 Solution

Finite numerical aperture and diffraction remove high spatial frequencies from a mask image. Neighboring features modify the aerial intensity, and the photoresist threshold turns this blurred intensity into biased edges, shortened lines and rounded corners. optical proximity correction deliberately predistorts the mask: line-end extensions and small serifs can compensate for local loss of exposure, while other edges are moved back where exposure spreads too far. The correction is calibrated for illumination, resist and focus; it does not restore arbitrarily high lost spatial frequencies.

double patterning separates a dense target pattern into two sparser patterns, each printable within the single-exposure process window. Two exposures with an intervening pattern-fixing or transfer step combine their features on the wafer. For regular lines, alternating line assignment can halve the final pitch while each exposure retains a larger pitch. optical proximity correction corrects local image bias; double patterning divides the density burden between exposures. Overlay error and the minimum printable isolated feature still constrain the result. Simply exposing the same unmodified resist twice without an appropriate process separation does not give the same independent thresholding.