Knowledge Center
Knowledge Center

Stochastics, Stochastic-Induced Defects

Random variables that cause defects on chips during EUV lithography.


In extreme ultraviolet (EUV) lithography, stochastics are events that have random variables. These variations, called stochastic effects, sometimes cause unwanted defects and pattern roughness in chips. Both can impact the performance of a chip or even cause a device to fail.

In EUV, stochastic effects are a major concern, and they have become more problematic at each node. The good news is that the industry has found ways to mitigate the problem by improving the resists and processes. But stochastic-induced defects can crop up, creating headaches for foundry vendors and their customers alike.

Sometime around the 10nm or 7nm nodes, stochastic variations became the dominant source of variations in patterning. That’s mainly because all the other sources of variation kept getting smaller. Stochastic variations didn’t — or at least it didn’t shrink as much or as fast. It’s becoming a larger percentage of the total budget that we allow for variations.

In operation, an EUV scanner is supposed to create various patterns in chips, such as tiny contact holes, lines, and vias, with good uniformity. But at times, the scanner may fail to pattern a required line, called a line break. The scanner can sometimes fail to print one or more of the contact holes, called a missing contact. In other cases, the process causes one or more holes to merge, sometimes called “kissing contacts.”

Stochastics-induced defects are line breaks, missing contacts, and kissing contacts are considered stochastic-induced defects. Another stochastic effect is line-edge roughness (LER). LER is defined as a deviation of a feature edge from an ideal shape. It is problematic because it doesn’t scale with the feature size.