Table 1.

Summary of M³ patterning capabilities

Pattern	Restrictions	Algorithm	UV exposure
Connected	Eulerian connectivity	Build a doubly-connected edge list (De Berg et al. 2008) and create an Eulerian circuit with Fleury’s algorithm (Fleury 1883)	ET for one exposure
Disconnected	Isolated points	Modification of a TSP approximating path	$\frac{(1+\delta )ET}{n}$ for n exposures
Composite	None known	Handle the disconnected components first and then expose connected components afterwards	ET for one exposure along connected components $\frac{(1+\delta )ET}{2}$ for two exposures at disconnected locations

^aET is the exposure threshold that induces feature creation in the photoresist (75 mJ/cm² ) and δ is an arbitrarily small positive value (e.g. 0.01–0.10) to ensure that exposure saturation is achieved