There is a significant gap between the internal efficiency of light‐emitting diodes (LEDs) and their external efficiency. The reason for this shortfall is the narrow escape cone for light in high refractive index semiconductors. We have found that by separating thin‐film LEDs from their substrates (by epitaxial lift‐off, for example), it is much easier for light to escape from the LED structure and thereby avoid absorption. Moreover, by nanotexturing the thin‐film surface using ‘‘natural lithography,’’ the light ray dynamics becomes chaotic, and the optical phase‐space distribution becomes ‘‘ergodic,’’ allowing even more of the light to find the escape cone. We have demonstrated 30% external efficiency in GaAs LEDs employing these principles.