Film Stress Characterization Using Substrate Shape Data and Numerical Techniques
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Film Stress Characterization Using Substrate Shape Data and Numerical Techniques Zhaohua Feng, Edward G. Lovell, Roxann L. Engelstad, Andrew R. Mikkelson, Phillip L. Reu and Jaewoong Sohn Computational Mechanics Center, Mechanical Engineering Department University of Wisconsin, Madison, WI 53706, U.S.A. ABSTRACT Intrinsic stress in a film-substrate system can have deleterious effects. To facilitate an understanding of stress generation and control film quality, measuring film stress is essential. In recent years research laboratories and industry have increasingly adopted indirect methods, which are usually based on the measurement of substrate deformation. The film stress is calculated by equations relating the stress to the deformation, such as the well-known Stoney’s equation. However, when the two principal stresses at each point in the film plane are not equal and their distribution is nonuniform, the local application of Stoney’s equation does not provide correct stress results. A numerical technique is presented, which overcomes these limitations and makes accurate stress determination possible. INTRODUCTION Intrinsic stress in thin films continues to be a persistent and pervasive surface engineering problem. For example, stress control is essential for material heteroepitaxy and the fabrication of viable MEMS devices. Likewise, in the semiconductor industry, image fidelity is becoming more important as integrated circuit feature sizes shrink below 100 nm. Film stress generated during the fabrication of advanced lithographic masks can cause mechanical distortions which compromise the accuracy of image resolution and placement. For such applications, dependable stress measurements are necessary before process control can be realized. Techniques for directly measuring localized thin-film strain, such as X-ray diffraction, have been used for many years, but the equipment is expensive and not well-suited for production environments. Indirect methods employ laser scanning or full-field measurement to determine the out-of-plane displacement (OPD) or the curvature generated by the intrinsic stress. The film stress is then computed from the measured data. Although most measuring tools provide accurate information about the induced substrate shape, the film stress magnitudes and distributions are not reliable. This is primarily due to the fact that the calculations are based upon the local application of Stoney’s equation, which is not valid for most real film-substrate systems. An alternative numerical technique based on finite element (FE) analysis was developed at the University of Wisconsin – Computational Mechanics Center (UW-CMC) and is discussed here. RELATING FILM STRESS TO SUBSTRATE DEFORMATION Stoney's equation is the most well-known expression linking film stress to substrate deformation. It was originally derived for a beam flexed by a uniformly stressed film [1], and
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was extended to determine two-dimensional film stress point-by-point from measured local substrate curvatures. For a unifo
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