Stress patterning systems and methods for manufacturing free-form deformations in thin substrates

1. A device, comprising:

a substrate; and

a stressed layer disposed on a first surface of the substrate, the stressed layer comprising:

a first set of patterns having a predetermined geometry, size, and arrangement selected to control an equibiaxial stress field of the stressed layer, wherein the equibiaxial stress field varies in magnitude over the first surface of the substrate, and

a second set of patterns etched into the first set of patterns and the substrate, the second set of patterns comprising a plurality of substantially parallel lines arranged to control at least a uniaxial stress field of the stressed layer, wherein the uniaxial stress field varies in magnitude over the first surface of the substrate.

2. The device of claim 1 wherein the stressed layer comprises a thermal oxide.

3. The device of claim 1 wherein the stressed layer comprises a second stressed layer disposed on a second surface of the substrate opposite from the first surface.

4. The device of claim 1 wherein the magnitude and an orientation of the uniaxial stress field varies according to a position on the substrate.

5. The device of claim 1 wherein the plurality of substantially parallel lines comprise a plurality of substantially parallel grating bars, wherein ones of the plurality of grating bars have an aspect ratio selected to induce a predetermined uniaxial stress within the stressed layer, wherein the aspect ratio for a grating bar is defined as a ratio of a height of the grating bar divided by a width of the grating bar.

6. The device of claim 5 wherein the aspect ratio is greater than or equal to 0.1.

7. The device of claim 1 wherein the first set of patterns comprises one or more geometric regions.

8. The device of claim 7 wherein the one or more geometric regions have varying dimensions.

9. The device of claim 7 wherein the second set of patterns comprises a first plurality of substantially parallel lines etched into a first one of the one or more geometric regions and a second plurality of substantially parallel lines etched into a second one of the one or more geometric regions, wherein the first and second pluralities of substantially parallel lines have different orientations.

10. The device of claim 1 wherein the substrate comprises a silicon wafer.

11. A method for fabricating a device, the method comprising:

providing a substrate having a stressed layer disposed on a first surface of the substrate;

etching a first set of patterns into the stressed layer, the first set of patterns having a predetermined geometry, size, and arrangement selected to control an equibiaxial stress field of the stressed layer, wherein the equibiaxial stress field varies in magnitude over the first surface of the substrate; and

etching a second set of patterns into the first set of patterns and the substrate, the second set of patterns comprising a plurality of substantially parallel lines arranged to control at least a uniaxial stress field of the stressed layer, wherein the uniaxial stress field varies in magnitude over the first surface of the substrate.

12. The method of claim 11 wherein etching the second set of patterns comprises:

using a first method to etch the second set of patterns into the stressed layer; and

using a second method to etch the second set of patterns into the substrate.

13. The method of claim 12 wherein using the first method comprises using wet etching.

14. The method of claim 12 wherein using the second method comprises using one of reactive ion etching or laser cutting.

15. The method of claim 12 wherein using the first method comprises using laser cutting.

16. The method of claim 11 wherein etching the second set of patterns comprises etching the second set of patterns into the substrate to a depth dictated by a predetermined aspect ratio.