Thickness Effects on the Plasticity of Gold Films
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LD films are found in many applications where their special properties enable advances in new technologies. They have high conductance making them ideal for critical microelectronics applications. Understanding other material properties, such as hardness and elastic modulus, as well as adhesion, friction, and wear properties are important for the design of structures with small volumes. Nanoindentation is a versatile technique that can be used to determine the mechanical properties of thin films. It allows for the probing of hardness, elastic modulus, and adhesion properties at length scales below 1 lm. Of interest with nanoindentation is the indentation size effect (ISE) that is observed during these experiments. The first observations of the ISE were by Gane and Cox[1] in 1970 in single-crystal gold. They demonstrated that measured hardness increased by a factor of 3 when decreasing the contact diameter of the indenter tip. With the advent of depth sensing instrumentation,[2] Stelmashenko et al.[3] showed a similar increase in measured hardness with a decrease in indentation depth on different orientations of single-crystal tungsten. This was attributed to the local dislocation hardening due to formation of geometrically necessary dislocations.[3] These findings, along with other observed material scale effects, led to phenomenological theories of strain gradient plasticity[4,5] and later a mechanism-based strain M.J. CORDILL, Postdoctoral Candidate and W.W. GERBERICH, Professor, are with Chemical Engineering and Materials Science Department, University of Minnesota, Minneapolis, MN 55455, USA. Contact e-mail: [email protected] D.M. HALLMAN, Mechanical Engineer, is with MTS Systems, Eden Prairie, MN, USA. N.R. MOODY, Distinguished Member of the Technical Staff, is with Sandia National Laboratories, Livermore, CA 94550, USA. D.P. ADAMS, Distinguished Member of the Technical Staff, is with Sandia National Laboratories, Albuquerque, NM, USA. This article is based on a presentation given in the symposium entitled ‘‘Deformation and Fracture from Nano to Macro: Honoring W.W. Gerberich’s 70th Birthday’’ which occurred during the TMS Annual Meeting, March 12–16, 2006 in San Antonio, Texas, and was sponsored by the Mechanical Behavior of Materials and Nanomechanical Behavior Committees of TMS. Article published online January 20, 2007. 2154—VOLUME 38A, SEPTEMBER 2007
gradient plasticity theory by Gao et al.[6] The use of the mechanism-based theory[6] at very shallow depths (less than 100 nm) is not ideal, because, at such small size scales, atomistic and surface effects may dominate where 1-nm penetrations are involved.[7] With this in mind, others,[8,9] at the suggestion of Baskes and Horstemeyer,[10] who considered the surface to volume (S/V) to be key, determined plastic zone sizes and surfaces of contact both experimentally and theoretically to assess the S/V’s importance. From these results, the S/V appeared to play a pivotal role for very shallow indentation contacts.[7] Previous research[8,11] used both the surface energy
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