Apparatus for use in forming an adaptive layer and a method of using the same

1. An apparatus comprising:

a logic element, wherein the logic element

obtains a raw overlay error between a first patterned layer and a second patterned layer over a first substrate, wherein the first patterned layer was patterned using a first substrate chuck, and the second patterned layer was patterned using a second substrate chuck;

determines a difference in flatness profiles associated with the first substrate chuck and the second substrate chuck, wherein the difference in flatness profiles is based at least in part on the raw overlay error between the first patterned layer and the second patterned layer;

generates information corresponding to an adaptive layer to be formed over a second substrate in response to the difference in flatness profiles associated with the first substrate chuck and the second substrate chuck; and

removes an imprint distortion contribution that corresponds to an imprint distortion associated with the difference in the flatness profiles in a first imprint template used to form the first patterned layer, a second imprint template used to form the second patterned layer, or the first and second imprint templates.

2. The apparatus of claim 1 , wherein the logic element is further configured to remove an alignment contribution that corresponds to a misalignment between the first and second patterned layers.

3. The apparatus of claim 1 , wherein the logic element is further configured to remove a mean field signature, wherein the mean field signature corresponds to repetitive errors that are averaged over all fields.

4. The apparatus of claim 1 , wherein the logic element is further configured to remove a flatness induced distortion contribution associated with the first and second substrate chucks.

5. The apparatus of claim 1 , wherein the information corresponding to an adaptive layer includes a fluid droplet pattern associated with the adaptive layer.

6. An apparatus comprising a logic element configured to:

obtain a raw overlay error between a first patterned layer and a second patterned layer over a first substrate, wherein the first patterned layer was patterned using a first substrate chuck, and the second patterned layer was patterned using a second substrate chuck;

generate information corresponding to an adaptive layer to be formed over a second substrate based at least in part on a difference in flatness profiles associated with a first substrate chuck and the second substrate chuck;

remove an alignment contribution corresponds to a misalignment between the first and second patterned layers;

remove an imprint distortion contribution that corresponds to an imprint distortion associated with the difference in the flatness profiles in a first imprint template used to form the first patterned layer, a second imprint template used to form the second patterned layer, or the first and second imprint templates; and

remove a flatness induced distortion contribution associated with the second substrate chuck.

7. The apparatus of claim 6 , wherein the logic element is further configured to:

remove a mean field signature, wherein the mean field signature corresponds to repetitive errors that are averaged over all fields.

8. A method, comprising:

determining a difference in flatness profiles associated with a first substrate chuck and a second substrate chuck; and

forming an adaptive layer over a first substrate, wherein the adaptive layer has a thickness profile that is a function of an inverse of the difference in the flatness profiles, and wherein determining the difference in flatness profiles comprises:

measuring a raw overlay error between a first patterned layer and a second patterned layer over a second substrate, wherein the first patterned layer was patterned using the first substrate chuck, and the second patterned layer was patterned using the second substrate chuck;

removing an alignment contribution that corresponds to a misalignment between the first and second patterned layers;

removing an imprint distortion contribution that corresponds to an imprint distortion associated with a first imprint template used to form the first patterned layer, a second imprint template used to form the second patterned layer, or the first and second imprint templates; and

estimating a distortion due to differences in flatness profiles of the first and second substrate chucks.

9. The method of claim 8 , wherein determining the difference in flatness profiles further comprises removing a mean field signature, wherein the mean field signature corresponds to repetitive errors that are averaged over all fields.

10. The method of claim 9 , wherein determining the difference in flatness profiles further comprising determining the mean field signature associated with a first imprint template used to form the first patterned layer, a second imprint template used to form the second patterned layer, or the first and second imprint templates.

11. The method of claim 8 , wherein determining the difference in flatness profiles further comprises removing a flatness induced distortion contribution associated with the first and second substrate chucks.

12. The method of claim 11 , wherein the estimated distortion corresponds to the flatness induced distortion contribution.

13. The method of claim 12 , wherein determining the difference in flatness profiles further comprises removing a mean field signature, wherein the mean field signature corresponds to repetitive errors that are averaged over all fields.

14. The method of claim 8 , further comprising:

forming a formable material over the adaptive layer and the current substrate.