Accuracy of the Fatigue Lifetime of Polysilicon Predicted from its Strength Distribution
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Accuracy of the Fatigue Lifetime of Polysilicon Predicted from its Strength Distribution Vu Le Huy1, Joao Gaspar2, Oliver Paul2, Shoji Kamiya1 1 Materials Nagoya Institute of Technology, Nagoya, Aichi, Japan. 2 Department of Microsystems Engineering (IMTEK), University of Freiburg, Germany ABSTRACT This paper discusses the accuracy of the distribution of the fatigue lifetime of polysilicon thin films predicted from their strength distribution. On the basis of the authors’ previous studies, where the fatigue process determining the lifetime was formulated using the well-known fatigue crack extension Paris’ law, prediction error ranges for polysilicon specimens with different levels of strength are determined. The errors of the predicted fatigue lifetime in the logarithmic scale, defined as logN = |log10Nexp-log10Npred| where Nexp and Npred were the experimental and predicted number of cycle, were found to be less than 1 in the range of the cumulative fracture probability F between 0.1 and 0.9. Therefore, based on the measured Paris’ law parameters of polysilicon, the fatigue lifetimes of different polysilicon thin film structures can be predicted from their strength distributions with errors of roughly 10% in the logarithmic scale, which was average of percentages of logN to log10N of experimental data. INTRODUCTION The fatigue lifetime of micro electro-mechanical systems (MEMS) structures is one of the most serious concerns for their long-term reliability in many applications. Silicon is the most common structural material in MEMS. It is typically brittle and was recently found to be susceptible to fatigue [1,2]. Tsuchiya et al. [3] discovered that fatigue lifetime under different stress levels could be statistically explained on the basis of Paris’ law, which is well suited to describe fatigue crack extension. On the other hand, Izumi et al. [4] performed static strength tests on monocrystalline silicon (c-Si) specimens shaped by etching under different conditions. They reported a clear correlation between the state of damage on etched surface and the strength. Recently, fatigue behavior of polycrystalline silicon (polysilicon, poly-Si) thin films was found to be formulated as a fatigue crack extension process starting from the initial damage and being controlled by Paris’ law [5]. Therefore, fatigue lifetime of polysilicon as well as ceramic materials could be predicted under cyclic loading condition from the static parameters [6]. Paris’ law has already been used with two unknown parameters to predict the fatigue behavior of polysilicon by using the results of fatigue experiment with constant amplitude [5,7]. The fatigue behavior was then predicted from static strength distributions under monotonically increasing stress. Based on these studies, where the fatigue process determining the lifetime was formulated by using Paris’ law, prediction error ranges for polysilicon specimens with different levels of strength are now examined. The accuracy of the prediction is discussed on the basis of the resul
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