Thin Film Characterization Using the Point-Deflection Method
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Thin Film Characterization Using the Point-Deflection Method
Ning Tang, Roxann L. Engelstad and Edward G. Lovell Computational Mechanics Center, Mechanical Engineering Department, University of Wisconsin, Madison, WI 53706, U. S. A. ABSTRACT The Point-Deflection Method is a potentially useful technique for measuring the internal stresses of freestanding thin films. By applying a small concentrated transverse load at the center of a pre-stretched film, and measuring the corresponding out-of-plane displacement at appropriate locations, the average internal stress can be readily determined. The load-deflection relationship has been derived for both circular and rectangular shapes. The method involves no additional micromachining in sample preparation and has low sensitivity to the variations in boundary constraints. Its feasibility has been further substantiated with finite element simulations from a variety of perspectives, as well as experimental correlations from the stress measurements of a photomask pellicle film.
INTRODUCTION The characterization of residual stresses in thin films is becoming increasingly important in the semiconductor industry, e.g., stressed layers of advanced lithographic masks are a source of pattern placement errors [1, 2]. Current stress measurement techniques specifically developed for thin films, such as the microbeam deflection test, the pressure bulge test, the substrate curvature test, etc., have inherent limitations. For example, the microbeam deflection test often involves additional micromachining during sample preparation, and consequently induces unwanted stresses. Also, the pressure bulge test is quite sensitive to boundary constraints, due to localized stresses induced during the mounting procedure which are very difficult to eliminate in practice. Likewise, the effectiveness of the substrate curvature test diminishes dramatically for films with lower stress and smaller thickness. The Point-Deflection Method (PDM) presented in this paper is a promising relatively new technique for stress measurement in that it overcomes such difficulties. The average stress value can be extracted from the force vs. out-of-plane deflection (OPD) curve, determined for preselected positions on a freestanding film loaded by a concentrated transverse force applied at the center. It should be noted that although both the PDM and traditional depth-sensing indentation techniques [3] use similar instruments to apply small concentrated loads, the mechanics behind the two methods are fundamentally different.
THEORETICAL DEVELOPMENTS In the PDM, a freestanding film is modeled as a thin stressed plate with boundaries either fixed (clamped) or simply-supported (hinged). Schematics of the films considered are shown in Figure 1. L3.27.1
y
R 2b
r
0
x
0
2a
Figure 1. Schematic of circular and rectangular films. From classic theory [4], the small OPD of a single-layer prestressed circular plate subjected to a central point load P0 (with fixed and simply-supported boundaries, respectively) is given by:
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