Methods and devices for light extraction from a group III-nitride volumetric LED using surface and sidewall roughening

1. A light emitting diode comprising:

a gallium and nitrogen containing substrate comprising a surface region;

an n-type epitaxial material overlying the surface region;

one or more active regions overlying the n-type epitaxial material;

a p-type epitaxial material overlying the one or more active regions;

a first electrode coupled to the n-type epitaxial material, to the substrate, or to both the n-type epitaxial material and to the substrate;

a second electrode coupled to the p-type epitaxial material;

a top surface region comprising a top textured surface characterized by a top surface roughness of about 80 nm to about 10,000 nm;

a base; and

at least three lateral surface regions coupling the top surface region to the base, wherein at least one of the three lateral surface regions is characterized by a lateral surface roughness, wherein the at least one lateral surface region comprises a first portion and a second portion, wherein, the first portion comprise a one-dimensional surface roughness; and the second portion comprises a two-dimensional surface roughness.

2. The light emitting diode of claim 1 , wherein,

the top surface region is triangular;

the base is triangular; and

the at least three lateral surface regions comprise three lateral surface regions.

3. The light emitting diode of claim 1 , wherein the light emitting diode has a thickness of at least 20 μm.

4. The light emitting diode of claim 1 , wherein the lateral surface roughness ranges from 80 nm to about 1000 nm.

5. The light emitting diode of claim 1 , wherein the lateral surface roughness ranges from about 1001 nm to about 10000 nm.

6. The light emitting diode of claim 1 , wherein the top surface roughness is configured to extract a substantial portion of electromagnetic radiation derived from the one or more active regions.

7. The light emitting diode of claim 1 , wherein the lateral surface roughness is configured to extract a substantial portion of electromagnetic radiation derived from the one or more active regions.

8. The light emitting diode of claim 1 , wherein the one or more active regions comprises two or more of indium, gallium, aluminum, and nitrogen.

9. The light emitting diode of claim 1 , wherein the at least one lateral surface region is configured in a non-polar orientation.

10. The device of claim 1 , wherein the at least one lateral surface region is configured in a semi-polar orientation.

11. The device of claim 1 , wherein the at least one lateral surface region is configured in a polar orientation.

12. The light emitting diode of claim 1 , wherein the at least one lateral surface region is slanted with respect to the base.

13. The light emitting diode of claim 1 , wherein the at least one lateral surface region is slanted at an angle from 5 degrees to 20 degrees with respect to the base.

14. The light emitting diode of claim 1 , wherein the average lateral size of the one-dimensional surface roughness is from 1 μm to 10 μm.

15. The light emitting diode of claim 1 , wherein the average vertical size of the one-dimensional surface roughness is between 100 nm and 10 μm.

16. The light emitting diode of claim 1 , wherein the top surface roughness is characterized by a two-dimensional surface roughness.

17. The light emitting diode of claim 1 , wherein the top surface roughness comprises greater than 15% of the area of the top surface region.

18. The light emitting diode of claim 1 , wherein the one-dimensional surface roughness is characterized by vertical striations.

19. The light emitting diode of claim 1 , wherein the one-dimensional surface roughness comprises vertical striations having a characteristic distance from 1 μm to 5 μm.

20. The light emitting diode of claim 1 , wherein each of the at least three lateral surface regions comprises:

a first portion comprising p-type gallium and nitrogen containing material characterized by a first surface roughness; and

a second portion comprising an n-type gallium and nitrogen containing material characterized by a second surface roughness,

wherein the first surface roughness is different than the second surface roughness.

21. The light emitting diode of claim 1 , wherein the at least one lateral surface region is misaligned with a crystallographic plane of the gallium and nitrogen containing substrate.

22. The light emitting diode of claim 1 , wherein the at least one lateral surface region is misaligned within +/−20 degrees with respect to a crystallographic plane of the gallium and nitrogen containing substrate.

23. The light emitting diode of claim 20 , wherein,

the first surface roughness is characterized by a two-dimensional surface roughness; and

the second surface roughness is characterized by a one-dimensional surface roughness.

24. The light emitting diode of claim 23 , wherein,

the one-dimensional surface roughness comprises vertical striations.

25. A light emitting diode comprising:

a gallium and nitrogen containing substrate comprising a surface region;

an n-type epitaxial material overlying the surface region;

one or more active regions overlying the n-type epitaxial material;

a p-type epitaxial material overlying the one or more active regions;

a first electrode coupled to the n-type epitaxial material, to the substrate, or to both the n-type epitaxial material and to the substrate;

a second electrode coupled to the p-type epitaxial material;

a triangular top surface region comprising a top textured surface;

a triangular base; and

three lateral surface regions coupling the top surface region to the base, wherein each of the at least three lateral surface regions comprises a first portion and a second portion, wherein, the first portion comprise a one-dimensional surface roughness; and the second portion comprises a two-dimensional surface roughness.