Robust optimization to generate drop patterns in imprint lithography which are tolerant of variations in drop volume and drop placement
View Patent ↗Imprint lithography may comprise generating a fluid map, generating a fluid drop pattern, and applying a fluid to a substrate according to the fluid drop pattern. The fluid drop pattern may be generated using a stochastic process such as a Monte Carlo or structured experiment over the expected range of process variability for drop locations and drop volumes. Thus, variability in drop placement, volume, or both may be compensated for, resulting in surface features being substantially filled with the fluid during imprint.
1. A method of generating a fluid drop pattern, the method comprising:
selecting a fluid dispense system for positioning a plurality of drops of a fluid on a substrate;
selecting an imprinting surface comprising features having a volume; and
generating an optimized fluid drop pattern of the plurality of drops on the substrate, such that the plurality of drops of the fluid are distributed to locations on the substrate based on a modified Voronoi diagram incorporating a robust optimization procedure to accommodate for variation of drop location, drop volume, or both; wherein generating the optimized fluid drop pattern comprises:
locating edges in a fluid map corresponding the imprinting surface to form an edge map;
applying a threshold to the edge map;
computing a volume weight between a generator point and a volumetric pixel;
initializing a scaling factor;
performing a line scan from a generator point to the fluid map volumetric pixel;
determining a transition type when an edge is crossed;
multiplying the scaling factor by a weight associated with the transition type;
calculating a distance from the generator point to the volumetric pixel;
multiplying the distance by a scale factor to yield a corrected distance;
building a modified Voronoi diagram based on the corrected distance;
updating the modified Voronoi diagram to incorporate a stochastic optimization, and
further comprising dispensing the fluid in accordance with the optimized fluid drop pattern.
2. The method of claim 1 wherein the modified Voronoi diagram comprises a weight associated with each generator location in the Voronoi diagram.
3. The method of claim 1 wherein the dispensing comprises delivering from the fluid dispense system a multiplicity of drops of substantially equal volume to the substrate.
4. The method of claim 1 , wherein the robust optimization comprises a Monte Carlo or structured experiment with a fractional factorial design.
5. The method of claim 1 , wherein the optimized fluid drop pattern comprises adjusting drop location based at least in part on a volume of the features.
6. The method of claim 1 , further comprising replicating the imprinting surface by substantially filling the features of the imprinting surface with polymerizable material.
7. The method of claim 1 , further comprising translating the fluid drop pattern to form a set of shifted fluid drop patterns.
8. The method of claim 7 , further comprising superimposing the shifted fluid drop patterns to form a superimposed drop pattern.