A Direct Method of Determining Complex Depth Profiles of Residual Stresses in Thin Films on a Nanoscale - Mechanics of R
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1052-DD03-06
A Direct Method of Determining Complex Depth Profiles of Residual Stresses in Thin Films on a Nanoscale - Mechanics of Residually Stressed Systems Stefan Massl1, Jozef Keckes2, and Reinhard Pippan1 1 Erich Schmid Institute, Austrian Academy of Sciences, Jahnstr. 12, Leoben, A-8700, Austria 2 Department Materials Physics, University of Leoben, Jahnstr. 12, Leoben, A-8700, Austria
ABSTRACT The basic ideas behind the calculation procedure of the developed ion beam layer removal method (ILR method) to determine complex depth profiles of residual stresses in thin films are explained. The mechanics of thin films on substrates in general and the effect of the substrate thickness on the stresses in particular are presented by means of a simple model system in order to improve the understanding and facilitate the application of the ILR method.
INTRODUCTION The distribution of residual stresses in thin films and structures is essential for the mechanical performance and the lifetime of coated components. Therefore, the ion beam layer removal (ILR method) was developed to allow the determination of stress profiles on a nanoscale in amorphous and crystalline thin films [1]. The procedure starts with the fabrication of a cantilever from the initial system with a focused ion beam workstation. It consists of the substrate and the thin film and deflects due to residual stresses. The thickness of the cantilever is reduced step by step by removing the thin film gradually top-down with the ion beam. This affects the stress distribution and therefore the deflection of the cantilever. The mean stress that acted in the removed sublayer is determined for each step from the actual deflection measured from SEM images, the Young’s moduli and the dimensions of the cantilever. The stress profile in the cantilever is determined by superimposing the previously removed sublayers and establishing the force and moment balances by means of the equations presented subsequently. The stress distribution in the initial system is calculated from the stress profile in the cantilever. The ideas presented below are essential for the understanding of the mechanics of thin films as well as the ILR method. A simple model system is introduced to explain the two ways of
describing coated systems and the corresponding equations. The same equations are necessary for the calculation procedure of the ILR method, where the sublayers removed previously from the cantilever are superimposed. The stress in the sublayer superimposed and the accumulated balanced stresses in the cantilever below are correlated with the actual curvature. Finally the procedure to determine the stress distribution in the initial system from the stress profile in the cantilever (and vice versa) is presented.
MECHANICS OF RESIDUALLY STRESSED THIN FILMS ON SUBSTRATES In order to understand the mechanical behavior of residually stressed systems the basic ideas and equations [2] are explained by means of the cross section of a linear elastic model system sketched schematically in
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