Ž . Thin Solid Films 319 1998 9–15 Limits of validity of the crystallite group method in stress determination of thin film structures P. Gergaud ) , S. Labat, O. Thomas MATOP, Unite Associee CNRS, Faculte des Sciences de Saint Jerome, F-13397 Marseille Cedex 20, France ´ ´ ´ ´ˆ Abstract The mechanical state of stress of thin films and multilayers is of great importance because of its influence on many physical properties: magnetic, dielectric, elastic, etc. For these reasons, the determination of stresses in these materials is becoming of increasing importance. Among the methods available for stress or strain determination, the X-ray technique, through the sin 2 c method, is of great interest because of the low mean depth penetration of X-ray and because it allows the strain measurements in different phases of a thin film, leading thus, for instance in a multilayer, to a complete knowledge of the state of stress. Usually, the thin films exhibit strong textures inducing some difficulties in the stress calculus. One easy way to solve the problem is to use the crystallite group method. It is a pseudo sin 2 c analysis based on the assumptions done in single crystal analysis. Of course, the stronger the texture, the better the validity Ž . of the measurements. In this work, we calculate using simulations and modelling based on the Voigt and the Reuss hypotheses the limit of this technique vs. the mosaicity of the texture around an ideal orientation for both fibre texture and single crystal-like texture. It is shown that the crystallite group method can be employed even for rather weak texture, allowing its use in a wide range of thin polycrystalline coatings. q 1998 Elsevier Science S.A. Keywords: Crystallite group method; Stress determination; Thin film structures 1. Introduction Most properties of materials are influenced by some factors such as crystalline structure, texture, or internal stresses. The knowledge of these parameters is of great interest for the understanding of the process involved or of the mechanical behaviour of the materials. A useful and powerful technique for stress determination is X-ray diffraction. Within the limits of the method it is quite easy to employ. Unfortunately, a lot of processes like skin-pass- ing, plastic deformation in steels, and in particular deposi- tion processes can induce highly textured materials. In this case the classical method further described is no more valid. A specific analysis must be engaged to get accurate Ž . results. Depending on the texture sharp or weak , different methods have been developed. The most complete one is based on the calculus of specific X-ray elastic constants Ž taking into account the ODF orientation distribution func- . w x tion of the material 1,2 . Unfortunately, this technique is rather long and hard to perform. So in a number of cases, when the texture is sharp enough, one can use techniques ) Corresponding author. which are similar to the one used for stress analysis in single crystal. They are based on the measurement of Ž . particular directions or with different hkl planes. It is the purpose of the following development to describe briefly these methods and to define their limits of validity vs. the sharpness of the texture. In the following, we will focus on the specific case of thin films where the problem is mostly encountered, making assumptions regarding the isotropic biaxial state of stress in the surface of the film. Moreover, w x the considered textures are cubic 001 fibre texture or ² :w x 100 001 single crystal-like texture. Nevertheless, the calculus and results can be easily extended to more general state of stress and whatever texture axis. 2. The methods of stress determination using X-ray diffraction 2.1. X-ray measurements on polycrystalline randomly tex- tured materials The best adapted technique for crystalline parameters determination is X-ray diffraction. The interatomic spacing d is taken as strain gauge and Bragg’s law provides a hkl 0040-6090r98r$19.00 q 1998 Elsevier Science S.A. All rights reserved.