Flexible mask modulation for controlling atmosphere between mask and substrate and methods of using the same

An apparatus comprising:

• a substrate holder configured to hold a substrate, the substrate holder comprising:
• a first chucking region having a first area;
• and
• an adjacent region extending laterally from the first chucking region, wherein a surface of the adjacent region is on a different plane than a surface of the first chucking region, wherein the adjacent region comprises a top surface with one or more conduit openings;
• a stage configured to hold the substrate holder;
• a superstrate holder configured to hold a superstrate, the superstrate holder comprising a second chucking region having a second area, wherein the second area is larger than the first area, and wherein the superstrate holder faces the substrate holder forming a first gap between the adjacent region surface and the superstrate and a second gap between the substrate and the superstrate;
• and
• a gas supply system configured to supply a gas within the first gap and the second gap through the one or more conduit openings, wherein the superstrate holder alters a shape of the held superstrate to decrease the first gap and increase the second gap, wherein after the superstrate is adjusted into a first shape so that the second gap is larger than the first gap, the superstrate is configured to be adjusted into a second shape so that the second gap is smaller than the first gap before the superstrate is brought in contact with a formable material on the substrate.