Optical properties of dielectric layers with CeO₂

The polycrystalline thin films CeO₂, WO₃, amorphous complex films WO₃ + CeO₂ with content of CeO₂ in the powder 10, 15 and 20 %, and CeO₂ + Dy₂O₃ with content of Dy₂O3 in the powder 10, 15 and 20 % are obtained by vacuum deposition method via powder evaporation. For the first time the optical charac...

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Дата:	2004
Автор:	Semikina, T.V.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2004
Назва видання:	Semiconductor Physics Quantum Electronics & Optoelectronics
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/119127
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Цитувати:	Optical properties of dielectric layers with CeO₂ / T.V. Semikina // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 291-296. — Бібліогр.: 18 назв. — англ.

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spelling	irk-123456789-1191272017-06-05T03:02:35Z Optical properties of dielectric layers with CeO₂ Semikina, T.V. The polycrystalline thin films CeO₂, WO₃, amorphous complex films WO₃ + CeO₂ with content of CeO₂ in the powder 10, 15 and 20 %, and CeO₂ + Dy₂O₃ with content of Dy₂O3 in the powder 10, 15 and 20 % are obtained by vacuum deposition method via powder evaporation. For the first time the optical characteristics of complex films WO₃ + CeO₂ and CeO₂+Dy₂O₃ are obtained. As a results of films investigation by ellipsometry the dependencies of refraction and extinction coefficients on incident beam energy are presented. The dielectric permittivity and energy band gapes are calculated. The refraction coefficients of films CeO₂ are 1.85–2.85 and are not more than 2.37 for complex films. Dielectric constant e of complex films are 3.57–4.16, and e =4.7 of CeO₂ film. The CeO₂, WO₃, and WO₃ + CeO₂ films have wide band gape Eg = 2.8–3.37 eV. 2004 Article Optical properties of dielectric layers with CeO₂ / T.V. Semikina // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 291-296. — Бібліогр.: 18 назв. — англ. 1560-8034 PACS: 77.55.+f, 78.66.-w http://dspace.nbuv.gov.ua/handle/123456789/119127 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The polycrystalline thin films CeO₂, WO₃, amorphous complex films WO₃ + CeO₂ with content of CeO₂ in the powder 10, 15 and 20 %, and CeO₂ + Dy₂O₃ with content of Dy₂O3 in the powder 10, 15 and 20 % are obtained by vacuum deposition method via powder evaporation. For the first time the optical characteristics of complex films WO₃ + CeO₂ and CeO₂+Dy₂O₃ are obtained. As a results of films investigation by ellipsometry the dependencies of refraction and extinction coefficients on incident beam energy are presented. The dielectric permittivity and energy band gapes are calculated. The refraction coefficients of films CeO₂ are 1.85–2.85 and are not more than 2.37 for complex films. Dielectric constant e of complex films are 3.57–4.16, and e =4.7 of CeO₂ film. The CeO₂, WO₃, and WO₃ + CeO₂ films have wide band gape Eg = 2.8–3.37 eV.
format	Article
author	Semikina, T.V.
spellingShingle	Semikina, T.V. Optical properties of dielectric layers with CeO₂ Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Semikina, T.V.
author_sort	Semikina, T.V.
title	Optical properties of dielectric layers with CeO₂
title_short	Optical properties of dielectric layers with CeO₂
title_full	Optical properties of dielectric layers with CeO₂
title_fullStr	Optical properties of dielectric layers with CeO₂
title_full_unstemmed	Optical properties of dielectric layers with CeO₂
title_sort	optical properties of dielectric layers with ceo₂
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	2004
url	http://dspace.nbuv.gov.ua/handle/123456789/119127
citation_txt	Optical properties of dielectric layers with CeO₂ / T.V. Semikina // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 291-296. — Бібліогр.: 18 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv	AT semikinatv opticalpropertiesofdielectriclayerswithceo2
first_indexed	2025-07-08T15:16:17Z
last_indexed	2025-07-08T15:16:17Z
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fulltext	291© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 3. P. 291-296. PACS: 77.55.+f, 78.66.-w Optical properties of dielectric layers with CeO2 T.V. Semikina Department of Environmental & Material Engineering, Teikyo University of Science & Technology, 2525 Yatsusawa, Uenohara-machi, Kitatsuru-gun, Yamanashi-pref., 409-0193 Japan, E-mail: semikina@edd.ntu-kpi.kiev.ua, tanyasemikina@rambler.ru Abstract. The polycrystalline thin films CeO2, WO3, amorphous complex films WO3 + CeO2 with content of CeO2 in the powder 10, 15 and 20 %, and CeO2 + Dy2O3 with content of Dy2O3 in the powder 10, 15 and 20 % are obtained by vacuum deposition method via powder evapo- ration. For the first time the optical characteristics of complex films WO3 + CeO2 and CeO2+Dy2O3 are obtained. As a results of films investigation by ellipsometry the dependen- cies of refraction and extinction coefficients on incident beam energy are presented. The di- electric permittivity and energy band gapes are calculated. The refraction coefficients of films CeO2 are 1.85�2.85 and are not more than 2.37 for complex films. Dielectric constant ε of complex films are 3.57�4.16, and ε =4.7 of CeO2 film. The CeO2, WO3, and WO3 + CeO2 films have wide band gape Eg = 2.8�3.37 eV. Keywords: oxide high-k materials, rare-earth elements, CeO2, optical characteristics, dielectric permittivity, and wide band gap. Paper received 22.05.04; accepted for publication 21.10.04. 1. Introduction The ways of microelectronics development are based on a permanent decrease in integrated circuit component dimensions. For metal-oxide semiconductor field effect transistors (MOSFET), first of all, the gate length should be reduced, which consequently results in scaling all oth- ers dimensions and is accompanied by appearance of new technological problems [1,2]. Because of the dimension decrease, which is related with, reduction of the dielec- tric thickness under the gate, there appear such problems as a drop of the breakdown voltage of this layer, increase in leakage current and operation voltage values. SiO2 is often used as a dielectric layer in silicon technology and certainly has excellent characteristics, namely: high qual- ity of the interface between oxide silicon and silicon with density of surface traps ~1010 cm�2eV�1, breakdown volt- age is 15 MV/cm, high thermodynamic and electrical properties stability. Even at SiO2 layer cutting down to 13 Å MOSFET operates rather successful by [1]. How- ever, at small thicknesses, there exist such undesirable effects as impurity penetration, especially boron from the high doped polysilicon gate. The problems of reliability stable and operation of transistor as well as undesirable leakage currents also appear. For example, in MOSFET with SiO2 thickness of 3.5 nm at the gate voltage of 1 V the leakage currents are 10�12 A/cm2 and at the thickness 1.5 nm the leakage currents increase by 13 orders and reach 10 A/cm2 [3]. For the normal operation of micro- processors and fast growing market of mobile phones and portable computers, there is strong demand to decrease the leakage current up to ~10�3A/cm2 [1]. The problem solution of gate capacity keeping without the gate volt- age increase can be provided by SiO2 layer change for dielectric having a higher value of the dielectric permit- tivity ε and higher breakdown voltage. Certainly, this new dielectric should be compatible with silicon technol- ogy to form the high quality interface with silicon, to be thermodynamic and structurally stable and technologi- cally reproducible. Nowadays, all over world the inves- tigations aimed at the change of the silicon oxide are carried out. The favorites of investigations are [1]: Ta2O5, SrTiO3, Al2O3, BaxSr1�xTiO3, PbxZr1�xTiO3, Y2O3, La2O3, Pr2O3, TiO2, ZrO2, and HfO2. But for all these materials, there is the problem of high quality interface with silicon formation. For the most cases, the density of trap states is ~1012 ñm�2 eV�1. One from perspective materials with the big ε value is cerium dioxide CeO2 that can be deposited by different methods [4-9]. E.g., in the work [6] it was obtained the perfect quality of the interface CeO2/Si with the state den- sity 6.8⋅1010 eV�1cm�2 after annealing the deposited film 292 SQO, 7(3), 2004 T.V. Semikina: Optical properties of dielectric layers with CeO2 in oxygen at temperature 500°C. Cerium dioxide was employed as a gate insulator for an enhancement-type n- channel metal-oxide semiconductor (MOS) transistor [10]. With CeO2 gate MOS device yielded an interface charge of 1.5⋅1010 Coul/cm2 with threshold voltage of 0.3 V. Because the threshold voltage was positive the CeO2 application rejected the problem of an additional processing step for charge reduction that exist for SiO2 dioxide. In the work [11], CeO2 film in the structure CeO2/Ge in MOSFET promoted the elimination of the native germanium oxide formation, which is an impor- tant result opposite to the case of usual uncontrolled na- tive substrate oxide growth. In this work, we propose the results of investigation of optical properties inherent to dielectric layers based on CeO2, namely: ÑåÎ2, WO3, WO3+CeO2, CeO2+Dy2O3 with the aim to get dielectric possessing a high ε value. This class of materials was chosen as based on previous investigations of electrical properties that showed the possibility to get the high quality interface with silicon, where the density of surface traps was ~1010 cm�2eV�1 [12] and breakdown voltage reached 3 � 3.2⋅106 V/cm. The obtained result of high quality interface is explained by small lattice mismatches between CeO2 and Si. It is known [3] that binary oxide CeO2 has the high value of dielectric permittivity ε = 18�26 that allows to hope on increase in CeO2 films in comparison with silicon diox- ide. Though it is known [1] that properties of thin films materials strongly differ from properties of volume mate- rials and under thickness reduction the ε value is also decreased. The incorporation of rare earth element Dy into the CeO2 film was fulfilled because Dy promotes the electric properties stabilization that is very important start to solve from the put problem for application of new dielectric material [1]. The optical properties were investigated by the meth- ods of infrared (IR), Raman spectroscopy and ellip- sometry. Infrared reflection spectra were measured at 20° angle of incidence using a Bruker IFS 66 Fourier Trans- form Infrared Spectrometer based on the Michelson Inter- ferometer. Raman spectra were excited using Kr+ Innova � 300 laser. Measurements were made using the, wave length 647.1 nm, resolution achieved 2.5 cm�1, ra- diation power was 15 mW. It was used nonpolarized ra- diation. The spectral analysis was performed by a Dilor XY 800 triple monochromator equipped with a Peltier cooled Wright CCD detector. Spectroscopic ellipsometry measurements were performed using a variable angle spectroscopic ellipsometer (VASE from J.A. Woollam Co., Inc.) equipped with a Xe-lamp source, single cham- ber monochromator, continuously rotating analyser and auto-retarder. The ellipsometric angles Ψ and ∆ were determined in the spectral range 0.8 to 5 eV at 65°, 70° and 75° angles of incidence. For data evaluation, the measured samples were described by a model taking into consideration the silicon substrate with an oxide layer on top, covered by the film containing CeO2 and an addi- tional top layer consisting of 50% film material and 50% void material for modeling the surface roughness. For the silicon and SiO2, optical constants data base values were used. From the measured data, the thickness of the SiO2 film, thickness and roughness of CeO2 containing films and their optical constants were determined. The standard X-ray diffractometr (Model DMAX-B, Rigaku, Tokyo, Japan) was used to determine the crys- talline phases present in the samples. To identify com- pounds, we used JCPDF card files to match peak posi- tions of possible ÑåÎ2, WO3 oxides. 2. Technology of deposition All the experiments were performed using commercially available p-Si (100) wafers (≈ 440 µm) with a resistance of 4�10 Ω⋅cm, oxidized at temperatures about 940°C at atmospheric pressure in dry O2. Thin evaporated layers of ÑåÎ2, WO3, WO3+CeO2, CeO2+Dy2O3 were depo- sited by technology of flash evaporation from powder original materials onto the oxidized Si substrate. Before the deposition process, the substrates were cleaned in the solution: 1part H2O2 + 1 part NH4OH + 4 part H2O and then washed in deionised water for 10 minutes. These Si substrates with different thicknesses of SiO2 were used to check SiO2 thickness influence on properties of depo- sited films. The powder of ÑåÎ2, WO3 and couple WO3+CeO2 (the powder concentration of CeO2 was 10, 15 and 20 % of the common powder amount), CeO2+Dy2O3 (concentration Dy2O3 was 10, 15, 20% of the common powder amount) were used as material sources. The substrate temperature during the evapora- tion was 170�180°C. The chamber pressure was 10�5 Pa. The light-doses of evaporated materials reached the tung- sten filament with definite frequency supplied for the keep- ing of stoichiometric composition of double systems, evaporated and deposited onto the substrate with SiO2. SiO2 layers were used because the interface SiO2/Si has the highest quality. However, the SiO2 presence leads to reduction of the equivalent thickness of CeO2+SiO2 struc- ture in comparison with the equivalent thickness of CeO2 film. 3. Investigation of films chemical content The results of X-ray diffraction demonstrate that ÑåÎ2 films have sharp peaks of cerium dioxide in crystalline phase (Fig. 1). As is known [1], the polycrystalline films have higher ε than the amorphous ones. However, the leakage current in polycrystalline films is also higher in comparison with that of the amorphous ones. Amorphous films are more homogeneous and better reproducible. Thus, it is more preferable to get amorphous films as gate dielectric in MOSFET, though the dependence on film structure and transistor operation is not studied well yet [1]. The task to prepare amorphous films based on CeO2 was solved by deposition of complex films WO3+CeO2. The films of pure WO3 possess an amorphous structure, T.V. Semikina: Optical properties of dielectric layers with CeO2 293SQO, 7(3), 2004 as it follows from X-ray diffraction results. It was ob- tained that after CeO2 introduction the resulting com- plex films WO3 + CeO2 also possess the amorphous struc- ture with impregnation of polycrystalline particles of CeO2. 4. Results of Raman spectroscopy All Raman spectra of investigated materials have the same character and show neither the presence of peak at the wavelength 466 cm�1 typical for nanocrystalline CeO2 films [13] no others peaks. The only peak of silicon was present. From the obtained results, it can be concluded that the energy of exciting radiation at the wavelength 647.1 nm is not enough to excite vibrations, and hence studied materials have the wide bandgap. 5. Results of infrared spectroscopy investigation From the IR reflection spectra of the researched materi- als (Fig. 2),it is seen that the deposited films have differ- ent thicknesses and deposited on the substrates with dif- ferent thicknesses of native oxide. The samples with CeO2 films (1, 2, 3) do not show the presence of Si�O oxides in the films. Their spectral behaviour indicates that only a very thin native oxide layer is on the top of substrates. There were not the peaks indicative of the presence of vibrations inherent to SiHx and Si�OH bonds and to wa- ter absorbed as free. The spectra of the samples with com- plex films WO3+20%CeO2 (7), CeO2+20%Dy2O3 (9,10) and CeO2+15% Dy2O3 (8) show the presence of thick native oxide on the substrates ( 462 nm). The strong fea- ture at 1100 cm�1 (sample WO3+20% CeO2, CeO2+15% Dy2O3 and CeO2+20% Dy2O3) and two weaker features at 466 cm�1 and 820 cm�1 are characteristic for SiO2. The weak peaks at 700 and 1600 cm�1 possibly concern with vibration modes of CeO2 element. The IR spectra of complex films WO3+CeO2 (5,6,7) at different cerium dioxide concentrations (10, 15, 20%) and pure WO3 (4) film are presented in Fig. 3. It is seen that CeO2 introduction into WO3 film does not essen- tially change the original dependence character. Only for the sample with CeO2 content 10 %, the peaks near 1600 cm�1 become more intensive. 6. Results of ellipsometry The film thickness and optical constants are determined by the ellipsometry method. There were used several simu- lation models applying point-by-point fit, model descrip- tion of optical constants, and Kramers-Kronig consist- ent. It is obtained that the film thickness varies in the range 72�154 nm at the surface roughness of 5�12 nm (Table 1). SiO2 thickness is 6 ± 1 to 464 ± 1 nm, which is in a good agreement with results of IR spectroscopy. 20 30 40 50 60 70 0 200 400 600 800 1000 1200 1400 x � CeO 2 In te n si ty , a . u . I x x x x x 2 Θ Fig. 1. X-ray diffraction spectrum of CeO2 film. 200 400 600 800 1000 1200 1400 1600 1800 2000 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 1 7 2 3 8 9 10 Wavenumber, cm R e fl ec ta n c e , a . u . �1 Fig. 2. IR-spectrums of the films: 1, 2, 3 � CeO2, 7 � WO3+20% CeO2, 8 � CeO2+15% Dy2O3, 9, 10 � CeO2+20% Dy2O3. Wavenumber, cm R e fl e c ta n c e , a r b . u n it s �1 200 600 1000 1400 1800 2200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 4 5 6 7 Fig. 3. IR-spectrums of the films: 4 � WO3, 5 � WO3+10% CeO2, 6 � WO3+15% CeO2, 7 � WO3+20% CeO2. 294 SQO, 7(3), 2004 T.V. Semikina: Optical properties of dielectric layers with CeO2 Under the usage of different simulation models for optical constant calculations it was obtained that the point-by-point approach gives more details for the char- acter of refraction and extinction coefficients behavior having non-monotonic character with absorption spec- trum broadening near the absorption edge. However, at this approach received is a plenty of noise signals, and parameters accuracy is 3�10 % for different films because of big number of unknowns. The results of optical con- stants evaluation by the point-by-point and Kramers- Kronig approaches are presented in Figs 4, 5 and Tab- le 2. From Fig. 4 (Kramers-Kronig approach), it is seen that CeO2 refraction coefficient varies from 2.17 to 2.85, which is a little bit higher than literature data (1.85�2.4) [14] and our previous results (2.2�2.4) [15]. This change of optical constants of complex WO3+CeO2 films do not depend on the cerium content in the film and dioxide sili- con thickness. On the base of obtained results of the point-by-point approach, it is plotted the dependence of wide bandgap Eg on absorption coefficient α1/2 presented in Fig. 6 (a�e). WO3 film has the biggest value ε =5.76 obtained by the Table 1. The thickness of silicon dioxide and deposited films obtained by ellipsometry method. Sample Thickness, nm Thickness non-uniformity SiO2 Film Surface roughness WO3+15%CeO2, (6) 143 ± 1 72 ± 1 5 ± 1 <5 WO3+20%CeO2, (7) 144 ± 1 102 ± 1 6 ± 1 <4 CeO2+20%Dy2O3, (9) 464 ± 1 35 ± 2 7 ± 1 <3 CeO2, (1) 6 ± 1 154 ± 1 12 ± 1 <14 WO3, (4) 138 ± 2 116 ± 1 9 ± 1 <5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Energy,eV R e fr a ct iv e i n d e x n 1 8 6 7 4 Fig. 4. Refractive coefficient dependence on photon energy for the films: 1 � ÑåÎ2, 4 � WO3, 6 � WO3+15% CeO2, 7 � WO3+20% CeO2, 8 � CeO2+15% Dy2O3. 1 8 6 7 4 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.1 0.2 0.3 0.4 0.5 Energy, eV E x ti n c ti o n c o ef fi c ie n t k Fig. 5. Extinction coefficient dependence on photon energy for the films: 1 � ÑåÎ2, 4 � WO3, 6 � WO3+15% CeO2, 7 � WO3+20% CeO2, 8 � CeO2+15% Dy2O3. Table 2. The films optical constants and energy band gaps. Sample nmin, hν = 1.0 eV ε = n2 � k2 Eg, eV Point-by- Kramers- Point-by- Kramers- Point-by- point fit Kronig model point fit Kronig model point fit CeO2 2.08 2.17 4.32 4.7 3.15 WO3 2.14 2.4 4.55 5.76 3.37 WO3+CeO2 (15%) 2.0 1.98 4.0 3.92 2.8 WO3+CeO2 (20%) 2.05 2.04 4.2 4.16 3.0 CeO2+Dy2O3 (20%) 1.89 1.89 3.57 3.57 2.3 T.V. Semikina: Optical properties of dielectric layers with CeO2 295SQO, 7(3), 2004 Kramers-Kronig simulation. The ε values 3.57-4.16 for complex films and ε = 4.7 of CeO2 are not high enough to change for the gate dioxide silicon film (ε = 3.9). The widths of bandgap (Table 2) are equal 2.3 to 3.37 eV. These data corresponds to literature data for CeO2 [16] where the bandgap for direct transition lies between 3.34 and 3.38 eV and the bandgap for indirect transitions lies between 3.02 and 3.20 eV. Consequently, the CeO2 films, amorphous films WO3 and amorphous complex films WO3+CeO2 have the wide bandgap that is the necessary requirement to new gate dielectric. 7. Conclusions As a result of fulfilled investigation, deposited are the polycrystalline thin films of CeO2, amorphous films WO3, amorphous complex films WO3+CeO2 and CeO2+Dy2O3. For the first time, the optical characteristics of complex films WO3+CeO2 and CeO2+Dy2O3 are presented. The IR results are indicative of SiO2 presence in the films except for CeO2. Water in the films is not found. The refraction coefficient (n = 1.85�2.85) for CeO2 films is a little bit higher than that presented in literature data. 1.0 1.5 2.0 2.5 3.0 3.5 4.0 a , m µ –1 / 1/ 2 2 1.5 2.0 2.5 3.0 3.5 4.0 4.5 E n erg y, eV 1.00.5 1.5 2.0 2.5 3.0 3.5 4.0 a , m µ –1 / 1/ 2 2 E n e rg y, eV 0 1 2 3 4 5 6 1.0 1.5 2.0 2.5 3.0 3.5 4.0 a , m µ –1 / 1/ 2 2 E n e rg y, eV 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 a , m µ –1 / 1/ 2 2 E n e rg y, eV a , m µ 1 /2 � 1 /2 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 Energy. eV Fig. 6. Plot of the absorption coefficient α1/2 versus photon en- ergy for different films: à � WO3; b � ÑåÎ2, ñ � WO3+CeO2 (15%); d � WO3+CeO2 (20%); å � ÑåÎ2+Dy2O3 (20%). The point of crossing of straight line and energy axis notes the energy band gap value. e a b c d 296 SQO, 7(3), 2004 T.V. Semikina: Optical properties of dielectric layers with CeO2 The n value of complex films is not more than 2.37. The calculated ε =3.57�4.16 of complex films and ε = 4.7 of CeO2 do not allow to change for the gate dioxide silicon film. The deposited new films CeO2, WO3 and WO3+CeO2 have wide bandgap Eg = 2.8�3.37 eV. To increase the dielectric permittivity ε , it is possible to introduce some changes into the technological process of film evaporation. For example, to carry out the evapo- ration in the environment of oxygen or nitrogen (NH3, N2) with annealing treatment that, as is known [6,17,18], leads to film defect reduction. Acknowledgment The author thanks A.N. Shmyryeva (NTUU �KPI�) for the given samples and long time heading the authores work, V.G. Litovchenko for the consultation under re- sults processing, Marion Friedrich and D.R.T. Zahn for the possibility to work in their laboratory of semiconduc- tor physics in TU-Chemnitz, Germany. This work was financially supported by the grant from Ministry of Edu- cation of Saxon, Germany. References 1. G.D. Wilk, R.M. Wallance, and J.M. 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Optical properties of dielectric layers with CeO₂

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