Estimation of contamination levels in a chemical recirculation system for semiconductor wafer processing

A theoretical analysis is presented of the contamination buildup in a generic chemical recirculation system used in semiconductor wafer processing. Mathematical expressions are derived for useful quantities, such as the maximum possible concentration of contaminant in the recirculation tank and the number of processes required to reach any particular concentration level. Recirculation systems are analyzed wherein the amount of chemical used and the amount of contaminant picked up per process cycle are either constant or process dependent. Sample calculations are presented for the two cases. The mathematical equations derived in the study are presented in a form that can be easily extended to the analysis of more complex recirculation systems and the optimization of chemical supplies and processes for maximum performance.