The influence of the strain on the optical properties of Si-SiO2 system has been investigated by spectroscopic ellipsometry (SE), interferometry and weighing methods. Subtle changes of densification (compaction degree) in silicon dioxide layers on silicon substrates have been determined by weight technique (relying on measurements of the silicon dioxide layer mass and calculations of the volume). Elastic stress in the oxide layers has been measured by Fizeau fringes image analysis method. A comparison is made between the density of the silicon dioxide (r) and the results of calculations made using r = f = (n) relations (where n is the refractive index) given in the literature

Panas, Andrzej

Rzodkiewicz, Witold

Biblioteka Cyfrowa Instytutu Łączności / National Institute of Telecomunications: Digital Library

Paper Ellipsometric spectroscopystudies of compaction and decompactionof Si-SiO2 systemsWitold Rzodkiewicz and Andrzej PanasAbstract— The influence of the strain on the optical propertiesof Si-SiO2 system has been investigated by spectroscopic ellip-sometry (SE), interferometry and weighing methods. Subtlechanges of densification (compaction degree) in silicon diox-ide layers on silicon substrates have been determined by weighttechnique (relying on measurements of the silicon dioxide layermass and calculations of the volume). Elastic stress in the ox-ide layers has been measured by Fizeau fringes image analysismethod. A comparison is made between the density of thesilicon dioxide (ρ ) and the results of calculations made usingρ = f (n) relations (where n is the refractive index) given in theliterature.Keywords— Si-SiO2 system, density, refractive index, spectro-scopic ellipsometry.1. IntroductionOxidation of silicon has attracted much attention in the lastdecades. Due to the continuous miniaturization of inte-grated circuits and increased functionality in the modernmicroelectronics technology, better understanding of themechanisms of elastic (instantaneous and reversible com-paction) and non-elastic (irreversible and permanent den-sification) strain generation in the Si-SiO2 system is nec-essary. Furthermore, when the structure size is reduced,their mechanical and optical properties may differ from thecorresponding values of the bulk medium. Therefore, stud-ies of both mechanical and optical properties of Si-SiO2system are of great importance.Several methods, such as spectroscopic ellipsometry (SE),interferometry and weight technique (WT) have been usedto determine these properties. In connection with this, themain goal of our work was to study the influence of strainon the optical properties of Si-SiO2 system using the tech-niques mentioned above.2. Experimental characteristicsCzochralski-grown, n-type (100) silicon substrates havebeen used in this study. We started with 4-inch waferspolished on both sides. Subsequently, the wafers were sub-jected to thermal oxidation process at 1000◦C in either dryoxygen (in order to grow silicon dioxide layers with thethickness of approximately 45, 95, and 170 nm) or watervapor (in order to grow oxide layers with the thickness ofapproximately 50, 90, and 165 nm).The thickness of SiO2 layers formed in the way describedabove and their refractive indexes were determined us-ing a variable angle spectroscopic ellipsometer (VASE) ofJ. A. Woollam Inc. Co.Ellipsometric measurements were carried out at 5 points foreach wafer in a wide spectral range (250–1000 nm) at threeangles of incidence (65◦; 70◦; 75◦). Interferometry wasused to determine the radius of curvature of the investigatedwafers.2.1. Experiment methodologyThe sequence of processing and measurement steps per-formed during our investigations was as follows:1. Oxidation of 4-inch, n-type Si (100) wafers polishedon both sides.2. Interferometric measurements of oxidized wafers.3. Ellipsometric measurements of oxidized wafers(to determine the thickness and refractive index ofoxide).4. Measurements of the mass of oxidized wafers.5. The removal of both front-side SiO2 layer and back-side SiO2 layer of each wafer by etching in HF solu-tion.6. Measurements of the mass of as-etched wafers.7. Interferometric measurements of as-etched wafers.8. Calculations of the oxide mass as the difference be-tween the wafer mass obtained before and after re-moval of both front-side and back-side oxide.9. Calculations of oxide density as the ratio of the deter-mined oxide mass to its calculated volume (productof oxide thickness and the surface area).2.2. Optical model for ellipsometric data analysisThe optical model which used for spectro-ellipsometric dataanalysis consisted of a silicon dioxide layer and a siliconsubstrate. The Cauchy dispersive model enabled the sil-icon dioxide refractive index and its thickness to be de-termined. Determination of the SiO2 index of refraction44Ellipsometric spectroscopy studies of compaction and decompaction of Si-SiO2 systemsis based on the he relationship represented by the Cauchydispersion formula:n(λ ) = A + Bλ 2 +Cλ 4 + . . . , (1)where A, B, C are fitting coefficients, and λ stands forwavelength, expressed in µm. In the applied model, thethree parameters of Eq. (1) and SiO2 layer thickness werefitted.3. Results and discussionDependence of silicon dioxide density, ρox on the oxide re-fractive index n is illustrated in Fig. 1. This figure clearlyshows that the refractive index is a measure of the densi-fication degree of SiO2 layers on silicon substrates. Themeasurement and calculation results for wafers with silicondioxide thickness tox ≈ 50 nm, 90 nm, 170 nm are presentedin Tables 1–4.Once the mass MSiO2 of an SiO2 layer is measured and itsvolume VSiO2 is known (calculated as the product of theoxide thickness and surface area of the layer), one maydetermine directly the density of the layer:ρSiO2 =MSiO2VSiO2. (2)Fig. 1. Dependence of silicon dioxide density, ρSiO2 (experi-mentally determined by weight technique) on the oxide refractiveindex, n (determined by spectroscopic ellipsometry).Table 1The mass, density and averaged thickness valuesdetermined for silicon wafers oxidized in water vaporatmosphereNo. of wafertox[nm]Mox[mg]ρox[g/cm3]1 50.07 1.00 2.572 90.17 1.58 2.263 165.12 2.86 2.23Table 2The mass, density and averaged thickness valuesdetermined for silicon wafers oxidized in dry atmosphereNo. of wafertox[nm]Mox[mg]ρox[g/cm3]4 45.16 0.81 2.315 93.96 1.64 2.246 172.02 2.97 2.22Table 3Comparative collection of theoretical and experimentaldensity values determined for the corresponding averagedrefractive indexes (determined by SE at λ = 630 nm)of the wet oxides (oxides grown in water vapor)No. of n630 ρL-L ρG-D ρTa ρEyk ρDrude ρwtwafer [g/cm3]1 1.4710 2.25 2.25 2.29 2.25 2.26 2.572 1.4630 2.21 2.22 2.23 2.21 2.22 2.263 1.4629 2.21 2.22 2.23 2.21 2.22 2.23Table 4Comparative collection of theoretical and experimentaldensity values determined for the corresponding averagedrefractive indexes (determined by SE at λ = 630 nm)of the dry oxides (oxides grown in dry oxygen)No. of n630 ρL-L ρG-D ρTa ρEyk ρDrude ρwtwafer [g/cm3]4 1.4738 2.26 2.27 2.31 2.26 2.28 2.315 1.4636 2.21 2.22 2.23 2.22 2.22 2.246 1.4634 2.21 2.22 2.23 2.22 2.22 2.22Next, the density of SiO2 layers obtained in this way werecompared with that determined from the value of the re-fractive index (established in the course of ellipsometricmeasurements). The Lorentz-Lorenz equation [1, 2] (L-L)is one of the most widely used formulae relating oxide den-sity to its refractive index:Π =13NAα =(n2−1)(n2 + 2)Mρ , (3)where: Π – molar polarization, NA – Avogadro’s num-ber, α – mean polarizibility, M – molecular mass,ρ – density.Substituting the following values: M = 60.08 g/mol(molecular mass of SiO2), ρ = 2.2 g/cm3 and n = 1.46(density and refractive index of the relaxed SiO2, re-spectively), we obtain molar polarization for SiO2 layerΠ = 7.4797 cm3/mol and Eq. (1) becomes:ρ = 8.0324 n2−1n2 + 2. (4)45Witold Rzodkiewicz and Andrzej PanasFig. 2. Interferograms and theirs sections along horizontal axis and the center of Fizeau fringes for front-side (a), (c) and back-side(b), (d), of wafer no. 5 after dry oxidation.Fig. 3. Radius of curvature versus distance for front-side (a) andback-side (b) of wafer no. 5 after dry oxidation.Other models of the relationship between oxide density andits refractive index include: Gladstone-Dale formula [2, 3](G-D):ρ = 4.785n−4.784 , (5)the empirical ρ(n) relationship for SiO2 layer derivedby Taniguchi [4] (Ta):ρ = 7.81(n−1)1.63, (6)Eykman equation [5] (Eyk):ρ = C n2−1n2 + 0.4 , (7)where C = 3.6161 (at room temperature) – empirical con-stant dependent on temperature; and Drude equation [2]:ρ = 1.944(n2−1) . (8)The last two equations have usually been used to study theoptical properties of various liquids (such as chlorobenzene,methanol, water, etc.).A comparison between values of SiO2 density obtainedboth experimentally and theoretically is shown in Tables 3and 4. It should be noticed that the results obtained for dryoxides by means of WT and calculated using Eq. (5) are ina good agreement (see Table 4).The results of interferometric measurements are illustratedin Figs. 2–5. Interferograms and theirs sections along hor-izontal axis and the center of Fizeau fringes for front-side46Ellipsometric spectroscopy studies of compaction and decompaction of Si-SiO2 systemsFig. 4. Interferograms and theirs sections along horizontal axis and the center of Fizeau fringes for front-side (a), (c) and back-side(b), (d), of wafer no. 5 after removal of dry oxide.Fig. 5. Radius of curvature versus distance for front-side (a) andback-side (b) of wafer no. 5 after removal of dry oxide.and back-side of wafer no. 5 after dry oxidation (thicknessof ∼ 90 nm) are shown in Fig. 2. Similar data obtainedafter removal of thick dry oxide is presented in Fig. 4.Using the results shown in Figs. 2 and 4, the approxima-tion function of curve of the sections, as well as the corre-sponding formula for reciprocal curvature Eq. (9), we havedetermined the radius of curvature R versus distance forfront-side and back-side of the oxidized wafer (dry SiO2thickness of ∼ 90 nm) (see Fig. 3):R =1κ=[1 +(dydx)2] 32d2ydx2, (9)where κ is the curvature.Similar results are shown in Fig. 5 for front-side and back-side of the wafer after dry oxide removal.Comparison of the results obtained from wafer no. 5 afteroxidation and after etching indicates that the curvature ofan oxidized wafer is considerably smaller than that of anetched wafer (Figs. 3 and 5).4. ConclusionsIn this work, we have investigated the influence of strain onthe optical properties of Si-SiO2 system by spectroscopicellipsometry and interferometry.47Witold Rzodkiewicz and Andrzej PanasOn the basis of the obtained results, we have drawn thefollowing conclusions:– refractive index of wet oxide is lower than that of dryoxide (Tables 3 and 4);– for refractive index higher than 1.47, the divergencebetween the density calculated from the Taniguchiformula and that calculated from Lorentz-Lorenz,Gladstone-Dale, Eykman, and Drude equations be-comes significant (Tables 3 and 4);– measurement of oxide mass and calculated volumeof the oxide layer enabled the densification degree ofthe oxide layers on silicon substrates to be properlydetermined for about 83% of the investigated wafers(with numbers: 2–6);– the local radii of curvature of oxidized wafer no. 5 areconsiderably higher than those of the etched wafers(Figs. 3 and 5);– interferometry and spectroscopic ellipsometry haveturned out to be helpful and suitable methods in ourstudies.References[1] G. M. Barrow, Chemia fizyczna. Warszawa: PWN, 1978 (in Polish).[2] K. Vedam and P. Limsuwan, “Piezo- and elasto-optic properties of liq-uids under high pressure. II. Refractive index vs density”, J. Chem.Phys., vol. 69, pp. 4772–4778, 1978.[3] W. A. Pliskin, “Comparison of properties of dielectric films depositedby various methods”, J. Vac. Sci. Technol., vol. 14, pp. 1064–1081,1977.[4] K. Taniguchi, M. Tanaka, and C. Hamaguchi, “Density relaxationof silicon dioxide on (100) silicon during thermal annealing”, J. Appl.Phys., vol. 67, pp. 2195–2198, 1990.[5] L. Lorenzi, M. Fermeglia, and G. Torriano, “Kinematic viscosity,and refractive index for bis (2-ethylexyl) adipate, tris (2-ethylhexyl)trimelitate, and dissonyl phthalate”, J. Chem. Eng. Data, vol. 43,pp. 183–185, 1998.Witold Rzodkiewicz was bornin Warsaw, Poland, in 1971. Hereceived the M.Sc. and M.Eng.degree in material science andengineering from Warsaw Uni-versity of Technology, Poland,in 1995. His Masters projectin “Studies of the structural per-fection of GaInAsSb quaternarylayers grown by LPE on GaSbsubstrates” was carried out atthe Institute of Electron Technology in Warsaw, Poland.From 1995 to 1998, he was with the Department of Mate-rials and Semiconductor Structures Research of the Instituteof Electron Technology in Warsaw as a Research Assistant,working in the area of process-induced defects in semicon-ductor structures. Since 1998, he is with the Departmentof the MOS System Studies in the above mentioned insti-tute as Research Assistant. Recently, he has taken up Ph.D.studies and is involved in optical studies with special em-phasis on spectroscopic ellipsometry and interferometry.e-mail: rzodki@ite.waw.plInstitute of Electron TechnologyLotników av. 32/4602-668 Warsaw, PolandAndrzej Panas received theEng.degree in UnorganicChemistry from Departamentof Chemistry, Warsaw Uni-versity of Technology, Poland.Recently, he works at Divisionof Silicon Microsystem andNanostructure Technology ofInstitute of Electron Technologyin Warsaw as technical-researchspecialist. He is involved inthermal processes of oxidation and diffusion.e-mail: panas@ite.waw.plInstitute of Electron TechnologyLotników av. 32/4602-668 Warsaw, Poland48

Ellipsometric spectroscopy studies of compaction and decompaction of Si-SiO2 systems, Journal of Telecommunications and Information Technology, 2007, nr 3

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Ellipsometric spectroscopy studies of compaction and decompaction of Si-SiO2 systems, Journal of Telecommunications and Information Technology, 2007, nr 3

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