Light-emitting device with patterned substrate

1. A lighting device comprising:

a substrate comprising a plurality of holes, wherein the holes extend from a top surface of the substrate;

a semiconductor structure grown on the top surface of the substrate, the semiconductor structure comprising a light emitting layer disposed between an n-type region and a p-type region, a portion of the semiconductor structure being disposed in the holes; and

a non-III-nitride material disposed within the plurality of holes and forming a gradient index optical interface between the semiconductor structure and the substrate, the top surface of the substrate being free of the non-III-nitride material, wherein the gradient index optical interface smoothly transitions from a first refractive index to a second refractive index between the semiconductor structure and the substrate, the second refractive index being closer to a refractive index of the substrate than is the first refractive index.

2. The lighting device of claim 1 wherein the plurality of holes have a triangular cross section.

3. The lighting device of claim 1 wherein the non-III-nitride material includes a stack of layers that forms the gradient index optical interface between the semiconductor structure and the substrate.

4. The lighting device of claim 1 wherein the plurality of holes have a width at the top surface between 1 μm and 20 μm.

5. The lighting device of claim 1 wherein the plurality of holes extend into the substrate a depth of between 1 μm and 20 μm.

6. The lighting device of claim 1 wherein a spacing between centers of nearest neighbor holes is between 2 μm and 50 μm.

7. The lighting device of claim 1 wherein the plurality of holes are arranged in an array.

8. The lighting device of claim 1 wherein an average of between 1 and 2 holes is formed in every 3 μm by 3 μm area of the substrate.

9. A lighting device comprising:

a sapphire substrate comprising a plurality of holes extending from a flat surface of the substrate, wherein the holes comprise sidewalls that are slanted relative to the flat surface of the substrate;

a dielectric material disposed on the slanted sidewalls and not on the flat surface of the substrate; and

a semiconductor structure grown on the flat surface of the substrate, the semiconductor structure comprising a III-nitride light emitting layer disposed between an n-type region and a p-type region;

wherein a portion of the semiconductor structure is disposed in the holes; and

the dielectric material includes a stack of layers that forms a gradient index optical interface between the semiconductor structure and the substrate, the gradient index optical interface smoothly transiting from a first refractive index to a second refractive index between the semiconductor structure and the substrate, the second refractive index being closer to a refractive index of the substrate than is the first refractive index.

10. The lighting device of claim 9 wherein the plurality of holes have a triangular cross section.

11. The lighting device of claim 9 wherein the plurality of holes are arranged in an array.

12. The lighting device of claim 9 wherein an average of between 1 and 2 holes is formed in every 3 μm by 3 μm area of the substrate.

13. The lighting device of claim 9 wherein the dielectric material is disposed in the plurality of holes, between the semiconductor structure and the substrate.

14. The lighting device of claim 1 , wherein the first refractive index is closer to a refractive index of the semiconductor structure than is the second refractive index.

15. The lighting device of claim 1 , wherein the gradient index optical interface is configured to receive light emitted from the light emitting layer and direct the light into the substrate.

16. The lighting device of claim 9 , wherein the gradient index optical interface is configured to receive light emitted from the III-nitride light emitting layer and direct the light into the substrate.