Nanopatterned sapphire substrates in deep-UV LEDs: is there an optical benefit?

Light emitting diodes (LEDs) in the deep ultra-violet (DUV) offer new perspectives for multiple applications ranging from 3D printing to sterilization. However, insufficient light extraction severely limits their efficiency. Nanostructured sapphire substrates in aluminum nitride based LED devices have recently shown to improve crystal growth properties, while their impact on light extraction has not been fully verified. We present a model for understanding the impact of nanostructures on the light extraction capability of DUV-LEDs. The model assumes an isotropic light source in the semiconductor layer stack and combines rigorously computed scattering matrices with a multilayer solver. We find that the optical benefit of using a nanopatterned as opposed to a planar sapphire substrate to be negligible, if parasitic absorption in the p-side of the LED is dominant. If losses in the p-side are reduced to 20%, then for a wavelength of 265 nm an increase of light extraction efficiency from 7.8% to 25.0% is possible due to nanostructuring. We introduce a concept using a diffuse ('Lambertian') reflector as p-contact, further increasing the light extraction efficiency to 34.2%. The results underline that transparent p-sides and reflective p-contacts in DUV-LEDs are indispensable for enhanced light extraction regardless of the interface texture between semiconductor and sapphire substrate. The optical design guidelines presented in this study will accelerate the development of high-efficiency DUV-LEDs. The model can be extended to other multilayer opto-electronic nanostructured devices such as photovoltaics or photodetectors.