The mechanical properties of freestanding electroplated Cu thin films
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T.Y. Tsui Texas Instruments, Inc., Dallas, Texas 75243
J.J. Vlassaka) Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (Received 30 December 2005; accepted 22 March 2006)
The plane-strain bulge test is used to investigate the mechanical behavior of freestanding electroplated Cu thin films as a function of film thickness and microstructure. The stiffness of the films increases slightly with decreasing film thickness because of changes in the crystallographic texture and the elastic anisotropy of Cu. Experimental stiffness values agree well with values derived from single-crystal elastic constants and the appropriate orientation distribution functions. No modulus deficit is observed. The yield stress of the films varies with film thickness and heat treatment as a result of changes in the grain size of the films. The yield stress follows typical Hall-Petch behavior if twins are counted as distinct grains, indicating that twin boundaries are effective barriers to dislocation motion. The Hall-Petch coefficient is in good agreement with values reported for bulk Cu. Film thickness and crystallographic texture have a negligible effect on the yield stress of the films.
I. INTRODUCTION
Over the last few decades, much work has gone into characterizing the mechanical behavior of thin metal films. It is found that thin-film mechanical properties are typically very different from those of bulk materials.1,2 For example, thin metal films are often found to support much higher stresses than their bulk counterparts. This strengthening has generally been attributed to dimensional and microstructural constraints on dislocation motion. Dimensional constraints are imposed by interfaces and the small dimensions typically encountered in thin films, whereas microstructural constraints arise from the very fine grains often found in thin films.3 In bulk materials, microstructural constraints dominate the plastic behavior of the material. However, when material dimensions are comparable with microstructural length scales, as is typically the case for thin films, free surfaces and interfaces are important as well. For example, dislocations can exit the material through free surfaces, and strong interfaces can prevent them from doing so. Consequently, strong interfaces may lead to a higher cumulative dislocation density in the film, resulting in higher
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0195 J. Mater. Res., Vol. 21, No. 6, Jun 2006
flow stresses and greater strain hardening rates. This strengthening behavior scales with film thickness and is often referred to in this article as the film thickness effect. The film thickness effect has been modeled by various researchers. Theoretical models generally fall into two main categories: The macroscopic models are based on the continuum theory of plasticity, such as the strain gradient plasticity theories by Aifantis4,5 or Fleck and Hutchison.6–9 The microscopic models are based
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