, extracted from the Tauc plots, and the energy of the CP1, extracted from the derivative analysis, exhibit minor variations with temperature in the range from 10 to 300 K and practically coincide at low temperatures [ Fig. 7 and Supplement 1 Table S2]. The observer behavior implies insignificant variations of the direct interband transitions with temperature. We believe that the remarkable thermal stability of the index of refraction in the transparency range [Fig. 2(d)] may be related to such thermally stable transitions [Fig. 4 and Fig. 5] in LAO below 300 K.
Fig. 7. The energy Eg of the direct bandgap and the energy E1 of the critical point CP1 as a function of temperature.
Thus, compared to the previously performed optical investigations of LAO in the limited spectral and temperature range, here, the expanded range ensured assessment of the interband transitions in this wide bandgap material. The direct transition and the CP1 were assessed owing to the VUV spectrum, not commonly available. Additionally, the low-temperature measurements made it possible to reduce phononic contributions to the absorption edge.
4. Conclusions
The low-temperature optical behavior of the (001) LAO crystal was examined using spectroscopic ellipsometry and transmission spectroscopy. The optical constants and dielectric functions were obtained in the NIR-VUV spectral range (photon energies 0.8-8.8 eV) at temperatures from 10 to 300 K. The performed Tauc and critical-point analyses revealed the indirect and direct transitions and their insignificant variations with temperature. The index of refraction in the transparency spectral range was found to be nearly temperature-independent that was ascribed the thermally stable interband transitions.
Funding
European Structural and Investment Funds and the Ministry of Education, Youth and Sports of the Czech Republic through Programme "Research, Development and Education" (SOLID21 - CZ.02.1.01/0.0/0.0/16_019/0000760); The Grant Agency of the Czech Technical University in Prague (SGS22/182/OHK4/3T/14).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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