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J. Micromech. Microeng. 9 (1999) 230–235. Printed in the UK PII: S0960-1317(99)98357-2Determination of the elastic modulusof thin film materials usingself-deformed micromachinedcantileversWeileun FangPower Mechanical Engineering Department, National Tsing Hwa University, Hsinchu,TaiwanReceived 13 October 1998Abstract. The elastic modulus is a very important mechanical property in micromachinedstructures. There are several design issues such as resonant frequencies and stiffness inmicromachined structures that are related to the elastic modulus. In addition, the accuracy ofthe results from a finite element model is highly dependent upon the elastic modulus. In thisstudy a simple technique to characterize the elastic moduli of thin films of any thickness wasdeveloped. The film to be measured formed a bilayer cantilever with another film throughstandard micromachining processes. Due to the residual stresses of these two films thebilayer cantilever was deformed without any external load. Through the deformation profileof this self-deformed bilayer cantilever, the elastic modulus of the deposited film wasdetermined. A theoretical model was developed to predict the variations of the elasticmodulus of a deposited film and the deformation profile of a bilayer cantilever. Experimentswere also conducted to demonstrate the applications of this approach. In the experiments,bilayer cantilevers constructed from thin films of different materials and residual stresseswere fabricated and measured.1. IntroductionThin film materials are used widely in the areas of microelectronics,magnetic recording systems, microelectromechanicalsystems, etc [1, 2]. The thickness of the thin film materialscan range from several hundred angstrom, for example theovercoat of a hard disk, to several microns, for example amicromotor. In order to improve the performance of thinfilm devices, it is necessary to characterize their mechanicalas well as electrical properties. The elastic modulus is avery important mechanical property. There are several designissues related to the elastic modulus such as resonantfrequencies and stiffness. In addition, the accuracy of theresults from finite element analysis is also very dependent onthe elastic modulus.Because thin films have thicknesses of the orderof microns, the traditional elastic modulus determinationtechniques used for bulk materials, such as the tensile test,are not applied extensively [3]. In addition, the test in [3]requires a special experimental setup and specimen. Onthe other hand, the elastic moduli for components on thedimensional scale of microns are not evident in advance,and particularly so, to the extent that the process by whichthe thin film is grown affects the material properties [4, 5].For instance, the ion bombardment effect may change theresidual stress and elastic modulus of a sputtered film [4].The elastic modulus of a thermal oxide depends upon thegrowing process (wet or dry) [5]. Therefore, it is not reliableto predict thin film material properties from bulk material orthrough extrapolations of thick film properties.Currently several techniques in addition to [3] havebeen developed to characterize the elastic moduli of thinfilm materials. For example, the load–deflection tests onmicrostructures through the load from electrostatic voltageand pressure have been discussed [6, 7]. Unfortunatelya complicated experimental setup is required for thesemeasurement techniques. The load–deflection tests using asurface profiler [8] and nanoindenter [9] are also available.In these two approaches, mechanical contact betweenthe probe and the micromachined structures during themeasurement is inevitable. This may lead to some unwantedeffects such as friction during the measurement. Indirectmethods devised for determining the elastic moduli of thinfilms include techniques that involve measurement of theresonant frequencies of micromachined beams [10–12]. Anadditional experimental setup is also required to excitethe micromachined structures for measuring their resonantfrequencies.This study intends to develop a simple technique tocharacterize the elastic moduli of thin films of any thickness.In this technique, the film to be measured will be depositedon top of a film with known material properties. As shown0960-1317/99/030230+06$30.00 © 1999 IOP Publishing Ltd

Weileun Fangbilayer cantilever [15],I effective = e 1h 3 (212 + e 1h 2 h 1 + h ) 222 −ȳ( ) 2+ h3 112 + h h112 −ȳȳ= e 1h 2 (h 1 +h 2 /2)+h 2 1 /2 . (4)e 1 h 2 +h 1If the thickness of the film to be measured is very small (i.e.h 2 ≪ h 1 ), it is obtained from (3) and (4) that ρ gradient ≈ ρ 1 .The uniform residual stress can be relieved through thefree end for a single-layer cantilever. However, for a bilayercantilever, it will be exposed to a bending moment by theuniform residual stresses if the uniform residual strains (ɛ 0 ) 1and (ɛ 0 ) 2 of the thin films are different. After the uniformresidual stresses are relieved from the films, there are resultantnormal forces P i and moments M i acting over each film asshown in figure 3(b). Since no external forces and momentsare applied to the films, the basic requirement for this bilayercantilever is to satisfy ∑ P = 0 and ∑ M = 0. It is evidentfor this self-deformed structure thatP 1 + P 2 = 0 M 1 + M 2 = P 1h 12 + P 2(h 1 + h )22hence P 1 =−P 2 and M 1 + M 2 = P 2 (h 1 + h 2 )/2. In order tosatisfy the equation of compatibility, the total strain for films1 and 2 must be equal at their interface. Since the cantileveris bent with a radius of curvature ρ uniform , the compatibilityequation becomes− (σ 0) 2+E 2P 2E 2 h 2 w + h 22ρ uniform=− (σ 0) 1E 1+P 1(5)E 1 h 1 w − h 12ρ uniform(6)where w is the width of the films. Note that there are negativesigns for both (σ 0 ) 1 and (σ 0 ) 2 , since they are residual stresses.The radius of curvature ρ uniform determined through (5) and(6) is⎛ρ uniform = ⎝ − 1/e1+H 13 − 1+e1H6(H 1+H1 2 13) 6(1+H − H11)(σ 0 ) 1 − (σ0)2e 12 − 1 2⎞⎠ E 1 h 1 (7)where H 1 = h 2 /h 1 is a non-dimensional parameter.Therefore, the net radius of curvature of the bent bilayer beamρ total is1 1 1= + . (8)ρ total ρ gradient ρ uniformSubstitution of (3), (4) and (7) into (8) results in the followingrelationshipE 2 = f(ρ total ,h 1 ,h 2 ,ρ 1 ,ρ 2 ,(σ 0 ) 1 ,(σ 0 ) 2 ,E 1 ). (9)Therefore, the biaxial elastic modulus E 2 can be determinedthrough (9).3. Applications and resultsIn applications of this technique, a PECVD nitride film hasbeen used in the case studies. Bilayer cantilevers with alength between 40 and 200 µm were fabricated throughconventional bulk micromachining in this experiment.Cantilevers of different lengths were used to check theuniformity of the fabrication and the repeatability andconsistency of the measurements. Since the materialproperties of the thermally grown SiO 2 have been extensivelystudied [5, 16, 17], it was chosen as the base layer of thebilayer cantilever. In short, the bilayer cantilevers consistedof thermal SiO 2 and PECVD nitride. As shown in figures 1(a)and (b), the SiO 2 film was thermally grown onto a (100)wafer at 1050 ◦ C first and then deposited with a nitride film.Both of these two films were patterned using lithography andbuffered hydrofluoric acid as illustrated in figure 1(c). Thebilayer cantilevers were suspended above a cavity as shown infigure 1(d), after the substrate was etched anisotropically withN 2 H 4 . Since the selectivity between single crystal siliconand the thin films is very large for N 2 H 4 , the removal of thethin films during the etching process is negligible. The SEMphotograph in figure 4 shows several typical micromachinedcantilevers.The deformation configuration of the micromachinedcantilevers was measured quantitatively using an interferrometricprofilometry. A typical deflection profile of a bilayermicromachined cantilever measured in this manner is shownin figure 5. Hence the radius of curvature of the bilayer cantileverρ total is determined from the measured profiles. Theradius of curvature of SiO 2 and PECVD nitride single-layercantilevers ρ 1 and ρ 2 were also characterized in the samemanner. In addition, the residual stresses (σ 0 ) 1 and (σ 0 ) 2 ofthe films was characterized using a commercialized thin filmstress measurement instrument in this experiment. The residualstresses were determined by measuring the change in theglobal curvature of a wafer after the deposition of the thinfilm [18]. In the experiment, the residual stress (σ 0 ) 1 of film1 is considered to be unchanged after the deposition of film2. With E 1 , h 1 and h 2 being determined from the measuredbiaxial elastic moduli and thicknesses, E 2 was found in turnthrough equation (9).In the case study, the SiO 2 film was 0.33 µm thick andthe PECVD nitride film was 0.30 µm thick. Figure 6(a) and(b) shows the measured configuration of SiO 2 and PECVDnitride single-layer cantilevers, respectively. According tothe measurements, the average radius of curvature for SiO 2and PECVD nitride cantilevers were ρ 1 = 360 µm and ρ 2 =780 µm, respectively. In addition, the radius of curvatureof the bilayer cantilever determined using the profile infigure 5 was ρ total =−190 µm. The residual stresses ofthe SiO 2 and PECVD nitride films characterized throughthe wafer curvature approach were (σ 0 ) 1 =−290 MPa and(σ 0 ) 2 =−1120 MPa, respectively. Since the elastic modulusand the Poisson’s ratio of the wet thermal SiO 2 is 70 GPa and0.15, respectively, the biaxial elastic modulus of film 1 isE 1 = 82 GPa. Therefore, the relationship between E 2 andρ total , shown in figure 7, is determined through (9).As indicated in figure 7, the bilayer cantilever is initiallybent downward with ρ total = −6 µmatE 2 = 10 GPa.The radius of curvature of the bilayer cantilever is changedto −2000 µm when E 2 is increased to 275 GPa. WhenE 2 is near 300 GPa, ρ total becomes very large; in otherwords, the bilayer cantilever is flat. After E 2 is greater than310 GPa, the bilayer cantilever is bent upward, and the radius232

Self-deformed micromachined cantileversFigure 4. SEM photograph of the bilayer cantilevers.Figure 5. The measured deformation configuration of a 25 µm long bilayer beam from interferometric profilometry.of curvature of the bilayer cantilever is decreased when E 2is increased. The configurations of the bilayer cantilever fordifferent E 2 are also depicted by the insets in figure 7. Sinceρ total =−190 µm, the biaxial elastic modulus of the PECVDnitride film in this experiment is E 2 = 182 GPa. Thus theelastic modulus of the PECVD nitride film is E f 2 = 137 GPafor the Poisson’s ratio of PECVD nitride film ν f 2 = 0.25 [19].By way of comparison with the existing results, the biaxialelastic modulus of the PECVD nitride film is distributed from85 GPa to 210 GPa [19].4. DiscussionIn general, micromachined structures are always deformedby the thin film residual stresses. The proposed techniqueexploits this characteristic to determine the elastic moduli ofthin films. The advantages of such an approach are twofold:first, the structure is self-deformed, hence no complicatedsetup for applying external loads is required; and second, theerror due to the initial deflection during measurement, such asthe deviation of the resonant frequencies, can be prevented.Furthermore, it is recommended to characterize the thin filmmaterial properties through multiple approaches in order toreach a reliable result. Thus, the existing techniques [5–12],in which the elastic modulus is determined by complicatedsetups, can be supplemented with the use of the bilayercantilever technique.The results according to the simulations of thin filmswith h 2 = 0.1 µm and 0.3 µm thick Si 3 N 4 film depositedonto a h 1 = 1 µm thick SiO 2 base layer is shown in figure 8.The three different curves in figure 8 represent the variationsof E 2 and ρ total for radii of curvature ρ 2 = 780 µm, 7800 µmand −780 µm, respectively. In comparisons with the resultsshown in figures 8(a) and (b), it is evident that the relationshipbetween ρ total and E 2 will not be influenced by ρ 2 for smallerh 2 . Thus, it is not necessary to characterize the radius of233

Weileun FangFigure 6. The measured deformation configuration of: (a) a SiO 2cantilever; and (b) a PECVD nitride cantilever.Figure 8. The variation of E 2 and ρ total for three different radii ofcurvature ρ 2 when the film thickness h 2 is: (a) 0.3 µm; and(b) 0.1 µm.Figure 7. The variation of the biaxial elastic modulus E 2 and theradius of curvature of the bilayer beam ρ total .curvature ρ 2 when the thickness of the film h 2 is very thin.The difficulty in determining the gradient residual stress offilm 2 when h 2 is very thin can be prevented.The residual stresses (σ 0 ) 1 and (σ 0 ) 2 of the thin filmswere determined through the variations of the wafer curvaturein this study. This approach only gives an average measureof the stress across the entire substrate. In addition, theirregular surface topology of the substrate may lead to anerror in stress measurement. Therefore errors of the biaxialelastic modulus E 2 determined through (9) are produced bythe error of the measured residual stress (σ 0 ) 2 . For instance,the error propagation between (σ 0 ) 2 and E 2 is(dE 2E 1 h 1= −E 2 6ρ total (σ 0 ) 2 (H 1 + H1 2)E 1 h 1 e1 2 +H 13 ) −16ρ total (σ 0 ) 2 (1+H 1 ) +1 d(σ0 ) 2. (10)(σ 0 ) 2It is obvious from (10) that a limiting case of the errorpropagation is dE 2 /E 2 ≈ d(σ 0 ) 2 /(σ 0 ) 2 . In order to preventthe error of the elastic modulus due to the measurement of(σ 0 ) 1 and (σ 0 ) 2 of the thin films, (7) can be rewritten as⎛ρ uniform = ⎝ − 1/e1+H 13 − 1+e1H6(H 1+H1 2 13) 6(1+H − H11) 2 − ⎞12⎠ h 1 . (11)(ε 0 ) 1 − (ε 0 ) 2In (11), the residual strains (ε 0 ) 1 and (ε 0 ) 2 of the thin films isused to replace the residual stresses of the thin films. Sincethe residual strains can be determined through diagnosticmicromachined beams [13], a more accurate measured value234

Self-deformed micromachined cantileversFigure 9. Fabrication processes of the bilayer cantilever through:(a) the fabrication of a single-layer cantilever; and (b) thedeposition of a second thin film.can be obtained. Moreover, the distribution of the residualstrain can also be measured through the same approach.However, this approach cannot be applied for a very thin film.In the presented case, the thin films of thebilayer cantilever were patterned first and then undercutsimultaneously as shown in figures 1(c) and 1(d). Thisis different from the case discussed in [20], where film 2was deposited after the cantilevers made from film 1 werefabricated as shown in figure 9. Therefore the uniformresidual stress of film 1 has no contribution to the bendingof the bilayer cantilever in [20]. In other words, (9) isnot appropriate for determining the biaxial elastic moduliof thin films fabricated through the processes illustrated infigure 9.AcknowledgmentsThis material is based (in part) upon work supported bythe National Science Council (Taiwan) under Grant NSC87-2218-E007-007. The author would also like to expresshis appreciation for the assistance of his graduate studentsJerwei Hsieh, Hung-Yi Lin and Hsing-Hua Hu of NationalTsing Hua University (Taiwan) in handling the fabricationprocesses.References[1] Petersen K E 1982 Silicon as a mechanical material Proc.IEEE 70 420–57[2] Nix W D 1991 Mechanical properties of thin films Metall.Trans. A 20 2217–45[3] SharpeWNJr,YuanBandEdwards R L 1997 A newtechnique for measuring the mechanical properties of thinfilms J. Microelectromech. Syst. 6 193–9[4] Thornton J A and Hoffman D W 1989 Stress-related effectsin thin film Thin Solid Films 171 5–31[5] Petersen K E and Guarnieri C R 1979 Young’s modulusmeasurements of thin films using micromechanics J. Appl.Phys. 50 6761–5[6] Najafi K and Suzuki K 1989 A novel technique and structurefor the measurement of intrinsic stress and Young’smodulus of thin films Proc. IEEE/MEMS (Salt Lake City,UT, February 1989) pp 96–7[7] Tabata O, Kawahata K, Sugiyama S and Igarashi I 1989Mechanical property measurements of thin films usingload–deflection of composite rectangular membraneSensors Actuators A 20 135–41[8] Tai Y-C and Muller R S 1990 Measurement of Young’smodulus on microfabricated structures using a surfaceprofiler Proc. IEEE/MEMS (Napa Valley, CA, February1990) pp 11–14[9] Doerner M F and Nix W D 1986 A method for interpretingthe data from depth-sensing indentation instrumentsJ. Mater. Res. 1 601–9[10] Kiesewetter L, Zhang J-M, Houdeau D and Steckenborn A1992 Determination of Young’s moduli ofmicromechanical thin films using the resonance methodSensors Actuators A 35 153–9[11] Zhang L M, Uttamchandani D and Culshaw B 1991Measurement of the mechanical properties of siliconmicroresonators Sensors Actuators A, 29 79–84[12] Zhang L M, Uttamchandani D, Culshaw B and Dobson P1990 Measurement of Young’s modulus and internalstress in silicon microresonators using a resonantfrequency technique Meas. Sci. Technol. 1 1343–6[13] Fang W and Wickert J A 1996 Determining mean andgradient residual stresses in thin films usingmicromachined cantilevers J. Micromech. Microeng. 6301–9[14] Chu W-H, Mehregany M and Mullen R L 1993 Analysis oftip deflection and force of a bimetallic cantilevermicroactuator J. Micromech. Microeng. 3 4–7[15] Beer F P and Johnston ERJr1981 Mechanics of Materials(New York: McGraw-Hill)[16] Jaccodine R J and Schlegel W A 1966 Measurement ofstrains at Si–SiO 2 interface J. Appl. Phys. 37 2429–34[17] Wolf S and Tauber R N 1986 Silicon Processing (SunsetBeach, CA: Lattice)[18] Rossnagel S M, Gilstrap P and Rujkorakarn R 1982 Stressmeasurement in thin films by geometrical optics J. Vac.Sci. Technol. B 21 1045–6[19] Stoffel A, Kovacs A, Kronast W and Muller B 1996 LPCVDagainst PECVD for micromechanical applicationsJ. Micromech. Microeng. 6 1–13[20] Fang W and Wickert J A 1995 Comments on measuringthin-film stresses using bi-layer micromachined beamsJ. Micromech. Microeng. 5 276–81235