Markov G/G/s model adaptation to factory operational curve though exponential correlation

In the current highly competitive environment of the NAND Flash/NVM/NOR flash market, cycle times (CT) are the key to success. CT performance depends on process time reduction, tool set (group of similar tool running same operations) performance, and WIP (Work In Process) management policy, but mainly on factory (fab) loading. Understanding factory CT variability is critical to meet customer commitments while maintaining optimized inventory levels. Tool set CT (sum of the operations step CT run on the tool set) is usually modeled by the P/K equation, a fundamental equation that provides insights into what affects CT. We extended this equation to model factory CT. The curve CT vs. loading is called the tool set operational curve. In this paper, we will define the logarithm factory operational curve based on 35 weeks of 200mm factory CT performance running at 65nm, during variable loading and capacity change. The operational curve was also validated using factory simulation.