Measurement Of Residual Stress In Ferroelectric Thin Films By Using X-ray Diffraction

The interest in ferroelectric thin films in recent years results from the numerous potential applications in micro electromechanical system(MEMS), micro-electronics and information storing which utilize the unique properties of the material, such as piezoelectricity, pyroelectricity, electro-opticity, acousto-opticsity, and dielectricity. Therefore, details on preparation, structural characteristic and property studies to ferroelectric thin films have attracted great interests. Because of the structural misfit and thermal misfit between the film/substrate systems, together with the cooling down procedure during the preparation process of thin films, residual stress is induced inevitably. Residual stress in thin films may lead to delamination, degradation or complete failure. Therefore, research upon residual stress in ferroelectric thin films is very important. In this paper, we investigate general techniques of residual stress measuring in thin films, and review the applications of several methods of residual stress measuring in ferroelectric thin films. Moreover, two new models based on X-ray diffraction are proposed to accurately measure the residual stress in ferroelectric thin films, taking account of the intrinsic characters of ferroelectric thin films such as isotropy, piezoelectricity and orientation-texture. The models are used to calculate residual stresses in PZT and BNT thin film samples, and the results are compared with those evaluated by existing methods. The main conclusions are given as follow(a) Ferroelectric thin films have their particular characters such as isotropy, piezoelectricity and mechanic-electric coupling, which make conventional sin 2? method inaccurate. Such properties must be taking into account when measuring residual stresses in ferroelectric thin films, and for polycrystalline thin films, the orientation-texture status is also important for the validity.(b) The cell-stress model is an innovative method in residual stress measuring of ferroelectric thin films. The main procedures can be described as follow. Firstly stress status in a crystal cell located on the film/substrate interface is calculated by analyzing the microscopic mechanism of stress sources, taking account properties of isotropy, piezoelectricity and mechanic-electric coupling. Secondly, an orientation average procedure is processed in frame of continuum micro-mechanics to obtain the average residual stresses in the film/substrate interface. Lastly, by utilizing the decline parameter of the in-plane stress along the film thickness, surfacial residual stresses of the ferroelectric thin films can also be evaluated. According to calculating results of several sets of samples, this model has a good consistency with previous methods on surfacial stresses, while our model can also give a credible result of interfacial residual stress, which to our knowledge can not be measured by any other conventional methods.(c) The out-of-plane strain model, which also takes account the particular properties of isotropy, piezoelectricity and mechanic-electric coupling, gives a simple and convenient routine to residual stress measuring of polycrystalline ferroelectric thin films. Firstly, out-of-plain strains for all orientation are respectively calculated via the peaks in XRD pattern. Secondly, in-plane stresses for each orientation are calculated via piezoelectric constitution. Lastly, the average stress in thin film is obtained by an orientation average procedure. The model is testified by calculations to several sets of ferroelectric thin films, results show that its accuracy is guaranteed and this model has a better adaptability for polycrystalline thin films.