Magnification correction employing out-of-plane distortion of a substrate
The present invention is directed to a method of controlling dimensional relations between an original pattern present in a mold and a recorded pattern formed in a layer of a substrate. In this manner, the size of the recorded pattern may appear to be magnified and/or reduced, when compared to the original pattern. To that end, the method comprises defining a region on the layer in which to produce the recorded pattern. The substrate is bent to produce a contoured surface in the region. Dimensional variations in the original pattern are produced by bending the mold, defining a varied pattern. The contoured surface and the mold are provided to have similar radii of curvatures. The varied pattern is then recorded in the layer. These and other embodiments of the present invention are discussed more fully below.
1. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a surface of a wafer, said method comprising:
defining a region on said surface in which to produce said recorded pattern;
creating dimensional variations in said original pattern by subjecting said mold to tensional stresses, defining a varied pattern;
bending said wafer to produce a contoured surface in said region, with said contoured surface and said mold having similar radii of curvatures, wherein bending said wafer further includes providing said contoured surface with an arcuate shape having a constant radius of curvature, with said mold conforming to said arcuate shape; and
recording said varied pattern in said region on said surface.
2. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a surface of a wafer, said method comprising:
defining a region on said surface in which to produce said recorded pattern;
creating dimensional variations in said original pattern by subjecting said mold to tensional stresses, defining a varied pattern;
recording said varied pattern in said region on said surface; and
bending said wafer to produce a contoured surface in said region, with said contoured surface and said mold having similar radii of curvatures, wherein defining further includes defining a plurality of regions on said surface in which to produce said recorded pattern and bending further includes bending said wafer to provide a plurality of contoured surfaces, each of which has a normal associated therewith centrally disposed therein, and creating further includes providing said mold with a curved profile that is radially and symmetrically disposed about an axis and successively orientating said axis to extend parallel to each said normal associated with each of said plurality of regions.
3. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a surface of a wafer, said method comprising:
defining a region on said surface in which to produce said recorded pattern;
creating dimensional variations in said original pattern by subjecting said mold to tensional stresses, defining a varied pattern;
recording said varied pattern in said region on said surface; and
bending said wafer to produce a contoured surface in said region, with said contoured surface and said mold having similar radii of curvatures, wherein creating further includes providing said mold with a curved profile having a first radius of curvature, and bending further includes providing said contoured surface with an arcuate shape having a second radius of curvature.
4. The method as recited in claim 1 wherein said mold includes a first surface and a first neutral axis, separated therefrom a first distance, and said wafer includes a second surface and a second neutral axis, separated therefrom a second distance, with control of said dimensional variations being dominated by a greater of said first and second distances.
5. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a surface of a wafer, said method comprising:
defining a region on said surface in which to produce said recorded pattern;
creating dimensional variations in said original pattern by subjecting said mold to tensional stresses, defining a varied pattern;
recording said varied pattern in said region on said surface; and
bending said wafer to produce a contoured surface in said region, with said contoured surface and said mold having similar radii of curvatures, wherein creating further includes providing said mold with a curved profile having a first radius of curvature, and bending further includes providing said contoured surface with an arcuate shape having a second radius of curvature, with said second radius of curvature matching said first radius of curvature.
6. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a surface of a wafer, said method comprising:
defining a region on said surface in which to produce said recorded pattern;
creating dimensional variations in said original pattern by subjecting said mold to tensional stresses, defining a varied pattern;
recording said varied pattern in said region on said surface; and
bending said wafer to produce a contoured surface in said region, with said contoured surface and said mold having similar radii of curvatures, wherein creating further includes providing said mold with a curved profile that is radially and symmetrically disposed about an axis to define a first radius of curvature, and bending further includes providing said contoured surface with an arcuate shape radially and symmetrically disposed about said axis to define a second radius of curvature.
7. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a surface of a wafer, said method comprising:
defining a region on said surface in which to produce said recorded pattern;
creating dimensional variations in said original pattern by subjecting said mold to tensional stresses, defining a varied pattern;
recording said varied pattern in said region on said surface; and
bending said wafer to produce a contoured surface in said region, with said contoured surface and said mold having similar radii of curvatures, wherein creating further includes providing said mold with a curved profile that is radially and symmetrically disposed about an axis to define a first radius of curvature, and bending further includes providing said contoured surface with an arcuate shape radially and symmetrically disposed about said axis to define a second radius of curvature, with said second radius of curvature matching said first radius of curvature.
8. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a surface of a wafer, said method comprising:
defining a region on said surface in which to produce said recorded pattern;
creating dimensional variations in said original pattern by subjecting said mold to tensional stresses, defining a varied pattern;
recording said varied pattern in said region on said surface; and
bending said wafer to produce a contoured surface in said region, with said contoured surface and said mold having similar radii of curvatures, wherein creating further includes providing said mold with a curved profile, while minimizing shear forces on said wafer, and bending further includes providing said contoured surface with an arcuate shape while minimizing shear forces on said wafer.
9. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a layer of a wafer, said method comprising:
defining a region on said layer in which to produce said recorded pattern;
bending said wafer to produce a contoured surface in said region, wherein bending said wafer further includes providing said contoured surface with an arcuate shape having a constant radius of curvature, with said mold conforming to said arcuate shape;
creating dimensional variations in said original pattern by bending said mold, defining a varied pattern, with said contoured surface and said mold having similar radii of curvatures; and
recording said varied pattern in said layer.
10. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a layer of a wafer, said method comprising:
defining a region on said layer in which to produce said recorded pattern;
bending said wafer to produce a contoured surface in said region;
creating dimensional variations in said original pattern by bending said mold, defining a varied pattern, with said contoured surface and said mold having similar radii of curvatures; and
recording said varied pattern in said region on said layer, wherein defining further includes defining a plurality of regions on said layer in which to produce said recorded pattern and bending further includes bending said wafer to provide a plurality of contoured surfaces, each of which has a normal associated therewith centrally disposed therein, and creating further includes providing said mold with a curved profile that is radially and symmetrically disposed about an axis and successively orientating said axis to extend parallel to each said normal associated with each of said plurality of regions.
11. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a layer of a wafer, said method comprising:
defining a region on said layer in which to produce said recorded pattern;
bending said wafer to produce a contoured surface in said region;
creating dimensional variations in said original pattern by bending said mold, defining a varied pattern, with said contoured surface and said mold having similar radii of curvatures; and
recording said varied pattern in said region on said layer, wherein creating further includes providing said mold with a curved profile, having a first radius of curvature, and bending further includes providing said contoured surface with an arcuate shape having a second radius of curvature.
12. The method as recited in claim 9 wherein said mold includes a first surface and a first neutral axis, separated therefrom a first distance, and said wafer includes a second surface and a second neutral axis, separated therefrom a second distance, with magnification control being defined by a greater of said first and second distances.
13. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a layer of a wafer, said method comprising:
defining a region on said layer in which to produce said recorded pattern;
bending said wafer to produce a contoured surface in said region;
creating dimensional variations in said original pattern by bending said mold, defining a varied pattern, with said contoured surface and said mold having similar radii of curvatures; and
recording said varied pattern in said region on said layer, wherein creating further includes providing said mold with a curved profile having a first radius of curvature, and bending further includes providing said contoured surface with an arcuate shape having a second radius of curvature, with said second radius of curvature matching said first radius of curvature.
14. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a layer of a wafer, said method comprising:
defining a region on said layer in which to produce said recorded pattern;
bending said wafer to produce a contoured surface in said region;
creating dimensional variations in said original pattern by bending said mold, defining a varied pattern, with said contoured surface and said mold having similar radii of curvatures; and
recording said varied pattern in said region on said layer, wherein creating further includes providing said mold with a curved profile that is radially and symmetrically disposed about an axis to define a first radius of curvature, and bending further includes providing said contoured surface with an arcuate shape radially and symmetrically disposed about said axis to define a second radius of curvature.
15. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a layer of a wafer, said method comprising:
defining a region on said layer in which to produce said recorded pattern;
bending said wafer to produce a contoured surface in said region;
creating dimensional variations in said original pattern by bending said mold, defining a varied pattern, with said contoured surface and said mold having similar radii of curvatures; and
recording said varied pattern in said region on said layer, wherein creating further includes providing said mold with a curved profile that is radially and symmetrically disposed about an axis to define a first radius of curvature, and bending further includes providing said contoured surface with an arcuate shape radially and symmetrically disposed about said axis to define a second radius of curvature, with said second radius of curvature matching said first radius of curvature.
16. A method of controlling relative dimensions between an original pattern present in a mold and a recorded pattern formed in a layer of a wafer, said method comprising:
defining a region on said layer in which to produce said recorded pattern;
bending said wafer to produce a contoured surface in said region;
creating dimensional variations in said original pattern by bending said mold, defining a varied pattern, with said contoured surface and said mold having similar radii of curvatures; and
recording said varied pattern in said region on said layer, wherein creating further includes providing said mold with a curved profile, while minimizing shear forces on said wafer, and bending further includes providing said contoured surface with an arcuate shape while minimizing shear forces on said wafer.