1. Introduction

Oxide-based transparent materials play a key role in various research and industry fields, which are focused on the construction of optical devices such as lasers, scintillators, telecommunications, etc. For these applications is critical to know the exact optical parameters of used materials for all operational photon energies.

Yttrium aluminum garnet Y₃Al₅O₁₂ and lutetium aluminum garnet Lu₃Al₅O₁₂ are important wide bandgap materials suitable for a wide range of optical applications such as laser host systems [1] or for optical lenses in semiconductor microlithography. This is connected chiefly with their excellent mechanical stability, low thermal expansion coefficient, low-acoustic loss, a high threshold for optical damage, stability against chemical and mechanical changes, and excellent optical properties [2]. With its high density (6.73 g/cm³) and high effective atomic number of Z_eff = 62 (compared to 30 in YAG) LuAG is also well-known as a material for scintillators [3] to detect high energy gamma or X-ray radiation. High index of refraction, wide bandgap, broad optical transparency range from 190 nm to 5 µm, and very low intrinsic birefringence [4] make undoped YAG or LuAG a convenient materials for applications in UV-C region for excimer lenses at λ = 193 nm, but also in the infrared range such as night vision devices, and represent suitable materials for various UV and IR elements (windows, lenses, or prisms).

On the other hand, YAG doped by rare earth elements (such as Nd, Er, etc.) plays an important role mainly in the construction of solid-state lasers as an active medium, where neodymium-YAG is still the most widely used active laser medium in solid-state lasers [5]. The detailed knowledge of spectrally dependent optical properties of these materials is therefore necessary to choose particular materials for desired application as well as to theoretically design novel devices.

So far the refractive index of YAG and LuAG was investigated only in visible and near IR spectral ranges [6,7]. To the best of our knowledge, any data are not available in the UV range between 193 and 400 nm (from 3.1 to 6.42 eV). The presented study thus fills the information gap in the experimental data. The refractive indices of undoped YAG and LuAG single crystals were measured using spectroscopy ellipsometry and Sellmeier coefficients that fit the data over the full experimental energy range from 0.73 to 6.42 eV were determined. In addition, the experimental data that describe optical reflectivity and transmission of the investigated samples in a wide spectral range are included as well. Together, the present study provides an important set of data to precisely design various optical devices operating in UV using YAG and LuAG as a host material.

2. Experimental

High-quality YAG and LuAG undoped single crystals were purchased from Crytur, Ltd. The crystals were prepared using the Czochralski method from 5N purity raw materials (Lu₂O₃, Y₂O₃, Al₂O₃) in reducing atmosphere. After the growth the crystals were annealed in an oxidizing atmosphere to get rid oxygen vacancies and related color centers, and to remove eventual residual mechanical stress in the samples. The single crystal rods were cut into disks with (111) orientation and dimensions of approximately 12 mm in diameter and 0.5 mm in thickness. Single crystal samples used for a material characterization were selected from a part of stress free crystal outside of a central core. Inspection in a polarizing microscope showed good sample quality and any mechanical stress was not observed in the samples The sample surfaces were polished to epitaxial quality on both faces for transmission measurements. For ellipsometry, only one side was epi-polished, the second one was matt. Ellipsometry measurements for two selected YAG and LuAG samples were carried out using the variable angle Mueller matrix spectroscopic ellipsometer J.A. Woollam Co. RC2 in the spectral range from 0.73 to 6.42 eV (193–1700 nm) and at angle of incidence from 55 to 75 deg with 5 deg steps. Optical transmission spectra were recorded using the UV-Vis-NIR spectrophotometer Perkin Elmer Lambda 12 in the spectral range from 1.24 to 6.52 eV (190 to 1000 nm).

3. Results and discussion

Measured ellipsometric parameters $\psi $ and $\mathrm{\Delta }$ are defined as ${r_p}/{r_s} = \tan (\psi )\textrm{exp}({i\; \Delta } )$, where r_p and r_s represent the Fresnell amplitude reflection coefficients for the p- and s-polarized light. Elipsometric spectra were fitted using the Woollam CompleteEase software with integrated Sellmeier model

The data fit is evaluated by the Root Mean Squared Error (MSE) value defined as described in supplementary section (Suppl. S1)

The experimental and simulated spectra ($\psi ,\; \mathrm{\Delta }$) for YAG and LuAG samples are depicted in Fig. 1, showing good agreement between them. This is also is demonstrated by low values of MSE where MSE_YAG=0.574 and MSE_LuAG= 1.148 (compare with other monocrystals of various materials [9,10]) (Tab.1)

 

Fig. 1. Plots of the experimental and simulated (model) spectroscopic ellipsometry spectra (psi and delta) of YAG and LuAG samples at angles of incidence 60, 65 and 70 deg.

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The spectra of refractive indices derived from the ellipsometric measurements of YAG and LuAG single crystals are shown in Fig. 2 together with literature data [4,6,7,11]. The Sellmeier coefficients A_E, B_E, C_E, $\varepsilon (\infty )$ and the surface roughness are summarized in Table 1. The table with obtained spectra of refractive indices is in Suppl. S2. In the visible and near IR spectral ranges the values of refractive indices are in a good agreement with those reported in the literature for YAG [6] and LuAG [4,7,11]. The observed maximal deviation from the reported reference values was 0.004 for LuAG and 0.002 for YAG. Mutual comparison of the refractive indices of YAG and LuAG samples (see Fig. 2 and data in Suppl. S2) shows that the values of the refractive index of LuAG are about ∼ 0.015 higher than those of YAG in the infrared and visible spectral region and are in agreement with the published results [4,6,7,11]. However, in the UV spectral region below 400 nm (i.e. above 3 eV), the refractive index of YAG increases more quickly compared to LuAG. At 6.42 eV (193 nm) both materials show almost the same value, n ≈ 2.142. This is worth a short comment. The bandgap of YAG is estimated to be around 8 eV (according to the VUV data [12,13]). The bandgap of LuAG is obviously at higher energy in 0.2–0.3 eV [4,14]. In strongly ionic compounds, such as garnets, an electron-hole bound state is formed at lower energy. Besides, the garnets are known for structural defects due to their high growth temperature. The antisite defects, where Y or Lu ions are situated in the aluminum octahedral sites, are the most frequent. Both impurities and structural defects lead to localized electronic states close to the band-gap. In fact, the exciton was observed near 7 eV in YAG and at an energy about 0.2–0.3 eV higher in LuAG [12,15]. Last but not least, at nonzero temperatures, due to the interaction with lattice distortions, the energy required for excitation is further decreased, which leads to absorption observed well below the band-gap. The steeply rising absorption tail observed above ∼6.4 eV is intrinsic to YAG or LuAG crystals and it is described by the Urbach rule [14,16], which scales the tail absorption coefficient near the band-gap (we note that only very initial part of the Urbach tail is observed in Fig. 4(b)). Summarizing, the onset of absorption in YAG and LuAG is well below band edge, which, due the the Kramers-Kronig relations, leads to an increase of the refractive index accordingly. In view of what has been said above, a slightly faster increase of n in YAG can therefore be expected in the UV below the band-gap.

 

Fig. 2. Refractive indices of YAG and LuAG crystals derived from ellipsometry data using Eq.2 (solid symbols) as a function of photon energy. Obtained data were compared with corresponding references (open symbols). See Data File 1 for underlying values [6,7,11].

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Fig. 3. Reflectivity dependence of YAG and LuAG crystals as a function angle of incidence from 20 deg to 75 deg for two reference wavelengths of 193 nm (6.42 eV) and 532 nm (2.33 eV).

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Fig. 4. Transmission spectra and spectra of the extinction coefficient of YAG and LuAG samples at normal incidence as a function of photon energy.

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Table 1. Summary of optical parameters of YAG and LuAG crystals derived from Eq.1. Numbers in parentheses represents the tolerance on the last digit.

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Reflectivity as one of the necessary parameters for the construction of optical devices was measured in the whole spectral region from 0.73 up to 6.42 eV at angles of incidence from 20 to 75 deg with 1 deg step. The obtained results for two wavelengths of 193 nm (6.42 eV) and 532 nm (2.33 eV) are plotted in Fig. 3 for s- and p-polarized light. In agreement with theory, values of the Brewster angle were estimated from the p-polarized reflectivity, where light is perfectly transmitted through a transparent dielectric surface, with no reflection. The Brewster angles for YAG (${\theta _{B:\; 193\; nm}} = \; 64.89.\; ^\circ $, ${\theta _{B:\; 532\; nm}} = \; 61.51^\circ $) and LuAG (${\theta _{B:\; 193\; nm}} = \; 64.71\; ^\circ $, ${\alpha _{B:\; 532\; nm}} = \; 61.47^\circ $) samples were estimated. The spectral dependence of the Brewster angle then exhibits a slow decrease with increasing incident wavelength. Experimental ellipsometric data obtained at an angle of incidence close to the Brewster angle (65°) were additionally fitted using standard two-oscillator Sellmeier model for better comparison with other materials and the results are shown in Suppl.3. It is good to say, that the observed difference within the two used Sellmeier models is negligible.

Additionally, the transmission spectra of both YAG and LuAG samples were measured and the values of the extinction coefficients k were derived. The spectra are plotted in Fig. 4 and demonstrate very low absorption of the samples, which is bellow the sensitivity limit of the spectroscopic ellipsometer (k < 10^–4). The absorption in YAG and LuAG crystals between 4.5 and 6.5 eV can be ascribed to the trace impurities in the samples of the order of units to ten of ppm coming from chemicals, crucible, furnace, or possible residual color centers, c.f. also Refs [17]. The small values of extinction coefficient, k = 1.5 × 10^–5 and 0.5 × 10^–5 at 4.8 and 6.4 eV, respectively, justify the use of Sellmeier parametrization as a good approximation for the description of optical properties of investigated materials, since the more complicated Kramers-Kronig consistent parametrization which accounts for absorption gives the same values of refractive index within three decimal digits.

4. Conclusion

We reported the spectral dependencies of optical properties of undoped LuAG and YAG single crystals in a wide spectral range from 0.73 up to 6.42 eV. Moreover, the spectral dependencies of optical reflectivities for s and p-polarized light and angles of incidence from 20 up to 75 deg were measured. The present study provides an important set of data for precise design of various optical devices operating in the UV spectral range using YAG and LuAG as host material.