The binomial test: a simple tool to identify process problems

The yield distribution of a batch of wafers is an indicator of the type and behavior of defect sources in the manufacturing process. In a stable process, defects generated by these sources are evenly and randomly distributed, repetitive from wafer-to-wafer. The yield distribution of wafers manufactured in such an environment follows the binomial distribution. If, on the other hand, wafers contain defects with systematic patterns that repeat from wafer-to-wafer, the yield distribution tends to be narrower than the binomial distribution. For defect sources that generate systematic wafer-to-wafer variations, the yield distribution widens if compared with the binomial distribution. The binomial distribution can be calculated from the mean yield and the number of dice per wafer. Thus, comparing the actual yield distribution with the corresponding binomial distribution (binomial test) gives the yield improvement engineer a simple first-order indicator of the behavior of defect sources. Since wafer yield data is routinely available from functional production tests, the binomial test can be performed with existing data. This paper describes the principle and use of the binomial test using visual analysis on graphical yield plots of simulated and actual production wafers