LED with patterned surface features based on emission field patterns

The escape surface of a light emitting element includes features that include sloped surfaces that have angles of inclination that are based on the direction of peak light output from the light emitting element. If the light output exhibits a number of lobes at different directions, the sloped surfaces may have a corresponding number of different angles of inclination. To minimize the re-injection of light into adjacent features, adjacent features may be positioned to avoid having surfaces that directly face each other. The features may be shaped or positioned to provide a pseudo-random distribution of inclined surfaces across the escape surface, and multiple roughening processes may be used.