What does this equation mean?

Frederick Chen’s analysis of a real 3-nanometer via layer measured this directly: at typical exposure conditions (roughly 60–89 mJ/cm² depending on resist chemistry), the observed missing-via rate came in at the parts-per-million level — “many orders of magnitude higher than expected from basic estimates” that treat each pixel’s exposure as statistically independent [ 3 ] . The gap between the naive estimate and the measured rate is explained by correlation between neighboring exposed pixels: a defect does not need every pixel in a feature to fail independently, it needs a contiguous cluster of neighboring pixels to under- or over-expose together, which happens far more often than independent-pixel statistics predict [ 3 ] . The practical lesson for a process engineer is blunt: doubling the dose does not buy proportional improvement. Raising exposure dose reduces the variance of the delivered dose roughly as the square root of photon count, so doubling dose only shrinks statistical spread to about 70% of its previous value — and doubling dose is expensive in throughput, in resist heating and outgassing, and in optics contamination, so the achievable stochastic-defect floor at a given throughput target is a genuine economic trade, not a solved problem. This is why in-line dose control is treated as a first-class process loop rather than a machine setting checked once at installation: the scanner’s dose sensors and the fab’s CD (critical dimension) metrology are in continuous conversation, adjusting exposure energy lot to lot to hold the delivered dose inside a tight band around the target the resist chemistry was qualified at.