In advanced semiconductor lithography, many process variations are statistical rather than deterministic. Even under identical process conditions, the printed results may vary due to fundamental physical and chemical randomness. These phenomena are commonly referred to as stochastic effects.
As feature sizes continue to shrink, especially for critical layers, lithography outcomes can no longer be described by a single expected value. Instead, they must be understood as distributions characterized by variability and tail risk.
Light exposure is quantized at the photon level. For a given exposure dose, the number of photons arriving at a local region follows a statistical distribution. As a result, local dose fluctuations occur even when the global dose is fixed.
Photoresist reactions such as acid generation, diffusion, and quenching occur at the molecular scale. These reactions are inherently random, leading to local variations in feature edges and critical dimensions.
The combined effect of photon and resist stochasticity can result in random printing failures. Examples include missing contacts, broken lines, or unintended bridges. These defects do not appear at fixed locations and cannot be predicted deterministically.