A new defect distribution metrology with a consistent discrete exponential formula and its applications

We have proposed a novel discrete exponential distribution function, which describes defect-count distributions on wafers and/or chips more accurately, especially for near-defect-free conditions. The conventional approach based on a gamma probability density function (g-PDF) is known to fail in terms of expressing defect-free wafers or chips, which always gives 0 PDF value. Since the number of faults/defects should be countable (discrete) and analyzed in terms of a nondefective chip yield, the g-PDF cannot be used due to its inaccuracy in near-defect-free conditions. A new discrete formula which is based on the idea of a discrete exponential PDF has been developed. It describes the situation of the defect-count distribution of near-defect-free wafers well. It is experimentally proved that defect-count distributions are approximated with the new model to within an average error of about 0.01 defects/wafer using film deposition process data