Capacity planning with sequential two-level time constraints in the back-end process of wafer fabrication

A time constraint is a queue-time boundary that is set between particular sequential operations to ensure final product yield. These time boundaries, called ‘sequential time constraints’, can be found in a series of operations on the back-end of wafer fabrication. Wafers exceeding the time constraints are traced through the fabrication process, but generally pass through the remaining processes. Nonetheless, it is a waste of capacity to continue processing wafers with unacceptable yield. Unfortunately, these unacceptable wafers cannot be identified before the wafer acceptance test using the current control policy. This work proposes a control rule for two-level time constraints with capacity planning methodology under this rule. Wafers exceeding the lower time constraints will be treated as normal wafers; however, once wafers exceed the upper time constraint, they will be scrapped immediately. In the capacity planning model, a GI/G/m queuing network is applied to determine the required number of machines. By pre-setting target yields, the rates of wafers being marked or scrapped can be controlled. Furthermore, a novel scheme–regarding machine failures as irregular customers–is introduced to describe the effect of service interruptions. The results show that the proposed control rule and capacity planning model can more effectively resolve the issues of sequential time constraints. Moreover, the results of the analysis indicate that the current capacity expansion policy of the semiconductor industry should be re-examined.