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

A theoretical analysis is presented of the contamination buildup in a gener ic chemical recirculation system used in semiconductor wafer processing. Ma thematical expressions are derived for useful quantities, such as the maxim um possible concentration of contaminant in the recirculation tank and the number of processes required to reach any particular concentration level, R ecirculation systems are analyzed wherein the amount of chemical used and t he amount of contaminant picked up per process cycle are either constant or process. dependent. Sample calculations are presented for the two cases. T he mathematical equations derived in the study are presented in a form that can be easily extended to the analysis of more complex recirculation syste ms and the optimization of chemical supplies and processes for maximum perf ormance.