Variable-etch-depth gratings

1. A method comprising:

forming a patterned etch mask on a substrate;

depositing a photoresist material layer on the patterned etch mask, the photoresist material layer sensitive to ultra-violet (UV) light and having a linear response to UV light dose;

exposing the photoresist material layer to UV light through a variable transparency photomask;

developing the photoresist material layer exposed to the UV light to form a patterned photoresist layer having a non-uniform thickness;

etching the patterned photoresist layer and the substrate to obtain a grating having a non-uniform etch depth in the substrate, wherein the patterned photoresist layer is characterized by an etch rate comparable to an etch rate of the substrate; and

removing the patterned photoresist layer and the patterned etch mask from the substrate.

2. The method of claim 1 , further comprising at least one of:

depositing, before depositing the photoresist material layer, a first anti-reflective coating layer on the patterned etch mask, or

depositing, after depositing the photoresist material layer, a second anti-reflective coating layer on the photoresist material layer.

3. The method of claim 1 , wherein etching the patterned photoresist layer and the substrate comprises:

etching the patterned photoresist layer and the substrate at a slant angle greater than 10° with respect to a surface normal of the substrate.

4. The method of claim 3 , wherein the slant angle is between 30° and 70°.

5. The method of claim 1 , wherein the photoresist material layer is sensitive to light having a wavelength shorter than 300 nm, 250 nm, 193 nm, or 157 nm.

6. The method of claim 1 , wherein the etch rate of the patterned photoresist layer is between 0.5 and 5 times of the etch rate of the substrate in a same etching process.

7. The method of claim 1 , wherein a depth of an exposed portion of the photoresist material layer is a linear function of the UV light dose.

8. The method of claim 1 , wherein the photoresist material layer includes a positive-tone photoresist.

9. The method of claim 1 , wherein the photoresist material layer includes Poly(methyl methacrylate) (PMMA) sensitized with a photosensitive group.

10. The method of claim 9 , wherein the photosensitive group includes at least one of:

an acyloximino group;

methacrylonitrile;

terpolymer of methyl methacrylate;

oximino methacrylate;

benzoic acids;

N-acetylcarbazole; or

indenone.

11. The method of claim 1 , wherein the photoresist material layer includes at least one of:

poly(methyl methacrylate)-r-poly(tert-butyl methacrylate)-r-poly(methyl methacrylate) and a photo acid generator;

poly(methyl methacrylate)-r-poly(methacrylic acid);

poly(α-methylstyrene-co-methyl chloroacrylate) and an acid generator;

polycarbonate and a photo acid or base generator;

polylactide and a photo acid or base generator; or

polyphthalaldehyde and a photo acid generator.

12. The method of claim 1 , wherein the non-uniform etch depth in the substrate includes at least 8 different depth levels.

13. The method of claim 1 , wherein a maximum depth of the non-uniform etch depth in the substrate is greater than 100 nm.

14. The method of claim 1 , wherein etching the patterned photoresist layer and the substrate includes etching the patterned photoresist layer and the substrate using at least one of:

an oxygen source including O 2 , N 2 O, CO 2 , or CO;

a nitrogen source including N 2 , N 2 O, or NH 3 ; or

ions with an energy between 100-500 eV.

15. The method of claim 1 , wherein the variable transparency photomask includes a gray-scale photomask.

16. The method of claim 15 , wherein the gray-scale photomask includes at least 8 different transmissivity levels.

17. A slanted surface-relief structure for waveguide display, the slanted surface-relief structure comprising:

a substrate; and

a slanted surface-relief optical grating in the substrate, the slanted surface-relief optical grating having a flat top surface and including a plurality of grating ridges and a plurality of grating grooves, each of the plurality of grating grooves characterized by a corresponding depth,

wherein depths of the plurality of grating grooves include at least 8 different depth levels and vary in two directions across the slanted surface-relief optical grating according to a predetermined profile; and

wherein a slant angle of at least one grating ridge in the plurality of grating ridges is greater than 30° with respect to a surface normal of the substrate.

18. The slanted surface-relief structure of claim 17 , wherein the depths of the plurality of grating grooves range from 0 nm to greater than 100 nm.

19. The slanted surface-relief structure of claim 17 , wherein the corresponding depth of a grating groove in the plurality of grating grooves varies across the slanted surface-relief optical grating.

20. The slanted surface-relief structure of claim 17 , wherein the slanted surface-relief optical grating has different grating duty cycles at different regions of the slanted surface-relief optical grating.

21. The slanted surface-relief structure of claim 20 , wherein the slanted surface-relief optical grating is characterized by a duty cycle greater than 70%.

22. The slanted surface-relief structure of claim 20 , wherein the slanted surface-relief optical grating is characterized by a duty cycle less than 30%.

23. The slanted surface-relief structure of claim 17 , wherein the slanted surface-relief optical grating has different grating periods at different regions of the slanted surface-relief optical grating.

24. A photoresist material for fabricating a variable-etch-depth grating, wherein:

the photoresist material is sensitive to light with a wavelength shorter than 300 nm;

the photoresist material is characterized by an etch rate that is between 0.5 and 5 times of an etch rate of a substrate; and

the photoresist material is characterized by a linear response to UV light dose such that a depth of an exposed portion of the photoresist material is a linear function of the UV light dose.

25. The photoresist material of claim 24 , wherein the photoresist material includes at least one of:

Poly(methyl methacrylate) (PMMA) sensitized with a photosensitive group;

poly(methyl methacrylate)-r-poly(tert-butyl methacrylate)-r-poly(methyl methacrylate) and a photo acid generator;

poly(methyl methacrylate)-r-poly(methacrylic acid);

poly(α-methylstyrene-co-methyl chloroacrylate) and an acid generator;

polycarbonate and a photo acid or base generator;

polylactide and a photo acid or base generator; or

polyphthalaldehyde and a photo acid generator.