Thin-Film-Edge-Induced Stresses in Substrates
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THIN-FILM-EDGE-INDUCED STRESSES IN SUBSTRATES S.P. Wong*#, H.J. Peng*, Shounan Zhao** *Department of Electronic Engineering and Materials Science and Technology Research Centre, The Chinese University of Hong Kong, Hong Kong, China **Department of Applied Physics, South China University of Technology, Guangzhou, China ABSTRACT We have obtained an analytic solution of linear elasticity for the stress distribution under a thin film edge in isotropic substrates of finite thickness and of infinite extent in the other two directions. The following boundary conditions are considered. At the film/substrate interface and the free surfaces at the top and bottom of the substrate, the normal stress component vanishes. Far from the film edge on the side without the film, all stress components are zero. Far from the film edge under the film, the stress distribution is in accordance with that given by the bimetallic strip theory. Two examples of comparison between theory and experiments were given to demonstrate the validity of this solution. The infrared photoelastic stress fringe pattern obtained by a dark-field plane polariscope in a Si substrate under an oxide film edge was successfully reproduced. The calculated and experimental results of Raman-shift of Si under patterned CoSi2 line structures also showed good agreement with each other. INTRODUCTION It is well known that stresses in the substrate are of importance in Si technology and film edge can produce large and localized stress in the silicon substrates [1]. There are many studies related to film-edge-induced stress effects in other semiconductor heterostructure systems, including GaAs stripes on Si [2], InP stripes on Si [3], GeSi stripes on Si [4], InGaAs stripes on GaAs [5], and amorphous carbon stripes on GaAs-AlGaAs quantum well structures [6]. More recent examples include the micro-Raman study of film-edge-induced stress in silicon substrates under metal and metal silicide stripes [7, 8]. Apart from the experimental studies, there are also many theoretical attempts to analyze the film-edgeinduced stress effects in the past two decades but so far a satisfactory analytical solution is still lacking. Several comprehensive review articles on this problem are available [1, 9, 10]. In this work, we shall report on an analytic solution we have obtained for the stress distribution under thin film edge in isotropic substrates satisfying the balance and compatibility equations of linear elasticity and the following boundary conditions. The substrate in consideration is of finite thickness H in the y direction and extends to infinity in the x and z directions (Fig. 1). It is half-covered by a thin film on the left half xz-plane (y = 0 and x < 0). Far from the film edge and on the side without the thin film, all stress components are zero. Far from the film edge and under the thin film, the stress distribution is in accordance with that given by the bimetallic strip theory [11]. That is, the non-vanishing stress components, σx and σz, vary linearly with depth when x approach
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