A Method to Simulate the Interface-Diffusion in Solid-State Bonding-Processes Considering the Elastic Deformation
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A Method to Simulate the Interface-Diffusion in Solid-State Bonding-Processes Considering the Elastic Deformation Takehiko Ito, Shigeki Saito, Kunio Takahashi and Tadao Onzawa Department of International Development Engineering, Faculty of Engineering, Tokyo Institute of Technology, 452, 1st Ishikawadai bldg., 2-12-1, O-okayama, Meguro-ku, Tokyo, Japan 152-8552 ABSTRACT We propose a new method to simulate the interface diffusion in the solid-state bondingprocess. This method is more significant under the condition of low pressure and low temperature. It is available for the bonding of two bodies which consist of the atoms of the same kind and have slight surface roughness. In a conventional method, the elastic deformation during the bonding process is considered. The interface diffusion is enhanced and the bonding time decreases when the external pressure changes at appropriate frequency. In order to clarify the enhancement effect of changing the pressure, we examine three cases, i.e., the 1st pressure type is constant pressure, the 2nd type is zero pressure, and the 3rd type is the on-off pressure. Our results suggest the on-off pressure decreases the required time for the perfect bonding if we choose on appropriate frequency. INTRODUCTION Conventional solid-state bonding-process is usually performed in vacuum at high temperature, at which the diffusion is activated. The rate of the bonding process is determined at least by four fundamental mechanisms; the plastic deformation, the creep deformation, the interface diffusion and the volume diffusion. A precise process is possible under the condition of low pressure and low temperature, under which the interface diffusion is dominant. Since the interface diffusion proceeds at a low rate, the bonding process requires an extremely long time under that condition. It is important to decrease the bonding time. We calculate the stress distribution at the interface between the bodies based on Jornson’s theory[1]. In the presence of the adhesion, Johnson showed the relation between the external pressure, the surface deformations and the contact width for the two elastic wavy surfaces, which have sinusoidal undulations. The flux of the interface diffusion is proportional to the gradient of the stress distribution. The stress distribution changes dramatically and the interface diffusion becomes large in the transient state compared to the steady state. The diffusion could be enhanced when the external pressure is changed at appropriate frequency according to the transient behavior. This method examines the enhancement effect and the decrease of the bonding time. We define the external pressure changing at high frequency as ’on-off pressure type’. In a conventional method, the elastic deformation during the bonding process is not perfectly considered[2]. We discuss the advantage of the on-off pressure type considering the elastic deformation during the process. THEORY Model We simulate the solid-state bonding-process for an ideal material in a two-dimensional model (Figure 1). We assume the bodies
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