Indentation Technique to Investigate Elastic Moduli of Thin Films on Substrates
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INDENTATION TECHNIQUE TO INVESTIGATE ELASTIC MODULI OF THIN FILMS ON SUBSTRATES D.S. STONE*, T.W. WUt, P.-S. ALEXOPOULOSt, and W.R. LAFONTAINEt *Materials Science and Engineering, Bard Hall, Cornell University, Ithaca, NY 14853; presently at Materials Science and Engineering, University of Wisconsin, 1509 University Avenue, Madison, WI 53706 tIBM Research Division, Almaden Research Center, IBM Magnetic Recording Institute, San Jose, CA 95120-6099 Cornell Bard Hall, tMaterials Science and Engineering, University, Ithaca, NY 14853 ABSTRACT Closed-form elasticity solutions are introduced, that predict the average displacement beneath square and triangular, The uniformly loaded areas at the surface of a bilayer. solutions aid in the application of depth-sensing indentation techniques for measuring thin film elastic moduli. The elasticity solutions agree closely with experimental data of Al, Si, 1 pm Al on Si, and 2 pm Cr on Si. The case of poor adhesion between the film and substrate is briefly examined. INTRODUCTION The principles of using depth-sensing indentation tests to measure elastic moduli are discussed by Doerner and Nix [1] and Loubet [2]. According to the former's analysis, the unloading compliance, C, and square root of the projected indent area, S, are related by: c
i/SEeff l
=
(l-vs 2 )/•SEs + (l-vd2 )/PSEd
(1)
where Es, VS, Ed and vd are the Young's Moduli and Poisson's Ratios of the substrate and diamond indentor, respectively, and f is a number near 1. Eeff is an effective elastic modulus. The two terms at right represent the specimen and indentor compliance, respectively. Equation 1 excludes the machine compliance, which can be accounted for in the data analysis [1], and it assumes the indentor and substrate are elastically isotropic. Based on Equation 1 and provided the modulus of the indentor is known, the elastic moduli of bulk specimens can be determined from the slope of C vs. 1/S. However, the compliance measured from a thin film on substrate reflects a combination of both film and substrate properties. This paper reports some elasticity solutions necessary for analysis of unloading data from thin film-substrate systems and compares these solutions with experimental data. ELASTICITY MODEL FOR INDENTATION OF BILAYER The model will be detailed elsewhere [6]. In the model, the average displacement of the surface beneath a region of uniformly distributed pressure is calculated. This approach for determining compliance contrasts with that of King [7], who Mat.Ras.Soc. Symp. Proc. Vot. 130. 019©9Materais Research Society
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Beneath a modeled indentation of a bilayer with a rigid punch. whereas the is uniform, punch the displacement rigid While the values of compliance distribution of pressure is not. predicted by the different approaches are similar, the present results can be approach is more convenient to use because its presented in closed-form. Based on Chou and Pagano [8] and the work of Burmister [9], displacements at the surface of a bilayered the elastic half-space can be found in the
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