Ultraviolet vacuum ultraviolet optical functions for

Ultraviolet vacuum ultraviolet optical functions for SrTiO3 and NdGaO3 crystals determined by spectroscopic ellipsometry K. Dorywalski, B. Andriyevsky, M. Piasecki, N. Lemee, A. Patryn, C. Cobet, and N. Esser Citation: Journal of Applied Physics 114, 043513 (2013); doi: 10.1063/1.4816624 View online: http://dx.doi.org/10.1063/1.4816624 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/114/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Intrinsic relationship between electronic structures and phase transition of SrBi2 x Nd x Nb2O9 ceramics from ultraviolet ellipsometry at elevated temperatures J. Appl. Phys. 115, 054107 (2014); 10.1063/1.4864715 Visible to vacuum ultraviolet dielectric functions of epitaxial graphene on 3C and 4H SiC polytypes determined by spectroscopic ellipsometry Appl. Phys. Lett. 101, 011912 (2012); 10.1063/1.4732159 Heteroepitaxial growth of SnO 2 thin films on SrTiO 3 (111) single crystal substrate by laser molecular beam epitaxy J. Appl. Phys. 107, 013515 (2010); 10.1063/1.3273494 Model dielectric function spectra of GaAsN for far-infrared and near-infrared to ultraviolet wavelengths J. Appl. Phys. 89, 4927 (2001); 10.1063/1.1359422 Ordinary optical dielectric functions of anisotropic hexagonal GaN film determined by variable angle spectroscopic ellipsometry J. Appl. Phys. 88, 3463 (2000); 10.1063/1.1289224

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JOURNAL OF APPLIED PHYSICS 114, 043513 (2013)

Ultraviolet vacuum ultraviolet optical functions for SrTiO3 and NdGaO3 crystals determined by spectroscopic ellipsometry K. Dorywalski,1,2,a) B. Andriyevsky,1 M. Piasecki,3 N. Lemee,4 A. Patryn,1 C. Cobet,5 and N. Esser6

1 Faculty of Electronics and Computer Sciences, Koszalin University of Technology, Sniadeckich Str. 2, PL-75-453 Koszalin, Poland 2 Institute of Technology and Education, Koszalin University of Technology, Sniadeckich Str. 2, PL-75-453 Koszalin, Poland 3 J. Długosz University, Al. Armii Krajowej 13/15, PL-42-200 CzeR stochowa, Poland 4 University of Picardie Jules Verne, 33 rue Saint-Leu, 800039 Amiens Cedex 1, France 5 Johannes Kepler Universit€ at Linz, Zentrum f€ ur Oberfl€ achen und Nanoanalytik (ZONA), Altenberger Str. 69, 4040 Linz, Austria 6 Lebniz-Institut f€ ur Analytische Wissenschaften – ISAS – e.V., Albert-Einstein-Str. 9, D-12489 Berlin, Germany

(Received 27 May 2013; accepted 10 July 2013; published online 25 July 2013) Complex dielectric functions e(E) ¼ e1(E) þ e2(E) were experimentally evaluated within the spectral range E ¼ 2–25 eV and E ¼ 2–20 eV for SrTiO3 and NdGaO3 single crystals, respectively, using synchrotron-based spectroscopic ellipsometry measurements. The ellipsometric spectra were evaluated within a framework of optical layer model taking into account sample surface roughness and anisotropy of NdGaO3. The parameters of Herzinger-Johs oscillator model were fitted to reproduce sufficiently all features of the optical spectra within the spectral range 2–10 eV. Only slight differences were revealed for spectra polarized along b and c crystallographic axes of the C 2013 AIP Publishing LLC. NdGaO3, which can confirm weak optical anisotropy. V [http://dx.doi.org/10.1063/1.4816624] I. INTRODUCTION

Oxide perovskites are one of the most significant materials for a wide range of applications in optoelectronics, microelectronics, and others.1,2 Among them, SrTiO3 (STO) and NdGaO3 (NGO), beyond many interesting physical properties, have very important role as platform materials for the epitaxial growth of a variety of technologically relevant complex oxide thin films and high-temperature superconductors.3,4 Particularly, the NGO crystals are promising for this purpose owing to the very small lattice mismatch between the NGO substrate and the most common YBa2Cu3Ox (YBCO) superconducting film near the deposition temperature as well as close thermal expansion coefficient of NGO to those of YBCO and absence of disruptive phase transition up to temperature of epitaxial growth. Besides, the NGO single crystal is promising substrate material also for GaN film deposition.5 Further applications of these materials require a knowledge of their band structures, which can be obtained from the data of fundamental inter-band optical transitions. Moreover, such data may be crucial as a reference for theoretical studies of the electronic properties of more wide class of the wide energy band gap oxides. The first report concerning the fundamental optical properties of STO was done by Cardona6 in which the normal incidence reflectance spectra were measured in the spectral range 2–22 eV and the optical constants were calculated in the spectral range 0–20 eV by the Kramers-Kronig transformation. Later, Ba€uerle et al.7 used the same technique and obtained optical functions for a)

Author to whom correspondence should be addressed. Electronic mail: [email protected].

0021-8979/2013/114(4)/043513/5/$30.00

STO in the same spectral range. All these data were afterwards summarized by Gervais in Palik’s Handbook of Optical Constants of Solids8 and hereafter are customarily used as a reference for the STO. More recently, optical spectra of STO were obtained by the valence electron-energy loss spectroscopy (VEELS), vacuum ultraviolet (VUV) spectroscopy,9 and spectroscopic ellipsometry9,10 (the latter up to 8.5 eV), which give more complete knowledge on the electronic properties of these materials. The corresponding spectra are however substantially different compared to those obtained earlier. This circumstance, as well as improved samples quality in recent years, inspired as for the verification of previous results. Contrary to the STO, optical properties of NGO single crystal were not studied sufficiently in the wide UV spectral range. Gibbons and Trolier-McKinstry11 has reported dispersion of the refractive index of NGO in the spectral range 1.65–4.96 eV, which is situated below the fundamental absorption edge. Afterwards, we have measured ellipsometric spectra of NGO in the region of electronic excitations 2–18 eV (Refs. 12 and 13) using synchrotron light source and presented them in the form of so called pseudo-dielectric functions14 calculated directly from the ellipsometric parameters using two-phase optical model (ambient/material). These results however do not take into account the expected surface inhomogeneity (roughness) of the measured specimens. As a consequence, these data are not sufficiently reliable as a precise reference source of the material optical constants, which can be used, e.g., in the ellipsometric data evaluation. A goal of the present study is to provide data for analysis of spectroscopic results on multilayer systems including the STO or NGO as a substrate. We employed spectroscopic

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ellipsometry with synchrotron radiation light source to determine the complex dielectric functions (DF) e(E) ¼ e1(E) þ ie2(E) of STO and NGO single crystals in the wide photon energy ranges E ¼ 2–25 eV (STO) and E ¼ 2–20 eV (NGO). The data obtained were evaluated taking into account the real surface roughness of samples, and the parametric oscillator model was introduced for better experimental spectra reproduction. II. EXPERIMENTAL DETAILS

Commercially purchased (001)-oriented STO and Czochralski-grown13 NGO (100) samples were prepared in the 8 5 1 mm platelet-shaped form. VUV spectroscopic ellipsometry was performed in the photon energy range 3–25 eV by manually manufactured rotating-polarizer type ellipsometric setup using synchrotron radiation of Berlin Electron Storage Ring for Synchrotron Radiation BESSY II as a light source. The apparatus allows to perform the measurements at fixed incident angle equal to 67.5 and 45 for 3–10 eV (BESSY monochromator NIM-3 m) and 10–25 eV (monochromator TGM-4 and U125/2-NIM) spectral range, respectively. A more detailed description of the experimental setup can be found elsewhere.15 All the measurements were performed at ambient temperature (296 K) with standard spectral resolution equal to 0.02 eV. Complementary experiments in the photon energy range 2–5 eV were done using of commercial ellipsometer (SENTECH) equipped with a retarder. In order to avoid any surface contaminations, the samples were washed by isopropyl alcohol in ultrasonic bath before experiments. Since STO has simple cubic structure at ambient temperature, optical response of them is isotropic. The NGO crystal belongs to the orthorhombic space group Pbmn (D16 2h ) with unit cell parameters a ¼ 0.5426 nm, b ¼ 0.5496 nm, c ¼ 0.7707 nm16 at ambient temperature. It should therefore have three different diagonal components of the dielectric tensor. Taking into account the two lattice constants a and b are almost equal that indicates for closeness to the tetragonal symmetry, dielectric tensor can be treated correspondingly, ea eb 6¼ ec. Hence, only two diagonal components of the dielectric tensor are expected to be different, eb and ec. Following this assumption, a-cut NGO single crystal sample was measured for two different azimuthal orientations with the crystallographic c-axis parallel and perpendicular to the plane of incidence. III. ELLIPSOMETRIC DATA EVALUATION

The complex pseudodielectric functions hei(E) of STO and NGO, which was calculated directly from the measured ellipsometric parameters W and D by the known Fresnel equations (two-phase ambient/material model),14 are denoted by dashed lines in Figure 1. Unfortunately, the transmission bandwidth of the polarizers employed in the Bessy ellipsometric setup (Rochon prism and Au-Si-Au reflection-type polarizer used for lower and upper energies, respectively) does not cover narrow range of 9.9–10.4 eV; hence, a corresponding gap is seen in the spectra. In the case of semi-infinite bulk sample with perfectly smooth and clean surface, the measured

FIG. 1. Experimental (dashed lines) and simulated (solid lines) pseudodielectric function for SrTiO3 (upper graph) and NdGaO3 (lower graph) single crystals.

hei(E) and the intrinsic DF are identical. In our case, however, the non-zero value of the imaginary part of the he2i(E) below the optical band gap clearly indicates presence of overlayers, i.e., surface roughness or contamination, which affect whole spectrum. Hence, data analysis procedure by three-phase model (ambient/overlayer/material) in a fitting procedure that minimizes the mean square error (MSE) is necessary in order to determine the “real” DF. Spectra recorded for two orthogonal orientation of NGO samples reveals only minor differences. Thus, only hei(E) spectra for one polarization (parallel to c-axis) are shown in Figure 1 for better clarity. Method known as a mathematical inversion14 was applied for ellipsometry data analysis. The procedure can be summarized in the following steps. First, assuming no absorption below the optical band gap, the optical response of the samples was described by a Cauchy dispersion formula14 for the real part of the complex dielectric function. The overlayer was approximated by the effective medium theory according to Bruggeman,17 assuming 50% of voids in a matrix of the sample. The thickness of the overlayer and the Cauchy model parameters were used as the starting fitting factors. Then, the determined thickness value was fixed and the complex DF is calculated from the model in the whole measured spectral range using Fresnel equations for the light reflection and transmission at two interfaces. In the case of NGO, a description derived from the extended Fresnel equation for anisotropic materials was used.14,18 Finally, the extracted dielectric functions for STO and NGO were parameterized in the spectral range 2–9.9 eV using the Herzinger-Johs oscillator model,19 which is known for its convenience in describing different ellipsometric data without need of additional “dummy” oscillators between critical-point (CP) structures. This model analytically describes DF as the summation of several energy-bounded Gaussian-broadened polynomials, whose detailed explanation is given in Ref. 19. A single oscillator structure described by the model is depicted in Fig. 2. The polynomials are grouped into four


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FIG. 2. A single CP structure described by Herzinger-Johs oscillator model (see Ref. 19 for details).

ensembles of 4th order polynomials, which are centered on CP structures with the overlapping tails of adjacent ensembles. The center energy EC corresponds to the CP energy, while the bounding energies EL and EU delineate adjacent CPs. The spectral position of the two control points, ELM and EUM, are the joining points of the four polynomials and are defined by the relation given in Fig. 2. The model parameters were varied to the imaginary part of the complex dielectric function using a Levenberg-Marquardt fitting algorithm.20 We started with minimum number of oscillators in simplest form (disc ¼ L2d ¼ U2d ¼ 0), gradually adding next oscillators until the modeled and the experimental data matched as close as possible. The real part of complex-DF is calculated by Kramers-Kronig formula. Some additional zero-width Sellmeier oscillators (poles)14 are added to simulate absorption outside measuring range in case of NGO. Unfortunately, we cannot get Kramers-Kronig consistence model DF that fit sufficiently good to the experimental spectra above 10 eV energies. The values of experimental data he2i(E) for spectral range about 10.4–15 eV tend to be

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FIG. 4. Real (e1) and imaginary (e2) parts of the complex dielectric function for (100) NdGaO3 crystal as determined from ellipsometric data analysis and contribution of each oscillator to the spectra in the range E < 9.9 eV. Solid lines correspond to the spectra obtained along crystallographic b-axes, while dashes to c-axes.

lower with respect to the modeled for both measured specimens. This is likely a consequence of the strong decrease in the overall intensity of reflected light observed for this spectral range. The intensity problem is related most likely to contamination on the gold surfaces of the rotating analyzer, which in combination with decrease in the first order intensity of the monochromator may produce the non KramersKronig consistent structures. The problem is not so critical in the higher energy range. Hence, the spectra in the mentioned energy range depicted in Figs. 3 and 4 originate from the calculations based on Fresnel equations, and it should be kept in mind that the corresponding absolute magnitudes contain some inaccuracies with respect to the “true” values. However, all spectral features are rather unaffected. The mentioned discrepancies will be further examined by comparing the results obtained to the available experimental and theoretical data for STO. IV. RESULTS AND DISCUSSION

Results of the fitting procedure are presented in Fig. 1, where solid lines correspond to modeled DF. The model fit agrees well with the experimental data recorded in the range 2–9.9 eV for both specimens. For the simulation of STO dielectric functions, eight oscillators were used, while for the NGO three (see Figs. 3 and 4). Resulting model parameters TABLE I. The parameters of SrTiO3 for the Herzinger-Johs parametric oscillator model.19 # EL EU

FIG. 3. Real (e1) and imaginary (e2) parts of the complex dielectric function for (001) SrTiO3 crystal as determined from ellipsometric data analysis and contribution of each oscillator to the spectra in the range E < 9.9 eV.

0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8

EC

1 3.312 3 3.848 3 4.218 4 4.727 5 5.290 6 6.246 7 8.123 8 8.848 9 10.351 9 22.620

A

R

3.294 6.991 6.292 4.999 5.675 2.222 4.604 2.353

87.89 156.29 133.38 543.99 170.80 420.12 177.66 83.52

disc Lpos

0 0 0 0 0 0 0 0

0.804 0.674 0.982 0.088 0.851 0.914 0.437 0.207

Lamp L2d Upos Uamp U2d

0.160 0.556 0.322 0.601 0.364 0.999 0.144 0.406

0 0 0 0 0 0 0 0

0.239 0.732 0.043 0.489 0.335 0.233 0.412 0.448

0.122 0.440 0.006 0.529 0.130 0.934 0.324 0.906

0 0 0 0 0 0 0 0


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TABLE II. The parameters of NdGaO3 for the Herzinger-Johs parametric oscillator model19 for DF along c (upper part) and b (lower part) crystallographic axes. # EL EU

EC

A

R

disc Lpos

Lamp L2d Upos Uamp U2d

0 1 2 3 4

0 0 1 2 3

Pole pos./magn.: (1) 13.01/123.41 and (2) 40.41/538.61 1 5.296 0 2 6.414 3.842 127.60 0 0.073 0.021 0 0.532 0.488 3 7.998 7.933 237.50 0 0.531 0.488 0 0.567 0.519 4 11.067 9.446 231.10 0 0.772 0.276 0 0.308 1.867 4 0.010 0

0 1 2 3 4

0 0 1 2 3

Pole pos./magn.: (1) 21.59/94.49 and (2) 32.49/789.77 1 5.272 0 2 6.430 4.015 121.70 0 0.007 0.01 0 0.541 0.489 3 7.906 7.906 208.50 0 0.543 0.505 0 0.528 0.495 4 11.305 14.105 209.20 0 0.566 0.116 0 0.940 0.736 4 0.706 0

0 0 0

0 0 0

for this spectral range are gathered in Table I (STO) and Table II (NGO), and the derived complex DF are shown in Figs. 3 and 4 for the STO and NGO, respectively. It is necessary to emphasize that we have used the convention where EL and EU parameters are referred to the EC value indicated by the oscillator number.19 Comparing our dielectric function for STO with those obtained by Zollner and coworkers10 (dashed lines in Fig. 3), one can see generally good agreement of both curves. Larger difference is observed only for the photon energies above 7.5 eV. Spectral positions of these bands are formed by excitations of deeper valence bands formed mainly by 2pO orbitals. Additionally, such spectra may also be disturbed by the influence of phonon subsystem21 and presence of intrinsic oxygen defect states.22 Taking into account the data in Ref. 10 were recorded by ellipsometric setup which was only purged with dry nitrogen gas, the mentioned discrepancy above 7.5 eV can be caused by the presence of residual amount of oxygen and water giving an absorption in this spectral range. This is not the case of the BESSY ellipsometric setup, where the measured sample is mounted in the UHV chamber (1010 millibars), that excludes influence of such residuals on the spectra measured. Additional prominent structure in e2(E) spectrum was revealed at 8.83 eV, which is out of the photon energy range of Zollner’s data.10 The early data tabulated by Gervais in Ref. 8 are also plotted in Fig. 3 (dots). These data are based on the reflectivity measurements combined with a Kramers-Kronig transformation.7 The spectra generally reveal similar structure to those obtained by ellipsometry. However, one can see for these data a substantial spectral shift of first band toward lower energies and relatively large differences of e2 absolute values. The parameters presented in Tables I and II are provided to easily reproduce all spectral features for STO and NGO in the range 2–9.9 eV. Additional analysis of DFs related to the interband electronic transitions (critical points) would be possible by calculating the second derivatives of e2(E).23 However, when compared oscillators EC values obtained here for STO with experimental and theoretical data for interband transition energies reported previously,9 one can

FIG. 5. Imaginary (e2) part of the complex dielectric function for (001) SrTiO3 in the photon energy range E > 10.4 eV and labeled peaks (notation follows van Benthem et al.9).

see good agreement of both (see Table III). To verify a statement that the mentioned measuring setup problem for the spectral range about 10.4–15 eV does not affect spectral features but only can change absolute values of e2(E), energy positions of distinct peaks seen in the imaginary part e2(E) of the complex DF (see Figure 5) were compared to the known experimental data obtained by van Benthem et al.9 with use of VUV reflectance spectroscopy, VEELS method, and DFT calculations as well as to the reflectance measurements of Ba€uerle et al.7 The agreement of both data is sufficiently good, which proves reliability of the measurements with use of BESSY ellipsometric setup also in the spectral range above E > 10 eV. Additional faint peaks denoted in Fig. 5 by asterisks were found in this spectral range. Only small differences are observed between DFs of NGO for polarizations along b (solid lines) and c (dashes) crystallographic axes (Fig. 4). It is hard to judge unambiguously whether these differences correspond to the real crystal’s anisotropy or they do not exceed experimental inaccuracy. The density functional calculations of NGO12 reveal only small anisotropy of DF, which are comparable to the experimentally observed one (Fig. 4). TABLE III. Comparison of peak energies (in eV) for SrTiO3 with interband transition energies reported by van Benthem et al.9 and Ba€uerle et al.7 For assignment of an individual transition, see Ref. 9. This VUV Transition work Ellipsometrya spectroscopya VEELSa LDFTa Reflectanceb A1 A2 A3 A4 B1 B2 C D1 D2 E1 E1* E2 E3 E4** E4* E4 a

4.21 4.73 5.29 6.24 8.83 10.33 11.99 12.9 13.75 16.4 17.1 19.6 21.2 22.8 23.4 24.2

4.2 4.9 5.4 6.3 ... ... ... ... ... ... ... ... ... ... ... ...

4.2 4.8 5.3 6.3 9.1 9.9 11.9 12.9 13.7 16.4 ... 19.7 21.7 ... ... 24.2

… 5.0 ... 6.4 ... 9.7 11.8 12.7 13.2 16.1 ... 18.7 21.7 ... ... 23.6

… 5.1 ... 6.7 ... 9.7 11.8 ... 13.1 16.7 ... 20.0 ... ... ... ...

4.0 4.86 5.5 6.52 9.2 10.2 12.0 13.0 – 13.8 13.0 – 13.8 16.4 ... 19.6 ... ... ... ...

See Ref. 9. See Ref. 7.

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V. CONCLUSIONS

The complex dielectric functions for SrTiO3 and NdGaO3 substrate crystals were determined in the wide UVVUV photon energy range (up to 25 eV) using spectroscopic ellipsometry and subsequent data analysis. Dielectric function obtained for SrTiO3 is in agreement with analogous dependencies obtained previously by ellipsometry in the range of E < 8.5 eV and is a first ellipsometric measurement of the crystal in the range of E > 8.5 eV. Accurate dielectric functions of NdGaO3 in the spectral range 2–20 eV are obtained by the ellipsometric method for the first time. The spectra obtained reveal small differences for the light polarizations along b and c crystallographic axes (small anisotropy), that is, generally in agreement with corresponding theoretical DFT based calculations. ACKNOWLEDGMENTS

The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 226716. We also want to thank the BESSY GmbH for help and support (project BESSY 2011_1_101284). K.D. appreciate the financial support of German Academic Exchange Service (DAAD) under Grant No. A/ 10/82079 1

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