Method and apparatus for embossing a deformable body
A deformable body is embossed using a stamp as a function of a pressure distribution. The pressure distribution is obtained by running a deformation model determined based on convolving a contact pressure distribution with a mechanical response of a surface topography of the deformable body and convolving the pressure distribution with a point load response of the stamp.
1. A method of embossing with a stamp a deformable body comprising a deformable layer on a substrate, the method comprising:
running a deformation model based on convolving a contact pressure distribution with a mechanical response of a surface topography of the deformable layer and convolving the contact pressure distribution with a point load response of the stamp; and
embossing the deformable body using the stamp as a function of the deformation model.
2. The method of claim 1 wherein the deformation model is further based on convolving the contact pressure distribution with a point load response of the substrate.
3. The method of claim 1 further including determining the point load response of the stamp based on bending of the stamp.
4. The method of claim 3 further including determining the bending of the stamp based on thickness of the stamp.
5. The method of claim 4 further including determining the bending of the stamp based on elasticity of the stamp.
6. The method of claim 3 further including determining the point load response of the stamp based on indentation of the stamp.
7. The method of claim 1 wherein the deformable body includes a polymeric layer comparable in thickness to lateral dimensions of features being embossed.
8. The method of claim 1 wherein the deformable body includes a polymeric layer of thickness substantially less than lateral dimensions of features being embossed.
9. The method of claim 1 further including determining the contact pressure distribution based on elastic deflections of stamp and substrate.
10. The method of claim 1 further including determining the contact pressure distribution based on stamp indentation and substrate indentation.
11. The method of claim 1 further including determining the contact pressure history distribution based on deformations of a layer of the deformable body.
12. The method of claim 1 further including determining the contact pressure distribution based on a zero-mean pressure distribution needed to bring all surfaces of the layer of the deformable body into contact with the stamp.
13. The method of claim 1 further including determining the contact pressure distribution based on a zero-mean pressure distribution needed for an incremental displacement of the stamp into the deformable body.
14. The method of claim 1 further including determining the contact pressure distribution based on a spatial variation of thickness of the layer of the deformable body.
15. The method of claim 1 further including determining the contact pressure distribution based on the point load response and an average pressure applied to the stamp.
16. The method of claim 1 further including determining the mechanical response of the surface topography of the deformable body based on an average layer thickness of layers of the deformable body.
17. The method of claim 1 wherein the mechanical response of the surface topography of the deformable body is anisotropic.
18. The method of claim 1 wherein the mechanical response of the surface topography is a spatial response.
19. The method of claim 18 wherein the mechanical response of the surface topography is a temporal response.