Chemical stresses induced by grain-boundary diffusion in thin films
- PDF / 300,913 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 82 Downloads / 242 Views
Y.T. Chou Department of Chemical and Biochemical Engineering and Materials Science, University of California at Irvine, Irvine, California 92697
Sanboh Lee Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu, Taiwan (Received 3 August 2000; accepted 12 April 2001)
Chemical stresses induced by grain-boundary diffusion in thin films were analyzed. The stress distribution consisted of both tension and compression fields, and its characteristics were similar to those obtained for a semi-infinite solid. At a given time, the maximum stress (tension or compression) increased with increasing film thickness for both constant and instantaneous sources; it was generally higher than that in the semi-infinite system. The maximum stress (tension or compression) decreased as the diffusion time increased and at a given time and film thickness it increased with decreasing diffusivity ratio. The buildup of local stress is likely to cause damage and malfunctions of the film when used in an electronic device.
I. INTRODUCTION
Since Darken’s analysis of the Kirkendall effect in interdiffusion,1,2 considerable attention has been given to the thermodynamics of stressed solids3–6 and to the interaction between stress and diffusion.7–10 In the latter studies, the internal stresses generated by the composition inhomogeneity during diffusion are of special interest because they could cause dislocation generation and changes in material properties.11–16 Such diffusioninduced stresses are termed chemical stresses, analogous to thermal stresses generated by temperature inhomogeneity during heat flow, and their distributions have been extensively studied.7,18–21 Recently, the present authors made a quantitative analysis on chemical stress induced by grain-boundary diffusion in a semi-infinite medium.22 This model is applicable to most engineering systems, but it may not be suitable for thin films such as those used in electronic devices where the diffusion path is extremely small. For this case, the film thickness must be taken into consideration in solving the diffusion equations. Grainboundary diffusion in thin films of finite thickness has been analyzed by Gilmer and Farrell,23 Campbell,24,25 and Wang et al.26 It was pointed out 23 that calculations of grainboundary diffusivity in thin films based on the semiinfinite model may be in error by several orders of magnitude. The aim of this investigation is to calculate J. Mater. Res., Vol. 16, No. 7, Jul 2001
http://journals.cambridge.org
Downloaded: 08 Dec 2014
the distribution of chemical stress in a thin film based on the finite thickness model and to compare the data of sufficiently thick samples with previous results obtained for the semi-infinite case.
II. ANALYSIS
Consider an isotropic elastic solid of thickness y0 containing a thin slab of grain boundary of width ␦ situated along the positive y axis of a Cartesian coordinate system 0xyz (Fig. 1). A layer of source diffusant is coated on the surface y ⳱ 0. During diffusion annealing, a concentrat
Data Loading...
