Computation of integrated-circuit yields from the distribution of slice yields for the individual devices

This correspondence calculates the average yield
\bar{Y_{N}}
for
N
multiple devices as a function of the average yield (
\bar{Y_{1}}
) of single devices assuming several simple forms of distribution function for slice yields. It shows that the usual calculation
\bar{Y_{N}}
= (
\bar{Y_{1}})^{N}
is too pessmistic by an appreciable factor even when no "within slice" correlation exists. Using an actual distribution of transistor slice yields, the (
\bar{Y_{1}})^{N}
calculation is shown to give a yield which is a factor of 5 too low for groups of eight good devices.