DEFORMATIONS AND STRESSES IN THE CONSOLE SYSTEM «FILM – SUBSTRATE»

The purpose of this publication is analysis of the stress-strain state in the console system «film – substrate». Deformations of the cantilever system «film – substrate» under the impact of stresses occurring upon film deposition are analyzed in beam approximation. General formulas are derived to calculate the angular and linear deformation of the system at various values of the module of elasticity of the materials of the substrate and film. In contrast to the well-known Stoney formula, the expression obtained in this paper for the angular deformation of the cantilever system is valid for different values of the film and substrate thickness. The Stoney formula is the limiting case of the derived general formula valid when the thickness of the film is several orders of magnitude less than the substrate thickness. The influence of various elastic moduli on the angular and linear deformation of the console, as well as on the stress distribution in the «film – substrate» system, is estimated. It is shown that if the substrate thickness is 100 times larger than the film thickness, the angular deformation changes approximately by a factor of two at 2-fold change in the ratio the moduli of elasticity. The measuring capabilities of the cantilever converter of stresses in the film into the angular deformation of the end of the console are analyzed. The sensitivity of the converter is estimated as a function of the ratio of film and substrate thicknesses. It is shown that the obtained expressions for the displacements and stresses can be used in studying temperature deformations and stresses in the «film – substrate» system. To do this, the stress in the film should be replaced by the product of the modulus of elasticity and the temperature change and the difference in the coefficients of thermal expansion of the materials of the film and substrate.

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