Ανάπτυξη μικρομηχανικού μοντέλου για τον υπολογισμό ιδιοτήτων λεπτών υμενίων στη μικρό και νανό – κλίμακα

Abstract

The material properties of thin films used in surface micromachined devices depend, to a large extend, on the deposition process, the physical and chemical processes characterizing film growth, and post-deposition thermal processing (annealing). Hence, although the properties of the bulk form of the material are well defined, the corresponding thin-film properties are not so well characterized. To this end, the first objective of this thesis is to examine the feasibility of using vibration characteristics of surface micromachined structures to determine the stiffness and Poisson’s ratio of thin films in the form of clamped rectangular plates. In addition, one must always bear in mind that a state of residual stress exists in all surface micro-machined structures. Residual stresses may be generated due to a variety of factors including a mismatch in the thermal expansion coefficients of a film and an adjacent one, or a film and the substrate, the presence of impurities, and chemical and physical processes accompanying film growth. A solid understanding of these stresses is important for improving the reliability and life-time of thin films. Appropriately, the second objective of this thesis is to study the effects of residual stresses on the natural frequencies of plates and beams and to examine how natural frequency measurements can lead to the determination of these residual stresses. To meet these objectives, equations of the fundamental frequency of a rectangular plate clamped on all four sides as well as a beam clamped on both ends, in terms of the material properties and the residual stresses are derived. These equations are then used to determine closed-form expressions for the Young’s Modulus and Poisson’s Ratio of the material of the plates and beams. In addition, natural frequency measurements will lead to the determination of residual stresses present in the aforementioned structures. The results of this work conform very well to their counterparts from various published models.