Study of the Yielding and Strain Hardening Behavior of a Copper Thin Film on a Silicon Substrate Using Microbeam Bending
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Study of the Yielding and Strain Hardening Behavior of a Copper Thin Film on a Silicon Substrate Using Microbeam Bending
Jeffrey N. Florando and William D. Nix Dept. of Materials Science and Engineering, Stanford University, Stanford, CA 94305
ABSTRACT Recently a new microbeam bending technique utilizing triangular beams was introduced. For this geometry, the film on top of the beam deforms uniformly when the beams are deflected, unlike the standard rectangular geometry in which the bending is concentrated at the support. The yielding behavior of the film can be modeled using average stress-strain equations to predict the stress-strain relation for the film while attached to its substrate. This model has also been used to show that the gradient of stress and strain through the thickness of the film, which occurs during beam bending, does not obscure the measurement of the yield stress in our analysis. Utilizing this technique, the yielding and strain hardening behavior of bare Cu thin films has been investigated. The Cu film was thermally cycled from room temperature to 500 oC, and from room temperature to –196 oC. The film was tested after each cycle. The thermal cycles were performed to examine the effect of thermal processing on the stress-strain behavior of the film. INTRODUCTION There is an ongoing need to understand how materials in small dimensions deform, especially in industrial applications. Many current techniques used in industry, such as nanoindentation and wafer curvature, provide some insight into this area. While indentation has proven to be a simple and easy-to-use technique, it fails to provide the fundamental data (yield strength, strain hardening rate) needed for the characterization and modeling of thin film structures. Wafer curvature provides useful information about the elastic and plastic behavior of thin films on substrates, but large temperature changes are required for these experiments. While the thermal cycles experienced during this experiment are similar to the cycles experienced during some chip operations, there is some debate as to how the stress data should be interpreted. One issue is whether the increase in the stress upon cooling is due to strain hardening in the film [1], or due to the temperature dependence of the yield stress [2-3]. An improved microbeam bending technique may be able to help answer this question. The method is similar to previous work done on microbeam bending [4-5], except that triangularshaped silicon microbeams are used. These triangular beams have the advantage that the entire film on the top surface of the beams is subjected to a uniform state of strain when the beams are deflected, unlike the standard rectangular geometry where the bending is concentrated at the support. The uniform strain state allows for the calculation of the stress-strain behavior of the film. Since the test is performed at room temperature, the film’s yielding behavior can be examined independent of temperature, leading to a possible method of determining the mechanism that caus
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