Wafer fabrication yield learning and cost analysis based on in-line inspection

Wafer fabrication is characterised with advanced equipment, complex processes and high cost. Good production output, measured by yield given total throughput, should rapidly increase while considering the associated cost. Yield improvement models based on inspection usually consider the effect of excursion monitoring, while this work considers the effect of learning from experience as well. It assumes a production model where each machines output is inspected via wafers it processes, triggering repair if required. The yield improvement is modelled as a function of machines quality performance, accumulated inspections, inspection capacity and inspection rate. It exhibits a sigmoid shape curve with slow rise in startup, acceleration in ramp and almost a plateau in high volume manufacturing. Higher inspection rate enables more inspections over time, faster learning and higher yield. Yet, higher inspection rate at constant capacity prolongs the response time and can further drive lower yield. Clearly, higher inspection capacity enables faster yield improvement, but also increases equipment and operations costs. The cost analysis developed here illustrates the preferred inspection capacity and inspection rate, for minimising the overall cost combined of yield loss and inspection cost. It also shows preference to error with higher, rather than with lower, inspection capacity.