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Embodiments of the invention include a substrate comprising a host and a seed layer bonded to the host, and a semiconductor structure comprising a light emitting layer disposed between an n-type region and a p-type region grown over the seed layer. A variation in index of refraction in a direction p

Embodiments of the invention include a substrate comprising a host and a seed layer bonded to the host, and a semiconductor structure comprising a light emitting layer disposed between an n-type region and a p-type region grown over the seed layer. A variation in index of refraction in a direction perpendicular to a growth direction of the semiconductor structure is disposed between the host and the light emitting layer.

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1. A structure comprising: a substrate comprising: a host; anda seed layer bonded to the host;a semiconductor structure grown over the seed layer, the semiconductor structure comprising a light emitting layer disposed between an n-type region and a p-type region; anda variation in index of refractio

1. A structure comprising: a substrate comprising: a host; anda seed layer bonded to the host;a semiconductor structure grown over the seed layer, the semiconductor structure comprising a light emitting layer disposed between an n-type region and a p-type region; anda variation in index of refraction disposed between the host and the light emitting layer, the variation in index of refraction comprising hills of first material having a first index of refraction separated by valleys of a second material having a second index of refraction. 2. The structure of claim 1 wherein the hills comprise pillars. 3. The structure of claim 1 wherein the hills comprise pyramids. 4. The structure of claim 1 wherein: one of the first and second materials is one of III-nitride material, high index glass, TiO2, and Ta2O5; andthe other of the first and second materials is one of SiO2, MgF2, CaF2, air, porous material, porous oxide, and porous dielectric. 5. The structure of claim 1 wherein a difference between the first index of refraction and the second index of refraction is at least 0.1. 6. The structure of claim 1 wherein a difference between the first index of refraction and the second index of refraction is at least 0.5. 7. The structure of claim 1 wherein the hills are between 100 nm and 10 microns high. 8. A structure comprising: a substrate comprising: a non-III-nitride host; anda III-nitride seed layer bonded to the host by a bonding layer;a semiconductor structure grown over the seed layer, the semiconductor structure comprising a light emitting layer disposed between an n-type region and a p-type region; anda variation in index of refraction disposed between the non-III-nitride host and the light emitting layer, the variation in index of refraction comprising one of a lattice of holes and a grid. 9. The structure of claim 8 wherein the variation in index of refraction is a lattice of holes and the holes are arranged periodically. 10. The structure of claim 8 wherein the variation in index of refraction is disposed in the bonding layer. 11. The structure of claim 10 wherein the bonding layer is one of glass and an oxide of silicon. 12. The structure of claim 10 wherein the variation in index of refraction is a lattice of holes filled with gas. 13. The structure of claim 8 wherein the variation in index of refraction is disposed in the III-nitride seed layer. 14. The structure of claim 8 wherein the variation in index of refraction is disposed on a surface of the III-nitride seed layer. 15. A method comprising: providing a substrate comprising: a host; anda seed layer bonded to the host by a bonding layer;growing on the substrate a semiconductor structure comprising a III-nitride light emitting layer disposed between an n-type region and a p-type region; andpatterning a layer to form one of a periodic lattice of holes and a grid, wherein the patterned layer is disposed between the host and the III-nitride light emitting layer and is configured to extract light from the semiconductor structure. 16. The method of claim 15 wherein patterning a layer to form one of a periodic lattice of holes and a grid comprises patterning the bonding layer. 17. The method of claim 15 wherein patterning a layer to form one of a periodic lattice of holes and a grid comprises patterning the seed layer. 18. The method of claim 15 further comprising forming a non-semiconductor layer on the seed layer, wherein patterning a layer to form one of a periodic lattice of holes and a grid comprises patterning the non-semiconductor layer.