Device including transparent layer with profiled surface for improved extraction

A method comprising:

• designing a profiled surface for an at least partially transparent substrate of a device, wherein the at least partially transparent substrate includes a first side and a second side, wherein a group Ill nitride heterostructure is located on the second side, and wherein radiation passes through the second side during operation of the device, wherein the profiled surface includes:
• a plurality of large roughness components providing a first variation of the profiled surface having a characteristic scale approximately an order of magnitude larger than a target wavelength of the radiation, wherein the plurality of large roughness components comprise a series of truncated shapes formed of a material of the at least partially transparent substrate, wherein at least one of the series of truncated shapes is inversely truncated with respect to a direction the radiation travels through the at least partially transparent substrate;
• and a plurality of small roughness components providing a second variation of the profiled surface having a characteristic scale on the order of the target wavelength of the radiation, wherein the plurality of small roughness components are superimposed on the plurality of large roughness components, wherein a graded refractive index along a height of each small roughness component in the plurality of small roughness components decreases substantially linearly along the height.

An emitting device comprising:

• an active region configured to generate radiation having a peak wavelength;
• and
• an at least partially transparent substrate having a first side and a second side, wherein the active region is located on the first side, wherein radiation generated in the active region passes through the second side, and wherein the at least partially transparent substrate includes a profiled surface, wherein the profiled surface includes:
• a plurality of large roughness components providing a first variation of the profiled surface having a characteristic scale approximately an order of magnitude larger than a target wavelength of the radiation, wherein the plurality of large roughness components comprise a series of truncated shapes formed of a material of the at least partially transparent substrate, wherein at least one of the series of truncated shapes is inversely truncated with respect to a direction the radiation travels through the at least partially transparent substrate;
• and
• a plurality of small roughness components providing a second variation of the profiled surface having a characteristic scale on the order of the target wavelength of the radiation, wherein the plurality of small roughness components are superimposed on the plurality of large roughness components, wherein a graded refractive index along a height of each small roughness component in the plurality of small roughness components decreases substantially linearly along the height.