Mathematical Modeling of Thermomechanical Stresses of Multilayer Erosion-Resistant Electrode Coatings of Magnetically Co
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Mathematical Modeling of Thermomechanical Stresses of Multilayer Erosion-Resistant Electrode Coatings of Magnetically Controlled MEMS Sergey Karabanov, Dmitriy Suvorov, Gennady Gololobov, Evgeny Slivkin, Dmitry Tarabrin Ryazan State Radio Engineering University, 59/1 Gagarina St., Ryazan 390005, Russia ABSTRACT The paper presents the results of numerical modeling of thermomechanical stresses and thermal fields for conditions of erosion-resistant electrode coatings of magnetically controlled MEMS switches with W-Ti-Cu structure at local temperature and electric current influence in axially symmetrical approximation. It is shown that the introduction of titan interlayer (30-100 nm) in the coating with W-Ti-Cu structure results in considerable (more than two times) decrease of internal thermomechanical stresses between layers that increases coating resistance to delamination. It is established that there is an optimum value of Ti layer thickness at which the minimum thermomechanical stresses are provided. INTRODUCTION Magnetically controlled MEMS switches are switching devices, the operating principle of which is based on switching of electrodes under the influence of a magnetic field [1-3]. The life time of these devices is defined, first of all, by electrodes erosion resistance. To provide the working capacity and durability of MEMS switches the erosion resistant materials are used: ruthenium, rhodium, gold alloys [5-6]. In some cases (large current density) the reason of MEMS switches breakdown, except surface erosion, is also the coating delamination from the substrate material. The main reason for delamination is considerable thermomechanical stresses on the substrate-coating border. The detailed calculation of thermomechanical stresses between various coating layers is necessary for the development of peeling resistant coatings. The coating structure optimization is carried out on the basis of the obtained data. The purpose of the paper is the numeric evaluation of the local temperature and electric current effect on the W-Ti-Cu film structure in axially symmetric approximation and provision of optimum structure parameters ensuring high coating erosion resistance. THEORY
For life time increase of MEMS switches their contact groups are made of high-melting and chemically resistant materials having high fusion temperature: ruthenium, rhodium, etc. The character and intensity of materials electric erosion depend on their connection polarity and thermophysical constants of electrodes materials. The materials erosion resistance is estimated by Palatnik’s criterion on the basis of thermophysical constants [4]:
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where Ст – heat capacity, cal·g/C; ρ — material density, g/sm3; λ — heat conductivity factor, cal·sm2/C; Тmelt — fusion temperature, °С. The negative factor of these materials application is the temperature increase of the electrodes surface due to their low heat conductivity and ohmic heating. Thus the local temperature increase of any sector enables the further erosion growth and local increase of surfa
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