The mask error factor in optical lithography

The primary cause of greater than unity mask error factor (MEF) is degradation of image integrity. Mathematical description of image formation reveals the gradual loss of image shape control by photomask features as the critical dimension decreases below 0.8(λ/NA). The growing contribution of mask critical dimension error to line-width variation prompts generalization of the conventional two-dimensional (2-D) exposure-defocus window (ED window) to a three-dimensional (3-D) mask-exposure-defocus volume (ED volume), adding mask tolerance to exposure latitude and depth-of-focus as the important parameters of a process. The increase in MEF with feature nesting means that the relative importance of sources of line-width variation changes with pattern pitch. Mask improvement is the most effective means to reduce line-width variation for dense features, but lens quality is the most significant factor affecting line-width control for sparse patterns. The approximately 20% higher MEF of dark-field masks, low MEF of alternating phase-shifting masks, and relatively high MEF of assist features all have ramifications on lithography strategies for printing sparse lines. The MEF does not simply indicate a need for high-quality masks, it also sheds light on the critical areas in which improvements are needed for successful lithography, and the disciplines that need to cooperate for successful device fabrication