Nanoindentation study of plasticity length scale effects in LIGA Ni microelectromechanical systems structures

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T. Buchheit Mechanical Reliability and Modeling Department, Sandia National Laboratories, Albuquerque, New Mexico 87185

D. Yang Hysitron, Inc., Minneapolis, Minnesota 55439

W.O. Soboyejo Princeton Materials Institute and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544 (Received 21 March 2002; accepted 31 December 2002)

This paper presents the results of a nanoindentation study of the effects of strain gradient plasticity on the elastic–plastic deformation of lithographie, galvanoformung, abformung (LIGA) Ni microelectromechanical systems (MEMS) structures plated from sulfamate baths. Both Berkovich and North Star/cube corner indenter tips were used in the study to investigate possible effects of residual indentation depth on the hardness of LIGA Ni MEMS structures between the micro- and nanoscales. A microstructural length scale parameter, ˆl ⳱ 2.2 ␮m, was determined for LIGA nickel films. This is shown to be consistent with a stretch gradient length-scale parameter, ls, of approximately 0.9 ␮m.

I. INTRODUCTION

In recent years, LIGA (an acronym of the German words “lithographie, galvanoformung, abformung”) nickel microelectromechanical systems (MEMS) structures have been developed for applications in larger and thicker devices.1–4 These include applications in microswitches2–4 and accelerometers1 that are used for the deployment of air bags. However, a basic understanding of the mechanical behavior of LIGA nickel MEMS structures is yet to be developed. Furthermore, the possible effects of size-scale on plasticity in LIGA Ni MEMS structures are yet to be fully explored. The nanoindentation method was chosen in this study of size effects because it is the simplest and most controllable experimental technique for the characterization of size effects on the plasticity of metals between the micro- and nanoscales. Traditionally, indentation tests can be used to estimate the yield stress by measuring the hardness at the macro- and microscales.5 In most of these studies, it has been assumed that the hardness is independent of indentation size. However, there have been ample studies5–10 that show that the measured hardness is dependent on the size of indent, when the residual indent size is on the order of tens of microns or less. This size J. Mater. Res., Vol. 18, No. 3, Mar 2003

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dependence cannot be explained by the conventional continuum plasticity theories in which there are no length scale parameters.9–11 During the last three decades, there have been significant efforts to develop new plasticity theories that include the effects of plasticity length scale parameters.9–11 Two classes of plasticity theories have been developed. These include the phenomenological strain gradient plasticity theories proposed by Fleck and Hutchinson11 and the mechanism-based strain gradient plasticity theory developed by Gao, Huang, and Nix.10,12,13 Most recently, microbend experiments have been conducted on LIGA Ni MEMS stru