In the previous chapters we described light and photoresist properties by continuous variables. Lithography in the range of a few tens of nanometers and below exhibits several effects and observations that cannot be explained by such a continuous description. Instead, the discrete nature of energy (light) and matter (photoresist) and the randomness of related events have to be recognized to understand stochastic phenomena such as the roughness of printed feature edges, small local variations of size and placement of nominally identical features, and rare non-systematic printing errors. This chapter provides an introduction to stochastic effects in advanced lithography.

An overview of the important discrete variables and processes, resulting lithographic phenomena, modeling approaches, and observed dependencies is presented. We will explain how to comprehend the statement of Chris Mack [1] that stochastic effects define the ultimate limits of lithography. The last section discusses several proposed mitigation strategies, especially the development and application of novel photoresist materials, to push this limit as far as possible. Numerous references for an in-depth study of this topic are provided.