초록
The packaging of the integrated circuits requires knowledge of ceramics and metals to accommodate the fabrication of modules that are used to construct subsystems and entire systems from extremely small components. Composite ceramics (Al$_2$O$_3$-SiO$_2$) were tested for substrates. A stress analysis was conducted for a linear work-hardening metal cylinder embedded in an infinite ceramic matrix. The bond between the metal and ceramic was established at high temperature and stresses developed during cooling to room temperature. The calculations showed that the stresses depend on the mismatch in thermal expansion, the elastic properties, and the yield strength and work hardening rate of the metal. Experimental measurements of the surface stresses have also been made on a Cu/Al$_2$O$_3$-SiO$_2$ceramic system, using an indentation technique. A comparison revealed that the calculated stresses were appreciably larger than the measured surface stresses, indicating an important difference between the bulk and surface residual stresses. However, it was also shown that porosity in the metal could plastically expand and permit substantial dilatational relaxation of the residual stresses. Conversely it was noted that pore clusters were capable of initiating ductile rupture, by means of a plastic instability, in the presence of appreciable tri-axiality. The role of ceramics for packaging of microelectronics will continue to be extremely challenging.