MEF in Theory and Practice

Ruth DeJule, Associate Editor -- Semiconductor International, 11/1/1999

The mask error enhancement factor (MEF) represents an additional distortion that must be considered in lithography, especially sub-wavelength lithography. As linewidths become significantly smaller than the exposure wavelength, the wafer CD becomes significantly different from the target CD, until the process fails entirely. The MEF represents the ratio of the wafer CD change to the corresponding change in the reticle CD, with an MEF of 1.0 indicating perfect linearity. MEF values as large as 8 have been observed, undermining the practical adoption of OPC and other resolution enhancement technologies that require small, controlled changes on the reticle. At this year's BACUS meeting in Monterey, Calif., Mentor Graphics (San Jose, Calif.) and FINLE (Austin, Texas) presented their examination of the underlying principle behind the MEF to gain a better understanding of the phenomenon. Comparing theoretical predictions to simulations, and in some cases to actual experiments, the results proved interesting.

Not surprisingly, the theoretical predictions were shown to be over-optimistic. Instead of falling off near 100 nm, as some theoretical predictions would suggest, DUV lithography in practice was limited to 170 nm for isolated lines and 300 nm for isolated posts because of resist thic kness and etch effects, according to Dr. Frank Schellenberg, product marketing manager at Mentor Graphics. This points out the limitation in relying solely on aerial image simulations as a predictor of practical process latitude and yield.

MEF typically is viewed as characteristic of a particular process. However, Schellenberg and FINLE's Chris Mack also looked at the MEF for isolated and dense lines of the same CD, and found surprising differences. While the MEF for isolated features was always larger than 1.0, the MEF for dense (1:1 duty cycle) lines was significantly smaller for features ranging from 248 nm (exposure wavelength) to 400 nm (Table). This creates a 'MEF gap' in which isolated lines are far more sensitive to reticle errors than dense features. 'This might explain why practical reports of MEF can differ widely, depending on the application -- for example, DRAM and ASIC', said Schellenberg. The consequences for OPC are not lost on the authors, who point out that the emphasis on sensitivity to iso-dense bias in OPC actually may be sensitivity to the iso-dense MEF difference in practice. Careful characterization of the MEF under these different conditions will become a necessary part of reticle enhancement strategies as Moore's Law continues to drive features smaller.