Thermal stress analysis for rapid thermal processor

Within the framework of linearized thermoelasticity theory, the temperature and thermal stresses on the wafer for the rapid thermal processor are solved by using the finite-difference approach and a trapezoidal integration technique, respectively. Although the equations governing the present thermoelastic system are coupled in nature, the temperature can still be obtained independently due to the fact that the coupling term is negligible as a result of the strain rate being extremely small as compared with unity. Based on the maximum shear stress failure criterion, the calculated results show that material failure always occurs at the edge of the wafer at the beginning of cooling processes. Furthermore, the maximum stress control scheme is proved to be more efficient that it can significantly reduce the required cooling time and thermal budgets. Thus, the conventional constant cooling-rate control scheme or linear temperature ramp-down scheme is not appropriate for the rapid thermal processor.