J. Micromech. Microeng. 9 (1999) 414–421. Printed in the UK PII: S0960-1317(99)06288-9 Energy study of buckled micromachined beams for thin-film stress measurements applied to SiO 2 Liviu Nicu, Pierre Temple-Boyer, Christian Bergaud, Emmanuel Scheid and Augustin Martinez Laboratoire d’Analyse et d’Architecture des Syst` emes (LAAS/CNRS), 7 Avenue du Colonel Roche, 31077 Toulouse, France Received 23 July 1999, in final form 2 September 1999 Abstract. Measurements of maximal deflection amplitude were carried out on arrays of clamped–clamped SiO 2 microfabricated beams buckling under the effect of thin-film built-in compressive stress. The experimental deflection determination of these deflections yields the residual stress value in the SiO 2 film. This proposal is confirmed by appropriate theory that considers the issue of microfabricated beam buckling from an energy point of view. In this model, the total potential energy stored in a buckled microbeam is computed and the residual stress value is given by considering the measured buckling maximal deflection and by making approximations about the shape of the microbeam deflection curve. The SiO 2 film residual stress evaluated with the help of the energy method is in good agreement with values reported in the literature. 1. Introduction Accurate testing of the mechanical properties of thin films as deposited is crucial to the development of the microelectromechanical systems (MEMS) field. Residual stress in thin films is one of the most common properties to be evaluated since it directly affects the device behaviour [1]. Specific deposition conditions as well as temperature changes during processing and in service often lead to high mechanical stress. This may even cause buckling, changes in dynamic response, adhesion failure or other types of damage. As a result adequate methods are urgently needed for an in- depth analysis of thin-film mechanical properties. The study of residual stresses has been appreciated since the early work on the mechanical properties of thin films following the theory of Stoney [2] on electrodeposited films in 1909. A summary of the major research trends in this field has been proposed by Hoffman [3] and Chopra [4]. They discussed mechanical measurements and the results obtained on stresses in films and on tensile strength and adhesion of films. They also reviewed various models proposed to explain the observed phenomena. More recently, in situ methods for determining residual stress in microelectronic films have been developed by relying on the deformation of microfabricated structures as suspended membranes, asymmetric released structures [5] or micromachined beams [6–8]. All these studies have focused on the static behaviour. It should be pointed out that measurement methods involving in-plane deformations such as elongation tests of clamped beam overhangs may be destructive. However, as noted by Lin and Pugacz-Muraszkievicz [9], out-of- plane deformations like buckling of beams or microbridges offer an option to accurately evaluate compressive stress in thin films. They determined the local stress in thin thermal SiO 2 films and noticed a substrate orientation dependence for very thin films (less than 0.03 μm). It should also be pointed out that the method proposed in [9] is accurate only for films thinner than 0.2 μm. Guckel et al [10] experimentally documented the determination of mechanical strain in polysilicon micromachined beams. Their approach was supported by an adequate theory applied to experimental structures that buckled at a critical geometry. Fang and Wickert [6] studied the static deformation of SiO 2 micromachined bridges. The originality of their model lies in explicitly considering the effect of net imperfections (fabrication defects, non-ideal loading etc) on the beam’s behaviour in the near-buckling regime. More recently, Chiskis and Parnes [11] have proposed a model which allows them to demonstrate nanobuckling of monomolecular layers adhering to a substrate. In the case of micromachined beams under compressive stress, linear buckling models cannot realistically account for the real static behaviour of the beam. The initial curvature of the wafer under the influence of the one-side-deposited, thin-film residual stress leads to a slightly curved initial state of the micromachined beams. In addition, as noted by Fang and Wickert, fabrication defects and geometric irregularities may complicate the distinction between unbuckled and buckled beams. For all these reasons, it is commonly assumed in the buckling theory of micromachined beams that Dickinson’s model [12, 13] of slightly curved beams 0960-1317/99/040414+08$30.00 © 1999 IOP Publishing Ltd